about summary refs log tree commit diff
path: root/sysdeps/ieee754/flt-32/s_sinf.c
blob: 8b98573ae476013f7264d8b09f86e126ccb9dde5 (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
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
/* Compute sine of argument.
   Copyright (C) 2017 Free Software Foundation, Inc.
   This file is part of the GNU C Library.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 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
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <http://www.gnu.org/licenses/>.  */

#include <errno.h>
#include <math.h>
#include <math_private.h>
#include <libm-alias-float.h>

#ifndef SINF
# define SINF_FUNC __sinf
#else
# define SINF_FUNC SINF
#endif

/* Chebyshev constants for cos, range -PI/4 - PI/4.  */
static const double C0 = -0x1.ffffffffe98aep-2;
static const double C1 =  0x1.55555545c50c7p-5;
static const double C2 = -0x1.6c16b348b6874p-10;
static const double C3 =  0x1.a00eb9ac43ccp-16;
static const double C4 = -0x1.23c97dd8844d7p-22;

/* Chebyshev constants for sin, range -PI/4 - PI/4.  */
static const double S0 = -0x1.5555555551cd9p-3;
static const double S1 =  0x1.1111110c2688bp-7;
static const double S2 = -0x1.a019f8b4bd1f9p-13;
static const double S3 =  0x1.71d7264e6b5b4p-19;
static const double S4 = -0x1.a947e1674b58ap-26;

/* Chebyshev constants for sin, range 2^-27 - 2^-5.  */
static const double SS0 = -0x1.555555543d49dp-3;
static const double SS1 =  0x1.110f475cec8c5p-7;

/* PI/2 with 98 bits of accuracy.  */
static const double PI_2_hi = -0x1.921fb544p+0;
static const double PI_2_lo = -0x1.0b4611a626332p-34;

static const double SMALL = 0x1p-50; /* 2^-50.  */
static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI.  */

#define FLOAT_EXPONENT_SHIFT 23
#define FLOAT_EXPONENT_BIAS 127

static const double pio2_table[] = {
  0 * M_PI_2,
  1 * M_PI_2,
  2 * M_PI_2,
  3 * M_PI_2,
  4 * M_PI_2,
  5 * M_PI_2
};

static const double invpio4_table[] = {
  0x0p+0,
  0x1.45f306cp+0,
  0x1.c9c882ap-28,
  0x1.4fe13a8p-58,
  0x1.f47d4dp-85,
  0x1.bb81b6cp-112,
  0x1.4acc9ep-142,
  0x1.0e4107cp-169
};

static const int ones[] = { +1, -1 };

/* Compute the sine value using Chebyshev polynomials where
   THETA is the range reduced absolute value of the input
   and it is less than Pi/4,
   N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
   whether a sine or cosine approximation is more accurate and
   SIGNBIT is used to add the correct sign after the Chebyshev
   polynomial is computed.  */
static inline float
reduced (const double theta, const unsigned int n,
	 const unsigned int signbit)
{
  double sx;
  const double theta2 = theta * theta;
  /* We are operating on |x|, so we need to add back the original
     signbit for sinf.  */
  int sign;
  /* Determine positive or negative primary interval.  */
  sign = ones[((n >> 2) & 1) ^ signbit];
  /* Are we in the primary interval of sin or cos?  */
  if ((n & 2) == 0)
    {
      /* Here sinf() is calculated using sin Chebyshev polynomial:
	x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */
      sx = S3 + theta2 * S4;     /* S3+x^2*S4.  */
      sx = S2 + theta2 * sx;     /* S2+x^2*(S3+x^2*S4).  */
      sx = S1 + theta2 * sx;     /* S1+x^2*(S2+x^2*(S3+x^2*S4)).  */
      sx = S0 + theta2 * sx;     /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))).  */
      sx = theta + theta * theta2 * sx;
    }
  else
    {
     /* Here sinf() is calculated using cos Chebyshev polynomial:
	1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).  */
      sx = C3 + theta2 * C4;     /* C3+x^2*C4.  */
      sx = C2 + theta2 * sx;     /* C2+x^2*(C3+x^2*C4).  */
      sx = C1 + theta2 * sx;     /* C1+x^2*(C2+x^2*(C3+x^2*C4)).  */
      sx = C0 + theta2 * sx;     /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))).  */
      sx = 1.0 + theta2 * sx;
    }

