sysdeps/ieee754/flt-32/s_sincosf.h

   1 /* Used by sinf, cosf and sincosf functions.
   2    Copyright (C) 2017 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, see
  17    <http://www.gnu.org/licenses/>.  */
  18
  19 /* Chebyshev constants for cos, range -PI/4 - PI/4.  */
  20 static const double C0 = -0x1.ffffffffe98aep-2;
  21 static const double C1 =  0x1.55555545c50c7p-5;
  22 static const double C2 = -0x1.6c16b348b6874p-10;
  23 static const double C3 =  0x1.a00eb9ac43ccp-16;
  24 static const double C4 = -0x1.23c97dd8844d7p-22;
  25
  26 /* Chebyshev constants for sin, range -PI/4 - PI/4.  */
  27 static const double S0 = -0x1.5555555551cd9p-3;
  28 static const double S1 =  0x1.1111110c2688bp-7;
  29 static const double S2 = -0x1.a019f8b4bd1f9p-13;
  30 static const double S3 =  0x1.71d7264e6b5b4p-19;
  31 static const double S4 = -0x1.a947e1674b58ap-26;
  32
  33 /* Chebyshev constants for sin, range 2^-27 - 2^-5.  */
  34 static const double SS0 = -0x1.555555543d49dp-3;
  35 static const double SS1 =  0x1.110f475cec8c5p-7;
  36
  37 /* Chebyshev constants for cos, range 2^-27 - 2^-5.  */
  38 static const double CC0 = -0x1.fffffff5cc6fdp-2;
  39 static const double CC1 =  0x1.55514b178dac5p-5;
  40
  41 /* PI/2 with 98 bits of accuracy.  */
  42 static const double PI_2_hi = 0x1.921fb544p+0;
  43 static const double PI_2_lo = 0x1.0b4611a626332p-34;
  44
  45 static const double SMALL = 0x1p-50; /* 2^-50.  */
  46 static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI.  */
  47
  48 #define FLOAT_EXPONENT_SHIFT 23
  49 #define FLOAT_EXPONENT_BIAS 127
  50
  51 static const double pio2_table[] = {
  52   0 * M_PI_2,
  53   1 * M_PI_2,
  54   2 * M_PI_2,
  55   3 * M_PI_2,
  56   4 * M_PI_2,
  57   5 * M_PI_2
  58 };
  59
  60 static const double invpio4_table[] = {
  61   0x0p+0,
  62   0x1.45f306cp+0,
  63   0x1.c9c882ap-28,
  64   0x1.4fe13a8p-58,
  65   0x1.f47d4dp-85,
  66   0x1.bb81b6cp-112,
  67   0x1.4acc9ep-142,
  68   0x1.0e4107cp-169
  69 };
  70
  71 static const double ones[] = { 1.0, -1.0 };
  72
  73 /* Compute the sine value using Chebyshev polynomials where
  74    THETA is the range reduced absolute value of the input
  75    and it is less than Pi/4,
  76    N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
  77    whether a sine or cosine approximation is more accurate and
  78    SIGNBIT is used to add the correct sign after the Chebyshev
  79    polynomial is computed.  */
  80 static inline float
  81 reduced_sin (const double theta, const unsigned int n,
  82          const unsigned int signbit)
  83 {
  84   double sx;
  85   const double theta2 = theta * theta;
  86   /* We are operating on |x|, so we need to add back the original
  87      signbit for sinf.  */
  88   double sign;
  89   /* Determine positive or negative primary interval.  */
  90   sign = ones[((n >> 2) & 1) ^ signbit];
  91   /* Are we in the primary interval of sin or cos?  */
  92   if ((n & 2) == 0)
  93     {
  94       /* Here sinf() is calculated using sin Chebyshev polynomial:
  95         x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */
  96       sx = S3 + theta2 * S4;     /* S3+x^2*S4.  */
  97       sx = S2 + theta2 * sx;     /* S2+x^2*(S3+x^2*S4).  */
  98       sx = S1 + theta2 * sx;     /* S1+x^2*(S2+x^2*(S3+x^2*S4)).  */
  99       sx = S0 + theta2 * sx;     /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))).  */
 100       sx = theta + theta * theta2 * sx;
 101     }
 102   else
 103     {
 104      /* Here sinf() is calculated using cos Chebyshev polynomial:
 105         1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).  */
 106       sx = C3 + theta2 * C4;     /* C3+x^2*C4.  */
 107       sx = C2 + theta2 * sx;     /* C2+x^2*(C3+x^2*C4).  */
 108       sx = C1 + theta2 * sx;     /* C1+x^2*(C2+x^2*(C3+x^2*C4)).  */
 109       sx = C0 + theta2 * sx;     /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))).  */
 110       sx = 1.0 + theta2 * sx;
 111     }
 112
 113   /* Add in the signbit and assign the result.  */
 114   return sign * sx;
 115 }
 116
 117 /* Compute the cosine value using Chebyshev polynomials where
 118    THETA is the range reduced absolute value of the input
 119    and it is less than Pi/4,
 120    N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
 121    whether a sine or cosine approximation is more accurate and
 122    the sign of the result.  */
 123 static inline float
 124 reduced_cos (double theta, unsigned int n)
 125 {
 126   double sign, cx;
 127   const double theta2 = theta * theta;
 128
 129   /* Determine positive or negative primary interval.  */
 130   n += 2;
 131   sign = ones[(n >> 2) & 1];
 132
 133   /* Are we in the primary interval of sin or cos?  */
 134   if ((n & 2) == 0)
 135     {
 136       /* Here cosf() is calculated using sin Chebyshev polynomial:
 137         x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */
 138       cx = S3 + theta2 * S4;
 139       cx = S2 + theta2 * cx;
 140       cx = S1 + theta2 * cx;
 141       cx = S0 + theta2 * cx;
 142       cx = theta + theta * theta2 * cx;
 143     }
 144   else
 145     {
 146      /* Here cosf() is calculated using cos Chebyshev polynomial:
 147         1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).  */
 148       cx = C3 + theta2 * C4;
 149       cx = C2 + theta2 * cx;
 150       cx = C1 + theta2 * cx;
 151       cx = C0 + theta2 * cx;
 152       cx = 1. + theta2 * cx;
 153     }
 154   return sign * cx;
 155 }