[444] | 1 | |
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| 2 | /* @(#)s_sin.c 5.1 93/09/24 */ |
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| 3 | /* |
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| 4 | * ==================================================== |
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 6 | * |
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| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 8 | * Permission to use, copy, modify, and distribute this |
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| 9 | * software is freely granted, provided that this notice |
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| 10 | * is preserved. |
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| 11 | * ==================================================== |
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| 12 | */ |
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| 13 | |
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| 14 | /* |
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| 15 | FUNCTION |
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| 16 | <<sin>>, <<sinf>>, <<cos>>, <<cosf>>---sine or cosine |
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| 17 | INDEX |
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| 18 | sin |
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| 19 | INDEX |
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| 20 | sinf |
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| 21 | INDEX |
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| 22 | cos |
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| 23 | INDEX |
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| 24 | cosf |
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| 25 | SYNOPSIS |
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| 26 | #include <math.h> |
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| 27 | double sin(double <[x]>); |
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| 28 | float sinf(float <[x]>); |
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| 29 | double cos(double <[x]>); |
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| 30 | float cosf(float <[x]>); |
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| 31 | |
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| 32 | DESCRIPTION |
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| 33 | <<sin>> and <<cos>> compute (respectively) the sine and cosine |
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| 34 | of the argument <[x]>. Angles are specified in radians. |
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| 35 | |
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| 36 | <<sinf>> and <<cosf>> are identical, save that they take and |
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| 37 | return <<float>> values. |
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| 38 | |
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| 39 | |
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| 40 | RETURNS |
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| 41 | The sine or cosine of <[x]> is returned. |
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| 42 | |
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| 43 | PORTABILITY |
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| 44 | <<sin>> and <<cos>> are ANSI C. |
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| 45 | <<sinf>> and <<cosf>> are extensions. |
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| 46 | |
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| 47 | QUICKREF |
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| 48 | sin ansi pure |
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| 49 | sinf - pure |
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| 50 | */ |
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| 51 | |
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| 52 | /* sin(x) |
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| 53 | * Return sine function of x. |
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| 54 | * |
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| 55 | * kernel function: |
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| 56 | * __kernel_sin ... sine function on [-pi/4,pi/4] |
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| 57 | * __kernel_cos ... cose function on [-pi/4,pi/4] |
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| 58 | * __ieee754_rem_pio2 ... argument reduction routine |
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| 59 | * |
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| 60 | * Method. |
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| 61 | * Let S,C and T denote the sin, cos and tan respectively on |
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| 62 | * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 |
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| 63 | * in [-pi/4 , +pi/4], and let n = k mod 4. |
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| 64 | * We have |
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| 65 | * |
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| 66 | * n sin(x) cos(x) tan(x) |
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| 67 | * ---------------------------------------------------------- |
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| 68 | * 0 S C T |
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| 69 | * 1 C -S -1/T |
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| 70 | * 2 -S -C T |
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| 71 | * 3 -C S -1/T |
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| 72 | * ---------------------------------------------------------- |
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| 73 | * |
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| 74 | * Special cases: |
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| 75 | * Let trig be any of sin, cos, or tan. |
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| 76 | * trig(+-INF) is NaN, with signals; |
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| 77 | * trig(NaN) is that NaN; |
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| 78 | * |
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| 79 | * Accuracy: |
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| 80 | * TRIG(x) returns trig(x) nearly rounded |
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| 81 | */ |
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| 82 | |
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| 83 | #include "fdlibm.h" |
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| 84 | |
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| 85 | #ifndef _DOUBLE_IS_32BITS |
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| 86 | |
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| 87 | #ifdef __STDC__ |
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| 88 | double sin(double x) |
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| 89 | #else |
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| 90 | double sin(x) |
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| 91 | double x; |
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| 92 | #endif |
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| 93 | { |
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| 94 | double y[2],z=0.0; |
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| 95 | __int32_t n,ix; |
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| 96 | |
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| 97 | /* High word of x. */ |
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| 98 | GET_HIGH_WORD(ix,x); |
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| 99 | |
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| 100 | /* |x| ~< pi/4 */ |
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| 101 | ix &= 0x7fffffff; |
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| 102 | if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); |
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| 103 | |
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| 104 | /* sin(Inf or NaN) is NaN */ |
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| 105 | else if (ix>=0x7ff00000) return x-x; |
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| 106 | |
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| 107 | /* argument reduction needed */ |
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| 108 | else { |
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| 109 | n = __ieee754_rem_pio2(x,y); |
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| 110 | switch(n&3) { |
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| 111 | case 0: return __kernel_sin(y[0],y[1],1); |
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| 112 | case 1: return __kernel_cos(y[0],y[1]); |
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| 113 | case 2: return -__kernel_sin(y[0],y[1],1); |
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| 114 | default: |
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| 115 | return -__kernel_cos(y[0],y[1]); |
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| 116 | } |
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| 117 | } |
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| 118 | } |
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| 119 | |
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| 120 | #endif /* _DOUBLE_IS_32BITS */ |
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