projects/ldc: lphobos/std/math.d annotate

annotate lphobos/std/math.d @ 883:b52d5de7783f

GC defines and linkage changes.

author	Christian Kamm <kamm incasoftware de>
date	Thu, 08 Jan 2009 18:20:02 +0100
parents	373489eeaf90
children

rev	line source
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1 // Written in the D programming language
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	2
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	3 /**
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	4 * Macros:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	5 * WIKI = Phobos/StdMath
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	6 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	7 * TABLE_SV = <table border=1 cellpadding=4 cellspacing=0>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	8 * <caption>Special Values</caption>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	9 * $0</table>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	10 * SVH = $(TR $(TH $1) $(TH $2))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	11 * SV = $(TR $(TD $1) $(TD $2))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	12 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	13 * NAN = $(RED NAN)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	14 * SUP = <span style="vertical-align:super;font-size:smaller">$0</span>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	15 * GAMMA = Γ
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	16 * INTEGRAL = ∫
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	17 * INTEGRATE = $(BIG ∫<sub>$(SMALL $1)</sub><sup>$2</sup>)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	18 * POWER = $1<sup>$2</sup>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	19 * BIGSUM = $(BIG Σ <sup>$2</sup><sub>$(SMALL $1)</sub>)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	20 * CHOOSE = $(BIG () <sup>$(SMALL $1)</sup><sub>$(SMALL $2)</sub> $(BIG ))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	21 * PLUSMN = ±
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	22 * INFIN = ∞
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	23 * PI = π
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	24 * LT = <
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	25 * GT = >
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	26 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	27
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	28 /*
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	29 * Author:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	30 * Walter Bright
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	31 * Copyright:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	32 * Copyright (c) 2001-2005 by Digital Mars,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	33 * All Rights Reserved,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	34 * www.digitalmars.com
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	35 * Copyright (c) 2007 by Tomas Lindquist Olsen
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	36 * License:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	37 * This software is provided 'as-is', without any express or implied
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	38 * warranty. In no event will the authors be held liable for any damages
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	39 * arising from the use of this software.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	40 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	41 * Permission is granted to anyone to use this software for any purpose,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	42 * including commercial applications, and to alter it and redistribute it
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	43 * freely, subject to the following restrictions:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	44 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	45 * <ul>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	46 * <li> The origin of this software must not be misrepresented; you must not
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	47 * claim that you wrote the original software. If you use this software
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	48 * in a product, an acknowledgment in the product documentation would be
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	49 * appreciated but is not required.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	50 * </li>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	51 * <li> Altered source versions must be plainly marked as such, and must not
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	52 * be misrepresented as being the original software.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	53 * </li>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	54 * <li> This notice may not be removed or altered from any source
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	55 * distribution.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	56 * </li>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	57 * </ul>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	58 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	59
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	60
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	61 module std.math;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	62
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	63 //debug=math; // uncomment to turn on debugging printf's
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	64
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	65 private import std.c.stdio;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	66 private import std.c.math;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	67
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	68 class NotImplemented : Error
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	69 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	70 this(string msg)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	71 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	72 super(msg ~ "not implemented");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	73 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	74 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	75
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	76 const real E = 2.7182818284590452354L; /** e */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	77 const real LOG2T = 0x1.a934f0979a3715fcp+1; /** log<sub>2</sub>10 */ // 3.32193 fldl2t
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	78 const real LOG2E = 0x1.71547652b82fe178p+0; /** log<sub>2</sub>e */ // 1.4427 fldl2e
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	79 const real LOG2 = 0x1.34413509f79fef32p-2; /** log<sub>10</sub>2 */ // 0.30103 fldlg2
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	80 const real LOG10E = 0.43429448190325182765; /** log<sub>10</sub>e */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	81 const real LN2 = 0x1.62e42fefa39ef358p-1; /** ln 2 */ // 0.693147 fldln2
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	82 const real LN10 = 2.30258509299404568402; /** ln 10 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	83 const real PI = 0x1.921fb54442d1846ap+1; /** $(PI) */ // 3.14159 fldpi
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	84 const real PI_2 = 1.57079632679489661923; /** $(PI) / 2 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	85 const real PI_4 = 0.78539816339744830962; /** $(PI) / 4 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	86 const real M_1_PI = 0.31830988618379067154; /** 1 / $(PI) */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	87 const real M_2_PI = 0.63661977236758134308; /** 2 / $(PI) */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	88 const real M_2_SQRTPI = 1.12837916709551257390; /** 2 / √$(PI) */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	89 const real SQRT2 = 1.41421356237309504880; /** √2 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	90 const real SQRT1_2 = 0.70710678118654752440; /** √½ */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	91
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	92 /*
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	93 Octal versions:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	94 PI/64800 0.00001 45530 36176 77347 02143 15351 61441 26767
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	95 PI/180 0.01073 72152 11224 72344 25603 54276 63351 22056
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	96 PI/8 0.31103 75524 21026 43021 51423 06305 05600 67016
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	97 SQRT(1/PI) 0.44067 27240 41233 33210 65616 51051 77327 77303
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	98 2/PI 0.50574 60333 44710 40522 47741 16537 21752 32335
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	99 PI/4 0.62207 73250 42055 06043 23046 14612 13401 56034
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	100 SQRT(2/PI) 0.63041 05147 52066 24106 41762 63612 00272 56161
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	101
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	102 PI 3.11037 55242 10264 30215 14230 63050 56006 70163
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	103 LOG2 0.23210 11520 47674 77674 61076 11263 26013 37111
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	104 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	105
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	106
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	107 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	108 * Calculates the absolute value
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	109 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	110 * For complex numbers, abs(z) = sqrt( $(POWER z.re, 2) + $(POWER z.im, 2) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	111 * = hypot(z.re, z.im).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	112 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	113 real abs(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	114 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	115 return fabs(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	116 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	117
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	118 /** ditto */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	119 long abs(long x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	120 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	121 return x>=0 ? x : -x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	122 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	123
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	124 /** ditto */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	125 int abs(int x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	126 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	127 return x>=0 ? x : -x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	128 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	129
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	130 /** ditto */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	131 real abs(creal z)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	132 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	133 return hypot(z.re, z.im);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	134 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	135
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	136 /** ditto */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	137 real abs(ireal y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	138 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	139 return fabs(y.im);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	140 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	141
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	142
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	143 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	144 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	145 assert(isPosZero(abs(-0.0L)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	146 assert(isnan(abs(real.nan)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	147 assert(abs(-real.infinity) == real.infinity);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	148 assert(abs(-3.2Li) == 3.2L);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	149 assert(abs(71.6Li) == 71.6L);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	150 assert(abs(-56) == 56);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	151 assert(abs(2321312L) == 2321312L);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	152 assert(abs(-1+1i) == sqrt(2.0));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	153 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	154
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	155 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	156 * Complex conjugate
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	157 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	158 * conj(x + iy) = x - iy
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	159 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	160 * Note that z * conj(z) = $(POWER z.re, 2) - $(POWER z.im, 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	161 * is always a real number
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	162 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	163 creal conj(creal z)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	164 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	165 return z.re - z.im*1i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	166 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	167
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	168 /** ditto */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	169 ireal conj(ireal y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	170 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	171 return -y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	172 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	173
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	174 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	175 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	176 assert(conj(7 + 3i) == 7-3i);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	177 ireal z = -3.2Li;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	178 assert(conj(z) == -z);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	179 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	180
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	181 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	182 * Returns cosine of x. x is in radians.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	183 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	184 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	185 * $(TR $(TH x) $(TH cos(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	186 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	187 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	188 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	189 * Bugs:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	190 * Results are undefined if \|x\| >= $(POWER 2,64).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	191 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	192
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	193 pragma(intrinsic, "llvm.cos.f32")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	194 float cos(float x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	195
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	196 pragma(intrinsic, "llvm.cos.f64")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	197 double cos(double x); // ditto
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	198
373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	199 pragma(intrinsic, "llvm.cos.f80")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	200 real cos(real x); /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	201
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	202
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	203 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	204 * Returns sine of x. x is in radians.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	205 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	206 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	207 * $(TR $(TH x) $(TH sin(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	208 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	209 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	210 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	211 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	212 * Bugs:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	213 * Results are undefined if \|x\| >= $(POWER 2,64).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	214 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	215
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	216 pragma(intrinsic, "llvm.sin.f32")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	217 float sin(float x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	218
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	219 pragma(intrinsic, "llvm.sin.f64")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	220 double sin(double x); // ditto
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	221
373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	222 pragma(intrinsic, "llvm.sin.f80")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	223 real sin(real x); /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	224
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	225
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	226 /****************************************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	227 * Returns tangent of x. x is in radians.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	228 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	229 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	230 * $(TR $(TH x) $(TH tan(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	231 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	232 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	233 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	234 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	235 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	236
