generic-library/opencv
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity
opencv/modules/core/src/mathfuncs_core.cpp
Maksim Shabunin 84f37d352f HAL moved back to core
2015-12-17 12:33:23 +03:00

1461 lines
62 KiB
C++
Raw Blame History

/*M///////////////////////////////////////////////////////////////////////////////////////
//
// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
//
// By downloading, copying, installing or using the software you agree to this license.
// If you do not agree to this license, do not download, install,
// copy or use the software.
//
//
// License Agreement
// For Open Source Computer Vision Library
//
// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
// Copyright (C) 2009-2011, Willow Garage Inc., all rights reserved.
// Third party copyrights are property of their respective owners.
//
// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:
//
// * Redistribution's of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
//
// * Redistribution's in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
//
// * The name of the copyright holders may not be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// This software is provided by the copyright holders and contributors "as is" and
// any express or implied warranties, including, but not limited to, the implied
// warranties of merchantability and fitness for a particular purpose are disclaimed.
// In no event shall the Intel Corporation or contributors be liable for any direct,
// indirect, incidental, special, exemplary, or consequential damages
// (including, but not limited to, procurement of substitute goods or services;
// loss of use, data, or profits; or business interruption) however caused
// and on any theory of liability, whether in contract, strict liability,
// or tort (including negligence or otherwise) arising in any way out of
// the use of this software, even if advised of the possibility of such damage.
//
//M*/
#include "precomp.hpp"
#undef HAVE_IPP
namespace cv { namespace hal {
///////////////////////////////////// ATAN2 ////////////////////////////////////
static const float atan2_p1 = 0.9997878412794807f*(float)(180/CV_PI);
static const float atan2_p3 = -0.3258083974640975f*(float)(180/CV_PI);
static const float atan2_p5 = 0.1555786518463281f*(float)(180/CV_PI);
static const float atan2_p7 = -0.04432655554792128f*(float)(180/CV_PI);
void fastAtan2(const float *Y, const float *X, float *angle, int len, bool angleInDegrees )
{
int i = 0;
float scale = angleInDegrees ? 1 : (float)(CV_PI/180);
#ifdef HAVE_TEGRA_OPTIMIZATION
if (tegra::useTegra() && tegra::FastAtan2_32f(Y, X, angle, len, scale))
return;
#endif
#if CV_SSE2
Cv32suf iabsmask; iabsmask.i = 0x7fffffff;
__m128 eps = _mm_set1_ps((float)DBL_EPSILON), absmask = _mm_set1_ps(iabsmask.f);
__m128 _90 = _mm_set1_ps(90.f), _180 = _mm_set1_ps(180.f), _360 = _mm_set1_ps(360.f);
__m128 z = _mm_setzero_ps(), scale4 = _mm_set1_ps(scale);
__m128 p1 = _mm_set1_ps(atan2_p1), p3 = _mm_set1_ps(atan2_p3);
__m128 p5 = _mm_set1_ps(atan2_p5), p7 = _mm_set1_ps(atan2_p7);
for( ; i <= len - 4; i += 4 )
{
__m128 x = _mm_loadu_ps(X + i), y = _mm_loadu_ps(Y + i);
__m128 ax = _mm_and_ps(x, absmask), ay = _mm_and_ps(y, absmask);
__m128 mask = _mm_cmplt_ps(ax, ay);
__m128 tmin = _mm_min_ps(ax, ay), tmax = _mm_max_ps(ax, ay);
__m128 c = _mm_div_ps(tmin, _mm_add_ps(tmax, eps));
__m128 c2 = _mm_mul_ps(c, c);
__m128 a = _mm_mul_ps(c2, p7);
a = _mm_mul_ps(_mm_add_ps(a, p5), c2);
a = _mm_mul_ps(_mm_add_ps(a, p3), c2);
a = _mm_mul_ps(_mm_add_ps(a, p1), c);
__m128 b = _mm_sub_ps(_90, a);
a = _mm_xor_ps(a, _mm_and_ps(_mm_xor_ps(a, b), mask));
b = _mm_sub_ps(_180, a);
mask = _mm_cmplt_ps(x, z);
a = _mm_xor_ps(a, _mm_and_ps(_mm_xor_ps(a, b), mask));
b = _mm_sub_ps(_360, a);
mask = _mm_cmplt_ps(y, z);
a = _mm_xor_ps(a, _mm_and_ps(_mm_xor_ps(a, b), mask));
a = _mm_mul_ps(a, scale4);
_mm_storeu_ps(angle + i, a);
}
#elif CV_NEON
float32x4_t eps = vdupq_n_f32((float)DBL_EPSILON);
float32x4_t _90 = vdupq_n_f32(90.f), _180 = vdupq_n_f32(180.f), _360 = vdupq_n_f32(360.f);
float32x4_t z = vdupq_n_f32(0.0f), scale4 = vdupq_n_f32(scale);
float32x4_t p1 = vdupq_n_f32(atan2_p1), p3 = vdupq_n_f32(atan2_p3);
float32x4_t p5 = vdupq_n_f32(atan2_p5), p7 = vdupq_n_f32(atan2_p7);
for( ; i <= len - 4; i += 4 )
{
float32x4_t x = vld1q_f32(X + i), y = vld1q_f32(Y + i);
float32x4_t ax = vabsq_f32(x), ay = vabsq_f32(y);
float32x4_t tmin = vminq_f32(ax, ay), tmax = vmaxq_f32(ax, ay);
float32x4_t c = vmulq_f32(tmin, cv_vrecpq_f32(vaddq_f32(tmax, eps)));
float32x4_t c2 = vmulq_f32(c, c);
float32x4_t a = vmulq_f32(c2, p7);
a = vmulq_f32(vaddq_f32(a, p5), c2);
a = vmulq_f32(vaddq_f32(a, p3), c2);
a = vmulq_f32(vaddq_f32(a, p1), c);
a = vbslq_f32(vcgeq_f32(ax, ay), a, vsubq_f32(_90, a));
a = vbslq_f32(vcltq_f32(x, z), vsubq_f32(_180, a), a);
a = vbslq_f32(vcltq_f32(y, z), vsubq_f32(_360, a), a);
vst1q_f32(angle + i, vmulq_f32(a, scale4));
}
#endif
for( ; i < len; i++ )
{
float x = X[i], y = Y[i];
float ax = std::abs(x), ay = std::abs(y);
float a, c, c2;
if( ax >= ay )
{
c = ay/(ax + (float)DBL_EPSILON);
c2 = c*c;
a = (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
}
else
{
c = ax/(ay + (float)DBL_EPSILON);
c2 = c*c;
a = 90.f - (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
}
if( x < 0 )
a = 180.f - a;
if( y < 0 )
a = 360.f - a;
angle[i] = (float)(a*scale);
}
}
void magnitude32f(const float* x, const float* y, float* mag, int len)
{
#if defined HAVE_IPP
CV_IPP_CHECK()
{
IppStatus status = ippsMagnitude_32f(x, y, mag, len);
if (status >= 0)
{
CV_IMPL_ADD(CV_IMPL_IPP);
return;
}
setIppErrorStatus();
}
#endif
int i = 0;
#if CV_SIMD128
for( ; i <= len - 8; i += 8 )
{
v_float32x4 x0 = v_load(x + i), x1 = v_load(x + i + 4);
v_float32x4 y0 = v_load(y + i), y1 = v_load(y + i + 4);
x0 = v_sqrt(v_muladd(x0, x0, y0*y0));
x1 = v_sqrt(v_muladd(x1, x1, y1*y1));
v_store(mag + i, x0);
v_store(mag + i + 4, x1);
}
#endif
for( ; i < len; i++ )
{
float x0 = x[i], y0 = y[i];
mag[i] = std::sqrt(x0*x0 + y0*y0);
}
}
void magnitude64f(const double* x, const double* y, double* mag, int len)
{
#if defined(HAVE_IPP)
CV_IPP_CHECK()
{
IppStatus status = ippsMagnitude_64f(x, y, mag, len);
if (status >= 0)
{
CV_IMPL_ADD(CV_IMPL_IPP);
return;
}
setIppErrorStatus();
}
#endif
int i = 0;
#if CV_SIMD128_64F
for( ; i <= len - 4; i += 4 )
{
v_float64x2 x0 = v_load(x + i), x1 = v_load(x + i + 2);
v_float64x2 y0 = v_load(y + i), y1 = v_load(y + i + 2);
x0 = v_sqrt(v_muladd(x0, x0, y0*y0));
x1 = v_sqrt(v_muladd(x1, x1, y1*y1));
v_store(mag + i, x0);
v_store(mag + i + 2, x1);
}
#endif
for( ; i < len; i++ )
{
double x0 = x[i], y0 = y[i];
mag[i] = std::sqrt(x0*x0 + y0*y0);
}
}
void invSqrt32f(const float* src, float* dst, int len)
{
#if defined(HAVE_IPP)
CV_IPP_CHECK()
{
if (ippsInvSqrt_32f_A21(src, dst, len) >= 0)
{
CV_IMPL_ADD(CV_IMPL_IPP);
return;
}
setIppErrorStatus();
}
#endif
int i = 0;
#if CV_SIMD128
for( ; i <= len - 8; i += 8 )
{
v_float32x4 t0 = v_load(src + i), t1 = v_load(src + i + 4);
t0 = v_invsqrt(t0);
