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annotate lphobos/std/math.d @ 108:288fe1029e1f trunk

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[svn r112] Fixed 'case 1,2,3:' style case statements. Fixed a bunch of bugs with return/break/continue in loops. Fixed support for the DMDFE hidden implicit return value variable. This can be needed for some foreach statements where the loop body is converted to a nested delegate, but also possibly returns from the function. Added std.math to phobos. Added AA runtime support code, done ground work for implementing AAs. Several other bugfixes.
author lindquist
date Tue, 20 Nov 2007 05:29:20 +0100
parents
children 373489eeaf90
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108
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1 // Written in the D programming language
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2
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3 /**
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4 * Macros:
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5 * WIKI = Phobos/StdMath
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6 *
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7 * TABLE_SV = <table border=1 cellpadding=4 cellspacing=0>
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8 * <caption>Special Values</caption>
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9 * $0</table>
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10 * SVH = $(TR $(TH $1) $(TH $2))
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11 * SV = $(TR $(TD $1) $(TD $2))
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12 *
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13 * NAN = $(RED NAN)
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14 * SUP = <span style="vertical-align:super;font-size:smaller">$0</span>
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15 * GAMMA = &#915;
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16 * INTEGRAL = &#8747;
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17 * INTEGRATE = $(BIG &#8747;<sub>$(SMALL $1)</sub><sup>$2</sup>)
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18 * POWER = $1<sup>$2</sup>
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19 * BIGSUM = $(BIG &Sigma; <sup>$2</sup><sub>$(SMALL $1)</sub>)
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20 * CHOOSE = $(BIG &#40;) <sup>$(SMALL $1)</sup><sub>$(SMALL $2)</sub> $(BIG &#41;)
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21 * PLUSMN = &plusmn;
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22 * INFIN = &infin;
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23 * PI = &pi;
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24 * LT = &lt;
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25 * GT = &gt;
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26 */
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27
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28 /*
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29 * Author:
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30 * Walter Bright
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31 * Copyright:
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32 * Copyright (c) 2001-2005 by Digital Mars,
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33 * All Rights Reserved,
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34 * www.digitalmars.com
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35 * Copyright (c) 2007 by Tomas Lindquist Olsen
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36 * License:
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37 * This software is provided 'as-is', without any express or implied
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38 * warranty. In no event will the authors be held liable for any damages
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39 * arising from the use of this software.
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40 *
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41 * Permission is granted to anyone to use this software for any purpose,
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42 * including commercial applications, and to alter it and redistribute it
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43 * freely, subject to the following restrictions:
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44 *
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45 * <ul>
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46 * <li> The origin of this software must not be misrepresented; you must not
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47 * claim that you wrote the original software. If you use this software
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48 * in a product, an acknowledgment in the product documentation would be
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49 * appreciated but is not required.
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50 * </li>
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51 * <li> Altered source versions must be plainly marked as such, and must not
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52 * be misrepresented as being the original software.
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53 * </li>
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54 * <li> This notice may not be removed or altered from any source
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55 * distribution.
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56 * </li>
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57 * </ul>
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58 */
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59
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60
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61 module std.math;
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62
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63 //debug=math; // uncomment to turn on debugging printf's
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64
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65 private import std.c.stdio;
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66 private import std.c.math;
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67
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68 class NotImplemented : Error
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69 {
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70 this(string msg)
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71 {
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72 super(msg ~ "not implemented");
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73 }
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74 }
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75
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76 const real E = 2.7182818284590452354L; /** e */
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77 const real LOG2T = 0x1.a934f0979a3715fcp+1; /** log<sub>2</sub>10 */ // 3.32193 fldl2t
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78 const real LOG2E = 0x1.71547652b82fe178p+0; /** log<sub>2</sub>e */ // 1.4427 fldl2e
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79 const real LOG2 = 0x1.34413509f79fef32p-2; /** log<sub>10</sub>2 */ // 0.30103 fldlg2
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80 const real LOG10E = 0.43429448190325182765; /** log<sub>10</sub>e */
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81 const real LN2 = 0x1.62e42fefa39ef358p-1; /** ln 2 */ // 0.693147 fldln2
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82 const real LN10 = 2.30258509299404568402; /** ln 10 */
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83 const real PI = 0x1.921fb54442d1846ap+1; /** $(PI) */ // 3.14159 fldpi
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84 const real PI_2 = 1.57079632679489661923; /** $(PI) / 2 */
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85 const real PI_4 = 0.78539816339744830962; /** $(PI) / 4 */
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86 const real M_1_PI = 0.31830988618379067154; /** 1 / $(PI) */
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87 const real M_2_PI = 0.63661977236758134308; /** 2 / $(PI) */
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88 const real M_2_SQRTPI = 1.12837916709551257390; /** 2 / &radic;$(PI) */
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89 const real SQRT2 = 1.41421356237309504880; /** &radic;2 */
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90 const real SQRT1_2 = 0.70710678118654752440; /** &radic;&frac12; */
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91
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92 /*
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93 Octal versions:
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94 PI/64800 0.00001 45530 36176 77347 02143 15351 61441 26767
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95 PI/180 0.01073 72152 11224 72344 25603 54276 63351 22056
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96 PI/8 0.31103 75524 21026 43021 51423 06305 05600 67016
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97 SQRT(1/PI) 0.44067 27240 41233 33210 65616 51051 77327 77303
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98 2/PI 0.50574 60333 44710 40522 47741 16537 21752 32335
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99 PI/4 0.62207 73250 42055 06043 23046 14612 13401 56034
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100 SQRT(2/PI) 0.63041 05147 52066 24106 41762 63612 00272 56161
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101
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102 PI 3.11037 55242 10264 30215 14230 63050 56006 70163
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103 LOG2 0.23210 11520 47674 77674 61076 11263 26013 37111
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104 */
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105
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106
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107 /***********************************
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108 * Calculates the absolute value
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109 *
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110 * For complex numbers, abs(z) = sqrt( $(POWER z.re, 2) + $(POWER z.im, 2) )
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111 * = hypot(z.re, z.im).