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	237 version(D_InlineAsm_X86)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	238 real tan(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	239 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	240
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	241 asm
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	242 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	243 fld x[EBP] ; // load theta
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	244 fxam ; // test for oddball values
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	245 fstsw AX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	246 sahf ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	247 jc trigerr ; // x is NAN, infinity, or empty
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	248 // 387's can handle denormals
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	249 SC18: fptan ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	250 fstp ST(0) ; // dump X, which is always 1
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	251 fstsw AX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	252 sahf ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	253 jnp Lret ; // C2 = 1 (x is out of range)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	254
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	255 // Do argument reduction to bring x into range
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	256 fldpi ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	257 fxch ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	258 SC17: fprem1 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	259 fstsw AX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	260 sahf ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	261 jp SC17 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	262 fstp ST(1) ; // remove pi from stack
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	263 jmp SC18 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	264
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	265 trigerr:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	266 jnp Lret ; // if theta is NAN, return theta
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	267 fstp ST(0) ; // dump theta
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	268 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	269 return real.nan;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	270
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	271 Lret:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	272 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	273 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	274 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	275 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	276 real tan(real x) { return std.c.math.atan(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	277 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	278
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	279
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	280 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	281 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	282 static real vals[][2] = // angle,tan
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	283 [
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	284 [ 0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	285 [ .5, .5463024898],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	286 [ 1, 1.557407725],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	287 [ 1.5, 14.10141995],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	288 [ 2, -2.185039863],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	289 [ 2.5,-.7470222972],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	290 [ 3, -.1425465431],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	291 [ 3.5, .3745856402],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	292 [ 4, 1.157821282],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	293 [ 4.5, 4.637332055],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	294 [ 5, -3.380515006],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	295 [ 5.5,-.9955840522],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	296 [ 6, -.2910061914],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	297 [ 6.5, .2202772003],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	298 [ 10, .6483608275],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	299
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	300 // special angles
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	301 [ PI_4, 1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	302 //[ PI_2, real.infinity],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	303 [ 3*PI_4, -1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	304 [ PI, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	305 [ 5*PI_4, 1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	306 //[ 3*PI_2, -real.infinity],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	307 [ 7*PI_4, -1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	308 [ 2*PI, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	309
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	310 // overflow
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	311 [ real.infinity, real.nan],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	312 [ real.nan, real.nan],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	313 //[ 1e+100, real.nan],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	314 ];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	315 int i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	316
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	317 for (i = 0; i < vals.length; i++)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	318 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	319 real x = vals[i][0];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	320 real r = vals[i][1];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	321 real t = tan(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	322
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	323 //printf("tan(%Lg) = %Lg, should be %Lg\n", x, t, r);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	324 assert(mfeq(r, t, .0000001));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	325
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	326 x = -x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	327 r = -r;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	328 t = tan(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	329 //printf("tan(%Lg) = %Lg, should be %Lg\n", x, t, r);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	330 assert(mfeq(r, t, .0000001));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	331 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	332 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	333
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	334 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	335 * Calculates the arc cosine of x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	336 * returning a value ranging from -$(PI)/2 to $(PI)/2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	337 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	338 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	339 * $(TR $(TH x) $(TH acos(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	340 * $(TR $(TD $(GT)1.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	341 * $(TR $(TD $(LT)-1.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	342 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	343 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	344 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	345 real acos(real x) { return std.c.math.acos(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	346
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	347 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	348 * Calculates the arc sine of x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	349 * returning a value ranging from -$(PI)/2 to $(PI)/2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	350 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	351 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	352 * $(TR $(TH x) $(TH asin(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	353 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	354 * $(TR $(TD $(GT)1.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	355 * $(TR $(TD $(LT)-1.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	356 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	357 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	358 real asin(real x) { return std.c.math.asin(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	359
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	360 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	361 * Calculates the arc tangent of x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	362 * returning a value ranging from -$(PI)/2 to $(PI)/2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	363 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	364 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	365 * $(TR $(TH x) $(TH atan(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	366 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	367 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	368 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	369 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	370 real atan(real x) { return std.c.math.atan(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	371
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	372 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	373 * Calculates the arc tangent of y / x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	374 * returning a value ranging from -$(PI)/2 to $(PI)/2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	375 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	376 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	377 * $(TR $(TH y) $(TH x) $(TH atan(y, x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	378 * $(TR $(TD $(NAN)) $(TD anything) $(TD $(NAN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	379 * $(TR $(TD anything) $(TD $(NAN)) $(TD $(NAN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	380 * $(TR $(TD $(PLUSMN)0.0) $(TD $(GT)0.0) $(TD $(PLUSMN)0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	381 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	382 * $(TR $(TD $(PLUSMN)0.0) $(TD $(LT)0.0) $(TD $(PLUSMN)$(PI)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	383 * $(TR $(TD $(PLUSMN)0.0) $(TD -0.0) $(TD $(PLUSMN)$(PI)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	384 * $(TR $(TD $(GT)0.0) $(TD $(PLUSMN)0.0) $(TD $(PI)/2) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	385 * $(TR $(TD $(LT)0.0) $(TD $(PLUSMN)0.0) $(TD $(PI)/2))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	386 * $(TR $(TD $(GT)0.0) $(TD $(INFIN)) $(TD $(PLUSMN)0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	387 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD anything) $(TD $(PLUSMN)$(PI)/2))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	388 * $(TR $(TD $(GT)0.0) $(TD -$(INFIN)) $(TD $(PLUSMN)$(PI)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	389 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(INFIN)) $(TD $(PLUSMN)$(PI)/4))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	390 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD -$(INFIN)) $(TD $(PLUSMN)3$(PI)/4))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	391 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	392 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	393 real atan2(real y, real x) { return std.c.math.atan2(y,x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	394
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	395 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	396 * Calculates the hyperbolic cosine of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	397 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	398 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	399 * $(TR $(TH x) $(TH cosh(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	400 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)0.0) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	401 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	402 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	403 real cosh(real x) { return std.c.math.cosh(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	404
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	405 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	406 * Calculates the hyperbolic sine of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	407 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	408 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	409 * $(TR $(TH x) $(TH sinh(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	410 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	411 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	412 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	413 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	414 real sinh(real x) { return std.c.math.sinh(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	415
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	416 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	417 * Calculates the hyperbolic tangent of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	418 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	419 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	420 * $(TR $(TH x) $(TH tanh(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	421 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	422 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)1.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	423 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	424 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	425 real tanh(real x) { return std.c.math.tanh(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	426
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	427 //real acosh(real x) { return std.c.math.acoshl(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	428 //real asinh(real x) { return std.c.math.asinhl(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	429 //real atanh(real x) { return std.c.math.atanhl(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	430
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	431 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	432 * Calculates the inverse hyperbolic cosine of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	433 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	434 * Mathematically, acosh(x) = log(x + sqrt( x*x - 1))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	435 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	436 * $(TABLE_DOMRG
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	437 * $(DOMAIN 1..$(INFIN))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	438 * $(RANGE 1..log(real.max), $(INFIN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	439 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	440 * $(SVH x, acosh(x) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	441 * $(SV $(NAN), $(NAN) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	442 * $(SV <1, $(NAN) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	443 * $(SV 1, 0 )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	444 * $(SV +$(INFIN),+$(INFIN))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	445 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	446 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	447 real acosh(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	448 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	449 if (x > 1/real.epsilon)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	450 return LN2 + log(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	451 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	452 return log(x + sqrt(x*x - 1));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	453 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	454
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	455 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	456 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	457 assert(isnan(acosh(0.9)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	458 assert(isnan(acosh(real.nan)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	459 assert(acosh(1)==0.0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	460 assert(acosh(real.infinity) == real.infinity);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	461 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	462
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	463 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	464 * Calculates the inverse hyperbolic sine of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	465 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	466 * Mathematically,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	467 * ---------------
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	468 * asinh(x) = log( x + sqrt( x*x + 1 )) // if x >= +0
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	469 * asinh(x) = -log(-x + sqrt( x*x + 1 )) // if x <= -0
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	470 * -------------
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	471 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	472 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	473 * $(SVH x, asinh(x) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	474 * $(SV $(NAN), $(NAN) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	475 * $(SV $(PLUSMN)0, $(PLUSMN)0 )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	476 * $(SV $(PLUSMN)$(INFIN),$(PLUSMN)$(INFIN))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	477 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	478 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	479 real asinh(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	480 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	481 if (fabs(x) > 1 / real.epsilon) // beyond this point, xx + 1 == xx
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	482 return copysign(LN2 + log(fabs(x)), x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	483 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	484 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	485 // sqrt(xx + 1) == 1 + x x / ( 1 + sqrt(x*x + 1) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	486 return copysign(log1p(fabs(x) + xx / (1 + sqrt(xx + 1)) ), x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	487 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	488 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	489
