| /* k_rem_pio2f.c -- float version of e_rem_pio2.c |
| Copyright (C) 2011-2014 Free Software Foundation, Inc. |
| This file is part of the GNU C Library. |
| Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011 |
| |
| The GNU C Library is free software; you can redistribute it and/or |
| modify it under the terms of the GNU Library General Public License as |
| published by the Free Software Foundation; either version 2 of the |
| License, or (at your option) any later version. |
| |
| The GNU C Library is distributed in the hope that it will be useful, |
| but WITHOUT ANY WARRANTY; without even the implied warranty of |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| Library General Public License for more details. |
| |
| You should have received a copy of the GNU Library General Public |
| License along with the GNU C Library; see the file COPYING.LIB. If |
| not, see <http://www.gnu.org/licenses/>. */ |
| |
| #include <math.h> |
| |
| #include <math_private.h> |
| #include "s_float_bitwise.h" |
| |
| |
| static const float two_over_pi[] = { |
| 1.62000000e+02, 2.49000000e+02, 1.31000000e+02, 1.10000000e+02, |
| 7.80000000e+01, 6.80000000e+01, 2.10000000e+01, 4.10000000e+01, |
| 2.52000000e+02, 3.90000000e+01, 8.70000000e+01, 2.09000000e+02, |
| 2.45000000e+02, 5.20000000e+01, 2.21000000e+02, 1.92000000e+02, |
| 2.19000000e+02, 9.80000000e+01, 1.49000000e+02, 1.53000000e+02, |
| 6.00000000e+01, 6.70000000e+01, 1.44000000e+02, 6.50000000e+01, |
| 2.54000000e+02, 8.10000000e+01, 9.90000000e+01, 1.71000000e+02, |
| 2.22000000e+02, 1.87000000e+02, 1.97000000e+02, 9.70000000e+01, |
| 1.83000000e+02, 3.60000000e+01, 1.10000000e+02, 5.80000000e+01, |
| 6.60000000e+01, 7.70000000e+01, 2.10000000e+02, 2.24000000e+02, |
| 6.00000000e+00, 7.30000000e+01, 4.60000000e+01, 2.34000000e+02, |
| 9.00000000e+00, 2.09000000e+02, 1.46000000e+02, 2.80000000e+01, |
| 2.54000000e+02, 2.90000000e+01, 2.35000000e+02, 2.80000000e+01, |
| 1.77000000e+02, 4.10000000e+01, 1.67000000e+02, 6.20000000e+01, |
| 2.32000000e+02, 1.30000000e+02, 5.30000000e+01, 2.45000000e+02, |
| 4.60000000e+01, 1.87000000e+02, 6.80000000e+01, 1.32000000e+02, |
| 2.33000000e+02, 1.56000000e+02, 1.12000000e+02, 3.80000000e+01, |
| 1.80000000e+02, 9.50000000e+01, 1.26000000e+02, 6.50000000e+01, |
| 5.70000000e+01, 1.45000000e+02, 2.14000000e+02, 5.70000000e+01, |
| 1.31000000e+02, 8.30000000e+01, 5.70000000e+01, 2.44000000e+02, |
| 1.56000000e+02, 1.32000000e+02, 9.50000000e+01, 1.39000000e+02, |
| 1.89000000e+02, 2.49000000e+02, 4.00000000e+01, 5.90000000e+01, |
| 3.10000000e+01, 2.48000000e+02, 1.51000000e+02, 2.55000000e+02, |
| 2.22000000e+02, 5.00000000e+00, 1.52000000e+02, 1.50000000e+01, |
| 2.39000000e+02, 4.70000000e+01, 1.70000000e+01, 1.39000000e+02, |
| 9.00000000e+01, 1.00000000e+01, 1.09000000e+02, 3.10000000e+01, |
| 1.09000000e+02, 5.40000000e+01, 1.26000000e+02, 2.07000000e+02, |