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112 */
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113 real abs(real x)
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114 {
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115 return fabs(x);
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116 }
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117
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118 /** ditto */
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119 long abs(long x)
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120 {
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121 return x>=0 ? x : -x;
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122 }
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123
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124 /** ditto */
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125 int abs(int x)
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126 {
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127 return x>=0 ? x : -x;
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128 }
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129
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130 /** ditto */
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131 real abs(creal z)
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132 {
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133 return hypot(z.re, z.im);
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134 }
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135
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136 /** ditto */
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137 real abs(ireal y)
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138 {
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139 return fabs(y.im);
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140 }
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141
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142
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143 unittest
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144 {
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145 assert(isPosZero(abs(-0.0L)));
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146 assert(isnan(abs(real.nan)));
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147 assert(abs(-real.infinity) == real.infinity);
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148 assert(abs(-3.2Li) == 3.2L);
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149 assert(abs(71.6Li) == 71.6L);
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150 assert(abs(-56) == 56);
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151 assert(abs(2321312L) == 2321312L);
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152 assert(abs(-1+1i) == sqrt(2.0));
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153 }
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154
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155 /***********************************
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156 * Complex conjugate
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157 *
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158 * conj(x + iy) = x - iy
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159 *
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160 * Note that z * conj(z) = $(POWER z.re, 2) - $(POWER z.im, 2)
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161 * is always a real number
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162 */
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163 creal conj(creal z)
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164 {
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165 return z.re - z.im*1i;
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166 }
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167
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168 /** ditto */
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169 ireal conj(ireal y)
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170 {
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171 return -y;
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172 }
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173
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174 unittest
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175 {
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176 assert(conj(7 + 3i) == 7-3i);
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177 ireal z = -3.2Li;
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178 assert(conj(z) == -z);
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179 }
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180
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181 /***********************************
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182 * Returns cosine of x. x is in radians.
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183 *
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184 * $(TABLE_SV
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185 * $(TR $(TH x) $(TH cos(x)) $(TH invalid?))
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186 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes) )
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187 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes) )
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188 * )
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189 * Bugs:
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190 * Results are undefined if |x| >= $(POWER 2,64).
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191 */
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192
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193 pragma(LLVM_internal, "intrinsic", "llvm.cos.f32")
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194 float cos(float x);
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195
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196 pragma(LLVM_internal, "intrinsic", "llvm.cos.f64") {
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197 double cos(double x); // ditto
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198 real cos(real x); /// ditto
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199 }
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200
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201
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202 /***********************************
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203 * Returns sine of x. x is in radians.
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204 *
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205 * $(TABLE_SV
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206 * $(TR $(TH x) $(TH sin(x)) $(TH invalid?))
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207 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
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208 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
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209 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes))
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210 * )
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211 * Bugs:
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212 * Results are undefined if |x| >= $(POWER 2,64).
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213 */
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214
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215 pragma(LLVM_internal, "intrinsic", "llvm.sin.f32")
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216 float sin(float x);
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217
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218 pragma(LLVM_internal, "intrinsic", "llvm.sin.f64") {
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219 double sin(double x); // ditto
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220 real sin(real x); /// ditto
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221 }
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222
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223
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224 /****************************************************************************
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225 * Returns tangent of x. x is in radians.
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226 *
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227 * $(TABLE_SV
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228 * $(TR $(TH x) $(TH tan(x)) $(TH invalid?))
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229 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
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230 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
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231 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes))
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232 * )
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233 */
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234
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235 version(D_InlineAsm_X86)
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236 real tan(real x)
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237 {
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238
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239 asm
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240 {
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241 fld x[EBP] ; // load theta
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242 fxam ; // test for oddball values
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243 fstsw AX ;
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244 sahf ;
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245 jc trigerr ; // x is NAN, infinity, or empty
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246 // 387's can handle denormals
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247 SC18: fptan ;
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248 fstp ST(0) ; // dump X, which is always 1
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249 fstsw AX ;
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250 sahf ;
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251 jnp Lret ; // C2 = 1 (x is out of range)
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252
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253 // Do argument reduction to bring x into range
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254 fldpi ;
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255 fxch ;
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256 SC17: fprem1 ;
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257 fstsw AX ;
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258 sahf ;
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259 jp SC17 ;
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260 fstp ST(1) ; // remove pi from stack
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261 jmp SC18 ;
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262
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263 trigerr:
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264 jnp Lret ; // if theta is NAN, return theta
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265 fstp ST(0) ; // dump theta
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266 }
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267 return real.nan;
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268
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269 Lret:
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270 ;
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271 }
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272 else
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273 {
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274 real tan(real x) { return std.c.math.atan(x); }
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275 }
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276
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277
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278 unittest
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279 {
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280 static real vals[][2] = // angle,tan
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281 [
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282 [ 0, 0],
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283 [ .5, .5463024898],
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284 [ 1, 1.557407725],
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285 [ 1.5, 14.10141995],
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286 [ 2, -2.185039863],
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287 [ 2.5,-.7470222972],
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288 [ 3, -.1425465431],
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289 [ 3.5, .3745856402],
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290 [ 4, 1.157821282],
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291 [ 4.5, 4.637332055],
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292 [ 5, -3.380515006],
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293 [ 5.5,-.9955840522],
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294 [ 6, -.2910061914],
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295 [ 6.5, .2202772003],
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296 [ 10, .6483608275],
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297
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298 // special angles
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299 [ PI_4, 1],
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300 //[ PI_2, real.infinity],
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parents:
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301 [ 3*PI_4, -1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
302 [ PI, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
303 [ 5*PI_4, 1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
304 //[ 3*PI_2, -real.infinity],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
305 [ 7*PI_4, -1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
306 [ 2*PI, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
307
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
308 // overflow
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
309 [ real.infinity, real.nan],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
310 [ real.nan, real.nan],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
311 //[ 1e+100, real.nan],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
312 ];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
313 int i;
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 for (i = 0; i < vals.length; 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 real x = vals[i][0];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
318 real r = vals[i][1];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
319 real t = tan(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
320
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
321 //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
322 assert(mfeq(r, t, .0000001));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
323
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
324 x = -x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
325 r = -r;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
326 t = tan(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
327 //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
328 assert(mfeq(r, t, .0000001));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
329 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
330 }
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 * Calculates the arc cosine of x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
334 * 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
335 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
336 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
337 * $(TR $(TH x) $(TH acos(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
338 * $(TR $(TD $(GT)1.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
339 * $(TR $(TD $(LT)-1.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
340 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
341 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
342 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
343 real acos(real x) { return std.c.math.acos(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
344
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
345 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
346 * Calculates the arc sine of x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
347 * returning a value ranging from -$(PI)/2 to $(PI)/2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
348 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
349 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
350 * $(TR $(TH x) $(TH asin(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
351 * $(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
352 * $(TR $(TD $(GT)1.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
353 * $(TR $(TD $(LT)-1.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
354 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
355 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
356 real asin(real x) { return std.c.math.asin(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
357
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
358 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
359 * Calculates the arc tangent of x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
360 * returning a value ranging from -$(PI)/2 to $(PI)/2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
361 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
362 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
363 * $(TR $(TH x) $(TH atan(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
364 * $(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
365 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
366 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
367 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
368 real atan(real x) { return std.c.math.atan(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
369
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
370 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
371 * Calculates the arc tangent of y / x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
372 * returning a value ranging from -$(PI)/2 to $(PI)/2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
373 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
374 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
375 * $(TR $(TH y) $(TH x) $(TH atan(y, x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
376 * $(TR $(TD $(NAN)) $(TD anything) $(TD $(NAN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
377 * $(TR $(TD anything) $(TD $(NAN)) $(TD $(NAN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
378 * $(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
379 * $(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
380 * $(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
381 * $(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
382 * $(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
383 * $(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
384 * $(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
385 * $(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
386 * $(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
387 * $(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
388 * $(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
389 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
390 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
391 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
392
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
393 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
394 * Calculates the hyperbolic cosine of x.
