1/* @(#)s_tanh.c 5.1 93/09/24 */ 2/* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13#ifndef lint
| 1/* @(#)s_tanh.c 5.1 93/09/24 */ 2/* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13#ifndef lint
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14static char rcsid[] = "$FreeBSD: head/lib/msun/src/s_tanh.c 97413 2002-05-28 18:15:04Z alfred $";
| 14static char rcsid[] = "$FreeBSD: head/lib/msun/src/s_tanh.c 160122 2006-07-05 22:59:33Z bde $";
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15#endif 16 17/* Tanh(x) 18 * Return the Hyperbolic Tangent of x 19 * 20 * Method : 21 * x -x 22 * e - e 23 * 0. tanh(x) is defined to be ----------- 24 * x -x 25 * e + e 26 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
| 15#endif 16 17/* Tanh(x) 18 * Return the Hyperbolic Tangent of x 19 * 20 * Method : 21 * x -x 22 * e - e 23 * 0. tanh(x) is defined to be ----------- 24 * x -x 25 * e + e 26 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
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27 * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
| 27 * 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0
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28 * -t
| 28 * -t
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29 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
| 29 * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x)
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30 * t + 2 31 * 2
| 30 * t + 2 31 * 2
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32 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
| 32 * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x)
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33 * t + 2
| 33 * t + 2
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34 * 22.0 < x <= INF : tanh(x) := 1.
| 34 * 22 <= x <= INF : tanh(x) := 1.
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35 * 36 * Special cases: 37 * tanh(NaN) is NaN; 38 * only tanh(0)=0 is exact for finite argument. 39 */ 40 41#include "math.h" 42#include "math_private.h" 43
| 35 * 36 * Special cases: 37 * tanh(NaN) is NaN; 38 * only tanh(0)=0 is exact for finite argument. 39 */ 40 41#include "math.h" 42#include "math_private.h" 43
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44static const double one=1.0, two=2.0, tiny = 1.0e-300;
| 44static const double one = 1.0, two = 2.0, tiny = 1.0e-300, huge = 1.0e300;
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45 46double 47tanh(double x) 48{ 49 double t,z; 50 int32_t jx,ix; 51
| 45 46double 47tanh(double x) 48{ 49 double t,z; 50 int32_t jx,ix; 51
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52 /* High word of |x|. */
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53 GET_HIGH_WORD(jx,x); 54 ix = jx&0x7fffffff; 55 56 /* x is INF or NaN */ 57 if(ix>=0x7ff00000) { 58 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 59 else return one/x-one; /* tanh(NaN) = NaN */ 60 } 61 62 /* |x| < 22 */ 63 if (ix < 0x40360000) { /* |x|<22 */
| 52 GET_HIGH_WORD(jx,x); 53 ix = jx&0x7fffffff; 54 55 /* x is INF or NaN */ 56 if(ix>=0x7ff00000) { 57 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 58 else return one/x-one; /* tanh(NaN) = NaN */ 59 } 60 61 /* |x| < 22 */ 62 if (ix < 0x40360000) { /* |x|<22 */
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64 if (ix<0x3c800000) /* |x|<2**-55 */ 65 return x*(one+x); /* tanh(small) = small */
| 63 if (ix<0x3e300000) { /* |x|<2**-28 */ 64 if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */ 65 }
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66 if (ix>=0x3ff00000) { /* |x|>=1 */ 67 t = expm1(two*fabs(x)); 68 z = one - two/(t+two); 69 } else { 70 t = expm1(-two*fabs(x)); 71 z= -t/(t+two); 72 }
| 66 if (ix>=0x3ff00000) { /* |x|>=1 */ 67 t = expm1(two*fabs(x)); 68 z = one - two/(t+two); 69 } else { 70 t = expm1(-two*fabs(x)); 71 z= -t/(t+two); 72 }
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73 /* |x| > 22, return +-1 */
| 73 /* |x| >= 22, return +-1 */
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74 } else {
| 74 } else {
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75 z = one - tiny; /* raised inexact flag */
| 75 z = one - tiny; /* raise inexact flag */
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76 } 77 return (jx>=0)? z: -z; 78}
| 76 } 77 return (jx>=0)? z: -z; 78}
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