diff options
Diffstat (limited to 'src/math/asinhl.c')
| -rw-r--r-- | src/math/asinhl.c | 72 |
1 files changed, 24 insertions, 48 deletions
diff --git a/src/math/asinhl.c b/src/math/asinhl.c index dc5dd71f..db966246 100644 --- a/src/math/asinhl.c +++ b/src/math/asinhl.c @@ -1,25 +1,3 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_asinhl.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. - * ==================================================== - */ -/* asinhl(x) - * Method : - * Based on - * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] - * we have - * asinhl(x) := x if 1+x*x=1, - * := signl(x)*(logl(x)+ln2)) for large |x|, else - * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else - * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) - */ - #include "libm.h" #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 @@ -28,35 +6,33 @@ long double asinhl(long double x) return asinh(x); } #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -static const long double -ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */ -huge = 1.000000000000000000e+4900L; - +/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ long double asinhl(long double x) { - long double t,w; - int32_t hx,ix; + union { + long double f; + struct{uint64_t m; uint16_t se; uint16_t pad;} i; + } u = {.f = x}; + unsigned e = u.i.se & 0x7fff; + unsigned s = u.i.se >> 15; - GET_LDOUBLE_EXP(hx, x); - ix = hx & 0x7fff; - if (ix == 0x7fff) - return x + x; /* x is inf or NaN */ - if (ix < 0x3fde) { /* |x| < 2**-34 */ - /* return x, raise inexact if x != 0 */ - if (huge+x > 1.0) - return x; - } - if (ix > 0x4020) { /* |x| > 2**34 */ - w = logl(fabsl(x)) + ln2; - } else if (ix > 0x4000) { /* 2**34 > |x| > 2.0 */ - t = fabsl(x); - w = logl(2.0*t + 1.0/(sqrtl(x*x + 1.0) + t)); - } else { /* 2.0 > |x| > 2**-28 */ - t = x*x; - w =log1pl(fabsl(x) + t/(1.0 + sqrtl(1.0 + t))); + /* |x| */ + u.i.se = e; + x = u.f; + + if (e >= 0x3fff + 32) { + /* |x| >= 0x1p32 or inf or nan */ + x = logl(x) + 0.693147180559945309417232121458176568L; + } else if (e >= 0x3fff + 1) { + /* |x| >= 2 */ + x = logl(2*x + 1/(sqrtl(x*x+1)+x)); + } else if (e >= 0x3fff - 32) { + /* |x| >= 0x1p-32 */ + x = log1pl(x + x*x/(sqrtl(x*x+1)+1)); + } else { + /* |x| < 0x1p-32, raise inexact if x!=0 */ + FORCE_EVAL(x + 0x1p1000); } - if (hx & 0x8000) - return -w; - return w; + return s ? -x : x; } #endif |