[444] | 1 | |
---|
| 2 | /* @(#)z_sineh.c 1.0 98/08/13 */ |
---|
| 3 | /****************************************************************** |
---|
| 4 | * The following routines are coded directly from the algorithms |
---|
| 5 | * and coefficients given in "Software Manual for the Elementary |
---|
| 6 | * Functions" by William J. Cody, Jr. and William Waite, Prentice |
---|
| 7 | * Hall, 1980. |
---|
| 8 | ******************************************************************/ |
---|
| 9 | |
---|
| 10 | /* |
---|
| 11 | FUNCTION |
---|
| 12 | <<sinh>>, <<sinhf>>, <<cosh>>, <<coshf>>, <<sineh>>---hyperbolic sine or cosine |
---|
| 13 | |
---|
| 14 | INDEX |
---|
| 15 | sinh |
---|
| 16 | INDEX |
---|
| 17 | sinhf |
---|
| 18 | INDEX |
---|
| 19 | cosh |
---|
| 20 | INDEX |
---|
| 21 | coshf |
---|
| 22 | |
---|
| 23 | SYNOPSIS |
---|
| 24 | #include <math.h> |
---|
| 25 | double sinh(double <[x]>); |
---|
| 26 | float sinhf(float <[x]>); |
---|
| 27 | double cosh(double <[x]>); |
---|
| 28 | float coshf(float <[x]>); |
---|
| 29 | |
---|
| 30 | DESCRIPTION |
---|
| 31 | <<sinh>> and <<cosh>> compute the hyperbolic sine or cosine |
---|
| 32 | of the argument <[x]>. |
---|
| 33 | Angles are specified in radians. <<sinh>>(<[x]>) is defined as |
---|
| 34 | @ifnottex |
---|
| 35 | . (exp(<[x]>) - exp(-<[x]>))/2 |
---|
| 36 | @end ifnottex |
---|
| 37 | @tex |
---|
| 38 | $${e^x - e^{-x}}\over 2$$ |
---|
| 39 | @end tex |
---|
| 40 | <<cosh>> is defined as |
---|
| 41 | @ifnottex |
---|
| 42 | . (exp(<[x]>) - exp(-<[x]>))/2 |
---|
| 43 | @end ifnottex |
---|
| 44 | @tex |
---|
| 45 | $${e^x + e^{-x}}\over 2$$ |
---|
| 46 | @end tex |
---|
| 47 | |
---|
| 48 | <<sinhf>> and <<coshf>> are identical, save that they take |
---|
| 49 | and returns <<float>> values. |
---|
| 50 | |
---|
| 51 | RETURNS |
---|
| 52 | The hyperbolic sine or cosine of <[x]> is returned. |
---|
| 53 | |
---|
| 54 | When the correct result is too large to be representable (an |
---|
| 55 | overflow), the functions return <<HUGE_VAL>> with the |
---|
| 56 | appropriate sign, and sets the global value <<errno>> to |
---|
| 57 | <<ERANGE>>. |
---|
| 58 | |
---|
| 59 | PORTABILITY |
---|
| 60 | <<sinh>> is ANSI C. |
---|
| 61 | <<sinhf>> is an extension. |
---|
| 62 | <<cosh>> is ANSI C. |
---|
| 63 | <<coshf>> is an extension. |
---|
| 64 | |
---|
| 65 | */ |
---|
| 66 | |
---|
| 67 | /****************************************************************** |
---|
| 68 | * Hyperbolic Sine |
---|
| 69 | * |
---|
| 70 | * Input: |
---|
| 71 | * x - floating point value |
---|
| 72 | * |
---|
| 73 | * Output: |
---|
| 74 | * hyperbolic sine of x |
---|
| 75 | * |
---|
| 76 | * Description: |
---|
| 77 | * This routine calculates hyperbolic sines. |
---|
| 78 | * |
---|
