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/* Used by sinf, cosf and sincosf functions.
Copyright (C) 2017-2018 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/>. */
/* 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;
/* Chebyshev constants for cos, range 2^-27 - 2^-5. */
static const double CC0 = -0x1.fffffff5cc6fdp-2;
static const double CC1 = 0x1.55514b178dac5p-5;
/* 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 double ones[] = { 1.0, -1.0 };
/* 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_sin (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. */
double 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;
}
/* Compute the cosine 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
the sign of the result. */
static inline float
reduced_cos (double theta, unsigned int n)
{
double sign, cx;
const double theta2 = theta * theta;
/* Determine positive or negative primary interval. */
n += 2;
sign = ones[(n >> 2) & 1];
/* Are we in the primary interval of sin or cos? */
if ((n & 2) == 0)
{
/* Here cosf() is calculated using sin Chebyshev polynomial:
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;
}
else
{
/* Here cosf() is calculated using cos Chebyshev polynomial:
1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
cx = C3 + theta2 * C4;
cx = C2 + theta2 * cx;
cx = C1 + theta2 * cx;
cx = C0 + theta2 * cx;
cx = 1. + theta2 * cx;
}
return sign * cx;
}
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