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Diffstat (limited to 'newlib/libm/mathfp/s_asinh.c')
| -rw-r--r-- | newlib/libm/mathfp/s_asinh.c | 107 |
1 files changed, 107 insertions, 0 deletions
diff --git a/newlib/libm/mathfp/s_asinh.c b/newlib/libm/mathfp/s_asinh.c new file mode 100644 index 00000000000..43b9d49fa5e --- /dev/null +++ b/newlib/libm/mathfp/s_asinh.c @@ -0,0 +1,107 @@ + +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * 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. + * ==================================================== + */ + +/* +FUNCTION + <<asinh>>, <<asinhf>>---inverse hyperbolic sine + +INDEX + asinh +INDEX + asinhf + +ANSI_SYNOPSIS + #include <math.h> + double asinh(double <[x]>); + float asinhf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double asinh(<[x]>) + double <[x]>; + + float asinhf(<[x]>) + float <[x]>; + +DESCRIPTION +<<asinh>> calculates the inverse hyperbolic sine of <[x]>. +<<asinh>> is defined as +@ifinfo +. sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>)) +@end ifinfo +@tex +$$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$ +@end tex + +<<asinhf>> is identical, other than taking and returning floats. + +RETURNS +<<asinh>> and <<asinhf>> return the calculated value. + +PORTABILITY +Neither <<asinh>> nor <<asinhf>> are ANSI C. + +*/ + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +huge= 1.00000000000000000000e+300; + +#ifdef __STDC__ + double asinh(double x) +#else + double asinh(x) + double x; +#endif +{ + double t,w; + __int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ + if(ix< 0x3e300000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x41b00000) { /* |x| > 2**28 */ + w = log(fabs(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabs(x); + w = log(2.0*t+one/(sqrt(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1p(fabs(x)+t/(one+sqrt(one+t))); + } + if(hx>0) return w; else return -w; +} + +#endif /* _DOUBLE_IS_32BITS */ |