Lines Matching +full:high +full:- +full:accuracy

1 /*-
29  * note that tanpi(-x) = -tanpi(x), so the algorithm considers only |x| and
34  *    threshold is |x| < 0x1pN with N = -(P/2+M).  P is the precision of the
35  *    floating-point type and M = 2 to 4.  To achieve high accuracy, pi is
36  *    decomposed into high and low parts with the high part containing a
37  *    number of trailing zero bits.  x is also split into high and low parts.
43  * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where
49  *    tanpi(x) = tan(pi*(j0+r)) = ---------------------------- = tanpi(r)
50  *                                 1 - tan(pi*j0) * tan(pi*r)
54  * 4. For |x| >= 0x1p(P-1), |x| is integral and tanpi(x) = copysign(0,x).
58  *    tanpi(+-0) = +-0
60  *    tanpi(n) = -0 for positive odd and negative even integer n.
61  *    tanpi(+-n+1/4) = +-1, for positive integers n.
64  *    tanpi(n+1/2) = -inf and raises the FE_DIVBYZERO exception for 
66  *    tanpi(+-inf) = NaN and raises the FE_INVALID exception.
76 pi_lo = -2.7818135228334233e-08;	/* 0xbe5dde97 0x3dcb3b3a */
79  * The kernel for tanpi(x) multiplies x by an 80-bit approximation of
89 		lo = x - hi;  in __kernel_tanpi()
95 		x = 0.5 - x;  in __kernel_tanpi()
97 		lo = x - hi;  in __kernel_tanpi()
101 		t = - __kernel_tan(hi, lo, -1);  in __kernel_tanpi()
122 			if (ix < 0x3e200000) {	/* |x| < 0x1p-29 */  in tanpi()
132 				lo = x * 0x1p53 - hi;  in tanpi()
135 				return (t * 0x1p-53);  in tanpi()
141 			t = - __kernel_tanpi(1 - ax);  in tanpi()
142 		return ((hx & 0x80000000) ? -t : t);  in tanpi()
147 		odd = (uint64_t)x & 1 ? -1 : 1;  in tanpi()
148 		ax -= x;  in tanpi()
156 			t = - __kernel_tanpi(1 - ax);  in tanpi()
158 		return ((hx & 0x80000000) ? -t : t);  in tanpi()
161 	/* x = +-inf or nan. */  in tanpi()
167 	 * or odd integer to set t = +0 or -0.  in tanpi()
170 	t = ix >= 0x43400000 ? 0 : (copysign(0, (lx & 1) ? -1 : 1));  in tanpi()
171 	return ((hx & 0x80000000) ? -t : t);  in tanpi()