diff options
Diffstat (limited to 'lib/mlibc/options/ansi/musl-generic-math/log1p.c')
| -rw-r--r-- | lib/mlibc/options/ansi/musl-generic-math/log1p.c | 122 |
1 files changed, 0 insertions, 122 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/log1p.c b/lib/mlibc/options/ansi/musl-generic-math/log1p.c deleted file mode 100644 index 0097134..0000000 --- a/lib/mlibc/options/ansi/musl-generic-math/log1p.c +++ /dev/null @@ -1,122 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */ -/* - * ==================================================== - * 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. - * ==================================================== - */ -/* double log1p(double x) - * Return the natural logarithm of 1+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 log(1+f): See log.c - * - * 3. Finally, log1p(x) = k*ln2 + log(1+f) + c/u. See log.c - * - * 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 "libm.h" - -static const double -ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ -ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ -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 */ - -double log1p(double x) -{ - union {double f; uint64_t i;} u = {x}; - double_t hfsq,f,c,s,z,R,w,t1,t2,dk; - uint32_t hx,hu; - int k; - - hx = u.i>>32; - k = 1; - if (hx < 0x3fda827a || hx>>31) { /* 1+x < sqrt(2)+ */ - if (hx >= 0xbff00000) { /* x <= -1.0 */ - if (x == -1) - return x/0.0; /* log1p(-1) = -inf */ - return (x-x)/0.0; /* log1p(x<-1) = NaN */ - } - if (hx<<1 < 0x3ca00000<<1) { /* |x| < 2**-53 */ - /* underflow if subnormal */ - if ((hx&0x7ff00000) == 0) - FORCE_EVAL((float)x); - return x; - } - if (hx <= 0xbfd2bec4) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ - k = 0; - c = 0; - f = x; - } - } else if (hx >= 0x7ff00000) - return x; - if (k) { - u.f = 1 + x; - hu = u.i>>32; - hu += 0x3ff00000 - 0x3fe6a09e; - k = (int)(hu>>20) - 0x3ff; - /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */ - if (k < 54) { - c = k >= 2 ? 1-(u.f-x) : x-(u.f-1); - c /= u.f; - } else - c = 0; - /* reduce u into [sqrt(2)/2, sqrt(2)] */ - hu = (hu&0x000fffff) + 0x3fe6a09e; - u.i = (uint64_t)hu<<32 | (u.i&0xffffffff); - f = u.f - 1; - } - hfsq = 0.5*f*f; - s = f/(2.0+f); - z = s*s; - w = z*z; - t1 = w*(Lg2+w*(Lg4+w*Lg6)); - t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); - R = t2 + t1; - dk = k; - return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi; -} |