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
397 * $(TR $(TH x) $(TH cosh(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
398 * $(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
399 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
400 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
401 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
402
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
403 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
404 * Calculates the hyperbolic sine of x.
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
407 * $(TR $(TH x) $(TH sinh(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
408 * $(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
409 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
410 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
411 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
412 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
413
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
414 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
415 * Calculates the hyperbolic tangent of x.
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
418 * $(TR $(TH x) $(TH tanh(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
419 * $(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
420 * $(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
421 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
422 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
423 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
424
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
425 //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
426 //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
427 //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
428
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
429 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
430 * Calculates the inverse hyperbolic cosine of x.
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 * Mathematically, acosh(x) = log(x + sqrt( x*x - 1))
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 * $(TABLE_DOMRG
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
435 * $(DOMAIN 1..$(INFIN))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
436 * $(RANGE 1..log(real.max), $(INFIN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
437 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
438 * $(SVH x, acosh(x) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
439 * $(SV $(NAN), $(NAN) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
440 * $(SV <1, $(NAN) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
441 * $(SV 1, 0 )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
442 * $(SV +$(INFIN),+$(INFIN))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
443 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
444 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
445 real acosh(real x)
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 if (x > 1/real.epsilon)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
448 return LN2 + log(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
449 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
450 return log(x + sqrt(x*x - 1));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
451 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
452
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
453 unittest
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 assert(isnan(acosh(0.9)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
456 assert(isnan(acosh(real.nan)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
457 assert(acosh(1)==0.0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
458 assert(acosh(real.infinity) == real.infinity);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
459 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
460
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 * Calculates the inverse hyperbolic sine of x.
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 * Mathematically,
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 * 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
467 * 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
468 * -------------
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
469 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
470 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
471 * $(SVH x, asinh(x) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
472 * $(SV $(NAN), $(NAN) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
473 * $(SV $(PLUSMN)0, $(PLUSMN)0 )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
474 * $(SV $(PLUSMN)$(INFIN),$(PLUSMN)$(INFIN))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
475 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
476 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
477 real asinh(real x)
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 if (fabs(x) > 1 / real.epsilon) // beyond this point, x*x + 1 == x*x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
480 return copysign(LN2 + log(fabs(x)), x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
481 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
482 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
483 // sqrt(x*x + 1) == 1 + x * x / ( 1 + sqrt(x*x + 1) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
484 return copysign(log1p(fabs(x) + x*x / (1 + sqrt(x*x + 1)) ), x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
485 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
486 }
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 unittest
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 assert(isPosZero(asinh(0.0)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
491 assert(isNegZero(asinh(-0.0)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
492 assert(asinh(real.infinity) == real.infinity);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
493 assert(asinh(-real.infinity) == -real.infinity);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
494 assert(isnan(asinh(real.nan)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
495 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
496
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 * Calculates the inverse hyperbolic tangent of x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
499 * returning a value from ranging from -1 to 1.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
500 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
501 * Mathematically, atanh(x) = log( (1+x)/(1-x) ) / 2
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 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
504 * $(TABLE_DOMRG
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
505 * $(DOMAIN -$(INFIN)..$(INFIN))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
506 * $(RANGE -1..1) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
507 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
508 * $(SVH x, acosh(x) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
509 * $(SV $(NAN), $(NAN) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
510 * $(SV $(PLUSMN)0, $(PLUSMN)0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
511 * $(SV -$(INFIN), -0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
512 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
513 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
514 real atanh(real x)
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 // 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
517 return 0.5 * log1p( 2 * x / (1 - x) );
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
518 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
519
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
520 unittest
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 assert(isPosZero(atanh(0.0)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
523 assert(isNegZero(atanh(-0.0)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
524 assert(isnan(atanh(real.nan)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
525 assert(isnan(atanh(-real.infinity)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
526 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
527
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 * 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
530 * If the integer value of x is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
531 * greater than long.max, the result is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
532 * indeterminate.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
533 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
534 long rndtol(real x); /* intrinsic */
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
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 * 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
539 * If the integer value of x is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
540 * greater than long.max, the result is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
541 * indeterminate.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
542 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
543 extern (C) real rndtonl(real x);
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 /***************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
546 * Compute square root of x.
