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Added test case for bug #100 Removed dubious check for not emitting static private global in other modules without access. This should be handled properly somewhere else, it's causing unresolved global errors for stuff that should work (in MiniD)
author Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
date Sun, 05 Oct 2008 17:28:15 +0200
parents 373489eeaf90
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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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(intrinsic, "llvm.cos.f32")
108
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194 float cos(float x);
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195
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196 pragma(intrinsic, "llvm.cos.f64")
108
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197 double cos(double x); // ditto
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198
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199 pragma(intrinsic, "llvm.cos.f80")
108
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200 real cos(real x); /// ditto
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201
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202
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203 /***********************************
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204 * Returns sine of x. x is in radians.
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205 *
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206 * $(TABLE_SV
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207 * $(TR $(TH x) $(TH sin(x)) $(TH invalid?))
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208 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
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209 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
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210 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes))
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211 * )
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212 * Bugs:
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213 * Results are undefined if |x| >= $(POWER 2,64).
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214 */
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215
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216 pragma(intrinsic, "llvm.sin.f32")
108
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217 float sin(float x);
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218
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219 pragma(intrinsic, "llvm.sin.f64")
108
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220 double sin(double x); // ditto
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221
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222 pragma(intrinsic, "llvm.sin.f80")
108
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223 real sin(real x); /// ditto
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224
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225
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226 /****************************************************************************
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227 * Returns tangent of x. x is in radians.
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228 *
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229 * $(TABLE_SV
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230 * $(TR $(TH x) $(TH tan(x)) $(TH invalid?))
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231 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
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232 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
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233 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes))
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234 * )
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235 */
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236
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237 version(D_InlineAsm_X86)
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238 real tan(real x)
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239 {
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240
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241 asm
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242 {
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243 fld x[EBP] ; // load theta
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244 fxam ; // test for oddball values
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245 fstsw AX ;
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246 sahf ;
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247 jc trigerr ; // x is NAN, infinity, or empty
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248 // 387's can handle denormals
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249 SC18: fptan ;
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250 fstp ST(0) ; // dump X, which is always 1
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251 fstsw AX ;
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252 sahf ;
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253 jnp Lret ; // C2 = 1 (x is out of range)
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254
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255 // Do argument reduction to bring x into range
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256 fldpi ;
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257 fxch ;
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258 SC17: fprem1 ;
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259 fstsw AX ;
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260 sahf ;
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261 jp SC17 ;
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262 fstp ST(1) ; // remove pi from stack
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263 jmp SC18 ;
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264
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265 trigerr:
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266 jnp Lret ; // if theta is NAN, return theta
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267 fstp ST(0) ; // dump theta
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268 }
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269 return real.nan;
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270
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271 Lret:
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272 ;
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273 }
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274 else
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275 {
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276 real tan(real x) { return std.c.math.atan(x); }
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277 }
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278
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279
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280 unittest
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281 {
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282 static real vals[][2] = // angle,tan
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283 [
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284 [ 0, 0],
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285 [ .5, .5463024898],
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286 [ 1, 1.557407725],
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287 [ 1.5, 14.10141995],
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288 [ 2, -2.185039863],
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289 [ 2.5,-.7470222972],
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290 [ 3, -.1425465431],
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291 [ 3.5, .3745856402],
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292 [ 4, 1.157821282],
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293 [ 4.5, 4.637332055],
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294 [ 5, -3.380515006],
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295 [ 5.5,-.9955840522],
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296 [ 6, -.2910061914],
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297 [ 6.5, .2202772003],
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298 [ 10, .6483608275],
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299
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300 // special angles
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301 [ PI_4, 1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
302 //[ PI_2, real.infinity],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
303 [ 3*PI_4, -1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
304 [ PI, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
305 [ 5*PI_4, 1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
306 //[ 3*PI_2, -real.infinity],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
307 [ 7*PI_4, -1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
308 [ 2*PI, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
309
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
310 // overflow
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
311 [ real.infinity, real.nan],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
312 [ real.nan, real.nan],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
313 //[ 1e+100, real.nan],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
314 ];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
315 int i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
316
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
317 for (i = 0; i < vals.length; i++)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
318 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
319 real x = vals[i][0];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
320 real r = vals[i][1];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
321 real t = tan(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
322
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
323 //printf("tan(%Lg) = %Lg, should be %Lg\n", x, t, r);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
324 assert(mfeq(r, t, .0000001));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
325
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
326 x = -x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
327 r = -r;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
328 t = tan(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
329 //printf("tan(%Lg) = %Lg, should be %Lg\n", x, t, r);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
330 assert(mfeq(r, t, .0000001));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
331 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
332 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
333
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
334 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
335 * Calculates the arc cosine of x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
336 * returning a value ranging from -$(PI)/2 to $(PI)/2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
337 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
338 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
339 * $(TR $(TH x) $(TH acos(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
340 * $(TR $(TD $(GT)1.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
341 * $(TR $(TD $(LT)-1.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
342 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
343 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
344 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
345 real acos(real x) { return std.c.math.acos(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
346
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
347 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
348 * Calculates the arc sine of x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
349 * returning a value ranging from -$(PI)/2 to $(PI)/2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
350 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
351 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
352 * $(TR $(TH x) $(TH asin(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
353 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
354 * $(TR $(TD $(GT)1.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
355 * $(TR $(TD $(LT)-1.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
356 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
357 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
358 real asin(real x) { return std.c.math.asin(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
359
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
360 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
361 * Calculates the arc tangent of x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
362 * returning a value ranging from -$(PI)/2 to $(PI)/2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
363 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
364 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
365 * $(TR $(TH x) $(TH atan(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
366 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
367 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
368 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
369 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
370 real atan(real x) { return std.c.math.atan(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
371
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
372 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
373 * Calculates the arc tangent of y / x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
374 * returning a value ranging from -$(PI)/2 to $(PI)/2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
375 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
376 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
377 * $(TR $(TH y) $(TH x) $(TH atan(y, x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
378 * $(TR $(TD $(NAN)) $(TD anything) $(TD $(NAN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
379 * $(TR $(TD anything) $(TD $(NAN)) $(TD $(NAN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
380 * $(TR $(TD $(PLUSMN)0.0) $(TD $(GT)0.0) $(TD $(PLUSMN)0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
381 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
382 * $(TR $(TD $(PLUSMN)0.0) $(TD $(LT)0.0) $(TD $(PLUSMN)$(PI)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
383 * $(TR $(TD $(PLUSMN)0.0) $(TD -0.0) $(TD $(PLUSMN)$(PI)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
384 * $(TR $(TD $(GT)0.0) $(TD $(PLUSMN)0.0) $(TD $(PI)/2) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
385 * $(TR $(TD $(LT)0.0) $(TD $(PLUSMN)0.0) $(TD $(PI)/2))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
386 * $(TR $(TD $(GT)0.0) $(TD $(INFIN)) $(TD $(PLUSMN)0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
387 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD anything) $(TD $(PLUSMN)$(PI)/2))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
388 * $(TR $(TD $(GT)0.0) $(TD -$(INFIN)) $(TD $(PLUSMN)$(PI)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
389 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(INFIN)) $(TD $(PLUSMN)$(PI)/4))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
390 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD -$(INFIN)) $(TD $(PLUSMN)3$(PI)/4))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
391 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
392 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
393 real atan2(real y, real x) { return std.c.math.atan2(y,x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
394
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
395 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
396 * Calculates the hyperbolic cosine of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
397 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
398 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
399 * $(TR $(TH x) $(TH cosh(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
400 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)0.0) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
401 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
402 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
403 real cosh(real x) { return std.c.math.cosh(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
404
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
405 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
406 * Calculates the hyperbolic sine of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
407 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
408 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
409 * $(TR $(TH x) $(TH sinh(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
410 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
