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gnss-sdr/src/algorithms/libs/volk_gnsssdr_module/volk_gnsssdr/kernels/volk_gnsssdr/volk_gnsssdr_32f_sincos_32fc.h

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/*!
* \file volk_gnsssdr_32f_sincos_32fc.h
* \brief VOLK_GNSSSDR kernel: Computes the sine and cosine of a vector of floats.
* \authors <ul>
* <li> Julien Pommier, 2007
* <li> Carles Fernandez-Prades, 2016. cfernandez(at)cttc.es
* </ul>
*
* VOLK_GNSSSDR kernel that computes the sine and cosine of a vector of floats.
*
* -------------------------------------------------------------------------
*
* Copyright (C) 2007 Julien Pommier
*
* This software is provided 'as-is', without any express or implied
* warranty. In no event will the authors be held liable for any damages
* arising from the use of this software.
*
* Permission is granted to anyone to use this software for any purpose,
* including commercial applications, and to alter it and redistribute it
* freely, subject to the following restrictions:
*
* 1. The origin of this software must not be misrepresented; you must not
* claim that you wrote the original software. If you use this software
* in a product, an acknowledgment in the product documentation would be
* appreciated but is not required.
* 2. Altered source versions must be plainly marked as such, and must not be
* misrepresented as being the original software.
* 3. This notice may not be removed or altered from any source distribution.
*
* (this is the zlib license)
*/
/*!
* \page volk_gnsssdr_32f_sincos_32fc
*
* \b Overview
*
* VOLK_GNSSSDR kernel that computes the sine and cosine of a vector
* of floats, providing the output in a complex vector (cosine, sine).
* WARNING: it is not IEEE compliant, but the max absolute error on sines is 2^-24 on the range [-8192, 8192].
*
* <b>Dispatcher Prototype</b>
* \code
* void volk_gnsssdr_32f_sincos_32fc(lv_32fc_t* out, const float* in, unsigned int num_points)
* \endcode
*
* \b Inputs
* \li in: Vector of floats, in radians.
* \li num_points: Number of components in \p in to be computed.
*
* \b Outputs
* \li out: Vector of the form lv_32fc_t out[n] = lv_cmake(cos(in[n]), sin(in[n]))
*
* Adapted from http://gruntthepeon.free.fr/ssemath/sse_mathfun.h, original code from Julien Pommier
* Based on algorithms from the cephes library https://www.netlib.org/cephes/
*/
#ifndef INCLUDED_volk_gnsssdr_32f_sincos_32fc_H
#define INCLUDED_volk_gnsssdr_32f_sincos_32fc_H
#include <volk_gnsssdr/volk_gnsssdr_common.h>
#include <volk_gnsssdr/volk_gnsssdr_complex.h>
#include <math.h>
#ifdef LV_HAVE_SSE4_1
#include <smmintrin.h>
/* Adapted from the original VOLK for comparison purposes.
* In turn based on algorithms from:
* Naoki Shibata, "Efficient Evaluation Methods of Elementary Functions Suitable for SIMD Computation,"
* Computer Science Research and Development, May 2010, Volume 25, Issue 1, pp 25-32. DOI 10.1007/s00450-010-0108-2 */
