2 /* @(#)e_rem_pio2.c 1.4 95/01/18 */
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
11 * ====================================================
13 * Optimized by Bruce D. Evans.
16 #include <sys/cdefs.h>
17 __FBSDID("$FreeBSD$");
19 /* __ieee754_rem_pio2(x,y)
21 * return the remainder of x rem pi/2 in y[0]+y[1]
22 * use __kernel_rem_pio2()
28 #include "math_private.h"
31 * invpio2: 53 bits of 2/pi
32 * pio2_1: first 33 bit of pi/2
33 * pio2_1t: pi/2 - pio2_1
34 * pio2_2: second 33 bit of pi/2
35 * pio2_2t: pi/2 - (pio2_1+pio2_2)
36 * pio2_3: third 33 bit of pi/2
37 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
41 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
42 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
43 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
44 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
45 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
46 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
47 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
48 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
49 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
51 #ifdef INLINE_REM_PIO2
52 static __inline __always_inline
55 __ieee754_rem_pio2(double x, double *y)
59 int32_t e0,i,j,nx,n,ix,hx;
62 GET_HIGH_WORD(hx,x); /* high word of x */
64 #if 0 /* Must be handled in caller. */
65 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
66 {y[0] = x; y[1] = 0; return 0;}
68 if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */
69 if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */
70 goto medium; /* cancellation -- use medium case */
71 if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */
73 z = x - pio2_1; /* one round good to 85 bits */
75 y[1] = (z-y[0])-pio2_1t;
80 y[1] = (z-y[0])+pio2_1t;
87 y[1] = (z-y[0])-2*pio2_1t;
92 y[1] = (z-y[0])+2*pio2_1t;
97 if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */
98 if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */
99 if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */
103 y[0] = z - 3*pio2_1t;
104 y[1] = (z-y[0])-3*pio2_1t;
108 y[0] = z + 3*pio2_1t;
109 y[1] = (z-y[0])+3*pio2_1t;
113 if (ix == 0x401921fb) /* |x| ~= 4pi/2 */
117 y[0] = z - 4*pio2_1t;
118 y[1] = (z-y[0])-4*pio2_1t;
122 y[0] = z + 4*pio2_1t;
123 y[1] = (z-y[0])+4*pio2_1t;
128 if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
130 /* Use a specialized rint() to get fn. Assume round-to-nearest. */
131 STRICT_ASSIGN(double,fn,x*invpio2+0x1.8p52);
133 #ifdef HAVE_EFFICIENT_IRINT
139 w = fn*pio2_1t; /* 1st round good to 85 bit */
144 GET_HIGH_WORD(high,y[0]);
145 i = j-((high>>20)&0x7ff);
146 if(i>16) { /* 2nd iteration needed, good to 118 */
150 w = fn*pio2_2t-((t-r)-w);
152 GET_HIGH_WORD(high,y[0]);
153 i = j-((high>>20)&0x7ff);
154 if(i>49) { /* 3rd iteration need, 151 bits acc */
155 t = r; /* will cover all possible cases */
158 w = fn*pio2_3t-((t-r)-w);
167 * all other (large) arguments
169 if(ix>=0x7ff00000) { /* x is inf or NaN */
170 y[0]=y[1]=x-x; return 0;
172 /* set z = scalbn(|x|,ilogb(x)-23) */
174 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
175 INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low);
177 tx[i] = (double)((int32_t)(z));
182 while(tx[nx-1]==zero) nx--; /* skip zero term */
183 n = __kernel_rem_pio2(tx,ty,e0,nx,1);
184 if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;}
185 y[0] = ty[0]; y[1] = ty[1]; return n;