411 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
412 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
413 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
414 real sinh(real x) { return std.c.math.sinh(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
415
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
416 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
417 * Calculates the hyperbolic tangent of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
418 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
419 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
420 * $(TR $(TH x) $(TH tanh(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
421 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
422 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)1.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
423 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
424 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
425 real tanh(real x) { return std.c.math.tanh(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
426
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
427 //real acosh(real x) { return std.c.math.acoshl(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
428 //real asinh(real x) { return std.c.math.asinhl(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
429 //real atanh(real x) { return std.c.math.atanhl(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
430
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
431 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
432 * Calculates the inverse hyperbolic cosine of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
433 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
434 * Mathematically, acosh(x) = log(x + sqrt( x*x - 1))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
435 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
436 * $(TABLE_DOMRG
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
437 * $(DOMAIN 1..$(INFIN))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
438 * $(RANGE 1..log(real.max), $(INFIN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
439 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
440 * $(SVH x, acosh(x) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
441 * $(SV $(NAN), $(NAN) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
442 * $(SV <1, $(NAN) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
443 * $(SV 1, 0 )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
444 * $(SV +$(INFIN),+$(INFIN))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
445 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
446 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
447 real acosh(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
448 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
449 if (x > 1/real.epsilon)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
450 return LN2 + log(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
451 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
452 return log(x + sqrt(x*x - 1));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
453 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
454
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
455 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
456 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
457 assert(isnan(acosh(0.9)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
458 assert(isnan(acosh(real.nan)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
459 assert(acosh(1)==0.0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
460 assert(acosh(real.infinity) == real.infinity);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
461 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
462
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
463 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
464 * Calculates the inverse hyperbolic sine of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
465 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
466 * Mathematically,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
467 * ---------------
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
468 * asinh(x) = log( x + sqrt( x*x + 1 )) // if x >= +0
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
469 * asinh(x) = -log(-x + sqrt( x*x + 1 )) // if x <= -0
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
470 * -------------
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
471 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
472 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
473 * $(SVH x, asinh(x) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
474 * $(SV $(NAN), $(NAN) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
475 * $(SV $(PLUSMN)0, $(PLUSMN)0 )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
476 * $(SV $(PLUSMN)$(INFIN),$(PLUSMN)$(INFIN))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
477 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
478 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
479 real asinh(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
480 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
481 if (fabs(x) > 1 / real.epsilon) // beyond this point, x*x + 1 == x*x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
482 return copysign(LN2 + log(fabs(x)), x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
483 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
484 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
485 // sqrt(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
486 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
487 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
488 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
489
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
490 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
491 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
492 assert(isPosZero(asinh(0.0)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
493 assert(isNegZero(asinh(-0.0)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
494 assert(asinh(real.infinity) == real.infinity);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
495 assert(asinh(-real.infinity) == -real.infinity);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
496 assert(isnan(asinh(real.nan)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
497 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
498
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
499 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
500 * Calculates the inverse hyperbolic tangent of x,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
501 * returning a value from ranging from -1 to 1.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
502 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
503 * Mathematically, atanh(x) = log( (1+x)/(1-x) ) / 2
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
504 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
505 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
506 * $(TABLE_DOMRG
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
507 * $(DOMAIN -$(INFIN)..$(INFIN))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
508 * $(RANGE -1..1) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
509 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
510 * $(SVH x, acosh(x) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
511 * $(SV $(NAN), $(NAN) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
512 * $(SV $(PLUSMN)0, $(PLUSMN)0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
513 * $(SV -$(INFIN), -0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
514 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
515 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
516 real atanh(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
517 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
518 // log( (1+x)/(1-x) ) == log ( 1 + (2*x)/(1-x) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
519 return 0.5 * log1p( 2 * x / (1 - x) );
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
520 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
521
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
522 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
523 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
524 assert(isPosZero(atanh(0.0)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
525 assert(isNegZero(atanh(-0.0)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
526 assert(isnan(atanh(real.nan)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
527 assert(isnan(atanh(-real.infinity)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
528 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
529
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
530 /*****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
531 * Returns x rounded to a long value using the current rounding mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
532 * If the integer value of x is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
533 * greater than long.max, the result is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
534 * indeterminate.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
535 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
536 long rndtol(real x); /* intrinsic */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
537
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
538
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
539 /*****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
540 * Returns x rounded to a long value using the FE_TONEAREST rounding mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
541 * If the integer value of x is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
542 * greater than long.max, the result is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
543 * indeterminate.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
544 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
545 extern (C) real rndtonl(real x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
546
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
547 /***************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
548 * Compute square root of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
549 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
550 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
551 * $(TR $(TH x) $(TH sqrt(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
552 * $(TR $(TD -0.0) $(TD -0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
553 * $(TR $(TD $(LT)0.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
554 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
555 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
556 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
557
473
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
558 pragma(intrinsic, "llvm.sqrt.f32")
108
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
559 float sqrt(float x); /* intrinsic */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
560
473
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
561 pragma(intrinsic, "llvm.sqrt.f64")
108
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
562 double sqrt(double x); /* intrinsic */ /// ditto
473
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
563
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
564 pragma(intrinsic, "llvm.sqrt.f80")
108
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
565 real sqrt(real x); /* intrinsic */ /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
566
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
567 creal sqrt(creal z)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
568 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
569 creal c;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
570 real x,y,w,r;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
571
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
572 if (z == 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
573 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
574 c = 0 + 0i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
575 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
576 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
577 { real z_re = z.re;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
578 real z_im = z.im;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
579
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
580 x = fabs(z_re);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
581 y = fabs(z_im);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
582 if (x >= y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
583 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
584 r = y / x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
585 w = sqrt(x) * sqrt(0.5 * (1 + sqrt(1 + r * r)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
586 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
587 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
588 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
589 r = x / y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
590 w = sqrt(y) * sqrt(0.5 * (r + sqrt(1 + r * r)));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
591 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
592
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
593 if (z_re >= 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
594 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
595 c = w + (z_im / (w + w)) * 1.0i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
596 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
597 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
598 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
599 if (z_im < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
600 w = -w;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
601 c = z_im / (w + w) + w * 1.0i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
602 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
603 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
604 return c;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
605 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
606
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
607 /**********************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
608 * Calculates e$(SUP x).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
609 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
610 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
611 * $(TR $(TH x) $(TH exp(x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
612 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
613 * $(TR $(TD -$(INFIN)) $(TD +0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
614 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
615 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
616 real exp(real x) { return std.c.math.exp(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
617
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
618 /**********************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
619 * Calculates 2$(SUP x).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
620 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
621 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
622 * $(TR $(TH x) $(TH exp2(x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
623 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
624 * $(TR $(TD -$(INFIN)) $(TD +0.0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
625 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
626 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
627 real exp2(real x) { return std.c.math.exp2(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
628
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
629 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
630 * Calculates the value of the natural logarithm base (e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
631 * raised to the power of x, minus 1.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
632 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
633 * For very small x, expm1(x) is more accurate
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
634 * than exp(x)-1.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
635 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
636 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
637 * $(TR $(TH x) $(TH e$(SUP x)-1))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
638 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
639 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
640 * $(TR $(TD -$(INFIN)) $(TD -1.0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
641 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
642 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
643
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
644 real expm1(real x) { return std.c.math.expm1(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
645
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
646
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
647 /*********************************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