static inline void volk_gnsssdr_32f_sincos_32fc_u_sse4_1(lv_32fc_t* out, const float* in, unsigned int num_points)
{
lv_32fc_t* bPtr = out;
const float* aPtr = in;
unsigned int number = 0;
unsigned int quarterPoints = num_points / 4;
unsigned int i = 0;
__m128 aVal, s, m4pi, pio4A, pio4B, cp1, cp2, cp3, cp4, cp5, ffours, ftwos, fones, fzeroes;
__m128 sine, cosine, condition1, condition2, condition3, cplxValue;
__m128i q, r, ones, twos, fours;
m4pi = _mm_set1_ps(1.273239545);
pio4A = _mm_set1_ps(0.78515625);
pio4B = _mm_set1_ps(0.241876e-3);
ffours = _mm_set1_ps(4.0);
ftwos = _mm_set1_ps(2.0);
fones = _mm_set1_ps(1.0);
fzeroes = _mm_setzero_ps();
ones = _mm_set1_epi32(1);
twos = _mm_set1_epi32(2);
fours = _mm_set1_epi32(4);
cp1 = _mm_set1_ps(1.0);
cp2 = _mm_set1_ps(0.83333333e-1);
cp3 = _mm_set1_ps(0.2777778e-2);
cp4 = _mm_set1_ps(0.49603e-4);
cp5 = _mm_set1_ps(0.551e-6);
for (; number < quarterPoints; number++)
{
aVal = _mm_loadu_ps(aPtr);
__VOLK_GNSSSDR_PREFETCH(aPtr + 8);
s = _mm_sub_ps(aVal, _mm_and_ps(_mm_mul_ps(aVal, ftwos), _mm_cmplt_ps(aVal, fzeroes)));
q = _mm_cvtps_epi32(_mm_floor_ps(_mm_mul_ps(s, m4pi)));
r = _mm_add_epi32(q, _mm_and_si128(q, ones));
s = _mm_sub_ps(s, _mm_mul_ps(_mm_cvtepi32_ps(r), pio4A));
s = _mm_sub_ps(s, _mm_mul_ps(_mm_cvtepi32_ps(r), pio4B));
s = _mm_div_ps(s, _mm_set1_ps(8.0)); // The constant is 2^N, for 3 times argument reduction
s = _mm_mul_ps(s, s);
// Evaluate Taylor series
s = _mm_mul_ps(_mm_add_ps(_mm_mul_ps(_mm_sub_ps(_mm_mul_ps(_mm_add_ps(_mm_mul_ps(_mm_sub_ps(_mm_mul_ps(s, cp5), cp4), s), cp3), s), cp2), s), cp1), s);
for (i = 0; i < 3; i++)
{
s = _mm_mul_ps(s, _mm_sub_ps(ffours, s));
}
s = _mm_div_ps(s, ftwos);
sine = _mm_sqrt_ps(_mm_mul_ps(_mm_sub_ps(ftwos, s), s));
cosine = _mm_sub_ps(fones, s);
condition1 = _mm_cmpneq_ps(_mm_cvtepi32_ps(_mm_and_si128(_mm_add_epi32(q, ones), twos)), fzeroes);
condition2 = _mm_cmpneq_ps(_mm_cmpneq_ps(_mm_cvtepi32_ps(_mm_and_si128(q, fours)), fzeroes), _mm_cmplt_ps(aVal, fzeroes));
condition3 = _mm_cmpneq_ps(_mm_cvtepi32_ps(_mm_and_si128(_mm_add_epi32(q, twos), fours)), fzeroes);
cplxValue = sine;
sine = _mm_add_ps(sine, _mm_and_ps(_mm_sub_ps(cosine, sine), condition1));
sine = _mm_sub_ps(sine, _mm_and_ps(_mm_mul_ps(sine, _mm_set1_ps(2.0f)), condition2));
cosine = _mm_add_ps(cosine, _mm_and_ps(_mm_sub_ps(cplxValue, cosine), condition1));
cosine = _mm_sub_ps(cosine, _mm_and_ps(_mm_mul_ps(cosine, _mm_set1_ps(2.0f)), condition3));
cplxValue = _mm_unpacklo_ps(cosine, sine);
_mm_storeu_ps((float*)bPtr, cplxValue);
bPtr += 2;
cplxValue = _mm_unpackhi_ps(cosine, sine);
_mm_storeu_ps((float*)bPtr, cplxValue);
bPtr += 2;
aPtr += 4;
}
number = quarterPoints * 4;
for (; number < num_points; number++)
{
float _in = *aPtr++;
*bPtr++ = lv_cmake(cosf(_in), sinf(_in));
}
}
#endif /* LV_HAVE_SSE4_1 for unaligned */
#ifdef LV_HAVE_SSE4_1
#include <smmintrin.h>
/* Adapted from the original VOLK for comparison purposes.
