about summary refs log tree commit diff
path: root/sysdeps/powerpc/fpu/e_rem_pio2f.c
blob: f277f862446d79c0a6137e2a166e898196b46443 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
/* e_rem_pio2f.c -- float version of e_rem_pio2.c
   Copyright (C) 2011-2015 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"

/* defined in sysdeps/powerpc/fpu/k_rem_pio2f.c */
int __fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx);

/* __ieee754_rem_pio2f(x,y)
 *
 * return the remainder of x rem pi/2 in y[0]+y[1]
 */

static const float npio2_hw[] = {
  1.57077026e+00, 3.14154053e+00, 4.71228027e+00, 6.28308105e+00,
  7.85388184e+00, 9.42456055e+00, 1.09953613e+01, 1.25661621e+01,
  1.41369629e+01, 1.57077637e+01, 1.72783203e+01, 1.88491211e+01,
  2.04199219e+01, 2.19907227e+01, 2.35615234e+01, 2.51323242e+01,
  2.67031250e+01, 2.82739258e+01, 2.98447266e+01, 3.14155273e+01,
  3.29863281e+01, 3.45566406e+01, 3.61279297e+01, 3.76982422e+01,
  3.92695312e+01, 4.08398438e+01, 4.24111328e+01, 4.39814453e+01,
  4.55527344e+01, 4.71230469e+01, 4.86943359e+01, 5.02646484e+01
};


static const float zero  = 0.0000000000e+00;
static const float two8  = 2.5600000000e+02;

static const float half    = 5.0000000000e-01;
static const float invpio2 = 6.3661980629e-01;
static const float pio2_1  = 1.5707855225e+00;
static const float pio2_1t = 1.0804334124e-05;
static const float pio2_2  = 1.0804273188e-05;
static const float pio2_2t = 6.0770999344e-11;
static const float pio2_3  = 6.0770943833e-11;
static const float pio2_3t = 6.1232342629e-17;

static const float pio4     = 7.8539801e-01;
static const float pio3_4   = 2.3561945e+00;
static const float pio2_24b = 1.5707951e+00;
static const float pio2_2e7 = 2.0106054e+02;


int32_t
__ieee754_rem_pio2f (float x, float *y)
{
  float ax, z, n, r, w, t, e0;
  float tx[3];
  int32_t i, nx;

  ax = __builtin_fabsf (x);
  if (ax <= pio4)
    {
      y[0] = x;
      y[1] = 0;
      return 0;
    }
  if (ax < pio3_4)
    {
      if (x > 0)
	{
	  z = x - pio2_1;
	  if (!__float_and_test28 (ax, pio2_24b))
	    {
	      y[0] = z - pio2_1t;
	      y[1] = (z - y[0]) - pio2_1t;
	    }
	  else
	    {
	      z -= pio2_2;
	      y[0] = z - pio2_2t;
	      y[1] = (z - y[0]) - pio2_2t;
	    }
	  return 1;
	}
      else
	{
	  z = x + pio2_1;
	  if (!__float_and_test28 (ax, pio2_24b))
	    {
	      y[0] = z + pio2_1t;
	      y[1] = (z - y[0]) + pio2_1t;
	    }
	  else
	    {
	      z += pio2_2;
	      y[0] = z + pio2_2t;
	      y[1] = (z - y[0]) + pio2_2t;
	    }
	  return -1;
	}
    }
  if (ax <= pio2_2e7)
    {
      n = __floorf (ax * invpio2 + half);
      i = (int32_t) n;
      r = ax - n * pio2_1;
      w = n * pio2_1t;		/* 1st round good to 40 bit */
      if (i < 32 && !__float_and_test24 (ax, npio2_hw[i - 1]))
	{
	  y[0] = r - w;
	}
      else
	{
	  float i, j;
	  j = __float_and8 (ax);
	  y[0] = r - w;
	  i = __float_and8 (y[0]);
	  if (j / i > 256.0 || j / i < 3.9062500e-3)
	    {			/* 2nd iterations needed, good to 57 */
	      t = r;
	      w = n * pio2_2;
	      r = t - w;
	      w = n * pio2_2t - ((t - r) - w);
	      y[0] = r - w;
	      i = __float_and8 (y[0]);
	      if (j / i > 33554432 || j / i < 2.9802322e-8)
		{		/* 3rd iteration needed, 74 bits acc */
		  t = r;
		  w = n * pio2_3;
		  r = t - w;
		  w = n * pio2_3t - ((t - r) - w);
		  y[0] = r - w;
		}
	    }
	}
      y[1] = (r - y[0]) - w;
      if (x < 0)
	{
	  y[0] = -y[0];
	  y[1] = -y[1];
	  return -i;
	}
      else
	{
	  return i;
	}
    }

  /* all other (large) arguments */
  if (isnanf (x) || isinff (x))
    {
      y[0] = y[1] = x - x;
      return 0;
    }

  /* set z = scalbn(|x|,ilogb(x)-7) */
  e0 = __float_and8 (ax / 128.0);
  z = ax / e0;

  tx[0] = __floorf (z);
  z = (z - tx[0]) * two8;
  tx[1] = __floorf (z);
  z = (z - tx[1]) * two8;
  tx[2] = __floorf (z);

  nx = 3;
  while (tx[nx - 1] == zero)
    nx--;

  i = __fp_kernel_rem_pio2f (tx, y, e0, nx);
  if (x < 0)
    {
      y[0] = -y[0];
      y[1] = -y[1];
      return -i;
    }
  return i;
}