t1 = v_invsqrt(t1);
v_store(dst + i, t0); v_store(dst + i + 4, t1);
}
#endif
for( ; i < len; i++ )
dst[i] = 1/std::sqrt(src[i]);
}
void invSqrt64f(const double* src, double* dst, int len)
{
int i = 0;
#if CV_SSE2
__m128d v_1 = _mm_set1_pd(1.0);
for ( ; i <= len - 2; i += 2)
_mm_storeu_pd(dst + i, _mm_div_pd(v_1, _mm_sqrt_pd(_mm_loadu_pd(src + i))));
#endif
for( ; i < len; i++ )
dst[i] = 1/std::sqrt(src[i]);
}
void sqrt32f(const float* src, float* dst, int len)
{
#if defined(HAVE_IPP)
CV_IPP_CHECK()
{
if (ippsSqrt_32f_A21(src, dst, len) >= 0)
{
CV_IMPL_ADD(CV_IMPL_IPP);
return;
}
setIppErrorStatus();
}
#endif
int i = 0;
#if CV_SIMD128
for( ; i <= len - 8; i += 8 )
{
v_float32x4 t0 = v_load(src + i), t1 = v_load(src + i + 4);
t0 = v_sqrt(t0);
t1 = v_sqrt(t1);
v_store(dst + i, t0); v_store(dst + i + 4, t1);
}
#endif
for( ; i < len; i++ )
dst[i] = std::sqrt(src[i]);
}
void sqrt64f(const double* src, double* dst, int len)
{
#if defined(HAVE_IPP)
CV_IPP_CHECK()
{
if (ippsSqrt_64f_A50(src, dst, len) >= 0)
{
CV_IMPL_ADD(CV_IMPL_IPP);
return;
}
setIppErrorStatus();
}
#endif
int i = 0;
#if CV_SIMD128_64F
for( ; i <= len - 4; i += 4 )
{
v_float64x2 t0 = v_load(src + i), t1 = v_load(src + i + 2);
t0 = v_sqrt(t0);
t1 = v_sqrt(t1);
v_store(dst + i, t0); v_store(dst + i + 2, t1);
}
#endif
for( ; i < len; i++ )
dst[i] = std::sqrt(src[i]);
}
////////////////////////////////////// EXP /////////////////////////////////////
typedef union
{
struct {
#if ( defined( WORDS_BIGENDIAN ) && !defined( OPENCV_UNIVERSAL_BUILD ) ) || defined( __BIG_ENDIAN__ )
int hi;
int lo;
#else
int lo;
int hi;
#endif
} i;
double d;
}
DBLINT;
#define EXPTAB_SCALE 6
#define EXPTAB_MASK ((1 << EXPTAB_SCALE) - 1)
#define EXPPOLY_32F_A0 .9670371139572337719125840413672004409288e-2
static const double expTab[] = {
1.0 * EXPPOLY_32F_A0,
1.0108892860517004600204097905619 * EXPPOLY_32F_A0,
1.0218971486541166782344801347833 * EXPPOLY_32F_A0,
1.0330248790212284225001082839705 * EXPPOLY_32F_A0,
1.0442737824274138403219664787399 * EXPPOLY_32F_A0,
1.0556451783605571588083413251529 * EXPPOLY_32F_A0,
1.0671404006768236181695211209928 * EXPPOLY_32F_A0,
1.0787607977571197937406800374385 * EXPPOLY_32F_A0,
1.0905077326652576592070106557607 * EXPPOLY_32F_A0,
1.1023825833078409435564142094256 * EXPPOLY_32F_A0,
1.1143867425958925363088129569196 * EXPPOLY_32F_A0,
1.126521618608241899794798643787 * EXPPOLY_32F_A0,
1.1387886347566916537038302838415 * EXPPOLY_32F_A0,
1.151189229952982705817759635202 * EXPPOLY_32F_A0,
1.1637248587775775138135735990922 * EXPPOLY_32F_A0,
1.1763969916502812762846457284838 * EXPPOLY_32F_A0,
1.1892071150027210667174999705605 * EXPPOLY_32F_A0,
1.2021567314527031420963969574978 * EXPPOLY_32F_A0,
1.2152473599804688781165202513388 * EXPPOLY_32F_A0,
1.2284805361068700056940089577928 * EXPPOLY_32F_A0,
1.2418578120734840485936774687266 * EXPPOLY_32F_A0,
1.2553807570246910895793906574423 * EXPPOLY_32F_A0,
1.2690509571917332225544190810323 * EXPPOLY_32F_A0,
1.2828700160787782807266697810215 * EXPPOLY_32F_A0,
1.2968395546510096659337541177925 * EXPPOLY_32F_A0,
1.3109612115247643419229917863308 * EXPPOLY_32F_A0,
1.3252366431597412946295370954987 * EXPPOLY_32F_A0,
1.3396675240533030053600306697244 * EXPPOLY_32F_A0,
1.3542555469368927282980147401407 * EXPPOLY_32F_A0,
1.3690024229745906119296011329822 * EXPPOLY_32F_A0,
1.3839098819638319548726595272652 * EXPPOLY_32F_A0,
1.3989796725383111402095281367152 * EXPPOLY_32F_A0,
1.4142135623730950488016887242097 * EXPPOLY_32F_A0,
1.4296133383919700112350657782751 * EXPPOLY_32F_A0,
1.4451808069770466200370062414717 * EXPPOLY_32F_A0,
1.4609177941806469886513028903106 * EXPPOLY_32F_A0,
1.476826145939499311386907480374 * EXPPOLY_32F_A0,
1.4929077282912648492006435314867 * EXPPOLY_32F_A0,
1.5091644275934227397660195510332 * EXPPOLY_32F_A0,
1.5255981507445383068512536895169 * EXPPOLY_32F_A0,
1.5422108254079408236122918620907 * EXPPOLY_32F_A0,
1.5590044002378369670337280894749 * EXPPOLY_32F_A0,
1.5759808451078864864552701601819 * EXPPOLY_32F_A0,
1.5931421513422668979372486431191 * EXPPOLY_32F_A0,
1.6104903319492543081795206673574 * EXPPOLY_32F_A0,
1.628027421857347766848218522014 * EXPPOLY_32F_A0,
1.6457554781539648445187567247258 * EXPPOLY_32F_A0,
1.6636765803267364350463364569764 * EXPPOLY_32F_A0,
1.6817928305074290860622509524664 * EXPPOLY_32F_A0,
1.7001063537185234695013625734975 * EXPPOLY_32F_A0,
1.7186192981224779156293443764563 * EXPPOLY_32F_A0,
1.7373338352737062489942020818722 * EXPPOLY_32F_A0,
1.7562521603732994831121606193753 * EXPPOLY_32F_A0,
1.7753764925265212525505592001993 * EXPPOLY_32F_A0,
1.7947090750031071864277032421278 * EXPPOLY_32F_A0,
1.8142521755003987562498346003623 * EXPPOLY_32F_A0,
1.8340080864093424634870831895883 * EXPPOLY_32F_A0,
1.8539791250833855683924530703377 * EXPPOLY_32F_A0,
1.8741676341102999013299989499544 * EXPPOLY_32F_A0,
1.8945759815869656413402186534269 * EXPPOLY_32F_A0,
1.9152065613971472938726112702958 * EXPPOLY_32F_A0,
1.9360617934922944505980559045667 * EXPPOLY_32F_A0,
1.9571441241754002690183222516269 * EXPPOLY_32F_A0,
1.9784560263879509682582499181312 * EXPPOLY_32F_A0,
};
// the code below uses _mm_cast* intrinsics, which are not avialable on VS2005
#if (defined _MSC_VER && _MSC_VER < 1500) || \
(!defined __APPLE__ && defined __GNUC__ && __GNUC__*100 + __GNUC_MINOR__ < 402)
#undef CV_SSE2
#define CV_SSE2 0
#endif
static const double exp_prescale = 1.4426950408889634073599246810019 * (1 << EXPTAB_SCALE);
static const double exp_postscale = 1./(1 << EXPTAB_SCALE);
static const double exp_max_val = 3000.*(1 << EXPTAB_SCALE); // log10(DBL_MAX) < 3000
void exp32f( const float *_x, float *y, int n )
{
static const float
A4 = (float)(1.000000000000002438532970795181890933776 / EXPPOLY_32F_A0),
A3 = (float)(.6931471805521448196800669615864773144641 / EXPPOLY_32F_A0),
A2 = (float)(.2402265109513301490103372422686535526573 / EXPPOLY_32F_A0),
A1 = (float)(.5550339366753125211915322047004666939128e-1 / EXPPOLY_32F_A0);
#undef EXPPOLY
#define EXPPOLY(x) \
(((((x) + A1)*(x) + A2)*(x) + A3)*(x) + A4)
int i = 0;
const Cv32suf* x = (const Cv32suf*)_x;
Cv32suf buf[4];
#if CV_SSE2
if( n >= 8 )
{
static const __m128d prescale2 = _mm_set1_pd(exp_prescale);
static const __m128 postscale4 = _mm_set1_ps((float)exp_postscale);
static const __m128 maxval4 = _mm_set1_ps((float)(exp_max_val/exp_prescale));
static const __m128 minval4 = _mm_set1_ps((float)(-exp_max_val/exp_prescale));
static const __m128 mA1 = _mm_set1_ps(A1);
static const __m128 mA2 = _mm_set1_ps(A2);
static const __m128 mA3 = _mm_set1_ps(A3);
static const __m128 mA4 = _mm_set1_ps(A4);
bool y_aligned = (size_t)(void*)y % 16 == 0;
ushort CV_DECL_ALIGNED(16) tab_idx[8];
for( ; i <= n - 8; i += 8 )
{
__m128 xf0, xf1;
xf0 = _mm_loadu_ps(&x[i].f);
xf1 = _mm_loadu_ps(&x[i+4].f);
__m128i xi0, xi1, xi2, xi3;
xf0 = _mm_min_ps(_mm_max_ps(xf0, minval4), maxval4);
xf1 = _mm_min_ps(_mm_max_ps(xf1, minval4), maxval4);
__m128d xd0 = _mm_cvtps_pd(xf0);
__m128d xd2 = _mm_cvtps_pd(_mm_movehl_ps(xf0, xf0));
__m128d xd1 = _mm_cvtps_pd(xf1);
__m128d xd3 = _mm_cvtps_pd(_mm_movehl_ps(xf1, xf1));
xd0 = _mm_mul_pd(xd0, prescale2);