648 * Separate floating point value into significand and exponent.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
649 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
650 * Returns:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
651 * Calculate and return <i>x</i> and exp such that
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
652 * value =<i>x</i>*2$(SUP exp) and
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
653 * .5 $(LT)= |<i>x</i>| $(LT) 1.0<br>
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
654 * <i>x</i> has same sign as value.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
655 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
656 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
657 * $(TR $(TH value) $(TH returns) $(TH exp))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
658 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
659 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD int.max))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
660 * $(TR $(TD -$(INFIN)) $(TD -$(INFIN)) $(TD int.min))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
661 * $(TR $(TD $(PLUSMN)$(NAN)) $(TD $(PLUSMN)$(NAN)) $(TD int.min))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
662 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
663 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
664
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
665
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
666 real frexp(real value, out int exp)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
667 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
668 ushort* vu = cast(ushort*)&value;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
669 long* vl = cast(long*)&value;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
670 uint ex;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
671
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
672 // If exponent is non-zero
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
673 ex = vu[4] & 0x7FFF;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
674 if (ex)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
675 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
676 if (ex == 0x7FFF)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
677 { // infinity or NaN
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
678 if (*vl & 0x7FFFFFFFFFFFFFFF) // if NaN
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
679 { *vl |= 0xC000000000000000; // convert $(NAN)S to $(NAN)Q
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
680 exp = int.min;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
681 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
682 else if (vu[4] & 0x8000)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
683 { // negative infinity
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
684 exp = int.min;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
685 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
686 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
687 { // positive infinity
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
688 exp = int.max;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
689 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
690 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
691 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
692 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
693 exp = ex - 0x3FFE;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
694 vu[4] = cast(ushort)((0x8000 & vu[4]) | 0x3FFE);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
695 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
696 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
697 else if (!*vl)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
698 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
699 // value is +-0.0
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
700 exp = 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
701 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
702 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
703 { // denormal
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
704 int i = -0x3FFD;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
705
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
706 do
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
707 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
708 i--;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
709 *vl <<= 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
710 } while (*vl > 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
711 exp = i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
712 vu[4] = cast(ushort)((0x8000 & vu[4]) | 0x3FFE);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
713 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
714 return value;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
715 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
716
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
717
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
718 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
719 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
720 static real vals[][3] = // x,frexp,exp
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
721 [
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
722 [0.0, 0.0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
723 [-0.0, -0.0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
724 [1.0, .5, 1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
725 [-1.0, -.5, 1],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
726 [2.0, .5, 2],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
727 [155.67e20, 0x1.A5F1C2EB3FE4Fp-1, 74], // normal
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
728 [1.0e-320, 0.98829225, -1063],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
729 [real.min, .5, -16381],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
730 [real.min/2.0L, .5, -16382], // denormal
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
731
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
732 [real.infinity,real.infinity,int.max],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
733 [-real.infinity,-real.infinity,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
734 [real.nan,real.nan,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
735 [-real.nan,-real.nan,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
736
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
737 // Don't really support signalling nan's in D
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
738 //[real.nans,real.nan,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
739 //[-real.nans,-real.nan,int.min],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
740 ];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
741 int i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
742
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
743 for (i = 0; i < vals.length; i++)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
744 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
745 real x = vals[i][0];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
746 real e = vals[i][1];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
747 int exp = cast(int)vals[i][2];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
748 int eptr;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
749 real v = frexp(x, eptr);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
750
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
751 //printf("frexp(%Lg) = %.8Lg, should be %.8Lg, eptr = %d, should be %d\n", x, v, e, eptr, exp);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
752 assert(mfeq(e, v, .0000001));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
753 assert(exp == eptr);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
754 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
755 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
756
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
757
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
758 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
759 * Extracts the exponent of x as a signed integral value.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
760 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
761 * If x is not a special value, the result is the same as
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
762 * <tt>cast(int)logb(x)</tt>.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
763 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
764 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
765 * $(TR $(TH x) $(TH ilogb(x)) $(TH Range error?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
766 * $(TR $(TD 0) $(TD FP_ILOGB0) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
767 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD int.max) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
768 * $(TR $(TD $(NAN)) $(TD FP_ILOGBNAN) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
769 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
770 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
771 int ilogb(real x) { return std.c.math.ilogb(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
772
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
773 alias std.c.math.FP_ILOGB0 FP_ILOGB0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
774 alias std.c.math.FP_ILOGBNAN FP_ILOGBNAN;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
775
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
776
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
777 /*******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
778 * Compute n * 2$(SUP exp)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
779 * References: frexp
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
780 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
781
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
782 real ldexp(real n, int exp) { return std.c.math.ldexp(n, exp); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
783
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
784 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
785 * Calculate the natural logarithm of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
786 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
787 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
788 * $(TR $(TH x) $(TH log(x)) $(TH divide by 0?) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
789 * $(TR $(TD $(PLUSMN)0.0) $(TD -$(INFIN)) $(TD yes) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
790 * $(TR $(TD $(LT)0.0) $(TD $(NAN)) $(TD no) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
791 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
792 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
793 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
794
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
795 real log(real x) { return std.c.math.log(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
796
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
797 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
798 * Calculate the base-10 logarithm of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
799 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
800 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
801 * $(TR $(TH x) $(TH log10(x)) $(TH divide by 0?) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
802 * $(TR $(TD $(PLUSMN)0.0) $(TD -$(INFIN)) $(TD yes) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
803 * $(TR $(TD $(LT)0.0) $(TD $(NAN)) $(TD no) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
804 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
805 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
806 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
807
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
808 real log10(real x) { return std.c.math.log10(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
809
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
810 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
811 * Calculates the natural logarithm of 1 + x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
812 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
813 * For very small x, log1p(x) will be more accurate than
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
814 * log(1 + x).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
815 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
816 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
817 * $(TR $(TH x) $(TH log1p(x)) $(TH divide by 0?) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
818 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
819 * $(TR $(TD -1.0) $(TD -$(INFIN)) $(TD yes) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
820 * $(TR $(TD $(LT)-1.0) $(TD $(NAN)) $(TD no) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
821 * $(TR $(TD +$(INFIN)) $(TD -$(INFIN)) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
822 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
823 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
824
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
825 real log1p(real x) { return std.c.math.log1p(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
826
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
827 /***************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
828 * Calculates the base-2 logarithm of x:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
829 * log<sub>2</sub>x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
830 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
831 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
832 * $(TR $(TH x) $(TH log2(x)) $(TH divide by 0?) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
833 * $(TR $(TD $(PLUSMN)0.0) $(TD -$(INFIN)) $(TD yes) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
834 * $(TR $(TD $(LT)0.0) $(TD $(NAN)) $(TD no) $(TD yes) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
835 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
836 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
837 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
838 real log2(real x) { return std.c.math.log2(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
839
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
840 /*****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
841 * Extracts the exponent of x as a signed integral value.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
842 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
843 * If x is subnormal, it is treated as if it were normalized.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
844 * For a positive, finite x:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
845 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
846 * -----
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
847 * 1 <= $(I x) * FLT_RADIX$(SUP -logb(x)) < FLT_RADIX
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
848 * -----
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
849 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
850 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
851 * $(TR $(TH x) $(TH logb(x)) $(TH divide by 0?) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
852 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
853 * $(TR $(TD $(PLUSMN)0.0) $(TD -$(INFIN)) $(TD yes) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
854 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
855 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
856 real logb(real x) { return std.c.math.logb(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
857
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
858 /************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
859 * Calculates the remainder from the calculation x/y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
860 * Returns:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
861 * The value of x - i * y, where i is the number of times that y can
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
862 * be completely subtracted from x. The result has the same sign as x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
863 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
864 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
865 * $(TR $(TH x) $(TH y) $(TH modf(x, y)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
866 * $(TR $(TD $(PLUSMN)0.0) $(TD no)t 0.0 $(TD $(PLUSMN)0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
867 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD anything) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
868 * $(TR $(TD anything) $(TD $(PLUSMN)0.0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
869 * $(TR $(TD !=$(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD x) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
870 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
871 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
872 real modf(real x, inout real y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
