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274 lines
8.2 KiB
C
274 lines
8.2 KiB
C
/* k_rem_pio2f.c -- float version of e_rem_pio2.c
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Copyright (C) 2011-2017 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Library General Public License as
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published by the Free Software Foundation; either version 2 of the
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License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Library General Public License for more details.
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You should have received a copy of the GNU Library General Public
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License along with the GNU C Library; see the file COPYING.LIB. If
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not, see <http://www.gnu.org/licenses/>. */
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#include <math.h>
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#include <math_private.h>
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#include "s_float_bitwise.h"
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static const float two_over_pi[] = {
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1.62000000e+02, 2.49000000e+02, 1.31000000e+02, 1.10000000e+02,
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7.80000000e+01, 6.80000000e+01, 2.10000000e+01, 4.10000000e+01,
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2.52000000e+02, 3.90000000e+01, 8.70000000e+01, 2.09000000e+02,
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2.45000000e+02, 5.20000000e+01, 2.21000000e+02, 1.92000000e+02,
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2.19000000e+02, 9.80000000e+01, 1.49000000e+02, 1.53000000e+02,
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6.00000000e+01, 6.70000000e+01, 1.44000000e+02, 6.50000000e+01,
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2.54000000e+02, 8.10000000e+01, 9.90000000e+01, 1.71000000e+02,
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2.22000000e+02, 1.87000000e+02, 1.97000000e+02, 9.70000000e+01,
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1.83000000e+02, 3.60000000e+01, 1.10000000e+02, 5.80000000e+01,
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6.60000000e+01, 7.70000000e+01, 2.10000000e+02, 2.24000000e+02,
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6.00000000e+00, 7.30000000e+01, 4.60000000e+01, 2.34000000e+02,
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9.00000000e+00, 2.09000000e+02, 1.46000000e+02, 2.80000000e+01,
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2.54000000e+02, 2.90000000e+01, 2.35000000e+02, 2.80000000e+01,
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1.77000000e+02, 4.10000000e+01, 1.67000000e+02, 6.20000000e+01,
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2.32000000e+02, 1.30000000e+02, 5.30000000e+01, 2.45000000e+02,
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4.60000000e+01, 1.87000000e+02, 6.80000000e+01, 1.32000000e+02,
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2.33000000e+02, 1.56000000e+02, 1.12000000e+02, 3.80000000e+01,
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1.80000000e+02, 9.50000000e+01, 1.26000000e+02, 6.50000000e+01,
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5.70000000e+01, 1.45000000e+02, 2.14000000e+02, 5.70000000e+01,
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1.31000000e+02, 8.30000000e+01, 5.70000000e+01, 2.44000000e+02,
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1.56000000e+02, 1.32000000e+02, 9.50000000e+01, 1.39000000e+02,
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1.89000000e+02, 2.49000000e+02, 4.00000000e+01, 5.90000000e+01,
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3.10000000e+01, 2.48000000e+02, 1.51000000e+02, 2.55000000e+02,
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2.22000000e+02, 5.00000000e+00, 1.52000000e+02, 1.50000000e+01,
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2.39000000e+02, 4.70000000e+01, 1.70000000e+01, 1.39000000e+02,
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9.00000000e+01, 1.00000000e+01, 1.09000000e+02, 3.10000000e+01,
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1.09000000e+02, 5.40000000e+01, 1.26000000e+02, 2.07000000e+02,
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3.90000000e+01, 2.03000000e+02, 9.00000000e+00, 1.83000000e+02,
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7.90000000e+01, 7.00000000e+01, 6.30000000e+01, 1.02000000e+02,
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1.58000000e+02, 9.50000000e+01, 2.34000000e+02, 4.50000000e+01,
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1.17000000e+02, 3.90000000e+01, 1.86000000e+02, 1.99000000e+02,
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2.35000000e+02, 2.29000000e+02, 2.41000000e+02, 1.23000000e+02,
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6.10000000e+01, 7.00000000e+00, 5.70000000e+01, 2.47000000e+02,
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1.38000000e+02, 8.20000000e+01, 1.46000000e+02, 2.34000000e+02,
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1.07000000e+02, 2.51000000e+02, 9.50000000e+01, 1.77000000e+02,
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3.10000000e+01, 1.41000000e+02, 9.30000000e+01, 8.00000000e+00,
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8.60000000e+01, 3.00000000e+00, 4.80000000e+01, 7.00000000e+01,
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2.52000000e+02, 1.23000000e+02, 1.07000000e+02, 1.71000000e+02,
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2.40000000e+02, 2.07000000e+02, 1.88000000e+02, 3.20000000e+01,
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1.54000000e+02, 2.44000000e+02, 5.40000000e+01, 2.90000000e+01,
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1.69000000e+02, 2.27000000e+02, 1.45000000e+02, 9.70000000e+01,
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9.40000000e+01, 2.30000000e+02, 2.70000000e+01, 8.00000000e+00,
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1.01000000e+02, 1.53000000e+02, 1.33000000e+02, 9.50000000e+01,
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2.00000000e+01, 1.60000000e+02, 1.04000000e+02, 6.40000000e+01,
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1.41000000e+02, 2.55000000e+02, 2.16000000e+02, 1.28000000e+02,
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7.70000000e+01, 1.15000000e+02, 3.90000000e+01, 4.90000000e+01,
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6.00000000e+00, 6.00000000e+00, 2.10000000e+01, 8.60000000e+01,
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2.02000000e+02, 1.15000000e+02, 1.68000000e+02, 2.01000000e+02,
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9.60000000e+01, 2.26000000e+02, 1.23000000e+02, 1.92000000e+02,
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1.40000000e+02, 1.07000000e+02
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};
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static const float PIo2[] = {
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1.5703125000e+00, /* 0x3fc90000 */
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4.5776367188e-04, /* 0x39f00000 */
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2.5987625122e-05, /* 0x37da0000 */
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7.5437128544e-08, /* 0x33a20000 */
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6.0026650317e-11, /* 0x2e840000 */
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7.3896444519e-13, /* 0x2b500000 */
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5.3845816694e-15, /* 0x27c20000 */
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5.6378512969e-18, /* 0x22d00000 */
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8.3009228831e-20, /* 0x1fc40000 */
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3.2756352257e-22, /* 0x1bc60000 */
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6.3331015649e-25, /* 0x17440000 */
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};
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static const float zero = 0.0000000000e+00;
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static const float one = 1.0000000000;
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static const float twon8 = 3.9062500000e-03;
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static const float two8 = 2.5600000000e+02;
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int32_t
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__fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx)
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{
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int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih, exp;
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float z, fw, f[20], fq[20], q[20];
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/* initialize jk */
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jp = jk = 9;
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/* determine jx,jv,q0, note that 3>q0 */
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jx = nx - 1;
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exp = __float_get_exp (e0) - 127;
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jv = (exp - 3) / 8;
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if (jv < 0)
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jv = 0;
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q0 = exp - 8 * (jv + 1);
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/* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */
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j = jv - jx;
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m = jx + jk;
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for (i = 0; i <= m; i++, j++)