| 3.90000000e+01, 2.03000000e+02, 9.00000000e+00, 1.83000000e+02, |
| 7.90000000e+01, 7.00000000e+01, 6.30000000e+01, 1.02000000e+02, |
| 1.58000000e+02, 9.50000000e+01, 2.34000000e+02, 4.50000000e+01, |
| 1.17000000e+02, 3.90000000e+01, 1.86000000e+02, 1.99000000e+02, |
| 2.35000000e+02, 2.29000000e+02, 2.41000000e+02, 1.23000000e+02, |
| 6.10000000e+01, 7.00000000e+00, 5.70000000e+01, 2.47000000e+02, |
| 1.38000000e+02, 8.20000000e+01, 1.46000000e+02, 2.34000000e+02, |
| 1.07000000e+02, 2.51000000e+02, 9.50000000e+01, 1.77000000e+02, |
| 3.10000000e+01, 1.41000000e+02, 9.30000000e+01, 8.00000000e+00, |
| 8.60000000e+01, 3.00000000e+00, 4.80000000e+01, 7.00000000e+01, |
| 2.52000000e+02, 1.23000000e+02, 1.07000000e+02, 1.71000000e+02, |
| 2.40000000e+02, 2.07000000e+02, 1.88000000e+02, 3.20000000e+01, |
| 1.54000000e+02, 2.44000000e+02, 5.40000000e+01, 2.90000000e+01, |
| 1.69000000e+02, 2.27000000e+02, 1.45000000e+02, 9.70000000e+01, |
| 9.40000000e+01, 2.30000000e+02, 2.70000000e+01, 8.00000000e+00, |
| 1.01000000e+02, 1.53000000e+02, 1.33000000e+02, 9.50000000e+01, |
| 2.00000000e+01, 1.60000000e+02, 1.04000000e+02, 6.40000000e+01, |
| 1.41000000e+02, 2.55000000e+02, 2.16000000e+02, 1.28000000e+02, |
| 7.70000000e+01, 1.15000000e+02, 3.90000000e+01, 4.90000000e+01, |
| 6.00000000e+00, 6.00000000e+00, 2.10000000e+01, 8.60000000e+01, |
| 2.02000000e+02, 1.15000000e+02, 1.68000000e+02, 2.01000000e+02, |
| 9.60000000e+01, 2.26000000e+02, 1.23000000e+02, 1.92000000e+02, |
| 1.40000000e+02, 1.07000000e+02 |
| }; |
| |
| |
| static const float PIo2[] = { |
| 1.5703125000e+00, /* 0x3fc90000 */ |
| 4.5776367188e-04, /* 0x39f00000 */ |
| 2.5987625122e-05, /* 0x37da0000 */ |
| 7.5437128544e-08, /* 0x33a20000 */ |
| 6.0026650317e-11, /* 0x2e840000 */ |
| 7.3896444519e-13, /* 0x2b500000 */ |
| 5.3845816694e-15, /* 0x27c20000 */ |
| 5.6378512969e-18, /* 0x22d00000 */ |
| 8.3009228831e-20, /* 0x1fc40000 */ |
| 3.2756352257e-22, /* 0x1bc60000 */ |
| 6.3331015649e-25, /* 0x17440000 */ |
| }; |
| |
| |
| static const float zero = 0.0000000000e+00; |
| static const float one = 1.0000000000; |
| static const float twon8 = 3.9062500000e-03; |
| static const float two8 = 2.5600000000e+02; |
| |
| |
| int32_t |
| __fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx) |
| { |
| int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih, exp; |
| float z, fw, f[20], fq[20], q[20]; |
| |
| /* initialize jk */ |
| jp = jk = 9; |
| |
| /* determine jx,jv,q0, note that 3>q0 */ |
| jx = nx - 1; |
| exp = __float_get_exp (e0) - 127; |
| jv = (exp - 3) / 8; |
| if (jv < 0) |
| jv = 0; |
| q0 = exp - 8 * (jv + 1); |
| |
| /* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */ |
| j = jv - jx; |
| m = jx + jk; |
| for (i = 0; i <= m; i++, j++) |
| f[i] = (j < 0) ? zero : two_over_pi[j]; |
| |
| /* compute q[0],q[1],...q[jk] */ |
| for (i = 0; i <= jk; i++) |
| { |