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	490 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	491 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	492 assert(isPosZero(asinh(0.0)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	493 assert(isNegZero(asinh(-0.0)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	494 assert(asinh(real.infinity) == real.infinity);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	495 assert(asinh(-real.infinity) == -real.infinity);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	496 assert(isnan(asinh(real.nan)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	497 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	498
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	499 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	500 * Calculates the inverse hyperbolic tangent of x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	501 * returning a value from ranging from -1 to 1.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	502 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	503 * Mathematically, atanh(x) = log( (1+x)/(1-x) ) / 2
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	504 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	505 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	506 * $(TABLE_DOMRG
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	507 * $(DOMAIN -$(INFIN)..$(INFIN))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	508 * $(RANGE -1..1) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	509 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	510 * $(SVH x, acosh(x) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	511 * $(SV $(NAN), $(NAN) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	512 * $(SV $(PLUSMN)0, $(PLUSMN)0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	513 * $(SV -$(INFIN), -0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	514 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	515 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	516 real atanh(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	517 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	518 // log( (1+x)/(1-x) ) == log ( 1 + (2*x)/(1-x) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	519 return 0.5 * log1p( 2 * x / (1 - x) );
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	520 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	521
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	522 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	523 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	524 assert(isPosZero(atanh(0.0)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	525 assert(isNegZero(atanh(-0.0)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	526 assert(isnan(atanh(real.nan)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	527 assert(isnan(atanh(-real.infinity)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	528 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	529
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	530 /*****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	531 * Returns x rounded to a long value using the current rounding mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	532 * If the integer value of x is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	533 * greater than long.max, the result is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	534 * indeterminate.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	535 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	536 long rndtol(real x); /* intrinsic */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	537
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	538
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	539 /*****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	540 * Returns x rounded to a long value using the FE_TONEAREST rounding mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	541 * If the integer value of x is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	542 * greater than long.max, the result is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	543 * indeterminate.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	544 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	545 extern (C) real rndtonl(real x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	546
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	547 /***************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	548 * Compute square root of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	549 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	550 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	551 * $(TR $(TH x) $(TH sqrt(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	552 * $(TR $(TD -0.0) $(TD -0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	553 * $(TR $(TD $(LT)0.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	554 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	555 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	556 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	557
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	558 pragma(intrinsic, "llvm.sqrt.f32")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	559 float sqrt(float x); /* intrinsic */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	560
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	561 pragma(intrinsic, "llvm.sqrt.f64")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	562 double sqrt(double x); /* intrinsic */ /// ditto
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	563
373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	564 pragma(intrinsic, "llvm.sqrt.f80")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	565 real sqrt(real x); /* intrinsic */ /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	566
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	567 creal sqrt(creal z)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	568 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	569 creal c;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	570 real x,y,w,r;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	571
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	572 if (z == 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	573 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	574 c = 0 + 0i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	575 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	576 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	577 { real z_re = z.re;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	578 real z_im = z.im;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	579
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	580 x = fabs(z_re);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	581 y = fabs(z_im);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	582 if (x >= y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	583 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	584 r = y / x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	585 w = sqrt(x) * sqrt(0.5 * (1 + sqrt(1 + r * r)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	586 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	587 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	588 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	589 r = x / y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	590 w = sqrt(y) * sqrt(0.5 * (r + sqrt(1 + r * r)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	591 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	592
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	593 if (z_re >= 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	594 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	595 c = w + (z_im / (w + w)) * 1.0i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	596 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	597 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	598 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	599 if (z_im < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	600 w = -w;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	601 c = z_im / (w + w) + w * 1.0i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	602 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	603 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	604 return c;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	605 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	606
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	607 /**********************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	608 * Calculates e$(SUP x).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	609 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	610 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	611 * $(TR $(TH x) $(TH exp(x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	612 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	613 * $(TR $(TD -$(INFIN)) $(TD +0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	614 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	615 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	616 real exp(real x) { return std.c.math.exp(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	617
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	618 /**********************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	619 * Calculates 2$(SUP x).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	620 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	621 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	622 * $(TR $(TH x) $(TH exp2(x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	623 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	624 * $(TR $(TD -$(INFIN)) $(TD +0.0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	625 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	626 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	627 real exp2(real x) { return std.c.math.exp2(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	628
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	629 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	630 * Calculates the value of the natural logarithm base (e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	631 * raised to the power of x, minus 1.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	632 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	633 * For very small x, expm1(x) is more accurate
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	634 * than exp(x)-1.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	635 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	636 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	637 * $(TR $(TH x) $(TH e$(SUP x)-1))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	638 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	639 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	640 * $(TR $(TD -$(INFIN)) $(TD -1.0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	641 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	642 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	643
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	644 real expm1(real x) { return std.c.math.expm1(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	645
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	646
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	647 /*********************************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	648 * Separate floating point value into significand and exponent.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	649 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	650 * Returns:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	651 * Calculate and return <i>x</i> and exp such that
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	652 * value =<i>x</i>*2$(SUP exp) and
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	653 * .5 $(LT)= \|<i>x</i>\| $(LT) 1.0<br>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	654 * <i>x</i> has same sign as value.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	655 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	656 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	657 * $(TR $(TH value) $(TH returns) $(TH exp))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	658 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	659 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD int.max))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	660 * $(TR $(TD -$(INFIN)) $(TD -$(INFIN)) $(TD int.min))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	661 * $(TR $(TD $(PLUSMN)$(NAN)) $(TD $(PLUSMN)$(NAN)) $(TD int.min))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	662 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	663 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	664
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	665
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	666 real frexp(real value, out int exp)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	667 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	668 ushort* vu = cast(ushort*)&value;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	669 long* vl = cast(long*)&value;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	670 uint ex;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	671
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	672 // If exponent is non-zero
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	673 ex = vu[4] & 0x7FFF;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	674 if (ex)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	675 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	676 if (ex == 0x7FFF)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	677 { // infinity or NaN
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	678 if (*vl & 0x7FFFFFFFFFFFFFFF) // if NaN
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	679 { *vl \|= 0xC000000000000000; // convert $(NAN)S to $(NAN)Q
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	680 exp = int.min;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	681 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	682 else if (vu[4] & 0x8000)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	683 { // negative infinity
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	684 exp = int.min;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	685 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	686 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	687 { // positive infinity
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	688 exp = int.max;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	689 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	690 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	691 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	692 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	693 exp = ex - 0x3FFE;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	694 vu[4] = cast(ushort)((0x8000 & vu[4]) \| 0x3FFE);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	695 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	696 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	697 else if (!*vl)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	698 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	699 // value is +-0.0
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	700 exp = 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	701 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	702 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	703 { // denormal
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	704 int i = -0x3FFD;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	705
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	706 do
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	707 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	708 i--;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	709 *vl <<= 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	710 } while (*vl > 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	711 exp = i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	712 vu[4] = cast(ushort)((0x8000 & vu[4]) \| 0x3FFE);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	713 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	714 return value;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	715 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	716
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	717
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	718 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	719 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	720 static real vals[][3] = // x,frexp,exp
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	721 [
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	722 [0.0, 0.0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	723 [-0.0, -0.0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	724 [1.0, .5, 1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	725 [-1.0, -.5, 1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	726 [2.0, .5, 2],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	727 [155.67e20, 0x1.A5F1C2EB3FE4Fp-1, 74], // normal
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	728 [1.0e-320, 0.98829225, -1063],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	729 [real.min, .5, -16381],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	730 [real.min/2.0L, .5, -16382], // denormal
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	731
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	732 [real.infinity,real.infinity,int.max],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	733 [-real.infinity,-real.infinity,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	734 [real.nan,real.nan,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	735 [-real.nan,-real.nan,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	736
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	737 // Don't really support signalling nan's in D
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	738 //[real.nans,real.nan,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	739 //[-real.nans,-real.nan,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	740 ];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	741 int i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	742