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
549 * $(TR $(TH x) $(TH sqrt(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
550 * $(TR $(TD -0.0) $(TD -0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
551 * $(TR $(TD $(LT)0.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
552 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
553 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
554 */
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 pragma(LLVM_internal, "intrinsic", "llvm.sqrt.f32")
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
557 float sqrt(float x); /* intrinsic */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
558
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
559 pragma(LLVM_internal, "intrinsic", "llvm.sqrt.f64") {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
560 double sqrt(double x); /* intrinsic */ /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
561 real sqrt(real x); /* intrinsic */ /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
562 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
563
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
564 creal sqrt(creal z)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
565 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
566 creal c;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
567 real x,y,w,r;
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 if (z == 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
570 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
571 c = 0 + 0i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
572 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
573 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
574 { real z_re = z.re;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
575 real z_im = z.im;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
576
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
577 x = fabs(z_re);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
578 y = fabs(z_im);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
579 if (x >= y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
580 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
581 r = y / x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
582 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
583 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
584 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
585 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
586 r = x / y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
587 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
588 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
589
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
590 if (z_re >= 0)
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 c = w + (z_im / (w + w)) * 1.0i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
593 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
594 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
595 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
596 if (z_im < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
597 w = -w;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
598 c = z_im / (w + w) + w * 1.0i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
599 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
600 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
601 return c;
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 /**********************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
605 * Calculates e$(SUP x).
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
608 * $(TR $(TH x) $(TH exp(x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
609 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
610 * $(TR $(TD -$(INFIN)) $(TD +0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
611 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
612 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
613 real exp(real x) { return std.c.math.exp(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
614
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
615 /**********************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
616 * Calculates 2$(SUP 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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
619 * $(TR $(TH x) $(TH exp2(x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
620 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
621 * $(TR $(TD -$(INFIN)) $(TD +0.0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
622 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
623 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
624 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
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 * Calculates the value of the natural logarithm base (e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
628 * raised to the power of x, minus 1.
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 * For very small x, expm1(x) is more accurate
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
631 * than exp(x)-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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
634 * $(TR $(TH x) $(TH e$(SUP x)-1))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
635 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
636 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
637 * $(TR $(TD -$(INFIN)) $(TD -1.0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
638 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
639 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
640
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
641 real expm1(real x) { return std.c.math.expm1(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
642
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
643
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
644 /*********************************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
645 * Separate floating point value into significand and exponent.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
646 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
647 * Returns:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
648 * Calculate and return <i>x</i> and exp such that
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
649 * value =<i>x</i>*2$(SUP exp) and
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
650 * .5 $(LT)= |<i>x</i>| $(LT) 1.0<br>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
651 * <i>x</i> has same sign as value.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
652 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
653 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
654 * $(TR $(TH value) $(TH returns) $(TH exp))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
655 * $(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
656 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD int.max))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
657 * $(TR $(TD -$(INFIN)) $(TD -$(INFIN)) $(TD int.min))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
658 * $(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
659 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
660 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
661
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 real frexp(real value, out int exp)
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 ushort* vu = cast(ushort*)&value;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
666 long* vl = cast(long*)&value;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
667 uint ex;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
668
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
669 // If exponent is non-zero
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
670 ex = vu[4] & 0x7FFF;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
671 if (ex)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
672 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
673 if (ex == 0x7FFF)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
674 { // infinity or NaN
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
675 if (*vl & 0x7FFFFFFFFFFFFFFF) // if NaN
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
676 { *vl |= 0xC000000000000000; // convert $(NAN)S to $(NAN)Q
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
677 exp = int.min;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
678 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
679 else if (vu[4] & 0x8000)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
680 { // negative infinity
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
681 exp = int.min;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
682 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
683 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
684 { // positive infinity
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
685 exp = int.max;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
686 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
687 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
688 else
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 exp = ex - 0x3FFE;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
691 vu[4] = cast(ushort)((0x8000 & vu[4]) | 0x3FFE);
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 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
694 else if (!*vl)
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 // value is +-0.0
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
697 exp = 0;
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 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
700 { // denormal
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
701 int i = -0x3FFD;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
702
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
703 do
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
704 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
705 i--;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
706 *vl <<= 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
707 } while (*vl > 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
708 exp = i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
709 vu[4] = cast(ushort)((0x8000 & vu[4]) | 0x3FFE);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
710 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
711 return value;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
712 }
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
715 unittest
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 static real vals[][3] = // x,frexp,exp
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
718 [
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
719 [0.0, 0.0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
720 [-0.0, -0.0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
721 [1.0, .5, 1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
722 [-1.0, -.5, 1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
723 [2.0, .5, 2],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
724 [155.67e20, 0x1.A5F1C2EB3FE4Fp-1, 74], // normal
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
725 [1.0e-320, 0.98829225, -1063],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
726 [real.min, .5, -16381],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
727 [real.min/2.0L, .5, -16382], // denormal
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
728
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
729 [real.infinity,real.infinity,int.max],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
730 [-real.infinity,-real.infinity,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
731 [real.nan,real.nan,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
732 [-real.nan,-real.nan,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
733
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
734 // Don't really support signalling nan's in D
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
735 //[real.nans,real.nan,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
736 //[-real.nans,-real.nan,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
737 ];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
738 int i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
739
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
740 for (i = 0; i < vals.length; i++)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
741 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
742 real x = vals[i][0];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
743 real e = vals[i][1];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
744 int exp = cast(int)vals[i][2];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
745 int eptr;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
746 real v = frexp(x, eptr);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
747
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
748 //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
749 assert(mfeq(e, v, .0000001));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
750 assert(exp == eptr);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
751 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
752 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
753
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 * 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
757 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
758 * 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
759 * <tt>cast(int)logb(x)</tt>.
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
762 * $(TR $(TH x) $(TH ilogb(x)) $(TH Range error?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
763 * $(TR $(TD 0) $(TD FP_ILOGB0) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
764 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD int.max) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
765 * $(TR $(TD $(NAN)) $(TD FP_ILOGBNAN) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
766 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
767 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
768 int ilogb(real x) { return std.c.math.ilogb(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
769
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
770 alias std.c.math.FP_ILOGB0 FP_ILOGB0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
771 alias std.c.math.FP_ILOGBNAN FP_ILOGBNAN;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
772
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
773
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
774 /*******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
775 * Compute n * 2$(SUP exp)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
776 * References: frexp
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
779 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
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 * Calculate the natural logarithm of x.
