| /* @(#)e_rem_pio2.c 5.1 93/09/24 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #if defined(LIBM_SCCS) && !defined(lint) |
| static const char rcsid[] = |
| "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $"; |
| #endif |
| |
| /* __ieee754_rem_pio2(x,y) |
| * |
| * return the remainder of x rem pi/2 in y[0]+y[1] |
| * use __kernel_rem_pio2() |
| */ |
| |
| #include "math_libm.h" |
| #include "math_private.h" |
| |
| libm_hidden_proto(fabs) |
| |
| /* |
| * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
| */ |
| #ifdef __STDC__ |
| static const int32_t two_over_pi[] = { |
| #else |
| static int32_t two_over_pi[] = { |
| #endif |
| 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, |
| 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, |
| 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, |
| 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, |
| 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, |
| 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, |
| 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, |
| 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, |
| 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, |
| 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, |
| 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, |
| }; |
| |
| #ifdef __STDC__ |
| static const int32_t npio2_hw[] = { |
| #else |
| static int32_t npio2_hw[] = { |
| #endif |
| 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, |
| 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, |
| 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, |
| 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, |
| 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, |
| 0x404858EB, 0x404921FB, |
| }; |
| |
| /* |
| * invpio2: 53 bits of 2/pi |
| * pio2_1: first 33 bit of pi/2 |
| * pio2_1t: pi/2 - pio2_1 |
| * pio2_2: second 33 bit of pi/2 |
| * pio2_2t: pi/2 - (pio2_1+pio2_2) |
| * pio2_3: third 33 bit of pi/2 |
| * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) |
| */ |
| |
| #ifdef __STDC__ |
| static const double |
| #else |
| static double |
| #endif |
| zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
| half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
| two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ |
| invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
| pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ |
| pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ |
| pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ |
| pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ |
| pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ |
| pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ |
| |
| #ifdef __STDC__ |
| int32_t attribute_hidden |
| __ieee754_rem_pio2(double x, double *y) |
| #else |
| int32_t attribute_hidden |
| __ieee754_rem_pio2(x, y) |
| double x, y[]; |
| #endif |
| { |
| double z = 0.0, w, t, r, fn; |
| double tx[3]; |
| int32_t e0, i, j, nx, n, ix, hx; |
| u_int32_t low; |
| |
| GET_HIGH_WORD(hx, x); /* high word of x */ |
| ix = hx & 0x7fffffff; |
| if (ix <= 0x3fe921fb) { /* |x| ~<= pi/4 , no need for reduction */ |
| y[0] = x; |
| y[1] = 0; |
| return 0; |
| } |
| if (ix < 0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ |
| if (hx > 0) { |
| z = x - pio2_1; |
| if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */ |
| y[0] = z - pio2_1t; |
| y[1] = (z - y[0]) - pio2_1t; |
| } else { /* near pi/2, use 33+33+53 bit pi */ |
| z -= pio2_2; |
| y[0] = z - pio2_2t; |
| y[1] = (z - y[0]) - pio2_2t; |
| } |
| return 1; |
| } else { /* negative x */ |
| z = x + pio2_1; |
| if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */ |
| y[0] = z + pio2_1t; |
| y[1] = (z - y[0]) + pio2_1t; |
| } else { /* near pi/2, use 33+33+53 bit pi */ |
| z += pio2_2; |
| y[0] = z + pio2_2t; |
| y[1] = (z - y[0]) + pio2_2t; |
| } |
| return -1; |
| } |
| } |
| if (ix <= 0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ |
| t = fabs(x); |
| n = (int32_t) (t * invpio2 + half); |
| fn = (double) n; |
| r = t - fn * pio2_1; |
| w = fn * pio2_1t; /* 1st round good to 85 bit */ |
| if (n < 32 && ix != npio2_hw[n - 1]) { |
| y[0] = r - w; /* quick check no cancellation */ |
| } else { |
| u_int32_t high; |
| j = ix >> 20; |
| y[0] = r - w; |
| GET_HIGH_WORD(high, y[0]); |
| i = j - ((high >> 20) & 0x7ff); |
| if (i > 16) { /* 2nd iteration needed, good to 118 */ |
| t = r; |
| w = fn * pio2_2; |
| r = t - w; |
| w = fn * pio2_2t - ((t - r) - w); |
| y[0] = r - w; |
| GET_HIGH_WORD(high, y[0]); |
| i = j - ((high >> 20) & 0x7ff); |
| if (i > 49) { /* 3rd iteration need, 151 bits acc */ |
| t = r; /* will cover all possible cases */ |
| w = fn * pio2_3; |
| r = t - w; |
| w = fn * pio2_3t - ((t - r) - w); |
| y[0] = r - w; |
| } |
| } |
| } |
| y[1] = (r - y[0]) - w; |
| if (hx < 0) { |
| y[0] = -y[0]; |
| y[1] = -y[1]; |
| return -n; |
| } else |
| return n; |
| } |
| /* |
| * all other (large) arguments |
| */ |
| if (ix >= 0x7ff00000) { /* x is inf or NaN */ |
| y[0] = y[1] = x - x; |
| return 0; |
| } |
| /* set z = scalbn(|x|,ilogb(x)-23) */ |
| GET_LOW_WORD(low, x); |
| SET_LOW_WORD(z, low); |
| e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */ |
| SET_HIGH_WORD(z, ix - ((int32_t) (e0 << 20))); |
| for (i = 0; i < 2; i++) { |
| tx[i] = (double) ((int32_t) (z)); |
| z = (z - tx[i]) * two24; |
| } |
| tx[2] = z; |
| nx = 3; |
| while (tx[nx - 1] == zero) |
| nx--; /* skip zero term */ |
| n = __kernel_rem_pio2(tx, y, e0, nx, 2, two_over_pi); |
| if (hx < 0) { |
| y[0] = -y[0]; |
| y[1] = -y[1]; |
| return -n; |
| } |
| return n; |
| } |