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	743 for (i = 0; i < vals.length; i++)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	744 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	745 real x = vals[i][0];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	746 real e = vals[i][1];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	747 int exp = cast(int)vals[i][2];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	748 int eptr;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	749 real v = frexp(x, eptr);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	750
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	751 //printf("frexp(%Lg) = %.8Lg, should be %.8Lg, eptr = %d, should be %d\n", x, v, e, eptr, exp);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	752 assert(mfeq(e, v, .0000001));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	753 assert(exp == eptr);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	754 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	755 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	756
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	757
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	758 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	759 * Extracts the exponent of x as a signed integral value.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	760 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	761 * If x is not a special value, the result is the same as
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	762 * <tt>cast(int)logb(x)</tt>.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	763 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	764 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	765 * $(TR $(TH x) $(TH ilogb(x)) $(TH Range error?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	766 * $(TR $(TD 0) $(TD FP_ILOGB0) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	767 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD int.max) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	768 * $(TR $(TD $(NAN)) $(TD FP_ILOGBNAN) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	769 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	770 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	771 int ilogb(real x) { return std.c.math.ilogb(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	772
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	773 alias std.c.math.FP_ILOGB0 FP_ILOGB0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	774 alias std.c.math.FP_ILOGBNAN FP_ILOGBNAN;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	775
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	776
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	777 /*******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	778 * Compute n * 2$(SUP exp)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	779 * References: frexp
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	780 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	781
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	782 real ldexp(real n, int exp) { return std.c.math.ldexp(n, exp); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	783
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	784 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	785 * Calculate the natural logarithm of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	786 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	787 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	788 * $(TR $(TH x) $(TH log(x)) $(TH divide by 0?) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	789 * $(TR $(TD $(PLUSMN)0.0) $(TD -$(INFIN)) $(TD yes) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	790 * $(TR $(TD $(LT)0.0) $(TD $(NAN)) $(TD no) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	791 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	792 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	793 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	794
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	795 real log(real x) { return std.c.math.log(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	796
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	797 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	798 * Calculate the base-10 logarithm of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	799 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	800 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	801 * $(TR $(TH x) $(TH log10(x)) $(TH divide by 0?) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	802 * $(TR $(TD $(PLUSMN)0.0) $(TD -$(INFIN)) $(TD yes) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	803 * $(TR $(TD $(LT)0.0) $(TD $(NAN)) $(TD no) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	804 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	805 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	806 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	807
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	808 real log10(real x) { return std.c.math.log10(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	809
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	810 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	811 * Calculates the natural logarithm of 1 + x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	812 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	813 * For very small x, log1p(x) will be more accurate than
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	814 * log(1 + x).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	815 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	816 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	817 * $(TR $(TH x) $(TH log1p(x)) $(TH divide by 0?) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	818 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	819 * $(TR $(TD -1.0) $(TD -$(INFIN)) $(TD yes) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	820 * $(TR $(TD $(LT)-1.0) $(TD $(NAN)) $(TD no) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	821 * $(TR $(TD +$(INFIN)) $(TD -$(INFIN)) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	822 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	823 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	824
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	825 real log1p(real x) { return std.c.math.log1p(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	826
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	827 /***************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	828 * Calculates the base-2 logarithm of x:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	829 * log<sub>2</sub>x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	830 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	831 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	832 * $(TR $(TH x) $(TH log2(x)) $(TH divide by 0?) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	833 * $(TR $(TD $(PLUSMN)0.0) $(TD -$(INFIN)) $(TD yes) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	834 * $(TR $(TD $(LT)0.0) $(TD $(NAN)) $(TD no) $(TD yes) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	835 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	836 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	837 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	838 real log2(real x) { return std.c.math.log2(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	839
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	840 /*****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	841 * Extracts the exponent of x as a signed integral value.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	842 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	843 * If x is subnormal, it is treated as if it were normalized.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	844 * For a positive, finite x:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	845 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	846 * -----
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	847 * 1 <= $(I x) * FLT_RADIX$(SUP -logb(x)) < FLT_RADIX
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	848 * -----
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	849 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	850 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	851 * $(TR $(TH x) $(TH logb(x)) $(TH divide by 0?) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	852 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	853 * $(TR $(TD $(PLUSMN)0.0) $(TD -$(INFIN)) $(TD yes) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	854 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	855 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	856 real logb(real x) { return std.c.math.logb(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	857
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	858 /************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	859 * Calculates the remainder from the calculation x/y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	860 * Returns:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	861 * The value of x - i * y, where i is the number of times that y can
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	862 * be completely subtracted from x. The result has the same sign as x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	863 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	864 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	865 * $(TR $(TH x) $(TH y) $(TH modf(x, y)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	866 * $(TR $(TD $(PLUSMN)0.0) $(TD no)t 0.0 $(TD $(PLUSMN)0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	867 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD anything) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	868 * $(TR $(TD anything) $(TD $(PLUSMN)0.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	869 * $(TR $(TD !=$(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD x) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	870 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	871 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	872 real modf(real x, inout real y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	873 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	874 double Y = y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	875 auto tmp = std.c.math.modf(x,&Y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	876 y = Y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	877 return tmp;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	878 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	879
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	880 /*************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	881 * Efficiently calculates x * 2$(SUP n).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	882 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	883 * scalbn handles underflow and overflow in
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	884 * the same fashion as the basic arithmetic operators.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	885 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	886 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	887 * $(TR $(TH x) $(TH scalb(x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	888 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	889 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	890 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	891 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	892 real scalbn(real x, int n)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	893 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	894 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	895 return std.c.math.scalbn(x, n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	896 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	897 throw new NotImplemented("scalbn");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	898 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	899
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	900 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	901 * Calculates the cube root x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	902 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	903 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	904 * $(TR $(TH $(I x)) $(TH cbrt(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	905 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	906 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	907 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	908 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	909 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	910 real cbrt(real x) { return std.c.math.cbrt(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	911
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	912
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	913 /*******************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	914 * Returns \|x\|
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	915 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	916 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	917 * $(TR $(TH x) $(TH fabs(x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	918 * $(TR $(TD $(PLUSMN)0.0) $(TD +0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	919 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	920 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	921 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	922 real fabs(real x) { return std.c.math.fabs(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	923
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	924
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	925 /***********************************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	926 * Calculates the length of the
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	927 * hypotenuse of a right-angled triangle with sides of length x and y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	928 * The hypotenuse is the value of the square root of
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	929 * the sums of the squares of x and y:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	930 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	931 * sqrt(x² + y²)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	932 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	933 * Note that hypot(x, y), hypot(y, x) and
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	934 * hypot(x, -y) are equivalent.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	935 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	936 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	937 * $(TR $(TH x) $(TH y) $(TH hypot(x, y)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	938 * $(TR $(TD x) $(TD $(PLUSMN)0.0) $(TD \|x\|) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	939 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD y) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	940 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	941 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	942 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	943
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	944 real hypot(real x, real y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	945 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	946 /*
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	947 * This is based on code from:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	948 * Cephes Math Library Release 2.1: January, 1989
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	949 * Copyright 1984, 1987, 1989 by Stephen L. Moshier
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	950 * Direct inquiries to 30 Frost Street, Cambridge, MA 02140
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	951 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	952
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	953 const int PRECL = 32;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	954 const int MAXEXPL = real.max_exp; //16384;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	955 const int MINEXPL = real.min_exp; //-16384;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	956
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	957 real xx, yy, b, re, im;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	958 int ex, ey, e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	959
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	960 // Note, hypot(INFINITY, NAN) = INFINITY.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	961 if (isinf(x) \|\| isinf(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	962 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	963
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	964 if (isnan(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	965 return x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	966 if (isnan(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	967 return y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	968
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	969 re = fabs(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	970 im = fabs(y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	971
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	972 if (re == 0.0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	973 return im;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	974 if (im == 0.0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	975 return re;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	976
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	977 // Get the exponents of the numbers
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	978 xx = frexp(re, ex);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	979 yy = frexp(im, ey);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	980
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	981 // Check if one number is tiny compared to the other
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	982 e = ex - ey;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	983 if (e > PRECL)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	984 return re;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	985 if (e < -PRECL)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	986 return im;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	987
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	988 // Find approximate exponent e of the geometric mean.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	989 e = (ex + ey) >> 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	990
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	991 // Rescale so mean is about 1
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	992 xx = ldexp(re, -e);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	993 yy = ldexp(im, -e);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	994
