| Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [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 | #include <sys/cdefs.h> |
| 15 | __FBSDID("$FreeBSD$"); |
| 16 | |
| 17 | /* |
| 18 | * Return the base 10 logarithm of x. See e_log.c and k_log.h for most |
| 19 | * comments. |
| 20 | * |
| 21 | * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2) |
| 22 | * in not-quite-routine extra precision. |
| 23 | */ |
| 24 | |
| 25 | #include "math.h" |
| 26 | #include "math_private.h" |
| 27 | #include "k_log.h" |
| 28 | |
| 29 | static const double |
| 30 | two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ |
| 31 | ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */ |
| 32 | ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */ |
| 33 | log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ |
| 34 | log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ |
| 35 | |
| 36 | static const double zero = 0.0; |
| 37 | |
| 38 | double |
| 39 | __ieee754_log10(double x) |
| 40 | { |
| 41 | double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2; |
| 42 | int32_t i,k,hx; |
| 43 | u_int32_t lx; |
| 44 | |
| 45 | EXTRACT_WORDS(hx,lx,x); |
| 46 | |
| 47 | k=0; |
| 48 | if (hx < 0x00100000) { /* x < 2**-1022 */ |
| 49 | if (((hx&0x7fffffff)|lx)==0) |
| 50 | return -two54/zero; /* log(+-0)=-inf */ |
| 51 | if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ |
| 52 | k -= 54; x *= two54; /* subnormal number, scale up x */ |
| 53 | GET_HIGH_WORD(hx,x); |
| 54 | } |
| 55 | if (hx >= 0x7ff00000) return x+x; |
| 56 | if (hx == 0x3ff00000 && lx == 0) |
| 57 | return zero; /* log(1) = +0 */ |
| 58 | k += (hx>>20)-1023; |
| 59 | hx &= 0x000fffff; |
| 60 | i = (hx+0x95f64)&0x100000; |
| 61 | SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ |
| 62 | k += (i>>20); |
| 63 | y = (double)k; |
| 64 | f = x - 1.0; |
| 65 | hfsq = 0.5*f*f; |
| 66 | r = k_log1p(f); |
| 67 | |
| 68 | /* See e_log2.c for most details. */ |
| 69 | hi = f - hfsq; |
| 70 | SET_LOW_WORD(hi,0); |
| 71 | lo = (f - hi) - hfsq + r; |
| 72 | val_hi = hi*ivln10hi; |
| 73 | y2 = y*log10_2hi; |
| 74 | val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi; |
| 75 | |
| 76 | /* |
| 77 | * Extra precision in for adding y*log10_2hi is not strictly needed |
| 78 | * since there is no very large cancellation near x = sqrt(2) or |
| 79 | * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs |
| 80 | * with some parallelism and it reduces the error for many args. |
| 81 | */ |
| 82 | w = y2 + val_hi; |
| 83 | val_lo += (y2 - w) + val_hi; |
| 84 | val_hi = w; |
| 85 | |
| 86 | return val_lo + val_hi; |
| 87 | } |