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annotate src/video/e_log.h @ 1643:51038e80ae59

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More general fix for bug #189 The clipping is done at a higher level, and the low level functions are passed clipped rectangles. Drivers which don't support source clipping have not been changed, so the image will be squished instead of clipped, but at least they will no longer crash when the destination rect was out of bounds.
author Sam Lantinga <slouken@libsdl.org>
date Mon, 17 Apr 2006 06:47:23 +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;
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
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,
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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,
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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,
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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:
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140 }