* In turn based on algorithms from:
* Naoki Shibata, "Efficient Evaluation Methods of Elementary Functions Suitable for SIMD Computation,"
* Computer Science Research and Development, May 2010, Volume 25, Issue 1, pp 25-32. DOI 10.1007/s00450-010-0108-2 */
static inline void volk_gnsssdr_32f_sincos_32fc_a_sse4_1(lv_32fc_t* out, const float* in, unsigned int num_points)
{
lv_32fc_t* bPtr = out;
const float* aPtr = in;
unsigned int number = 0;
unsigned int quarterPoints = num_points / 4;
unsigned int i = 0;
__m128 aVal, s, m4pi, pio4A, pio4B, cp1, cp2, cp3, cp4, cp5, ffours, ftwos, fones, fzeroes;
__m128 sine, cosine, condition1, condition2, condition3, cplxValue;
__m128i q, r, ones, twos, fours;
m4pi = _mm_set1_ps(1.273239545);
pio4A = _mm_set1_ps(0.78515625);
pio4B = _mm_set1_ps(0.241876e-3);
ffours = _mm_set1_ps(4.0);
ftwos = _mm_set1_ps(2.0);
fones = _mm_set1_ps(1.0);
fzeroes = _mm_setzero_ps();
ones = _mm_set1_epi32(1);
twos = _mm_set1_epi32(2);
fours = _mm_set1_epi32(4);
cp1 = _mm_set1_ps(1.0);
cp2 = _mm_set1_ps(0.83333333e-1);
cp3 = _mm_set1_ps(0.2777778e-2);
cp4 = _mm_set1_ps(0.49603e-4);
cp5 = _mm_set1_ps(0.551e-6);
for (; number < quarterPoints; number++)
{
aVal = _mm_load_ps(aPtr);
__VOLK_GNSSSDR_PREFETCH(aPtr + 8);
s = _mm_sub_ps(aVal, _mm_and_ps(_mm_mul_ps(aVal, ftwos), _mm_cmplt_ps(aVal, fzeroes)));
q = _mm_cvtps_epi32(_mm_floor_ps(_mm_mul_ps(s, m4pi)));
r = _mm_add_epi32(q, _mm_and_si128(q, ones));
s = _mm_sub_ps(s, _mm_mul_ps(_mm_cvtepi32_ps(r), pio4A));
s = _mm_sub_ps(s, _mm_mul_ps(_mm_cvtepi32_ps(r), pio4B));
s = _mm_div_ps(s, _mm_set1_ps(8.0)); // The constant is 2^N, for 3 times argument reduction
s = _mm_mul_ps(s, s);
// Evaluate Taylor series
s = _mm_mul_ps(_mm_add_ps(_mm_mul_ps(_mm_sub_ps(_mm_mul_ps(_mm_add_ps(_mm_mul_ps(_mm_sub_ps(_mm_mul_ps(s, cp5), cp4), s), cp3), s), cp2), s), cp1), s);
for (i = 0; i < 3; i++)
{
s = _mm_mul_ps(s, _mm_sub_ps(ffours, s));
}
s = _mm_div_ps(s, ftwos);
sine = _mm_sqrt_ps(_mm_mul_ps(_mm_sub_ps(ftwos, s), s));
cosine = _mm_sub_ps(fones, s);
condition1 = _mm_cmpneq_ps(_mm_cvtepi32_ps(_mm_and_si128(_mm_add_epi32(q, ones), twos)), fzeroes);
condition2 = _mm_cmpneq_ps(_mm_cmpneq_ps(_mm_cvtepi32_ps(_mm_and_si128(q, fours)), fzeroes), _mm_cmplt_ps(aVal, fzeroes));
condition3 = _mm_cmpneq_ps(_mm_cvtepi32_ps(_mm_and_si128(_mm_add_epi32(q, twos), fours)), fzeroes);
cplxValue = sine;
sine = _mm_add_ps(sine, _mm_and_ps(_mm_sub_ps(cosine, sine), condition1));
sine = _mm_sub_ps(sine, _mm_and_ps(_mm_mul_ps(sine, _mm_set1_ps(2.0f)), condition2));
cosine = _mm_add_ps(cosine, _mm_and_ps(_mm_sub_ps(cplxValue, cosine), condition1));
cosine = _mm_sub_ps(cosine, _mm_and_ps(_mm_mul_ps(cosine, _mm_set1_ps(2.0f)), condition3));
cplxValue = _mm_unpacklo_ps(cosine, sine);
_mm_store_ps((float*)bPtr, cplxValue);
bPtr += 2;
cplxValue = _mm_unpackhi_ps(cosine, sine);
_mm_store_ps((float*)bPtr, cplxValue);
bPtr += 2;
aPtr += 4;
}
number = quarterPoints * 4;
for (; number < num_points; number++)
{
float _in = *aPtr++;
*bPtr++ = lv_cmake(cosf(_in), sinf(_in));
}
}
#endif /* LV_HAVE_SSE4_1 for aligned */
#ifdef LV_HAVE_SSE2
#include <emmintrin.h>
static inline void volk_gnsssdr_32f_sincos_32fc_a_sse2(lv_32fc_t* out, const float* in, unsigned int num_points)
