95 lines
2.5 KiB
C
95 lines
2.5 KiB
C
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/* @(#)e_log10.c 1.3 95/01/18 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/*
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* Return the base 10 logarithm of x. See e_log.c and k_log.h for most
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* comments.
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*
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* log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2)
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* in not-quite-routine extra precision.
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*/
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#include <float.h>
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#include "math.h"
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#include "math_private.h"
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#include "k_log.h"
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static const double
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two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
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ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
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ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
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log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
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log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
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static const double zero = 0.0;
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static volatile double vzero = 0.0;
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double
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__ieee754_log10(double x)
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{
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double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2;
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int32_t i,k,hx;
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u_int32_t lx;
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EXTRACT_WORDS(hx,lx,x);
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k=0;
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if (hx < 0x00100000) { /* x < 2**-1022 */
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if (((hx&0x7fffffff)|lx)==0)
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return -two54/vzero; /* log(+-0)=-inf */
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if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
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k -= 54; x *= two54; /* subnormal number, scale up x */
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GET_HIGH_WORD(hx,x);
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}
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if (hx >= 0x7ff00000) return x+x;
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if (hx == 0x3ff00000 && lx == 0)
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return zero; /* log(1) = +0 */
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k += (hx>>20)-1023;
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hx &= 0x000fffff;
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i = (hx+0x95f64)&0x100000;
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SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
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k += (i>>20);
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y = (double)k;
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f = x - 1.0;
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hfsq = 0.5*f*f;
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r = k_log1p(f);
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/* See e_log2.c for most details. */
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hi = f - hfsq;
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SET_LOW_WORD(hi,0);
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lo = (f - hi) - hfsq + r;
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val_hi = hi*ivln10hi;
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y2 = y*log10_2hi;
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val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
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/*
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* Extra precision in for adding y*log10_2hi is not strictly needed
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* since there is no very large cancellation near x = sqrt(2) or
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* x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
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* with some parallelism and it reduces the error for many args.
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*/
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w = y2 + val_hi;
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val_lo += (y2 - w) + val_hi;
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val_hi = w;
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return val_lo + val_hi;
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}
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#if (LDBL_MANT_DIG == 53)
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__weak_reference(log10, log10l);
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#endif
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