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98 lines
1.6 KiB
C
98 lines
1.6 KiB
C
/* acosh.c
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*
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* Inverse hyperbolic cosine
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*
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*
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*
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* SYNOPSIS:
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*
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* float x, y, acosh();
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*
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* y = acosh( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns inverse hyperbolic cosine of argument.
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*
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* If 1 <= x < 1.5, a polynomial approximation
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*
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* sqrt(z) * P(z)
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*
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* where z = x-1, is used. Otherwise,
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*
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* acosh(x) = log( x + sqrt( (x-1)(x+1) ).
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE 1,3 100000 1.8e-7 3.9e-8
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* IEEE 1,2000 100000 3.0e-8
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*
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* acosh domain |x| < 1 0.0
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*
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*/
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/* acosh.c */
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/*
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Cephes Math Library Release 2.2: June, 1992
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Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
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Direct inquiries to 30 Frost Street, Cambridge, MA 02140
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*/
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/* Single precision inverse hyperbolic cosine
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* test interval: [1.0, 1.5]
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* trials: 10000
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* peak relative error: 1.7e-7
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* rms relative error: 5.0e-8
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*
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* Copyright (C) 1989 by Stephen L. Moshier. All rights reserved.
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*/
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#include "mconf.h"
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#include "stabs.h"
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float acosh( float xx )
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{
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float x, z;
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x = xx;
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if( x < 1.0f )
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{
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mtherr( "acosh", DOMAIN );
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return(0.0f);
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}
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if( x > 1500.0f )
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return( log(x) + LOGE2F );
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z = x - 1.0f;
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if( z < 0.5f )
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{
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z =
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(((( 1.7596881071E-3f * z
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- 7.5272886713E-3f) * z
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+ 2.6454905019E-2f) * z
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- 1.1784741703E-1f) * z
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+ 1.4142135263E0f) * sqrt( z );
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}
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else
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{
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z = sqrt( z*(x+1.0f) );
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z = log(x + z);
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}
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return( z );
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}
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ALIAS(acoshf,acosh);
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ALIAS(acoshl,acosh);
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