{
lv_32fc_t* bPtr = out;
const float* aPtr = in;
const unsigned int sse_iters = num_points / 4;
unsigned int number = 0;
float _in;
__m128 sine, cosine, aux, x;
__m128 xmm1, xmm2, xmm3 = _mm_setzero_ps(), sign_bit_sin, y;
__m128i emm0, emm2, emm4;
/* declare some SSE constants */
__VOLK_ATTR_ALIGNED(16)
static const int _ps_inv_sign_mask[4] = {~0x80000000, ~0x80000000, ~0x80000000, ~0x80000000};
__VOLK_ATTR_ALIGNED(16)
static const int _ps_sign_mask[4] = {(int)0x80000000, (int)0x80000000, (int)0x80000000, (int)0x80000000};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_cephes_FOPI[4] = {1.27323954473516, 1.27323954473516, 1.27323954473516, 1.27323954473516};
__VOLK_ATTR_ALIGNED(16)
static const int _pi32_1[4] = {1, 1, 1, 1};
__VOLK_ATTR_ALIGNED(16)
static const int _pi32_inv1[4] = {~1, ~1, ~1, ~1};
__VOLK_ATTR_ALIGNED(16)
static const int _pi32_2[4] = {2, 2, 2, 2};
__VOLK_ATTR_ALIGNED(16)
static const int _pi32_4[4] = {4, 4, 4, 4};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_minus_cephes_DP1[4] = {-0.78515625, -0.78515625, -0.78515625, -0.78515625};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_minus_cephes_DP2[4] = {-2.4187564849853515625e-4, -2.4187564849853515625e-4, -2.4187564849853515625e-4, -2.4187564849853515625e-4};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_minus_cephes_DP3[4] = {-3.77489497744594108e-8, -3.77489497744594108e-8, -3.77489497744594108e-8, -3.77489497744594108e-8};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_coscof_p0[4] = {2.443315711809948E-005, 2.443315711809948E-005, 2.443315711809948E-005, 2.443315711809948E-005};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_coscof_p1[4] = {-1.388731625493765E-003, -1.388731625493765E-003, -1.388731625493765E-003, -1.388731625493765E-003};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_coscof_p2[4] = {4.166664568298827E-002, 4.166664568298827E-002, 4.166664568298827E-002, 4.166664568298827E-002};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_sincof_p0[4] = {-1.9515295891E-4, -1.9515295891E-4, -1.9515295891E-4, -1.9515295891E-4};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_sincof_p1[4] = {8.3321608736E-3, 8.3321608736E-3, 8.3321608736E-3, 8.3321608736E-3};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_sincof_p2[4] = {-1.6666654611E-1, -1.6666654611E-1, -1.6666654611E-1, -1.6666654611E-1};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_0p5[4] = {0.5f, 0.5f, 0.5f, 0.5f};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_1[4] = {1.0f, 1.0f, 1.0f, 1.0f};
for (; number < sse_iters; number++)
{
x = _mm_load_ps(aPtr);
__VOLK_GNSSSDR_PREFETCH(aPtr + 8);
sign_bit_sin = x;
/* take the absolute value */
x = _mm_and_ps(x, *(__m128*)_ps_inv_sign_mask);
/* extract the sign bit (upper one) */
sign_bit_sin = _mm_and_ps(sign_bit_sin, *(__m128*)_ps_sign_mask);
/* scale by 4/Pi */
y = _mm_mul_ps(x, *(__m128*)_ps_cephes_FOPI);
/* store the integer part of y in emm2 */
emm2 = _mm_cvttps_epi32(y);
/* j=(j+1) & (~1) (see the cephes sources) */
emm2 = _mm_add_epi32(emm2, *(__m128i*)_pi32_1);
emm2 = _mm_and_si128(emm2, *(__m128i*)_pi32_inv1);
y = _mm_cvtepi32_ps(emm2);
