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ClickHouse/libs/libvectorclass/vectorf256.h

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dbms: vectorize math functions. [#METR-13613]
2014-12-01 13:48:31 +00:00
/**************************** vectorf256.h *******************************
* Author: Agner Fog
* Date created: 2012-05-30
* Last modified: 2014-10-22
* Version: 1.16
* Project: vector classes
* Description:
* Header file defining 256-bit floating point vector classes as interface
* to intrinsic functions in x86 microprocessors with AVX instruction set.
*
* Instructions:
* Use Gnu, Intel or Microsoft C++ compiler. Compile for the desired
* instruction set, which must be at least AVX.
*
* The following vector classes are defined here:
* Vec8f Vector of 8 single precision floating point numbers
* Vec8fb Vector of 8 Booleans for use with Vec8f
* Vec4d Vector of 4 double precision floating point numbers
* Vec4db Vector of 4 Booleans for use with Vec4d
*
* Each vector object is represented internally in the CPU as a 256-bit register.
* This header file defines operators and functions for these vectors.
*
* For example:
* Vec4d a(1., 2., 3., 4.), b(5., 6., 7., 8.), c;
* c = a + b; // now c contains (6., 8., 10., 12.)
*
* For detailed instructions, see VectorClass.pdf
*
* (c) Copyright 2012 - 2014 GNU General Public License http://www.gnu.org/licenses
*****************************************************************************/
// check combination of header files
#if defined (VECTORF256_H)
#if VECTORF256_H != 2
#error Two different versions of vectorf256.h included
#endif
#else
#define VECTORF256_H 2
#if INSTRSET < 7 // AVX required
#error Please compile for the AVX instruction set or higher
#endif
#include "vectorf128.h" // Define 128-bit vectors
/*****************************************************************************
*
* select functions
*
*****************************************************************************/
// Select between two __m256 sources, element by element. Used in various functions
// and operators. Corresponds to this pseudocode:
// for (int i = 0; i < 8; i++) result[i] = s[i] ? a[i] : b[i];
// Each element in s must be either 0 (false) or 0xFFFFFFFF (true).
static inline __m256 selectf (__m256 const & s, __m256 const & a, __m256 const & b) {
return _mm256_blendv_ps (b, a, s);
}
// Same, with two __m256d sources.
// and operators. Corresponds to this pseudocode:
// for (int i = 0; i < 4; i++) result[i] = s[i] ? a[i] : b[i];
// Each element in s must be either 0 (false) or 0xFFFFFFFFFFFFFFFF (true). No other
// values are allowed.
static inline __m256d selectd (__m256d const & s, __m256d const & a, __m256d const & b) {
return _mm256_blendv_pd (b, a, s);
}
/*****************************************************************************
*
* Generate compile-time constant vector
*
*****************************************************************************/
// Generate a constant vector of 8 integers stored in memory,
// load as __m256
template <int i0, int i1, int i2, int i3, int i4, int i5, int i6, int i7>
static inline __m256 constant8f() {
static const union {
int i[8];
__m256 ymm;
} u = {{i0,i1,i2,i3,i4,i5,i6,i7}};
return u.ymm;
}
/*****************************************************************************
*
* Join two 128-bit vectors
*
*****************************************************************************/
#define set_m128r(lo,hi) _mm256_insertf128_ps(_mm256_castps128_ps256(lo),(hi),1)
// _mm256_set_m128(hi,lo); // not defined in all versions of immintrin.h
/*****************************************************************************
*
* Vec8fb: Vector of 8 Booleans for use with Vec8f
*
*****************************************************************************/
class Vec8fb {
protected:
__m256 ymm; // Float vector
public:
// Default constructor:
Vec8fb() {
}
// Constructor to build from all elements:
Vec8fb(bool b0, bool b1, bool b2, bool b3, bool b4, bool b5, bool b6, bool b7) {
#if INSTRSET >= 8 // AVX2
ymm = _mm256_castsi256_ps(_mm256_setr_epi32(-(int)b0, -(int)b1, -(int)b2, -(int)b3, -(int)b4, -(int)b5, -(int)b6, -(int)b7));
#else
__m128 blo = _mm_castsi128_ps(_mm_setr_epi32(-(int)b0, -(int)b1, -(int)b2, -(int)b3));
__m128 bhi = _mm_castsi128_ps(_mm_setr_epi32(-(int)b4, -(int)b5, -(int)b6, -(int)b7));
ymm = set_m128r(blo,bhi);
#endif
}
// Constructor to build from two Vec4fb:
Vec8fb(Vec4fb const & a0, Vec4fb const & a1) {
ymm = set_m128r(a0, a1);
}
// Constructor to convert from type __m256 used in intrinsics:
Vec8fb(__m256 const & x) {
ymm = x;
}
// Assignment operator to convert from type __m256 used in intrinsics:
Vec8fb & operator = (__m256 const & x) {
ymm = x;
return *this;
}
// Constructor to broadcast the same value into all elements:
Vec8fb(bool b) {
#if INSTRSET >= 8 // AVX2
ymm = _mm256_castsi256_ps(_mm256_set1_epi32(-(int)b));
#else
__m128 b1 = _mm_castsi128_ps(_mm_set1_epi32(-(int)b));
//ymm = _mm256_set_m128(b1,b1);
ymm = set_m128r(b1,b1);
#endif
}
// Assignment operator to broadcast scalar value:
Vec8fb & operator = (bool b) {
*this = Vec8fb(b);
return *this;
}
private: // Prevent constructing from int, etc.
Vec8fb(int b);
Vec8fb & operator = (int x);
public:
// Type cast operator to convert to __m256 used in intrinsics
operator __m256() const {
return ymm;
}
#if defined (VECTORI256_H)
#if VECTORI256_H >= 2 // AVX2 version
// Constructor to convert from type Vec8ib used as Boolean for integer vectors
Vec8fb(Vec8ib const & x) {
ymm = _mm256_castsi256_ps(x);
}
// Assignment operator to convert from type Vec8ib used as Boolean for integer vectors
Vec8fb & operator = (Vec8ib const & x) {
ymm = _mm256_castsi256_ps(x);
return *this;
}
#ifndef FIX_CLANG_VECTOR_ALIAS_AMBIGUITY
// Type cast operator to convert to type Vec8ib used as Boolean for integer vectors
operator Vec8ib() const {
return _mm256_castps_si256(ymm);
}
#endif
#else
// Constructor to convert from type Vec8ib used as Boolean for integer vectors
Vec8fb(Vec8ib const & x) {
ymm = set_m128r(_mm_castsi128_ps(x.get_low()), _mm_castsi128_ps(x.get_high()));
}
// Assignment operator to convert from type Vec8ib used as Boolean for integer vectors
Vec8fb & operator = (Vec8ib const & x) {
ymm = set_m128r(_mm_castsi128_ps(x.get_low()), _mm_castsi128_ps(x.get_high()));
return *this;
}
// Type cast operator to convert to type Vec8ib used as Boolean for integer vectors
operator Vec8ib() const {
return Vec8i(_mm_castps_si128(get_low()), _mm_castps_si128(get_high()));
}
#endif
#endif // VECTORI256_H
// Member function to change a single element in vector
// Note: This function is inefficient. Use load function if changing more than one element
Vec8fb const & insert(uint32_t index, bool value) {
static const int32_t maskl[16] = {0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0};
__m256 mask = _mm256_loadu_ps((float const*)(maskl+8-(index & 7))); // mask with FFFFFFFF at index position
if (value) {
ymm = _mm256_or_ps(ymm,mask);
}
else {
ymm = _mm256_andnot_ps(mask,ymm);
}
return *this;
}
// Member function extract a single element from vector
bool extract(uint32_t index) const {
union {
float f[8];
int32_t i[8];
} u;
_mm256_storeu_ps(u.f, ymm);
return u.i[index & 7] != 0;
}
// Extract a single element. Operator [] can only read an element, not write.
bool operator [] (uint32_t index) const {
return extract(index);
}
// Member functions to split into two Vec4fb:
Vec4fb get_low() const {
return _mm256_castps256_ps128(ymm);
}
Vec4fb get_high() const {
return _mm256_extractf128_ps(ymm,1);
}
static int size () {
return 8;
}
};
/*****************************************************************************
*
* Operators for Vec8fb
*
*****************************************************************************/
// vector operator & : bitwise and
static inline Vec8fb operator & (Vec8fb const & a, Vec8fb const & b) {
return _mm256_and_ps(a, b);
}
static inline Vec8fb operator && (Vec8fb const & a, Vec8fb const & b) {
return a & b;
}
// vector operator &= : bitwise and
static inline Vec8fb & operator &= (Vec8fb & a, Vec8fb const & b) {
a = a & b;
return a;
}
// vector operator | : bitwise or
static inline Vec8fb operator | (Vec8fb const & a, Vec8fb const & b) {
return _mm256_or_ps(a, b);
}
static inline Vec8fb operator || (Vec8fb const & a, Vec8fb const & b) {
return a | b;
}
// vector operator |= : bitwise or
static inline Vec8fb & operator |= (Vec8fb & a, Vec8fb const & b) {
a = a | b;
return a;
}
// vector operator ^ : bitwise xor
static inline Vec8fb operator ^ (Vec8fb const & a, Vec8fb const & b) {
return _mm256_xor_ps(a, b);
}
// vector operator ^= : bitwise xor
static inline Vec8fb & operator ^= (Vec8fb & a, Vec8fb const & b) {
a = a ^ b;
return a;
}
// vector operator ~ : bitwise not
static inline Vec8fb operator ~ (Vec8fb const & a) {
return _mm256_xor_ps(a, constant8f<-1,-1,-1,-1,-1,-1,-1,-1>());
}
// vector operator ! : logical not
// (operator ! is less efficient than operator ~. Use only where not
// all bits in an element are the same)
static inline Vec8fb operator ! (Vec8fb const & a) {
return Vec8fb( !Vec8ib(a));
}
// Functions for Vec8fb
// andnot: a & ~ b
static inline Vec8fb andnot(Vec8fb const & a, Vec8fb const & b) {
return _mm256_andnot_ps(b, a);
}
/*****************************************************************************
*
* Horizontal Boolean functions
*
*****************************************************************************/
// horizontal_and. Returns true if all bits are 1
static inline bool horizontal_and (Vec8fb const & a) {
return _mm256_testc_ps(a,constant8f<-1,-1,-1,-1,-1,-1,-1,-1>()) != 0;
}
// horizontal_or. Returns true if at least one bit is 1
static inline bool horizontal_or (Vec8fb const & a) {
return ! _mm256_testz_ps(a,a);
}
/*****************************************************************************
*
* Vec4db: Vector of 4 Booleans for use with Vec4d
*
*****************************************************************************/
class Vec4db {
protected:
__m256d ymm; // double vector
public:
// Default constructor:
Vec4db() {
}
// Constructor to build from all elements:
Vec4db(bool b0, bool b1, bool b2, bool b3) {
#if INSTRSET >= 8 // AVX2
ymm = _mm256_castsi256_pd(_mm256_setr_epi64x(-(int64_t)b0, -(int64_t)b1, -(int64_t)b2, -(int64_t)b3));
#else
__m128 blo = _mm_castsi128_ps(_mm_setr_epi32(-(int)b0, -(int)b0, -(int)b1, -(int)b1));
__m128 bhi = _mm_castsi128_ps(_mm_setr_epi32(-(int)b2, -(int)b2, -(int)b3, -(int)b3));
ymm = _mm256_castps_pd(set_m128r(bhi,blo));
#endif
}
// Constructor to build from two Vec2db:
Vec4db(Vec2db const & a0, Vec2db const & a1) {
ymm = _mm256_castps_pd(set_m128r(_mm_castpd_ps(a0),_mm_castpd_ps(a1)));
//ymm = _mm256_set_m128d(a1, a0);
}
// Constructor to convert from type __m256d used in intrinsics:
Vec4db(__m256d const & x) {
ymm = x;
}
// Assignment operator to convert from type __m256d used in intrinsics:
Vec4db & operator = (__m256d const & x) {
ymm = x;
return *this;
}
// Constructor to broadcast the same value into all elements:
Vec4db(bool b) {
#if INSTRSET >= 8 // AVX2
ymm = _mm256_castsi256_pd(_mm256_set1_epi64x(-(int64_t)b));
#else
__m128 b1 = _mm_castsi128_ps(_mm_set1_epi32(-(int)b));
ymm = _mm256_castps_pd(set_m128r(b1,b1));
#endif
}
// Assignment operator to broadcast scalar value:
Vec4db & operator = (bool b) {
ymm = _mm256_castsi256_pd(_mm256_set1_epi32(-int32_t(b)));
return *this;
}
private: // Prevent constructing from int, etc.
Vec4db(int b);
Vec4db & operator = (int x);
public:
// Type cast operator to convert to __m256d used in intrinsics
operator __m256d() const {
return ymm;
}
#ifdef VECTORI256_H
#if VECTORI256_H == 2 // 256 bit integer vectors are available, AVX2
// Constructor to convert from type Vec4qb used as Boolean for integer vectors
Vec4db(Vec4qb const & x) {
ymm = _mm256_castsi256_pd(x);
}
// Assignment operator to convert from type Vec4qb used as Boolean for integer vectors
Vec4db & operator = (Vec4qb const & x) {
ymm = _mm256_castsi256_pd(x);
return *this;
}
#ifndef FIX_CLANG_VECTOR_ALIAS_AMBIGUITY
// Type cast operator to convert to type Vec4qb used as Boolean for integer vectors
operator Vec4qb() const {
return _mm256_castpd_si256(ymm);
}
#endif
#else // 256 bit integer vectors emulated without AVX2
// Constructor to convert from type Vec4qb used as Boolean for integer vectors
Vec4db(Vec4qb const & x) {
*this = Vec4db(_mm_castsi128_pd(x.get_low()), _mm_castsi128_pd(x.get_high()));
}
// Assignment operator to convert from type Vec4qb used as Boolean for integer vectors
Vec4db & operator = (Vec4qb const & x) {
*this = Vec4db(_mm_castsi128_pd(x.get_low()), _mm_castsi128_pd(x.get_high()));
return *this;
}
// Type cast operator to convert to type Vec4qb used as Boolean for integer vectors
operator Vec4qb() const {
return Vec4q(_mm_castpd_si128(get_low()), _mm_castpd_si128(get_high()));
}
#endif
#endif // VECTORI256_H
// Member function to change a single element in vector
// Note: This function is inefficient. Use load function if changing more than one element
Vec4db const & insert(uint32_t index, bool value) {
static const int32_t maskl[16] = {0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0};
__m256d mask = _mm256_loadu_pd((double const*)(maskl+8-(index&3)*2)); // mask with FFFFFFFFFFFFFFFF at index position
if (value) {
ymm = _mm256_or_pd(ymm,mask);
}
else {
ymm = _mm256_andnot_pd(mask,ymm);
}
return *this;
}
// Member function extract a single element from vector
bool extract(uint32_t index) const {
union {
double f[8];
int32_t i[16];
} u;
_mm256_storeu_pd(u.f, ymm);
return u.i[(index & 3) * 2 + 1] != 0;
}
// Extract a single element. Operator [] can only read an element, not write.