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
785 * $(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
786 * $(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
787 * $(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
788 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
789 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
790 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
791
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
792 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
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 * Calculate the base-10 logarithm of 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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
798 * $(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
799 * $(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
800 * $(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
801 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
802 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
803 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
804
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
805 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
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 * Calculates the natural logarithm of 1 + 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 * 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
811 * log(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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
814 * $(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
815 * $(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
816 * $(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
817 * $(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
818 * $(TR $(TD +$(INFIN)) $(TD -$(INFIN)) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
819 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
820 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
821
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
822 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
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 * Calculates the base-2 logarithm of x:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
826 * log<sub>2</sub>x
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
829 * $(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
830 * $(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
831 * $(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
832 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
833 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
834 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
835 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
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 * 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
839 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
840 * 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
841 * For a positive, finite x:
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 * -----
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
844 * 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
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
848 * $(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
849 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
850 * $(TR $(TD $(PLUSMN)0.0) $(TD -$(INFIN)) $(TD yes) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
851 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
852 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
853 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
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 * Calculates the remainder from the calculation x/y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
857 * Returns:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
858 * 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
859 * 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
860 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
861 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
862 * $(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
863 * $(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
864 * $(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
865 * $(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
866 * $(TR $(TD !=$(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD x) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
867 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
868 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
869 real modf(real x, inout real y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
870 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
871 double Y = y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
872 auto tmp = std.c.math.modf(x,&Y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
873 y = Y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
874 return tmp;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
875 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
876
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
877 /*************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
878 * Efficiently calculates x * 2$(SUP n).
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 * scalbn handles underflow and overflow in
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
881 * the same fashion as the basic arithmetic operators.
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
884 * $(TR $(TH x) $(TH scalb(x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
885 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
886 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
887 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
888 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
889 real scalbn(real x, int n)
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 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
892 return std.c.math.scalbn(x, n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
893 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
894 throw new NotImplemented("scalbn");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
895 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
896
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
897 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
898 * Calculates the cube root x.
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
901 * $(TR $(TH $(I x)) $(TH cbrt(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
902 * $(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
903 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
904 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
905 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
906 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
907 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
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 /*******************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
911 * Returns |x|
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
914 * $(TR $(TH x) $(TH fabs(x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
915 * $(TR $(TD $(PLUSMN)0.0) $(TD +0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
916 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
917 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
918 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
919 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
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 /***********************************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
923 * Calculates the length of the
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
924 * 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
925 * 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
926 * the sums of the squares of x and y:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
927 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
928 * sqrt(x&sup2; + y&sup2;)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
929 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
930 * Note that hypot(x, y), hypot(y, x) and
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
931 * hypot(x, -y) are equivalent.
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 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
934 * $(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
935 * $(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
936 * $(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
937 * $(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
938 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
939 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
940
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
941 real hypot(real x, real y)
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 * This is based on code from:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
945 * Cephes Math Library Release 2.1: January, 1989
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
946 * Copyright 1984, 1987, 1989 by Stephen L. Moshier
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
947 * Direct inquiries to 30 Frost Street, Cambridge, MA 02140
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
948 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
949
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
950 const int PRECL = 32;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
951 const int MAXEXPL = real.max_exp; //16384;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
952 const int MINEXPL = real.min_exp; //-16384;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
953
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
954 real xx, yy, b, re, im;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
955 int ex, ey, e;
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 // Note, hypot(INFINITY, NAN) = INFINITY.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
958 if (isinf(x) || isinf(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
959 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
960
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
961 if (isnan(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
962 return x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
963 if (isnan(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
964 return y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
965
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
966 re = fabs(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
967 im = fabs(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 if (re == 0.0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
970 return im;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
971 if (im == 0.0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
972 return re;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
973
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
974 // Get the exponents of the numbers
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
975 xx = frexp(re, ex);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
976 yy = frexp(im, ey);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
977
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
978 // 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
979 e = ex - ey;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
980 if (e > PRECL)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
981 return re;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
982 if (e < -PRECL)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
983 return im;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
984
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
985 // Find approximate exponent e of the geometric mean.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
986 e = (ex + ey) >> 1;
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 // Rescale so mean is about 1
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
989 xx = ldexp(re, -e);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
990 yy = ldexp(im, -e);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
991
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
992 // Hypotenuse of the right triangle
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
993 b = sqrt(xx * xx + yy * yy);
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 // Compute the exponent of the answer.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
996 yy = frexp(b, ey);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
997 ey = e + ey;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
998
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
999 // Check it for overflow and underflow.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1000 if (ey > MAXEXPL + 2)
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 //return __matherr(_OVERFLOW, INFINITY, x, y, "hypotl");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1003 return real.infinity;
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 if (ey < MINEXPL - 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1006 return 0.0;
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 // Undo the scaling
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1009 b = ldexp(b, e);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1010 return b;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1011 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1012
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1013 unittest
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 static real vals[][3] = // x,y,hypot
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1016 [
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1017 [ 0, 0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1018 [ 0, -0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1019 [ 3, 4, 5],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1020 [ -300, -400, 500],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1021 [ real.min, real.min, 4.75473e-4932L],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1022 [ 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
1023 [ real.infinity, real.nan, real.infinity],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1024 [ real.nan, real.nan, real.nan],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1025 ];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1026 int i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1027
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1028 for (i = 0; i < vals.length; i++)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1029 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1030 real x = vals[i][0];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1031 real y = vals[i][1];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1032 real z = vals[i][2];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1033 real h = hypot(x, y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1034
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1035 //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
1036 //if (!mfeq(z, h, .0000001))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1037 //printf("%La\n", h);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1038 assert(mfeq(z, h, .0000001));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1039 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1040 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1041
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 * Returns the error function of x.
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 * <img src="erf.gif" alt="error function">
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1046 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1047 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
1048
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 * 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
1051 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1052 * <img src="erfc.gif" alt="complementary error function">
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1053 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1054 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
1055
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 * Natural logarithm of gamma function.
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 * 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
1060 * value of the gamma function of the argument.
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 * 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
1063 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1064 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1065 * $(TR $(TH x) $(TH lgamma(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1066 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1067 * $(TR $(TD integer <= 0) $(TD +$(INFIN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1068 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1069 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1070 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1071 /* Documentation prepared by Don Clugston */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1072 real lgamma(real x)
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 return std.c.math.lgamma(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1075
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1076 // 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
1077 }
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 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1080 * The Gamma function, $(GAMMA)(x)
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 * $(GAMMA)(x) is a generalisation of the factorial function
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1083 * to real and complex numbers.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1084 * Like x!, $(GAMMA)(x+1) = x*$(GAMMA)(x).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1085 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1086 * Mathematically, if z.re > 0 then
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1087 * $(GAMMA)(z) =<big>$(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
1088 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1089 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1090 * $(TR $(TH x) $(TH $(GAMMA)(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1091 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1092 * $(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
1093 * $(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
1094 * $(TR $(TD integer $(LT)0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1095 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1096 * $(TR $(TD -$(INFIN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1097 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1098 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1099 * References:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1100 * $(LINK http://en.wikipedia.org/wiki/Gamma_function),
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1101 * $(LINK http://www.netlib.org/cephes/ldoubdoc.html#gamma)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1102 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1103 /* Documentation prepared by Don Clugston */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1104 real tgamma(real x)
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 return std.c.math.tgamma(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1107
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1108 // 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
1109 }
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 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1112 * 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
1113 * (toward positive infinity).