emm4 = emm2;
/* get the swap sign flag for the sine */
emm0 = _mm_and_si128(emm2, *(__m128i*)_pi32_4);
emm0 = _mm_slli_epi32(emm0, 29);
__m128 swap_sign_bit_sin = _mm_castsi128_ps(emm0);
/* get the polynom selection mask for the sine*/
emm2 = _mm_and_si128(emm2, *(__m128i*)_pi32_2);
emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
__m128 poly_mask = _mm_castsi128_ps(emm2);
/* The magic pass: "Extended precision modular arithmetic”
x = ((x - y * DP1) - y * DP2) - y * DP3; */
xmm1 = *(__m128*)_ps_minus_cephes_DP1;
xmm2 = *(__m128*)_ps_minus_cephes_DP2;
xmm3 = *(__m128*)_ps_minus_cephes_DP3;
xmm1 = _mm_mul_ps(y, xmm1);
xmm2 = _mm_mul_ps(y, xmm2);
xmm3 = _mm_mul_ps(y, xmm3);
x = _mm_add_ps(x, xmm1);
x = _mm_add_ps(x, xmm2);
x = _mm_add_ps(x, xmm3);
emm4 = _mm_sub_epi32(emm4, *(__m128i*)_pi32_2);
emm4 = _mm_andnot_si128(emm4, *(__m128i*)_pi32_4);
emm4 = _mm_slli_epi32(emm4, 29);
__m128 sign_bit_cos = _mm_castsi128_ps(emm4);
sign_bit_sin = _mm_xor_ps(sign_bit_sin, swap_sign_bit_sin);
/* Evaluate the first polynom (0 <= x <= Pi/4) */
__m128 z = _mm_mul_ps(x, x);
y = *(__m128*)_ps_coscof_p0;
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(__m128*)_ps_coscof_p1);
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(__m128*)_ps_coscof_p2);
y = _mm_mul_ps(y, z);
y = _mm_mul_ps(y, z);
__m128 tmp = _mm_mul_ps(z, *(__m128*)_ps_0p5);
y = _mm_sub_ps(y, tmp);
y = _mm_add_ps(y, *(__m128*)_ps_1);
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
__m128 y2 = *(__m128*)_ps_sincof_p0;
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(__m128*)_ps_sincof_p1);
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(__m128*)_ps_sincof_p2);
y2 = _mm_mul_ps(y2, z);
y2 = _mm_mul_ps(y2, x);
y2 = _mm_add_ps(y2, x);
/* select the correct result from the two polynoms */
xmm3 = poly_mask;
__m128 ysin2 = _mm_and_ps(xmm3, y2);
__m128 ysin1 = _mm_andnot_ps(xmm3, y);
y2 = _mm_sub_ps(y2, ysin2);
y = _mm_sub_ps(y, ysin1);
xmm1 = _mm_add_ps(ysin1, ysin2);
xmm2 = _mm_add_ps(y, y2);
/* update the sign */
sine = _mm_xor_ps(xmm1, sign_bit_sin);
cosine = _mm_xor_ps(xmm2, sign_bit_cos);
/* write the output */
aux = _mm_unpacklo_ps(cosine, sine);
_mm_store_ps((float*)bPtr, aux);
bPtr += 2;
aux = _mm_unpackhi_ps(cosine, sine);
_mm_store_ps((float*)bPtr, aux);
bPtr += 2;
aPtr += 4;
}
for (number = sse_iters * 4; number < num_points; number++)
{
_in = *aPtr++;
*bPtr++ = lv_cmake((float)cosf(_in), (float)sinf(_in));
}
}
#endif /* LV_HAVE_SSE2 */
#ifdef LV_HAVE_SSE2
#include <emmintrin.h>
static inline void volk_gnsssdr_32f_sincos_32fc_u_sse2(lv_32fc_t* out, const float* in, unsigned int num_points)
{
lv_32fc_t* bPtr = out;
const float* aPtr = in;
const unsigned int sse_iters = num_points / 4;
unsigned int number = 0;
float _in;
__m128 sine, cosine, aux, x;
__m128 xmm1, xmm2, xmm3 = _mm_setzero_ps(), sign_bit_sin, y;
__m128i emm0, emm2, emm4;
/* declare some SSE constants */
__VOLK_ATTR_ALIGNED(16)
static const int _ps_inv_sign_mask[4] = {~0x80000000, ~0x80000000, ~0x80000000, ~0x80000000};
__VOLK_ATTR_ALIGNED(16)
static const int _ps_sign_mask[4] = {(int)0x80000000, (int)0x80000000, (int)0x80000000, (int)0x80000000};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_cephes_FOPI[4] = {1.27323954473516, 1.27323954473516, 1.27323954473516, 1.27323954473516};