873 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
874 double Y = y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
875 auto tmp = std.c.math.modf(x,&Y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
876 y = Y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
877 return tmp;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
878 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
879
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
880 /*************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
881 * Efficiently calculates x * 2$(SUP n).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
882 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
883 * scalbn handles underflow and overflow in
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
884 * the same fashion as the basic arithmetic operators.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
885 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
886 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
887 * $(TR $(TH x) $(TH scalb(x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
888 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
889 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
890 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
891 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
892 real scalbn(real x, int n)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
893 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
894 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
895 return std.c.math.scalbn(x, n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
896 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
897 throw new NotImplemented("scalbn");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
898 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
899
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
900 /***************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
901 * Calculates the cube root x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
902 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
903 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
904 * $(TR $(TH $(I x)) $(TH cbrt(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
905 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
906 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
907 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
908 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
909 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
910 real cbrt(real x) { return std.c.math.cbrt(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
911
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
912
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
913 /*******************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
914 * Returns |x|
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
915 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
916 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
917 * $(TR $(TH x) $(TH fabs(x)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
918 * $(TR $(TD $(PLUSMN)0.0) $(TD +0.0) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
919 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
920 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
921 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
922 real fabs(real x) { return std.c.math.fabs(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
923
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
924
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
925 /***********************************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
926 * Calculates the length of the
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
927 * hypotenuse of a right-angled triangle with sides of length x and y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
928 * The hypotenuse is the value of the square root of
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
929 * the sums of the squares of x and y:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
930 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
931 * sqrt(x&sup2; + y&sup2;)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
932 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
933 * Note that hypot(x, y), hypot(y, x) and
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
934 * hypot(x, -y) are equivalent.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
935 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
936 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
937 * $(TR $(TH x) $(TH y) $(TH hypot(x, y)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
938 * $(TR $(TD x) $(TD $(PLUSMN)0.0) $(TD |x|) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
939 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD y) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
940 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
941 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
942 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
943
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
944 real hypot(real x, real y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
945 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
946 /*
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
947 * This is based on code from:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
948 * Cephes Math Library Release 2.1: January, 1989
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
949 * Copyright 1984, 1987, 1989 by Stephen L. Moshier
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
950 * Direct inquiries to 30 Frost Street, Cambridge, MA 02140
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
951 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
952
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
953 const int PRECL = 32;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
954 const int MAXEXPL = real.max_exp; //16384;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
955 const int MINEXPL = real.min_exp; //-16384;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
956
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
957 real xx, yy, b, re, im;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
958 int ex, ey, e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
959
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
960 // Note, hypot(INFINITY, NAN) = INFINITY.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
961 if (isinf(x) || isinf(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
962 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
963
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
964 if (isnan(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
965 return x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
966 if (isnan(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
967 return y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
968
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
969 re = fabs(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
970 im = fabs(y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
971
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
972 if (re == 0.0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
973 return im;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
974 if (im == 0.0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
975 return re;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
976
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
977 // Get the exponents of the numbers
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
978 xx = frexp(re, ex);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
979 yy = frexp(im, ey);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
980
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
981 // Check if one number is tiny compared to the other
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
982 e = ex - ey;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
983 if (e > PRECL)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
984 return re;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
985 if (e < -PRECL)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
986 return im;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
987
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
988 // Find approximate exponent e of the geometric mean.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
989 e = (ex + ey) >> 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
990
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
991 // Rescale so mean is about 1
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
992 xx = ldexp(re, -e);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
993 yy = ldexp(im, -e);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
994
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
995 // Hypotenuse of the right triangle
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
996 b = sqrt(xx * xx + yy * yy);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
997
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
998 // Compute the exponent of the answer.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
999 yy = frexp(b, ey);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1000 ey = e + ey;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1001
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1002 // Check it for overflow and underflow.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1003 if (ey > MAXEXPL + 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1004 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1005 //return __matherr(_OVERFLOW, INFINITY, x, y, "hypotl");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1006 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1007 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1008 if (ey < MINEXPL - 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1009 return 0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1010
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1011 // Undo the scaling
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1012 b = ldexp(b, e);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1013 return b;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1014 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1015
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1016 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1017 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1018 static real vals[][3] = // x,y,hypot
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1019 [
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1020 [ 0, 0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1021 [ 0, -0, 0],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1022 [ 3, 4, 5],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1023 [ -300, -400, 500],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1024 [ real.min, real.min, 4.75473e-4932L],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1025 [ real.max/2, real.max/2, 0x1.6a09e667f3bcc908p+16383L /*8.41267e+4931L*/],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1026 [ real.infinity, real.nan, real.infinity],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1027 [ real.nan, real.nan, real.nan],
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1028 ];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1029 int i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1030
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1031 for (i = 0; i < vals.length; i++)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1032 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1033 real x = vals[i][0];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1034 real y = vals[i][1];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1035 real z = vals[i][2];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1036 real h = hypot(x, y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1037
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1038 //printf("hypot(%Lg, %Lg) = %Lg, should be %Lg\n", x, y, h, z);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1039 //if (!mfeq(z, h, .0000001))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1040 //printf("%La\n", h);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1041 assert(mfeq(z, h, .0000001));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1042 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1043 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1044
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1045 /**********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1046 * Returns the error function of x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1047 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1048 * <img src="erf.gif" alt="error function">
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1049 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1050 real erf(real x) { return std.c.math.erf(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1051
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1052 /**********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1053 * Returns the complementary error function of x, which is 1 - erf(x).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1054 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1055 * <img src="erfc.gif" alt="complementary error function">
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1056 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1057 real erfc(real x) { return std.c.math.erfc(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1058
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1059 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1060 * Natural logarithm of gamma function.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1061 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1062 * Returns the base e (2.718...) logarithm of the absolute
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1063 * value of the gamma function of the argument.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1064 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1065 * For reals, lgamma is equivalent to log(fabs(gamma(x))).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1066 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1067 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1068 * $(TR $(TH x) $(TH lgamma(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1069 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1070 * $(TR $(TD integer <= 0) $(TD +$(INFIN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1071 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1072 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1073 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1074 /* Documentation prepared by Don Clugston */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1075 real lgamma(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1076 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1077 return std.c.math.lgamma(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1078
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1079 // Use etc.gamma.lgamma for those C systems that are missing it
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1080 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1081
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1082 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1083 * The Gamma function, $(GAMMA)(x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1084 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1085 * $(GAMMA)(x) is a generalisation of the factorial function
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1086 * to real and complex numbers.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1087 * Like x!, $(GAMMA)(x+1) = x*$(GAMMA)(x).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1088 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1089 * Mathematically, if z.re > 0 then
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1090 * $(GAMMA)(z) =<big>$(INTEGRAL)<sub><small>0</small></sub><sup>$(INFIN)</sup></big>t<sup>z-1</sup>e<sup>-t</sup>dt
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1091 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1092 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1093 * $(TR $(TH x) $(TH $(GAMMA)(x)) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1094 * $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1095 * $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)$(INFIN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1096 * $(TR $(TD integer $(GT)0) $(TD (x-1)!) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1097 * $(TR $(TD integer $(LT)0) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1098 * $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1099 * $(TR $(TD -$(INFIN)) $(TD $(NAN)) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1100 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1101 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1102 * References:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1103 * $(LINK http://en.wikipedia.org/wiki/Gamma_function),
