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annotate src/video/e_pow.h @ 2190:eff1ccd88273

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author Patrice Mandin <patmandin@gmail.com>
date Fri, 13 Jul 2007 22:55:54 +0000
parents c121d94672cb
children edd2839b36f7
rev   line source
1330
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
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1 /* @(#)e_pow.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 char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $";
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15 #endif
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16
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17 /* __ieee754_pow(x,y) return x**y
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18 *
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19 * n
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20 * Method: Let x = 2 * (1+f)
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21 * 1. Compute and return log2(x) in two pieces:
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22 * log2(x) = w1 + w2,
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23 * where w1 has 53-24 = 29 bit trailing zeros.
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24 * 2. Perform y*log2(x) = n+y' by simulating muti-precision
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25 * arithmetic, where |y'|<=0.5.
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26 * 3. Return x**y = 2**n*exp(y'*log2)
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27 *
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28 * Special cases:
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29 * 1. (anything) ** 0 is 1
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30 * 2. (anything) ** 1 is itself
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31 * 3. (anything) ** NAN is NAN
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32 * 4. NAN ** (anything except 0) is NAN
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33 * 5. +-(|x| > 1) ** +INF is +INF
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34 * 6. +-(|x| > 1) ** -INF is +0
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35 * 7. +-(|x| < 1) ** +INF is +0
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36 * 8. +-(|x| < 1) ** -INF is +INF
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37 * 9. +-1 ** +-INF is NAN
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38 * 10. +0 ** (+anything except 0, NAN) is +0
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39 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
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40 * 12. +0 ** (-anything except 0, NAN) is +INF
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41 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
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42 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
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43 * 15. +INF ** (+anything except 0,NAN) is +INF
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44 * 16. +INF ** (-anything except 0,NAN) is +0
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45 * 17. -INF ** (anything) = -0 ** (-anything)
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46 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
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47 * 19. (-anything except 0 and inf) ** (non-integer) is NAN
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48 *
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49 * Accuracy:
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50 * pow(x,y) returns x**y nearly rounded. In particular
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51 * pow(integer,integer)
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52 * always returns the correct integer provided it is
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53 * representable.
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54 *
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55 * Constants :
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56 * The hexadecimal values are the intended ones for the following
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57 * constants. The decimal values may be used, provided that the
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58 * compiler will convert from decimal to binary accurately enough
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59 * to produce the hexadecimal values shown.
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60 */
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61
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62 /*#include "math.h"*/
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63 #include "math_private.h"
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64
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65 #ifdef __STDC__
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66 static const double
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67 #else
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68 static double
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69 #endif
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70 bp[] = { 1.0, 1.5, }, dp_h[] = {
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71 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
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72
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73 dp_l[] = {
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74 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
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75
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76 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
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77 L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
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78 L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
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79 L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
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80 L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
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81 L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
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82 L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
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83 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
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84 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
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85 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
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86 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
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87 P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
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88 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
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89 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
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90 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
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91 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
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92 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
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93 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
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94 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h */
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95 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
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96 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2 */
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97 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail */
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98
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99 #ifdef __STDC__
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100 double
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101 __ieee754_pow(double x, double y)
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102 #else
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103 double
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104 __ieee754_pow(x, y)
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105 double x, y;
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106 #endif
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107 {
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108 double z, ax, z_h, z_l, p_h, p_l;
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109 double y1, t1, t2, r, s, t, u, v, w;
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110 int32_t i, j, k, yisint, n;
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111 int32_t hx, hy, ix, iy;
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112 u_int32_t lx, ly;
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113
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114 EXTRACT_WORDS(hx, lx, x);
