mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-04 10:50:07 +00:00
984ae9967b
This implementation is based on generic s_sinf.c and s_cosf.c. Tested on s390x, powerpc64le and powerpc32.
156 lines
5.2 KiB
C
156 lines
5.2 KiB
C
/* Used by sinf, cosf and sincosf functions.
|
|
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/>. */
|
|
|
|
/* 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;
|
|
}
|