| /* @(#)e_log10.c 5.1 93/09/24 */ |
| /* |
| * ==================================================== |
| * 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_log10(x) |
| * Return the base 10 logarithm of x |
| * |
| * Method : |
| * Let log10_2hi = leading 40 bits of log10(2) and |
| * log10_2lo = log10(2) - log10_2hi, |
| * ivln10 = 1/log(10) rounded. |
| * Then |
| * n = ilogb(x), |
| * if(n<0) n = n+1; |
| * x = scalbn(x,-n); |
| * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) |
| * |
| * Note 1: |
| * To guarantee log10(10**n)=n, where 10**n is normal, the rounding |
| * mode must set to Round-to-Nearest. |
| * Note 2: |
| * [1/log(10)] rounded to 53 bits has error .198 ulps; |
| * log10 is monotonic at all binary break points. |
| * |
| * Special cases: |
| * log10(x) is NaN with signal if x < 0; |
| * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; |
| * log10(NaN) is that NaN with no signal; |
| * log10(10**N) = N for N=0,1,...,22. |
| * |
| * 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 <stdint.h> |
| |
| static const double two54 = 1.80143985094819840000e+16; /* 0x4350000000000000 */ |
| static const double ivln10 = 4.34294481903251816668e-01; /* 0x3FDBCB7B1526E50E */ |
| static const double log10_2hi = 3.01029995663611771306e-01; /* 0x3FD34413509F6000 */ |
| static const double log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF311F12B36 */ |
| |
| double |
| __ieee754_log10 (double x) |
| { |
| double y, z; |
| int64_t i, hx; |
| int32_t k; |
| |
| EXTRACT_WORDS64 (hx, x); |
| |
| k = 0; |
| if (hx < INT64_C(0x0010000000000000)) |
| { /* x < 2**-1022 */ |
| if (__builtin_expect ((hx & UINT64_C(0x7fffffffffffffff)) == 0, 0)) |
| return -two54 / (x - x); /* log(+-0)=-inf */ |
| if (__builtin_expect (hx < 0, 0)) |
| return (x - x) / (x - x); /* log(-#) = NaN */ |
| k -= 54; |
| x *= two54; /* subnormal number, scale up x */ |
| EXTRACT_WORDS64 (hx, x); |
| } |
| /* scale up resulted in a NaN number */ |
| if (__builtin_expect (hx >= UINT64_C(0x7ff0000000000000), 0)) |
| return x + x; |
| k += (hx >> 52) - 1023; |
| i = ((uint64_t) k & UINT64_C(0x8000000000000000)) >> 63; |
| hx = (hx & UINT64_C(0x000fffffffffffff)) | ((0x3ff - i) << 52); |
| y = (double) (k + i); |
| INSERT_WORDS64 (x, hx); |
| z = y * log10_2lo + ivln10 * __ieee754_log (x); |
| return z + y * log10_2hi; |
| } |
| |
| strong_alias (__ieee754_log10, __log10_finite) |
