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 __FBSDID("$FreeBSD$"); 15 16 /* sin(x) 17 * Return sine function of x. 18 * 19 * kernel function: 20 * __kernel_sin ... sine function on [-pi/4,pi/4] 21 * __kernel_cos ... cose function on [-pi/4,pi/4] 22 * __ieee754_rem_pio2 ... argument reduction routine 23 * 24 * Method. 25 * Let S,C and T denote the sin, cos and tan respectively on 26 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 27 * in [-pi/4 , +pi/4], and let n = k mod 4. 28 * We have 29 * 30 * n sin(x) cos(x) tan(x) 31 * ---------------------------------------------------------- 32 * 0 S C T 33 * 1 C -S -1/T 34 * 2 -S -C T 35 * 3 -C S -1/T 36 * ---------------------------------------------------------- 37 * 38 * Special cases: 39 * Let trig be any of sin, cos, or tan. 40 * trig(+-INF) is NaN, with signals; 41 * trig(NaN) is that NaN; 42 * 43 * Accuracy: 44 * TRIG(x) returns trig(x) nearly rounded 45 */ 46 47 #include <float.h> 48 49 #include "math.h" 50 #define INLINE_REM_PIO2 51 #include "math_private.h" 52 #include "e_rem_pio2.c" 53 54 double 55 sin(double x) 56 { 57 double y[2],z=0.0; 58 int32_t n, ix; 59 60 /* High word of x. */ 61 GET_HIGH_WORD(ix,x); 62 63 /* |x| ~< pi/4 */ 64 ix &= 0x7fffffff; 65 if(ix <= 0x3fe921fb) { 66 if(ix<0x3e500000) /* |x| < 2**-26 */ 67 {if((int)x==0) return x;} /* generate inexact */ 68 return __kernel_sin(x,z,0); 69 } 70 71 /* sin(Inf or NaN) is NaN */ 72 else if (ix>=0x7ff00000) return x-x; 73 74 /* argument reduction needed */ 75 else { 76 n = __ieee754_rem_pio2(x,y); 77 switch(n&3) { 78 case 0: return __kernel_sin(y[0],y[1],1); 79 case 1: return __kernel_cos(y[0],y[1]); 80 case 2: return -__kernel_sin(y[0],y[1],1); 81 default: 82 return -__kernel_cos(y[0],y[1]); 83 } 84 } 85 } 86 87 #if (LDBL_MANT_DIG == 53) 88 __weak_reference(sin, sinl); 89 #endif 90