xd2 = _mm_mul_pd(xd2, prescale2);
xd1 = _mm_mul_pd(xd1, prescale2);
xd3 = _mm_mul_pd(xd3, prescale2);
xi0 = _mm_cvtpd_epi32(xd0);
xi2 = _mm_cvtpd_epi32(xd2);
xi1 = _mm_cvtpd_epi32(xd1);
xi3 = _mm_cvtpd_epi32(xd3);
xd0 = _mm_sub_pd(xd0, _mm_cvtepi32_pd(xi0));
xd2 = _mm_sub_pd(xd2, _mm_cvtepi32_pd(xi2));
xd1 = _mm_sub_pd(xd1, _mm_cvtepi32_pd(xi1));
xd3 = _mm_sub_pd(xd3, _mm_cvtepi32_pd(xi3));
xf0 = _mm_movelh_ps(_mm_cvtpd_ps(xd0), _mm_cvtpd_ps(xd2));
xf1 = _mm_movelh_ps(_mm_cvtpd_ps(xd1), _mm_cvtpd_ps(xd3));
xf0 = _mm_mul_ps(xf0, postscale4);
xf1 = _mm_mul_ps(xf1, postscale4);
xi0 = _mm_unpacklo_epi64(xi0, xi2);
xi1 = _mm_unpacklo_epi64(xi1, xi3);
xi0 = _mm_packs_epi32(xi0, xi1);
_mm_store_si128((__m128i*)tab_idx, _mm_and_si128(xi0, _mm_set1_epi16(EXPTAB_MASK)));
xi0 = _mm_add_epi16(_mm_srai_epi16(xi0, EXPTAB_SCALE), _mm_set1_epi16(127));
xi0 = _mm_max_epi16(xi0, _mm_setzero_si128());
xi0 = _mm_min_epi16(xi0, _mm_set1_epi16(255));
xi1 = _mm_unpackhi_epi16(xi0, _mm_setzero_si128());
xi0 = _mm_unpacklo_epi16(xi0, _mm_setzero_si128());
__m128d yd0 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[0]), _mm_load_sd(expTab + tab_idx[1]));
__m128d yd1 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[2]), _mm_load_sd(expTab + tab_idx[3]));
__m128d yd2 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[4]), _mm_load_sd(expTab + tab_idx[5]));
__m128d yd3 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[6]), _mm_load_sd(expTab + tab_idx[7]));
__m128 yf0 = _mm_movelh_ps(_mm_cvtpd_ps(yd0), _mm_cvtpd_ps(yd1));
__m128 yf1 = _mm_movelh_ps(_mm_cvtpd_ps(yd2), _mm_cvtpd_ps(yd3));
yf0 = _mm_mul_ps(yf0, _mm_castsi128_ps(_mm_slli_epi32(xi0, 23)));
yf1 = _mm_mul_ps(yf1, _mm_castsi128_ps(_mm_slli_epi32(xi1, 23)));
__m128 zf0 = _mm_add_ps(xf0, mA1);
__m128 zf1 = _mm_add_ps(xf1, mA1);
zf0 = _mm_add_ps(_mm_mul_ps(zf0, xf0), mA2);
zf1 = _mm_add_ps(_mm_mul_ps(zf1, xf1), mA2);
zf0 = _mm_add_ps(_mm_mul_ps(zf0, xf0), mA3);
zf1 = _mm_add_ps(_mm_mul_ps(zf1, xf1), mA3);
zf0 = _mm_add_ps(_mm_mul_ps(zf0, xf0), mA4);
zf1 = _mm_add_ps(_mm_mul_ps(zf1, xf1), mA4);
zf0 = _mm_mul_ps(zf0, yf0);
zf1 = _mm_mul_ps(zf1, yf1);
if( y_aligned )
{
_mm_store_ps(y + i, zf0);
_mm_store_ps(y + i + 4, zf1);
}
else
{
_mm_storeu_ps(y + i, zf0);
_mm_storeu_ps(y + i + 4, zf1);
}
}
}
else
#endif
for( ; i <= n - 4; i += 4 )
{
double x0 = x[i].f * exp_prescale;
double x1 = x[i + 1].f * exp_prescale;
double x2 = x[i + 2].f * exp_prescale;
double x3 = x[i + 3].f * exp_prescale;
int val0, val1, val2, val3, t;
if( ((x[i].i >> 23) & 255) > 127 + 10 )
x0 = x[i].i < 0 ? -exp_max_val : exp_max_val;
if( ((x[i+1].i >> 23) & 255) > 127 + 10 )
x1 = x[i+1].i < 0 ? -exp_max_val : exp_max_val;
if( ((x[i+2].i >> 23) & 255) > 127 + 10 )
x2 = x[i+2].i < 0 ? -exp_max_val : exp_max_val;
if( ((x[i+3].i >> 23) & 255) > 127 + 10 )
x3 = x[i+3].i < 0 ? -exp_max_val : exp_max_val;
val0 = cvRound(x0);
val1 = cvRound(x1);
val2 = cvRound(x2);
val3 = cvRound(x3);
x0 = (x0 - val0)*exp_postscale;
x1 = (x1 - val1)*exp_postscale;
x2 = (x2 - val2)*exp_postscale;
x3 = (x3 - val3)*exp_postscale;
t = (val0 >> EXPTAB_SCALE) + 127;
t = !(t & ~255) ? t : t < 0 ? 0 : 255;
buf[0].i = t << 23;
t = (val1 >> EXPTAB_SCALE) + 127;
t = !(t & ~255) ? t : t < 0 ? 0 : 255;
buf[1].i = t << 23;
t = (val2 >> EXPTAB_SCALE) + 127;
t = !(t & ~255) ? t : t < 0 ? 0 : 255;
buf[2].i = t << 23;
t = (val3 >> EXPTAB_SCALE) + 127;
t = !(t & ~255) ? t : t < 0 ? 0 : 255;
buf[3].i = t << 23;
x0 = buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY( x0 );
x1 = buf[1].f * expTab[val1 & EXPTAB_MASK] * EXPPOLY( x1 );
y[i] = (float)x0;
y[i + 1] = (float)x1;
x2 = buf[2].f * expTab[val2 & EXPTAB_MASK] * EXPPOLY( x2 );
x3 = buf[3].f * expTab[val3 & EXPTAB_MASK] * EXPPOLY( x3 );
y[i + 2] = (float)x2;
y[i + 3] = (float)x3;
}
for( ; i < n; i++ )
{
double x0 = x[i].f * exp_prescale;
int val0, t;
if( ((x[i].i >> 23) & 255) > 127 + 10 )
x0 = x[i].i < 0 ? -exp_max_val : exp_max_val;
val0 = cvRound(x0);
t = (val0 >> EXPTAB_SCALE) + 127;
t = !(t & ~255) ? t : t < 0 ? 0 : 255;
buf[0].i = t << 23;
x0 = (x0 - val0)*exp_postscale;
y[i] = (float)(buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY(x0));
}
}
void exp64f( const double *_x, double *y, int n )
{
static const double
A5 = .99999999999999999998285227504999 / EXPPOLY_32F_A0,
A4 = .69314718055994546743029643825322 / EXPPOLY_32F_A0,
A3 = .24022650695886477918181338054308 / EXPPOLY_32F_A0,
A2 = .55504108793649567998466049042729e-1 / EXPPOLY_32F_A0,
A1 = .96180973140732918010002372686186e-2 / EXPPOLY_32F_A0,
A0 = .13369713757180123244806654839424e-2 / EXPPOLY_32F_A0;
#undef EXPPOLY
#define EXPPOLY(x) (((((A0*(x) + A1)*(x) + A2)*(x) + A3)*(x) + A4)*(x) + A5)
int i = 0;
Cv64suf buf[4];
const Cv64suf* x = (const Cv64suf*)_x;
#if CV_SSE2
static const __m128d prescale2 = _mm_set1_pd(exp_prescale);
static const __m128d postscale2 = _mm_set1_pd(exp_postscale);
static const __m128d maxval2 = _mm_set1_pd(exp_max_val);
static const __m128d minval2 = _mm_set1_pd(-exp_max_val);
static const __m128d mA0 = _mm_set1_pd(A0);
static const __m128d mA1 = _mm_set1_pd(A1);
static const __m128d mA2 = _mm_set1_pd(A2);
static const __m128d mA3 = _mm_set1_pd(A3);
static const __m128d mA4 = _mm_set1_pd(A4);
static const __m128d mA5 = _mm_set1_pd(A5);
int CV_DECL_ALIGNED(16) tab_idx[4];
for( ; i <= n - 4; i += 4 )
{
__m128d xf0 = _mm_loadu_pd(&x[i].f), xf1 = _mm_loadu_pd(&x[i+2].f);
__m128i xi0, xi1;
xf0 = _mm_min_pd(_mm_max_pd(xf0, minval2), maxval2);
xf1 = _mm_min_pd(_mm_max_pd(xf1, minval2), maxval2);
xf0 = _mm_mul_pd(xf0, prescale2);
xf1 = _mm_mul_pd(xf1, prescale2);
xi0 = _mm_cvtpd_epi32(xf0);
xi1 = _mm_cvtpd_epi32(xf1);
xf0 = _mm_mul_pd(_mm_sub_pd(xf0, _mm_cvtepi32_pd(xi0)), postscale2);
xf1 = _mm_mul_pd(_mm_sub_pd(xf1, _mm_cvtepi32_pd(xi1)), postscale2);
xi0 = _mm_unpacklo_epi64(xi0, xi1);
_mm_store_si128((__m128i*)tab_idx, _mm_and_si128(xi0, _mm_set1_epi32(EXPTAB_MASK)));
xi0 = _mm_add_epi32(_mm_srai_epi32(xi0, EXPTAB_SCALE), _mm_set1_epi32(1023));
xi0 = _mm_packs_epi32(xi0, xi0);
xi0 = _mm_max_epi16(xi0, _mm_setzero_si128());
xi0 = _mm_min_epi16(xi0, _mm_set1_epi16(2047));
xi0 = _mm_unpacklo_epi16(xi0, _mm_setzero_si128());
xi1 = _mm_unpackhi_epi32(xi0, _mm_setzero_si128());
xi0 = _mm_unpacklo_epi32(xi0, _mm_setzero_si128());
__m128d yf0 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[0]), _mm_load_sd(expTab + tab_idx[1]));
__m128d yf1 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[2]), _mm_load_sd(expTab + tab_idx[3]));
yf0 = _mm_mul_pd(yf0, _mm_castsi128_pd(_mm_slli_epi64(xi0, 52)));
yf1 = _mm_mul_pd(yf1, _mm_castsi128_pd(_mm_slli_epi64(xi1, 52)));
__m128d zf0 = _mm_add_pd(_mm_mul_pd(mA0, xf0), mA1);
__m128d zf1 = _mm_add_pd(_mm_mul_pd(mA0, xf1), mA1);
zf0 = _mm_add_pd(_mm_mul_pd(zf0, xf0), mA2);
zf1 = _mm_add_pd(_mm_mul_pd(zf1, xf1), mA2);
zf0 = _mm_add_pd(_mm_mul_pd(zf0, xf0), mA3);
zf1 = _mm_add_pd(_mm_mul_pd(zf1, xf1), mA3);
zf0 = _mm_add_pd(_mm_mul_pd(zf0, xf0), mA4);
zf1 = _mm_add_pd(_mm_mul_pd(zf1, xf1), mA4);
