[444] | 1 | |
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| 2 | /* @(#)z_sine.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 | FUNCTION |
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| 12 | <<sin>>, <<cos>>, <<sine>>, <<sinf>>, <<cosf>>, <<sinef>>---sine or cosine |
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| 13 | INDEX |
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| 14 | sin |
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| 15 | INDEX |
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| 16 | sinf |
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| 17 | INDEX |
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| 18 | cos |
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| 19 | INDEX |
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| 20 | cosf |
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| 21 | SYNOPSIS |
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| 22 | #include <math.h> |
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| 23 | double sin(double <[x]>); |
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| 24 | float sinf(float <[x]>); |
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| 25 | double cos(double <[x]>); |
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| 26 | float cosf(float <[x]>); |
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| 27 | |
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| 28 | DESCRIPTION |
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| 29 | <<sin>> and <<cos>> compute (respectively) the sine and cosine |
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| 30 | of the argument <[x]>. Angles are specified in radians. |
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| 31 | RETURNS |
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| 32 | The sine or cosine of <[x]> is returned. |
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| 33 | |
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| 34 | PORTABILITY |
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| 35 | <<sin>> and <<cos>> are ANSI C. |
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| 36 | <<sinf>> and <<cosf>> are extensions. |
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| 37 | |
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| 38 | QUICKREF |
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| 39 | sin ansi pure |
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| 40 | sinf - pure |
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| 41 | */ |
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| 42 | |
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| 43 | /****************************************************************** |
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| 44 | * sine |
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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 | * cosine - indicates cosine value |
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| 49 | * |
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| 50 | * Output: |
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| 51 | * Sine of x. |
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| 52 | * |
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| 53 | * Description: |
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| 54 | * This routine calculates sines and cosines. |
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| 55 | * |
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| 56 | *****************************************************************/ |
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| 57 | |
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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 HALF_PI = 1.57079632679489661923; |
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| 64 | static const double ONE_OVER_PI = 0.31830988618379067154; |
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| 65 | static const double r[] = { -0.16666666666666665052, |
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| 66 | 0.83333333333331650314e-02, |
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| 67 | -0.19841269841201840457e-03, |
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| 68 | 0.27557319210152756119e-05, |
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| 69 | -0.25052106798274584544e-07, |
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| 70 | 0.16058936490371589114e-09, |
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| 71 | -0.76429178068910467734e-12, |
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| 72 | 0.27204790957888846175e-14 }; |
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| 73 | |
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| 74 | double |
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| 75 | sine (double x, |
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| 76 | int cosine) |
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| 77 | { |
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| 78 | int sgn, N; |
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| 79 | double y, XN, g, R, res; |
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| 80 | double YMAX = 210828714.0; |
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| 81 | |
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| 82 | switch (numtest (x)) |
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| 83 | { |
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| 84 | case NAN: |
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| 85 | errno = EDOM; |
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| 86 | return (x); |
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| 87 | case INF: |
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| 88 | errno = EDOM; |
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| 89 | return (z_notanum.d); |
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| 90 | } |
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| 91 | |
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| 92 | /* Use sin and cos properties to ease computations. */ |
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| 93 | if (cosine) |
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| 94 | { |
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| 95 | sgn = 1; |
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| 96 | y = fabs (x) + HALF_PI; |
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| 97 | } |
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| 98 | else |
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| 99 | { |
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| 100 | if (x < 0.0) |
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| 101 | { |
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| 102 | sgn = -1; |
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| 103 | y = -x; |
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| 104 | } |
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| 105 | else |
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| 106 | { |
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| 107 | sgn = 1; |
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| 108 | y = x; |
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| 109 | } |
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| 110 | } |
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| 111 | |
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| 112 | /* Check for values of y that will overflow here. */ |
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| 113 | if (y > YMAX) |
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| 114 | { |
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| 115 | errno = ERANGE; |
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| 116 | return (x); |
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| 117 | } |
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| 118 | |
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| 119 | /* Calculate the exponent. */ |
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| 120 | if (y < 0.0) |
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| 121 | N = (int) (y * ONE_OVER_PI - 0.5); |
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| 122 | else |
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| 123 | N = (int) (y * ONE_OVER_PI + 0.5); |
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| 124 | XN = (double) N; |
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| 125 | |
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| 126 | if (N & 1) |
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| 127 | sgn = -sgn; |
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| 128 | |
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| 129 | if (cosine) |
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| 130 | XN -= 0.5; |
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| 131 | |
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| 132 | y = fabs (x) - XN * __PI; |
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| 133 | |
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| 134 | if (-z_rooteps < y && y < z_rooteps) |
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| 135 | res = y; |
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| 136 | |
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| 137 | else |
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| 138 | { |
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| 139 | g = y * y; |
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| 140 | |
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| 141 | /* Calculate the Taylor series. */ |
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| 142 | R = (((((((r[6] * g + r[5]) * g + r[4]) * g + r[3]) * g + r[2]) * g + r[1]) * g + r[0]) * g); |
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| 143 | |
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| 144 | /* Finally, compute the result. */ |
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| 145 | res = y + y * R; |
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| 146 | } |
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| 147 | |
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| 148 | res *= sgn; |
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| 149 | |
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| 150 | return (res); |
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| 151 | } |
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| 152 | |
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| 153 | #endif /* _DOUBLE_IS_32BITS */ |
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