  /* Add in the signbit and assign the result.  */
  return sign * sx;
}

float
SINF_FUNC (float x)
{
  double cx;
  double theta = x;
  double abstheta = fabs (theta);
  /* If |x|< Pi/4.  */
  if (isless (abstheta, M_PI_4))
    {
      if (abstheta >= 0x1p-5) /* |x| >= 2^-5.  */
	{
	  const double theta2 = theta * theta;
	  /* Chebyshev polynomial of the form for sin
	     x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */
	  cx = S3 + theta2 * S4;
	  cx = S2 + theta2 * cx;
	  cx = S1 + theta2 * cx;
	  cx = S0 + theta2 * cx;
	  cx = theta + theta * theta2 * cx;
	  return cx;
	}
      else if (abstheta >= 0x1p-27)     /* |x| >= 2^-27.  */
	{
	  /* A simpler Chebyshev approximation is close enough for this range:
	     for sin: x+x^3*(SS0+x^2*SS1).  */
	  const double theta2 = theta * theta;
	  cx = SS0 + theta2 * SS1;
	  cx = theta + theta * theta2 * cx;
	  return cx;
	}
      else
	{
	  /* Handle some special cases.  */
	  if (theta)
	    return theta - (theta * SMALL);
	  else
	    return theta;
	}
    }
  else                          /* |x| >= Pi/4.  */
    {
      unsigned int signbit = isless (x, 0);
      if (isless (abstheta, 9 * M_PI_4))        /* |x| < 9*Pi/4.  */
	{
	  /* There are cases where FE_UPWARD rounding mode can
	     produce a result of abstheta * inv_PI_4 == 9,
	     where abstheta < 9pi/4, so the domain for
	     pio2_table must go to 5 (9 / 2 + 1).  */
	  unsigned int n = (abstheta * inv_PI_4) + 1;
	  theta = abstheta - pio2_table[n / 2];
	  return reduced (theta, n, signbit);
	}
      else if (isless (abstheta, INFINITY))
	{
	  if (abstheta < 0x1p+23)     /* |x| < 2^23.  */
	    {
	      unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
	      double x = n / 2;
	      theta = x * PI_2_lo + (x * PI_2_hi + abstheta);
	      /* Argument reduction needed.  */
	      return reduced (theta, n, signbit);
	    }
	  else                  /* |x| >= 2^23.  */
	    {
	      x = fabsf (x);
	      int exponent;
	      GET_FLOAT_WORD (exponent, x);
	      exponent
	        = (exponent >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
	      exponent += 3;
	      exponent /= 28;
	      double a = invpio4_table[exponent] * x;
	      double b = invpio4_table[exponent + 1] * x;
	      double c = invpio4_table[exponent + 2] * x;
	      double d = invpio4_table[exponent + 3] * x;
	      uint64_t l = a;
	      l &= ~0x7;
	      a -= l;
	      double e = a + b;
	      l = e;
	      e = a - l;
	      if (l & 1)
	        {
	          e -= 1.0;
	          e += b;
	          e += c;
	          e += d;
	          e *= M_PI_4;
	          return reduced (e, l + 1, signbit);
	        }
	      else
		{
		  e += b;
		  e += c;
		  e += d;
		  if (e <= 1.0)
		    {
		      e *= M_PI_4;
		      return reduced (e, l + 1, signbit);
		    }
		  else
		    {
		      l++;
		      e -= 2.0;
		      e *= M_PI_4;
		      return reduced (e, l + 1, signbit);
		    }
		}
	    }
	}
      else
	{
	  int32_t ix;
	  /* High word of x.  */
	  GET_FLOAT_WORD (ix, abstheta);
	  /* Sin(Inf or NaN) is NaN.  */
	  if (ix == 0x7f800000)
	    __set_errno (EDOM);
	  return x - x;
	}
    }
}

#ifndef SINF
libm_alias_float (__sin, sin)
#endif