projects / unix-history / blame
| Commit | Line | Data |
|---|---|---|
| 9b525f39 | 1 | /* |
| 06b452f6 | 2 | * Copyright (c) 1985 Regents of the University of California. |
| 9b525f39 KB |
3 | * All rights reserved. |
| 4 | * | |
| 7e3eac84 | 5 | * %sccs.include.redist.c% |
| 06b452f6 ZAL |
6 | */ |
| 7 | ||
| 8 | #ifndef lint | |
| 2bc65d90 | 9 | static char sccsid[] = "@(#)tanh.c 5.5 (Berkeley) %G%"; |
| 9b525f39 | 10 | #endif /* not lint */ |
| 06b452f6 ZAL |
11 | |
| 12 | /* TANH(X) | |
| 13 | * RETURN THE HYPERBOLIC TANGENT OF X | |
| 14 | * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) | |
| 15 | * CODED IN C BY K.C. NG, 1/8/85; | |
| 16 | * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85. | |
| 17 | * | |
| 18 | * Required system supported functions : | |
| 19 | * copysign(x,y) | |
| 20 | * finite(x) | |
| 21 | * | |
| 22 | * Required kernel function: | |
| 23 | * expm1(x) ...exp(x)-1 | |
| 24 | * | |
| 25 | * Method : | |
| 26 | * 1. reduce x to non-negative by tanh(-x) = - tanh(x). | |
| 27 | * 2. | |
| 28 | * 0 < x <= 1.e-10 : tanh(x) := x | |
| 29 | * -expm1(-2x) | |
| 30 | * 1.e-10 < x <= 1 : tanh(x) := -------------- | |
| 31 | * expm1(-2x) + 2 | |
| 32 | * 2 | |
| 33 | * 1 <= x <= 22.0 : tanh(x) := 1 - --------------- | |
| 34 | * expm1(2x) + 2 | |
| 35 | * 22.0 < x <= INF : tanh(x) := 1. | |
| 36 | * | |
| 37 | * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1. | |
| 38 | * | |
| 39 | * Special cases: | |
| 40 | * tanh(NaN) is NaN; | |
| 41 | * only tanh(0)=0 is exact for finite argument. | |
| 42 | * | |
| 43 | * Accuracy: | |
| 44 | * tanh(x) returns the exact hyperbolic tangent of x nealy rounded. | |
| 45 | * In a test run with 1,024,000 random arguments on a VAX, the maximum | |
| 46 | * observed error was 2.22 ulps (units in the last place). | |
| 47 | */ | |
| 48 | ||
| 49 | double tanh(x) | |
| 50 | double x; | |
| 51 | { | |
| 52 | static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10; | |
| 53 | double expm1(), t, copysign(), sign; | |
| 54 | int finite(); | |
| 55 | ||
| 859dc438 | 56 | #if !defined(vax)&&!defined(tahoe) |
| 06b452f6 | 57 | if(x!=x) return(x); /* x is NaN */ |
| 859dc438 | 58 | #endif /* !defined(vax)&&!defined(tahoe) */ |
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59 | |
| 60 | sign=copysign(one,x); | |
| 61 | x=copysign(x,one); | |
| 62 | if(x < 22.0) | |
| 63 | if( x > one ) | |
| 64 | return(copysign(one-two/(expm1(x+x)+two),sign)); | |
| 65 | else if ( x > small ) | |
| 66 | {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));} | |
| 67 | else /* raise the INEXACT flag for non-zero x */ | |
| 68 | {big+x; return(copysign(x,sign));} | |
| 69 | else if(finite(x)) | |
| 70 | return (sign+1.0E-37); /* raise the INEXACT flag */ | |
| 71 | else | |
| 72 | return(sign); /* x is +- INF */ | |
| 73 | } |