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annotate src/video/e_pow.h @ 4170:092c0bc69155 SDL-1.2

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Fixed bug #618 Description From Tim Angus 2008-08-30 12:23:56 (-) [reply] As we all know SDL 1.2 doesn't handle dead keys well since one key press potentially equals two (or more) characters. For example, on many layouts, keying <backquote>,<space> results in <no character>,<backquote><space>. Since the unicode member of the SDL_keysym struct only has room for one character, only one can be returned. On Linux, the first character is returned. On Windows however, unless the exact number of characters generated by the keypress is 1, nothing is returned. The following patch addresses this inconsistency. Updated patch which includes a further fix to the handling of the numpad when numlock is on. This further fix is courtesy Amanieu d'Antras.
author Sam Lantinga <slouken@libsdl.org>
date Mon, 13 Apr 2009 08:42:09 +0000
parents 7a610f25c12f
children 782fd950bd46 c121d94672cb
rev   line source
1330
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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,},
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71 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
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72 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
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73 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
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74 L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
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75 L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
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76 L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
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77 L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
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78 L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
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79 L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
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80 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
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81 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
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82 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
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83 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
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84 P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
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85 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
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86 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
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87 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
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88 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
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89 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
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90 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
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91 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
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92 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
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93 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
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94 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
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95
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96 #ifdef __STDC__
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97 double __ieee754_pow(double x, double y)
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98 #else
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99 double __ieee754_pow(x,y)
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100 double x, y;
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101 #endif
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102 {
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103 double z,ax,z_h,z_l,p_h,p_l;
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104 double y1,t1,t2,r,s,t,u,v,w;
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105 int32_t i,j,k,yisint,n;
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106 int32_t hx,hy,ix,iy;
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107 u_int32_t lx,ly;
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108
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109 EXTRACT_WORDS(hx,lx,x);
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110 EXTRACT_WORDS(hy,ly,y);
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111 ix = hx&0x7fffffff; iy = hy&0x7fffffff;
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112
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113 /* y==zero: x**0 = 1 */
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114 if((iy|ly)==0) return one;
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115
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116 /* +-NaN return x+y */
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117 if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
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diff changeset
118 iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
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diff changeset
119 return x+y;
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diff changeset
120
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diff changeset
121 /* determine if y is an odd int when x < 0
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diff changeset
122 * yisint = 0 ... y is not an integer
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diff changeset
123 * yisint = 1 ... y is an odd int
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
124 * yisint = 2 ... y is an even int
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diff changeset
125 */
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diff changeset
126 yisint = 0;
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diff changeset
127 if(hx<0) {
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diff changeset
128 if(iy>=0x43400000) yisint = 2; /* even integer y */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
129 else if(iy>=0x3ff00000) {
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diff changeset
130 k = (iy>>20)-0x3ff; /* exponent */
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diff changeset
131 if(k>20) {
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diff changeset
132 j = ly>>(52-k);
1345
7f32b9bede06 Fixes for Visual C++ 6.0
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parents: 1330
diff changeset
133 if((u_int32_t)(j<<(52-k))==ly) yisint = 2-(j&1);
1330
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diff changeset
134 } else if(ly==0) {
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diff changeset
135 j = iy>>(20-k);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
136 if((j<<(20-k))==iy) yisint = 2-(j&1);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
137 }
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
138 }
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
139 }
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
140
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
141 /* special value of y */
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diff changeset
142 if(ly==0) {
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parents:
diff changeset
143 if (iy==0x7ff00000) { /* y is +-inf */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
144 if(((ix-0x3ff00000)|lx)==0)
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
145 return y - y; /* inf**+-1 is NaN */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
146 else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
147 return (hy>=0)? y: zero;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
148 else /* (|x|<1)**-,+inf = inf,0 */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
149 return (hy<0)?-y: zero;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
150 }
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
151 if(iy==0x3ff00000) { /* y is +-1 */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
152 if(hy<0) return one/x; else return x;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
153 }
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
154 if(hy==0x40000000) return x*x; /* y is 2 */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
155 if(hy==0x3fe00000) { /* y is 0.5 */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
156 if(hx>=0) /* x >= +0 */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
157 return __ieee754_sqrt(x);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
158 }
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
159 }
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
160
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
161 ax = x < 0 ? -x : x; /*fabs(x);*/
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
162 /* special value of x */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
163 if(lx==0) {
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
164 if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
165 z = ax; /*x is +-0,+-inf,+-1*/
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
166 if(hy<0) z = one/z; /* z = (1/|x|) */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
167 if(hx<0) {
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
168 if(((ix-0x3ff00000)|yisint)==0) {
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
169 z = (z-z)/(z-z); /* (-1)**non-int is NaN */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
170 } else if(yisint==1)
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
171 z = -z; /* (x<0)**odd = -(|x|**odd) */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