zf0 = _mm_add_pd(_mm_mul_pd(zf0, xf0), mA5);
zf1 = _mm_add_pd(_mm_mul_pd(zf1, xf1), mA5);
zf0 = _mm_mul_pd(zf0, yf0);
zf1 = _mm_mul_pd(zf1, yf1);
_mm_storeu_pd(y + i, zf0);
_mm_storeu_pd(y + i + 2, zf1);
}
#endif
for( ; i <= n - 4; i += 4 )
{
double x0 = x[i].f * exp_prescale;
double x1 = x[i + 1].f * exp_prescale;
double x2 = x[i + 2].f * exp_prescale;
double x3 = x[i + 3].f * exp_prescale;
double y0, y1, y2, y3;
int val0, val1, val2, val3, t;
t = (int)(x[i].i >> 52);
if( (t & 2047) > 1023 + 10 )
x0 = t < 0 ? -exp_max_val : exp_max_val;
t = (int)(x[i+1].i >> 52);
if( (t & 2047) > 1023 + 10 )
x1 = t < 0 ? -exp_max_val : exp_max_val;
t = (int)(x[i+2].i >> 52);
if( (t & 2047) > 1023 + 10 )
x2 = t < 0 ? -exp_max_val : exp_max_val;
t = (int)(x[i+3].i >> 52);
if( (t & 2047) > 1023 + 10 )
x3 = t < 0 ? -exp_max_val : exp_max_val;
val0 = cvRound(x0);
val1 = cvRound(x1);
val2 = cvRound(x2);
val3 = cvRound(x3);
x0 = (x0 - val0)*exp_postscale;
x1 = (x1 - val1)*exp_postscale;
x2 = (x2 - val2)*exp_postscale;
x3 = (x3 - val3)*exp_postscale;
t = (val0 >> EXPTAB_SCALE) + 1023;
t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
buf[0].i = (int64)t << 52;
t = (val1 >> EXPTAB_SCALE) + 1023;
t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
buf[1].i = (int64)t << 52;
t = (val2 >> EXPTAB_SCALE) + 1023;
t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
buf[2].i = (int64)t << 52;
t = (val3 >> EXPTAB_SCALE) + 1023;
t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
buf[3].i = (int64)t << 52;
y0 = buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY( x0 );
y1 = buf[1].f * expTab[val1 & EXPTAB_MASK] * EXPPOLY( x1 );
y[i] = y0;
y[i + 1] = y1;
y2 = buf[2].f * expTab[val2 & EXPTAB_MASK] * EXPPOLY( x2 );
y3 = buf[3].f * expTab[val3 & EXPTAB_MASK] * EXPPOLY( x3 );
y[i + 2] = y2;
y[i + 3] = y3;
}
for( ; i < n; i++ )
{
double x0 = x[i].f * exp_prescale;
int val0, t;
t = (int)(x[i].i >> 52);
if( (t & 2047) > 1023 + 10 )
x0 = t < 0 ? -exp_max_val : exp_max_val;
val0 = cvRound(x0);
t = (val0 >> EXPTAB_SCALE) + 1023;
t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
buf[0].i = (int64)t << 52;
x0 = (x0 - val0)*exp_postscale;
y[i] = buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY( x0 );
}
}
#undef EXPTAB_SCALE
#undef EXPTAB_MASK
#undef EXPPOLY_32F_A0
/////////////////////////////////////////// LOG ///////////////////////////////////////
#define LOGTAB_SCALE 8
#define LOGTAB_MASK ((1 << LOGTAB_SCALE) - 1)
#define LOGTAB_MASK2 ((1 << (20 - LOGTAB_SCALE)) - 1)
#define LOGTAB_MASK2_32F ((1 << (23 - LOGTAB_SCALE)) - 1)
static const double CV_DECL_ALIGNED(16) icvLogTab[] = {
0.0000000000000000000000000000000000000000, 1.000000000000000000000000000000000000000,
.00389864041565732288852075271279318258166, .9961089494163424124513618677042801556420,
.00778214044205494809292034119607706088573, .9922480620155038759689922480620155038760,
.01165061721997527263705585198749759001657, .9884169884169884169884169884169884169884,
.01550418653596525274396267235488267033361, .9846153846153846153846153846153846153846,
.01934296284313093139406447562578250654042, .9808429118773946360153256704980842911877,
.02316705928153437593630670221500622574241, .9770992366412213740458015267175572519084,
.02697658769820207233514075539915211265906, .9733840304182509505703422053231939163498,
.03077165866675368732785500469617545604706, .9696969696969696969696969696969696969697,
.03455238150665972812758397481047722976656, .9660377358490566037735849056603773584906,
.03831886430213659461285757856785494368522, .9624060150375939849624060150375939849624,
.04207121392068705056921373852674150839447, .9588014981273408239700374531835205992509,
.04580953603129420126371940114040626212953, .9552238805970149253731343283582089552239,
.04953393512227662748292900118940451648088, .9516728624535315985130111524163568773234,
.05324451451881227759255210685296333394944, .9481481481481481481481481481481481481481,
.05694137640013842427411105973078520037234, .9446494464944649446494464944649446494465,
.06062462181643483993820353816772694699466, .9411764705882352941176470588235294117647,
.06429435070539725460836422143984236754475, .9377289377289377289377289377289377289377,
.06795066190850773679699159401934593915938, .9343065693430656934306569343065693430657,
.07159365318700880442825962290953611955044, .9309090909090909090909090909090909090909,
.07522342123758751775142172846244648098944, .9275362318840579710144927536231884057971,
.07884006170777602129362549021607264876369, .9241877256317689530685920577617328519856,
.08244366921107458556772229485432035289706, .9208633093525179856115107913669064748201,
.08603433734180314373940490213499288074675, .9175627240143369175627240143369175627240,
.08961215868968712416897659522874164395031, .9142857142857142857142857142857142857143,
.09317722485418328259854092721070628613231, .9110320284697508896797153024911032028470,
.09672962645855109897752299730200320482256, .9078014184397163120567375886524822695035,
.10026945316367513738597949668474029749630, .9045936395759717314487632508833922261484,
.10379679368164355934833764649738441221420, .9014084507042253521126760563380281690141,
.10731173578908805021914218968959175981580, .8982456140350877192982456140350877192982,
.11081436634029011301105782649756292812530, .8951048951048951048951048951048951048951,
.11430477128005862852422325204315711744130, .8919860627177700348432055749128919860627,
.11778303565638344185817487641543266363440, .8888888888888888888888888888888888888889,
.12124924363286967987640707633545389398930, .8858131487889273356401384083044982698962,
.12470347850095722663787967121606925502420, .8827586206896551724137931034482758620690,
.12814582269193003360996385708858724683530, .8797250859106529209621993127147766323024,
.13157635778871926146571524895989568904040, .8767123287671232876712328767123287671233,
.13499516453750481925766280255629681050780, .8737201365187713310580204778156996587031,
.13840232285911913123754857224412262439730, .8707482993197278911564625850340136054422,
.14179791186025733629172407290752744302150, .8677966101694915254237288135593220338983,
.14518200984449788903951628071808954700830, .8648648648648648648648648648648648648649,
.14855469432313711530824207329715136438610, .8619528619528619528619528619528619528620,
.15191604202584196858794030049466527998450, .8590604026845637583892617449664429530201,
.15526612891112392955683674244937719777230, .8561872909698996655518394648829431438127,
.15860503017663857283636730244325008243330, .8533333333333333333333333333333333333333,
.16193282026931324346641360989451641216880, .8504983388704318936877076411960132890365,
.16524957289530714521497145597095368430010, .8476821192052980132450331125827814569536,
.16855536102980664403538924034364754334090, .8448844884488448844884488448844884488449,
.17185025692665920060697715143760433420540, .8421052631578947368421052631578947368421,
.17513433212784912385018287750426679849630, .8393442622950819672131147540983606557377,
.17840765747281828179637841458315961062910, .8366013071895424836601307189542483660131,
