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 #include <sys/cdefs.h> 14 /* sin(x) 15 * Return sine function of x. 16 * 17 * kernel function: 18 * __kernel_sin ... sine function on [-pi/4,pi/4] 19 * __kernel_cos ... cose function on [-pi/4,pi/4] 20 * __ieee754_rem_pio2 ... argument reduction routine 21 * 22 * Method. 23 * Let S,C and T denote the sin, cos and tan respectively on 24 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 25 * in [-pi/4 , +pi/4], and let n = k mod 4. 26 * We have 27 * 28 * n sin(x) cos(x) tan(x) 29 * ---------------------------------------------------------- 30 * 0 S C T 31 * 1 C -S -1/T 32 * 2 -S -C T 33 * 3 -C S -1/T 34 * ---------------------------------------------------------- 35 * 36 * Special cases: 37 * Let trig be any of sin, cos, or tan. 38 * trig(+-INF) is NaN, with signals; 39 * trig(NaN) is that NaN; 40 * 41 * Accuracy: 42 * TRIG(x) returns trig(x) nearly rounded 43 */ 44 45 #include <float.h> 46 47 #include "math.h" 48 #define INLINE_REM_PIO2 49 #include "math_private.h" 50 #include "e_rem_pio2.c" 51 52 double 53 sin(double x) 54 { 55 double y[2],z=0.0; 56 int32_t n, ix; 57 58 /* High word of x. */ 59 GET_HIGH_WORD(ix,x); 60 61 /* |x| ~< pi/4 */ 62 ix &= 0x7fffffff; 63 if(ix <= 0x3fe921fb) { 64 if(ix<0x3e500000) /* |x| < 2**-26 */ 65 {if((int)x==0) return x;} /* generate inexact */ 66 return __kernel_sin(x,z,0); 67 } 68 69 /* sin(Inf or NaN) is NaN */ 70 else if (ix>=0x7ff00000) return x-x; 71 72 /* argument reduction needed */ 73 else { 74 n = __ieee754_rem_pio2(x,y); 75 switch(n&3) { 76 case 0: return __kernel_sin(y[0],y[1],1); 77 case 1: return __kernel_cos(y[0],y[1]); 78 case 2: return -__kernel_sin(y[0],y[1],1); 79 default: 80 return -__kernel_cos(y[0],y[1]); 81 } 82 } 83 } 84 85 #if (LDBL_MANT_DIG == 53) 86 __weak_reference(sin, sinl); 87 #endif 88