bool operator [] (uint32_t index) const {
return extract(index);
}
// Member functions to split into two Vec4fb:
Vec2db get_low() const {
return _mm256_castpd256_pd128(ymm);
}
Vec2db get_high() const {
return _mm256_extractf128_pd(ymm,1);
}
static int size () {
return 4;
}
};
/*****************************************************************************
*
* Operators for Vec4db
*
*****************************************************************************/
// vector operator & : bitwise and
static inline Vec4db operator & (Vec4db const & a, Vec4db const & b) {
return _mm256_and_pd(a, b);
}
static inline Vec4db operator && (Vec4db const & a, Vec4db const & b) {
return a & b;
}
// vector operator &= : bitwise and
static inline Vec4db & operator &= (Vec4db & a, Vec4db const & b) {
a = a & b;
return a;
}
// vector operator | : bitwise or
static inline Vec4db operator | (Vec4db const & a, Vec4db const & b) {
return _mm256_or_pd(a, b);
}
static inline Vec4db operator || (Vec4db const & a, Vec4db const & b) {
return a | b;
}
// vector operator |= : bitwise or
static inline Vec4db & operator |= (Vec4db & a, Vec4db const & b) {
a = a | b;
return a;
}
// vector operator ^ : bitwise xor
static inline Vec4db operator ^ (Vec4db const & a, Vec4db const & b) {
return _mm256_xor_pd(a, b);
}
// vector operator ^= : bitwise xor
static inline Vec4db & operator ^= (Vec4db & a, Vec4db const & b) {
a = a ^ b;
return a;
}
// vector operator ~ : bitwise not
static inline Vec4db operator ~ (Vec4db const & a) {
return _mm256_xor_pd(a, _mm256_castps_pd (constant8f<-1,-1,-1,-1,-1,-1,-1,-1>()));
}
// vector operator ! : logical not
// (operator ! is less efficient than operator ~. Use only where not
// all bits in an element are the same)
static inline Vec4db operator ! (Vec4db const & a) {
return Vec4db( ! Vec4qb(a));
}
// Functions for Vec8fb
// andnot: a & ~ b
static inline Vec4db andnot(Vec4db const & a, Vec4db const & b) {
return _mm256_andnot_pd(b, a);
}
/*****************************************************************************
*
* Horizontal Boolean functions
*
*****************************************************************************/
// horizontal_and. Returns true if all bits are 1
static inline bool horizontal_and (Vec4db const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
return horizontal_and(Vec256b(_mm256_castpd_si256(a)));
#else // split into 128 bit vectors
return horizontal_and(a.get_low() & a.get_high());
#endif
}
// horizontal_or. Returns true if at least one bit is 1
static inline bool horizontal_or (Vec4db const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
return horizontal_or(Vec256b(_mm256_castpd_si256(a)));
#else // split into 128 bit vectors
return horizontal_or(a.get_low() | a.get_high());
#endif
}
/*****************************************************************************
*
* Vec8f: Vector of 8 single precision floating point values
*
*****************************************************************************/
class Vec8f {
protected:
__m256 ymm; // Float vector
public:
// Default constructor:
Vec8f() {
}
// Constructor to broadcast the same value into all elements:
Vec8f(float f) {
ymm = _mm256_set1_ps(f);
}
// Constructor to build from all elements:
Vec8f(float f0, float f1, float f2, float f3, float f4, float f5, float f6, float f7) {
ymm = _mm256_setr_ps(f0, f1, f2, f3, f4, f5, f6, f7);
}
// Constructor to build from two Vec4f:
Vec8f(Vec4f const & a0, Vec4f const & a1) {
ymm = set_m128r(a0, a1);
//ymm = _mm256_set_m128(a1, a0);
}
// Constructor to convert from type __m256 used in intrinsics:
Vec8f(__m256 const & x) {
ymm = x;
}
// Assignment operator to convert from type __m256 used in intrinsics:
Vec8f & operator = (__m256 const & x) {
ymm = x;
return *this;
}
// Type cast operator to convert to __m256 used in intrinsics
operator __m256() const {
return ymm;
}
// Member function to load from array (unaligned)
Vec8f & load(float const * p) {
ymm = _mm256_loadu_ps(p);
return *this;
}
// Member function to load from array, aligned by 32
// You may use load_a instead of load if you are certain that p points to an address
// divisible by 32.
Vec8f & load_a(float const * p) {
ymm = _mm256_load_ps(p);
return *this;
}
// Member function to store into array (unaligned)
void store(float * p) const {
_mm256_storeu_ps(p, ymm);
}
// Member function to store into array, aligned by 32
// You may use store_a instead of store if you are certain that p points to an address
// divisible by 32.
void store_a(float * p) const {
_mm256_store_ps(p, ymm);
}
// Partial load. Load n elements and set the rest to 0
Vec8f & load_partial(int n, float const * p) {
if (n > 0 && n <= 4) {
*this = Vec8f(Vec4f().load_partial(n, p), _mm_setzero_ps());
// ymm = _mm256_castps128_ps256(Vec4f().load_partial<n>(p)); (this doesn't work on MS compiler due to sloppy definition of the cast)
}
else if (n > 4 && n <= 8) {
*this = Vec8f(Vec4f().load(p), Vec4f().load_partial(n - 4, p + 4));
}
else {
ymm = _mm256_setzero_ps();
}
return *this;
}
// Partial store. Store n elements
void store_partial(int n, float * p) const {
if (n <= 4) {
get_low().store_partial(n, p);
}
else if (n <= 8) {
get_low().store(p);
get_high().store_partial(n - 4, p + 4);
}
}
// cut off vector to n elements. The last 8-n elements are set to zero
Vec8f & cutoff(int n) {
if (uint32_t(n) >= 8) return *this;
static const union {
int32_t i[16];
float f[16];
} mask = {{-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0}};
*this = Vec8fb(*this) & Vec8fb(Vec8f().load(mask.f + 8 - n));
return *this;
}
// Member function to change a single element in vector
// Note: This function is inefficient. Use load function if changing more than one element
Vec8f const & insert(uint32_t index, float value) {
__m256 v0 = _mm256_broadcast_ss(&value);
switch (index) {
case 0:
ymm = _mm256_blend_ps (ymm, v0, 1); break;
case 1:
ymm = _mm256_blend_ps (ymm, v0, 2); break;
case 2:
ymm = _mm256_blend_ps (ymm, v0, 4); break;
case 3:
ymm = _mm256_blend_ps (ymm, v0, 8); break;
case 4:
ymm = _mm256_blend_ps (ymm, v0, 0x10); break;
case 5:
ymm = _mm256_blend_ps (ymm, v0, 0x20); break;
case 6:
ymm = _mm256_blend_ps (ymm, v0, 0x40); break;
default:
ymm = _mm256_blend_ps (ymm, v0, 0x80); break;
}
return *this;
}
// Member function extract a single element from vector
float extract(uint32_t index) const {
float x[8];
store(x);
return x[index & 7];
}
// Extract a single element. Use store function if extracting more than one element.
// Operator [] can only read an element, not write.
float operator [] (uint32_t index) const {
return extract(index);
}
// Member functions to split into two Vec4f:
Vec4f get_low() const {
return _mm256_castps256_ps128(ymm);
}
Vec4f get_high() const {
return _mm256_extractf128_ps(ymm,1);
}
static int size () {
return 8;
}
};
/*****************************************************************************
*
* Operators for Vec8f
*
*****************************************************************************/
// vector operator + : add element by element
static inline Vec8f operator + (Vec8f const & a, Vec8f const & b) {
return _mm256_add_ps(a, b);
}
// vector operator + : add vector and scalar
static inline Vec8f operator + (Vec8f const & a, float b) {
return a + Vec8f(b);
}
static inline Vec8f operator + (float a, Vec8f const & b) {
return Vec8f(a) + b;
}
// vector operator += : add
static inline Vec8f & operator += (Vec8f & a, Vec8f const & b) {
a = a + b;
return a;
}
// postfix operator ++
static inline Vec8f operator ++ (Vec8f & a, int) {
Vec8f a0 = a;
a = a + 1.0f;
return a0;
}
// prefix operator ++
static inline Vec8f & operator ++ (Vec8f & a) {
a = a + 1.0f;
return a;
}
// vector operator - : subtract element by element
static inline Vec8f operator - (Vec8f const & a, Vec8f const & b) {
return _mm256_sub_ps(a, b);
}
// vector operator - : subtract vector and scalar
static inline Vec8f operator - (Vec8f const & a, float b) {
return a - Vec8f(b);
}
static inline Vec8f operator - (float a, Vec8f const & b) {
return Vec8f(a) - b;
}
// vector operator - : unary minus
// Change sign bit, even for 0, INF and NAN
static inline Vec8f operator - (Vec8f const & a) {
return _mm256_xor_ps(a, constant8f<(int)0x80000000,(int)0x80000000,(int)0x80000000,(int)0x80000000,(int)0x80000000,(int)0x80000000,(int)0x80000000,(int)0x80000000> ());
}
// vector operator -= : subtract
static inline Vec8f & operator -= (Vec8f & a, Vec8f const & b) {
a = a - b;
return a;
}
// postfix operator --
static inline Vec8f operator -- (Vec8f & a, int) {
Vec8f a0 = a;
a = a - 1.0f;
return a0;
}
// prefix operator --
static inline Vec8f & operator -- (Vec8f & a) {
a = a - 1.0f;
return a;
}
// vector operator * : multiply element by element
static inline Vec8f operator * (Vec8f const & a, Vec8f const & b) {
return _mm256_mul_ps(a, b);
}
// vector operator * : multiply vector and scalar
static inline Vec8f operator * (Vec8f const & a, float b) {
return a * Vec8f(b);
}
static inline Vec8f operator * (float a, Vec8f const & b) {
return Vec8f(a) * b;
}
// vector operator *= : multiply
static inline Vec8f & operator *= (Vec8f & a, Vec8f const & b) {
a = a * b;
return a;
}
// vector operator / : divide all elements by same integer
static inline Vec8f operator / (Vec8f const & a, Vec8f const & b) {
return _mm256_div_ps(a, b);
}
// vector operator / : divide vector and scalar
static inline Vec8f operator / (Vec8f const & a, float b) {
return a / Vec8f(b);
}
static inline Vec8f operator / (float a, Vec8f const & b) {
return Vec8f(a) / b;
}
// vector operator /= : divide
static inline Vec8f & operator /= (Vec8f & a, Vec8f const & b) {
a = a / b;
return a;
}
// vector operator == : returns true for elements for which a == b
static inline Vec8fb operator == (Vec8f const & a, Vec8f const & b) {
return _mm256_cmp_ps(a, b, 0);
}
// vector operator != : returns true for elements for which a != b
static inline Vec8fb operator != (Vec8f const & a, Vec8f const & b) {
return _mm256_cmp_ps(a, b, 4);
}
// vector operator < : returns true for elements for which a < b
static inline Vec8fb operator < (Vec8f const & a, Vec8f const & b) {
return _mm256_cmp_ps(a, b, 1);
}
// vector operator <= : returns true for elements for which a <= b
static inline Vec8fb operator <= (Vec8f const & a, Vec8f const & b) {
return _mm256_cmp_ps(a, b, 2);
}
// vector operator > : returns true for elements for which a > b
static inline Vec8fb operator > (Vec8f const & a, Vec8f const & b) {
return b < a;
}
// vector operator >= : returns true for elements for which a >= b
static inline Vec8fb operator >= (Vec8f const & a, Vec8f const & b) {
return b <= a;
}
// Bitwise logical operators
// vector operator & : bitwise and
static inline Vec8f operator & (Vec8f const & a, Vec8f const & b) {
return _mm256_and_ps(a, b);
}
// vector operator &= : bitwise and
static inline Vec8f & operator &= (Vec8f & a, Vec8f const & b) {
a = a & b;
return a;
}
// vector operator & : bitwise and of Vec8f and Vec8fb
static inline Vec8f operator & (Vec8f const & a, Vec8fb const & b) {
return _mm256_and_ps(a, b);
}
static inline Vec8f operator & (Vec8fb const & a, Vec8f const & b) {
return _mm256_and_ps(a, b);
}
// vector operator | : bitwise or
static inline Vec8f operator | (Vec8f const & a, Vec8f const & b) {
return _mm256_or_ps(a, b);
}
// vector operator |= : bitwise or
static inline Vec8f & operator |= (Vec8f & a, Vec8f const & b) {
a = a | b;
return a;
}
// vector operator ^ : bitwise xor
static inline Vec8f operator ^ (Vec8f const & a, Vec8f const & b) {
return _mm256_xor_ps(a, b);
}
// vector operator ^= : bitwise xor
static inline Vec8f & operator ^= (Vec8f & a, Vec8f const & b) {
a = a ^ b;
return a;
}
// vector operator ! : logical not. Returns Boolean vector
static inline Vec8fb operator ! (Vec8f const & a) {
return a == Vec8f(0.0f);
}
/*****************************************************************************
*
* Functions for Vec8f
*
*****************************************************************************/
// Select between two operands. Corresponds to this pseudocode:
// for (int i = 0; i < 8; i++) result[i] = s[i] ? a[i] : b[i];
// Each byte in s must be either 0 (false) or 0xFFFFFFFF (true). No other values are allowed.
static inline Vec8f select (Vec8fb const & s, Vec8f const & a, Vec8f const & b) {
return _mm256_blendv_ps (b, a, s);
}
// Conditional add: For all vector elements i: result[i] = f[i] ? (a[i] + b[i]) : a[i]
static inline Vec8f if_add (Vec8fb const & f, Vec8f const & a, Vec8f const & b) {
return a + (Vec8f(f) & b);
}
// Conditional multiply: For all vector elements i: result[i] = f[i] ? (a[i] * b[i]) : a[i]
static inline Vec8f if_mul (Vec8fb const & f, Vec8f const & a, Vec8f const & b) {
return a * select(f, b, 1.f);
}
// General arithmetic functions, etc.
