diff options
Diffstat (limited to 'src/math/asinhf.c')
| -rw-r--r-- | src/math/asinhf.c | 62 |
1 files changed, 21 insertions, 41 deletions
diff --git a/src/math/asinhf.c b/src/math/asinhf.c index efe3af94..fc9f0911 100644 --- a/src/math/asinhf.c +++ b/src/math/asinhf.c @@ -1,48 +1,28 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_asinhf.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" -static const float -ln2 = 6.9314718246e-01, /* 0x3f317218 */ -huge= 1.0000000000e+30; - +/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ float asinhf(float x) { - float t,w; - int32_t hx,ix; + union {float f; uint32_t i;} u = {.f = x}; + uint32_t i = u.i & 0x7fffffff; + unsigned s = u.i >> 31; - GET_FLOAT_WORD(hx, x); - ix = hx & 0x7fffffff; - if (ix >= 0x7f800000) /* x is inf or NaN */ - return x+x; - if (ix < 0x31800000) { /* |x| < 2**-28 */ - /* return x inexact except 0 */ - if (huge+x > 1.0f) - return x; - } - if (ix > 0x4d800000) { /* |x| > 2**28 */ - w = logf(fabsf(x)) + ln2; - } else if (ix > 0x40000000) { /* 2**28 > |x| > 2.0 */ - t = fabsf(x); - w = logf(2.0f*t + 1.0f/(sqrtf(x*x+1.0f)+t)); - } else { /* 2.0 > |x| > 2**-28 */ - t = x*x; - w =log1pf(fabsf(x) + t/(1.0f+sqrtf(1.0f+t))); + /* |x| */ + u.i = i; + x = u.f; + + if (i >= 0x3f800000 + (12<<23)) { + /* |x| >= 0x1p12 or inf or nan */ + x = logf(x) + 0.693147180559945309417232121458176568f; + } else if (i >= 0x3f800000 + (1<<23)) { + /* |x| >= 2 */ + x = logf(2*x + 1/(sqrtf(x*x+1)+x)); + } else if (i >= 0x3f800000 - (12<<23)) { + /* |x| >= 0x1p-12, up to 1.6ulp error in [0.125,0.5] */ + x = log1pf(x + x*x/(sqrtf(x*x+1)+1)); + } else { + /* |x| < 0x1p-12, raise inexact if x!=0 */ + FORCE_EVAL(x + 0x1p120f); } - if (hx > 0) - return w; - return -w; + return s ? -x : x; } |