From: Szabolcs Nagy Date: Sun, 16 Dec 2012 18:23:51 +0000 (+0100) Subject: math: finished cosh.c cleanup X-Git-Tag: v0.9.9~53 X-Git-Url: https://git.librecmc.org/?a=commitdiff_plain;h=1aec620f9366c29d761fe42b3e02bd8024685db3;p=oweals%2Fmusl.git math: finished cosh.c cleanup changed the algorithm: large input is not special cased (when exp(-x) is small compared to exp(x)) and the threshold values are reevaluated (fdlibm code had a log(2)/2 cutoff for which i could not find justification, log(2) seems to be a better threshold and this was verified empirically) the new code is simpler, makes smaller binaries and should be faster for common cases the old comments were removed as they are no longer true for the new algorithm and the fdlibm copyright was dropped as well because there is no common code or idea with the original anymore except for trivial ones. --- diff --git a/src/math/cosh.c b/src/math/cosh.c index 2fcdea8f..100f8231 100644 --- a/src/math/cosh.c +++ b/src/math/cosh.c @@ -1,71 +1,40 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_cosh.c */ -/* - * ==================================================== - * 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. - * ==================================================== - */ -/* cosh(x) - * Method : - * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 - * 1. Replace x by |x| (cosh(x) = cosh(-x)). - * 2. - * [ exp(x) - 1 ]^2 - * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- - * 2*exp(x) - * - * exp(x) + 1/exp(x) - * ln2/2 <= x <= 22 : cosh(x) := ------------------- - * 2 - * 22 <= x <= lnovft : cosh(x) := exp(x)/2 - * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) - * ln2ovft < x : cosh(x) := inf (overflow) - * - * Special cases: - * cosh(x) is |x| if x is +INF, -INF, or NaN. - * only cosh(0)=1 is exact for finite x. - */ - #include "libm.h" +/* cosh(x) = (exp(x) + 1/exp(x))/2 + * = 1 + 0.5*(exp(x)-1)*(exp(x)-1)/exp(x) + * = 1 + x*x/2 + o(x^4) + */ double cosh(double x) { union {double f; uint64_t i;} u = {.f = x}; - uint32_t ix; + uint32_t w; double t; /* |x| */ u.i &= (uint64_t)-1/2; x = u.f; - ix = u.i >> 32; + w = u.i >> 32; - /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ - if (ix < 0x3fd62e43) { - t = expm1(x); - if (ix < 0x3c800000) + /* |x| < log(2) */ + if (w < 0x3fe62e42) { + if (w < 0x3ff00000 - (26<<20)) { + /* raise inexact if x!=0 */ + FORCE_EVAL(x + 0x1p120f); return 1; + } + t = expm1(x); return 1 + t*t/(2*(1+t)); } - /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|))/2; */ - if (ix < 0x40360000) { + /* |x| < log(DBL_MAX) */ + if (w < 0x40862e42) { t = exp(x); - return 0.5*t + 0.5/t; + /* note: if x>log(0x1p26) then the 1/t is not needed */ + return 0.5*(t + 1/t); } - /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ - if (ix < 0x40862e42) - return 0.5*exp(x); - - /* |x| in [log(maxdouble), overflowthresold] */ - if (ix <= 0x408633ce) - return __expo2(x); - - /* overflow (or nan) */ - x *= 0x1p1023; - return x; + /* |x| > log(DBL_MAX) or nan */ + /* note: the result is stored to handle overflow */ + t = __expo2(x); + return t; } diff --git a/src/math/coshf.c b/src/math/coshf.c index 2bed1258..b09f2ee5 100644 --- a/src/math/coshf.c +++ b/src/math/coshf.c @@ -1,54 +1,33 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_coshf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * 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. - * ==================================================== - */ - #include "libm.h" float coshf(float x) { union {float f; uint32_t i;} u = {.f = x}; - uint32_t ix; + uint32_t w; float t; /* |x| */ u.i &= 0x7fffffff; x = u.f; - ix = u.i; + w = u.i; - /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ - if (ix < 0x3eb17218) { - t = expm1f(x); - if (ix < 0x39800000) + /* |x| < log(2) */ + if (w < 0x3f317217) { + if (w < 0x3f800000 - (12<<23)) { + FORCE_EVAL(x + 0x1p120f); return 1; + } + t = expm1f(x); return 1 + t*t/(2*(1+t)); } - /* |x| in [0.5*ln2,9], return (exp(|x|)+1/exp(|x|))/2; */ - if (ix < 0x41100000) { + /* |x| < log(FLT_MAX) */ + if (w < 0x42b17217) { t = expf(x); - return 0.5f*t + 0.5f/t; + return 0.5f*(t + 1/t); } - /* |x| in [9, log(maxfloat)] return 0.5f*exp(|x|) */ - if (ix < 0x42b17217) - return 0.5f*expf(x); - - /* |x| in [log(maxfloat), overflowthresold] */ - if (ix <= 0x42b2d4fc) - return __expo2f(x); - - /* |x| > overflowthresold or nan */ - x *= 0x1p127f; - return x; + /* |x| > log(FLT_MAX) or nan */ + t = __expo2f(x); + return t; } diff --git a/src/math/coshl.c b/src/math/coshl.c index 3ea56e00..d09070bb 100644 --- a/src/math/coshl.c +++ b/src/math/coshl.c @@ -1,35 +1,3 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_coshl.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. - * ==================================================== - */ -/* coshl(x) - * Method : - * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2 - * 1. Replace x by |x| (coshl(x) = coshl(-x)). - * 2. - * [ exp(x) - 1 ]^2 - * 0 <= x <= ln2/2 : coshl(x) := 1 + ------------------- - * 2*exp(x) - * - * exp(x) + 1/exp(x) - * ln2/2 <= x <= 22 : coshl(x) := ------------------- - * 2 - * 22 <= x <= lnovft : coshl(x) := expl(x)/2 - * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) - * ln2ovft < x : coshl(x) := inf (overflow) - * - * Special cases: - * coshl(x) is |x| if x is +INF, -INF, or NaN. - * only coshl(0)=1 is exact for finite x. - */ - #include "libm.h" #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 @@ -45,41 +13,32 @@ long double coshl(long double x) struct{uint64_t m; uint16_t se; uint16_t pad;} i; } u = {.f = x}; unsigned ex = u.i.se & 0x7fff; + uint32_t w; long double t; - uint32_t mx,lx; /* |x| */ u.i.se = ex; x = u.f; - mx = u.i.m >> 32; - lx = u.i.m; + w = u.i.m >> 32; - /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ - if (ex < 0x3fff-2 || (ex == 0x3fff-2 && mx < 0xb17217f7)) { - t = expm1l(x); - if (ex < 0x3fff-64) + /* |x| < log(2) */ + if (ex < 0x3fff-1 || (ex == 0x3fff-1 && w < 0xb17217f7)) { + if (ex < 0x3fff-32) { + FORCE_EVAL(x + 0x1p120f); return 1; + } + t = expm1l(x); return 1 + t*t/(2*(1+t)); } - /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ - if (ex < 0x3fff+4 || (ex == 0x3fff+4 && mx < 0xb0000000)) { + /* |x| < log(LDBL_MAX) */ + if (ex < 0x3fff+13 || (ex == 0x3fff+13 && w < 0xb17217f7)) { t = expl(x); - return 0.5*t + 0.5/t; - } - - /* |x| in [22, ln(maxdouble)] return 0.5*exp(|x|) */ - if (ex < 0x3fff+13 || (ex == 0x3fff+13 && mx < 0xb1700000)) - return 0.5*expl(x); - - /* |x| in [log(maxdouble), log(2*maxdouble)) */ - if (ex == 0x3fff+13 && (mx < 0xb174ddc0 || - (mx == 0xb174ddc0 && lx < 0x31aec0eb))) { - t = expl(0.5*x); - return 0.5*t*t; + return 0.5*(t + 1/t); } - /* |x| >= log(2*maxdouble) or nan */ - return x*0x1p16383L; + /* |x| > log(LDBL_MAX) or nan */ + t = expl(0.5*x); + return 0.5*t*t; } #endif