// Horizontal add: Calculates the sum of all vector elements.
static inline float horizontal_add (Vec8f const & a) {
__m256 t1 = _mm256_hadd_ps(a,a);
__m256 t2 = _mm256_hadd_ps(t1,t1);
__m128 t3 = _mm256_extractf128_ps(t2,1);
__m128 t4 = _mm_add_ss(_mm256_castps256_ps128(t2),t3);
return _mm_cvtss_f32(t4);
}
// function max: a > b ? a : b
static inline Vec8f max(Vec8f const & a, Vec8f const & b) {
return _mm256_max_ps(a,b);
}
// function min: a < b ? a : b
static inline Vec8f min(Vec8f const & a, Vec8f const & b) {
return _mm256_min_ps(a,b);
}
// function abs: absolute value
// Removes sign bit, even for -0.0f, -INF and -NAN
static inline Vec8f abs(Vec8f const & a) {
__m256 mask = constant8f<0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF> ();
return _mm256_and_ps(a,mask);
}
// function sqrt: square root
static inline Vec8f sqrt(Vec8f const & a) {
return _mm256_sqrt_ps(a);
}
// function square: a * a
static inline Vec8f square(Vec8f const & a) {
return a * a;
}
// pow(Vec8f, int):
template <typename TT> static Vec8f pow(Vec8f const & a, TT n);
// Raise floating point numbers to integer power n
template <>
inline Vec8f pow<int>(Vec8f const & x0, int n) {
return pow_template_i<Vec8f>(x0, n);
}
// allow conversion from unsigned int
template <>
inline Vec8f pow<uint32_t>(Vec8f const & x0, uint32_t n) {
return pow_template_i<Vec8f>(x0, (int)n);
}
// Raise floating point numbers to integer power n, where n is a compile-time constant
template <int n>
static inline Vec8f pow_n(Vec8f const & a) {
if (n < 0) return Vec8f(1.0f) / pow_n<-n>(a);
if (n == 0) return Vec8f(1.0f);
if (n >= 256) return pow(a, n);
Vec8f x = a; // a^(2^i)
Vec8f y; // accumulator
const int lowest = n - (n & (n-1));// lowest set bit in n
if (n & 1) y = x;
if (n < 2) return y;
x = x*x; // x^2
if (n & 2) {
if (lowest == 2) y = x; else y *= x;
}
if (n < 4) return y;
x = x*x; // x^4
if (n & 4) {
if (lowest == 4) y = x; else y *= x;
}
if (n < 8) return y;
x = x*x; // x^8
if (n & 8) {
if (lowest == 8) y = x; else y *= x;
}
if (n < 16) return y;
x = x*x; // x^16
if (n & 16) {
if (lowest == 16) y = x; else y *= x;
}
if (n < 32) return y;
x = x*x; // x^32
if (n & 32) {
if (lowest == 32) y = x; else y *= x;
}
if (n < 64) return y;
x = x*x; // x^64
if (n & 64) {
if (lowest == 64) y = x; else y *= x;
}
if (n < 128) return y;
x = x*x; // x^128
if (n & 128) {
if (lowest == 128) y = x; else y *= x;
}
return y;
}
template <int n>
static inline Vec8f pow(Vec8f const & a, Const_int_t<n>) {
return pow_n<n>(a);
}
// function round: round to nearest integer (even). (result as float vector)
static inline Vec8f round(Vec8f const & a) {
return _mm256_round_ps(a, 0);
}
// function truncate: round towards zero. (result as float vector)
static inline Vec8f truncate(Vec8f const & a) {
return _mm256_round_ps(a, 3);
}
// function floor: round towards minus infinity. (result as float vector)
static inline Vec8f floor(Vec8f const & a) {
return _mm256_round_ps(a, 1);
}
// function ceil: round towards plus infinity. (result as float vector)
static inline Vec8f ceil(Vec8f const & a) {
return _mm256_round_ps(a, 2);
}
#ifdef VECTORI256_H // 256 bit integer vectors are available
#if VECTORI256_H > 1 // AVX2
// function round_to_int: round to nearest integer (even). (result as integer vector)
static inline Vec8i round_to_int(Vec8f const & a) {
// Note: assume MXCSR control register is set to rounding
return _mm256_cvtps_epi32(a);
}
// function truncate_to_int: round towards zero. (result as integer vector)
static inline Vec8i truncate_to_int(Vec8f const & a) {
return _mm256_cvttps_epi32(a);
}
// function to_float: convert integer vector to float vector
static inline Vec8f to_float(Vec8i const & a) {
return _mm256_cvtepi32_ps(a);
}
#else // no AVX2
// function round_to_int: round to nearest integer (even). (result as integer vector)
static inline Vec8i round_to_int(Vec8f const & a) {
// Note: assume MXCSR control register is set to rounding
return Vec8i(_mm_cvtps_epi32(a.get_low()), _mm_cvtps_epi32(a.get_high()));
}
// function truncate_to_int: round towards zero. (result as integer vector)
static inline Vec8i truncate_to_int(Vec8f const & a) {
return Vec8i(_mm_cvttps_epi32(a.get_low()), _mm_cvttps_epi32(a.get_high()));
}
// function to_float: convert integer vector to float vector
static inline Vec8f to_float(Vec8i const & a) {
return Vec8f(_mm_cvtepi32_ps(a.get_low()), _mm_cvtepi32_ps(a.get_high()));
}
#endif
#endif // VECTORI256_H
// Fused multiply and add functions
// Multiply and add
static inline Vec8f mul_add(Vec8f const & a, Vec8f const & b, Vec8f const & c) {
#ifdef __FMA__
return _mm256_fmadd_ps(a, b, c);
#elif defined (__FMA4__)
return _mm256_macc_ps(a, b, c);
#else
return a * b + c;
#endif
}
// Multiply and subtract
static inline Vec8f mul_sub(Vec8f const & a, Vec8f const & b, Vec8f const & c) {
#ifdef __FMA__
return _mm256_fmsub_ps(a, b, c);
#elif defined (__FMA4__)
return _mm256_msub_ps(a, b, c);
#else
return a * b - c;
#endif
}
// Multiply and inverse subtract
static inline Vec8f nmul_add(Vec8f const & a, Vec8f const & b, Vec8f const & c) {
#ifdef __FMA__
return _mm256_fnmadd_ps(a, b, c);
#elif defined (__FMA4__)
return _mm256_nmacc_ps(a, b, c);
#else
return c - a * b;
#endif
}
// Multiply and subtract with extra precision on the intermediate calculations,
// even if FMA instructions not supported, using Veltkamp-Dekker split
static inline Vec8f mul_sub_x(Vec8f const & a, Vec8f const & b, Vec8f const & c) {
#ifdef __FMA__
return _mm256_fmsub_ps(a, b, c);
#elif defined (__FMA4__)
return _mm256_msub_ps(a, b, c);
#else
// calculate a * b - c with extra precision
const int b12 = -(1 << 12); // mask to remove lower 12 bits
Vec8f upper_mask = constant8f<b12,b12,b12,b12,b12,b12,b12,b12>();
Vec8f a_high = a & upper_mask; // split into high and low parts
Vec8f b_high = b & upper_mask;
Vec8f a_low = a - a_high;
Vec8f b_low = b - b_high;
Vec8f r1 = a_high * b_high; // this product is exact
Vec8f r2 = r1 - c; // subtract c from high product
Vec8f r3 = r2 + (a_high * b_low + b_high * a_low) + a_low * b_low; // add rest of product
return r3; // + ((r2 - r1) + c);
#endif
}
// Approximate math functions
// approximate reciprocal (Faster than 1.f / a. relative accuracy better than 2^-11)
static inline Vec8f approx_recipr(Vec8f const & a) {
return _mm256_rcp_ps(a);
}
// approximate reciprocal squareroot (Faster than 1.f / sqrt(a). Relative accuracy better than 2^-11)
static inline Vec8f approx_rsqrt(Vec8f const & a) {
return _mm256_rsqrt_ps(a);
}
// Math functions using fast bit manipulation
#ifdef VECTORI256_H // 256 bit integer vectors are available, AVX2
// Extract the exponent as an integer
// exponent(a) = floor(log2(abs(a)));
// exponent(1.0f) = 0, exponent(0.0f) = -127, exponent(INF) = +128, exponent(NAN) = +128
static inline Vec8i exponent(Vec8f const & a) {
#if VECTORI256_H > 1 // AVX2
Vec8ui t1 = _mm256_castps_si256(a);// reinterpret as 32-bit integer
Vec8ui t2 = t1 << 1; // shift out sign bit
Vec8ui t3 = t2 >> 24; // shift down logical to position 0
Vec8i t4 = Vec8i(t3) - 0x7F; // subtract bias from exponent
return t4;
#else // no AVX2
return Vec8i(exponent(a.get_low()), exponent(a.get_high()));
#endif
}
#endif
// Extract the fraction part of a floating point number
// a = 2^exponent(a) * fraction(a), except for a = 0
// fraction(1.0f) = 1.0f, fraction(5.0f) = 1.25f
static inline Vec8f fraction(Vec8f const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 2 // 256 bit integer vectors are available, AVX2
Vec8ui t1 = _mm256_castps_si256(a); // reinterpret as 32-bit integer
Vec8ui t2 = (t1 & 0x007FFFFF) | 0x3F800000; // set exponent to 0 + bias
return _mm256_castsi256_ps(t2);
#else
return Vec8f(fraction(a.get_low()), fraction(a.get_high()));
#endif
}
#ifdef VECTORI256_H // 256 bit integer vectors are available, AVX2
// Fast calculation of pow(2,n) with n integer
// n = 0 gives 1.0f
// n >= 128 gives +INF
// n <= -127 gives 0.0f
// This function will never produce denormals, and never raise exceptions
static inline Vec8f exp2(Vec8i const & n) {
#if VECTORI256_H > 1 // AVX2
Vec8i t1 = max(n, -0x7F); // limit to allowed range
Vec8i t2 = min(t1, 0x80);
Vec8i t3 = t2 + 0x7F; // add bias
Vec8i t4 = t3 << 23; // put exponent into position 23
return _mm256_castsi256_ps(t4); // reinterpret as float
#else
return Vec8f(exp2(n.get_low()), exp2(n.get_high()));
#endif
}
//static inline Vec8f exp2(Vec8f const & x); // defined in vectormath_exp.h
#endif // VECTORI256_H
// Categorization functions
// Function sign_bit: gives true for elements that have the sign bit set
// even for -0.0f, -INF and -NAN
// Note that sign_bit(Vec8f(-0.0f)) gives true, while Vec8f(-0.0f) < Vec8f(0.0f) gives false
// (the underscore in the name avoids a conflict with a macro in Intel's mathimf.h)
static inline Vec8fb sign_bit(Vec8f const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
Vec8i t1 = _mm256_castps_si256(a); // reinterpret as 32-bit integer
Vec8i t2 = t1 >> 31; // extend sign bit
return _mm256_castsi256_ps(t2); // reinterpret as 32-bit Boolean
#else
return Vec8fb(sign_bit(a.get_low()), sign_bit(a.get_high()));
#endif
}
// Function sign_combine: changes the sign of a when b has the sign bit set
// same as select(sign_bit(b), -a, a)
static inline Vec8f sign_combine(Vec8f const & a, Vec8f const & b) {
Vec8f signmask = constant8f<(int)0x80000000,(int)0x80000000,(int)0x80000000,(int)0x80000000,(int)0x80000000,(int)0x80000000,(int)0x80000000,(int)0x80000000>(); // -0.0
return a ^ (b & signmask);
}
// Function is_finite: gives true for elements that are normal, denormal or zero,
// false for INF and NAN
// (the underscore in the name avoids a conflict with a macro in Intel's mathimf.h)
static inline Vec8fb is_finite(Vec8f const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
Vec8i t1 = _mm256_castps_si256(a); // reinterpret as 32-bit integer
Vec8i t2 = t1 << 1; // shift out sign bit
Vec8ib t3 = Vec8i(t2 & 0xFF000000) != 0xFF000000; // exponent field is not all 1s
return t3;
#else
return Vec8fb(is_finite(a.get_low()), is_finite(a.get_high()));
#endif
}
// Function is_inf: gives true for elements that are +INF or -INF
// false for finite numbers and NAN
// (the underscore in the name avoids a conflict with a macro in Intel's mathimf.h)
static inline Vec8fb is_inf(Vec8f const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
Vec8i t1 = _mm256_castps_si256(a); // reinterpret as 32-bit integer
Vec8i t2 = t1 << 1; // shift out sign bit
return t2 == 0xFF000000; // exponent is all 1s, fraction is 0
#else
return Vec8fb(is_inf(a.get_low()), is_inf(a.get_high()));
#endif
}
// Function is_nan: gives true for elements that are +NAN or -NAN
// false for finite numbers and +/-INF
// (the underscore in the name avoids a conflict with a macro in Intel's mathimf.h)
static inline Vec8fb is_nan(Vec8f const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
Vec8i t1 = _mm256_castps_si256(a); // reinterpret as 32-bit integer
Vec8i t2 = t1 << 1; // shift out sign bit
Vec8i t3 = 0xFF000000; // exponent mask
Vec8i t4 = t2 & t3; // exponent
Vec8i t5 = _mm256_andnot_si256(t3,t2);// fraction
return Vec8ib(t4 == t3 && t5 != 0);// exponent = all 1s and fraction != 0
#else
return Vec8fb(is_nan(a.get_low()), is_nan(a.get_high()));
#endif
}
// Function is_subnormal: gives true for elements that are denormal (subnormal)
// false for finite numbers, zero, NAN and INF
static inline Vec8fb is_subnormal(Vec8f const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
Vec8i t1 = _mm256_castps_si256(a); // reinterpret as 32-bit integer
Vec8i t2 = t1 << 1; // shift out sign bit
Vec8i t3 = 0xFF000000; // exponent mask
Vec8i t4 = t2 & t3; // exponent
Vec8i t5 = _mm256_andnot_si256(t3,t2);// fraction
return Vec8ib(t4 == 0 && t5 != 0); // exponent = 0 and fraction != 0
#else
return Vec8fb(is_subnormal(a.get_low()), is_subnormal(a.get_high()));
#endif
}
// Function is_zero_or_subnormal: gives true for elements that are zero or subnormal (denormal)
// false for finite numbers, NAN and INF
static inline Vec8fb is_zero_or_subnormal(Vec8f const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
Vec8i t = _mm256_castps_si256(a); // reinterpret as 32-bit integer
t &= 0x7F800000; // isolate exponent
return t == 0; // exponent = 0
#else
return Vec8fb(is_zero_or_subnormal(a.get_low()), is_zero_or_subnormal(a.get_high()));
#endif
}
// Function infinite4f: returns a vector where all elements are +INF
static inline Vec8f infinite8f() {
return constant8f<0x7F800000,0x7F800000,0x7F800000,0x7F800000,0x7F800000,0x7F800000,0x7F800000,0x7F800000>();
}
// Function nan4f: returns a vector where all elements are +NAN (quiet)
static inline Vec8f nan8f(int n = 0x10) {
return _mm256_castsi256_ps(_mm256_set1_epi32(0x7FC00000 + n));
}
// change signs on vectors Vec8f
// Each index i0 - i7 is 1 for changing sign on the corresponding element, 0 for no change
template <int i0, int i1, int i2, int i3, int i4, int i5, int i6, int i7>
static inline Vec8f change_sign(Vec8f const & a) {
if ((i0 | i1 | i2 | i3 | i4 | i5 | i6 | i7) == 0) return a;
__m256 mask = constant8f<i0 ? 0x80000000 : 0, i1 ? 0x80000000 : 0, i2 ? 0x80000000 : 0, i3 ? 0x80000000 : 0,
i4 ? 0x80000000 : 0, i5 ? 0x80000000 : 0, i6 ? 0x80000000 : 0, i7 ? 0x80000000 : 0> ();
return _mm256_xor_ps(a, mask);
}
/*****************************************************************************
*
* Vec4d: Vector of 4 double precision floating point values
*
*****************************************************************************/
class Vec4d {
protected:
__m256d ymm; // double vector
public:
// Default constructor:
Vec4d() {
}
// Constructor to broadcast the same value into all elements:
Vec4d(double d) {
ymm = _mm256_set1_pd(d);
}
// Constructor to build from all elements:
Vec4d(double d0, double d1, double d2, double d3) {
ymm = _mm256_setr_pd(d0, d1, d2, d3);
}
// Constructor to build from two Vec2d:
Vec4d(Vec2d const & a0, Vec2d const & a1) {
ymm = _mm256_castps_pd(set_m128r(_mm_castpd_ps(a0), _mm_castpd_ps(a1)));
//ymm = _mm256_set_m128d(a1, a0);
}
// Constructor to convert from type __m256d used in intrinsics:
Vec4d(__m256d const & x) {
ymm = x;
}
// Assignment operator to convert from type __m256d used in intrinsics:
Vec4d & operator = (__m256d const & x) {
ymm = x;
return *this;
}
// Type cast operator to convert to __m256d used in intrinsics
operator __m256d() const {
return ymm;
}
// Member function to load from array (unaligned)
Vec4d & load(double const * p) {
ymm = _mm256_loadu_pd(p);
return *this;
}
// Member function to load from array, aligned by 32
// You may use load_a instead of load if you are certain that p points to an address
// divisible by 32
Vec4d & load_a(double const * p) {
ymm = _mm256_load_pd(p);
return *this;
}
// Member function to store into array (unaligned)
void store(double * p) const {
_mm256_storeu_pd(p, ymm);
}
// Member function to store into array, aligned by 32
// You may use store_a instead of store if you are certain that p points to an address
// divisible by 32
void store_a(double * p) const {
_mm256_store_pd(p, ymm);
}
// Partial load. Load n elements and set the rest to 0
Vec4d & load_partial(int n, double const * p) {
if (n > 0 && n <= 2) {
*this = Vec4d(Vec2d().load_partial(n, p), _mm_setzero_pd());
}
else if (n > 2 && n <= 4) {
*this = Vec4d(Vec2d().load(p), Vec2d().load_partial(n - 2, p + 2));
}
else {
ymm = _mm256_setzero_pd();
}
return *this;
}
// Partial store. Store n elements
void store_partial(int n, double * p) const {
if (n <= 2) {
get_low().store_partial(n, p);
}
else if (n <= 4) {
get_low().store(p);
get_high().store_partial(n - 2, p + 2);
}
}
// cut off vector to n elements. The last 4-n elements are set to zero
Vec4d & cutoff(int n) {
ymm = _mm256_castps_pd(Vec8f(_mm256_castpd_ps(ymm)).cutoff(n*2));
return *this;
}
// Member function to change a single element in vector
// Note: This function is inefficient. Use load function if changing more than one element
Vec4d const & insert(uint32_t index, double value) {
__m256d v0 = _mm256_broadcast_sd(&value);
switch (index) {
case 0:
ymm = _mm256_blend_pd (ymm, v0, 1); break;
case 1:
ymm = _mm256_blend_pd (ymm, v0, 2); break;
case 2:
ymm = _mm256_blend_pd (ymm, v0, 4); break;
default:
ymm = _mm256_blend_pd (ymm, v0, 8); break;
}
return *this;
}
// Member function extract a single element from vector
double extract(uint32_t index) const {
double x[4];
store(x);
return x[index & 3];
}
// Extract a single element. Use store function if extracting more than one element.