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115 EXTRACT_WORDS(hy, ly, y);
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116 ix = hx & 0x7fffffff;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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117 iy = hy & 0x7fffffff;
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diff changeset
118
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diff changeset
119 /* y==zero: x**0 = 1 */
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120 if ((iy | ly) == 0)
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diff changeset
121 return one;
1330
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diff changeset
122
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diff changeset
123 /* +-NaN return x+y */
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124 if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) ||
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
125 iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0)))
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
126 return x + y;
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diff changeset
127
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diff changeset
128 /* determine if y is an odd int when x < 0
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129 * yisint = 0 ... y is not an integer
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130 * yisint = 1 ... y is an odd int
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131 * yisint = 2 ... y is an even int
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132 */
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133 yisint = 0;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
134 if (hx < 0) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
135 if (iy >= 0x43400000)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
136 yisint = 2; /* even integer y */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
137 else if (iy >= 0x3ff00000) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
138 k = (iy >> 20) - 0x3ff; /* exponent */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
139 if (k > 20) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
140 j = ly >> (52 - k);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
141 if ((u_int32_t) (j << (52 - k)) == ly)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
142 yisint = 2 - (j & 1);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
143 } else if (ly == 0) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
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144 j = iy >> (20 - k);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
145 if ((j << (20 - k)) == iy)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
146 yisint = 2 - (j & 1);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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147 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
148 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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149 }
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150
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diff changeset
151 /* special value of y */
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152 if (ly == 0) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
153 if (iy == 0x7ff00000) { /* y is +-inf */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
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154 if (((ix - 0x3ff00000) | lx) == 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
155 return y - y; /* inf**+-1 is NaN */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
156 else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
157 return (hy >= 0) ? y : zero;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
158 else /* (|x|<1)**-,+inf = inf,0 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
159 return (hy < 0) ? -y : zero;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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160 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
161 if (iy == 0x3ff00000) { /* y is +-1 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
162 if (hy < 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
163 return one / x;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
164 else
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
165 return x;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
166 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
167 if (hy == 0x40000000)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
168 return x * x; /* y is 2 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
169 if (hy == 0x3fe00000) { /* y is 0.5 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
170 if (hx >= 0) /* x >= +0 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
171 return __ieee754_sqrt(x);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
172 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
173 }
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174
1895
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175 ax = x < 0 ? -x : x; /*fabs(x); */
1330
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diff changeset
176 /* special value of x */
1895
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parents: 1424
diff changeset
177 if (lx == 0) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
178 if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
179 z = ax; /*x is +-0,+-inf,+-1 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
180 if (hy < 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
181 z = one / z; /* z = (1/|x|) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
182 if (hx < 0) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
183 if (((ix - 0x3ff00000) | yisint) == 0) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
184 z = (z - z) / (z - z); /* (-1)**non-int is NaN */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
185 } else if (yisint == 1)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
186 z = -z; /* (x<0)**odd = -(|x|**odd) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
187 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
188 return z;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
189 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
190 }
1330
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diff changeset
191
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
192 /* (x<0)**(non-int) is NaN */
1895
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diff changeset
193 if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
194 return (x - x) / (x - x);
1330
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diff changeset
195
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Sam Lantinga <slouken@libsdl.org>
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diff changeset
196 /* |y| is huge */
1895
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diff changeset
197 if (iy > 0x41e00000) { /* if |y| > 2**31 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
198 if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
199 if (ix <= 0x3fefffff)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
200 return (hy < 0) ? huge * huge : tiny * tiny;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
201 if (ix >= 0x3ff00000)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
202 return (hy > 0) ? huge * huge : tiny * tiny;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
203 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
204 /* over/underflow if x is not close to one */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
205 if (ix < 0x3fefffff)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
206 return (hy < 0) ? huge * huge : tiny * tiny;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
207 if (ix > 0x3ff00000)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
208 return (hy > 0) ? huge * huge : tiny * tiny;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
209 /* now |1-x| is tiny <= 2**-20, suffice to compute
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
210 log(x) by x-x^2/2+x^3/3-x^4/4 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
211 t = x - 1; /* t has 20 trailing zeros */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
212 w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
213 u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
214 v = t * ivln2_l - w * ivln2;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
215 t1 = u + v;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
216 SET_LOW_WORD(t1, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
217 t2 = v - (t1 - u);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
218 } else {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
219 double s2, s_h, s_l, t_h, t_l;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
220 n = 0;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
221 /* take care subnormal number */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
222 if (ix < 0x00100000) {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
223 ax *= two53;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
224 n -= 53;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
225 GET_HIGH_WORD(ix, ax);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
