| The Android Open Source Project | a27d2ba | 2008-10-21 07:00:00 -0700 | [diff] [blame^] | 1 | |
| 2 | /* @(#)e_log10.c 1.3 95/01/18 */ |
| 3 | /* |
| 4 | * ==================================================== |
| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 6 | * |
| 7 | * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| 8 | * Permission to use, copy, modify, and distribute this |
| 9 | * software is freely granted, provided that this notice |
| 10 | * is preserved. |
| 11 | * ==================================================== |
| 12 | */ |
| 13 | |
| 14 | #ifndef lint |
| 15 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_log10.c,v 1.11 2005/02/04 18:26:06 das Exp $"; |
| 16 | #endif |
| 17 | |
| 18 | /* __ieee754_log10(x) |
| 19 | * Return the base 10 logarithm of x |
| 20 | * |
| 21 | * Method : |
| 22 | * Let log10_2hi = leading 40 bits of log10(2) and |
| 23 | * log10_2lo = log10(2) - log10_2hi, |
| 24 | * ivln10 = 1/log(10) rounded. |
| 25 | * Then |
| 26 | * n = ilogb(x), |
| 27 | * if(n<0) n = n+1; |
| 28 | * x = scalbn(x,-n); |
| 29 | * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) |
| 30 | * |
| 31 | * Note 1: |
| 32 | * To guarantee log10(10**n)=n, where 10**n is normal, the rounding |
| 33 | * mode must set to Round-to-Nearest. |
| 34 | * Note 2: |
| 35 | * [1/log(10)] rounded to 53 bits has error .198 ulps; |
| 36 | * log10 is monotonic at all binary break points. |
| 37 | * |
| 38 | * Special cases: |
| 39 | * log10(x) is NaN with signal if x < 0; |
| 40 | * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; |
| 41 | * log10(NaN) is that NaN with no signal; |
| 42 | * log10(10**N) = N for N=0,1,...,22. |
| 43 | * |
| 44 | * Constants: |
| 45 | * The hexadecimal values are the intended ones for the following constants. |
| 46 | * The decimal values may be used, provided that the compiler will convert |
| 47 | * from decimal to binary accurately enough to produce the hexadecimal values |
| 48 | * shown. |
| 49 | */ |
| 50 | |
| 51 | #include "math.h" |
| 52 | #include "math_private.h" |
| 53 | |
| 54 | static const double |
| 55 | two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ |
| 56 | ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ |
| 57 | log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ |
| 58 | log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ |
| 59 | |
| 60 | static const double zero = 0.0; |
| 61 | |
| 62 | double |
| 63 | __ieee754_log10(double x) |
| 64 | { |
| 65 | double y,z; |
| 66 | int32_t i,k,hx; |
| 67 | u_int32_t lx; |
| 68 | |
| 69 | EXTRACT_WORDS(hx,lx,x); |
| 70 | |
| 71 | k=0; |
| 72 | if (hx < 0x00100000) { /* x < 2**-1022 */ |
| 73 | if (((hx&0x7fffffff)|lx)==0) |
| 74 | return -two54/zero; /* log(+-0)=-inf */ |
| 75 | if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ |
| 76 | k -= 54; x *= two54; /* subnormal number, scale up x */ |
| 77 | GET_HIGH_WORD(hx,x); |
| 78 | } |
| 79 | if (hx >= 0x7ff00000) return x+x; |
| 80 | k += (hx>>20)-1023; |
| 81 | i = ((u_int32_t)k&0x80000000)>>31; |
| 82 | hx = (hx&0x000fffff)|((0x3ff-i)<<20); |
| 83 | y = (double)(k+i); |
| 84 | SET_HIGH_WORD(x,hx); |
| 85 | z = y*log10_2lo + ivln10*__ieee754_log(x); |
| 86 | return z+y*log10_2hi; |
| 87 | } |