// Operator [] can only read an element, not write.
double operator [] (uint32_t index) const {
return extract(index);
}
// Member functions to split into two Vec2d:
Vec2d get_low() const {
return _mm256_castpd256_pd128(ymm);
}
Vec2d get_high() const {
return _mm256_extractf128_pd(ymm,1);
}
static int size () {
return 4;
}
};
/*****************************************************************************
*
* Operators for Vec4d
*
*****************************************************************************/
// vector operator + : add element by element
static inline Vec4d operator + (Vec4d const & a, Vec4d const & b) {
return _mm256_add_pd(a, b);
}
// vector operator + : add vector and scalar
static inline Vec4d operator + (Vec4d const & a, double b) {
return a + Vec4d(b);
}
static inline Vec4d operator + (double a, Vec4d const & b) {
return Vec4d(a) + b;
}
// vector operator += : add
static inline Vec4d & operator += (Vec4d & a, Vec4d const & b) {
a = a + b;
return a;
}
// postfix operator ++
static inline Vec4d operator ++ (Vec4d & a, int) {
Vec4d a0 = a;
a = a + 1.0;
return a0;
}
// prefix operator ++
static inline Vec4d & operator ++ (Vec4d & a) {
a = a + 1.0;
return a;
}
// vector operator - : subtract element by element
static inline Vec4d operator - (Vec4d const & a, Vec4d const & b) {
return _mm256_sub_pd(a, b);
}
// vector operator - : subtract vector and scalar
static inline Vec4d operator - (Vec4d const & a, double b) {
return a - Vec4d(b);
}
static inline Vec4d operator - (double a, Vec4d const & b) {
return Vec4d(a) - b;
}
// vector operator - : unary minus
// Change sign bit, even for 0, INF and NAN
static inline Vec4d operator - (Vec4d const & a) {
return _mm256_xor_pd(a, _mm256_castps_pd(constant8f<0,(int)0x80000000,0,(int)0x80000000,0,(int)0x80000000,0,(int)0x80000000> ()));
}
// vector operator -= : subtract
static inline Vec4d & operator -= (Vec4d & a, Vec4d const & b) {
a = a - b;
return a;
}
// postfix operator --
static inline Vec4d operator -- (Vec4d & a, int) {
Vec4d a0 = a;
a = a - 1.0;
return a0;
}
// prefix operator --
static inline Vec4d & operator -- (Vec4d & a) {
a = a - 1.0;
return a;
}
// vector operator * : multiply element by element
static inline Vec4d operator * (Vec4d const & a, Vec4d const & b) {
return _mm256_mul_pd(a, b);
}
// vector operator * : multiply vector and scalar
static inline Vec4d operator * (Vec4d const & a, double b) {
return a * Vec4d(b);
}
static inline Vec4d operator * (double a, Vec4d const & b) {
return Vec4d(a) * b;
}
// vector operator *= : multiply
static inline Vec4d & operator *= (Vec4d & a, Vec4d const & b) {
a = a * b;
return a;
}
// vector operator / : divide all elements by same integer
static inline Vec4d operator / (Vec4d const & a, Vec4d const & b) {
return _mm256_div_pd(a, b);
}
// vector operator / : divide vector and scalar
static inline Vec4d operator / (Vec4d const & a, double b) {
return a / Vec4d(b);
}
static inline Vec4d operator / (double a, Vec4d const & b) {
return Vec4d(a) / b;
}
// vector operator /= : divide
static inline Vec4d & operator /= (Vec4d & a, Vec4d const & b) {
a = a / b;
return a;
}
// vector operator == : returns true for elements for which a == b
static inline Vec4db operator == (Vec4d const & a, Vec4d const & b) {
return _mm256_cmp_pd(a, b, 0);
}
// vector operator != : returns true for elements for which a != b
static inline Vec4db operator != (Vec4d const & a, Vec4d const & b) {
return _mm256_cmp_pd(a, b, 4);
}
// vector operator < : returns true for elements for which a < b
static inline Vec4db operator < (Vec4d const & a, Vec4d const & b) {
return _mm256_cmp_pd(a, b, 1);
}
// vector operator <= : returns true for elements for which a <= b
static inline Vec4db operator <= (Vec4d const & a, Vec4d const & b) {
return _mm256_cmp_pd(a, b, 2);
}
// vector operator > : returns true for elements for which a > b
static inline Vec4db operator > (Vec4d const & a, Vec4d const & b) {
return b < a;
}
// vector operator >= : returns true for elements for which a >= b
static inline Vec4db operator >= (Vec4d const & a, Vec4d const & b) {
return b <= a;
}
// Bitwise logical operators
// vector operator & : bitwise and
static inline Vec4d operator & (Vec4d const & a, Vec4d const & b) {
return _mm256_and_pd(a, b);
}
// vector operator &= : bitwise and
static inline Vec4d & operator &= (Vec4d & a, Vec4d const & b) {
a = a & b;
return a;
}
// vector operator & : bitwise and of Vec4d and Vec4db
static inline Vec4d operator & (Vec4d const & a, Vec4db const & b) {
return _mm256_and_pd(a, b);
}
static inline Vec4d operator & (Vec4db const & a, Vec4d const & b) {
return _mm256_and_pd(a, b);
}
// vector operator | : bitwise or
static inline Vec4d operator | (Vec4d const & a, Vec4d const & b) {
return _mm256_or_pd(a, b);
}
// vector operator |= : bitwise or
static inline Vec4d & operator |= (Vec4d & a, Vec4d const & b) {
a = a | b;
return a;
}
// vector operator ^ : bitwise xor
static inline Vec4d operator ^ (Vec4d const & a, Vec4d const & b) {
return _mm256_xor_pd(a, b);
}
// vector operator ^= : bitwise xor
static inline Vec4d & operator ^= (Vec4d & a, Vec4d const & b) {
a = a ^ b;
return a;
}
// vector operator ! : logical not. Returns Boolean vector
static inline Vec4db operator ! (Vec4d const & a) {
return a == Vec4d(0.0);
}
/*****************************************************************************
*
* Functions for Vec4d
*
*****************************************************************************/
// Select between two operands. Corresponds to this pseudocode:
// for (int i = 0; i < 2; i++) result[i] = s[i] ? a[i] : b[i];
// Each byte in s must be either 0 (false) or 0xFFFFFFFFFFFFFFFF (true).
// No other values are allowed.
static inline Vec4d select (Vec4db const & s, Vec4d const & a, Vec4d const & b) {
return _mm256_blendv_pd(b, a, s);
}
// Conditional add: For all vector elements i: result[i] = f[i] ? (a[i] + b[i]) : a[i]
static inline Vec4d if_add (Vec4db const & f, Vec4d const & a, Vec4d const & b) {
return a + (Vec4d(f) & b);
}
// Conditional multiply: For all vector elements i: result[i] = f[i] ? (a[i] * b[i]) : a[i]
static inline Vec4d if_mul (Vec4db const & f, Vec4d const & a, Vec4d const & b) {
return a * select(f, b, 1.);
}
// General arithmetic functions, etc.
// Horizontal add: Calculates the sum of all vector elements.
static inline double horizontal_add (Vec4d const & a) {
__m256d t1 = _mm256_hadd_pd(a,a);
__m128d t2 = _mm256_extractf128_pd(t1,1);
__m128d t3 = _mm_add_sd(_mm256_castpd256_pd128(t1),t2);
return _mm_cvtsd_f64(t3);
}
// function max: a > b ? a : b
static inline Vec4d max(Vec4d const & a, Vec4d const & b) {
return _mm256_max_pd(a,b);
}
// function min: a < b ? a : b
static inline Vec4d min(Vec4d const & a, Vec4d const & b) {
return _mm256_min_pd(a,b);
}
// function abs: absolute value
// Removes sign bit, even for -0.0f, -INF and -NAN
static inline Vec4d abs(Vec4d const & a) {
__m256d mask = _mm256_castps_pd(constant8f<-1,0x7FFFFFFF,-1,0x7FFFFFFF,-1,0x7FFFFFFF,-1,0x7FFFFFFF> ());
return _mm256_and_pd(a,mask);
}
// function sqrt: square root
static inline Vec4d sqrt(Vec4d const & a) {
return _mm256_sqrt_pd(a);
}
// function square: a * a
static inline Vec4d square(Vec4d const & a) {
return a * a;
}
// pow(Vec4d, int):
template <typename TT> static Vec4d pow(Vec4d const & a, TT n);
// Raise floating point numbers to integer power n
template <>
inline Vec4d pow<int>(Vec4d const & x0, int n) {
return pow_template_i<Vec4d>(x0, n);
}
// allow conversion from unsigned int
template <>
inline Vec4d pow<uint32_t>(Vec4d const & x0, uint32_t n) {
return pow_template_i<Vec4d>(x0, (int)n);
}
// Raise floating point numbers to integer power n, where n is a compile-time constant
template <int n>
static inline Vec4d pow_n(Vec4d const & a) {
if (n < 0) return Vec4d(1.0) / pow_n<-n>(a);
if (n == 0) return Vec4d(1.0);
if (n >= 256) return pow(a, n);
Vec4d x = a; // a^(2^i)
Vec4d y; // accumulator
const int lowest = n - (n & (n-1));// lowest set bit in n
if (n & 1) y = x;
if (n < 2) return y;
x = x*x; // x^2
if (n & 2) {
if (lowest == 2) y = x; else y *= x;
}
if (n < 4) return y;
x = x*x; // x^4
if (n & 4) {
if (lowest == 4) y = x; else y *= x;
}
if (n < 8) return y;
x = x*x; // x^8
if (n & 8) {
if (lowest == 8) y = x; else y *= x;
}
if (n < 16) return y;
x = x*x; // x^16
if (n & 16) {
if (lowest == 16) y = x; else y *= x;
}
if (n < 32) return y;
x = x*x; // x^32
if (n & 32) {
if (lowest == 32) y = x; else y *= x;
}
if (n < 64) return y;
x = x*x; // x^64
if (n & 64) {
if (lowest == 64) y = x; else y *= x;
}
if (n < 128) return y;
x = x*x; // x^128
if (n & 128) {
if (lowest == 128) y = x; else y *= x;
}
return y;
}
template <int n>
static inline Vec4d pow(Vec4d const & a, Const_int_t<n>) {
return pow_n<n>(a);
}
// function round: round to nearest integer (even). (result as double vector)
static inline Vec4d round(Vec4d const & a) {
return _mm256_round_pd(a, 0);
}
// function truncate: round towards zero. (result as double vector)
static inline Vec4d truncate(Vec4d const & a) {
return _mm256_round_pd(a, 3);
}
// function floor: round towards minus infinity. (result as double vector)
static inline Vec4d floor(Vec4d const & a) {
return _mm256_round_pd(a, 1);
}
// function ceil: round towards plus infinity. (result as double vector)
static inline Vec4d ceil(Vec4d const & a) {
return _mm256_round_pd(a, 2);
}
// function round_to_int: round to nearest integer (even). (result as integer vector)
static inline Vec4i round_to_int(Vec4d const & a) {
// Note: assume MXCSR control register is set to rounding
return _mm256_cvtpd_epi32(a);
}
// function truncate_to_int: round towards zero. (result as integer vector)
static inline Vec4i truncate_to_int(Vec4d const & a) {
return _mm256_cvttpd_epi32(a);
}
#ifdef VECTORI256_H // 256 bit integer vectors are available
// function truncate_to_int64: round towards zero. (inefficient)
static inline Vec4q truncate_to_int64(Vec4d const & a) {
double aa[4];
a.store(aa);
return Vec4q(int64_t(aa[0]), int64_t(aa[1]), int64_t(aa[2]), int64_t(aa[3]));
}
// function truncate_to_int64_limited: round towards zero.
