math: rewrite inverse hyperbolic functions to be simpler/smaller

[musl] / src / math / atanhl.c

diff --git a/src/math/atanhl.c b/src/math/atanhl.c
index 931bae3..b4c5e58 100644 (file)
--- a/src/math/atanhl.c
+++ b/src/math/atanhl.c
@@ -1,31 +1,3 @@
-/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_atanh.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.
- * ====================================================
- */
-/* atanhl(x)
- * Method :
- *    1.Reduced x to positive by atanh(-x) = -atanh(x)
- *    2.For x>=0.5
- *                   1              2x                          x
- *      atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
- *                   2             1 - x                      1 - x
- *
- *      For x<0.5
- *      atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
- *
- * Special cases:
- *      atanhl(x) is NaN if |x| > 1 with signal;
- *      atanhl(NaN) is that NaN with no signal;
- *      atanhl(+-1) is +-INF with signal.
- */
-
 #include "libm.h"
 
 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@@ -34,31 +6,26 @@ long double atanhl(long double x)
        return atanh(x);
 }
 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
-static const long double huge = 1e4900L;
-
+/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
 long double atanhl(long double x)
 {
-       long double t;
-       int32_t ix;
-       uint32_t se,i0,i1;
+       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;
+
+       /* |x| */
+       u.i.se = e;
+       x = u.f;
 
-       GET_LDOUBLE_WORDS(se, i0, i1, x);
-       ix = se & 0x7fff;
-       if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31)) > 0x3fff)
-               /* |x| > 1 */
-               return (x-x)/(x-x);
-       if (ix == 0x3fff)
-               return x/0.0;
-       if (ix < 0x3fe3 && huge+x > 0.0)  /* x < 2**-28 */
-               return x;
-       SET_LDOUBLE_EXP(x, ix);
-       if (ix < 0x3ffe) {  /* x < 0.5 */
-               t = x + x;
-               t = 0.5*log1pl(t + t*x/(1.0 - x));
-       } else
-               t = 0.5*log1pl((x + x)/(1.0 - x));
-       if (se <= 0x7fff)
-               return t;
-       return -t;
+       if (e < 0x3fff - 1) {
+               /* |x| < 0.5, up to 1.7ulp error */
+               x = 0.5*log1pl(2*x + 2*x*x/(1-x));
+       } else {
+               x = 0.5*log1pl(2*x/(1-x));
+       }
+       return s ? -x : x;
 }
 #endif