diff options
Diffstat (limited to 'newlib/libm/mathfp/e_acosh.c')
| -rw-r--r-- | newlib/libm/mathfp/e_acosh.c | 135 |
1 files changed, 135 insertions, 0 deletions
diff --git a/newlib/libm/mathfp/e_acosh.c b/newlib/libm/mathfp/e_acosh.c new file mode 100644 index 00000000000..a48420304a1 --- /dev/null +++ b/newlib/libm/mathfp/e_acosh.c @@ -0,0 +1,135 @@ + +/* @(#)e_acosh.c 5.1 93/09/24 */ + +/* +FUNCTION +<<acosh>>, <<acoshf>>---inverse hyperbolic cosine + +INDEX +acosh +INDEX +acoshf + +ANSI_SYNOPSIS + #include <math.h> + double acosh(double <[x]>); + float acoshf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double acosh(<[x]>) + double <[x]>; + + float acoshf(<[x]>) + float <[x]>; + +DESCRIPTION +<<acosh>> calculates the inverse hyperbolic cosine of <[x]>. +<<acosh>> is defined as +@ifinfo +. log(<[x]> + sqrt(<[x]>*<[x]>-1)) +@end ifinfo +@tex +$$ln\Bigl(x + \sqrt{x^2-1}\Bigr)$$ +@end tex + +<[x]> must be a number greater than or equal to 1. + +<<acoshf>> is identical, other than taking and returning floats. + +RETURNS +<<acosh>> and <<acoshf>> return the calculated value. If <[x]> +less than 1, the return value is NaN and <<errno>> is set to <<EDOM>>. + +You can change the error-handling behavior with the non-ANSI +<<matherr>> function. + +PORTABILITY +Neither <<acosh>> nor <<acoshf>> are ANSI C. They are not recommended +for portable programs. + + +QUICKREF ANSI SVID POSIX RENTRANT + acos n,n,n,m + acosf n,n,n,m + +MATHREF + acosh, NAN, arg,DOMAIN,EDOM + acosh, < 1.0, NAN,DOMAIN,EDOM + acosh, >=1.0, acosh(arg),,, + +MATHREF + acoshf, NAN, arg,DOMAIN,EDOM + acoshf, < 1.0, NAN,DOMAIN,EDOM + acoshf, >=1.0, acosh(arg),,, + +*/ + +/* + * ==================================================== + * 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. + * ==================================================== + * + */ + +/* acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.0, +ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +#ifdef __STDC__ + double acosh(double x) +#else + double acosh(x) + double x; +#endif +{ + double t; + __int32_t hx; + __uint32_t lx; + EXTRACT_WORDS(hx,lx,x); + if(hx<0x3ff00000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x41b00000) { /* x > 2**28 */ + if(hx >=0x7ff00000) { /* x is inf of NaN */ + return x+x; + } else + return log(x)+ln2; /* acosh(huge)=log(2x) */ + } else if(((hx-0x3ff00000)|lx)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return log(2.0*x-one/(x+sqrt(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return log1p(t+sqrt(2.0*t+t*t)); + } +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ |