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Diffstat (limited to 'libm/float/acoshf.c')
-rw-r--r-- | libm/float/acoshf.c | 97 |
1 files changed, 97 insertions, 0 deletions
diff --git a/libm/float/acoshf.c b/libm/float/acoshf.c new file mode 100644 index 000000000..c45206125 --- /dev/null +++ b/libm/float/acoshf.c @@ -0,0 +1,97 @@ +/* acoshf.c + * + * Inverse hyperbolic cosine + * + * + * + * SYNOPSIS: + * + * float x, y, acoshf(); + * + * y = acoshf( x ); + * + * + * + * DESCRIPTION: + * + * Returns inverse hyperbolic cosine of argument. + * + * If 1 <= x < 1.5, a polynomial approximation + * + * sqrt(z) * P(z) + * + * where z = x-1, is used. Otherwise, + * + * acosh(x) = log( x + sqrt( (x-1)(x+1) ). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 1,3 100000 1.8e-7 3.9e-8 + * IEEE 1,2000 100000 3.0e-8 + * + * + * ERROR MESSAGES: + * + * message condition value returned + * acoshf domain |x| < 1 0.0 + * + */ + +/* acosh.c */ + +/* +Cephes Math Library Release 2.2: June, 1992 +Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier +Direct inquiries to 30 Frost Street, Cambridge, MA 02140 +*/ + +/* Single precision inverse hyperbolic cosine + * test interval: [1.0, 1.5] + * trials: 10000 + * peak relative error: 1.7e-7 + * rms relative error: 5.0e-8 + * + * Copyright (C) 1989 by Stephen L. Moshier. All rights reserved. + */ +#include <math.h> +extern float LOGE2F; + +float sqrtf( float ); +float logf( float ); + +float acoshf( float xx ) +{ +float x, z; + +x = xx; +if( x < 1.0 ) + { + mtherr( "acoshf", DOMAIN ); + return(0.0); + } + +if( x > 1500.0 ) + return( logf(x) + LOGE2F ); + +z = x - 1.0; + +if( z < 0.5 ) + { + z = + (((( 1.7596881071E-3 * z + - 7.5272886713E-3) * z + + 2.6454905019E-2) * z + - 1.1784741703E-1) * z + + 1.4142135263E0) * sqrtf( z ); + } +else + { + z = sqrtf( z*(x+1.0) ); + z = logf(x + z); + } +return( z ); +} |