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annotate src/libm/e_log.c @ 3294:470d0a416aa7

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Fixed bug #714 fuzzyTew@gmail.com 2009-03-14 15:18:45 PDT patch to change HAVE_ICONV to HAVE_ICONV_H There are two separate iconv checks in configure -- one for the header file and one for the library. include/SDL_stdinc.h uses the library define to see whether or not it should reference the types defined in the header, which naturally breaks if the library exists and the header does not.
author Sam Lantinga <slouken@libsdl.org>
date Mon, 21 Sep 2009 11:04:01 +0000
parents dc1eb82ffdaa
children
rev   line source
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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 const char rcsid[] =
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15 "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";
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16 #endif
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17
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18 /* __ieee754_log(x)
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19 * Return the logrithm of x
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20 *
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21 * Method :
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22 * 1. Argument Reduction: find k and f such that
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23 * x = 2^k * (1+f),
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24 * where sqrt(2)/2 < 1+f < sqrt(2) .
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25 *
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26 * 2. Approximation of log(1+f).
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27 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
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28 * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
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29 * = 2s + s*R
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30 * We use a special Reme algorithm on [0,0.1716] to generate
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31 * a polynomial of degree 14 to approximate R The maximum error
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32 * of this polynomial approximation is bounded by 2**-58.45. In
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33 * other words,
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34 * 2 4 6 8 10 12 14
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35 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
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36 * (the values of Lg1 to Lg7 are listed in the program)
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37 * and
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38 * | 2 14 | -58.45
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39 * | Lg1*s +...+Lg7*s - R(z) | <= 2
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40 * | |
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41 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
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42 * In order to guarantee error in log below 1ulp, we compute log
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43 * by
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44 * log(1+f) = f - s*(f - R) (if f is not too large)
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45 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
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46 *
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47 * 3. Finally, log(x) = k*ln2 + log(1+f).
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48 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
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49 * Here ln2 is split into two floating point number:
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50 * ln2_hi + ln2_lo,
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51 * where n*ln2_hi is always exact for |n| < 2000.
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52 *
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53 * Special cases:
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54 * log(x) is NaN with signal if x < 0 (including -INF) ;
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55 * log(+INF) is +INF; log(0) is -INF with signal;
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56 * log(NaN) is that NaN with no signal.
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57 *
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58 * Accuracy:
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59 * according to an error analysis, the error is always less than
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60 * 1 ulp (unit in the last place).
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61 *
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62 * Constants:
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63 * The hexadecimal values are the intended ones for the following
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64 * constants. The decimal values may be used, provided that the
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65 * compiler will convert from decimal to binary accurately enough
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66 * to produce the hexadecimal values shown.
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67 */
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68
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69 #include "math.h"
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70 #include "math_private.h"
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71
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72 #ifdef __STDC__
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73 static const double
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74 #else
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75 static double
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76 #endif
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77 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
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78 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
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79 two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
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80 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
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81 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
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82 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
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83 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
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84 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
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85 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
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86 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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87
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88 #ifdef __STDC__
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89 static const double zero = 0.0;
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90 #else
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91 static double zero = 0.0;
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92 #endif
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93
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94 #ifdef __STDC__
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95 double attribute_hidden
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96 __ieee754_log(double x)
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97 #else
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98 double attribute_hidden
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99 __ieee754_log(x)
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100 double x;
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101 #endif
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102 {
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103 double hfsq, f, s, z, R, w, t1, t2, dk;
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104 int32_t k, hx, i, j;
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105 u_int32_t lx;
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106
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107 EXTRACT_WORDS(hx, lx, x);
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108
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109 k = 0;
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110 if (hx < 0x00100000) { /* x < 2**-1022 */
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111 if (((hx & 0x7fffffff) | lx) == 0)
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112 return -two54 / zero; /* log(+-0)=-inf */
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113 if (hx < 0)
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114 return (x - x) / zero; /* log(-#) = NaN */
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115 k -= 54;
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116 x *= two54; /* subnormal number, scale up x */
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117 GET_HIGH_WORD(hx, x);
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118 }
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119 if (hx >= 0x7ff00000)
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120 return x + x;
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121 k += (hx >> 20) - 1023;
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122 hx &= 0x000fffff;
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123 i = (hx + 0x95f64) & 0x100000;
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124 SET_HIGH_WORD(x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */
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125 k += (i >> 20);
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126 f = x - 1.0;
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127 if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */
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128 if (f == zero) {
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129 if (k == 0)
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130 return zero;
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131 else {
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132 dk = (double) k;
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133 return dk * ln2_hi + dk * ln2_lo;
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134 }
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135 }
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136 R = f * f * (0.5 - 0.33333333333333333 * f);
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137 if (k == 0)
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138 return f - R;
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139 else {
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140 dk = (double) k;
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141 return dk * ln2_hi - ((R - dk * ln2_lo) - f);
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142 }
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143 }
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144 s = f / (2.0 + f);
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145 dk = (double) k;
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146 z = s * s;
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147 i = hx - 0x6147a;
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148 w = z * z;
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149 j = 0x6b851 - hx;
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150 t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
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151 t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
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152 i |= j;
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153 R = t2 + t1;
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154 if (i > 0) {
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155 hfsq = 0.5 * f * f;
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156 if (k == 0)
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157 return f - (hfsq - s * (hfsq + R));
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158 else
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159 return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) -
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160 f);
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161 } else {
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162 if (k == 0)
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163 return f - s * (f - R);
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164 else
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165 return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
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166 }
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parents:
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167 }