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	995 // Hypotenuse of the right triangle
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	996 b = sqrt(xx * xx + yy * yy);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	997
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	998 // Compute the exponent of the answer.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	999 yy = frexp(b, ey);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1000 ey = e + ey;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1001
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1002 // Check it for overflow and underflow.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1003 if (ey > MAXEXPL + 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1004 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1005 //return __matherr(_OVERFLOW, INFINITY, x, y, "hypotl");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1006 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1007 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1008 if (ey < MINEXPL - 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1009 return 0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1010
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1011 // Undo the scaling
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1012 b = ldexp(b, e);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1013 return b;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1014 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1015
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1016 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1017 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1018 static real vals[][3] = // x,y,hypot
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1019 [
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1020 [ 0, 0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1021 [ 0, -0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1022 [ 3, 4, 5],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1023 [ -300, -400, 500],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1024 [ real.min, real.min, 4.75473e-4932L],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1025 [ real.max/2, real.max/2, 0x1.6a09e667f3bcc908p+16383L /8.41267e+4931L/],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1026 [ real.infinity, real.nan, real.infinity],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1027 [ real.nan, real.nan, real.nan],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1028 ];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1029 int i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1030
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1031 for (i = 0; i < vals.length; i++)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1032 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1033 real x = vals[i][0];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1034 real y = vals[i][1];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1035 real z = vals[i][2];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1036 real h = hypot(x, y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1037
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1038 //printf("hypot(%Lg, %Lg) = %Lg, should be %Lg\n", x, y, h, z);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1039 //if (!mfeq(z, h, .0000001))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1040 //printf("%La\n", h);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1041 assert(mfeq(z, h, .0000001));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1042 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1043 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1044
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1045 /**********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1046 * Returns the error function of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1047 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1048 * <img src="erf.gif" alt="error function">
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1049 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1050 real erf(real x) { return std.c.math.erf(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1051
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1052 /**********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1053 * Returns the complementary error function of x, which is 1 - erf(x).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1054 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1055 * <img src="erfc.gif" alt="complementary error function">
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1056 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1057 real erfc(real x) { return std.c.math.erfc(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1058
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1059 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1060 * Natural logarithm of gamma function.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1061 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1062 * Returns the base e (2.718...) logarithm of the absolute
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1063 * value of the gamma function of the argument.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1064 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1065 * For reals, lgamma is equivalent to log(fabs(gamma(x))).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1066 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1067 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1068 * $(TR $(TH x) $(TH lgamma(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1069 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1070 * $(TR $(TD integer <= 0) $(TD +$(INFIN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1071 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1072 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1073 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1074 /* Documentation prepared by Don Clugston */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1075 real lgamma(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1076 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1077 return std.c.math.lgamma(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1078
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1079 // Use etc.gamma.lgamma for those C systems that are missing it
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1080 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1081
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1082 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1083 * The Gamma function, $(GAMMA)(x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1084 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1085 * $(GAMMA)(x) is a generalisation of the factorial function
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1086 * to real and complex numbers.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1087 * Like x!, $(GAMMA)(x+1) = x*$(GAMMA)(x).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1088 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1089 * Mathematically, if z.re > 0 then
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1090 * $(GAMMA)(z) =<big>$(INTEGRAL)<sub><small>0</small></sub><sup>$(INFIN)</sup></big>t<sup>z-1</sup>e<sup>-t</sup>dt
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1091 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1092 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1093 * $(TR $(TH x) $(TH $(GAMMA)(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1094 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1095 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)$(INFIN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1096 * $(TR $(TD integer $(GT)0) $(TD (x-1)!) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1097 * $(TR $(TD integer $(LT)0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1098 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1099 * $(TR $(TD -$(INFIN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1100 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1101 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1102 * References:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1103 * $(LINK http://en.wikipedia.org/wiki/Gamma_function),
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1104 * $(LINK http://www.netlib.org/cephes/ldoubdoc.html#gamma)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1105 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1106 /* Documentation prepared by Don Clugston */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1107 real tgamma(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1108 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1109 return std.c.math.tgamma(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1110
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1111 // Use etc.gamma.tgamma for those C systems that are missing it
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1112 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1113
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1114 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1115 * Returns the value of x rounded upward to the next integer
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1116 * (toward positive infinity).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1117 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1118 real ceil(real x) { return std.c.math.ceil(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1119
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1120 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1121 * Returns the value of x rounded downward to the next integer
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1122 * (toward negative infinity).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1123 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1124 real floor(real x) { return std.c.math.floor(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1125
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1126 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1127 * Rounds x to the nearest integer value, using the current rounding
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1128 * mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1129 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1130 * Unlike the rint functions, nearbyint does not raise the
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1131 * FE_INEXACT exception.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1132 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1133 real nearbyint(real x) { return std.c.math.nearbyint(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1134
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1135 /**********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1136 * Rounds x to the nearest integer value, using the current rounding
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1137 * mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1138 * If the return value is not equal to x, the FE_INEXACT
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1139 * exception is raised.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1140 * <b>nearbyint</b> performs
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1141 * the same operation, but does not set the FE_INEXACT exception.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1142 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1143 real rint(real x) { return std.c.math.rint(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1144
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1145 /***************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1146 * Rounds x to the nearest integer value, using the current rounding
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1147 * mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1148 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1149 long lrint(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1150 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1151 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1152 return std.c.math.llrint(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1153 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1154 throw new NotImplemented("lrint");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1155 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1156
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1157 /*******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1158 * Return the value of x rounded to the nearest integer.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1159 * If the fractional part of x is exactly 0.5, the return value is rounded to
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1160 * the even integer.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1161 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1162 real round(real x) { return std.c.math.round(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1163
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1164 /**********************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1165 * Return the value of x rounded to the nearest integer.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1166 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1167 * If the fractional part of x is exactly 0.5, the return value is rounded
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1168 * away from zero.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1169 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1170 long lround(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1171 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1172 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1173 return std.c.math.llround(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1174 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1175 throw new NotImplemented("lround");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1176 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1177
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1178 /****************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1179 * Returns the integer portion of x, dropping the fractional portion.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1180 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1181 * This is also known as "chop" rounding.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1182 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1183 real trunc(real x) { return std.c.math.trunc(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1184
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1185 /****************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1186 * Calculate the remainder x REM y, following IEC 60559.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1187 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1188 * REM is the value of x - y * n, where n is the integer nearest the exact
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1189 * value of x / y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1190 * If \|n - x / y\| == 0.5, n is even.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1191 * If the result is zero, it has the same sign as x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1192 * Otherwise, the sign of the result is the sign of x / y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1193 * Precision mode has no effect on the remainder functions.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1194 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1195 * remquo returns n in the parameter n.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1196 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1197 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1198 * $(TR $(TH x) $(TH y) $(TH remainder(x, y)) $(TH n) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1199 * $(TR $(TD $(PLUSMN)0.0) $(TD no)t 0.0 $(TD $(PLUSMN)0.0) $(TD 0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1200 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD anything) $(TD $(NAN)) $(TD ?) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1201 * $(TR $(TD anything) $(TD $(PLUSMN)0.0) $(TD $(NAN)) $(TD ?) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1202 * $(TR $(TD != $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD x) $(TD ?) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1203 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1204 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1205 real remainder(real x, real y) { return std.c.math.remainder(x, y); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1206
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1207 real remquo(real x, real y, out int n) /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1208 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1209 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1210 return std.c.math.remquo(x, y, &n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1211 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1212 throw new NotImplemented("remquo");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1213 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1214
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1215 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1216 * Returns !=0 if e is a NaN.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1217 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1218
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1219 int isnan(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1220 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1221 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1222 ulong* ps = cast(ulong *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1223
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1224 return (pe[4] & 0x7FFF) == 0x7FFF &&
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1225 *ps & 0x7FFFFFFFFFFFFFFF;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1226 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1227
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1228 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1229 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1230 assert(isnan(float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1231 assert(isnan(-double.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1232 assert(isnan(real.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1233