| for (j = 0, fw = 0.0; j <= jx; j++) |
| fw += x[j] * f[jx + i - j]; |
| q[i] = fw; |
| } |
| |
| jz = jk; |
| recompute: |
| /* distill q[] into iq[] reversingly */ |
| for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--) |
| { |
| fw = __truncf (twon8 * z); |
| iq[i] = (int32_t) (z - two8 * fw); |
| z = q[j - 1] + fw; |
| } |
| |
| /* compute n */ |
| z = __scalbnf (z, q0); /* actual value of z */ |
| z -= 8.0 * __floorf (z * 0.125); /* trim off integer >= 8 */ |
| n = (int32_t) z; |
| z -= __truncf (z); |
| ih = 0; |
| if (q0 > 0) |
| { /* need iq[jz-1] to determine n */ |
| i = (iq[jz - 1] >> (8 - q0)); |
| n += i; |
| iq[jz - 1] -= i << (8 - q0); |
| ih = iq[jz - 1] >> (7 - q0); |
| } |
| else if (q0 == 0) |
| ih = iq[jz - 1] >> 7; |
| else if (z >= 0.5) |
| ih = 2; |
| |
| if (ih > 0) |
| { /* q > 0.5 */ |
| n += 1; |
| carry = 0; |
| for (i = 0; i < jz; i++) |
| { /* compute 1-q */ |
| j = iq[i]; |
| if (carry == 0) |
| { |
| if (j != 0) |
| { |
| carry = 1; |
| iq[i] = 0x100 - j; |
| } |
| } |
| else |
| iq[i] = 0xff - j; |
| } |
| if (q0 > 0) |
| { /* rare case: chance is 1 in 12 */ |
| switch (q0) |
| { |
| case 1: |
| iq[jz - 1] &= 0x7f; |
| break; |
| case 2: |
| iq[jz - 1] &= 0x3f; |
| break; |
| } |
| } |
| if (ih == 2) |
| { |
| z = one - z; |
| if (carry != 0) |
| z -= __scalbnf (one, q0); |
| } |
| } |
| |
| /* check if recomputation is needed */ |
| if (z == zero) |
| { |
| j = 0; |
| for (i = jz - 1; i >= jk; i--) |
| j |= iq[i]; |
| if (j == 0) |
| { /* need recomputation */ |
| for (k = 1; iq[jk - k] == 0; k++); /* k = no. of terms needed */ |
| |
| for (i = jz + 1; i <= jz + k; i++) |
| { /* add q[jz+1] to q[jz+k] */ |
| f[jx + i] = two_over_pi[jv + i]; |
| for (j = 0, fw = 0.0; j <= jx; j++) |
| fw += x[j] * f[jx + i - j]; |
| q[i] = fw; |
| } |
| jz += k; |
| goto recompute; |
| } |
| } |
| |
| /* chop off zero terms */ |
| if (z == 0.0) |
| { |
| jz -= 1; |
| q0 -= 8; |
| while (iq[jz] == 0) |
| { |
| jz--; |
| q0 -= 8; |
| } |
| } |
| else |
| { /* break z into 8-bit if necessary */ |
| z = __scalbnf (z, -q0); |
| if (z >= two8) |
| { |
| fw = __truncf (twon8 * z); |
| iq[jz] = (int32_t) (z - two8 * fw); |
| jz += 1; |
| q0 += 8; |
| iq[jz] = (int32_t) fw; |
| } |
| else |
| iq[jz] = (int32_t) z; |
| } |
| |
| /* convert integer "bit" chunk to floating-point value */ |
| fw = __scalbnf (one, q0); |
| for (i = jz; i >= 0; i--) |
| { |
| q[i] = fw * (float) iq[i]; |
| fw *= twon8; |
| } |
| |
| /* compute PIo2[0,...,jp]*q[jz,...,0] */ |
| for (i = jz; i >= 0; i--) |
| { |
| for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++) |
| fw += PIo2[k] * q[i + k]; |
| fq[jz - i] = fw; |
| } |
| |
| /* compress fq[] into y[] */ |
| fw = 0.0; |
| for (i = jz; i >= 0; i--) |
| fw += fq[i]; |
| y[0] = (ih == 0) ? fw : -fw; |
| fw = fq[0] - fw; |
| for (i = 1; i <= jz; i++) |
| fw += fq[i]; |
| y[1] = (ih == 0) ? fw : -fw; |
| |
| return n & 7; |
| } |