diff options
Diffstat (limited to 'libc-top-half/musl/src/math/log1p.c')
| -rw-r--r-- | libc-top-half/musl/src/math/log1p.c | 122 |
1 files changed, 122 insertions, 0 deletions
diff --git a/libc-top-half/musl/src/math/log1p.c b/libc-top-half/musl/src/math/log1p.c new file mode 100644 index 0000000..0097134 --- /dev/null +++ b/libc-top-half/musl/src/math/log1p.c @@ -0,0 +1,122 @@ +/* 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; +} |