226 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
227 n += ((ix) >> 20) - 0x3ff;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
228 j = ix & 0x000fffff;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
229 /* determine interval */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
230 ix = j | 0x3ff00000; /* normalize ix */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
231 if (j <= 0x3988E)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
232 k = 0; /* |x|<sqrt(3/2) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
233 else if (j < 0xBB67A)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
234 k = 1; /* |x|<sqrt(3) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
235 else {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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236 k = 0;
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237 n += 1;
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238 ix -= 0x00100000;
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239 }
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diff changeset
240 SET_HIGH_WORD(ax, ix);
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241
1895
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242 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
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243 u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
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244 v = one / (ax + bp[k]);
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diff changeset
245 s = u * v;
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diff changeset
246 s_h = s;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
247 SET_LOW_WORD(s_h, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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248 /* t_h=ax+bp[k] High */
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249 t_h = zero;
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diff changeset
250 SET_HIGH_WORD(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
251 t_l = ax - (t_h - bp[k]);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
252 s_l = v * ((u - s_h * t_h) - s_h * t_l);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
253 /* compute log(ax) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
254 s2 = s * s;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
255 r = s2 * s2 * (L1 +
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
256 s2 * (L2 +
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
257 s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
258 r += s_l * (s_h + s);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
259 s2 = s_h * s_h;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
260 t_h = 3.0 + s2 + r;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
261 SET_LOW_WORD(t_h, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
262 t_l = r - ((t_h - 3.0) - s2);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
263 /* u+v = s*(1+...) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
264 u = s_h * t_h;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
265 v = s_l * t_h + t_l * s;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
266 /* 2/(3log2)*(s+...) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
267 p_h = u + v;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
268 SET_LOW_WORD(p_h, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
269 p_l = v - (p_h - u);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
270 z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
271 z_l = cp_l * p_h + p_l * cp + dp_l[k];
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
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272 /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
273 t = (double) n;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
274 t1 = (((z_h + z_l) + dp_h[k]) + t);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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275 SET_LOW_WORD(t1, 0);
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diff changeset
276 t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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277 }
1330
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diff changeset
278
1895
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diff changeset
279 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
280 if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
281 s = -one; /* (-ve)**(odd int) */
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diff changeset
282
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diff changeset
283 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
1895
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diff changeset
284 y1 = y;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
285 SET_LOW_WORD(y1, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
286 p_l = (y - y1) * t1 + y * t2;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
287 p_h = y1 * t1;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
288 z = p_l + p_h;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
289 EXTRACT_WORDS(j, i, z);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
290 if (j >= 0x40900000) { /* z >= 1024 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
291 if (((j - 0x40900000) | i) != 0) /* if z > 1024 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
292 return s * huge * huge; /* overflow */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
293 else {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
294 if (p_l + ovt > z - p_h)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
295 return s * huge * huge; /* overflow */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
296 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
297 } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
298 if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
299 return s * tiny * tiny; /* underflow */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
300 else {
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
301 if (p_l <= z - p_h)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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parents: 1424
diff changeset
302 return s * tiny * tiny; /* underflow */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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diff changeset
303 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
304 }
1330
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diff changeset
305 /*
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
306 * compute 2**(p_h+p_l)
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Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
307 */
1895
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
308 i = j & 0x7fffffff;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
309 k = (i >> 20) - 0x3ff;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
310 n = 0;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
311 if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
312 n = j + (0x00100000 >> (k + 1));
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
313 k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
314 t = zero;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
315 SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
316 n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
317 if (j < 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
318 n = -n;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
319 p_h -= t;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
320 }
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
321 t = p_l + p_h;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
322 SET_LOW_WORD(t, 0);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
323 u = t * lg2_h;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
324 v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
325 z = u + v;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
326 w = v - (z - u);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
327 t = z * z;
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
328 t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
329 r = (z * t1) / (t1 - two) - (w + z * w);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
330 z = one - (r - z);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
331 GET_HIGH_WORD(j, z);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
332 j += (n << 20);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
333 if ((j >> 20) <= 0)
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
334 z = SDL_NAME(scalbn) (z, n); /* subnormal output */
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
335 else
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
336 SET_HIGH_WORD(z, j);
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
337 return s * z;
1330
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
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diff changeset
338 }
1895
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
parents: 1424
diff changeset
339
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
Sam Lantinga <slouken@libsdl.org>
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diff changeset
340 /* vi: set ts=4 sw=4 expandtab: */