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 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
1116
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 * 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
1119 * (toward negative infinity).
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 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
1122
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 * 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
1125 * mode.
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 * Unlike the rint functions, nearbyint does not raise the
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1128 * FE_INEXACT exception.
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 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
1131
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 * 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
1134 * mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1135 * 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
1136 * exception is raised.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1137 * <b>nearbyint</b> performs
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1138 * 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
1139 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1140 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
1141
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 * 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
1144 * mode.
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 long lrint(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1147 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1148 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1149 return std.c.math.llrint(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1150 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1151 throw new NotImplemented("lrint");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1152 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1153
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1154 /*******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1155 * 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
1156 * 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
1157 * the even integer.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1158 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1159 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
1160
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 * 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
1163 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1164 * 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
1165 * away from zero.
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 long lround(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1168 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1169 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1170 return std.c.math.llround(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1171 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1172 throw new NotImplemented("lround");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1173 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1174
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1175 /****************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1176 * 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
1177 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1178 * This is also known as "chop" rounding.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1179 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1180 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
1181
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 * Calculate the remainder x REM y, following IEC 60559.
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 * 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
1186 * value of x / y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1187 * If |n - x / y| == 0.5, n is even.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1188 * 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
1189 * 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
1190 * Precision mode has no effect on the remainder functions.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1191 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1192 * remquo returns n in the parameter n.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1193 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1194 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1195 * $(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
1196 * $(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
1197 * $(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
1198 * $(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
1199 * $(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
1200 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1201 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1202 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
1203
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1204 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
1205 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1206 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1207 return std.c.math.remquo(x, y, &n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1208 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1209 throw new NotImplemented("remquo");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1210 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1211
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1212 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1213 * Returns !=0 if e is a NaN.
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 int isnan(real e)
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 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1219 ulong* ps = cast(ulong *)&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 return (pe[4] & 0x7FFF) == 0x7FFF &&
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1222 *ps & 0x7FFFFFFFFFFFFFFF;
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1225 unittest
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 assert(isnan(float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1228 assert(isnan(-double.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1229 assert(isnan(real.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1230
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1231 assert(!isnan(53.6));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1232 assert(!isnan(float.infinity));
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1235 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1236 * Returns !=0 if e is finite.
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 int isfinite(real e)
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 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1242
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1243 return (pe[4] & 0x7FFF) != 0x7FFF;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1244 }
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 unittest
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 assert(isfinite(1.23));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1249 assert(!isfinite(double.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1250 assert(!isfinite(float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1251 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1252
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1253
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 * Returns !=0 if x is normalized.
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 /* Need one for each format because subnormal floats might
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1259 * be converted to normal reals.
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1262 int isnormal(float x)
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 uint *p = cast(uint *)&x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1265 uint e;
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 e = *p & 0x7F800000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1268 //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
1269 return e && e != 0x7F800000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1270 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1271
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1272 /// ditto
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 int isnormal(double d)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1275 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1276 uint *p = cast(uint *)&d;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1277 uint e;
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 e = p[1] & 0x7FF00000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1280 return e && e != 0x7FF00000;
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1283 /// ditto
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 int isnormal(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1286 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1287 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1288 long* ps = cast(long *)&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 return (pe[4] & 0x7FFF) != 0x7FFF && *ps < 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1291 }
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 unittest
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 float f = 3;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1296 double d = 500;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1297 real e = 10e+48;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1298
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1299 assert(isnormal(f));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1300 assert(isnormal(d));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1301 assert(isnormal(e));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1302 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1303
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1304 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1305 * Is number subnormal? (Also called "denormal".)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1306 * 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
1307 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1308
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1309 /* Need one for each format because subnormal floats might
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1310 * be converted to normal reals.
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1313 int issubnormal(float f)
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 uint *p = cast(uint *)&f;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1316
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1317 //printf("*p = x%x\n", *p);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1318 return (*p & 0x7F800000) == 0 && *p & 0x007FFFFF;
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1321 unittest
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 float f = 3.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1324
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1325 for (f = 1.0; !issubnormal(f); f /= 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1326 assert(f != 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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1329 /// ditto
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 int issubnormal(double d)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1332 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1333 uint *p = cast(uint *)&d;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1334
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1335 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
1336 }
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 unittest
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 double f;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1341
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1342 for (f = 1; !issubnormal(f); f /= 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1343 assert(f != 0);
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1346 /// ditto
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 int issubnormal(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1349 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1350 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1351 long* ps = cast(long *)&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 return (pe[4] & 0x7FFF) == 0 && *ps > 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1354 }
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 unittest
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 real f;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1359
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1360 for (f = 1; !issubnormal(f); f /= 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1361 assert(f != 0);
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1364 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1365 * Return !=0 if e is $(PLUSMN)$(INFIN).
