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authorSzabolcs Nagy <nsz@port70.net>2012-12-11 23:06:20 +0100
committerSzabolcs Nagy <nsz@port70.net>2012-12-11 23:06:20 +0100
commit482ccd2f7497a79ca83e998f54e823e7cedaaa6e (patch)
tree0e2e1fd4db0a277ece85e32a23ecc68997404514 /src/math/acoshf.c
parent64623cd59a5e72c6322548bca3827a75d5d11918 (diff)
downloadmusl-482ccd2f7497a79ca83e998f54e823e7cedaaa6e.tar.gz
math: rewrite inverse hyperbolic functions to be simpler/smaller
modifications: * avoid unsigned->signed integer conversion * do not handle special cases when they work correctly anyway * more strict threshold values (0x1p26 instead of 0x1p28 etc) * smaller code, cleaner branching logic * same precision as the old code: acosh(x) has up to 2ulp error in [1,1.125] asinh(x) has up to 1.6ulp error in [0.125,0.5], [-0.5,-0.125] atanh(x) has up to 1.7ulp error in [0.125,0.5], [-0.5,-0.125]
Diffstat (limited to 'src/math/acoshf.c')
-rw-r--r--src/math/acoshf.c47
1 files changed, 11 insertions, 36 deletions
diff --git a/src/math/acoshf.c b/src/math/acoshf.c
index 0f7aae2a..4596085e 100644
--- a/src/math/acoshf.c
+++ b/src/math/acoshf.c
@@ -1,42 +1,17 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/e_acoshf.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 */
-
+/* acosh(x) = log(x + sqrt(x*x-1)) */
float acoshf(float x)
{
- float t;
- int32_t hx;
+ union {float f; int32_t i;} u = {.f = x};
- GET_FLOAT_WORD(hx, x);
- if (hx < 0x3f800000) { /* x < 1 */
- return (x-x)/(x-x);
- } else if (hx >= 0x4d800000) { /* x > 2**28 */
- if (hx >= 0x7f800000) /* x is inf of NaN */
- return x + x;
- return logf(x) + ln2; /* acosh(huge)=log(2x) */
- } else if (hx == 0x3f800000) {
- return 0.0f; /* acosh(1) = 0 */
- } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
- t = x*x;
- return logf(2.0f*x - 1.0f/(x+sqrtf(t-1.0f)));
- } else { /* 1 < x < 2 */
- t = x-1.0f;
- return log1pf(t + sqrtf(2.0f*t+t*t));
- }
+ if (u.i < 0x3f800000+(1<<23))
+ /* x < 2, invalid if x < 1 or nan */
+ /* up to 2ulp error in [1,1.125] */
+ return log1pf(x-1 + sqrtf((x-1)*(x-1)+2*(x-1)));
+ if (u.i < 0x3f800000+(12<<23))
+ /* x < 0x1p12 */
+ return logf(2*x - 1/(x+sqrtf(x*x-1)));
+ /* x >= 0x1p12 */
+ return logf(x) + 0.693147180559945309417232121458176568f;
}