34  *    threshold is |x| < 0x1pN with N = -(P/2+M).  P is the precision of the
43  * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where
45  *    0 <= r < 1.  With the given domain, a simplified inline floor(x)
56  * 4. For |x| >= 0x1p(P-1), |x| is integral and sinpi(x) = copysign(0,x).
60  *    sinpi(+-0) = +-0
61  *    sinpi(+-n) = +-0, for positive integers n.
71 pi_hi = 3.1415926814079285e+00,	/* 0x400921fb 0x58000000 */
72 pi_lo =-2.7818135228334233e-08;	/* 0xbe5dde97 0x3dcb3b3a */
77 volatile static const double vzero = 0;
86 	ix = hx & 0x7fffffff;  in sinpi()
89 	if (ix < 0x3ff00000) {			/* |x| < 1 */  in sinpi()
90 		if (ix < 0x3fd00000) {		/* |x| < 0.25 */  in sinpi()
91 			if (ix < 0x3e200000) {	/* |x| < 0x1p-29 */  in sinpi()
92 				if (x == 0)  in sinpi()
99 				INSERT_WORDS(hi, hx, 0);  in sinpi()
100 				hi *= 0x1p53;  in sinpi()
101 				lo = x * 0x1p53 - hi;  in sinpi()
104 				return (s * 0x1p-53);  in sinpi()
108 			return ((hx & 0x80000000) ? -s : s);  in sinpi()
111 		if (ix < 0x3fe00000)		/* |x| < 0.5 */  in sinpi()
113 		else if (ix < 0x3fe80000)	/* |x| < 0.75 */  in sinpi()
117 		return ((hx & 0x80000000) ? -s : s);  in sinpi()
120 	if (ix < 0x43300000) {			/* 1 <= |x| < 0x1p52 */  in sinpi()
125 		if (ix == 0)  in sinpi()
126 			s = 0;  in sinpi()
128 			if (ix < 0x3fe00000) {		/* |x| < 0.5 */  in sinpi()
129 				if (ix < 0x3fd00000)	/* |x| < 0.25 */  in sinpi()
134 				if (ix < 0x3fe80000)	/* |x| < 0.75 */  in sinpi()
141 				x -= 0x1p30;  in sinpi()
146 		return ((hx & 0x80000000) ? -s : s);  in sinpi()
150 	if (ix >= 0x7ff00000)  in sinpi()
154 	 * |x| >= 0x1p52 is always an integer, so return +-0.  in sinpi()
156 	return (copysign(0, x));  in sinpi()