1 /* @(#)s_sin.c 5.1 93/09/24 */ 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 13 /* sin(x) 14 * Return sine function of x. 15 * 16 * kernel function: 17 * __kernel_sin ... sine function on [-pi/4,pi/4] 18 * __kernel_cos ... cose function on [-pi/4,pi/4] 19 * __ieee754_rem_pio2 ... argument reduction routine 20 * 21 * Method. 22 * Let S,C and T denote the sin, cos and tan respectively on 23 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 24 * in [-pi/4 , +pi/4], and let n = k mod 4. 25 * We have 26 * 27 * n sin(x) cos(x) tan(x) 28 * ---------------------------------------------------------- 29 * 0 S C T 30 * 1 C -S -1/T 31 * 2 -S -C T 32 * 3 -C S -1/T 33 * ---------------------------------------------------------- 34 * 35 * Special cases: 36 * Let trig be any of sin, cos, or tan. 37 * trig(+-INF) is NaN, with signals; 38 * trig(NaN) is that NaN; 39 * 40 * Accuracy: 41 * TRIG(x) returns trig(x) nearly rounded 42 */ 43 44 #include <float.h> 45 #include <math.h> 46 47 #include "math_private.h" 48 49 double 50 sin(double x) 51 { 52 double y[2],z=0.0; 53 int32_t n, ix; 54 55 /* High word of x. */ 56 GET_HIGH_WORD(ix,x); 57 58 /* |x| ~< pi/4 */ 59 ix &= 0x7fffffff; 60 if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); 61 62 /* sin(Inf or NaN) is NaN */ 63 else if (ix>=0x7ff00000) return x-x; 64 65 /* argument reduction needed */ 66 else { 67 n = __ieee754_rem_pio2(x,y); 68 switch(n&3) { 69 case 0: return __kernel_sin(y[0],y[1],1); 70 case 1: return __kernel_cos(y[0],y[1]); 71 case 2: return -__kernel_sin(y[0],y[1],1); 72 default: 73 return -__kernel_cos(y[0],y[1]); 74 } 75 } 76 } 77 78 #if LDBL_MANT_DIG == DBL_MANT_DIG 79 __strong_alias(sinl, sin); 80 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 81