.18167030310763465639212199675966985523700, .8338762214983713355048859934853420195440,
.18492233849401198964024217730184318497780, .8311688311688311688311688311688311688312,
.18816383241818296356839823602058459073300, .8284789644012944983818770226537216828479,
.19139485299962943898322009772527962923050, .8258064516129032258064516129032258064516,
.19461546769967164038916962454095482826240, .8231511254019292604501607717041800643087,
.19782574332991986754137769821682013571260, .8205128205128205128205128205128205128205,
.20102574606059073203390141770796617493040, .8178913738019169329073482428115015974441,
.20421554142869088876999228432396193966280, .8152866242038216560509554140127388535032,
.20739519434607056602715147164417430758480, .8126984126984126984126984126984126984127,
.21056476910734961416338251183333341032260, .8101265822784810126582278481012658227848,
.21372432939771812687723695489694364368910, .8075709779179810725552050473186119873817,
.21687393830061435506806333251006435602900, .8050314465408805031446540880503144654088,
.22001365830528207823135744547471404075630, .8025078369905956112852664576802507836991,
.22314355131420973710199007200571941211830, .8000000000000000000000000000000000000000,
.22626367865045338145790765338460914790630, .7975077881619937694704049844236760124611,
.22937410106484582006380890106811420992010, .7950310559006211180124223602484472049689,
.23247487874309405442296849741978803649550, .7925696594427244582043343653250773993808,
.23556607131276688371634975283086532726890, .7901234567901234567901234567901234567901,
.23864773785017498464178231643018079921600, .7876923076923076923076923076923076923077,
.24171993688714515924331749374687206000090, .7852760736196319018404907975460122699387,
.24478272641769091566565919038112042471760, .7828746177370030581039755351681957186544,
.24783616390458124145723672882013488560910, .7804878048780487804878048780487804878049,
.25088030628580937353433455427875742316250, .7781155015197568389057750759878419452888,
.25391520998096339667426946107298135757450, .7757575757575757575757575757575757575758,
.25694093089750041913887912414793390780680, .7734138972809667673716012084592145015106,
.25995752443692604627401010475296061486000, .7710843373493975903614457831325301204819,
.26296504550088134477547896494797896593800, .7687687687687687687687687687687687687688,
.26596354849713793599974565040611196309330, .7664670658682634730538922155688622754491,
.26895308734550393836570947314612567424780, .7641791044776119402985074626865671641791,
.27193371548364175804834985683555714786050, .7619047619047619047619047619047619047619,
.27490548587279922676529508862586226314300, .7596439169139465875370919881305637982196,
.27786845100345625159121709657483734190480, .7573964497041420118343195266272189349112,
.28082266290088775395616949026589281857030, .7551622418879056047197640117994100294985,
.28376817313064456316240580235898960381750, .7529411764705882352941176470588235294118,
.28670503280395426282112225635501090437180, .7507331378299120234604105571847507331378,
.28963329258304265634293983566749375313530, .7485380116959064327485380116959064327485,
.29255300268637740579436012922087684273730, .7463556851311953352769679300291545189504,
.29546421289383584252163927885703742504130, .7441860465116279069767441860465116279070,
.29836697255179722709783618483925238251680, .7420289855072463768115942028985507246377,
.30126133057816173455023545102449133992200, .7398843930635838150289017341040462427746,
.30414733546729666446850615102448500692850, .7377521613832853025936599423631123919308,
.30702503529491181888388950937951449304830, .7356321839080459770114942528735632183908,
.30989447772286465854207904158101882785550, .7335243553008595988538681948424068767908,
.31275571000389684739317885942000430077330, .7314285714285714285714285714285714285714,
.31560877898630329552176476681779604405180, .7293447293447293447293447293447293447293,
.31845373111853458869546784626436419785030, .7272727272727272727272727272727272727273,
.32129061245373424782201254856772720813750, .7252124645892351274787535410764872521246,
.32411946865421192853773391107097268104550, .7231638418079096045197740112994350282486,
.32694034499585328257253991068864706903700, .7211267605633802816901408450704225352113,
.32975328637246797969240219572384376078850, .7191011235955056179775280898876404494382,
.33255833730007655635318997155991382896900, .7170868347338935574229691876750700280112,
.33535554192113781191153520921943709254280, .7150837988826815642458100558659217877095,
.33814494400871636381467055798566434532400, .7130919220055710306406685236768802228412,
.34092658697059319283795275623560883104800, .7111111111111111111111111111111111111111,
.34370051385331840121395430287520866841080, .7091412742382271468144044321329639889197,
.34646676734620857063262633346312213689100, .7071823204419889502762430939226519337017,
.34922538978528827602332285096053965389730, .7052341597796143250688705234159779614325,
.35197642315717814209818925519357435405250, .7032967032967032967032967032967032967033,
.35471990910292899856770532096561510115850, .7013698630136986301369863013698630136986,
.35745588892180374385176833129662554711100, .6994535519125683060109289617486338797814,
.36018440357500774995358483465679455548530, .6975476839237057220708446866485013623978,
.36290549368936841911903457003063522279280, .6956521739130434782608695652173913043478,
.36561919956096466943762379742111079394830, .6937669376693766937669376693766937669377,
.36832556115870762614150635272380895912650, .6918918918918918918918918918918918918919,
.37102461812787262962487488948681857436900, .6900269541778975741239892183288409703504,
.37371640979358405898480555151763837784530, .6881720430107526881720430107526881720430,
.37640097516425302659470730759494472295050, .6863270777479892761394101876675603217158,
.37907835293496944251145919224654790014030, .6844919786096256684491978609625668449198,
.38174858149084833769393299007788300514230, .6826666666666666666666666666666666666667,
.38441169891033200034513583887019194662580, .6808510638297872340425531914893617021277,
.38706774296844825844488013899535872042180, .6790450928381962864721485411140583554377,
.38971675114002518602873692543653305619950, .6772486772486772486772486772486772486772,
.39235876060286384303665840889152605086580, .6754617414248021108179419525065963060686,
.39499380824086893770896722344332374632350, .6736842105263157894736842105263157894737,
.39762193064713846624158577469643205404280, .6719160104986876640419947506561679790026,
.40024316412701266276741307592601515352730, .6701570680628272251308900523560209424084,
.40285754470108348090917615991202183067800, .6684073107049608355091383812010443864230,
.40546510810816432934799991016916465014230, .6666666666666666666666666666666666666667,
.40806588980822172674223224930756259709600, .6649350649350649350649350649350649350649,
.41065992498526837639616360320360399782650, .6632124352331606217616580310880829015544,
.41324724855021932601317757871584035456180, .6614987080103359173126614987080103359173,