__VOLK_ATTR_ALIGNED(16)
static const int _pi32_1[4] = {1, 1, 1, 1};
__VOLK_ATTR_ALIGNED(16)
static const int _pi32_inv1[4] = {~1, ~1, ~1, ~1};
__VOLK_ATTR_ALIGNED(16)
static const int _pi32_2[4] = {2, 2, 2, 2};
__VOLK_ATTR_ALIGNED(16)
static const int _pi32_4[4] = {4, 4, 4, 4};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_minus_cephes_DP1[4] = {-0.78515625, -0.78515625, -0.78515625, -0.78515625};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_minus_cephes_DP2[4] = {-2.4187564849853515625e-4, -2.4187564849853515625e-4, -2.4187564849853515625e-4, -2.4187564849853515625e-4};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_minus_cephes_DP3[4] = {-3.77489497744594108e-8, -3.77489497744594108e-8, -3.77489497744594108e-8, -3.77489497744594108e-8};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_coscof_p0[4] = {2.443315711809948E-005, 2.443315711809948E-005, 2.443315711809948E-005, 2.443315711809948E-005};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_coscof_p1[4] = {-1.388731625493765E-003, -1.388731625493765E-003, -1.388731625493765E-003, -1.388731625493765E-003};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_coscof_p2[4] = {4.166664568298827E-002, 4.166664568298827E-002, 4.166664568298827E-002, 4.166664568298827E-002};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_sincof_p0[4] = {-1.9515295891E-4, -1.9515295891E-4, -1.9515295891E-4, -1.9515295891E-4};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_sincof_p1[4] = {8.3321608736E-3, 8.3321608736E-3, 8.3321608736E-3, 8.3321608736E-3};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_sincof_p2[4] = {-1.6666654611E-1, -1.6666654611E-1, -1.6666654611E-1, -1.6666654611E-1};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_0p5[4] = {0.5f, 0.5f, 0.5f, 0.5f};
__VOLK_ATTR_ALIGNED(16)
static const float _ps_1[4] = {1.0f, 1.0f, 1.0f, 1.0f};
for (; number < sse_iters; number++)
{
x = _mm_loadu_ps(aPtr);
__VOLK_GNSSSDR_PREFETCH(aPtr + 8);
sign_bit_sin = x;
/* take the absolute value */
x = _mm_and_ps(x, *(__m128*)_ps_inv_sign_mask);
/* extract the sign bit (upper one) */
sign_bit_sin = _mm_and_ps(sign_bit_sin, *(__m128*)_ps_sign_mask);
/* scale by 4/Pi */
y = _mm_mul_ps(x, *(__m128*)_ps_cephes_FOPI);
/* store the integer part of y in emm2 */
emm2 = _mm_cvttps_epi32(y);
/* j=(j+1) & (~1) (see the cephes sources) */
emm2 = _mm_add_epi32(emm2, *(__m128i*)_pi32_1);
emm2 = _mm_and_si128(emm2, *(__m128i*)_pi32_inv1);
y = _mm_cvtepi32_ps(emm2);
emm4 = emm2;
/* get the swap sign flag for the sine */
emm0 = _mm_and_si128(emm2, *(__m128i*)_pi32_4);
emm0 = _mm_slli_epi32(emm0, 29);
__m128 swap_sign_bit_sin = _mm_castsi128_ps(emm0);
/* get the polynom selection mask for the sine*/
emm2 = _mm_and_si128(emm2, *(__m128i*)_pi32_2);
emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
__m128 poly_mask = _mm_castsi128_ps(emm2);
/* The magic pass: "Extended precision modular arithmetic”
x = ((x - y * DP1) - y * DP2) - y * DP3; */
xmm1 = *(__m128*)_ps_minus_cephes_DP1;
xmm2 = *(__m128*)_ps_minus_cephes_DP2;
xmm3 = *(__m128*)_ps_minus_cephes_DP3;
xmm1 = _mm_mul_ps(y, xmm1);