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f[i] = (j < 0) ? zero : two_over_pi[j];
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/* compute q[0],q[1],...q[jk] */
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for (i = 0; i <= jk; i++)
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{
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for (j = 0, fw = 0.0; j <= jx; j++)
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fw += x[j] * f[jx + i - j];
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q[i] = fw;
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}
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jz = jk;
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recompute:
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/* distill q[] into iq[] reversingly */
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for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--)
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{
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fw = __truncf (twon8 * z);
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iq[i] = (int32_t) (z - two8 * fw);
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z = q[j - 1] + fw;
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}
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/* compute n */
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z = __scalbnf (z, q0); /* actual value of z */
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z -= 8.0 * __floorf (z * 0.125); /* trim off integer >= 8 */
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n = (int32_t) z;
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z -= __truncf (z);
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ih = 0;
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if (q0 > 0)
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{ /* need iq[jz-1] to determine n */
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i = (iq[jz - 1] >> (8 - q0));
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n += i;
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iq[jz - 1] -= i << (8 - q0);
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ih = iq[jz - 1] >> (7 - q0);
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}
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else if (q0 == 0)
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ih = iq[jz - 1] >> 7;
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else if (z >= 0.5)
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ih = 2;
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if (ih > 0)
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{ /* q > 0.5 */
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n += 1;
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carry = 0;
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for (i = 0; i < jz; i++)
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{ /* compute 1-q */
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j = iq[i];
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if (carry == 0)
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{
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if (j != 0)
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{
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carry = 1;
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iq[i] = 0x100 - j;
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}
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}
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else
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iq[i] = 0xff - j;
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}
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if (q0 > 0)
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{ /* rare case: chance is 1 in 12 */
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switch (q0)
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{
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case 1:
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iq[jz - 1] &= 0x7f;
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break;
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case 2:
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iq[jz - 1] &= 0x3f;
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break;
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}
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}
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if (ih == 2)
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{
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z = one - z;
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if (carry != 0)
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z -= __scalbnf (one, q0);
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}
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}
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/* check if recomputation is needed */
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if (z == zero)
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{
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j = 0;
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for (i = jz - 1; i >= jk; i--)
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j |= iq[i];
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if (j == 0)
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{ /* need recomputation */
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for (k = 1; iq[jk - k] == 0; k++); /* k = no. of terms needed */
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for (i = jz + 1; i <= jz + k; i++)
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{ /* add q[jz+1] to q[jz+k] */
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f[jx + i] = two_over_pi[jv + i];
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for (j = 0, fw = 0.0; j <= jx; j++)
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fw += x[j] * f[jx + i - j];
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q[i] = fw;
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}
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jz += k;
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goto recompute;
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}
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}
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/* chop off zero terms */
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if (z == 0.0)
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{
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jz -= 1;
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q0 -= 8;
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while (iq[jz] == 0)
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{
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jz--;
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q0 -= 8;
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}
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}
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else
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{ /* break z into 8-bit if necessary */
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z = __scalbnf (z, -q0);
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if (z >= two8)
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{
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fw = __truncf (twon8 * z);
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iq[jz] = (int32_t) (z - two8 * fw);
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jz += 1;
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q0 += 8;
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iq[jz] = (int32_t) fw;
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}
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else
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iq[jz] = (int32_t) z;
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}
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/* convert integer "bit" chunk to floating-point value */
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fw = __scalbnf (one, q0);
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for (i = jz; i >= 0; i--)
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{
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q[i] = fw * (float) iq[i];
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fw *= twon8;
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}
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/* compute PIo2[0,...,jp]*q[jz,...,0] */
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for (i = jz; i >= 0; i--)
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{
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for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++)
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fw += PIo2[k] * q[i + k];
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fq[jz - i] = fw;
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}
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/* compress fq[] into y[] */
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fw = 0.0;
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for (i = jz; i >= 0; i--)
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fw += fq[i];
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y[0] = (ih == 0) ? fw : -fw;
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fw = fq[0] - fw;
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for (i = 1; i <= jz; i++)
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fw += fq[i];
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y[1] = (ih == 0) ? fw : -fw;
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return n & 7;
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}
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