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Diffstat (limited to 'libm/src/s_log1p.c')
| -rw-r--r-- | libm/src/s_log1p.c | 168 |
1 files changed, 0 insertions, 168 deletions
diff --git a/libm/src/s_log1p.c b/libm/src/s_log1p.c deleted file mode 100644 index 56e1516..0000000 --- a/libm/src/s_log1p.c +++ /dev/null @@ -1,168 +0,0 @@ -/* @(#)s_log1p.c 5.1 93/09/24 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#ifndef lint -static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_log1p.c,v 1.8 2005/12/04 12:28:33 bde Exp $"; -#endif - -/* double log1p(double x) - * - * Method : - * 1. Argument Reduction: find k and f such that - * 1+x = 2^k * (1+f), - * where sqrt(2)/2 < 1+f < sqrt(2) . - * - * Note. If k=0, then f=x is exact. However, if k!=0, then f - * may not be representable exactly. In that case, a correction - * term is need. Let u=1+x rounded. Let c = (1+x)-u, then - * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), - * and add back the correction term c/u. - * (Note: when x > 2**53, one can simply return log(x)) - * - * 2. Approximation of log1p(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) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s - * (the values of Lp1 to Lp7 are listed in the program) - * and - * | 2 14 | -58.45 - * | Lp1*s +...+Lp7*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 - * log1p(f) = f - (hfsq - s*(hfsq+R)). - * - * 3. Finally, log1p(x) = k*ln2 + log1p(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: - * log1p(x) is NaN with signal if x < -1 (including -INF) ; - * log1p(+INF) is +INF; log1p(-1) is -INF with signal; - * log1p(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. - * - * Note: Assuming log() return accurate answer, the following - * algorithm can be used to compute log1p(x) to within a few ULP: - * - * u = 1+x; - * if(u==1.0) return x ; else - * return log(u)*(x/(u-1.0)); - * - * See HP-15C Advanced Functions Handbook, p.193. - */ - -#include "math.h" -#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 */ -Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ -Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ -Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ -Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ -Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ -Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ -Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ - -static const double zero = 0.0; - -double -log1p(double x) -{ - double hfsq,f,c,s,z,R,u; - int32_t k,hx,hu,ax; - - GET_HIGH_WORD(hx,x); - ax = hx&0x7fffffff; - - k = 1; - if (hx < 0x3FDA827A) { /* 1+x < sqrt(2)+ */ - if(ax>=0x3ff00000) { /* x <= -1.0 */ - if(x==-1.0) return -two54/zero; /* log1p(-1)=+inf */ - else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ - } - if(ax<0x3e200000) { /* |x| < 2**-29 */ - if(two54+x>zero /* raise inexact */ - &&ax<0x3c900000) /* |x| < 2**-54 */ - return x; - else - return x - x*x*0.5; - } - if(hx>0||hx<=((int32_t)0xbfd2bec4)) { - k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ - } - if (hx >= 0x7ff00000) return x+x; - if(k!=0) { - if(hx<0x43400000) { - u = 1.0+x; - GET_HIGH_WORD(hu,u); - k = (hu>>20)-1023; - c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */ - c /= u; - } else { - u = x; - GET_HIGH_WORD(hu,u); - k = (hu>>20)-1023; - c = 0; - } - hu &= 0x000fffff; - /* - * The approximation to sqrt(2) used in thresholds is not - * critical. However, the ones used above must give less - * strict bounds than the one here so that the k==0 case is - * never reached from here, since here we have committed to - * using the correction term but don't use it if k==0. - */ - if(hu<0x6a09e) { /* u ~< sqrt(2) */ - SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */ - } else { - k += 1; - SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */ - hu = (0x00100000-hu)>>2; - } - f = u-1.0; - } - hfsq=0.5*f*f; - if(hu==0) { /* |f| < 2**-20 */ - if(f==zero) if(k==0) return zero; - else {c += k*ln2_lo; return k*ln2_hi+c;} - R = hfsq*(1.0-0.66666666666666666*f); - if(k==0) return f-R; else - return k*ln2_hi-((R-(k*ln2_lo+c))-f); - } - s = f/(2.0+f); - z = s*s; - R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); - if(k==0) return f-(hfsq-s*(hfsq+R)); else - return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); -} |