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Diffstat (limited to 'sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c | 128 |
1 files changed, 0 insertions, 128 deletions
diff --git a/sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c b/sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c deleted file mode 100644 index 5ccb78cf03..0000000000 --- a/sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c +++ /dev/null @@ -1,128 +0,0 @@ -/* - * ==================================================== - * 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> - -static const double ln2 = 0.69314718055994530942; -static const double two54 = 1.80143985094819840000e+16; /* 4350000000000000 */ -static const double Lg1 = 6.666666666666735130e-01; /* 3FE5555555555593 */ -static const double Lg2 = 3.999999999940941908e-01; /* 3FD999999997FA04 */ -static const double Lg3 = 2.857142874366239149e-01; /* 3FD2492494229359 */ -static const double Lg4 = 2.222219843214978396e-01; /* 3FCC71C51D8E78AF */ -static const double Lg5 = 1.818357216161805012e-01; /* 3FC7466496CB03DE */ -static const double Lg6 = 1.531383769920937332e-01; /* 3FC39A09D078C69F */ -static const double Lg7 = 1.479819860511658591e-01; /* 3FC2F112DF3E5244 */ - -static const double zero = 0.0; - -double -__ieee754_log2 (double x) -{ - double hfsq, f, s, z, R, w, t1, t2, dk; - int64_t hx, i, j; - int32_t k; - - EXTRACT_WORDS64 (hx, x); - - k = 0; - if (hx < INT64_C(0x0010000000000000)) - { /* x < 2**-1022 */ - if (__glibc_unlikely ((hx & UINT64_C(0x7fffffffffffffff)) == 0)) - return -two54 / (x - 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 */ - EXTRACT_WORDS64 (hx, x); - } - if (__glibc_unlikely (hx >= UINT64_C(0x7ff0000000000000))) - return x + x; - k += (hx >> 52) - 1023; - hx &= UINT64_C(0x000fffffffffffff); - i = (hx + UINT64_C(0x95f6400000000)) & UINT64_C(0x10000000000000); - /* normalize x or x/2 */ - INSERT_WORDS64 (x, hx | (i ^ UINT64_C(0x3ff0000000000000))); - k += (i >> 52); - dk = (double) k; - f = x - 1.0; - if ((UINT64_C(0x000fffffffffffff) & (2 + hx)) < 3) - { /* |f| < 2**-20 */ - if (f == zero) - 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 - UINT64_C(0x6147a00000000); - w = z * z; - j = UINT64_C(0x6b85100000000) - 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) |