1 /* 2 * Copyright (c) 1985 Regents of the University of California. 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms are permitted 6 * provided that the above copyright notice and this paragraph are 7 * duplicated in all such forms and that any documentation, 8 * advertising materials, and other materials related to such 9 * distribution and use acknowledge that the software was developed 10 * by the University of California, Berkeley. The name of the 11 * University may not be used to endorse or promote products derived 12 * from this software without specific prior written permission. 13 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR 14 * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED 15 * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE. 16 * 17 * All recipients should regard themselves as participants in an ongoing 18 * research project and hence should feel obligated to report their 19 * experiences (good or bad) with these elementary function codes, using 20 * the sendbug(8) program, to the authors. 21 */ 22 23 #ifndef lint 24 static char sccsid[] = "@(#)tanh.c 5.3 (Berkeley) 06/30/88"; 25 #endif /* not lint */ 26 27 /* TANH(X) 28 * RETURN THE HYPERBOLIC TANGENT OF X 29 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) 30 * CODED IN C BY K.C. NG, 1/8/85; 31 * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85. 32 * 33 * Required system supported functions : 34 * copysign(x,y) 35 * finite(x) 36 * 37 * Required kernel function: 38 * expm1(x) ...exp(x)-1 39 * 40 * Method : 41 * 1. reduce x to non-negative by tanh(-x) = - tanh(x). 42 * 2. 43 * 0 < x <= 1.e-10 : tanh(x) := x 44 * -expm1(-2x) 45 * 1.e-10 < x <= 1 : tanh(x) := -------------- 46 * expm1(-2x) + 2 47 * 2 48 * 1 <= x <= 22.0 : tanh(x) := 1 - --------------- 49 * expm1(2x) + 2 50 * 22.0 < x <= INF : tanh(x) := 1. 51 * 52 * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1. 53 * 54 * Special cases: 55 * tanh(NaN) is NaN; 56 * only tanh(0)=0 is exact for finite argument. 57 * 58 * Accuracy: 59 * tanh(x) returns the exact hyperbolic tangent of x nealy rounded. 60 * In a test run with 1,024,000 random arguments on a VAX, the maximum 61 * observed error was 2.22 ulps (units in the last place). 62 */ 63 64 double tanh(x) 65 double x; 66 { 67 static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10; 68 double expm1(), t, copysign(), sign; 69 int finite(); 70 71 #if !defined(vax)&&!defined(tahoe) 72 if(x!=x) return(x); /* x is NaN */ 73 #endif /* !defined(vax)&&!defined(tahoe) */ 74 75 sign=copysign(one,x); 76 x=copysign(x,one); 77 if(x < 22.0) 78 if( x > one ) 79 return(copysign(one-two/(expm1(x+x)+two),sign)); 80 else if ( x > small ) 81 {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));} 82 else /* raise the INEXACT flag for non-zero x */ 83 {big+x; return(copysign(x,sign));} 84 else if(finite(x)) 85 return (sign+1.0E-37); /* raise the INEXACT flag */ 86 else 87 return(sign); /* x is +- INF */ 88 } 89