tanhl.c revision 61ec6b12089c560a32ebd9efdbb057ff92665e60
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Use is subject to license terms.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * tanhl(x) returns the hyperbolic tangent of x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 1. reduce x to non-negative: tanhl(-x) = - tanhl(x).
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 0 < x <= small : tanhl(x) := x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * -expm1l(-2x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * small < x <= 1 : tanhl(x) := --------------
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * expm1l(-2x) + 2
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 1 <= x <= threshold : tanhl(x) := 1 - ---------------
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * expm1l(2x) + 2
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * threshold < x <= INF : tanhl(x) := 1.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * single : small = 1.e-5 threshold = 11.0
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * double : small = 1.e-10 threshold = 22.0
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * quad : small = 1.e-20 threshold = 45.0
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Note: threshold was chosen so that
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * fl(1.0+2/(expm1(2*threshold)+2)) == 1.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Special cases:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * tanhl(NaN) is NaN;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * only tanhl(0.0)=0.0 is exact for finite argument.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisstatic const long double small = 1.0e-20L, one = 1.0, two = 2.0,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtistanhl(long double x) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis long double t, y, z;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis volatile long double dummy;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (x + x); /* x is NaN */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis else if (t > small) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis z = -y / (y + two);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis /* inexact if t != 0 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis } else if (!finitel(t))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (signx ? -z + small * small : z - small * small);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (signx ? -z : z);