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1234 assert(!isnan(53.6));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1235 assert(!isnan(float.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1236 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1237
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1238 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1239 * Returns !=0 if e is finite.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1240 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1241
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1242 int isfinite(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1243 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1244 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1245
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1246 return (pe[4] & 0x7FFF) != 0x7FFF;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1247 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1248
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1249 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1250 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1251 assert(isfinite(1.23));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1252 assert(!isfinite(double.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1253 assert(!isfinite(float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1254 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1255
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1256
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1257 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1258 * Returns !=0 if x is normalized.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1259 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1260
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1261 /* Need one for each format because subnormal floats might
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1262 * be converted to normal reals.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1263 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1264
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1265 int isnormal(float x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1266 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1267 uint p = cast(uint )&x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1268 uint e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1269
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1270 e = *p & 0x7F800000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1271 //printf("e = x%x, p = x%x\n", e, p);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1272 return e && e != 0x7F800000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1273 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1274
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1275 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1276
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1277 int isnormal(double d)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1278 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1279 uint p = cast(uint )&d;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1280 uint e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1281
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1282 e = p[1] & 0x7FF00000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1283 return e && e != 0x7FF00000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1284 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1285
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1286 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1287
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1288 int isnormal(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1289 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1290 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1291 long* ps = cast(long *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1292
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1293 return (pe[4] & 0x7FFF) != 0x7FFF && *ps < 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1294 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1295
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1296 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1297 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1298 float f = 3;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1299 double d = 500;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1300 real e = 10e+48;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1301
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1302 assert(isnormal(f));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1303 assert(isnormal(d));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1304 assert(isnormal(e));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1305 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1306
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1307 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1308 * Is number subnormal? (Also called "denormal".)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1309 * Subnormals have a 0 exponent and a 0 most significant mantissa bit.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1310 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1311
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1312 /* Need one for each format because subnormal floats might
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1313 * be converted to normal reals.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1314 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1315
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1316 int issubnormal(float f)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1317 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1318 uint p = cast(uint )&f;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1319
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1320 //printf("p = x%x\n", p);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1321 return (p & 0x7F800000) == 0 && p & 0x007FFFFF;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1322 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1323
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1324 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1325 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1326 float f = 3.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1327
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1328 for (f = 1.0; !issubnormal(f); f /= 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1329 assert(f != 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1330 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1331
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1332 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1333
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1334 int issubnormal(double d)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1335 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1336 uint p = cast(uint )&d;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1337
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1338 return (p[1] & 0x7FF00000) == 0 && (p[0] \|\| p[1] & 0x000FFFFF);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1339 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1340
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1341 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1342 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1343 double f;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1344
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1345 for (f = 1; !issubnormal(f); f /= 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1346 assert(f != 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1347 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1348
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1349 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1350
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1351 int issubnormal(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1352 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1353 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1354 long* ps = cast(long *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1355
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1356 return (pe[4] & 0x7FFF) == 0 && *ps > 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1357 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1358
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1359 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1360 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1361 real f;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1362
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1363 for (f = 1; !issubnormal(f); f /= 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1364 assert(f != 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1365 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1366
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1367 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1368 * Return !=0 if e is $(PLUSMN)$(INFIN).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1369 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1370
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1371 int isinf(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1372 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1373 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1374 ulong* ps = cast(ulong *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1375
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1376 return (pe[4] & 0x7FFF) == 0x7FFF &&
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1377 *ps == 0x8000000000000000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1378 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1379
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1380 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1381 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1382 assert(isinf(float.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1383 assert(!isinf(float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1384 assert(isinf(double.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1385 assert(isinf(-real.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1386
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1387 assert(isinf(-1.0 / 0.0));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1388 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1389
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1390 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1391 * Return 1 if sign bit of e is set, 0 if not.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1392 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1393
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1394 int signbit(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1395 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1396 ubyte* pe = cast(ubyte *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1397
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1398 //printf("e = %Lg\n", e);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1399 return (pe[9] & 0x80) != 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1400 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1401
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1402 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1403 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1404 debug (math) printf("math.signbit.unittest\n");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1405 assert(!signbit(float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1406 assert(signbit(-float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1407 assert(!signbit(168.1234));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1408 assert(signbit(-168.1234));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1409 assert(!signbit(0.0));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1410 assert(signbit(-0.0));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1411 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1412
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1413 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1414 * Return a value composed of to with from's sign bit.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1415 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1416
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1417 real copysign(real to, real from)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1418 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1419 ubyte* pto = cast(ubyte *)&to;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1420 ubyte* pfrom = cast(ubyte *)&from;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1421
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1422 pto[9] &= 0x7F;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1423 pto[9] \|= pfrom[9] & 0x80;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1424
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1425 return to;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1426 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1427
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1428 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1429 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1430 real e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1431
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1432 e = copysign(21, 23.8);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1433 assert(e == 21);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1434
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1435 e = copysign(-21, 23.8);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1436 assert(e == 21);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1437
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1438 e = copysign(21, -23.8);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1439 assert(e == -21);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1440
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1441 e = copysign(-21, -23.8);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1442 assert(e == -21);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1443
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1444 e = copysign(real.nan, -23.8);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1445 assert(isnan(e) && signbit(e));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1446 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1447
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1448 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1449 * Creates a quiet NAN with the information from tagp[] embedded in it.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1450 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1451 real nan(char[] tagp) { return std.c.math.nan((tagp~\0).ptr); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1452
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1453 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1454 * Calculates the next representable value after x in the direction of y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1455 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1456 * If y $(GT) x, the result will be the next largest floating-point value;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1457 * if y $(LT) x, the result will be the next smallest value.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1458 * If x == y, the result is y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1459 * The FE_INEXACT and FE_OVERFLOW exceptions will be raised if x is finite and
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1460 * the function result is infinite. The FE_INEXACT and FE_UNDERFLOW
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1461 * exceptions will be raised if the function value is subnormal, and x is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1462 * not equal to y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1463 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1464 real nextafter(real x, real y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1465 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1466 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1467 return std.c.math.nextafterl(x, y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1468 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1469 throw new NotImplemented("nextafter");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1470 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1471
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1472 //real nexttoward(real x, real y) { return std.c.math.nexttowardl(x, y); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1473
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1474 /*******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1475 * Returns the positive difference between x and y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1476 * Returns:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1477 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1478 * $(TR $(TH x, y) $(TH fdim(x, y)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1479 * $(TR $(TD x $(GT) y) $(TD x - y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1480 * $(TR $(TD x $(LT)= y) $(TD +0.0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1481 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1482 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1483 real fdim(real x, real y) { return (x > y) ? x - y : +0.0; }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1484
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1485 /****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1486 * Returns the larger of x and y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1487 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1488 real fmax(real x, real y) { return x > y ? x : y; }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1489
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1490 /****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1491 * Returns the smaller of x and y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1492 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1493 real fmin(real x, real y) { return x < y ? x : y; }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1494
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1495 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1496 * Returns (x * y) + z, rounding only once according to the