// result as 64-bit integer vector, but with limited range
static inline Vec4q truncate_to_int64_limited(Vec4d const & a) {
#if VECTORI256_H > 1
// Note: assume MXCSR control register is set to rounding
Vec2q b = _mm256_cvttpd_epi32(a); // round to 32-bit integers
__m256i c = permute4q<0,-256,1,-256>(Vec4q(b,b)); // get bits 64-127 to position 128-191
__m256i s = _mm256_srai_epi32(c, 31); // sign extension bits
return _mm256_unpacklo_epi32(c, s); // interleave with sign extensions
#else
return Vec4q(truncate_to_int64_limited(a.get_low()), truncate_to_int64_limited(a.get_high()));
#endif
}
// function round_to_int64: round to nearest or even. (inefficient)
static inline Vec4q round_to_int64(Vec4d const & a) {
return truncate_to_int64(round(a));
}
// function round_to_int64_limited: round to nearest integer (even)
// result as 64-bit integer vector, but with limited range
static inline Vec4q round_to_int64_limited(Vec4d const & a) {
#if VECTORI256_H > 1
// Note: assume MXCSR control register is set to rounding
Vec2q b = _mm256_cvtpd_epi32(a); // round to 32-bit integers
__m256i c = permute4q<0,-256,1,-256>(Vec4q(b,b)); // get bits 64-127 to position 128-191
__m256i s = _mm256_srai_epi32(c, 31); // sign extension bits
return _mm256_unpacklo_epi32(c, s); // interleave with sign extensions
#else
return Vec4q(round_to_int64_limited(a.get_low()), round_to_int64_limited(a.get_high()));
#endif
}
// function to_double: convert integer vector elements to double vector (inefficient)
static inline Vec4d to_double(Vec4q const & a) {
int64_t aa[4];
a.store(aa);
return Vec4d(double(aa[0]), double(aa[1]), double(aa[2]), double(aa[3]));
}
// function to_double_limited: convert integer vector elements to double vector
// limited to abs(x) < 2^31
static inline Vec4d to_double_limited(Vec4q const & x) {
Vec8i compressed = permute8i<0,2,4,6,-256,-256,-256,-256>(Vec8i(x));
return _mm256_cvtepi32_pd(compressed.get_low()); // AVX
}
#endif // VECTORI256_H
// function to_double: convert integer vector to double vector
static inline Vec4d to_double(Vec4i const & a) {
return _mm256_cvtepi32_pd(a);
}
// function compress: convert two Vec4d to one Vec8f
static inline Vec8f compress (Vec4d const & low, Vec4d const & high) {
__m128 t1 = _mm256_cvtpd_ps(low);
__m128 t2 = _mm256_cvtpd_ps(high);
return Vec8f(t1, t2);
}
// Function extend_low : convert Vec8f vector elements 0 - 3 to Vec4d
static inline Vec4d extend_low(Vec8f const & a) {
return _mm256_cvtps_pd(_mm256_castps256_ps128(a));
}
// Function extend_high : convert Vec8f vector elements 4 - 7 to Vec4d
static inline Vec4d extend_high (Vec8f const & a) {
return _mm256_cvtps_pd(_mm256_extractf128_ps(a,1));
}
// Fused multiply and add functions
// Multiply and add
static inline Vec4d mul_add(Vec4d const & a, Vec4d const & b, Vec4d const & c) {
#ifdef __FMA__
return _mm256_fmadd_pd(a, b, c);
#elif defined (__FMA4__)
return _mm256_macc_pd(a, b, c);
#else
return a * b + c;
#endif
}
// Multiply and subtract
static inline Vec4d mul_sub(Vec4d const & a, Vec4d const & b, Vec4d const & c) {
#ifdef __FMA__
return _mm256_fmsub_pd(a, b, c);
#elif defined (__FMA4__)
return _mm256_msub_pd(a, b, c);
#else
return a * b - c;
#endif
}
// Multiply and inverse subtract
static inline Vec4d nmul_add(Vec4d const & a, Vec4d const & b, Vec4d const & c) {
#ifdef __FMA__
return _mm256_fnmadd_pd(a, b, c);
#elif defined (__FMA4__)
return _mm256_nmacc_pd(a, b, c);
#else
return c - a * b;
#endif
}
// Multiply and subtract with extra precision on the intermediate calculations,
// even if FMA instructions not supported, using Veltkamp-Dekker split
static inline Vec4d mul_sub_x(Vec4d const & a, Vec4d const & b, Vec4d const & c) {
#ifdef __FMA__
return _mm256_fmsub_pd(a, b, c);
#elif defined (__FMA4__)
return _mm256_msub_pd(a, b, c);
#else
// calculate a * b - c with extra precision
// mask to remove lower 27 bits
Vec4d upper_mask = _mm256_castps_pd(constant8f<(int)0xF8000000,-1,(int)0xF8000000,-1,(int)0xF8000000,-1,(int)0xF8000000,-1>());
Vec4d a_high = a & upper_mask; // split into high and low parts
Vec4d b_high = b & upper_mask;
Vec4d a_low = a - a_high;
Vec4d b_low = b - b_high;
Vec4d r1 = a_high * b_high; // this product is exact
Vec4d r2 = r1 - c; // subtract c from high product
Vec4d r3 = r2 + (a_high * b_low + b_high * a_low) + a_low * b_low; // add rest of product
return r3; // + ((r2 - r1) + c);
#endif
}
// Math functions using fast bit manipulation
#ifdef VECTORI256_H // 256 bit integer vectors are available
// Extract the exponent as an integer
// exponent(a) = floor(log2(abs(a)));
// exponent(1.0) = 0, exponent(0.0) = -1023, exponent(INF) = +1024, exponent(NAN) = +1024
static inline Vec4q exponent(Vec4d const & a) {
#if VECTORI256_H > 1 // AVX2
Vec4uq t1 = _mm256_castpd_si256(a);// reinterpret as 64-bit integer
Vec4uq t2 = t1 << 1; // shift out sign bit
Vec4uq t3 = t2 >> 53; // shift down logical to position 0
Vec4q t4 = Vec4q(t3) - 0x3FF; // subtract bias from exponent
return t4;
#else
return Vec4q(exponent(a.get_low()), exponent(a.get_high()));
#endif
}
// Extract the fraction part of a floating point number
// a = 2^exponent(a) * fraction(a), except for a = 0
// fraction(1.0) = 1.0, fraction(5.0) = 1.25
static inline Vec4d fraction(Vec4d const & a) {
#if VECTORI256_H > 1 // AVX2
Vec4uq t1 = _mm256_castpd_si256(a); // reinterpret as 64-bit integer
Vec4uq t2 = Vec4uq((t1 & 0x000FFFFFFFFFFFFF) | 0x3FF0000000000000); // set exponent to 0 + bias
return _mm256_castsi256_pd(t2);
#else
return Vec4d(fraction(a.get_low()), fraction(a.get_high()));
#endif
}
// Fast calculation of pow(2,n) with n integer
// n = 0 gives 1.0
// n >= 1024 gives +INF
// n <= -1023 gives 0.0
// This function will never produce denormals, and never raise exceptions
static inline Vec4d exp2(Vec4q const & n) {
#if VECTORI256_H > 1 // AVX2
Vec4q t1 = max(n, -0x3FF); // limit to allowed range
Vec4q t2 = min(t1, 0x400);
Vec4q t3 = t2 + 0x3FF; // add bias
Vec4q t4 = t3 << 52; // put exponent into position 52
return _mm256_castsi256_pd(t4); // reinterpret as double
#else
return Vec4d(exp2(n.get_low()), exp2(n.get_high()));
#endif
}
//static inline Vec4d exp2(Vec4d const & x); // defined in vectormath_exp.h
#endif
// Categorization functions
// Function sign_bit: gives true for elements that have the sign bit set
// even for -0.0, -INF and -NAN
// Note that sign_bit(Vec4d(-0.0)) gives true, while Vec4d(-0.0) < Vec4d(0.0) gives false
static inline Vec4db sign_bit(Vec4d const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
Vec4q t1 = _mm256_castpd_si256(a); // reinterpret as 64-bit integer
Vec4q t2 = t1 >> 63; // extend sign bit
return _mm256_castsi256_pd(t2); // reinterpret as 64-bit Boolean
#else
return Vec4db(sign_bit(a.get_low()),sign_bit(a.get_high()));
#endif
}
// Function sign_combine: changes the sign of a when b has the sign bit set
// same as select(sign_bit(b), -a, a)
static inline Vec4d sign_combine(Vec4d const & a, Vec4d const & b) {
Vec4d signmask = _mm256_castps_pd(constant8f<0,(int)0x80000000,0,(int)0x80000000,0,(int)0x80000000,0,(int)0x80000000>()); // -0.0
return a ^ (b & signmask);
}
// Function is_finite: gives true for elements that are normal, denormal or zero,
// false for INF and NAN
static inline Vec4db is_finite(Vec4d const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
Vec4q t1 = _mm256_castpd_si256(a); // reinterpret as 64-bit integer
Vec4q t2 = t1 << 1; // shift out sign bit
Vec4q t3 = 0xFFE0000000000000; // exponent mask
Vec4qb t4 = Vec4q(t2 & t3) != t3; // exponent field is not all 1s
return t4;
#else
return Vec4db(is_finite(a.get_low()),is_finite(a.get_high()));
#endif
}
// Function is_inf: gives true for elements that are +INF or -INF
// false for finite numbers and NAN
static inline Vec4db is_inf(Vec4d const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
Vec4q t1 = _mm256_castpd_si256(a); // reinterpret as 64-bit integer
Vec4q t2 = t1 << 1; // shift out sign bit
return t2 == 0xFFE0000000000000; // exponent is all 1s, fraction is 0
#else
return Vec4db(is_inf(a.get_low()),is_inf(a.get_high()));
#endif
}
// Function is_nan: gives true for elements that are +NAN or -NAN
// false for finite numbers and +/-INF
static inline Vec4db is_nan(Vec4d const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
Vec4q t1 = _mm256_castpd_si256(a); // reinterpret as 64-bit integer
Vec4q t2 = t1 << 1; // shift out sign bit
Vec4q t3 = 0xFFE0000000000000; // exponent mask
Vec4q t4 = t2 & t3; // exponent
Vec4q t5 = _mm256_andnot_si256(t3,t2);// fraction
return Vec4qb(t4 == t3 && t5 != 0);// exponent = all 1s and fraction != 0
#else
return Vec4db(is_nan(a.get_low()),is_nan(a.get_high()));
#endif
}
// Function is_subnormal: gives true for elements that are denormal (subnormal)
// false for finite numbers, zero, NAN and INF
static inline Vec4db is_subnormal(Vec4d const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
Vec4q t1 = _mm256_castpd_si256(a); // reinterpret as 64-bit integer
Vec4q t2 = t1 << 1; // shift out sign bit
Vec4q t3 = 0xFFE0000000000000; // exponent mask
Vec4q t4 = t2 & t3; // exponent
Vec4q t5 = _mm256_andnot_si256(t3,t2);// fraction
return Vec4qb(t4 == 0 && t5 != 0); // exponent = 0 and fraction != 0
#else
return Vec4db(is_subnormal(a.get_low()),is_subnormal(a.get_high()));
#endif
}
// Function is_zero_or_subnormal: gives true for elements that are zero or subnormal (denormal)
// false for finite numbers, NAN and INF
static inline Vec4db is_zero_or_subnormal(Vec4d const & a) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
Vec4q t = _mm256_castpd_si256(a); // reinterpret as 32-bit integer
t &= 0x7FF0000000000000ll; // isolate exponent
return t == 0; // exponent = 0
#else
return Vec4db(is_zero_or_subnormal(a.get_low()),is_zero_or_subnormal(a.get_high()));
#endif
}
// Function infinite2d: returns a vector where all elements are +INF
static inline Vec4d infinite4d() {
return _mm256_castps_pd(constant8f<0,0x7FF00000,0,0x7FF00000,0,0x7FF00000,0,0x7FF00000>());
}
// Function nan4d: returns a vector where all elements are +NAN (quiet)
static inline Vec4d nan4d(int n = 0x10) {
#if defined (VECTORI256_H) && VECTORI256_H > 1 // 256 bit integer vectors are available, AVX2
return _mm256_castsi256_pd(Vec4q(0x7FF8000000000000 + n));
#else
return Vec4d(nan2d(n),nan2d(n));
#endif
}
// change signs on vectors Vec4d
// Each index i0 - i3 is 1 for changing sign on the corresponding element, 0 for no change
template <int i0, int i1, int i2, int i3>
static inline Vec4d change_sign(Vec4d const & a) {
if ((i0 | i1 | i2 | i3) == 0) return a;
__m256 mask = constant8f<0, i0 ? 0x80000000 : 0, 0, i1 ? 0x80000000 : 0, 0, i2 ? 0x80000000 : 0, 0, i3 ? 0x80000000 : 0> ();
return _mm256_xor_pd(a, _mm256_castps_pd(mask));
}
/*****************************************************************************
*
* Functions for reinterpretation between vector types
*
*****************************************************************************/
#if defined (VECTORI256_H) && VECTORI256_H >= 2
// AVX2 vectors defined
// ABI version 4 or later needed on Gcc for correct mangling of 256-bit intrinsic vectors.
// It is recommended to compile with -fabi-version=0 to get the latest abi version
#if !defined (GCC_VERSION) || (defined (__GXX_ABI_VERSION) && __GXX_ABI_VERSION >= 1004)
static inline __m256i reinterpret_i (__m256i const & x) {
return x;
}
static inline __m256i reinterpret_i (__m256 const & x) {
return _mm256_castps_si256(x);
}
static inline __m256i reinterpret_i (__m256d const & x) {
return _mm256_castpd_si256(x);
}
static inline __m256 reinterpret_f (__m256i const & x) {
return _mm256_castsi256_ps(x);
}
static inline __m256 reinterpret_f (__m256 const & x) {
return x;
}
static inline __m256 reinterpret_f (__m256d const & x) {
return _mm256_castpd_ps(x);
}
static inline __m256d reinterpret_d (__m256i const & x) {
return _mm256_castsi256_pd(x);
}
static inline __m256d reinterpret_d (__m256 const & x) {
return _mm256_castps_pd(x);
}
static inline __m256d reinterpret_d (__m256d const & x) {
return x;
}
#else // __GXX_ABI_VERSION < 1004
static inline __m256i reinterpret_i (Vec32c const & x) {
return x;
}
static inline __m256i reinterpret_i (Vec16s const & x) {
return x;
}
static inline __m256i reinterpret_i (Vec8i const & x) {
return x;
}
static inline __m256i reinterpret_i (Vec4q const & x) {
return x;
}
static inline __m256i reinterpret_i (Vec8f const & x) {
return _mm256_castps_si256(x);
}
static inline __m256i reinterpret_i (Vec4d const & x) {
return _mm256_castpd_si256(x);
}
static inline __m256 reinterpret_f (Vec32c const & x) {
return _mm256_castsi256_ps(x);
}
static inline __m256 reinterpret_f (Vec16s const & x) {
return _mm256_castsi256_ps(x);
}
static inline __m256 reinterpret_f (Vec8i const & x) {
return _mm256_castsi256_ps(x);
}
static inline __m256 reinterpret_f (Vec4q const & x) {
return _mm256_castsi256_ps(x);
}
static inline __m256 reinterpret_f (Vec8f const & x) {
return x;
}
static inline __m256 reinterpret_f (Vec4d const & x) {
return _mm256_castpd_ps(x);
}
static inline __m256d reinterpret_d (Vec32c const & x) {
return _mm256_castsi256_pd(x);
}
static inline __m256d reinterpret_d (Vec16s const & x) {
return _mm256_castsi256_pd(x);
}
static inline __m256d reinterpret_d (Vec8i const & x) {
return _mm256_castsi256_pd(x);
}
static inline __m256d reinterpret_d (Vec4q const & x) {
return _mm256_castsi256_pd(x);
}
static inline __m256d reinterpret_d (Vec8f const & x) {
return _mm256_castps_pd(x);
}
static inline __m256d reinterpret_d (Vec4d const & x) {
return x;
}
#endif // __GXX_ABI_VERSION
#else
// AVX2 emulated in vectori256e.h, AVX supported
// ABI version 4 or later needed on Gcc for correct mangling of 256-bit intrinsic vectors.