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 int isinf(real e)
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 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1371 ulong* ps = cast(ulong *)&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 return (pe[4] & 0x7FFF) == 0x7FFF &&
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1374 *ps == 0x8000000000000000;
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1377 unittest
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 assert(isinf(float.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1380 assert(!isinf(float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1381 assert(isinf(double.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1382 assert(isinf(-real.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1383
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1384 assert(isinf(-1.0 / 0.0));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1385 }
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 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1388 * 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
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 int signbit(real e)
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 ubyte* pe = cast(ubyte *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1394
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1395 //printf("e = %Lg\n", e);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1396 return (pe[9] & 0x80) != 0;
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1399 unittest
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 debug (math) printf("math.signbit.unittest\n");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1402 assert(!signbit(float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1403 assert(signbit(-float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1404 assert(!signbit(168.1234));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1405 assert(signbit(-168.1234));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1406 assert(!signbit(0.0));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1407 assert(signbit(-0.0));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1408 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1409
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1410 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1411 * 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
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 real copysign(real to, real from)
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 ubyte* pto = cast(ubyte *)&to;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1417 ubyte* pfrom = cast(ubyte *)&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 pto[9] &= 0x7F;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1420 pto[9] |= pfrom[9] & 0x80;
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 return to;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1423 }
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 unittest
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 real e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1428
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1429 e = copysign(21, 23.8);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1430 assert(e == 21);
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(real.nan, -23.8);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1442 assert(isnan(e) && signbit(e));
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1445 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1446 * 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
1447 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1448 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
1449
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 * 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
1452 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1453 * 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
1454 * 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
1455 * If x == y, the result is y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1456 * 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
1457 * 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
1458 * 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
1459 * not equal to y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1460 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1461 real nextafter(real x, real y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1462 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1463 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1464 return std.c.math.nextafterl(x, y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1465 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1466 throw new NotImplemented("nextafter");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1467 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1468
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1469 //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
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 * Returns the positive difference between x and y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1473 * Returns:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1474 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1475 * $(TR $(TH x, y) $(TH fdim(x, y)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1476 * $(TR $(TD x $(GT) y) $(TD x - y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1477 * $(TR $(TD x $(LT)= y) $(TD +0.0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1478 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1479 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1480 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
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 * Returns the larger of x and y.
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 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
1486
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 * Returns the smaller of x and 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 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
1491
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 * 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
1494 * current rounding mode.
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 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
1497
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 * Fast integral powers.
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 pragma(LLVM_internal, "intrinsic", "llvm.powi.f32")
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 float pow(float x, uint n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1505 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1506 float pow(float x, int n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1507 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1508
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1509 pragma(LLVM_internal, "intrinsic", "llvm.powi.f64")
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 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1512 double pow(double x, uint n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1513 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1514 double pow(double x, int n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1515 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1516 real pow(real x, uint n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1517 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1518 real pow(real x, int n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1519 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1520
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1521 /+
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1522 real pow(real x, uint n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1523 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1524 real p;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1525
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1526 switch (n)
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 case 0:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1529 p = 1.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1530 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1531
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1532 case 1:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1533 p = x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1534 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1535
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1536 case 2:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1537 p = x * x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1538 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1539
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1540 default:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1541 p = 1.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1542 while (1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1543 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1544 if (n & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1545 p *= x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1546 n >>= 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1547 if (!n)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1548 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1549 x *= x;
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 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1552 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1553 return p;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1554 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1555
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1556 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1557 real pow(real x, int n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1558 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1559 if (n < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1560 return pow(x, cast(real)n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1561 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1562 return pow(x, cast(uint)n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1563 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1564 +/
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 /*********************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1567 * Calculates x$(SUP y).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1568 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1569 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1570 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1571 * $(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
1572 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1573 * $(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
1574 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1575 * $(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
1576 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1577 * $(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
1578 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1579 * $(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
1580 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1581 * $(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
1582 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1583 * $(TD +$(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
1584 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1585 * $(TD +$(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
1586 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1587 * $(TD -$(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
1588 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1589 * $(TD -$(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
1590 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1591 * $(TD -$(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
1592 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1593 * $(TD -$(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
1594 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1595 * $(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
1596 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1597 * $(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
1598 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1599 * $(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
1600 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1601 * $(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
1602 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1603 * $(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
1604 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1605 * $(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
1606 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1607 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1608
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1609 pragma(LLVM_internal, "intrinsic", "llvm.pow.f32")
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1610 float pow(float x, float y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1611
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1612 pragma(LLVM_internal, "intrinsic", "llvm.pow.f64")
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 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1615 double pow(double x, double y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1616 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1617 real pow(real x, real y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1618 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1619
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1620 /+
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1621 real pow(real x, real y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1622 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1623 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
1624 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1625 if (isnan(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1626 return 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 if (y == 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1629 return 1; // even if x is $(NAN)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1630 if (isnan(x) && y != 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1631 return x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1632 if (isinf(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1633 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1634 if (fabs(x) > 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1635 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1636 if (signbit(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1637 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1638 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1639 return real.infinity;
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 else if (fabs(x) == 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1642 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1643 return real.nan;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1644 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1645 else // < 1
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1646 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1647 if (signbit(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1648 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1649 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1650 return +0.0;
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 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1653 if (isinf(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1654 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1655 if (signbit(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1656 { long i;
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 i = cast(long)y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1659 if (y > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1660 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1661 if (i == y && i & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1662 return -real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1663 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1664 return real.infinity;
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 else if (y < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1667 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1668 if (i == y && i & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1669 return -0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1670 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1671 return +0.0;
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 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1674 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1675 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1676 if (y > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1677 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1678 else if (y < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1679 return +0.0;
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 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1682
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1683 if (x == 0.0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1684 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1685 if (signbit(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1686 { long i;
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 i = cast(long)y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1689 if (y > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1690 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1691 if (i == y && i & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1692 return -0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1693 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1694 return +0.0;
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 else if (y < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1697 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1698 if (i == y && i & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1699 return -real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1700 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1701 return real.infinity;
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 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1704 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1705 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1706 if (y > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1707 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1708 else if (y < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1709 return real.infinity;
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 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1712 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1713 return std.c.math.powl(x, y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1714 }
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 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1718 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1719 real x = 46;
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 assert(pow(x,0) == 1.0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1722 assert(pow(x,1) == x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1723 assert(pow(x,2) == x * x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1724 assert(pow(x,3) == x * x * x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1725 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
1726 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1727
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1728 /****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1729 * Simple function to compare two floating point values
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1730 * to a specified precision.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1731 * Returns:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1732 * 1 match
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1733 * 0 nomatch
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1734 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1735
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1736 private int mfeq(real x, real y, real precision)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1737 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1738 if (x == y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1739 return 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1740 if (isnan(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1741 return isnan(y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1742 if (isnan(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1743 return 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1744 return fabs(x - y) <= precision;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1745 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1746
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1747 // 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
1748 bool isPosZero(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1749 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1750 return (x == 0) && (signbit(x) == 0);
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1753 // 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
1754 bool isNegZero(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1755 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1756 return (x == 0) && signbit(x);
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
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1759 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1760 * To what precision is x equal to y?
