1 /* e_rem_pio2f.c -- float version of e_rem_pio2.c
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 * Conversion to not use float except for the arg by Bruce Evans.
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
14 * ====================================================
18 static char rcsid[] = "$FreeBSD$";
21 /* __ieee754_rem_pio2f(x,y)
23 * return the remainder of x rem pi/2 in y[0]+y[1]
24 * use __kernel_rem_pio2f()
28 #include "math_private.h"
31 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
33 static const int32_t two_over_pi[] = {
34 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
35 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
36 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
37 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
38 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
39 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
40 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
41 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
42 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
43 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
44 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
48 * invpio2: 53 bits of 2/pi
49 * pio2_1: first 33 bit of pi/2
50 * pio2_1t: pi/2 - pio2_1
54 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
55 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
56 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
57 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
58 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
59 pio2_1t = 6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */
61 int32_t __ieee754_rem_pio2f(float x, float *y)
65 int32_t e0,i,nx,n,ix,hx;
69 if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
70 {y[0] = x; y[1] = 0; return 0;}
71 /* 33+53 bit pi is good enough for special and medium size cases */
72 if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
76 y[1] = (z-y[0])-pio2_1t;
78 } else { /* negative x */
81 y[1] = (z-y[0])+pio2_1t;
85 if(ix<=0x49490f80) { /* |x| ~<= 2^19*(pi/2), medium size */
87 n = (int32_t) (t*invpio2+half);
93 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
97 * all other (large) arguments
99 if(ix>=0x7f800000) { /* x is inf or NaN */
100 y[0]=y[1]=x-x; return 0;
102 /* set z = scalbn(|x|,ilogb(x)-23) */
106 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
107 SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
109 tx[i] = (double)((int32_t)(z));
114 while(tx[nx-1]==zero) nx--; /* skip zero term */
115 n = __kernel_rem_pio2(tx,&z,e0,nx,1,two_over_pi);
118 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}