| 79 | *****************************************************************/ |
---|
| 80 | |
---|
| 81 | #include <float.h> |
---|
| 82 | #include "fdlibm.h" |
---|
| 83 | #include "zmath.h" |
---|
| 84 | |
---|
| 85 | static const double q[] = { -0.21108770058106271242e+7, |
---|
| 86 | 0.36162723109421836460e+5, |
---|
| 87 | -0.27773523119650701667e+3 }; |
---|
| 88 | static const double p[] = { -0.35181283430177117881e+6, |
---|
| 89 | -0.11563521196851768270e+5, |
---|
| 90 | -0.16375798202630751372e+3, |
---|
| 91 | -0.78966127417357099479 }; |
---|
| 92 | static const double LNV = 0.6931610107421875000; |
---|
| 93 | static const double INV_V2 = 0.24999308500451499336; |
---|
| 94 | static const double V_OVER2_MINUS1 = 0.13830277879601902638e-4; |
---|
| 95 | |
---|
| 96 | double |
---|
| 97 | sineh (double x, |
---|
| 98 | int cosineh) |
---|
| 99 | { |
---|
| 100 | double y, f, P, Q, R, res, z, w; |
---|
| 101 | int sgn = 1; |
---|
| 102 | double WBAR = 18.55; |
---|
| 103 | |
---|
| 104 | /* Check for special values. */ |
---|
| 105 | switch (numtest (x)) |
---|
| 106 | { |
---|
| 107 | case NAN: |
---|
| 108 | errno = EDOM; |
---|
| 109 | return (x); |
---|
| 110 | case INF: |
---|
| 111 | errno = ERANGE; |
---|
| 112 | return (ispos (x) ? z_infinity.d : -z_infinity.d); |
---|
| 113 | } |
---|
| 114 | |
---|
| 115 | y = fabs (x); |
---|
| 116 | |
---|
| 117 | if (!cosineh && x < 0.0) |
---|
| 118 | sgn = -1; |
---|
| 119 | |
---|
| 120 | if ((y > 1.0 && !cosineh) || cosineh) |
---|
| 121 | { |
---|
| 122 | if (y > BIGX) |
---|
| 123 | { |
---|
| 124 | w = y - LNV; |
---|
| 125 | |
---|
| 126 | /* Check for w > maximum here. */ |
---|
| 127 | if (w > BIGX) |
---|
| 128 | { |
---|
| 129 | errno = ERANGE; |
---|
| 130 | return (x); |
---|
| 131 | } |
---|
| 132 | |
---|
| 133 | z = exp (w); |
---|
| 134 | |
---|
| 135 | if (w > WBAR) |
---|
| 136 | res = z * (V_OVER2_MINUS1 + 1.0); |
---|
| 137 | } |
---|
| 138 | |
---|
| 139 | else |
---|
| 140 | { |
---|
| 141 | z = exp (y); |
---|
| 142 | if (cosineh) |
---|
| 143 | res = (z + 1 / z) / 2.0; |
---|
| 144 | else |
---|
| 145 | res = (z - 1 / z) / 2.0; |
---|
| 146 | } |
---|
| 147 | |
---|
| 148 | if (sgn < 0) |
---|
| 149 | res = -res; |
---|
| 150 | } |
---|
| 151 | else |
---|
| 152 | { |
---|
| 153 | /* Check for y being too small. */ |
---|
| 154 | if (y < z_rooteps) |
---|
| 155 | { |
---|
| 156 | res = x; |
---|
| 157 | } |
---|
| 158 | /* Calculate the Taylor series. */ |
---|
| 159 | else |
---|
| 160 | { |
---|
| 161 | f = x * x; |
---|
| 162 | Q = ((f + q[2]) * f + q[1]) * f + q[0]; |
---|
| 163 | P = ((p[3] * f + p[2]) * f + p[1]) * f + p[0]; |
---|
| 164 | R = f * (P / Q); |
---|
| 165 | |
---|
| 166 | res = x + x * R; |
---|
| 167 | } |
---|
| 168 | } |
---|
| 169 | |
---|
| 170 | return (res); |
---|
| 171 | } |
---|