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1761 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1762 * 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
1763 * 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
1764 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1765 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1766 * $(TR $(TH x) $(TH y) $(TH feqrel(x, y)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1767 * $(TR $(TD x) $(TD x) $(TD real.mant_dig))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1768 * $(TR $(TD x) $(TD $(GT)= 2*x) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1769 * $(TR $(TD x) $(TD $(LT)= x/2) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1770 * $(TR $(TD $(NAN)) $(TD any) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1771 * $(TR $(TD any) $(TD $(NAN)) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1772 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1773 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1774
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1775 int feqrel(real x, real y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1776 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1777 /* Public Domain. Author: Don Clugston, 18 Aug 2005.
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 if (x == y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1781 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
1782
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1783 real diff = fabs(x - y);
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 ushort *pa = cast(ushort *)(&x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1786 ushort *pb = cast(ushort *)(&y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1787 ushort *pd = cast(ushort *)(&diff);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1788
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1789 // 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
1790 // 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
1791 // 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
1792 // 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
1793 // AND with 0x7FFF to form the absolute value.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1794 // 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
1795 // if the exponents were different. This means 'bitsdiff' is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1796 // 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
1797 // they could have 0 or 1 bits in common.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1798 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
1799
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1800 if (pd[4] == 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1801 { // Difference is denormal
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1802 // 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
1803 // lie at the start of diff's mantissa.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1804 // 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
1805 diff *= 0x1p+63;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1806 return bitsdiff + real.mant_dig - pd[4];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1807 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1808
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1809 if (bitsdiff > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1810 return bitsdiff + 1; // add the 1 we subtracted before
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1811
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1812 // 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
1813 return (bitsdiff == 0) ? (pa[4] == pb[4]) : 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1814 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1815
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1816 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1817 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1818 // Exact equality
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1819 assert(feqrel(real.max,real.max)==real.mant_dig);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1820 assert(feqrel(0,0)==real.mant_dig);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1821 assert(feqrel(7.1824,7.1824)==real.mant_dig);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1822 assert(feqrel(real.infinity,real.infinity)==real.mant_dig);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1823
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1824 // a few bits away from exact equality
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1825 real w=1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1826 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
1827 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
1828 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
1829 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
1830 w*=2;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1831 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1832 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
1833 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
1834 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
1835
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1836 // Numbers that are close
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1837 assert(feqrel(0x1.Bp+84, 0x1.B8p+84)==5);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1838 assert(feqrel(0x1.8p+10, 0x1.Cp+10)==2);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1839 assert(feqrel(1.5*(1-real.epsilon), 1)==2);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1840 assert(feqrel(1.5, 1)==1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1841 assert(feqrel(2*(1-real.epsilon), 1)==1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1842
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1843 // Factors of 2
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1844 assert(feqrel(real.max,real.infinity)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1845 assert(feqrel(2*(1-real.epsilon), 1)==1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1846 assert(feqrel(1, 2)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1847 assert(feqrel(4, 1)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1848
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1849 // Extreme inequality
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1850 assert(feqrel(real.nan,real.nan)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1851 assert(feqrel(0,-real.nan)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1852 assert(feqrel(real.nan,real.infinity)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1853 assert(feqrel(real.infinity,-real.infinity)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1854 assert(feqrel(-real.max,real.infinity)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1855 assert(feqrel(real.max,-real.max)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1856 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1857
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1858
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1859 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1860 * Evaluate polynomial A(x) = a<sub>0</sub> + a<sub>1</sub>x + a<sub>2</sub>x&sup2; + a<sub>3</sub>x&sup3; ...
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 * 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
1863 * Params:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1864 * 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
1865 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1866 real poly(real x, real[] A)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1867 in
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1868 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1869 assert(A.length > 0);
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 body
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1872 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1873 version (D_InlineAsm_X86)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1874 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1875 version (Windows)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1876 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1877 asm // assembler by W. Bright
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1878 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1879 // EDX = (A.length - 1) * real.sizeof
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1880 mov ECX,A[EBP] ; // ECX = A.length
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1881 dec ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1882 lea EDX,[ECX][ECX*8] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1883 add EDX,ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1884 add EDX,A+4[EBP] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1885 fld real ptr [EDX] ; // ST0 = coeff[ECX]
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1886 jecxz return_ST ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1887 fld x[EBP] ; // ST0 = x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1888 fxch ST(1) ; // ST1 = x, ST0 = r
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1889 align 4 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1890 L2: fmul ST,ST(1) ; // r *= x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1891 fld real ptr -10[EDX] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1892 sub EDX,10 ; // deg--
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1893 faddp ST(1),ST ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1894 dec ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1895 jne L2 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1896 fxch ST(1) ; // ST1 = r, ST0 = x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1897 fstp ST(0) ; // dump x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1898 align 4 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1899 return_ST: ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1900 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1901 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1902 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1903 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1904 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1905 asm // assembler by W. Bright
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 // EDX = (A.length - 1) * real.sizeof
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1908 mov ECX,A[EBP] ; // ECX = A.length
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1909 dec ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1910 lea EDX,[ECX*8] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1911 lea EDX,[EDX][ECX*4] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1912 add EDX,A+4[EBP] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1913 fld real ptr [EDX] ; // ST0 = coeff[ECX]
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1914 jecxz return_ST ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1915 fld x[EBP] ; // ST0 = x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1916 fxch ST(1) ; // ST1 = x, ST0 = r
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1917 align 4 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1918 L2: fmul ST,ST(1) ; // r *= x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1919 fld real ptr -12[EDX] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1920 sub EDX,12 ; // deg--
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1921 faddp ST(1),ST ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1922 dec ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1923 jne L2 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1924 fxch ST(1) ; // ST1 = r, ST0 = x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1925 fstp ST(0) ; // dump x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1926 align 4 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1927 return_ST: ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1928 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1929 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1930 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1931 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1932 else
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 int i = A.length - 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1935 real r = A[i];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1936 while (--i >= 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1937 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1938 r *= x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1939 r += A[i];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1940 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1941 return r;
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 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1944
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1945 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1946 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1947 debug (math) printf("math.poly.unittest\n");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1948 real x = 3.1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1949 static real pp[] = [56.1, 32.7, 6];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1950
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1951 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
1952 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1953
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1954