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1497 * current rounding mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1498 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1499 real fma(real x, real y, real z) { return (x * y) + z; }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1500
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1501 /*******************************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1502 * Fast integral powers.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1503 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1504
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	1505 pragma(intrinsic, "llvm.powi.f32")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1506 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1507 float pow(float x, uint n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1508 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1509 float pow(float x, int n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1510 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1511
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	1512 pragma(intrinsic, "llvm.powi.f64")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1513 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1514 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1515 double pow(double x, uint n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1516 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1517 double pow(double x, int n);
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	1518 }
373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	1519
373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	1520 pragma(intrinsic, "llvm.powi.f80")
373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	1521 {
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1522 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1523 real pow(real x, uint n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1524 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1525 real pow(real x, int n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1526 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1527
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1528 /+
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1529 real pow(real x, uint n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1530 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1531 real p;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1532
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1533 switch (n)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1534 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1535 case 0:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1536 p = 1.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1537 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1538
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1539 case 1:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1540 p = x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1541 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1542
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1543 case 2:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1544 p = x * x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1545 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1546
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1547 default:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1548 p = 1.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1549 while (1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1550 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1551 if (n & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1552 p *= x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1553 n >>= 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1554 if (!n)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1555 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1556 x *= x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1557 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1558 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1559 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1560 return p;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1561 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1562
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1563 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1564 real pow(real x, int n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1565 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1566 if (n < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1567 return pow(x, cast(real)n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1568 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1569 return pow(x, cast(uint)n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1570 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1571 +/
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1572
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1573 /*********************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1574 * Calculates x$(SUP y).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1575 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1576 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1577 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1578 * $(TH x) $(TH y) $(TH pow(x, y)) $(TH div 0) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1579 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1580 * $(TD anything) $(TD $(PLUSMN)0.0) $(TD 1.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1581 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1582 * $(TD \|x\| $(GT) 1) $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1583 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1584 * $(TD \|x\| $(LT) 1) $(TD +$(INFIN)) $(TD +0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1585 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1586 * $(TD \|x\| $(GT) 1) $(TD -$(INFIN)) $(TD +0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1587 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1588 * $(TD \|x\| $(LT) 1) $(TD -$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1589 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1590 * $(TD +$(INFIN)) $(TD $(GT) 0.0) $(TD +$(INFIN)) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1591 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1592 * $(TD +$(INFIN)) $(TD $(LT) 0.0) $(TD +0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1593 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1594 * $(TD -$(INFIN)) $(TD odd integer $(GT) 0.0) $(TD -$(INFIN)) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1595 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1596 * $(TD -$(INFIN)) $(TD $(GT) 0.0, not odd integer) $(TD +$(INFIN)) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1597 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1598 * $(TD -$(INFIN)) $(TD odd integer $(LT) 0.0) $(TD -0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1599 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1600 * $(TD -$(INFIN)) $(TD $(LT) 0.0, not odd integer) $(TD +0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1601 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1602 * $(TD $(PLUSMN)1.0) $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD no) $(TD yes) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1603 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1604 * $(TD $(LT) 0.0) $(TD finite, nonintegral) $(TD $(NAN)) $(TD no) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1605 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1606 * $(TD $(PLUSMN)0.0) $(TD odd integer $(LT) 0.0) $(TD $(PLUSMN)$(INFIN)) $(TD yes) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1607 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1608 * $(TD $(PLUSMN)0.0) $(TD $(LT) 0.0, not odd integer) $(TD +$(INFIN)) $(TD yes) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1609 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1610 * $(TD $(PLUSMN)0.0) $(TD odd integer $(GT) 0.0) $(TD $(PLUSMN)0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1611 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1612 * $(TD $(PLUSMN)0.0) $(TD $(GT) 0.0, not odd integer) $(TD +0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1613 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1614 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1615
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	1616 pragma(intrinsic, "llvm.pow.f32")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1617 float pow(float x, float y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1618
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	1619 pragma(intrinsic, "llvm.pow.f64")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1620 double pow(double x, double y);
473 373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	1621
373489eeaf90 Applied downs' lphobos update Tomas Lindquist Olsen <tomas.l.olsen@gmail.com> parents: 108 diff changeset	1622 pragma(intrinsic, "llvm.pow.f80")
108 288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1623 real pow(real x, real y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1624
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1625 /+
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1626 real pow(real x, real y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1627 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1628 version (linux) // C pow() often does not handle special values correctly
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1629 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1630 if (isnan(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1631 return y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1632
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1633 if (y == 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1634 return 1; // even if x is $(NAN)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1635 if (isnan(x) && y != 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1636 return x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1637 if (isinf(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1638 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1639 if (fabs(x) > 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1640 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1641 if (signbit(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1642 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1643 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1644 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1645 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1646 else if (fabs(x) == 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1647 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1648 return real.nan;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1649 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1650 else // < 1
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1651 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1652 if (signbit(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1653 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1654 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1655 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1656 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1657 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1658 if (isinf(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1659 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1660 if (signbit(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1661 { long i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1662
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1663 i = cast(long)y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1664 if (y > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1665 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1666 if (i == y && i & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1667 return -real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1668 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1669 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1670 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1671 else if (y < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1672 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1673 if (i == y && i & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1674 return -0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1675 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1676 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1677 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1678 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1679 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1680 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1681 if (y > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1682 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1683 else if (y < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1684 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1685 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1686 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1687
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1688 if (x == 0.0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1689 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1690 if (signbit(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1691 { long i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1692
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1693 i = cast(long)y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1694 if (y > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1695 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1696 if (i == y && i & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1697 return -0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1698 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1699 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1700 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1701 else if (y < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1702 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1703 if (i == y && i & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1704 return -real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1705 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1706 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1707 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1708 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1709 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1710 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1711 if (y > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1712 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1713 else if (y < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1714 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1715 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1716 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1717 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1718 return std.c.math.powl(x, y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1719 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1720 +/
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1721
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1722 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1723 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1724 real x = 46;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1725
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1726 assert(pow(x,0) == 1.0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1727 assert(pow(x,1) == x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1728 assert(pow(x,2) == x * x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1729 assert(pow(x,3) == x * x * x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1730 assert(pow(x,8) == (x * x) * (x * x) * (x * x) * (x * x));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1731 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1732
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1733 /****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1734 * Simple function to compare two floating point values
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1735 * to a specified precision.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1736 * Returns:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1737 * 1 match
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1738 * 0 nomatch
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1739 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1740
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1741 private int mfeq(real x, real y, real precision)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1742 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1743 if (x == y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1744 return 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1745 if (isnan(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1746 return isnan(y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1747 if (isnan(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1748 return 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1749 return fabs(x - y) <= precision;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1750 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1751
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1752 // Returns true if x is +0.0 (This function is used in unit tests)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1753 bool isPosZero(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1754 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1755 return (x == 0) && (signbit(x) == 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1756 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1757
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1758 // Returns true if x is -0.0 (This function is used in unit tests)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1759 bool isNegZero(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1760 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1761 return (x == 0) && signbit(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1762 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1763
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1764 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1765 * To what precision is x equal to y?