// It is recommended to compile with -fabi-version=0 to get the latest abi version
#if !defined (GCC_VERSION) || (defined (__GXX_ABI_VERSION) && __GXX_ABI_VERSION >= 1004)
static inline Vec256ie reinterpret_i (__m256 const & x) {
Vec8f xx(x);
return Vec256ie(reinterpret_i(xx.get_low()), reinterpret_i(xx.get_high()));
}
static inline Vec256ie reinterpret_i (__m256d const & x) {
Vec4d xx(x);
return Vec256ie(reinterpret_i(xx.get_low()), reinterpret_i(xx.get_high()));
}
static inline __m256 reinterpret_f (__m256 const & x) {
return x;
}
static inline __m256 reinterpret_f (__m256d const & x) {
return _mm256_castpd_ps(x);
}
static inline __m256d reinterpret_d (__m256 const & x) {
return _mm256_castps_pd(x);
}
static inline __m256d reinterpret_d (__m256d const & x) {
return x;
}
#else // __GXX_ABI_VERSION < 1004
static inline Vec256ie reinterpret_i (Vec8f const & x) {
Vec8f xx(x);
return Vec256ie(reinterpret_i(xx.get_low()), reinterpret_i(xx.get_high()));
}
static inline Vec256ie reinterpret_i (Vec4d const & x) {
Vec4d xx(x);
return Vec256ie(reinterpret_i(xx.get_low()), reinterpret_i(xx.get_high()));
}
static inline __m256 reinterpret_f (Vec8f const & x) {
return x;
}
static inline __m256 reinterpret_f (Vec4d const & x) {
return _mm256_castpd_ps(x);
}
static inline __m256d reinterpret_d (Vec8f const & x) {
return _mm256_castps_pd(x);
}
static inline __m256d reinterpret_d (Vec4d const & x) {
return x;
}
#endif // __GXX_ABI_VERSION
static inline Vec256ie reinterpret_i (Vec256ie const & x) {
return x;
}
static inline __m256 reinterpret_f (Vec256ie const & x) {
return Vec8f(Vec4f(reinterpret_f(x.get_low())), Vec4f(reinterpret_f(x.get_high())));
}
static inline __m256d reinterpret_d (Vec256ie const & x) {
return Vec4d(Vec2d(reinterpret_d(x.get_low())), Vec2d(reinterpret_d(x.get_high())));
}
#endif // VECTORI256_H
/*****************************************************************************
*
* Vector permute and blend functions
*
******************************************************************************
*
* The permute function can reorder the elements of a vector and optionally
* set some elements to zero.
*
* The indexes are inserted as template parameters in <>. These indexes must be
* constants. Each template parameter is an index to the element you want to
* select. An index of -1 will generate zero. An index of -256 means don't care.
*
* Example:
* Vec4d a(10., 11., 12., 13.); // a is (10, 11, 12, 13)
* Vec4d b;
* b = permute4d<1,0,-1,3>(a); // b is (11, 10, 0, 13)
*
*
* The blend function can mix elements from two different vectors and
* optionally set some elements to zero.
*
* The indexes are inserted as template parameters in <>. These indexes must be
* constants. Each template parameter is an index to the element you want to
* select, where indexes 0 - 3 indicate an element from the first source
* vector and indexes 4 - 7 indicate an element from the second source vector.
* A negative index will generate zero.
*
*
* Example:
* Vec4d a(10., 11., 12., 13.); // a is (10, 11, 12, 13)
* Vec4d b(20., 21., 22., 23.); // a is (20, 21, 22, 23)
* Vec4d c;
* c = blend4d<4,3,7,-1> (a,b); // c is (20, 13, 23, 0)
*
* A lot of the code here is metaprogramming aiming to find the instructions
* that best fit the template parameters and instruction set. The metacode
* will be reduced out to leave only a few vector instructions in release
* mode with optimization on.
*****************************************************************************/
// permute vector Vec4d
template <int i0, int i1, int i2, int i3>
static inline Vec4d permute4d(Vec4d const & a) {
const int ior = i0 | i1 | i2 | i3; // OR indexes
// is zeroing needed
const bool do_zero = ior < 0 && (ior & 0x80); // at least one index is negative, and not -0x100
// is shuffling needed
const bool do_shuffle = (i0>0) || (i1!=1 && i1>=0) || (i2!=2 && i2>=0) || (i3!=3 && i3>=0);
if (!do_shuffle) { // no shuffling needed
if (do_zero) { // zeroing
if ((i0 & i1 & i2 & i3) < 0) {
return _mm256_setzero_pd(); // zero everything
}
// zero some elements
__m256d const mask = _mm256_castps_pd (
constant8f< -int(i0>=0), -int(i0>=0), -int(i1>=0), -int(i1>=0), -int(i2>=0), -int(i2>=0), -int(i3>=0), -int(i3>=0) > ());
return _mm256_and_pd(a, mask); // zero with AND mask
}
else {
return a; // do nothing
}
}
#if INSTRSET >= 8 // AVX2: use VPERMPD
__m256d x = _mm256_permute4x64_pd(a, (i0&3) | (i1&3)<<2 | (i2&3)<<4 | (i3&3)<<6);
if (do_zero) { // zeroing
// zero some elements
__m256d const mask2 = _mm256_castps_pd (
constant8f< -int(i0>=0), -int(i0>=0), -int(i1>=0), -int(i1>=0), -int(i2>=0), -int(i2>=0), -int(i3>=0), -int(i3>=0) > ());
x = _mm256_and_pd(x, mask2); // zero with AND mask
}
return x;
#else // AVX
// Needed contents of low/high part of each source register in VSHUFPD
// 0: a.low, 1: a.high, 3: zero
const int s1 = (i0 < 0 ? 3 : (i0 & 2) >> 1) | (i2 < 0 ? 0x30 : (i2 & 2) << 3);
const int s2 = (i1 < 0 ? 3 : (i1 & 2) >> 1) | (i3 < 0 ? 0x30 : (i3 & 2) << 3);
// permute mask
const int sm = (i0 < 0 ? 0 : (i0 & 1)) | (i1 < 0 ? 1 : (i1 & 1)) << 1 | (i2 < 0 ? 0 : (i2 & 1)) << 2 | (i3 < 0 ? 1 : (i3 & 1)) << 3;
if (s1 == 0x01 || s1 == 0x11 || s2 == 0x01 || s2 == 0x11) {
// too expensive to use 256 bit permute, split into two 128 bit permutes
Vec2d alo = a.get_low();
Vec2d ahi = a.get_high();
Vec2d rlo = blend2d<i0, i1> (alo, ahi);
Vec2d rhi = blend2d<i2, i3> (alo, ahi);
return Vec4d(rlo, rhi);
}
// make operands for VSHUFPD
__m256d r1, r2;
switch (s1) {
case 0x00: // LL
r1 = _mm256_insertf128_pd(a,_mm256_castpd256_pd128(a),1); break;
case 0x03: // LZ
r1 = _mm256_insertf128_pd(do_zero ? _mm256_setzero_pd() : __m256d(a), _mm256_castpd256_pd128(a), 1);
break;
case 0x10: // LH
r1 = a; break;
case 0x13: // ZH
r1 = do_zero ? _mm256_and_pd(a, _mm256_castps_pd(constant8f<0,0,0,0,-1,-1,-1,-1>())) : __m256d(a); break;
case 0x30: // LZ
if (do_zero) {
__m128d t = _mm256_castpd256_pd128(a);
t = _mm_and_pd(t,t);
r1 = _mm256_castpd128_pd256(t);
}
else r1 = a;
break;
case 0x31: // HZ
r1 = _mm256_castpd128_pd256(_mm256_extractf128_pd(a,1)); break;
case 0x33: // ZZ
r1 = do_zero ? _mm256_setzero_pd() : __m256d(a); break;
}
if (s2 == s1) {
if (sm == 0x0A) return r1;
r2 = r1;
}
else {
switch (s2) {
case 0x00: // LL
r2 = _mm256_insertf128_pd(a,_mm256_castpd256_pd128(a),1); break;
case 0x03: // ZL
r2 = _mm256_insertf128_pd(do_zero ? _mm256_setzero_pd() : __m256d(a), _mm256_castpd256_pd128(a), 1);
break;
case 0x10: // LH
r2 = a; break;
case 0x13: // ZH
r2 = do_zero ? _mm256_and_pd(a,_mm256_castps_pd(constant8f<0,0,0,0,-1,-1,-1,-1>())) : __m256d(a); break;
case 0x30: // LZ
if (do_zero) {
__m128d t = _mm256_castpd256_pd128(a);
t = _mm_and_pd(t,t);
r2 = _mm256_castpd128_pd256(t);
}
else r2 = a;
break;
case 0x31: // HZ
r2 = _mm256_castpd128_pd256(_mm256_extractf128_pd(a,1)); break;
case 0x33: // ZZ
r2 = do_zero ? _mm256_setzero_pd() : __m256d(a); break;
}
}
return _mm256_shuffle_pd(r1, r2, sm);
#endif // INSTRSET >= 8
}
// blend vectors Vec4d
template <int i0, int i1, int i2, int i3>
static inline Vec4d blend4d(Vec4d const & a, Vec4d const & b) {
// Combine all the indexes into a single bitfield, with 8 bits for each
const int m1 = (i0 & 7) | (i1 & 7) << 8 | (i2 & 7) << 16 | (i3 & 7) << 24;
// Mask to zero out negative indexes
const uint32_t mz = (i0 < 0 ? 0 : 0xFF) | (i1 < 0 ? 0 : 0xFF) << 8 | (i2 < 0 ? 0 : 0xFF) << 16 | (i3 < 0 ? 0 : 0xFF) << 24;
if (mz == 0) return _mm256_setzero_pd(); // all zero
__m256d t1;
if ((((m1 & 0xFEFEFEFE) ^ 0x06020400) & mz) == 0) {
// fits VSHUFPD(a,b)
t1 = _mm256_shuffle_pd(a, b, (i0 & 1) | (i1 & 1) << 1 | (i2 & 1) << 2 | (i3 & 1) << 3);
if (mz == 0xFFFFFFFF) return t1;
return permute4d<i0 < 0 ? -1 : 0, i1 < 0 ? -1 : 1, i2 < 0 ? -1 : 2, i3 < 0 ? -1 : 3> (t1);
}
if ((((m1 & 0xFEFEFEFE) ^0x02060004) & mz) == 0) {
// fits VSHUFPD(b,a)
t1 = _mm256_shuffle_pd(b, a, (i0 & 1) | (i1 & 1) << 1 | (i2 & 1) << 2 | (i3 & 1) << 3);
if (mz == 0xFFFFFFFF) return t1;
return permute4d<i0 < 0 ? -1 : 0, i1 < 0 ? -1 : 1, i2 < 0 ? -1 : 2, i3 < 0 ? -1 : 3> (t1);
}
if ((((m1 & 0x03030303) ^ 0x03020100) & mz) == 0) {
// blend and zero, no permute
if ((m1 & 0x04040404 & mz) == 0) {
t1 = a;
}
else if (((m1 ^ 0x04040404) & 0x04040404 & mz) == 0) {
t1 = b;
}
else {
t1 = _mm256_blend_pd(a, b, (i0&4)>>2 | (i1&4)>>1 | (i2&4) | (i3&4) << 1);
}
if (mz == 0xFFFFFFFF) return t1;
return permute4d<i0 < 0 ? -1 : 0, i1 < 0 ? -1 : 1, i2 < 0 ? -1 : 2, i3 < 0 ? -1 : 3> (t1);
}
if ((m1 & 0x04040404 & mz) == 0) {
// all from a
return permute4d<i0, i1, i2, i3> (a);
}
if (((m1 ^ 0x04040404) & 0x04040404 & mz) == 0) {
// all from b
return permute4d<i0 ^ 4, i1 ^ 4, i2 ^ 4, i3 ^ 4> (b);
}
// check if we can do 128-bit blend/permute
if (((m1 ^ 0x01000100) & 0x01010101 & mz) == 0) {
const uint32_t j0 = uint32_t((i0 >= 0 ? i0 : i1 >= 0 ? i1 : -1) >> 1);
const uint32_t j1 = uint32_t((i2 >= 0 ? i2 : i3 >= 0 ? i3 : -1) >> 1);
if (((m1 ^ ((j0 & 3) * 0x00000202 | (j1 & 3) * 0x02020000)) & 0x06060606 & mz) == 0) {
t1 = _mm256_permute2f128_pd(a, b, (j0 & 0x0F) | (j1 & 0x0F) << 4);
const bool partialzero = (((i0 | i1) ^ j0) & 0x80) != 0 || (((i2 | i3) ^ j1) & 0x80) != 0;
if (partialzero) {
// zero some elements
__m256d mask = _mm256_castps_pd (constant8f <
i0 < 0 ? 0 : -1, i0 < 0 ? 0 : -1, i1 < 0 ? 0 : -1, i1 < 0 ? 0 : -1,
i2 < 0 ? 0 : -1, i2 < 0 ? 0 : -1, i3 < 0 ? 0 : -1, i3 < 0 ? 0 : -1 > ());
return _mm256_and_pd(t1, mask);
}
else return t1;
}
}
// general case. combine two permutes
Vec4d a1 = permute4d <
(uint32_t)i0 < 4 ? i0 : -0x100,
(uint32_t)i1 < 4 ? i1 : -0x100,
(uint32_t)i2 < 4 ? i2 : -0x100,
(uint32_t)i3 < 4 ? i3 : -0x100 > (a);
Vec4d b1 = permute4d <
(uint32_t)(i0^4) < 4 ? (i0^4) : -0x100,
(uint32_t)(i1^4) < 4 ? (i1^4) : -0x100,
(uint32_t)(i2^4) < 4 ? (i2^4) : -0x100,
(uint32_t)(i3^4) < 4 ? (i3^4) : -0x100 > (b);
t1 = _mm256_blend_pd(a1, b1, (i0&4)>>2 | (i1&4)>>1 | (i2&4) | (i3&4) << 1);
if (mz == 0xFFFFFFFF) return t1;
return permute4d<i0 < 0 ? -1 : 0, i1 < 0 ? -1 : 1, i2 < 0 ? -1 : 2, i3 < 0 ? -1 : 3> (t1);
}
/*****************************************************************************
*
* Vector Vec8f permute and blend functions
*
*****************************************************************************/
// permute vector Vec8f
template <int i0, int i1, int i2, int i3, int i4, int i5, int i6, int i7>
static inline Vec8f permute8f(Vec8f const & a) {
__m256 t1, mask;
const int ior = i0 | i1 | i2 | i3 | i4 | i5 | i6 | i7; // OR indexes
// is zeroing needed
const bool do_zero = ior < 0 && (ior & 0x80); // at least one index is negative, and not -0x100
// is shuffling needed
const bool do_shuffle = (i0>0) || (i1!=1 && i1>=0) || (i2!=2 && i2>=0) || (i3!=3 && i3>=0) ||
(i4!=4 && i4>=0) || (i5!=5 && i5>=0) || (i6!=6 && i6>=0) || (i7!=7 && i7>=0);
if (!do_shuffle) { // no shuffling needed
if (do_zero) { // zeroing
if ((i0 & i1 & i2 & i3 & i4 & i5 & i6 & i7) < 0) {
return _mm256_setzero_ps(); // zero everything
}
// zero some elements
mask = constant8f< -int(i0>=0), -int(i1>=0), -int(i2>=0), -int(i3>=0), -int(i4>=0), -int(i5>=0), -int(i6>=0), -int(i7>=0) > ();
return _mm256_and_ps(a, mask); // zero with AND mask
}
else {
return a; // do nothing
}
}
#if INSTRSET >= 8 // AVX2: use VPERMPS
if (do_shuffle) { // shuffling
mask = constant8f< i0 & 7, i1 & 7, i2 & 7, i3 & 7, i4 & 7, i5 & 7, i6 & 7, i7 & 7 > ();
#if defined (_MSC_VER) && _MSC_VER < 1700 && ! defined(__INTEL_COMPILER)
// bug in MS VS 11 beta: operands in wrong order. fixed in 11.0