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1104 * $(LINK http://www.netlib.org/cephes/ldoubdoc.html#gamma)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1105 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1106 /* Documentation prepared by Don Clugston */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1107 real tgamma(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1108 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1109 return std.c.math.tgamma(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1110
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1111 // Use etc.gamma.tgamma for those C systems that are missing it
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1112 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1113
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1114 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1115 * Returns the value of x rounded upward to the next integer
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1116 * (toward positive infinity).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1117 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1118 real ceil(real x) { return std.c.math.ceil(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1119
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1120 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1121 * Returns the value of x rounded downward to the next integer
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1122 * (toward negative infinity).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1123 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1124 real floor(real x) { return std.c.math.floor(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1125
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1126 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1127 * Rounds x to the nearest integer value, using the current rounding
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1128 * mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1129 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1130 * Unlike the rint functions, nearbyint does not raise the
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1131 * FE_INEXACT exception.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1132 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1133 real nearbyint(real x) { return std.c.math.nearbyint(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1134
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1135 /**********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1136 * Rounds x to the nearest integer value, using the current rounding
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1137 * mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1138 * If the return value is not equal to x, the FE_INEXACT
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1139 * exception is raised.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1140 * <b>nearbyint</b> performs
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1141 * the same operation, but does not set the FE_INEXACT exception.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1142 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1143 real rint(real x) { return std.c.math.rint(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1144
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1145 /***************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1146 * Rounds x to the nearest integer value, using the current rounding
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1147 * mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1148 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1149 long lrint(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1150 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1151 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1152 return std.c.math.llrint(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1153 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1154 throw new NotImplemented("lrint");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1155 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1156
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1157 /*******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1158 * Return the value of x rounded to the nearest integer.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1159 * If the fractional part of x is exactly 0.5, the return value is rounded to
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1160 * the even integer.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1161 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1162 real round(real x) { return std.c.math.round(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1163
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1164 /**********************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1165 * Return the value of x rounded to the nearest integer.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1166 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1167 * If the fractional part of x is exactly 0.5, the return value is rounded
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1168 * away from zero.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1169 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1170 long lround(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1171 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1172 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1173 return std.c.math.llround(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1174 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1175 throw new NotImplemented("lround");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1176 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1177
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1178 /****************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1179 * Returns the integer portion of x, dropping the fractional portion.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1180 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1181 * This is also known as "chop" rounding.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1182 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1183 real trunc(real x) { return std.c.math.trunc(x); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1184
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1185 /****************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1186 * Calculate the remainder x REM y, following IEC 60559.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1187 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1188 * REM is the value of x - y * n, where n is the integer nearest the exact
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1189 * value of x / y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1190 * If |n - x / y| == 0.5, n is even.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1191 * If the result is zero, it has the same sign as x.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1192 * Otherwise, the sign of the result is the sign of x / y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1193 * Precision mode has no effect on the remainder functions.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1194 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1195 * remquo returns n in the parameter n.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1196 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1197 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1198 * $(TR $(TH x) $(TH y) $(TH remainder(x, y)) $(TH n) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1199 * $(TR $(TD $(PLUSMN)0.0) $(TD no)t 0.0 $(TD $(PLUSMN)0.0) $(TD 0.0) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1200 * $(TR $(TD $(PLUSMN)$(INFIN)) $(TD anything) $(TD $(NAN)) $(TD ?) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1201 * $(TR $(TD anything) $(TD $(PLUSMN)0.0) $(TD $(NAN)) $(TD ?) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1202 * $(TR $(TD != $(PLUSMN)$(INFIN)) $(TD $(PLUSMN)$(INFIN)) $(TD x) $(TD ?) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1203 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1204 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1205 real remainder(real x, real y) { return std.c.math.remainder(x, y); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1206
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1207 real remquo(real x, real y, out int n) /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1208 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1209 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1210 return std.c.math.remquo(x, y, &n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1211 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1212 throw new NotImplemented("remquo");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1213 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1214
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1215 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1216 * Returns !=0 if e is a NaN.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1217 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1218
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1219 int isnan(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1220 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1221 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1222 ulong* ps = cast(ulong *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1223
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1224 return (pe[4] & 0x7FFF) == 0x7FFF &&
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1225 *ps & 0x7FFFFFFFFFFFFFFF;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1226 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1227
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1228 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1229 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1230 assert(isnan(float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1231 assert(isnan(-double.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1232 assert(isnan(real.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1233
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1234 assert(!isnan(53.6));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1235 assert(!isnan(float.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1236 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1237
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1238 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1239 * Returns !=0 if e is finite.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1240 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1241
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1242 int isfinite(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1243 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1244 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1245
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1246 return (pe[4] & 0x7FFF) != 0x7FFF;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1247 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1248
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1249 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1250 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1251 assert(isfinite(1.23));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1252 assert(!isfinite(double.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1253 assert(!isfinite(float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1254 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1255
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1256
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1257 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1258 * Returns !=0 if x is normalized.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1259 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1260
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1261 /* Need one for each format because subnormal floats might
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1262 * be converted to normal reals.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1263 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1264
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1265 int isnormal(float x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1266 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1267 uint *p = cast(uint *)&x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1268 uint e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1269
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1270 e = *p & 0x7F800000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1271 //printf("e = x%x, *p = x%x\n", e, *p);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1272 return e && e != 0x7F800000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1273 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1274
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1275 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1276
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1277 int isnormal(double d)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1278 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1279 uint *p = cast(uint *)&d;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1280 uint e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1281
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1282 e = p[1] & 0x7FF00000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1283 return e && e != 0x7FF00000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1284 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1285
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1286 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1287
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1288 int isnormal(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1289 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1290 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1291 long* ps = cast(long *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1292
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1293 return (pe[4] & 0x7FFF) != 0x7FFF && *ps < 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1294 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1295
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1296 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1297 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1298 float f = 3;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1299 double d = 500;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1300 real e = 10e+48;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1301
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1302 assert(isnormal(f));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1303 assert(isnormal(d));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1304 assert(isnormal(e));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1305 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1306
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1307 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1308 * Is number subnormal? (Also called "denormal".)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1309 * Subnormals have a 0 exponent and a 0 most significant mantissa bit.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1310 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1311
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1312 /* Need one for each format because subnormal floats might
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1313 * be converted to normal reals.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1314 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1315
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1316 int issubnormal(float f)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1317 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1318 uint *p = cast(uint *)&f;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1319
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1320 //printf("*p = x%x\n", *p);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1321 return (*p & 0x7F800000) == 0 && *p & 0x007FFFFF;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1322 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1323
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1324 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1325 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1326 float f = 3.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1327
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1328 for (f = 1.0; !issubnormal(f); f /= 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1329 assert(f != 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1330 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1331
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1332 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1333
