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annotate src/video/e_log.h @ 1810:4c270c3a88ed

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Fixed bug #225 Making the old code limp along, for Carbon builds.
author Sam Lantinga <slouken@libsdl.org>
date Thu, 11 May 2006 03:19:03 +0000
parents 450721ad5436
children 782fd950bd46 c121d94672cb
rev   line source
1330
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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1 /* @(#)e_log.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_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";
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15 #endif
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16
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17 /* __ieee754_log(x)
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18 * Return the logrithm of x
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19 *
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20 * Method :
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21 * 1. Argument Reduction: find k and f such that
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22 * x = 2^k * (1+f),
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23 * where sqrt(2)/2 < 1+f < sqrt(2) .
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24 *
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25 * 2. Approximation of log(1+f).
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26 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
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27 * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
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28 * = 2s + s*R
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29 * We use a special Reme algorithm on [0,0.1716] to generate
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30 * a polynomial of degree 14 to approximate R The maximum error
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31 * of this polynomial approximation is bounded by 2**-58.45. In
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32 * other words,
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33 * 2 4 6 8 10 12 14
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34 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
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35 * (the values of Lg1 to Lg7 are listed in the program)
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36 * and
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37 * | 2 14 | -58.45
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38 * | Lg1*s +...+Lg7*s - R(z) | <= 2
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39 * | |
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40 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
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41 * In order to guarantee error in log below 1ulp, we compute log
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42 * by
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43 * log(1+f) = f - s*(f - R) (if f is not too large)
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44 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
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45 *
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46 * 3. Finally, log(x) = k*ln2 + log(1+f).
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47 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
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48 * Here ln2 is split into two floating point number:
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49 * ln2_hi + ln2_lo,
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50 * where n*ln2_hi is always exact for |n| < 2000.
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51 *
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52 * Special cases:
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53 * log(x) is NaN with signal if x < 0 (including -INF) ;
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54 * log(+INF) is +INF; log(0) is -INF with signal;
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55 * log(NaN) is that NaN with no signal.
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56 *
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57 * Accuracy:
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58 * according to an error analysis, the error is always less than
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59 * 1 ulp (unit in the last place).
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60 *
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61 * Constants:
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62 * The hexadecimal values are the intended ones for the following
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63 * constants. The decimal values may be used, provided that the
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64 * compiler will convert from decimal to binary accurately enough
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65 * to produce the hexadecimal values shown.
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66 */
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67
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68 /*#include "math.h"*/
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69 #include "math_private.h"
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70
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71 #ifdef __STDC__
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72 static const double
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73 #else
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74 static double
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75 #endif
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76 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
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77 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
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78 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
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79 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
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80 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
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81 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
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82 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
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83 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
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84 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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85
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86 #ifdef __STDC__
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87 double __ieee754_log(double x)
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88 #else
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89 double __ieee754_log(x)
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90 double x;
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91 #endif
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92 {
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93 double hfsq,f,s,z,R,w,t1,t2,dk;
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94 int32_t k,hx,i,j;
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95 u_int32_t lx;
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96
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97 EXTRACT_WORDS(hx,lx,x);
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98
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99 k=0;
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100 if (hx < 0x00100000) { /* x < 2**-1022 */
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101 if (((hx&0x7fffffff)|lx)==0)
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102 return -two54/zero; /* log(+-0)=-inf */
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103 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
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104 k -= 54; x *= two54; /* subnormal number, scale up x */
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105 GET_HIGH_WORD(hx,x);
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106 }
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107 if (hx >= 0x7ff00000) return x+x;
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108 k += (hx>>20)-1023;
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109 hx &= 0x000fffff;
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110 i = (hx+0x95f64)&0x100000;
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111 SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
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112 k += (i>>20);
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113 f = x-1.0;
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114 if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
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115 if(f==zero) {if(k==0) return zero; else {dk=(double)k;
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116 return dk*ln2_hi+dk*ln2_lo;}
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117 }
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118 R = f*f*(0.5-0.33333333333333333*f);
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119 if(k==0) return f-R; else {dk=(double)k;
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120 return dk*ln2_hi-((R-dk*ln2_lo)-f);}
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121 }
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122 s = f/(2.0+f);
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123 dk = (double)k;
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124 z = s*s;
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125 i = hx-0x6147a;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
126 w = z*z;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
127 j = 0x6b851-hx;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
128 t1= w*(Lg2+w*(Lg4+w*Lg6));
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
129 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
130 i |= j;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
131 R = t2+t1;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
132 if(i>0) {
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
133 hfsq=0.5*f*f;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
134 if(k==0) return f-(hfsq-s*(hfsq+R)); else
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
135 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
136 } else {
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
137 if(k==0) return f-s*(f-R); else
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
138 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
139 }
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
140 }