1*24607Szliu /* 2*24607Szliu * Copyright (c) 1985 Regents of the University of California. 3*24607Szliu * 4*24607Szliu * Use and reproduction of this software are granted in accordance with 5*24607Szliu * the terms and conditions specified in the Berkeley Software License 6*24607Szliu * Agreement (in particular, this entails acknowledgement of the programs' 7*24607Szliu * source, and inclusion of this notice) with the additional understanding 8*24607Szliu * that all recipients should regard themselves as participants in an 9*24607Szliu * ongoing research project and hence should feel obligated to report 10*24607Szliu * their experiences (good or bad) with these elementary function codes, 11*24607Szliu * using "sendbug 4bsd-bugs@BERKELEY", to the authors. 12*24607Szliu */ 13*24607Szliu 14*24607Szliu #ifndef lint 15*24607Szliu static char sccsid[] = "@(#)tanh.c 1.1 (ELEFUNT) 09/06/85"; 16*24607Szliu #endif not lint 17*24607Szliu 18*24607Szliu /* TANH(X) 19*24607Szliu * RETURN THE HYPERBOLIC TANGENT OF X 20*24607Szliu * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) 21*24607Szliu * CODED IN C BY K.C. NG, 1/8/85; 22*24607Szliu * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85. 23*24607Szliu * 24*24607Szliu * Required system supported functions : 25*24607Szliu * copysign(x,y) 26*24607Szliu * finite(x) 27*24607Szliu * 28*24607Szliu * Required kernel function: 29*24607Szliu * expm1(x) ...exp(x)-1 30*24607Szliu * 31*24607Szliu * Method : 32*24607Szliu * 1. reduce x to non-negative by tanh(-x) = - tanh(x). 33*24607Szliu * 2. 34*24607Szliu * 0 < x <= 1.e-10 : tanh(x) := x 35*24607Szliu * -expm1(-2x) 36*24607Szliu * 1.e-10 < x <= 1 : tanh(x) := -------------- 37*24607Szliu * expm1(-2x) + 2 38*24607Szliu * 2 39*24607Szliu * 1 <= x <= 22.0 : tanh(x) := 1 - --------------- 40*24607Szliu * expm1(2x) + 2 41*24607Szliu * 22.0 < x <= INF : tanh(x) := 1. 42*24607Szliu * 43*24607Szliu * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1. 44*24607Szliu * 45*24607Szliu * Special cases: 46*24607Szliu * tanh(NaN) is NaN; 47*24607Szliu * only tanh(0)=0 is exact for finite argument. 48*24607Szliu * 49*24607Szliu * Accuracy: 50*24607Szliu * tanh(x) returns the exact hyperbolic tangent of x nealy rounded. 51*24607Szliu * In a test run with 1,024,000 random arguments on a VAX, the maximum 52*24607Szliu * observed error was 2.22 ulps (units in the last place). 53*24607Szliu */ 54*24607Szliu 55*24607Szliu double tanh(x) 56*24607Szliu double x; 57*24607Szliu { 58*24607Szliu static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10; 59*24607Szliu double expm1(), t, copysign(), sign; 60*24607Szliu int finite(); 61*24607Szliu 62*24607Szliu #ifndef VAX 63*24607Szliu if(x!=x) return(x); /* x is NaN */ 64*24607Szliu #endif 65*24607Szliu 66*24607Szliu sign=copysign(one,x); 67*24607Szliu x=copysign(x,one); 68*24607Szliu if(x < 22.0) 69*24607Szliu if( x > one ) 70*24607Szliu return(copysign(one-two/(expm1(x+x)+two),sign)); 71*24607Szliu else if ( x > small ) 72*24607Szliu {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));} 73*24607Szliu else /* raise the INEXACT flag for non-zero x */ 74*24607Szliu {big+x; return(copysign(x,sign));} 75*24607Szliu else if(finite(x)) 76*24607Szliu return (sign+1.0E-37); /* raise the INEXACT flag */ 77*24607Szliu else 78*24607Szliu return(sign); /* x is +- INF */ 79*24607Szliu } 80