/* Compute sine and cosine of argument optimized with vector.
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 <x86intrin.h>
#include <libm-alias-float.h>
#include "s_sincosf.h"
#define SINCOSF __sincosf_fma
#ifndef SINCOSF
# define SINCOSF_FUNC __sincosf
#else
# define SINCOSF_FUNC SINCOSF
#endif
/* Chebyshev constants for sin and cos, range -PI/4 - PI/4. */
static const __v2df V0 = { -0x1.5555555551cd9p-3, -0x1.ffffffffe98aep-2};
static const __v2df V1 = { 0x1.1111110c2688bp-7, 0x1.55555545c50c7p-5 };
static const __v2df V2 = { -0x1.a019f8b4bd1f9p-13, -0x1.6c16b348b6874p-10 };
static const __v2df V3 = { 0x1.71d7264e6b5b4p-19, 0x1.a00eb9ac43ccp-16 };
static const __v2df V4 = { -0x1.a947e1674b58ap-26, -0x1.23c97dd8844d7p-22 };
/* Chebyshev constants for sin and cos, range 2^-27 - 2^-5. */
static const __v2df VC0 = { -0x1.555555543d49dp-3, -0x1.fffffff5cc6fdp-2 };
static const __v2df VC1 = { 0x1.110f475cec8c5p-7, 0x1.55514b178dac5p-5 };
static const __v2df v2ones = { 1.0, 1.0 };
/* Compute the sine and cosine values 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 void
reduced_sincos (const double theta, const unsigned int n,
const unsigned int signbit, float *sinx, float *cosx)
{
__v2df v2x, v2sx, v2cx;
const __v2df v2theta = { theta, theta };
const __v2df v2theta2 = v2theta * v2theta;
/* Here sinf() and cosf() are calculated using sin Chebyshev polynomial:
x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
v2x = V3 + v2theta2 * V4; /* S3+x^2*S4. */
v2x = V2 + v2theta2 * v2x; /* S2+x^2*(S3+x^2*S4). */
v2x = V1 + v2theta2 * v2x; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */
v2x = V0 + v2theta2 * v2x; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */
v2x = v2theta2 * v2x;
v2cx = v2ones + v2x;
v2sx = v2theta + v2theta * v2x;
/* We are operating on |x|, so we need to add back the original
signbit for sinf. */
/* Determine positive or negative primary interval. */
/* Are we in the primary interval of sin or cos? */
if ((n & 2) == 0)
{
const __v2df v2sign =
{
ones[((n >> 2) & 1) ^ signbit],
ones[((n + 2) >> 2) & 1]
};
v2cx[0] = v2sx[0];
v2cx *= v2sign;
__v4sf v4sx = _mm_cvtpd_ps (v2cx);
*sinx = v4sx[0];
*cosx = v4sx[1];
}
else
{
const __v2df v2sign =
{
ones[((n + 2) >> 2) & 1],
ones[((n >> 2) & 1) ^ signbit]
};
v2cx[0] = v2sx[0];
v2cx *= v2sign;
__v4sf v4sx = _mm_cvtpd_ps (v2cx);
*sinx = v4sx[1];
*cosx = v4sx[0];
}
}
void
SINCOSF_FUNC (float x, float *sinx, float *cosx)
{
double theta = x;
double abstheta = fabs (theta);
uint32_t ix, xi;
GET_FLOAT_WORD (xi, x);
/* |x| */
ix = xi & 0x7fffffff;
/* If |x|< Pi/4. */
if (ix < 0x3f490fdb)
{
if (ix >= 0x3d000000) /* |x| >= 2^-5. */
{
__v2df v2x, v2sx, v2cx;
const __v2df v2theta = { theta, theta };
const __v2df v2theta2 = v2theta * v2theta;
/* Chebyshev polynomial of the form for sin and cos. */
v2x = V3 + v2theta2 * V4;
v2x = V2 + v2theta2 * v2x;
v2x = V1 + v2theta2 * v2x;
v2x = V0 + v2theta2 * v2x;
v2x = v2theta2 * v2x;
v2cx = v2ones + v2x;
v2sx = v2theta + v2theta * v2x;
v2cx[0] = v2sx[0];
__v4sf v4sx = _mm_cvtpd_ps (v2cx);
*sinx = v4sx[0];
*cosx = v4sx[1];
}
else if (ix >= 0x32000000) /* |x| >= 2^-27. */
{
/* A simpler Chebyshev approximation is close enough for this range:
for sin: x+x^3*(SS0+x^2*SS1)
for cos: 1.0+x^2*(CC0+x^3*CC1). */
__v2df v2x, v2sx, v2cx;
const __v2df v2theta = { theta, theta };
const __v2df v2theta2 = v2theta * v2theta;
v2x = VC0 + v2theta * v2theta2 * VC1;
v2x = v2theta2 * v2x;
v2cx = v2ones + v2x;
v2sx = v2theta + v2theta * v2x;
v2cx[0] = v2sx[0];
__v4sf v4sx = _mm_cvtpd_ps (v2cx);
*sinx = v4sx[0];
*cosx = v4sx[1];
}
else
{
/* Handle some special cases. */
if (ix)
*sinx = theta - (theta * SMALL);
else
*sinx = theta;
*cosx = 1.0 - abstheta;
}
}
else /* |x| >= Pi/4. */
{
unsigned int signbit = xi >> 31;
if (ix < 0x40e231d6) /* |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];
reduced_sincos (theta, n, signbit, sinx, cosx);
}
else if (ix < 0x7f800000)
{
if (ix < 0x4b000000) /* |x| < 2^23. */
{
unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
double x = n / 2;
theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
/* Argument reduction needed. */
reduced_sincos (theta, n, signbit, sinx, cosx);
}
else /* |x| >= 2^23. */
{
x = fabsf (x);
int exponent
= (ix >> 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;
reduced_sincos (e, l + 1, signbit, sinx, cosx);
}
else
{
e += b;
e += c;
e += d;
if (e <= 1.0)
{
e *= M_PI_4;
reduced_sincos (e, l + 1, signbit, sinx, cosx);
}
else
{
l++;
e -= 2.0;
e *= M_PI_4;
reduced_sincos (e, l + 1, signbit, sinx, cosx);
}
}
}
}
else
{
if (ix == 0x7f800000)
__set_errno (EDOM);
/* sin/cos(Inf or NaN) is NaN. */
*sinx = *cosx = x - x;
}
}
}
#ifndef SINCOSF
libm_alias_float (__sincos, sincos)
#endif