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annotate src/libm/e_rem_pio2.c @ 4573:6399178be313

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Completed work on X11_CreateTexture. Added lots of safety features. These include support for drawing a texture using the core protocol while other textures are drawn using Xrender if Xrender does not support the color format of the said texture or any other fault with Xrender.
author Sunny Sachanandani <sunnysachanandani@gmail.com>
date Fri, 28 May 2010 20:40:09 +0530
parents dc1eb82ffdaa
children
rev   line source
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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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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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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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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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190 tx[2] = z;
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191 nx = 3;
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diff changeset
192 while (tx[nx - 1] == zero)
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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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diff changeset
195 if (hx < 0) {
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196 y[0] = -y[0];
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197 y[1] = -y[1];
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198 return -n;
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199 }
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200 return n;
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Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
201 }