X-Git-Url: http://nsz.repo.hu/git/?a=blobdiff_plain;f=src%2Fmath%2Fe_log.c;fp=src%2Fmath%2Fe_log.c;h=0000000000000000000000000000000000000000;hb=b69f695acedd4ce2798ef9ea28d834ceccc789bd;hp=9eb0e4448064c05be3e8f16c20e5dfc095ed1ce4;hpb=d46cf2e14cc4df7cc75e77d7009fcb6df1f48a33;p=musl diff --git a/src/math/e_log.c b/src/math/e_log.c deleted file mode 100644 index 9eb0e444..00000000 --- a/src/math/e_log.c +++ /dev/null @@ -1,131 +0,0 @@ - -/* @(#)e_log.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* log(x) - * Return the logrithm of x - * - * Method : - * 1. Argument Reduction: find k and f such that - * x = 2^k * (1+f), - * where sqrt(2)/2 < 1+f < sqrt(2) . - * - * 2. Approximation of log(1+f). - * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) - * = 2s + 2/3 s**3 + 2/5 s**5 + ....., - * = 2s + s*R - * We use a special Reme algorithm on [0,0.1716] to generate - * a polynomial of degree 14 to approximate R The maximum error - * of this polynomial approximation is bounded by 2**-58.45. In - * other words, - * 2 4 6 8 10 12 14 - * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s - * (the values of Lg1 to Lg7 are listed in the program) - * and - * | 2 14 | -58.45 - * | Lg1*s +...+Lg7*s - R(z) | <= 2 - * | | - * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. - * In order to guarantee error in log below 1ulp, we compute log - * by - * log(1+f) = f - s*(f - R) (if f is not too large) - * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) - * - * 3. Finally, log(x) = k*ln2 + log(1+f). - * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) - * Here ln2 is split into two floating point number: - * ln2_hi + ln2_lo, - * where n*ln2_hi is always exact for |n| < 2000. - * - * Special cases: - * log(x) is NaN with signal if x < 0 (including -INF) ; - * log(+INF) is +INF; log(0) is -INF with signal; - * log(NaN) is that NaN with no signal. - * - * Accuracy: - * according to an error analysis, the error is always less than - * 1 ulp (unit in the last place). - * - * 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 -#include "math_private.h" - -static const double -ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ -ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ -two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ -Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ -Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ -Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ -Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ -Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ -Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ -Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ - -static const double zero = 0.0; - -double -log(double x) -{ - double hfsq,f,s,z,R,w,t1,t2,dk; - int32_t k,hx,i,j; - uint32_t lx; - - EXTRACT_WORDS(hx,lx,x); - - k=0; - if (hx < 0x00100000) { /* x < 2**-1022 */ - if (((hx&0x7fffffff)|lx)==0) - return -two54/zero; /* log(+-0)=-inf */ - if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ - k -= 54; x *= two54; /* subnormal number, scale up x */ - GET_HIGH_WORD(hx,x); - } - if (hx >= 0x7ff00000) return x+x; - k += (hx>>20)-1023; - hx &= 0x000fffff; - i = (hx+0x95f64)&0x100000; - SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ - k += (i>>20); - f = x-1.0; - if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ - if(f==zero) { if(k==0) return zero; else {dk=(double)k; - return dk*ln2_hi+dk*ln2_lo;} } - R = f*f*(0.5-0.33333333333333333*f); - if(k==0) return f-R; else {dk=(double)k; - return dk*ln2_hi-((R-dk*ln2_lo)-f);} - } - s = f/(2.0+f); - dk = (double)k; - z = s*s; - i = hx-0x6147a; - w = z*z; - j = 0x6b851-hx; - t1= w*(Lg2+w*(Lg4+w*Lg6)); - t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); - i |= j; - R = t2+t1; - if(i>0) { - hfsq=0.5*f*f; - if(k==0) return f-(hfsq-s*(hfsq+R)); else - return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); - } else { - if(k==0) return f-s*(f-R); else - return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); - } -}