t1 = _mm256_permutevar8x32_ps(mask, _mm256_castps_si256(a)); // problem in immintrin.h
#elif defined (GCC_VERSION) && GCC_VERSION <= 40700 && !defined(__INTEL_COMPILER) && !defined(__clang__)
// Gcc 4.7.0 has wrong parameter type and operands in wrong order. fixed in version 4.7.1
t1 = _mm256_permutevar8x32_ps(mask, a);
#else // no bug version
t1 = _mm256_permutevar8x32_ps(a, _mm256_castps_si256(mask));
#endif
}
else {
t1 = a; // no shuffling
}
if (do_zero) { // zeroing
if ((i0 & i1 & i2 & i3 & i4 & i5 & i6 & i7) < 0) {
return _mm256_setzero_ps(); // zero everything
}
// zero some elements
mask = constant8f< -int(i0>=0), -int(i1>=0), -int(i2>=0), -int(i3>=0), -int(i4>=0), -int(i5>=0), -int(i6>=0), -int(i7>=0) > ();
t1 = _mm256_and_ps(t1, mask); // zero with AND mask
}
return t1;
#else // AVX
// Combine all the indexes into a single bitfield, with 4 bits for each
const int m1 = (i0&7) | (i1&7)<<4 | (i2&7)<<8 | (i3&7)<<12 | (i4&7)<<16 | (i5&7)<<20 | (i6&7)<<24 | (i7&7)<<28;
// Mask to zero out negative indexes
const int m2 = (i0<0?0:0xF) | (i1<0?0:0xF)<<4 | (i2<0?0:0xF)<<8 | (i3<0?0:0xF)<<12 | (i4<0?0:0xF)<<16 | (i5<0?0:0xF)<<20 | (i6<0?0:0xF)<<24 | (i7<0?0:0xF)<<28;
// Check if it is possible to use VSHUFPS. Index n must match index n+4 on bit 0-1, and even index n must match odd index n+1 on bit 2
const bool sps = ((m1 ^ (m1 >> 16)) & 0x3333 & m2 & (m2 >> 16)) == 0 && ((m1 ^ (m1 >> 4)) & 0x04040404 & m2 & m2 >> 4) == 0;
if (sps) { // can use VSHUFPS
// Index of each pair (i[n],i[n+1])
const int j0 = i0 >= 0 ? i0 : i1;
const int j1 = i2 >= 0 ? i2 : i3;
const int j2 = i4 >= 0 ? i4 : i5;
const int j3 = i6 >= 0 ? i6 : i7;
// Index of each pair (i[n],i[n+4])
const int k0 = i0 >= 0 ? i0 : i4;
const int k1 = i1 >= 0 ? i1 : i5;
const int k2 = i2 >= 0 ? i2 : i6;
const int k3 = i3 >= 0 ? i3 : i7;
// Needed contents of low/high part of each source register in VSHUFPS
// 0: a.low, 1: a.high, 3: zero or don't care
const int s1 = (j0 < 0 ? 3 : (j0 & 4) >> 2) | (j2 < 0 ? 0x30 : (j2 & 4) << 2);
const int s2 = (j1 < 0 ? 3 : (j1 & 4) >> 2) | (j3 < 0 ? 0x30 : (j3 & 4) << 2);
// calculate cost of using VSHUFPS
const int cost1 = (s1 == 0x01 || s1 == 0x11) ? 2 : (s1 == 0x00 || s1 == 0x03 || s1 == 0x31) ? 1 : 0;
const int cost2 = (s2 == s1) ? 0 : (s2 == 0x01 || s2 == 0x11) ? 2 : (s2 == 0x00 || (s2 == 0x03 && (s1 & 0xF0) != 0x00) || (s2 == 0x31 && (s1 & 0x0F) != 0x01)) ? 1 : 0;
if (cost1 + cost2 <= 3) {
// permute mask
const int sm = (k0 < 0 ? 0 : (k0 & 3)) | (k1 < 0 ? 1 : (k1 & 3)) << 2 | (k2 < 0 ? 2 : (k2 & 3)) << 4 | (k3 < 0 ? 3 : (k3 & 3)) << 6;
// make operands for VSHUFPS
__m256 r1, r2;
switch (s1) {
case 0x00: // LL
case 0x03: // ZL
r1 = _mm256_insertf128_ps(a,_mm256_castps256_ps128(a),1); break;
case 0x01: // HL
r1 = _mm256_castps128_ps256(_mm256_extractf128_ps(a,1));
r1 = _mm256_insertf128_ps(r1,_mm256_castps256_ps128(a),1); break;
case 0x10: // LH
case 0x13: // ZH
case 0x30: // LZ
case 0x33: // ZZ
r1 = a; break;
case 0x11: // HH
r1 = _mm256_castps128_ps256(_mm256_extractf128_ps(a,1));
r1 = _mm256_insertf128_ps(r1,_mm256_castps256_ps128(r1),1); break;
case 0x31: // HZ
r1 = _mm256_castps128_ps256(_mm256_extractf128_ps(a,1)); break;
}
if (s2 == s1) {
if (sm == 0xE4) return r1;
r2 = r1;
}
else {
switch (s2) {
case 0x00: // LL
r2 = _mm256_insertf128_ps(a,_mm256_castps256_ps128(a),1); break;
case 0x03: // ZL
if ((s1 & 0xF0) == 0x00) r2 = r1;
else {
r2 = _mm256_insertf128_ps(a,_mm256_castps256_ps128(a),1);
}
break;
case 0x01: // HL
r2 = _mm256_castps128_ps256(_mm256_extractf128_ps(a,1));
r2 = _mm256_insertf128_ps(r1,_mm256_castps256_ps128(a),1); break;
case 0x10: // LH
case 0x13: // ZH
case 0x30: // LZ
case 0x33: // ZZ
r2 = a; break;
case 0x11: // HH
r2 = _mm256_castps128_ps256(_mm256_extractf128_ps(a,1));
r2 = _mm256_insertf128_ps(r2,_mm256_castps256_ps128(r2),1); break;
case 0x31: // HZ
if ((s1 & 0x0F) == 0x01) r2 = r1;
else {
r2 = _mm256_castps128_ps256(_mm256_extractf128_ps(a,1));
}
break;
}
}
// now the permute instruction
t1 = _mm256_shuffle_ps(r1, r2, sm);
if (do_zero) {
// zero some elements
mask = constant8f< -int(i0>=0), -int(i1>=0), -int(i2>=0), -int(i3>=0), -int(i4>=0), -int(i5>=0), -int(i6>=0), -int(i7>=0) > ();
t1 = _mm256_and_ps(t1, mask); // zero with AND mask
}
return t1;
}
}
// not using VSHUFPS. Split into low and high part
Vec4f alo = a.get_low();
Vec4f ahi = a.get_high();
Vec4f rlo = blend4f<i0, i1, i2, i3> (alo, ahi);
Vec4f rhi = blend4f<i4, i5, i6, i7> (alo, ahi);
return Vec8f(rlo, rhi);
#endif
}
// blend vectors Vec8f
template <int i0, int i1, int i2, int i3, int i4, int i5, int i6, int i7>
static inline Vec8f blend8f(Vec8f const & a, Vec8f const & b) {
const int ior = i0 | i1 | i2 | i3 | i4 | i5 | i6 | i7; // OR indexes
// is zeroing needed
const bool do_zero = ior < 0 && (ior & 0x80); // at least one index is negative, and not -0x100
// Combine all the indexes into a single bitfield, with 4 bits for each
const int m1 = (i0&0xF) | (i1&0xF)<<4 | (i2&0xF)<<8 | (i3&0xF)<<12 | (i4&0xF)<<16 | (i5&0xF)<<20 | (i6&0xF)<<24 | (i7&0xF)<<28;
// Mask to zero out negative indexes
const int mz = (i0<0?0:0xF) | (i1<0?0:0xF)<<4 | (i2<0?0:0xF)<<8 | (i3<0?0:0xF)<<12 | (i4<0?0:0xF)<<16 | (i5<0?0:0xF)<<20 | (i6<0?0:0xF)<<24 | (i7<0?0:0xF)<<28;
__m256 t1, mask;
if (mz == 0) return _mm256_setzero_ps(); // all zero
if ((m1 & 0x88888888 & mz) == 0) {
// all from a
return permute8f<i0, i1, i2, i3, i4, i5, i6, i7> (a);
}
if (((m1 ^ 0x88888888) & 0x88888888 & mz) == 0) {
// all from b
return permute8f<i0&~8, i1&~8, i2&~8, i3&~8, i4&~8, i5&~8, i6&~8, i7&~8> (b);
}
if ((((m1 & 0x77777777) ^ 0x76543210) & mz) == 0) {
// blend and zero, no permute
mask = constant8f<(i0&8)?0:-1, (i1&8)?0:-1, (i2&8)?0:-1, (i3&8)?0:-1, (i4&8)?0:-1, (i5&8)?0:-1, (i6&8)?0:-1, (i7&8)?0:-1> ();
t1 = select(mask, a, b);
if (!do_zero) return t1;
// zero some elements
mask = constant8f< (i0<0&&(i0&8)) ? 0 : -1, (i1<0&&(i1&8)) ? 0 : -1, (i2<0&&(i2&8)) ? 0 : -1, (i3<0&&(i3&8)) ? 0 : -1,
(i4<0&&(i4&8)) ? 0 : -1, (i5<0&&(i5&8)) ? 0 : -1, (i6<0&&(i6&8)) ? 0 : -1, (i7<0&&(i7&8)) ? 0 : -1 > ();
return _mm256_and_ps(t1, mask);
}
// check if we can do 128-bit blend/permute
if (((m1 ^ 0x32103210) & 0x33333333 & mz) == 0) {
const uint32_t j0 = (i0 >= 0 ? i0 : i1 >= 0 ? i1 : i2 >= 0 ? i2 : i3 >= 0 ? i3 : -1) >> 2;
const uint32_t j1 = (i4 >= 0 ? i4 : i5 >= 0 ? i5 : i6 >= 0 ? i6 : i7 >= 0 ? i7 : -1) >> 2;
if (((m1 ^ ((j0 & 3) * 0x00004444 | (j1 & 3) * 0x44440000)) & 0xCCCCCCCC & mz) == 0) {
t1 = _mm256_permute2f128_ps(a, b, (j0 & 0x0F) | (j1 & 0x0F) << 4);
const bool partialzero = (((i0 | i1 | i2 | i3) ^ j0) & 0x80) != 0 || (((i4 | i5 | i6 | i7) ^ j1) & 0x80) != 0;
if (partialzero) {
// zero some elements
mask = constant8f< i0 < 0 ? 0 : -1, i1 < 0 ? 0 : -1, i2 < 0 ? 0 : -1, i3 < 0 ? 0 : -1,
i4 < 0 ? 0 : -1, i5 < 0 ? 0 : -1, i6 < 0 ? 0 : -1, i7 < 0 ? 0 : -1 > ();
return _mm256_and_ps(t1, mask);
}
else return t1;
}
}
// Not checking special cases for vunpckhps, vunpcklps: they are too rare
// Check if it is possible to use VSHUFPS.
// Index n must match index n+4 on bit 0-1, and even index n must match odd index n+1 on bit 2-3
const bool sps = ((m1 ^ (m1 >> 16)) & 0x3333 & mz & (mz >> 16)) == 0 && ((m1 ^ (m1 >> 4)) & 0x0C0C0C0C & mz & mz >> 4) == 0;
if (sps) { // can use VSHUFPS
// Index of each pair (i[n],i[n+1])
const int j0 = i0 >= 0 ? i0 : i1;
const int j1 = i2 >= 0 ? i2 : i3;
const int j2 = i4 >= 0 ? i4 : i5;
const int j3 = i6 >= 0 ? i6 : i7;
// Index of each pair (i[n],i[n+4])
const int k0 = i0 >= 0 ? i0 : i4;
const int k1 = i1 >= 0 ? i1 : i5;
const int k2 = i2 >= 0 ? i2 : i6;
const int k3 = i3 >= 0 ? i3 : i7;
// Needed contents of low/high part of each source register in VSHUFPS
// 0: a.low, 1: a.high, 2: b.low, 3: b.high, 4: zero or don't care
const int s1 = (j0 < 0 ? 4 : (j0 & 0xC) >> 2) | (j2 < 0 ? 0x30 : (j2 & 0xC) << 2);
const int s2 = (j1 < 0 ? 3 : (j1 & 0xC) >> 2) | (j3 < 0 ? 0x30 : (j3 & 0xC) << 2);
// permute mask
const int sm = (k0 < 0 ? 0 : (k0 & 3)) | (k1 < 0 ? 1 : (k1 & 3)) << 2 | (k2 < 0 ? 2 : (k2 & 3)) << 4 | (k3 < 0 ? 3 : (k3 & 3)) << 6;
__m256 r1, r2;
__m128 ahi = _mm256_extractf128_ps(a,1); // 1
__m128 bhi = _mm256_extractf128_ps(b,1); // 3
switch (s1) {
case 0x00: case 0x04:
r1 = _mm256_insertf128_ps(a,_mm256_castps256_ps128(a),1); break;
case 0x01: case 0x41:
r1 = _mm256_insertf128_ps(_mm256_castps128_ps256(ahi),_mm256_castps256_ps128(a),1); break;
case 0x02:
r1 = _mm256_insertf128_ps(b,_mm256_castps256_ps128(a),1); break;
case 0x03:
r1 = _mm256_insertf128_ps(_mm256_castps128_ps256(bhi),_mm256_castps256_ps128(a),1); break;
case 0x10: case 0x14: case 0x40: case 0x44:
r1 = a; break;
case 0x11:
r1 = _mm256_insertf128_ps(_mm256_castps128_ps256(ahi),ahi,1); break;
case 0x12:
r1 = _mm256_insertf128_ps(b,ahi,1); break;
case 0x13:
r1 = _mm256_insertf128_ps(_mm256_castps128_ps256(bhi),ahi,1); break;
case 0x20:
r1 = _mm256_insertf128_ps(a,_mm256_castps256_ps128(b),1); break;
case 0x21:
r1 = _mm256_insertf128_ps(_mm256_castps128_ps256(ahi),_mm256_castps256_ps128(b),1); break;
case 0x22: case 0x24: case 0x42:
r1 = _mm256_insertf128_ps(b,_mm256_castps256_ps128(b),1); break;
case 0x23: case 0x43:
r1 = _mm256_insertf128_ps(_mm256_castps128_ps256(bhi),_mm256_castps256_ps128(b),1); break;
case 0x30:
r1 = _mm256_insertf128_ps(a,bhi,1); break;
case 0x31:
r1 = _mm256_insertf128_ps(_mm256_castps128_ps256(ahi),bhi,1); break;
case 0x32: case 0x34:
r1 = b; break;
case 0x33:
r1 = _mm256_insertf128_ps(_mm256_castps128_ps256(bhi),bhi,1); break;
}
if (s2 == s1 || ((s2 & 0x04) && ((s1 ^ s2) & 0xF0) == 0) || ((s2 & 0x40) && ((s1 ^ s2) & 0x0F) == 0)) {
// can use r2 = r1
if (sm == 0xE4) return r1; // no shuffling needed
r2 = r1;
}
else {
switch (s2) {
case 0x00: case 0x04:
r2 = _mm256_insertf128_ps(a,_mm256_castps256_ps128(a),1); break;
case 0x01: case 0x41:
r2 = _mm256_insertf128_ps(_mm256_castps128_ps256(ahi),_mm256_castps256_ps128(a),1); break;
case 0x02:
r2 = _mm256_insertf128_ps(b,_mm256_castps256_ps128(a),1); break;
case 0x03:
r2 = _mm256_insertf128_ps(_mm256_castps128_ps256(bhi),_mm256_castps256_ps128(a),1); break;
case 0x10: case 0x14: case 0x40: case 0x44:
r2 = a; break;
case 0x11:
r2 = _mm256_insertf128_ps(_mm256_castps128_ps256(ahi),ahi,1); break;
case 0x12:
r2 = _mm256_insertf128_ps(b,ahi,1); break;
case 0x13:
r2 = _mm256_insertf128_ps(_mm256_castps128_ps256(bhi),ahi,1); break;
case 0x20:
r2 = _mm256_insertf128_ps(a,_mm256_castps256_ps128(b),1); break;
case 0x21:
r2 = _mm256_insertf128_ps(_mm256_castps128_ps256(ahi),_mm256_castps256_ps128(b),1); break;
case 0x22: case 0x24: case 0x42:
r2 = _mm256_insertf128_ps(b,_mm256_castps256_ps128(b),1); break;
case 0x23: case 0x43:
r2 = _mm256_insertf128_ps(_mm256_castps128_ps256(bhi),_mm256_castps256_ps128(b),1); break;
case 0x30:
r2 = _mm256_insertf128_ps(a,bhi,1); break;
case 0x31:
r2 = _mm256_insertf128_ps(_mm256_castps128_ps256(ahi),bhi,1); break;
case 0x32: case 0x34:
r2 = b; break;
case 0x33:
r2 = _mm256_insertf128_ps(_mm256_castps128_ps256(bhi),bhi,1); break;
}
}
// now the shuffle instruction
t1 = _mm256_shuffle_ps(r1, r2, sm);
if (do_zero) {
// zero some elements
mask = constant8f< -int(i0>=0), -int(i1>=0), -int(i2>=0), -int(i3>=0), -int(i4>=0), -int(i5>=0), -int(i6>=0), -int(i7>=0) > ();
t1 = _mm256_and_ps(t1, mask); // zero with AND mask
}
return t1;
}
// Check if we can use 64-bit blend. Even numbered indexes must be even and odd numbered
// indexes must be equal to the preceding index + 1, except for negative indexes.