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1766 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1767 * Returns: the number of mantissa bits which are equal in x and y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1768 * eg, 0x1.F8p+60 and 0x1.F1p+60 are equal to 5 bits of precision.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1769 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1770 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1771 * $(TR $(TH x) $(TH y) $(TH feqrel(x, y)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1772 * $(TR $(TD x) $(TD x) $(TD real.mant_dig))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1773 * $(TR $(TD x) $(TD $(GT)= 2*x) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1774 * $(TR $(TD x) $(TD $(LT)= x/2) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1775 * $(TR $(TD $(NAN)) $(TD any) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1776 * $(TR $(TD any) $(TD $(NAN)) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1777 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1778 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1779
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1780 int feqrel(real x, real y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1781 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1782 /* Public Domain. Author: Don Clugston, 18 Aug 2005.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1783 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1784
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1785 if (x == y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1786 return real.mant_dig; // ensure diff!=0, cope with INF.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1787
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1788 real diff = fabs(x - y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1789
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1790 ushort pa = cast(ushort )(&x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1791 ushort pb = cast(ushort )(&y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1792 ushort pd = cast(ushort )(&diff);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1793
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1794 // The difference in abs(exponent) between x or y and abs(x-y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1795 // is equal to the number of mantissa bits of x which are
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1796 // equal to y. If negative, x and y have different exponents.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1797 // If positive, x and y are equal to 'bitsdiff' bits.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1798 // AND with 0x7FFF to form the absolute value.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1799 // To avoid out-by-1 errors, we subtract 1 so it rounds down
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1800 // if the exponents were different. This means 'bitsdiff' is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1801 // always 1 lower than we want, except that if bitsdiff==0,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1802 // they could have 0 or 1 bits in common.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1803 int bitsdiff = ( ((pa[4]&0x7FFF) + (pb[4]&0x7FFF)-1)>>1) - pd[4];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1804
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1805 if (pd[4] == 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1806 { // Difference is denormal
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1807 // For denormals, we need to add the number of zeros that
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1808 // lie at the start of diff's mantissa.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1809 // We do this by multiplying by 2^real.mant_dig
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1810 diff *= 0x1p+63;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1811 return bitsdiff + real.mant_dig - pd[4];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1812 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1813
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1814 if (bitsdiff > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1815 return bitsdiff + 1; // add the 1 we subtracted before
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1816
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1817 // Avoid out-by-1 errors when factor is almost 2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1818 return (bitsdiff == 0) ? (pa[4] == pb[4]) : 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1819 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1820
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1821 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1822 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1823 // Exact equality
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1824 assert(feqrel(real.max,real.max)==real.mant_dig);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1825 assert(feqrel(0,0)==real.mant_dig);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1826 assert(feqrel(7.1824,7.1824)==real.mant_dig);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1827 assert(feqrel(real.infinity,real.infinity)==real.mant_dig);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1828
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1829 // a few bits away from exact equality
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1830 real w=1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1831 for (int i=1; i<real.mant_dig-1; ++i) {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1832 assert(feqrel(1+w*real.epsilon,1)==real.mant_dig-i);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1833 assert(feqrel(1-w*real.epsilon,1)==real.mant_dig-i);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1834 assert(feqrel(1,1+(w-1)*real.epsilon)==real.mant_dig-i+1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1835 w*=2;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1836 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1837 assert(feqrel(1.5+real.epsilon,1.5)==real.mant_dig-1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1838 assert(feqrel(1.5-real.epsilon,1.5)==real.mant_dig-1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1839 assert(feqrel(1.5-real.epsilon,1.5+real.epsilon)==real.mant_dig-2);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1840
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1841 // Numbers that are close
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1842 assert(feqrel(0x1.Bp+84, 0x1.B8p+84)==5);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1843 assert(feqrel(0x1.8p+10, 0x1.Cp+10)==2);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1844 assert(feqrel(1.5*(1-real.epsilon), 1)==2);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1845 assert(feqrel(1.5, 1)==1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1846 assert(feqrel(2*(1-real.epsilon), 1)==1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1847
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1848 // Factors of 2
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1849 assert(feqrel(real.max,real.infinity)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1850 assert(feqrel(2*(1-real.epsilon), 1)==1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1851 assert(feqrel(1, 2)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1852 assert(feqrel(4, 1)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1853
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1854 // Extreme inequality
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1855 assert(feqrel(real.nan,real.nan)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1856 assert(feqrel(0,-real.nan)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1857 assert(feqrel(real.nan,real.infinity)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1858 assert(feqrel(real.infinity,-real.infinity)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1859 assert(feqrel(-real.max,real.infinity)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1860 assert(feqrel(real.max,-real.max)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1861 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1862
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1863
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1864 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1865 * Evaluate polynomial A(x) = a<sub>0</sub> + a<sub>1</sub>x + a<sub>2</sub>x² + a<sub>3</sub>x³ ...
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1866 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1867 * Uses Horner's rule A(x) = a<sub>0</sub> + x(a<sub>1</sub> + x(a<sub>2</sub> + x(a<sub>3</sub> + ...)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1868 * Params:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1869 * A = array of coefficients a<sub>0</sub>, a<sub>1</sub>, etc.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1870 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1871 real poly(real x, real[] A)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1872 in
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1873 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1874 assert(A.length > 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1875 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1876 body
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1877 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1878 version (D_InlineAsm_X86)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1879 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1880 version (Windows)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1881 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1882 asm // assembler by W. Bright
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1883 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1884 // EDX = (A.length - 1) * real.sizeof
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1885 mov ECX,A[EBP] ; // ECX = A.length
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1886 dec ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1887 lea EDX,[ECX][ECX*8] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1888 add EDX,ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1889 add EDX,A+4[EBP] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1890 fld real ptr [EDX] ; // ST0 = coeff[ECX]
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1891 jecxz return_ST ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1892 fld x[EBP] ; // ST0 = x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1893 fxch ST(1) ; // ST1 = x, ST0 = r
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1894 align 4 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1895 L2: fmul ST,ST(1) ; // r *= x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1896 fld real ptr -10[EDX] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1897 sub EDX,10 ; // deg--
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1898 faddp ST(1),ST ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1899 dec ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1900 jne L2 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1901 fxch ST(1) ; // ST1 = r, ST0 = x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1902 fstp ST(0) ; // dump x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1903 align 4 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1904 return_ST: ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1905 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1906 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1907 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1908 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1909 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1910 asm // assembler by W. Bright
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1911 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1912 // EDX = (A.length - 1) * real.sizeof
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1913 mov ECX,A[EBP] ; // ECX = A.length
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1914 dec ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1915 lea EDX,[ECX*8] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1916 lea EDX,[EDX][ECX*4] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1917 add EDX,A+4[EBP] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1918 fld real ptr [EDX] ; // ST0 = coeff[ECX]
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1919 jecxz return_ST ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1920 fld x[EBP] ; // ST0 = x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1921 fxch ST(1) ; // ST1 = x, ST0 = r
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1922 align 4 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1923 L2: fmul ST,ST(1) ; // r *= x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1924 fld real ptr -12[EDX] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1925 sub EDX,12 ; // deg--
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1926 faddp ST(1),ST ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1927 dec ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1928 jne L2 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1929 fxch ST(1) ; // ST1 = r, ST0 = x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1930 fstp ST(0) ; // dump x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1931 align 4 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1932 return_ST: ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1933 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1934 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1935 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1936 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1937 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1938 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1939 int i = A.length - 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1940 real r = A[i];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1941 while (--i >= 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1942 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1943 r *= x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1944 r += A[i];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1945 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1946 return r;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1947 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1948 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1949
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1950 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1951 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1952 debug (math) printf("math.poly.unittest\n");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1953 real x = 3.1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1954 static real pp[] = [56.1, 32.7, 6];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1955
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1956 assert( poly(x, pp) == (56.1L + (32.7L + 6L * x) * x) );
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1957 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1958
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements. lindquist parents: diff changeset	1959

Mercurial > projects > ldc

annotate lphobos/std/math.d @ 883:b52d5de7783f