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1334 int issubnormal(double d)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1335 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1336 uint *p = cast(uint *)&d;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1337
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1338 return (p[1] & 0x7FF00000) == 0 && (p[0] || p[1] & 0x000FFFFF);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1339 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1340
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1341 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1342 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1343 double f;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1344
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1345 for (f = 1; !issubnormal(f); f /= 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1346 assert(f != 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1347 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1348
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1349 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1350
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1351 int issubnormal(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1352 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1353 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1354 long* ps = cast(long *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1355
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1356 return (pe[4] & 0x7FFF) == 0 && *ps > 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1357 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1358
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1359 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1360 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1361 real f;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1362
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1363 for (f = 1; !issubnormal(f); f /= 2)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1364 assert(f != 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1365 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1366
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1367 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1368 * Return !=0 if e is $(PLUSMN)$(INFIN).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1369 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1370
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1371 int isinf(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1372 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1373 ushort* pe = cast(ushort *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1374 ulong* ps = cast(ulong *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1375
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1376 return (pe[4] & 0x7FFF) == 0x7FFF &&
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1377 *ps == 0x8000000000000000;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1378 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1379
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1380 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1381 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1382 assert(isinf(float.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1383 assert(!isinf(float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1384 assert(isinf(double.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1385 assert(isinf(-real.infinity));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1386
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1387 assert(isinf(-1.0 / 0.0));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1388 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1389
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1390 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1391 * Return 1 if sign bit of e is set, 0 if not.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1392 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1393
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1394 int signbit(real e)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1395 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1396 ubyte* pe = cast(ubyte *)&e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1397
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1398 //printf("e = %Lg\n", e);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1399 return (pe[9] & 0x80) != 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1400 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1401
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1402 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1403 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1404 debug (math) printf("math.signbit.unittest\n");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1405 assert(!signbit(float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1406 assert(signbit(-float.nan));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1407 assert(!signbit(168.1234));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1408 assert(signbit(-168.1234));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1409 assert(!signbit(0.0));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1410 assert(signbit(-0.0));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1411 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1412
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1413 /*********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1414 * Return a value composed of to with from's sign bit.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1415 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1416
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1417 real copysign(real to, real from)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1418 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1419 ubyte* pto = cast(ubyte *)&to;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1420 ubyte* pfrom = cast(ubyte *)&from;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1421
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1422 pto[9] &= 0x7F;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1423 pto[9] |= pfrom[9] & 0x80;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1424
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1425 return to;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1426 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1427
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1428 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1429 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1430 real e;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1431
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1432 e = copysign(21, 23.8);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1433 assert(e == 21);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1434
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1435 e = copysign(-21, 23.8);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1436 assert(e == 21);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1437
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1438 e = copysign(21, -23.8);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1439 assert(e == -21);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1440
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1441 e = copysign(-21, -23.8);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1442 assert(e == -21);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1443
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1444 e = copysign(real.nan, -23.8);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1445 assert(isnan(e) && signbit(e));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1446 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1447
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1448 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1449 * Creates a quiet NAN with the information from tagp[] embedded in it.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1450 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1451 real nan(char[] tagp) { return std.c.math.nan((tagp~\0).ptr); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1452
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1453 /******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1454 * Calculates the next representable value after x in the direction of y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1455 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1456 * If y $(GT) x, the result will be the next largest floating-point value;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1457 * if y $(LT) x, the result will be the next smallest value.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1458 * If x == y, the result is y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1459 * The FE_INEXACT and FE_OVERFLOW exceptions will be raised if x is finite and
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1460 * the function result is infinite. The FE_INEXACT and FE_UNDERFLOW
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1461 * exceptions will be raised if the function value is subnormal, and x is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1462 * not equal to y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1463 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1464 real nextafter(real x, real y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1465 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1466 version (linux)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1467 return std.c.math.nextafterl(x, y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1468 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1469 throw new NotImplemented("nextafter");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1470 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1471
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1472 //real nexttoward(real x, real y) { return std.c.math.nexttowardl(x, y); }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1473
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1474 /*******************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1475 * Returns the positive difference between x and y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1476 * Returns:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1477 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1478 * $(TR $(TH x, y) $(TH fdim(x, y)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1479 * $(TR $(TD x $(GT) y) $(TD x - y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1480 * $(TR $(TD x $(LT)= y) $(TD +0.0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1481 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1482 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1483 real fdim(real x, real y) { return (x > y) ? x - y : +0.0; }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1484
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1485 /****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1486 * Returns the larger of x and y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1487 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1488 real fmax(real x, real y) { return x > y ? x : y; }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1489
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1490 /****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1491 * Returns the smaller of x and y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1492 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1493 real fmin(real x, real y) { return x < y ? x : y; }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1494
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1495 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1496 * Returns (x * y) + z, rounding only once according to the
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1497 * current rounding mode.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1498 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1499 real fma(real x, real y, real z) { return (x * y) + z; }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1500
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1501 /*******************************************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1502 * Fast integral powers.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1503 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1504
473
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
1505 pragma(intrinsic, "llvm.powi.f32")
108
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1506 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1507 float pow(float x, uint n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1508 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1509 float pow(float x, int n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1510 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1511
473
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
1512 pragma(intrinsic, "llvm.powi.f64")
108
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1513 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1514 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1515 double pow(double x, uint n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1516 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1517 double pow(double x, int n);
473
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
1518 }
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
1519
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
1520 pragma(intrinsic, "llvm.powi.f80")
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
1521 {
108
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1522 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1523 real pow(real x, uint n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1524 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1525 real pow(real x, int n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1526 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1527
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1528 /+
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1529 real pow(real x, uint n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1530 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1531 real p;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1532
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1533 switch (n)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1534 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1535 case 0:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1536 p = 1.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1537 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1538
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1539 case 1:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1540 p = x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1541 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1542
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1543 case 2:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1544 p = x * x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1545 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1546
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1547 default:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1548 p = 1.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1549 while (1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1550 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1551 if (n & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1552 p *= x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1553 n >>= 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1554 if (!n)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1555 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1556 x *= x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1557 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1558 break;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1559 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1560 return p;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1561 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1562
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1563 /// ditto
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1564 real pow(real x, int n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1565 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1566 if (n < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1567 return pow(x, cast(real)n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1568 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1569 return pow(x, cast(uint)n);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1570 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1571 +/
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1572
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1573 /*********************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1574 * Calculates x$(SUP y).
