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[/] [openrisc/] [trunk/] [gnu-stable/] [newlib-1.18.0/] [newlib/] [libm/] [mathfp/] [e_acosh.c] - Rev 207
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/* @(#)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 @ifnottex . log(<[x]> + sqrt(<[x]>*<[x]>-1)) @end ifnottex @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) */
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