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annotate src/libm/e_rem_pio2.c @ 3409:c8f580ebc96a

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Adam Strzelecki to SDL Sending a patch for fullscreen Mac OS X SDL 1.3 (SVN) Cocoa mouse position handling. In fullscreen mouse coordinates should be relative to SCREEN not to the window, which doesn't really occupy fullscreen. Without this patch mouse position (especially Y) was totally incorrect (shifted) in fullscreen.
author Sam Lantinga <slouken@libsdl.org>
date Thu, 22 Oct 2009 04:46:11 +0000
parents dc1eb82ffdaa
children
rev   line source
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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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diff changeset
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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Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
174 /*
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175 * all other (large) arguments
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176 */
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diff changeset
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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parents:
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182 GET_LOW_WORD(low, x);
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Sam Lantinga <slouken@libsdl.org>
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diff changeset
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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parents:
diff changeset
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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diff changeset
187 tx[i] = (double) ((int32_t) (z));
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parents:
diff changeset
188 z = (z - tx[i]) * two24;
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Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
189 }
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Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
190 tx[2] = z;
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Sam Lantinga <slouken@libsdl.org>
parents:
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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Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
194 n = __kernel_rem_pio2(tx, y, e0, nx, 2, two_over_pi);
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Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
195 if (hx < 0) {
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Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
196 y[0] = -y[0];
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Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
197 y[1] = -y[1];
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Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
198 return -n;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
199 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
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 }