.41582789514371093497757669865677598863850, .6597938144329896907216494845360824742268,
.41840189913888381489925905043492093682300, .6580976863753213367609254498714652956298,
.42096929464412963239894338585145305842150, .6564102564102564102564102564102564102564,
.42353011550580327293502591601281892508280, .6547314578005115089514066496163682864450,
.42608439531090003260516141381231136620050, .6530612244897959183673469387755102040816,
.42863216738969872610098832410585600882780, .6513994910941475826972010178117048346056,
.43117346481837132143866142541810404509300, .6497461928934010152284263959390862944162,
.43370832042155937902094819946796633303180, .6481012658227848101265822784810126582278,
.43623676677491801667585491486534010618930, .6464646464646464646464646464646464646465,
.43875883620762790027214350629947148263450, .6448362720403022670025188916876574307305,
.44127456080487520440058801796112675219780, .6432160804020100502512562814070351758794,
.44378397241030093089975139264424797147500, .6416040100250626566416040100250626566416,
.44628710262841947420398014401143882423650, .6400000000000000000000000000000000000000,
.44878398282700665555822183705458883196130, .6384039900249376558603491271820448877805,
.45127464413945855836729492693848442286250, .6368159203980099502487562189054726368159,
.45375911746712049854579618113348260521900, .6352357320099255583126550868486352357320,
.45623743348158757315857769754074979573500, .6336633663366336633663366336633663366337,
.45870962262697662081833982483658473938700, .6320987654320987654320987654320987654321,
.46117571512217014895185229761409573256980, .6305418719211822660098522167487684729064,
.46363574096303250549055974261136725544930, .6289926289926289926289926289926289926290,
.46608972992459918316399125615134835243230, .6274509803921568627450980392156862745098,
.46853771156323925639597405279346276074650, .6259168704156479217603911980440097799511,
.47097971521879100631480241645476780831830, .6243902439024390243902439024390243902439,
.47341577001667212165614273544633761048330, .6228710462287104622871046228710462287105,
.47584590486996386493601107758877333253630, .6213592233009708737864077669902912621359,
.47827014848147025860569669930555392056700, .6198547215496368038740920096852300242131,
.48068852934575190261057286988943815231330, .6183574879227053140096618357487922705314,
.48310107575113581113157579238759353756900, .6168674698795180722891566265060240963855,
.48550781578170076890899053978500887751580, .6153846153846153846153846153846153846154,
.48790877731923892879351001283794175833480, .6139088729016786570743405275779376498801,
.49030398804519381705802061333088204264650, .6124401913875598086124401913875598086124,
.49269347544257524607047571407747454941280, .6109785202863961813842482100238663484487,
.49507726679785146739476431321236304938800, .6095238095238095238095238095238095238095,
.49745538920281889838648226032091770321130, .6080760095011876484560570071258907363420,
.49982786955644931126130359189119189977650, .6066350710900473933649289099526066350711,
.50219473456671548383667413872899487614650, .6052009456264775413711583924349881796690,
.50455601075239520092452494282042607665050, .6037735849056603773584905660377358490566,
.50691172444485432801997148999362252652650, .6023529411764705882352941176470588235294,
.50926190178980790257412536448100581765150, .6009389671361502347417840375586854460094,
.51160656874906207391973111953120678663250, .5995316159250585480093676814988290398126,
.51394575110223428282552049495279788970950, .5981308411214953271028037383177570093458,
.51627947444845445623684554448118433356300, .5967365967365967365967365967365967365967,
.51860776420804555186805373523384332656850, .5953488372093023255813953488372093023256,
.52093064562418522900344441950437612831600, .5939675174013921113689095127610208816705,
.52324814376454775732838697877014055848100, .5925925925925925925925925925925925925926,
.52556028352292727401362526507000438869000, .5912240184757505773672055427251732101617,
.52786708962084227803046587723656557500350, .5898617511520737327188940092165898617512,
.53016858660912158374145519701414741575700, .5885057471264367816091954022988505747126,
.53246479886947173376654518506256863474850, .5871559633027522935779816513761467889908,
.53475575061602764748158733709715306758900, .5858123569794050343249427917620137299771,
.53704146589688361856929077475797384977350, .5844748858447488584474885844748858447489,
.53932196859560876944783558428753167390800, .5831435079726651480637813211845102505695,
.54159728243274429804188230264117009937750, .5818181818181818181818181818181818181818,
.54386743096728351609669971367111429572100, .5804988662131519274376417233560090702948,
.54613243759813556721383065450936555862450, .5791855203619909502262443438914027149321,
.54839232556557315767520321969641372561450, .5778781038374717832957110609480812641084,
.55064711795266219063194057525834068655950, .5765765765765765765765765765765765765766,
.55289683768667763352766542084282264113450, .5752808988764044943820224719101123595506,
.55514150754050151093110798683483153581600, .5739910313901345291479820627802690582960,
.55738115013400635344709144192165695130850, .5727069351230425055928411633109619686801,
.55961578793542265941596269840374588966350, .5714285714285714285714285714285714285714,
.56184544326269181269140062795486301183700, .5701559020044543429844097995545657015590,
.56407013828480290218436721261241473257550, .5688888888888888888888888888888888888889,
.56628989502311577464155334382667206227800, .5676274944567627494456762749445676274945,
.56850473535266865532378233183408156037350, .5663716814159292035398230088495575221239,
.57071468100347144680739575051120482385150, .5651214128035320088300220750551876379691,
.57291975356178548306473885531886480748650, .5638766519823788546255506607929515418502,
.57511997447138785144460371157038025558000, .5626373626373626373626373626373626373626,
.57731536503482350219940144597785547375700, .5614035087719298245614035087719298245614,
.57950594641464214795689713355386629700650, .5601750547045951859956236323851203501094,
.58169173963462239562716149521293118596100, .5589519650655021834061135371179039301310,
.58387276558098266665552955601015128195300, .5577342047930283224400871459694989106754,
.58604904500357812846544902640744112432000, .5565217391304347826086956521739130434783,
.58822059851708596855957011939608491957200, .5553145336225596529284164859002169197397,
.59038744660217634674381770309992134571100, .5541125541125541125541125541125541125541,
.59254960960667157898740242671919986605650, .5529157667386609071274298056155507559395,
.59470710774669277576265358220553025603300, .5517241379310344827586206896551724137931,
.59685996110779382384237123915227130055450, .5505376344086021505376344086021505376344,
.59900818964608337768851242799428291618800, .5493562231759656652360515021459227467811,
.60115181318933474940990890900138765573500, .5481798715203426124197002141327623126338,
.60329085143808425240052883964381180703650, .5470085470085470085470085470085470085470,
