[398] | 1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */
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| 2 | /*
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| 3 | * ====================================================
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| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 5 | *
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| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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| 7 | * Permission to use, copy, modify, and distribute this
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| 8 | * software is freely granted, provided that this notice
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| 9 | * is preserved.
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| 10 | * ====================================================
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| 11 | */
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| 12 | /* sin(x)
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| 13 | * Return sine function of x.
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| 14 | *
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| 15 | * kernel function:
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| 16 | * __sin ... sine function on [-pi/4,pi/4]
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| 17 | * __cos ... cose function on [-pi/4,pi/4]
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| 18 | * __rem_pio2 ... argument reduction routine
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| 19 | *
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| 20 | * Method.
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| 21 | * Let S,C and T denote the sin, cos and tan respectively on
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| 22 | * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
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| 23 | * in [-pi/4 , +pi/4], and let n = k mod 4.
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| 24 | * We have
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| 25 | *
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| 26 | * n sin(x) cos(x) tan(x)
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| 27 | * ----------------------------------------------------------
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| 28 | * 0 S C T
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| 29 | * 1 C -S -1/T
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| 30 | * 2 -S -C T
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| 31 | * 3 -C S -1/T
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| 32 | * ----------------------------------------------------------
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| 33 | *
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| 34 | * Special cases:
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| 35 | * Let trig be any of sin, cos, or tan.
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| 36 | * trig(+-INF) is NaN, with signals;
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| 37 | * trig(NaN) is that NaN;
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| 38 | *
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| 39 | * Accuracy:
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| 40 | * TRIG(x) returns trig(x) nearly rounded
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| 41 | */
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| 42 |
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| 43 | #include "libm.h"
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| 44 |
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| 45 | double sin(double x)
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| 46 | {
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| 47 | double y[2];
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| 48 | uint32_t ix;
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| 49 | unsigned n;
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| 50 |
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| 51 | /* High word of x. */
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| 52 | GET_HIGH_WORD(ix, x);
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| 53 | ix &= 0x7fffffff;
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| 54 |
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| 55 | /* |x| ~< pi/4 */
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| 56 | if (ix <= 0x3fe921fb) {
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| 57 | if (ix < 0x3e500000) { /* |x| < 2**-26 */
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| 58 | /* raise inexact if x != 0 and underflow if subnormal*/
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| 59 | FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
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| 60 | return x;
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| 61 | }
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| 62 | return __sin(x, 0.0, 0);
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| 63 | }
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| 64 |
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| 65 | /* sin(Inf or NaN) is NaN */
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| 66 | if (ix >= 0x7ff00000)
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| 67 | return x - x;
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| 68 |
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| 69 | /* argument reduction needed */
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| 70 | n = __rem_pio2(x, y);
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| 71 | switch (n&3) {
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| 72 | case 0: return __sin(y[0], y[1], 1);
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| 73 | case 1: return __cos(y[0], y[1]);
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| 74 | case 2: return -__sin(y[0], y[1], 1);
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| 75 | default:
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| 76 | return -__cos(y[0], y[1]);
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| 77 | }
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| 78 | }
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