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1575 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1576 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1577 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1578 * $(TH x) $(TH y) $(TH pow(x, y)) $(TH div 0) $(TH invalid?))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1579 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1580 * $(TD anything) $(TD $(PLUSMN)0.0) $(TD 1.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1581 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1582 * $(TD |x| $(GT) 1) $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1583 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1584 * $(TD |x| $(LT) 1) $(TD +$(INFIN)) $(TD +0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1585 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1586 * $(TD |x| $(GT) 1) $(TD -$(INFIN)) $(TD +0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1587 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1588 * $(TD |x| $(LT) 1) $(TD -$(INFIN)) $(TD +$(INFIN)) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1589 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1590 * $(TD +$(INFIN)) $(TD $(GT) 0.0) $(TD +$(INFIN)) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1591 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1592 * $(TD +$(INFIN)) $(TD $(LT) 0.0) $(TD +0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1593 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1594 * $(TD -$(INFIN)) $(TD odd integer $(GT) 0.0) $(TD -$(INFIN)) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1595 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1596 * $(TD -$(INFIN)) $(TD $(GT) 0.0, not odd integer) $(TD +$(INFIN)) $(TD no) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1597 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1598 * $(TD -$(INFIN)) $(TD odd integer $(LT) 0.0) $(TD -0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1599 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1600 * $(TD -$(INFIN)) $(TD $(LT) 0.0, not odd integer) $(TD +0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1601 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1602 * $(TD $(PLUSMN)1.0) $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD no) $(TD yes) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1603 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1604 * $(TD $(LT) 0.0) $(TD finite, nonintegral) $(TD $(NAN)) $(TD no) $(TD yes))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1605 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1606 * $(TD $(PLUSMN)0.0) $(TD odd integer $(LT) 0.0) $(TD $(PLUSMN)$(INFIN)) $(TD yes) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1607 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1608 * $(TD $(PLUSMN)0.0) $(TD $(LT) 0.0, not odd integer) $(TD +$(INFIN)) $(TD yes) $(TD no))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1609 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1610 * $(TD $(PLUSMN)0.0) $(TD odd integer $(GT) 0.0) $(TD $(PLUSMN)0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1611 * $(TR
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1612 * $(TD $(PLUSMN)0.0) $(TD $(GT) 0.0, not odd integer) $(TD +0.0) $(TD no) $(TD no) )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1613 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1614 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1615
473
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
1616 pragma(intrinsic, "llvm.pow.f32")
108
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1617 float pow(float x, float y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1618
473
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
1619 pragma(intrinsic, "llvm.pow.f64")
108
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1620 double pow(double x, double y);
473
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
1621
373489eeaf90 Applied downs' lphobos update
Tomas Lindquist Olsen <tomas.l.olsen@gmail.com>
parents: 108
diff changeset
1622 pragma(intrinsic, "llvm.pow.f80")
108
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1623 real pow(real x, real y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1624
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1625 /+
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1626 real pow(real x, real y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1627 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1628 version (linux) // C pow() often does not handle special values correctly
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1629 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1630 if (isnan(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1631 return y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1632
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1633 if (y == 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1634 return 1; // even if x is $(NAN)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1635 if (isnan(x) && y != 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1636 return x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1637 if (isinf(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1638 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1639 if (fabs(x) > 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1640 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1641 if (signbit(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1642 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1643 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1644 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1645 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1646 else if (fabs(x) == 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1647 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1648 return real.nan;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1649 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1650 else // < 1
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1651 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1652 if (signbit(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1653 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1654 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1655 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1656 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1657 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1658 if (isinf(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1659 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1660 if (signbit(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1661 { long i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1662
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1663 i = cast(long)y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1664 if (y > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1665 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1666 if (i == y && i & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1667 return -real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1668 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1669 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1670 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1671 else if (y < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1672 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1673 if (i == y && i & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1674 return -0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1675 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1676 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1677 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1678 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1679 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1680 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1681 if (y > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1682 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1683 else if (y < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1684 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1685 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1686 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1687
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1688 if (x == 0.0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1689 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1690 if (signbit(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1691 { long i;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1692
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1693 i = cast(long)y;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1694 if (y > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1695 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1696 if (i == y && i & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1697 return -0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1698 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1699 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1700 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1701 else if (y < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1702 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1703 if (i == y && i & 1)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1704 return -real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1705 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1706 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1707 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1708 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1709 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1710 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1711 if (y > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1712 return +0.0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1713 else if (y < 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1714 return real.infinity;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1715 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1716 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1717 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1718 return std.c.math.powl(x, y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1719 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1720 +/
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1721
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1722 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1723 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1724 real x = 46;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1725
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1726 assert(pow(x,0) == 1.0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1727 assert(pow(x,1) == x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1728 assert(pow(x,2) == x * x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1729 assert(pow(x,3) == x * x * x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1730 assert(pow(x,8) == (x * x) * (x * x) * (x * x) * (x * x));
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1731 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1732
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1733 /****************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1734 * Simple function to compare two floating point values
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1735 * to a specified precision.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1736 * Returns:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1737 * 1 match
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1738 * 0 nomatch
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1739 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1740
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1741 private int mfeq(real x, real y, real precision)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1742 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1743 if (x == y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1744 return 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1745 if (isnan(x))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1746 return isnan(y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1747 if (isnan(y))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1748 return 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1749 return fabs(x - y) <= precision;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1750 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1751
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1752 // Returns true if x is +0.0 (This function is used in unit tests)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1753 bool isPosZero(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1754 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1755 return (x == 0) && (signbit(x) == 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1756 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1757
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1758 // Returns true if x is -0.0 (This function is used in unit tests)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1759 bool isNegZero(real x)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1760 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1761 return (x == 0) && signbit(x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1762 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1763
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1764 /**************************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1765 * To what precision is x equal to y?