.60542532396671688843525771517306566238400, .5458422174840085287846481876332622601279,
.60755525022454170969155029524699784815300, .5446808510638297872340425531914893617021,
.60968064953685519036241657886421307921400, .5435244161358811040339702760084925690021,
.61180154110599282990534675263916142284850, .5423728813559322033898305084745762711864,
.61391794401237043121710712512140162289150, .5412262156448202959830866807610993657505,
.61602987721551394351138242200249806046500, .5400843881856540084388185654008438818565,
.61813735955507864705538167982012964785100, .5389473684210526315789473684210526315789,
.62024040975185745772080281312810257077200, .5378151260504201680672268907563025210084,
.62233904640877868441606324267922900617100, .5366876310272536687631027253668763102725,
.62443328801189346144440150965237990021700, .5355648535564853556485355648535564853556,
.62652315293135274476554741340805776417250, .5344467640918580375782881002087682672234,
.62860865942237409420556559780379757285100, .5333333333333333333333333333333333333333,
.63068982562619868570408243613201193511500, .5322245322245322245322245322245322245322,
.63276666957103777644277897707070223987100, .5311203319502074688796680497925311203320,
.63483920917301017716738442686619237065300, .5300207039337474120082815734989648033126,
.63690746223706917739093569252872839570050, .5289256198347107438016528925619834710744,
.63897144645792069983514238629140891134750, .5278350515463917525773195876288659793814,
.64103117942093124081992527862894348800200, .5267489711934156378600823045267489711934,
.64308667860302726193566513757104985415950, .5256673511293634496919917864476386036961,
.64513796137358470073053240412264131009600, .5245901639344262295081967213114754098361,
.64718504499530948859131740391603671014300, .5235173824130879345603271983640081799591,
.64922794662510974195157587018911726772800, .5224489795918367346938775510204081632653,
.65126668331495807251485530287027359008800, .5213849287169042769857433808553971486762,
.65330127201274557080523663898929953575150, .5203252032520325203252032520325203252033,
.65533172956312757406749369692988693714150, .5192697768762677484787018255578093306288,
.65735807270835999727154330685152672231200, .5182186234817813765182186234817813765182,
.65938031808912778153342060249997302889800, .5171717171717171717171717171717171717172,
.66139848224536490484126716182800009846700, .5161290322580645161290322580645161290323,
.66341258161706617713093692145776003599150, .5150905432595573440643863179074446680080,
.66542263254509037562201001492212526500250, .5140562248995983935742971887550200803213,
.66742865127195616370414654738851822912700, .5130260521042084168336673346693386773547,
.66943065394262923906154583164607174694550, .5120000000000000000000000000000000000000,
.67142865660530226534774556057527661323550, .5109780439121756487025948103792415169661,
.67342267521216669923234121597488410770900, .5099601593625498007968127490039840637450,
.67541272562017662384192817626171745359900, .5089463220675944333996023856858846918489,
.67739882359180603188519853574689477682100, .5079365079365079365079365079365079365079,
.67938098479579733801614338517538271844400, .5069306930693069306930693069306930693069,
.68135922480790300781450241629499942064300, .5059288537549407114624505928853754940711,
.68333355911162063645036823800182901322850, .5049309664694280078895463510848126232742,
.68530400309891936760919861626462079584600, .5039370078740157480314960629921259842520,
.68727057207096020619019327568821609020250, .5029469548133595284872298624754420432220,
.68923328123880889251040571252815425395950, .5019607843137254901960784313725490196078,
.69314718055994530941723212145818, 5.0e-01,
};
#define LOGTAB_TRANSLATE(x,h) (((x) - 1.)*icvLogTab[(h)+1])
static const double ln_2 = 0.69314718055994530941723212145818;
void log32f( const float *_x, float *y, int n )
{
static const float shift[] = { 0, -1.f/512 };
static const float
A0 = 0.3333333333333333333333333f,
A1 = -0.5f,
A2 = 1.f;
#undef LOGPOLY
#define LOGPOLY(x) (((A0*(x) + A1)*(x) + A2)*(x))
int i = 0;
Cv32suf buf[4];
const int* x = (const int*)_x;
#if CV_SSE2
static const __m128d ln2_2 = _mm_set1_pd(ln_2);
static const __m128 _1_4 = _mm_set1_ps(1.f);
static const __m128 shift4 = _mm_set1_ps(-1.f/512);
static const __m128 mA0 = _mm_set1_ps(A0);
static const __m128 mA1 = _mm_set1_ps(A1);
static const __m128 mA2 = _mm_set1_ps(A2);
int CV_DECL_ALIGNED(16) idx[4];
for( ; i <= n - 4; i += 4 )
{
__m128i h0 = _mm_loadu_si128((const __m128i*)(x + i));
__m128i yi0 = _mm_sub_epi32(_mm_and_si128(_mm_srli_epi32(h0, 23), _mm_set1_epi32(255)), _mm_set1_epi32(127));
__m128d yd0 = _mm_mul_pd(_mm_cvtepi32_pd(yi0), ln2_2);
__m128d yd1 = _mm_mul_pd(_mm_cvtepi32_pd(_mm_unpackhi_epi64(yi0,yi0)), ln2_2);
__m128i xi0 = _mm_or_si128(_mm_and_si128(h0, _mm_set1_epi32(LOGTAB_MASK2_32F)), _mm_set1_epi32(127 << 23));
h0 = _mm_and_si128(_mm_srli_epi32(h0, 23 - LOGTAB_SCALE - 1), _mm_set1_epi32(LOGTAB_MASK*2));
_mm_store_si128((__m128i*)idx, h0);
h0 = _mm_cmpeq_epi32(h0, _mm_set1_epi32(510));
__m128d t0, t1, t2, t3, t4;
t0 = _mm_load_pd(icvLogTab + idx[0]);
t2 = _mm_load_pd(icvLogTab + idx[1]);
t1 = _mm_unpackhi_pd(t0, t2);
t0 = _mm_unpacklo_pd(t0, t2);
t2 = _mm_load_pd(icvLogTab + idx[2]);
t4 = _mm_load_pd(icvLogTab + idx[3]);
t3 = _mm_unpackhi_pd(t2, t4);
t2 = _mm_unpacklo_pd(t2, t4);
yd0 = _mm_add_pd(yd0, t0);
yd1 = _mm_add_pd(yd1, t2);
__m128 yf0 = _mm_movelh_ps(_mm_cvtpd_ps(yd0), _mm_cvtpd_ps(yd1));
__m128 xf0 = _mm_sub_ps(_mm_castsi128_ps(xi0), _1_4);
xf0 = _mm_mul_ps(xf0, _mm_movelh_ps(_mm_cvtpd_ps(t1), _mm_cvtpd_ps(t3)));
xf0 = _mm_add_ps(xf0, _mm_and_ps(_mm_castsi128_ps(h0), shift4));
__m128 zf0 = _mm_mul_ps(xf0, mA0);
zf0 = _mm_mul_ps(_mm_add_ps(zf0, mA1), xf0);
zf0 = _mm_mul_ps(_mm_add_ps(zf0, mA2), xf0);
yf0 = _mm_add_ps(yf0, zf0);
_mm_storeu_ps(y + i, yf0);
}
#endif
for( ; i <= n - 4; i += 4 )
{
double x0, x1, x2, x3;
double y0, y1, y2, y3;
int h0, h1, h2, h3;
h0 = x[i];
h1 = x[i+1];
buf[0].i = (h0 & LOGTAB_MASK2_32F) | (127 << 23);
buf[1].i = (h1 & LOGTAB_MASK2_32F) | (127 << 23);
y0 = (((h0 >> 23) & 0xff) - 127) * ln_2;
y1 = (((h1 >> 23) & 0xff) - 127) * ln_2;
h0 = (h0 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
h1 = (h1 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
y0 += icvLogTab[h0];
y1 += icvLogTab[h1];
h2 = x[i+2];
h3 = x[i+3];
x0 = LOGTAB_TRANSLATE( buf[0].f, h0 );
x1 = LOGTAB_TRANSLATE( buf[1].f, h1 );
buf[2].i = (h2 & LOGTAB_MASK2_32F) | (127 << 23);
buf[3].i = (h3 & LOGTAB_MASK2_32F) | (127 << 23);
y2 = (((h2 >> 23) & 0xff) - 127) * ln_2;
y3 = (((h3 >> 23) & 0xff) - 127) * ln_2;
h2 = (h2 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
h3 = (h3 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
y2 += icvLogTab[h2];
y3 += icvLogTab[h3];
x2 = LOGTAB_TRANSLATE( buf[2].f, h2 );
x3 = LOGTAB_TRANSLATE( buf[3].f, h3 );
x0 += shift[h0 == 510];
x1 += shift[h1 == 510];
y0 += LOGPOLY( x0 );
y1 += LOGPOLY( x1 );
y[i] = (float) y0;
y[i + 1] = (float) y1;