if (((m1 ^ 0x10101010) & 0x11111111 & mz) == 0 && ((m1 ^ m1 >> 4) & 0x0E0E0E0E & mz & mz >> 4) == 0) {
const bool partialzero = int((i0 ^ i1) | (i2 ^ i3) | (i4 ^ i5) | (i6 ^ i7)) < 0; // part of a 64-bit block is zeroed
const int blank1 = partialzero ? -0x100 : -1; // ignore or zero
const int n0 = i0 > 0 ? i0/2 : i1 > 0 ? i1/2 : blank1; // indexes for 64 bit blend
const int n1 = i2 > 0 ? i2/2 : i3 > 0 ? i3/2 : blank1;
const int n2 = i4 > 0 ? i4/2 : i5 > 0 ? i5/2 : blank1;
const int n3 = i6 > 0 ? i6/2 : i7 > 0 ? i7/2 : blank1;
t1 = _mm256_castpd_ps (blend4d<n0,n1,n2,n3> (_mm256_castps_pd(a), _mm256_castps_pd(b)));
if (blank1 == -1 || !do_zero) {
return t1;
}
// need more zeroing
mask = constant8f< -int(i0>=0), -int(i1>=0), -int(i2>=0), -int(i3>=0), -int(i4>=0), -int(i5>=0), -int(i6>=0), -int(i7>=0) > ();
return _mm256_and_ps(t1, mask); // zero with AND mask
}
// general case: permute and blend and possible zero
const int blank2 = do_zero ? -1 : -0x100; // ignore or zero
Vec8f ta = permute8f <
(uint32_t)i0 < 8 ? i0 : blank2,
(uint32_t)i1 < 8 ? i1 : blank2,
(uint32_t)i2 < 8 ? i2 : blank2,
(uint32_t)i3 < 8 ? i3 : blank2,
(uint32_t)i4 < 8 ? i4 : blank2,
(uint32_t)i5 < 8 ? i5 : blank2,
(uint32_t)i6 < 8 ? i6 : blank2,
(uint32_t)i7 < 8 ? i7 : blank2 > (a);
Vec8f tb = permute8f <
(uint32_t)(i0^8) < 8 ? (i0^8) : blank2,
(uint32_t)(i1^8) < 8 ? (i1^8) : blank2,
(uint32_t)(i2^8) < 8 ? (i2^8) : blank2,
(uint32_t)(i3^8) < 8 ? (i3^8) : blank2,
(uint32_t)(i4^8) < 8 ? (i4^8) : blank2,
(uint32_t)(i5^8) < 8 ? (i5^8) : blank2,
(uint32_t)(i6^8) < 8 ? (i6^8) : blank2,
(uint32_t)(i7^8) < 8 ? (i7^8) : blank2 > (b);
if (blank2 == -1) {
return _mm256_or_ps(ta, tb);
}
// no zeroing, need to blend
const int maskb = ((i0 >> 3) & 1) | ((i1 >> 2) & 2) | ((i2 >> 1) & 4) | (i3 & 8) |
((i4 << 1) & 0x10) | ((i5 << 2) & 0x20) | ((i6 << 3) & 0x40) | ((i7 << 4) & 0x80);
return _mm256_blend_ps(ta, tb, maskb); // blend
}
/*****************************************************************************
*
* Vector lookup functions
*
******************************************************************************
*
* These functions use vector elements as indexes into a table.
* The table is given as one or more vectors or as an array.
*
* This can be used for several purposes:
* - table lookup
* - permute or blend with variable indexes
* - blend from more than two sources
* - gather non-contiguous data
*
* An index out of range may produce any value - the actual value produced is
* implementation dependent and may be different for different instruction
* sets. An index out of range does not produce an error message or exception.
*
* Example:
* Vec4i a(2,0,0,3); // index a is ( 2, 0, 0, 3)
* Vec4f b(1.0f,1.1f,1.2f,1.3f); // table b is (1.0, 1.1, 1.2, 1.3)
* Vec4f c;
* c = lookup4 (a,b); // result c is (1.2, 1.0, 1.0, 1.3)
*
*****************************************************************************/
#ifdef VECTORI256_H // Vec8i and Vec4q must be defined
static inline Vec8f lookup8(Vec8i const & index, Vec8f const & table) {
#if INSTRSET >= 8 && VECTORI256_H > 1 // AVX2
#if defined (_MSC_VER) && _MSC_VER < 1700 && ! defined(__INTEL_COMPILER)
// bug in MS VS 11 beta: operands in wrong order. fixed in 11.0
return _mm256_permutevar8x32_ps(_mm256_castsi256_ps(index), _mm256_castps_si256(table));
#elif defined (GCC_VERSION) && GCC_VERSION <= 40700 && !defined(__INTEL_COMPILER) && !defined(__clang__)
// Gcc 4.7.0 has wrong parameter type and operands in wrong order. fixed in version 4.7.1
return _mm256_permutevar8x32_ps(_mm256_castsi256_ps(index), table);
#else
// no bug version
return _mm256_permutevar8x32_ps(table, index);
#endif
#else // AVX
// swap low and high part of table
__m256 t1 = _mm256_castps128_ps256(_mm256_extractf128_ps(table, 1));
__m256 t2 = _mm256_insertf128_ps(t1, _mm256_castps256_ps128(table), 1);
// join index parts
__m256i index2 = _mm256_insertf128_si256(_mm256_castsi128_si256(index.get_low()), index.get_high(), 1);
// permute within each 128-bit part
__m256 r0 = _mm256_permutevar_ps(table, index2);
__m256 r1 = _mm256_permutevar_ps(t2, index2);
// high index bit for blend
__m128i k1 = _mm_slli_epi32(index.get_high() ^ 4, 29);
__m128i k0 = _mm_slli_epi32(index.get_low(), 29);
__m256 kk = _mm256_insertf128_ps(_mm256_castps128_ps256(_mm_castsi128_ps(k0)), _mm_castsi128_ps(k1), 1);
// blend the two permutes
return _mm256_blendv_ps(r0, r1, kk);
#endif
}
template <int n>
static inline Vec8f lookup(Vec8i const & index, float const * table) {
if (n <= 0) return 0;
if (n <= 4) {
Vec4f table1 = Vec4f().load(table);
return Vec8f(
lookup4 (index.get_low(), table1),
lookup4 (index.get_high(), table1));
}
#if INSTRSET < 8 // not AVX2
if (n <= 8) {
return lookup8(index, Vec8f().load(table));
}
#endif
// Limit index
Vec8ui index1;
if ((n & (n-1)) == 0) {
// n is a power of 2, make index modulo n
index1 = Vec8ui(index) & (n-1);
}
else {
// n is not a power of 2, limit to n-1
index1 = min(Vec8ui(index), n-1);
}
#if INSTRSET >= 8 && VECTORI256_H > 1 // AVX2
return _mm256_i32gather_ps(table, index1, 4);
#else // AVX
return Vec8f(table[index1[0]],table[index1[1]],table[index1[2]],table[index1[3]],
table[index1[4]],table[index1[5]],table[index1[6]],table[index1[7]]);
#endif
}
static inline Vec4d lookup4(Vec4q const & index, Vec4d const & table) {
#if INSTRSET >= 8 && VECTORI256_H > 1 // AVX2
// We can't use VPERMPD because it has constant indexes.
// Convert the index to fit VPERMPS
Vec8i index1 = permute8i<0,0,2,2,4,4,6,6> (Vec8i(index+index));
Vec8i index2 = index1 + Vec8i(constant8i<0,1,0,1,0,1,0,1>());
#if defined (_MSC_VER) && _MSC_VER < 1700 && ! defined(__INTEL_COMPILER)
// bug in MS VS 11 beta: operands in wrong order. fixed in 11.0
return _mm256_castps_pd(_mm256_permutevar8x32_ps(_mm256_castsi256_ps(index2), _mm256_castpd_si256(table)));
#elif defined (GCC_VERSION) && GCC_VERSION <= 40700 && !defined(__INTEL_COMPILER) && !defined(__clang__)
// Gcc 4.7.0 has wrong parameter type and operands in wrong order
return _mm256_castps_pd(_mm256_permutevar8x32_ps(_mm256_castsi256_ps(index2), _mm256_castpd_ps(table)));
#else
// no bug version
return _mm256_castps_pd(_mm256_permutevar8x32_ps(_mm256_castpd_ps(table), index2));
#endif
#else // AVX
// swap low and high part of table
__m256d t1 = _mm256_castpd128_pd256(_mm256_extractf128_pd(table, 1));
__m256d t2 = _mm256_insertf128_pd(t1, _mm256_castpd256_pd128(table), 1);
// index << 1
__m128i index2lo = index.get_low() + index.get_low();
__m128i index2hi = index.get_high() + index.get_high();
// join index parts
__m256i index3 = _mm256_insertf128_si256(_mm256_castsi128_si256(index2lo), index2hi, 1);
// permute within each 128-bit part
__m256d r0 = _mm256_permutevar_pd(table, index3);
__m256d r1 = _mm256_permutevar_pd(t2, index3);
// high index bit for blend
__m128i k1 = _mm_slli_epi64(index.get_high() ^ 2, 62);
__m128i k0 = _mm_slli_epi64(index.get_low(), 62);
__m256d kk = _mm256_insertf128_pd(_mm256_castpd128_pd256(_mm_castsi128_pd(k0)), _mm_castsi128_pd(k1), 1);
// blend the two permutes
return _mm256_blendv_pd(r0, r1, kk);
#endif
}
template <int n>
static inline Vec4d lookup(Vec4q const & index, double const * table) {
if (n <= 0) return 0;
if (n <= 2) {
Vec2d table1 = Vec2d().load(table);
return Vec4d(
lookup2 (index.get_low(), table1),
lookup2 (index.get_high(), table1));
}
#if INSTRSET < 8 // not AVX2
if (n <= 4) {
return lookup4(index, Vec4d().load(table));
}
#endif
// Limit index
Vec8ui index1;
if ((n & (n-1)) == 0) {
// n is a power of 2, make index modulo n
index1 = Vec8ui(index) & constant8i<n-1, 0, n-1, 0, n-1, 0, n-1, 0>();
}
else {
// n is not a power of 2, limit to n-1
index1 = min(Vec8ui(index), constant8i<n-1, 0, n-1, 0, n-1, 0, n-1, 0>() );
}
#if INSTRSET >= 8 && VECTORI256_H > 1 // AVX2
return _mm256_i64gather_pd(table, index1, 8);
#else // AVX
Vec4q index2 = Vec4q(index1);
return Vec4d(table[index2[0]],table[index2[1]],table[index2[2]],table[index2[3]]);
#endif
}
#endif // VECTORI256_H
/*****************************************************************************
*
* Gather functions with fixed indexes
*
*****************************************************************************/
// Load elements from array a with indices i0, i1, i2, i3, ..
template <int i0, int i1, int i2, int i3, int i4, int i5, int i6, int i7>
static inline Vec8f gather8f(void const * a) {
return reinterpret_f(gather8i<i0, i1, i2, i3, i4, i5, i6, i7>(a));
}
// Load elements from array a with indices i0, i1, i2, i3
template <int i0, int i1, int i2, int i3>
static inline Vec4d gather4d(void const * a) {
return reinterpret_d(gather4q<i0, i1, i2, i3>(a));
}
/*****************************************************************************
*
* Horizontal scan functions
*
*****************************************************************************/
// Get index to the first element that is true. Return -1 if all are false
static inline int horizontal_find_first(Vec8fb const & x) {
return horizontal_find_first(Vec8ib(x));
}
static inline int horizontal_find_first(Vec4db const & x) {
return horizontal_find_first(Vec4qb(x));
}
// Count the number of elements that are true
static inline uint32_t horizontal_count(Vec8fb const & x) {
return horizontal_count(Vec8ib(x));
}
static inline uint32_t horizontal_count(Vec4db const & x) {
return horizontal_count(Vec4qb(x));
}
/*****************************************************************************
*
* Boolean <-> bitfield conversion functions
*
*****************************************************************************/
// to_bits: convert boolean vector to integer bitfield
static inline uint8_t to_bits(Vec8fb const & x) {
return to_bits(Vec8ib(x));
}
// to_Vec8fb: convert integer bitfield to boolean vector
static inline Vec8fb to_Vec8fb(uint8_t x) {
return Vec8fb(to_Vec8ib(x));
}
// to_bits: convert boolean vector to integer bitfield
static inline uint8_t to_bits(Vec4db const & x) {
return to_bits(Vec4qb(x));
}
// to_Vec4db: convert integer bitfield to boolean vector
static inline Vec4db to_Vec4db(uint8_t x) {
return Vec4db(to_Vec4qb(x));
}
#endif // VECTORF256_H
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