xmm2 = _mm_mul_ps(y, xmm2);
xmm3 = _mm_mul_ps(y, xmm3);
x = _mm_add_ps(x, xmm1);
x = _mm_add_ps(x, xmm2);
x = _mm_add_ps(x, xmm3);
emm4 = _mm_sub_epi32(emm4, *(__m128i*)_pi32_2);
emm4 = _mm_andnot_si128(emm4, *(__m128i*)_pi32_4);
emm4 = _mm_slli_epi32(emm4, 29);
__m128 sign_bit_cos = _mm_castsi128_ps(emm4);
sign_bit_sin = _mm_xor_ps(sign_bit_sin, swap_sign_bit_sin);
/* Evaluate the first polynom (0 <= x <= Pi/4) */
__m128 z = _mm_mul_ps(x, x);
y = *(__m128*)_ps_coscof_p0;
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(__m128*)_ps_coscof_p1);
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(__m128*)_ps_coscof_p2);
y = _mm_mul_ps(y, z);
y = _mm_mul_ps(y, z);
__m128 tmp = _mm_mul_ps(z, *(__m128*)_ps_0p5);
y = _mm_sub_ps(y, tmp);
y = _mm_add_ps(y, *(__m128*)_ps_1);
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
__m128 y2 = *(__m128*)_ps_sincof_p0;
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(__m128*)_ps_sincof_p1);
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(__m128*)_ps_sincof_p2);
y2 = _mm_mul_ps(y2, z);
y2 = _mm_mul_ps(y2, x);
y2 = _mm_add_ps(y2, x);
/* select the correct result from the two polynoms */
xmm3 = poly_mask;
__m128 ysin2 = _mm_and_ps(xmm3, y2);
__m128 ysin1 = _mm_andnot_ps(xmm3, y);
y2 = _mm_sub_ps(y2, ysin2);
y = _mm_sub_ps(y, ysin1);
xmm1 = _mm_add_ps(ysin1, ysin2);
xmm2 = _mm_add_ps(y, y2);
/* update the sign */
sine = _mm_xor_ps(xmm1, sign_bit_sin);
cosine = _mm_xor_ps(xmm2, sign_bit_cos);
/* write the output */
aux = _mm_unpacklo_ps(cosine, sine);
_mm_storeu_ps((float*)bPtr, aux);
bPtr += 2;
aux = _mm_unpackhi_ps(cosine, sine);
_mm_storeu_ps((float*)bPtr, aux);
bPtr += 2;
aPtr += 4;
}
for (number = sse_iters * 4; number < num_points; number++)
{
_in = *aPtr++;
*bPtr++ = lv_cmake((float)cosf(_in), (float)sinf(_in));
}
}
#endif /* LV_HAVE_SSE2 */
#ifdef LV_HAVE_GENERIC
static inline void volk_gnsssdr_32f_sincos_32fc_generic(lv_32fc_t* out, const float* in, unsigned int num_points)
{
float _in;
unsigned int i;
for (i = 0; i < num_points; i++)
{
_in = *in++;
*out++ = lv_cmake((float)cosf(_in), (float)sinf(_in));
}
}
#endif /* LV_HAVE_GENERIC */
#ifdef LV_HAVE_GENERIC
#include <volk_gnsssdr/volk_gnsssdr_sine_table.h>
#include <stdint.h>
static inline void volk_gnsssdr_32f_sincos_32fc_generic_fxpt(lv_32fc_t* out, const float* in, unsigned int num_points)
{
float _in, s, c;
int32_t x, sin_index, cos_index, d;
const float PI = 3.14159265358979323846;
const float TWO_TO_THE_31_DIV_PI = 2147483648.0 / PI;
const float TWO_PI = PI * 2;
const int32_t bitlength = 32;
const int32_t Nbits = 10;
const int32_t diffbits = bitlength - Nbits;
uint32_t ux;
unsigned int i;
for (i = 0; i < num_points; i++)
{
_in = *in++;
d = (int32_t)floor(_in / TWO_PI + 0.5);
_in -= d * TWO_PI;
x = (int32_t)((float)_in * TWO_TO_THE_31_DIV_PI);
ux = x;
sin_index = ux >> diffbits;
s = sine_table_10bits[sin_index][0] * (ux >> 1) + sine_table_10bits[sin_index][1];
ux = x + 0x40000000;
cos_index = ux >> diffbits;
c = sine_table_10bits[cos_index][0] * (ux >> 1) + sine_table_10bits[cos_index][1];
*out++ = lv_cmake((float)c, (float)s);
}
}
#endif /* LV_HAVE_GENERIC */
#ifdef LV_HAVE_NEONV7
#include <arm_neon.h>
