1 /* derived from /netlib/fdlibm */ 2 3 /* @(#)s_sin.c 1.3 95/01/18 */ 4 /* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunSoft, a Sun Microsystems, Inc. business. 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 */ 14 15 /* sin(x) 16 * Return sine function of x. 17 * 18 * kernel function: 19 * __kernel_sin ... sine function on [-pi/4,pi/4] 20 * __kernel_cos ... cose function on [-pi/4,pi/4] 21 * __ieee754_rem_pio2 ... argument reduction routine 22 * 23 * Method. 24 * Let S,C and T denote the sin, cos and tan respectively on 25 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 26 * in [-pi/4 , +pi/4], and let n = k mod 4. 27 * We have 28 * 29 * n sin(x) cos(x) tan(x) 30 * ---------------------------------------------------------- 31 * 0 S C T 32 * 1 C -S -1/T 33 * 2 -S -C T 34 * 3 -C S -1/T 35 * ---------------------------------------------------------- 36 * 37 * Special cases: 38 * Let trig be any of sin, cos, or tan. 39 * trig(+-INF) is NaN, with signals; 40 * trig(NaN) is that NaN; 41 * 42 * Accuracy: 43 * TRIG(x) returns trig(x) nearly rounded 44 */ 45 46 #include "fdlibm.h" 47 48 double sin(double x) 49 { 50 double y[2],z=0.0; 51 int n, ix; 52 53 /* High word of x. */ 54 ix = __HI(x); 55 56 /* |x| ~< pi/4 */ 57 ix &= 0x7fffffff; 58 if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); 59 60 /* sin(Inf or NaN) is NaN */ 61 else if (ix>=0x7ff00000) return x-x; 62 63 /* argument reduction needed */ 64 else { 65 n = __ieee754_rem_pio2(x,y); 66 switch(n&3) { 67 case 0: return __kernel_sin(y[0],y[1],1); 68 case 1: return __kernel_cos(y[0],y[1]); 69 case 2: return -__kernel_sin(y[0],y[1],1); 70 default: 71 return -__kernel_cos(y[0],y[1]); 72 } 73 } 74 } 75