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Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/dbl-64/e_log2.c')
| -rw-r--r-- | REORG.TODO/sysdeps/ieee754/dbl-64/e_log2.c | 133 |
1 files changed, 133 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_log2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log2.c new file mode 100644 index 0000000000..5af68d8ecc --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_log2.c @@ -0,0 +1,133 @@ +/* Adapted for log2 by Ulrich Drepper <drepper@cygnus.com>. */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_log2(x) + * Return the logarithm to base 2 of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k + log(1+f). + * = k+(f-(hfsq-(s*(hfsq+R)))) + * + * Special cases: + * log2(x) is NaN with signal if x < 0 (including -INF) ; + * log2(+INF) is +INF; log(0) is -INF with signal; + * log2(NaN) is that NaN with no signal. + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include <math.h> +#include <math_private.h> +#include <fix-int-fp-convert-zero.h> + +static const double ln2 = 0.69314718055994530942; +static const double two54 = 1.80143985094819840000e+16; /* 43500000 00000000 */ +static const double Lg1 = 6.666666666666735130e-01; /* 3FE55555 55555593 */ +static const double Lg2 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */ +static const double Lg3 = 2.857142874366239149e-01; /* 3FD24924 94229359 */ +static const double Lg4 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */ +static const double Lg5 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */ +static const double Lg6 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */ +static const double Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; + +double +__ieee754_log2 (double x) +{ + double hfsq, f, s, z, R, w, t1, t2, dk; + int32_t k, hx, i, j; + u_int32_t lx; + + EXTRACT_WORDS (hx, lx, x); + + k = 0; + if (hx < 0x00100000) + { /* x < 2**-1022 */ + if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0)) + return -two54 / __fabs (x); /* log(+-0)=-inf */ + if (__glibc_unlikely (hx < 0)) + return (x - x) / (x - x); /* log(-#) = NaN */ + k -= 54; + x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD (hx, x); + } + if (__glibc_unlikely (hx >= 0x7ff00000)) + return x + x; + k += (hx >> 20) - 1023; + hx &= 0x000fffff; + i = (hx + 0x95f64) & 0x100000; + SET_HIGH_WORD (x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */ + k += (i >> 20); + dk = (double) k; + f = x - 1.0; + if ((0x000fffff & (2 + hx)) < 3) + { /* |f| < 2**-20 */ + if (f == zero) + { + if (FIX_INT_FP_CONVERT_ZERO && dk == 0.0) + dk = 0.0; + return dk; + } + R = f * f * (0.5 - 0.33333333333333333 * f); + return dk - (R - f) / ln2; + } + s = f / (2.0 + f); + z = s * s; + i = hx - 0x6147a; + w = z * z; + j = 0x6b851 - hx; + t1 = w * (Lg2 + w * (Lg4 + w * Lg6)); + t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); + i |= j; + R = t2 + t1; + if (i > 0) + { + hfsq = 0.5 * f * f; + return dk - ((hfsq - (s * (hfsq + R))) - f) / ln2; + } + else + { + return dk - ((s * (f - R)) - f) / ln2; + } +} + +strong_alias (__ieee754_log2, __log2_finite) |