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1766 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1767 * Returns: the number of mantissa bits which are equal in x and y.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1768 * eg, 0x1.F8p+60 and 0x1.F1p+60 are equal to 5 bits of precision.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1769 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1770 * $(TABLE_SV
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1771 * $(TR $(TH x) $(TH y) $(TH feqrel(x, y)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1772 * $(TR $(TD x) $(TD x) $(TD real.mant_dig))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1773 * $(TR $(TD x) $(TD $(GT)= 2*x) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1774 * $(TR $(TD x) $(TD $(LT)= x/2) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1775 * $(TR $(TD $(NAN)) $(TD any) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1776 * $(TR $(TD any) $(TD $(NAN)) $(TD 0))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1777 * )
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1778 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1779
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1780 int feqrel(real x, real y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1781 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1782 /* Public Domain. Author: Don Clugston, 18 Aug 2005.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1783 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1784
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1785 if (x == y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1786 return real.mant_dig; // ensure diff!=0, cope with INF.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1787
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1788 real diff = fabs(x - y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1789
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1790 ushort *pa = cast(ushort *)(&x);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1791 ushort *pb = cast(ushort *)(&y);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1792 ushort *pd = cast(ushort *)(&diff);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1793
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1794 // The difference in abs(exponent) between x or y and abs(x-y)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1795 // is equal to the number of mantissa bits of x which are
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1796 // equal to y. If negative, x and y have different exponents.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1797 // If positive, x and y are equal to 'bitsdiff' bits.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1798 // AND with 0x7FFF to form the absolute value.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1799 // To avoid out-by-1 errors, we subtract 1 so it rounds down
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1800 // if the exponents were different. This means 'bitsdiff' is
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1801 // always 1 lower than we want, except that if bitsdiff==0,
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1802 // they could have 0 or 1 bits in common.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1803 int bitsdiff = ( ((pa[4]&0x7FFF) + (pb[4]&0x7FFF)-1)>>1) - pd[4];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1804
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1805 if (pd[4] == 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1806 { // Difference is denormal
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1807 // For denormals, we need to add the number of zeros that
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1808 // lie at the start of diff's mantissa.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1809 // We do this by multiplying by 2^real.mant_dig
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1810 diff *= 0x1p+63;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1811 return bitsdiff + real.mant_dig - pd[4];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1812 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1813
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1814 if (bitsdiff > 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1815 return bitsdiff + 1; // add the 1 we subtracted before
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1816
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1817 // Avoid out-by-1 errors when factor is almost 2.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1818 return (bitsdiff == 0) ? (pa[4] == pb[4]) : 0;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1819 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1820
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1821 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1822 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1823 // Exact equality
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1824 assert(feqrel(real.max,real.max)==real.mant_dig);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1825 assert(feqrel(0,0)==real.mant_dig);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1826 assert(feqrel(7.1824,7.1824)==real.mant_dig);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1827 assert(feqrel(real.infinity,real.infinity)==real.mant_dig);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1828
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1829 // a few bits away from exact equality
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1830 real w=1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1831 for (int i=1; i<real.mant_dig-1; ++i) {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1832 assert(feqrel(1+w*real.epsilon,1)==real.mant_dig-i);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1833 assert(feqrel(1-w*real.epsilon,1)==real.mant_dig-i);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1834 assert(feqrel(1,1+(w-1)*real.epsilon)==real.mant_dig-i+1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1835 w*=2;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1836 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1837 assert(feqrel(1.5+real.epsilon,1.5)==real.mant_dig-1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1838 assert(feqrel(1.5-real.epsilon,1.5)==real.mant_dig-1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1839 assert(feqrel(1.5-real.epsilon,1.5+real.epsilon)==real.mant_dig-2);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1840
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1841 // Numbers that are close
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1842 assert(feqrel(0x1.Bp+84, 0x1.B8p+84)==5);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1843 assert(feqrel(0x1.8p+10, 0x1.Cp+10)==2);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1844 assert(feqrel(1.5*(1-real.epsilon), 1)==2);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1845 assert(feqrel(1.5, 1)==1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1846 assert(feqrel(2*(1-real.epsilon), 1)==1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1847
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1848 // Factors of 2
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1849 assert(feqrel(real.max,real.infinity)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1850 assert(feqrel(2*(1-real.epsilon), 1)==1);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1851 assert(feqrel(1, 2)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1852 assert(feqrel(4, 1)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1853
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1854 // Extreme inequality
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1855 assert(feqrel(real.nan,real.nan)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1856 assert(feqrel(0,-real.nan)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1857 assert(feqrel(real.nan,real.infinity)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1858 assert(feqrel(real.infinity,-real.infinity)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1859 assert(feqrel(-real.max,real.infinity)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1860 assert(feqrel(real.max,-real.max)==0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1861 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1862
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1863
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1864 /***********************************
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1865 * Evaluate polynomial A(x) = a<sub>0</sub> + a<sub>1</sub>x + a<sub>2</sub>x&sup2; + a<sub>3</sub>x&sup3; ...
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1866 *
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1867 * Uses Horner's rule A(x) = a<sub>0</sub> + x(a<sub>1</sub> + x(a<sub>2</sub> + x(a<sub>3</sub> + ...)))
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1868 * Params:
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1869 * A = array of coefficients a<sub>0</sub>, a<sub>1</sub>, etc.
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1870 */
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1871 real poly(real x, real[] A)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1872 in
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1873 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1874 assert(A.length > 0);
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1875 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1876 body
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1877 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1878 version (D_InlineAsm_X86)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1879 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1880 version (Windows)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1881 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1882 asm // assembler by W. Bright
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1883 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1884 // EDX = (A.length - 1) * real.sizeof
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1885 mov ECX,A[EBP] ; // ECX = A.length
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1886 dec ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1887 lea EDX,[ECX][ECX*8] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1888 add EDX,ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1889 add EDX,A+4[EBP] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1890 fld real ptr [EDX] ; // ST0 = coeff[ECX]
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1891 jecxz return_ST ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1892 fld x[EBP] ; // ST0 = x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1893 fxch ST(1) ; // ST1 = x, ST0 = r
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1894 align 4 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1895 L2: fmul ST,ST(1) ; // r *= x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1896 fld real ptr -10[EDX] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1897 sub EDX,10 ; // deg--
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1898 faddp ST(1),ST ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1899 dec ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1900 jne L2 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1901 fxch ST(1) ; // ST1 = r, ST0 = x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1902 fstp ST(0) ; // dump x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1903 align 4 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1904 return_ST: ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1905 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1906 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1907 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1908 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1909 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1910 asm // assembler by W. Bright
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1911 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1912 // EDX = (A.length - 1) * real.sizeof
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1913 mov ECX,A[EBP] ; // ECX = A.length
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1914 dec ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1915 lea EDX,[ECX*8] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1916 lea EDX,[EDX][ECX*4] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1917 add EDX,A+4[EBP] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1918 fld real ptr [EDX] ; // ST0 = coeff[ECX]
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1919 jecxz return_ST ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1920 fld x[EBP] ; // ST0 = x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1921 fxch ST(1) ; // ST1 = x, ST0 = r
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1922 align 4 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1923 L2: fmul ST,ST(1) ; // r *= x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1924 fld real ptr -12[EDX] ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1925 sub EDX,12 ; // deg--
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1926 faddp ST(1),ST ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1927 dec ECX ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1928 jne L2 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1929 fxch ST(1) ; // ST1 = r, ST0 = x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1930 fstp ST(0) ; // dump x
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1931 align 4 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1932 return_ST: ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1933 ;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1934 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1935 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1936 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1937 else
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1938 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1939 int i = A.length - 1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1940 real r = A[i];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1941 while (--i >= 0)
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1942 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1943 r *= x;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1944 r += A[i];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1945 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1946 return r;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1947 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1948 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1949
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1950 unittest
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1951 {
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1952 debug (math) printf("math.poly.unittest\n");
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1953 real x = 3.1;
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1954 static real pp[] = [56.1, 32.7, 6];
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1955
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1956 assert( poly(x, pp) == (56.1L + (32.7L + 6L * x) * x) );
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1957 }
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1958
288fe1029e1f [svn r112] Fixed 'case 1,2,3:' style case statements.
lindquist
parents:
diff changeset
1959