1 /* 2 * ==================================================== 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * 5 * Developed at SunPro, a Sun Microsystems, Inc. business. 6 * Permission to use, copy, modify, and distribute this 7 * software is freely granted, provided that this notice 8 * is preserved. 9 * ==================================================== 10 */ 11 12 #include <sys/cdefs.h> 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 46 #include "math.h" 47 #define INLINE_REM_PIO2 48 #include "math_private.h" 49 #include "e_rem_pio2.c" 50 51 double 52 sin(double x) 53 { 54 double y[2],z=0.0; 55 int32_t n, ix; 56 57 /* High word of x. */ 58 GET_HIGH_WORD(ix,x); 59 60 /* |x| ~< pi/4 */ 61 ix &= 0x7fffffff; 62 if(ix <= 0x3fe921fb) { 63 if(ix<0x3e500000) /* |x| < 2**-26 */ 64 {if((int)x==0) return x;} /* generate inexact */ 65 return __kernel_sin(x,z,0); 66 } 67 68 /* sin(Inf or NaN) is NaN */ 69 else if (ix>=0x7ff00000) return x-x; 70 71 /* argument reduction needed */ 72 else { 73 n = __ieee754_rem_pio2(x,y); 74 switch(n&3) { 75 case 0: return __kernel_sin(y[0],y[1],1); 76 case 1: return __kernel_cos(y[0],y[1]); 77 case 2: return -__kernel_sin(y[0],y[1],1); 78 default: 79 return -__kernel_cos(y[0],y[1]); 80 } 81 } 82 } 83 84 #if (LDBL_MANT_DIG == 53) 85 __weak_reference(sin, sinl); 86 #endif 87