1 /* origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 /* sin(x) 13 * Return sine function of x. 14 * 15 * kernel function: 16 * __sin ... sine function on [-pi/4,pi/4] 17 * __cos ... cose function on [-pi/4,pi/4] 18 * __rem_pio2 ... argument reduction routine 19 * 20 * Method. 21 * Let S,C and T denote the sin, cos and tan respectively on 22 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 23 * in [-pi/4 , +pi/4], and let n = k mod 4. 24 * We have 25 * 26 * n sin(x) cos(x) tan(x) 27 * ---------------------------------------------------------- 28 * 0 S C T 29 * 1 C -S -1/T 30 * 2 -S -C T 31 * 3 -C S -1/T 32 * ---------------------------------------------------------- 33 * 34 * Special cases: 35 * Let trig be any of sin, cos, or tan. 36 * trig(+-INF) is NaN, with signals; 37 * trig(NaN) is that NaN; 38 * 39 * Accuracy: 40 * TRIG(x) returns trig(x) nearly rounded 41 */ 42 43 #include "libm.h" 44 45 double sin(double x) 46 { 47 double y[2]; 48 uint32_t ix; 49 unsigned n; 50 51 /* High word of x. */ 52 GET_HIGH_WORD(ix, x); 53 ix &= 0x7fffffff; 54 55 /* |x| ~< pi/4 */ 56 if (ix <= 0x3fe921fb) { 57 if (ix < 0x3e500000) { /* |x| < 2**-26 */ 58 /* raise inexact if x != 0 and underflow if subnormal*/ 59 FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f); 60 return x; 61 } 62 return __sin(x, 0.0, 0); 63 } 64 65 /* sin(Inf or NaN) is NaN */ 66 if (ix >= 0x7ff00000) 67 return x - x; 68 69 /* argument reduction needed */ 70 n = __rem_pio2(x, y); 71 switch (n&3) { 72 case 0: return __sin(y[0], y[1], 1); 73 case 1: return __cos(y[0], y[1]); 74 case 2: return -__sin(y[0], y[1], 1); 75 default: 76 return -__cos(y[0], y[1]); 77 } 78 } 79