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author | Zack Weinberg <zackw@panix.com> | 2017-06-08 15:39:03 -0400 |
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committer | Zack Weinberg <zackw@panix.com> | 2017-06-08 15:39:03 -0400 |
commit | 5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 (patch) | |
tree | 4470480d904b65cf14ca524f96f79eca818c3eaf /REORG.TODO/sysdeps/ieee754/dbl-64/e_rem_pio2.c | |
parent | 199fc19d3aaaf57944ef036e15904febe877fc93 (diff) | |
download | glibc-5046dbb4a7eba5eccfd258f92f4735c9ffc8d069.tar.gz glibc-5046dbb4a7eba5eccfd258f92f4735c9ffc8d069.tar.xz glibc-5046dbb4a7eba5eccfd258f92f4735c9ffc8d069.zip |
Prepare for radical source tree reorganization. zack/build-layout-experiment
All top-level files and directories are moved into a temporary storage directory, REORG.TODO, except for files that will certainly still exist in their current form at top level when we're done (COPYING, COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which are moved to the new directory OldChangeLogs, instead), and the generated file INSTALL (which is just deleted; in the new order, there will be no generated files checked into version control).
Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/dbl-64/e_rem_pio2.c')
-rw-r--r-- | REORG.TODO/sysdeps/ieee754/dbl-64/e_rem_pio2.c | 193 |
1 files changed, 193 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_rem_pio2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_rem_pio2.c new file mode 100644 index 0000000000..2f55ca294b --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_rem_pio2.c @@ -0,0 +1,193 @@ +#ifdef NOT_NEEDED_ANYMORE + +/* + * ==================================================== + * 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. + * ==================================================== + */ + +/* __ieee754_rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include <math.h> +#include <math_private.h> + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +static const int32_t two_over_pi[] = { +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, +}; + +static const int32_t npio2_hw[] = { +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) + */ + +static const double + 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 */ + +int32_t +__ieee754_rem_pio2 (double x, double *y) +{ + double z, 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; +} +#endif |