/* asinhf.c * * Inverse hyperbolic sine * * * * SYNOPSIS: * * float x, y, asinhf(); * * y = asinhf( x ); * * * * DESCRIPTION: * * Returns inverse hyperbolic sine of argument. * * If |x| < 0.5, the function is approximated by a rational * form x + x**3 P(x)/Q(x). Otherwise, * * asinh(x) = log( x + sqrt(1 + x*x) ). * * * * ACCURACY: * * Relative error: * arithmetic domain # trials peak rms * IEEE -3,3 100000 2.4e-7 4.1e-8 * */ /* asinh.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 sine * test interval: [-0.5, +0.5] * trials: 10000 * peak relative error: 8.8e-8 * rms relative error: 3.2e-8 */ #include <math.h> extern float LOGE2F; float logf( float ); float sqrtf( float ); float asinhf( float xx ) { float x, z; if( xx < 0 ) x = -xx; else x = xx; if( x > 1500.0 ) { z = logf(x) + LOGE2F; goto done; } z = x * x; if( x < 0.5 ) { z = ((( 2.0122003309E-2 * z - 4.2699340972E-2) * z + 7.4847586088E-2) * z - 1.6666288134E-1) * z * x + x; } else { z = sqrtf( z + 1.0 ); z = logf( x + z ); } done: if( xx < 0 ) z = -z; return( z ); }