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Diffstat (limited to 'gcc-4.9/libquadmath/math/coshq.c')
| -rw-r--r-- | gcc-4.9/libquadmath/math/coshq.c | 108 |
1 files changed, 108 insertions, 0 deletions
diff --git a/gcc-4.9/libquadmath/math/coshq.c b/gcc-4.9/libquadmath/math/coshq.c new file mode 100644 index 000000000..77f4b9833 --- /dev/null +++ b/gcc-4.9/libquadmath/math/coshq.c @@ -0,0 +1,108 @@ +/* + * ==================================================== + * 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. + * ==================================================== + */ + +/* Changes for 128-bit __float128 are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under + the following terms: + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, write to the Free Software + Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ + +/* coshq(x) + * Method : + * mathematically coshq(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (coshq(x) = coshq(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : coshq(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : coshq(x) := ------------------- + * 2 + * 22 <= x <= lnovft : coshq(x) := expq(x)/2 + * lnovft <= x <= ln2ovft: coshq(x) := expq(x/2)/2 * expq(x/2) + * ln2ovft < x : coshq(x) := huge*huge (overflow) + * + * Special cases: + * coshq(x) is |x| if x is +INF, -INF, or NaN. + * only coshq(0)=1 is exact for finite x. + */ + +#include "quadmath-imp.h" + +static const __float128 one = 1.0Q, half = 0.5Q, huge = 1.0e4900Q, + ovf_thresh = 1.1357216553474703894801348310092223067821E4Q; + +__float128 +coshq (__float128 x) +{ + __float128 t, w; + int32_t ex; + ieee854_float128 u; + + u.value = x; + ex = u.words32.w0 & 0x7fffffff; + + /* Absolute value of x. */ + u.words32.w0 = ex; + + /* x is INF or NaN */ + if (ex >= 0x7fff0000) + return x * x; + + /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expq(|x|)) */ + if (ex < 0x3ffd62e4) /* 0.3465728759765625 */ + { + t = expm1q (u.value); + w = one + t; + if (ex < 0x3fb80000) /* |x| < 2^-116 */ + return w; /* cosh(tiny) = 1 */ + + return one + (t * t) / (w + w); + } + + /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */ + if (ex < 0x40044000) + { + t = expq (u.value); + return half * t + half / t; + } + + /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ + if (ex <= 0x400c62e3) /* 11356.375 */ + return half * expq (u.value); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (u.value <= ovf_thresh) + { + w = expq (half * u.value); + t = half * w; + return t * w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge * huge; +} |