x2 += shift[h2 == 510];
x3 += shift[h3 == 510];
y2 += LOGPOLY( x2 );
y3 += LOGPOLY( x3 );
y[i + 2] = (float) y2;
y[i + 3] = (float) y3;
}
for( ; i < n; i++ )
{
int h0 = x[i];
double y0;
float x0;
y0 = (((h0 >> 23) & 0xff) - 127) * ln_2;
buf[0].i = (h0 & LOGTAB_MASK2_32F) | (127 << 23);
h0 = (h0 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
y0 += icvLogTab[h0];
x0 = (float)LOGTAB_TRANSLATE( buf[0].f, h0 );
x0 += shift[h0 == 510];
y0 += LOGPOLY( x0 );
y[i] = (float)y0;
}
}
void log64f( const double *x, double *y, int n )
{
static const double shift[] = { 0, -1./512 };
static const double
A7 = 1.0,
A6 = -0.5,
A5 = 0.333333333333333314829616256247390992939472198486328125,
A4 = -0.25,
A3 = 0.2,
A2 = -0.1666666666666666574148081281236954964697360992431640625,
A1 = 0.1428571428571428769682682968777953647077083587646484375,
A0 = -0.125;
#undef LOGPOLY
#define LOGPOLY(x,k) ((x)+=shift[k], xq = (x)*(x),\
(((A0*xq + A2)*xq + A4)*xq + A6)*xq + \
(((A1*xq + A3)*xq + A5)*xq + A7)*(x))
int i = 0;
DBLINT buf[4];
DBLINT *X = (DBLINT *) x;
#if CV_SSE2
static const __m128d ln2_2 = _mm_set1_pd(ln_2);
static const __m128d _1_2 = _mm_set1_pd(1.);
static const __m128d shift2 = _mm_set1_pd(-1./512);
static const __m128i log_and_mask2 = _mm_set_epi32(LOGTAB_MASK2, 0xffffffff, LOGTAB_MASK2, 0xffffffff);
static const __m128i log_or_mask2 = _mm_set_epi32(1023 << 20, 0, 1023 << 20, 0);
static const __m128d mA0 = _mm_set1_pd(A0);
static const __m128d mA1 = _mm_set1_pd(A1);
static const __m128d mA2 = _mm_set1_pd(A2);
static const __m128d mA3 = _mm_set1_pd(A3);
static const __m128d mA4 = _mm_set1_pd(A4);
static const __m128d mA5 = _mm_set1_pd(A5);
static const __m128d mA6 = _mm_set1_pd(A6);
static const __m128d mA7 = _mm_set1_pd(A7);
int CV_DECL_ALIGNED(16) idx[4];
for( ; i <= n - 4; i += 4 )
{
__m128i h0 = _mm_loadu_si128((const __m128i*)(x + i));
__m128i h1 = _mm_loadu_si128((const __m128i*)(x + i + 2));
__m128d xd0 = _mm_castsi128_pd(_mm_or_si128(_mm_and_si128(h0, log_and_mask2), log_or_mask2));
__m128d xd1 = _mm_castsi128_pd(_mm_or_si128(_mm_and_si128(h1, log_and_mask2), log_or_mask2));
h0 = _mm_unpackhi_epi32(_mm_unpacklo_epi32(h0, h1), _mm_unpackhi_epi32(h0, h1));
__m128i yi0 = _mm_sub_epi32(_mm_and_si128(_mm_srli_epi32(h0, 20),
_mm_set1_epi32(2047)), _mm_set1_epi32(1023));
__m128d yd0 = _mm_mul_pd(_mm_cvtepi32_pd(yi0), ln2_2);
__m128d yd1 = _mm_mul_pd(_mm_cvtepi32_pd(_mm_unpackhi_epi64(yi0, yi0)), ln2_2);
h0 = _mm_and_si128(_mm_srli_epi32(h0, 20 - LOGTAB_SCALE - 1), _mm_set1_epi32(LOGTAB_MASK * 2));
_mm_store_si128((__m128i*)idx, h0);
h0 = _mm_cmpeq_epi32(h0, _mm_set1_epi32(510));
__m128d t0, t1, t2, t3, t4;
t0 = _mm_load_pd(icvLogTab + idx[0]);
t2 = _mm_load_pd(icvLogTab + idx[1]);
t1 = _mm_unpackhi_pd(t0, t2);
t0 = _mm_unpacklo_pd(t0, t2);
t2 = _mm_load_pd(icvLogTab + idx[2]);
t4 = _mm_load_pd(icvLogTab + idx[3]);
t3 = _mm_unpackhi_pd(t2, t4);
t2 = _mm_unpacklo_pd(t2, t4);
yd0 = _mm_add_pd(yd0, t0);
yd1 = _mm_add_pd(yd1, t2);
xd0 = _mm_mul_pd(_mm_sub_pd(xd0, _1_2), t1);
xd1 = _mm_mul_pd(_mm_sub_pd(xd1, _1_2), t3);
xd0 = _mm_add_pd(xd0, _mm_and_pd(_mm_castsi128_pd(_mm_unpacklo_epi32(h0, h0)), shift2));
xd1 = _mm_add_pd(xd1, _mm_and_pd(_mm_castsi128_pd(_mm_unpackhi_epi32(h0, h0)), shift2));
__m128d zd0 = _mm_mul_pd(xd0, mA0);
__m128d zd1 = _mm_mul_pd(xd1, mA0);
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA1), xd0);
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA1), xd1);
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA2), xd0);
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA2), xd1);
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA3), xd0);
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA3), xd1);
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA4), xd0);
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA4), xd1);
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA5), xd0);
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA5), xd1);
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA6), xd0);
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA6), xd1);
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA7), xd0);
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA7), xd1);
yd0 = _mm_add_pd(yd0, zd0);
yd1 = _mm_add_pd(yd1, zd1);
_mm_storeu_pd(y + i, yd0);
_mm_storeu_pd(y + i + 2, yd1);
}
#endif
for( ; i <= n - 4; i += 4 )
{
double xq;
double x0, x1, x2, x3;
double y0, y1, y2, y3;
int h0, h1, h2, h3;
h0 = X[i].i.lo;
h1 = X[i + 1].i.lo;
buf[0].i.lo = h0;
buf[1].i.lo = h1;
h0 = X[i].i.hi;
h1 = X[i + 1].i.hi;
buf[0].i.hi = (h0 & LOGTAB_MASK2) | (1023 << 20);
buf[1].i.hi = (h1 & LOGTAB_MASK2) | (1023 << 20);
y0 = (((h0 >> 20) & 0x7ff) - 1023) * ln_2;
y1 = (((h1 >> 20) & 0x7ff) - 1023) * ln_2;
h2 = X[i + 2].i.lo;
h3 = X[i + 3].i.lo;
buf[2].i.lo = h2;
buf[3].i.lo = h3;
h0 = (h0 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
h1 = (h1 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
y0 += icvLogTab[h0];
y1 += icvLogTab[h1];
h2 = X[i + 2].i.hi;
h3 = X[i + 3].i.hi;
x0 = LOGTAB_TRANSLATE( buf[0].d, h0 );
x1 = LOGTAB_TRANSLATE( buf[1].d, h1 );
buf[2].i.hi = (h2 & LOGTAB_MASK2) | (1023 << 20);
buf[3].i.hi = (h3 & LOGTAB_MASK2) | (1023 << 20);
y2 = (((h2 >> 20) & 0x7ff) - 1023) * ln_2;
y3 = (((h3 >> 20) & 0x7ff) - 1023) * ln_2;
h2 = (h2 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
h3 = (h3 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
y2 += icvLogTab[h2];
y3 += icvLogTab[h3];
x2 = LOGTAB_TRANSLATE( buf[2].d, h2 );
x3 = LOGTAB_TRANSLATE( buf[3].d, h3 );
y0 += LOGPOLY( x0, h0 == 510 );
y1 += LOGPOLY( x1, h1 == 510 );
y[i] = y0;
y[i + 1] = y1;
y2 += LOGPOLY( x2, h2 == 510 );
y3 += LOGPOLY( x3, h3 == 510 );
y[i + 2] = y2;
y[i + 3] = y3;
}
for( ; i < n; i++ )
{
int h0 = X[i].i.hi;
double xq;
double x0, y0 = (((h0 >> 20) & 0x7ff) - 1023) * ln_2;
buf[0].i.hi = (h0 & LOGTAB_MASK2) | (1023 << 20);
buf[0].i.lo = X[i].i.lo;
h0 = (h0 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
y0 += icvLogTab[h0];
x0 = LOGTAB_TRANSLATE( buf[0].d, h0 );
y0 += LOGPOLY( x0, h0 == 510 );
y[i] = y0;
}
}
//=============================================================================
// for compatibility with 3.0
void exp(const float* src, float* dst, int n)
{
exp32f(src, dst, n);
}
void exp(const double* src, double* dst, int n)
{
exp64f(src, dst, n);
}
void log(const float* src, float* dst, int n)
{
log32f(src, dst, n);
}
void log(const double* src, double* dst, int n)
{
log64f(src, dst, n);
}
void magnitude(const float* x, const float* y, float* dst, int n)
{
magnitude32f(x, y, dst, n);
}
void magnitude(const double* x, const double* y, double* dst, int n)
{
magnitude64f(x, y, dst, n);
}
void sqrt(const float* src, float* dst, int len)
{
sqrt32f(src, dst, len);
}
void sqrt(const double* src, double* dst, int len)
{
sqrt64f(src, dst, len);
}
void invSqrt(const float* src, float* dst, int len)
{
invSqrt32f(src, dst, len);
}
void invSqrt(const double* src, double* dst, int len)
{
invSqrt64f(src, dst, len);
}
}} // cv::hal::
Reference in New Issue View Git Blame Copy Permalink