| 1 | |
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| 2 | /* @(#)z_tanh.c 1.0 98/08/13 */ |
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| 3 | /***************************************************************** |
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| 4 | * The following routines are coded directly from the algorithms |
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| 5 | * and coefficients given in "Software Manual for the Elementary |
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| 6 | * Functions" by William J. Cody, Jr. and William Waite, Prentice |
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| 7 | * Hall, 1980. |
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| 8 | *****************************************************************/ |
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| 9 | |
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| 10 | /* |
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| 11 | |
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| 12 | FUNCTION |
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| 13 | <<tanh>>, <<tanhf>>---hyperbolic tangent |
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| 14 | |
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| 15 | INDEX |
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| 16 | tanh |
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| 17 | INDEX |
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| 18 | tanhf |
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| 19 | |
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| 20 | SYNOPSIS |
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| 21 | #include <math.h> |
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| 22 | double tanh(double <[x]>); |
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| 23 | float tanhf(float <[x]>); |
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| 24 | |
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| 25 | DESCRIPTION |
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| 26 | |
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| 27 | <<tanh>> computes the hyperbolic tangent of |
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| 28 | the argument <[x]>. Angles are specified in radians. |
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| 29 | |
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| 30 | <<tanh(<[x]>)>> is defined as |
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| 31 | . sinh(<[x]>)/cosh(<[x]>) |
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| 32 | |
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| 33 | <<tanhf>> is identical, save that it takes and returns <<float>> values. |
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| 34 | |
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| 35 | RETURNS |
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| 36 | The hyperbolic tangent of <[x]> is returned. |
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| 37 | |
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| 38 | PORTABILITY |
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| 39 | <<tanh>> is ANSI C. <<tanhf>> is an extension. |
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| 40 | |
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| 41 | */ |
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| 42 | |
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| 43 | /****************************************************************** |
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| 44 | * Hyperbolic Tangent |
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| 45 | * |
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| 46 | * Input: |
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| 47 | * x - floating point value |
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| 48 | * |
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| 49 | * Output: |
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| 50 | * hyperbolic tangent of x |
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| 51 | * |
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| 52 | * Description: |
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| 53 | * This routine calculates hyperbolic tangent. |
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| 54 | * |
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| 55 | *****************************************************************/ |
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| 56 | |
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| 57 | #include <float.h> |
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| 58 | #include "fdlibm.h" |
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| 59 | #include "zmath.h" |
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| 60 | |
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| 61 | #ifndef _DOUBLE_IS_32BITS |
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| 62 | |
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| 63 | static const double LN3_OVER2 = 0.54930614433405484570; |
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| 64 | static const double p[] = { -0.16134119023996228053e+4, |
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| 65 | -0.99225929672236083313e+2, |
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| 66 | -0.96437492777225469787 }; |
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| 67 | static const double q[] = { 0.48402357071988688686e+4, |
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| 68 | 0.22337720718962312926e+4, |
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| 69 | 0.11274474380534949335e+3 }; |
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| 70 | |
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| 71 | double |
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| 72 | tanh (double x) |
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| 73 | { |
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| 74 | double f, res, g, P, Q, R; |
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| 75 | |
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| 76 | f = fabs (x); |
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| 77 | |
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| 78 | /* Check if the input is too big. */ |
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| 79 | if (f > BIGX) |
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| 80 | res = 1.0; |
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| 81 | |
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| 82 | else if (f > LN3_OVER2) |
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| 83 | res = 1.0 - 2.0 / (exp (2 * f) + 1.0); |
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| 84 | |
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| 85 | /* Check if the input is too small. */ |
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| 86 | else if (f < z_rooteps) |
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| 87 | res = f; |
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| 88 | |
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| 89 | /* Calculate the Taylor series. */ |
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| 90 | else |
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| 91 | { |
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| 92 | g = f * f; |
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| 93 | |
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| 94 | P = (p[2] * g + p[1]) * g + p[0]; |
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| 95 | Q = ((g + q[2]) * g + q[1]) * g + q[0]; |
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| 96 | R = g * (P / Q); |
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| 97 | |
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| 98 | res = f + f * R; |
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| 99 | } |
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| 100 | |
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| 101 | if (x < 0.0) |
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| 102 | res = -res; |
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| 103 | |
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| 104 | return (res); |
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| 105 | } |
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| 106 | |
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| 107 | #endif /* _DOUBLE_IS_32BITS */ |
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