static inline void volk_gnsssdr_32f_sincos_32fc_neon(lv_32fc_t* out, const float* in, unsigned int num_points)
{
lv_32fc_t* bPtr = out;
const float* aPtr = in;
const unsigned int neon_iters = num_points / 4;
const float32_t c_minus_cephes_DP1 = -0.78515625;
const float32_t c_minus_cephes_DP2 = -2.4187564849853515625e-4;
const float32_t c_minus_cephes_DP3 = -3.77489497744594108e-8;
const float32_t c_sincof_p0 = -1.9515295891E-4;
const float32_t c_sincof_p1 = 8.3321608736E-3;
const float32_t c_sincof_p2 = -1.6666654611E-1;
const float32_t c_coscof_p0 = 2.443315711809948E-005;
const float32_t c_coscof_p1 = -1.388731625493765E-003;
const float32_t c_coscof_p2 = 4.166664568298827E-002;
const float32_t c_cephes_FOPI = 1.27323954473516;
unsigned int number = 0;
float _in;
float32x4_t x, xmm1, xmm2, xmm3, y, y1, y2, ys, yc, z;
float32x4x2_t result;
uint32x4_t emm2, poly_mask, sign_mask_sin, sign_mask_cos;
for (; number < neon_iters; number++)
{
x = vld1q_f32(aPtr);
__VOLK_GNSSSDR_PREFETCH(aPtr + 8);
sign_mask_sin = vcltq_f32(x, vdupq_n_f32(0));
x = vabsq_f32(x);
/* scale by 4/Pi */
y = vmulq_f32(x, vdupq_n_f32(c_cephes_FOPI));
/* store the integer part of y in mm0 */
emm2 = vcvtq_u32_f32(y);
/* j=(j+1) & (~1) (see the cephes sources) */
emm2 = vaddq_u32(emm2, vdupq_n_u32(1));
emm2 = vandq_u32(emm2, vdupq_n_u32(~1));
y = vcvtq_f32_u32(emm2);
/* get the polynom selection mask
there is one polynom for 0 <= x <= Pi/4
and another one for Pi/4<x<=Pi/2
Both branches will be computed.
*/
poly_mask = vtstq_u32(emm2, vdupq_n_u32(2));
/* The magic pass: "Extended precision modular arithmetic"
x = ((x - y * DP1) - y * DP2) - y * DP3; */
xmm1 = vmulq_n_f32(y, c_minus_cephes_DP1);
xmm2 = vmulq_n_f32(y, c_minus_cephes_DP2);
xmm3 = vmulq_n_f32(y, c_minus_cephes_DP3);
x = vaddq_f32(x, xmm1);
x = vaddq_f32(x, xmm2);
x = vaddq_f32(x, xmm3);
sign_mask_sin = veorq_u32(sign_mask_sin, vtstq_u32(emm2, vdupq_n_u32(4)));
sign_mask_cos = vtstq_u32(vsubq_u32(emm2, vdupq_n_u32(2)), vdupq_n_u32(4));
/* Evaluate the first polynom (0 <= x <= Pi/4) in y1,
and the second polynom (Pi/4 <= x <= 0) in y2 */
z = vmulq_f32(x, x);
y1 = vmulq_n_f32(z, c_coscof_p0);
y2 = vmulq_n_f32(z, c_sincof_p0);
y1 = vaddq_f32(y1, vdupq_n_f32(c_coscof_p1));
y2 = vaddq_f32(y2, vdupq_n_f32(c_sincof_p1));
y1 = vmulq_f32(y1, z);
y2 = vmulq_f32(y2, z);
y1 = vaddq_f32(y1, vdupq_n_f32(c_coscof_p2));
y2 = vaddq_f32(y2, vdupq_n_f32(c_sincof_p2));
y1 = vmulq_f32(y1, z);
y2 = vmulq_f32(y2, z);
y1 = vmulq_f32(y1, z);
y2 = vmulq_f32(y2, x);
y1 = vsubq_f32(y1, vmulq_f32(z, vdupq_n_f32(0.5f)));
y2 = vaddq_f32(y2, x);
y1 = vaddq_f32(y1, vdupq_n_f32(1));
/* select the correct result from the two polynoms */
ys = vbslq_f32(poly_mask, y1, y2);
yc = vbslq_f32(poly_mask, y2, y1);
result.val[1] = vbslq_f32(sign_mask_sin, vnegq_f32(ys), ys);
result.val[0] = vbslq_f32(sign_mask_cos, yc, vnegq_f32(yc));
vst2q_f32((float32_t*)bPtr, result);
bPtr += 4;
aPtr += 4;
}
for (number = neon_iters * 4; number < num_points; number++)
{
_in = *aPtr++;
*bPtr++ = lv_cmake((float)cosf(_in), (float)sinf(_in));
}
}
#endif /* LV_HAVE_NEONV7 */
#endif /* INCLUDED_volk_gnsssdr_32f_sincos_32fc_H */
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