172 }
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
173 return z;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
174 }
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
175 }
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
176
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
177 /* (x<0)**(non-int) is NaN */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
178 if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
179
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
180 /* |y| is huge */
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parents:
diff changeset
181 if(iy>0x41e00000) { /* if |y| > 2**31 */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
182 if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
183 if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
184 if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
185 }
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
186 /* over/underflow if x is not close to one */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
187 if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
188 if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
189 /* now |1-x| is tiny <= 2**-20, suffice to compute
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parents:
diff changeset
190 log(x) by x-x^2/2+x^3/3-x^4/4 */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
191 t = x-1; /* t has 20 trailing zeros */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
192 w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
193 u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
194 v = t*ivln2_l-w*ivln2;
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diff changeset
195 t1 = u+v;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
196 SET_LOW_WORD(t1,0);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
197 t2 = v-(t1-u);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
198 } else {
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
199 double s2,s_h,s_l,t_h,t_l;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
200 n = 0;
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diff changeset
201 /* take care subnormal number */
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diff changeset
202 if(ix<0x00100000)
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
203 {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
204 n += ((ix)>>20)-0x3ff;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
205 j = ix&0x000fffff;
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
206 /* determine interval */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
207 ix = j|0x3ff00000; /* normalize ix */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
208 if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
209 else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
210 else {k=0;n+=1;ix -= 0x00100000;}
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
211 SET_HIGH_WORD(ax,ix);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
212
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
213 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
214 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
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diff changeset
215 v = one/(ax+bp[k]);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
216 s = u*v;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
217 s_h = s;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
218 SET_LOW_WORD(s_h,0);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
219 /* t_h=ax+bp[k] High */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
220 t_h = zero;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
221 SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
222 t_l = ax - (t_h-bp[k]);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
223 s_l = v*((u-s_h*t_h)-s_h*t_l);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
224 /* compute log(ax) */
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
225 s2 = s*s;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
226 r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
227 r += s_l*(s_h+s);
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
228 s2 = s_h*s_h;
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
229 t_h = 3.0+s2+r;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
230 SET_LOW_WORD(t_h,0);
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
231 t_l = r-((t_h-3.0)-s2);
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
232 /* u+v = s*(1+...) */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
233 u = s_h*t_h;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
234 v = s_l*t_h+t_l*s;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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diff changeset
235 /* 2/(3log2)*(s+...) */
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
236 p_h = u+v;
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
237 SET_LOW_WORD(p_h,0);
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
238 p_l = v-(p_h-u);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
239 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
240 z_l = cp_l*p_h+p_l*cp+dp_l[k];
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
241 /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
242 t = (double)n;
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243 t1 = (((z_h+z_l)+dp_h[k])+t);
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244 SET_LOW_WORD(t1,0);
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245 t2 = z_l-(((t1-t)-dp_h[k])-z_h);
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246 }
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247
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248 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
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249 if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
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250 s = -one;/* (-ve)**(odd int) */
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251
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252 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
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253 y1 = y;
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254 SET_LOW_WORD(y1,0);
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255 p_l = (y-y1)*t1+y*t2;
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256 p_h = y1*t1;
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257 z = p_l+p_h;
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258 EXTRACT_WORDS(j,i,z);
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259 if (j>=0x40900000) { /* z >= 1024 */
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260 if(((j-0x40900000)|i)!=0) /* if z > 1024 */
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261 return s*huge*huge; /* overflow */
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262 else {
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263 if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
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264 }
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265 } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
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266 if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
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267 return s*tiny*tiny; /* underflow */
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268 else {
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269 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
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270 }
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271 }
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272 /*
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273 * compute 2**(p_h+p_l)
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274 */
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275 i = j&0x7fffffff;
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276 k = (i>>20)-0x3ff;
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277 n = 0;
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278 if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
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279 n = j+(0x00100000>>(k+1));
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280 k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
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281 t = zero;
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282 SET_HIGH_WORD(t,n&~(0x000fffff>>k));
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283 n = ((n&0x000fffff)|0x00100000)>>(20-k);
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284 if(j<0) n = -n;
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285 p_h -= t;
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286 }
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287 t = p_l+p_h;
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288 SET_LOW_WORD(t,0);
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289 u = t*lg2_h;
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290 v = (p_l-(t-p_h))*lg2+t*lg2_l;
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291 z = u+v;
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292 w = v-(z-u);
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293 t = z*z;
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294 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
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295 r = (z*t1)/(t1-two)-(w+z*w);
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296 z = one-(r-z);
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297 GET_HIGH_WORD(j,z);
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298 j += (n<<20);
1424
7a610f25c12f Updated MacOS Classic MPW build
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299 if((j>>20)<=0) z = SDL_NAME(scalbn)(z,n); /* subnormal output */
1330
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300 else SET_HIGH_WORD(z,j);
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301 return s*z;
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302 }