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annotate src/libm/e_rem_pio2.c @ 4834:fd5bb97ec05d

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Improving Cocoa implementation and fixed a small bug in SDL_shape.c.
author egottlieb
date Thu, 05 Aug 2010 18:58:45 -0400
parents dc1eb82ffdaa
children
rev   line source
2756
a98604b691c8 Expanded the libm support and put it into a separate directory.
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1 /* @(#)e_rem_pio2.c 5.1 93/09/24 */
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2 /*
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3 * ====================================================
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4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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5 *
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6 * Developed at SunPro, a Sun Microsystems, Inc. business.
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7 * Permission to use, copy, modify, and distribute this
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8 * software is freely granted, provided that this notice
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9 * is preserved.
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10 * ====================================================
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11 */
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12
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13 #if defined(LIBM_SCCS) && !defined(lint)
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dc1eb82ffdaa Von: Thomas Zimmermann
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14 static const char rcsid[] =
2756
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15 "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $";
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16 #endif
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17
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18 /* __ieee754_rem_pio2(x,y)
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19 *
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20 * return the remainder of x rem pi/2 in y[0]+y[1]
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21 * use __kernel_rem_pio2()
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22 */
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23
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24 #include "math.h"
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25 #include "math_private.h"
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26
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27 libm_hidden_proto(fabs)
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28
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29 /*
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30 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
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31 */
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32 #ifdef __STDC__
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33 static const int32_t two_over_pi[] = {
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34 #else
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35 static int32_t two_over_pi[] = {
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36 #endif
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37 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
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38 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
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39 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
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40 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
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41 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
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42 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
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43 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
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44 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
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45 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
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46 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
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47 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
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48 };
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49
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50 #ifdef __STDC__
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51 static const int32_t npio2_hw[] = {
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52 #else
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53 static int32_t npio2_hw[] = {
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54 #endif
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55 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
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56 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
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57 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
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58 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
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59 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
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60 0x404858EB, 0x404921FB,
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61 };
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62
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63 /*
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64 * invpio2: 53 bits of 2/pi
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65 * pio2_1: first 33 bit of pi/2
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66 * pio2_1t: pi/2 - pio2_1
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67 * pio2_2: second 33 bit of pi/2
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68 * pio2_2t: pi/2 - (pio2_1+pio2_2)
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69 * pio2_3: third 33 bit of pi/2
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70 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
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71 */
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72
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73 #ifdef __STDC__
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74 static const double
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75 #else
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76 static double
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77 #endif
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78 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
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79 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
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80 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
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81 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
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82 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
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83 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
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84 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
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85 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
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86 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
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87 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
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88
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89 #ifdef __STDC__
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90 int32_t attribute_hidden
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91 __ieee754_rem_pio2(double x, double *y)
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92 #else
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93 int32_t attribute_hidden
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94 __ieee754_rem_pio2(x, y)
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95 double x, y[];
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96 #endif
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97 {
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98 double z = 0.0, w, t, r, fn;
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99 double tx[3];
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100 int32_t e0, i, j, nx, n, ix, hx;
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101 u_int32_t low;
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102
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103 GET_HIGH_WORD(hx, x); /* high word of x */
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104 ix = hx & 0x7fffffff;
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105 if (ix <= 0x3fe921fb) { /* |x| ~<= pi/4 , no need for reduction */
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106 y[0] = x;
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107 y[1] = 0;
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108 return 0;
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109 }
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110 if (ix < 0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
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111 if (hx > 0) {
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112 z = x - pio2_1;
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113 if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */
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114 y[0] = z - pio2_1t;
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115 y[1] = (z - y[0]) - pio2_1t;
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116 } else { /* near pi/2, use 33+33+53 bit pi */
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117 z -= pio2_2;
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118 y[0] = z - pio2_2t;
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119 y[1] = (z - y[0]) - pio2_2t;
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120 }
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121 return 1;
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122 } else { /* negative x */
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123 z = x + pio2_1;
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124 if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */
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125 y[0] = z + pio2_1t;
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126 y[1] = (z - y[0]) + pio2_1t;
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127 } else { /* near pi/2, use 33+33+53 bit pi */
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128 z += pio2_2;
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129 y[0] = z + pio2_2t;
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130 y[1] = (z - y[0]) + pio2_2t;
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131 }
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132 return -1;
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133 }
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134 }
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135 if (ix <= 0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
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136 t = fabs(x);
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137 n = (int32_t) (t * invpio2 + half);
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138 fn = (double) n;
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139 r = t - fn * pio2_1;
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140 w = fn * pio2_1t; /* 1st round good to 85 bit */
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141 if (n < 32 && ix != npio2_hw[n - 1]) {
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142 y[0] = r - w; /* quick check no cancellation */
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143 } else {
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144 u_int32_t high;
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145 j = ix >> 20;
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146 y[0] = r - w;
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147 GET_HIGH_WORD(high, y[0]);
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148 i = j - ((high >> 20) & 0x7ff);
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149 if (i > 16) { /* 2nd iteration needed, good to 118 */
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150 t = r;
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151 w = fn * pio2_2;
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152 r = t - w;
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153 w = fn * pio2_2t - ((t - r) - w);
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154 y[0] = r - w;
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155 GET_HIGH_WORD(high, y[0]);
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156 i = j - ((high >> 20) & 0x7ff);
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157 if (i > 49) { /* 3rd iteration need, 151 bits acc */
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158 t = r; /* will cover all possible cases */
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159 w = fn * pio2_3;
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160 r = t - w;
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161 w = fn * pio2_3t - ((t - r) - w);
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162 y[0] = r - w;
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163 }
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164 }
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165 }
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166 y[1] = (r - y[0]) - w;
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167 if (hx < 0) {
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168 y[0] = -y[0];
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169 y[1] = -y[1];
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170 return -n;
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171 } else
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172 return n;
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173 }
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174 /*
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175 * all other (large) arguments
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176 */
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177 if (ix >= 0x7ff00000) { /* x is inf or NaN */
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178 y[0] = y[1] = x - x;
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179 return 0;
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180 }
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181 /* set z = scalbn(|x|,ilogb(x)-23) */
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182 GET_LOW_WORD(low, x);
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183 SET_LOW_WORD(z, low);
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diff changeset
184 e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */
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185 SET_HIGH_WORD(z, ix - ((int32_t) (e0 << 20)));
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parents:
diff changeset
186 for (i = 0; i < 2; i++) {
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187 tx[i] = (double) ((int32_t) (z));
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188 z = (z - tx[i]) * two24;
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diff changeset
189 }
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diff changeset
190 tx[2] = z;
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Sam Lantinga <slouken@libsdl.org>
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diff changeset
191 nx = 3;
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Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
192 while (tx[nx - 1] == zero)
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Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
193 nx--; /* skip zero term */
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diff changeset
194 n = __kernel_rem_pio2(tx, y, e0, nx, 2, two_over_pi);
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parents:
diff changeset
195 if (hx < 0) {
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diff changeset
196 y[0] = -y[0];
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diff changeset
197 y[1] = -y[1];
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diff changeset
198 return -n;
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Sam Lantinga <slouken@libsdl.org>
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diff changeset
199 }
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Sam Lantinga <slouken@libsdl.org>
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diff changeset
200 return n;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
201 }