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>
| 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>
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15__FBSDID("$FreeBSD: head/lib/msun/src/e_log10.c 176451 2008-02-22 02:30:36Z das $");
| 15__FBSDID("$FreeBSD: head/lib/msun/src/e_log2.c 216211 2010-12-05 22:11:22Z das $");
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16
| 16
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17/* __ieee754_log10(x) 18 * Return the base 10 logarithm of x 19 * 20 * Method : 21 * Let log10_2hi = leading 40 bits of log10(2) and 22 * log10_2lo = log10(2) - log10_2hi, 23 * ivln10 = 1/log(10) rounded. 24 * Then 25 * n = ilogb(x), 26 * if(n<0) n = n+1; 27 * x = scalbn(x,-n); 28 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) 29 * 30 * Note 1: 31 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding 32 * mode must set to Round-to-Nearest. 33 * Note 2: 34 * [1/log(10)] rounded to 53 bits has error .198 ulps; 35 * log10 is monotonic at all binary break points. 36 * 37 * Special cases: 38 * log10(x) is NaN with signal if x < 0; 39 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 40 * log10(NaN) is that NaN with no signal; 41 * log10(10**N) = N for N=0,1,...,22. 42 * 43 * Constants: 44 * The hexadecimal values are the intended ones for the following constants. 45 * The decimal values may be used, provided that the compiler will convert 46 * from decimal to binary accurately enough to produce the hexadecimal values 47 * shown.
| 17/* log2(x) 18 * Return the base 2 logarithm of x.
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48 */ 49 50#include "math.h" 51#include "math_private.h"
| 19 */ 20 21#include "math.h" 22#include "math_private.h"
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| 23#include "k_log.h"
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52 53static const double 54two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
| 24 25static const double 26two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
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55ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ 56log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ 57log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
| 27ivln2hi = 0x1.71547652000p+0, 28ivln2lo = 0x1.705fc2eefa2p-33;
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58 59static const double zero = 0.0; 60 61double
| 29 30static const double zero = 0.0; 31 32double
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62__ieee754_log10(double x)
| 33__ieee754_log2(double x)
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63{
| 34{
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64 double y,z;
| 35 double f,hi,lo;
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65 int32_t i,k,hx; 66 u_int32_t lx; 67 68 EXTRACT_WORDS(hx,lx,x); 69 70 k=0; 71 if (hx < 0x00100000) { /* x < 2**-1022 */ 72 if (((hx&0x7fffffff)|lx)==0) 73 return -two54/zero; /* log(+-0)=-inf */ 74 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 75 k -= 54; x *= two54; /* subnormal number, scale up x */ 76 GET_HIGH_WORD(hx,x); 77 } 78 if (hx >= 0x7ff00000) return x+x; 79 k += (hx>>20)-1023;
| 36 int32_t i,k,hx; 37 u_int32_t lx; 38 39 EXTRACT_WORDS(hx,lx,x); 40 41 k=0; 42 if (hx < 0x00100000) { /* x < 2**-1022 */ 43 if (((hx&0x7fffffff)|lx)==0) 44 return -two54/zero; /* log(+-0)=-inf */ 45 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ 46 k -= 54; x *= two54; /* subnormal number, scale up x */ 47 GET_HIGH_WORD(hx,x); 48 } 49 if (hx >= 0x7ff00000) return x+x; 50 k += (hx>>20)-1023;
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80 i = ((u_int32_t)k&0x80000000)>>31; 81 hx = (hx&0x000fffff)|((0x3ff-i)<<20); 82 y = (double)(k+i); 83 SET_HIGH_WORD(x,hx); 84 z = y*log10_2lo + ivln10*__ieee754_log(x); 85 return z+y*log10_2hi;
| 51 hx &= 0x000fffff; 52 i = (hx+0x95f64)&0x100000; 53 SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ 54 k += (i>>20); 55 f = __kernel_log(x); 56 hi = x = x - 1; 57 SET_LOW_WORD(hi,0); 58 lo = x - hi; 59 return (x+f)*ivln2lo + (lo+f)*ivln2hi + hi*ivln2hi + k;
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86}
| 60}
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