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2070 lines
70 KiB
C++
2070 lines
70 KiB
C++
/**************************** vectorf256e.h *******************************
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* Author: Agner Fog
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* Date created: 2012-05-30
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* Last modified: 2014-10-22
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* Version: 1.16
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* Project: vector classes
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* Description:
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* Header file defining 256-bit floating point vector classes as interface
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* to intrinsic functions. Emulated for processors without AVX instruction set.
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*
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* The following vector classes are defined here:
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* Vec8f Vector of 8 single precision floating point numbers
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* Vec8fb Vector of 8 Booleans for use with Vec8f
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* Vec4d Vector of 4 double precision floating point numbers
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* Vec4db Vector of 4 Booleans for use with Vec4d
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*
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* For detailed instructions, see VectorClass.pdf
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*
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* (c) Copyright 2012 - 2014 GNU General Public License http://www.gnu.org/licenses
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*****************************************************************************/
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// check combination of header files
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#ifdef VECTORF256_H
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#if VECTORF256_H != 1
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#error Two different versions of vectorf256.h included
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#endif
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#else
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#define VECTORF256_H 1
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#if defined (VECTORI256_H) && VECTORI256_H >= 2
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#error wrong combination of header files. Use vectorf256.h instead of vectorf256e.h if you have AVX2
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#endif
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#include "vectorf128.h" // Define 128-bit vectors
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/*****************************************************************************
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*
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* base class Vec256fe and Vec256de
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*
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*****************************************************************************/
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// base class to replace __m256 when AVX is not supported
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class Vec256fe {
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protected:
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__m128 y0; // low half
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__m128 y1; // high half
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public:
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Vec256fe(void) {}; // default constructor
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Vec256fe(__m128 x0, __m128 x1) { // constructor to build from two __m128
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y0 = x0; y1 = x1;
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}
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__m128 get_low() const { // get low half
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return y0;
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}
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__m128 get_high() const { // get high half
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return y1;
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}
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};
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// base class to replace __m256d when AVX is not supported
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class Vec256de {
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public:
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Vec256de() {}; // default constructor
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Vec256de(__m128d x0, __m128d x1) { // constructor to build from two __m128d
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y0 = x0; y1 = x1;
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}
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__m128d get_low() const { // get low half
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return y0;
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}
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__m128d get_high() const { // get high half
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return y1;
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}
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protected:
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__m128d y0; // low half
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__m128d y1; // high half
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};
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/*****************************************************************************
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*
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* select functions
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*
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*****************************************************************************/
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// Select between two Vec256fe sources, element by element. Used in various functions
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// and operators. Corresponds to this pseudocode:
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// for (int i = 0; i < 8; i++) result[i] = s[i] ? a[i] : b[i];
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// Each element in s must be either 0 (false) or 0xFFFFFFFF (true).
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static inline Vec256fe selectf (Vec256fe const & s, Vec256fe const & a, Vec256fe const & b) {
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return Vec256fe(selectf(b.get_low(), a.get_low(), s.get_low()), selectf(b.get_high(), a.get_high(), s.get_high()));
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}
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// Same, with two Vec256de sources.
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// and operators. Corresponds to this pseudocode:
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// for (int i = 0; i < 4; i++) result[i] = s[i] ? a[i] : b[i];
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// Each element in s must be either 0 (false) or 0xFFFFFFFFFFFFFFFF (true). No other
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// values are allowed.
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static inline Vec256de selectd (Vec256de const & s, Vec256de const & a, Vec256de const & b) {
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return Vec256de(selectd(b.get_low(), a.get_low(), s.get_low()), selectd(b.get_high(), a.get_high(), s.get_high()));
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}
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/*****************************************************************************
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*
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* Generate compile-time constant vector
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*
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*****************************************************************************/
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// Generate a constant vector of 8 integers stored in memory,
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// load as __m256
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template <int i0, int i1, int i2, int i3, int i4, int i5, int i6, int i7>
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static inline Vec256fe constant8f() {
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static const union {
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int i[8];
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__m128 y[2];
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} u = {{i0,i1,i2,i3,i4,i5,i6,i7}};
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return Vec256fe(u.y[0], u.y[1]);
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}
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/*****************************************************************************
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*
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* Vec8fb: Vector of 8 Booleans for use with Vec8f
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*
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*****************************************************************************/
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class Vec8fb : public Vec256fe {
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public:
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// Default constructor:
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Vec8fb() {
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}
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// Constructor to build from all elements:
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Vec8fb(bool b0, bool b1, bool b2, bool b3, bool b4, bool b5, bool b6, bool b7) {
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y0 = Vec4fb(b0, b1, b2, b3);
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y1 = Vec4fb(b4, b5, b6, b7);
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}
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// Constructor to build from two Vec4fb:
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Vec8fb(Vec4fb const & a0, Vec4fb const & a1) {
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y0 = a0; y1 = a1;
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}
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// Constructor to convert from type Vec256fe
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Vec8fb(Vec256fe const & x) {
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y0 = x.get_low(); y1 = x.get_high();
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}
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// Assignment operator to convert from type Vec256fe
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Vec8fb & operator = (Vec256fe const & x) {
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y0 = x.get_low(); y1 = x.get_high();
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return *this;
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}
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#ifdef VECTORI256_H // 256 bit integer vectors are available
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// Constructor to convert from type Vec8ib used as Boolean for integer vectors
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Vec8fb(Vec8ib const & x) {
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y0 = _mm_castsi128_ps(Vec8i(x).get_low());
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y1 = _mm_castsi128_ps(Vec8i(x).get_high());
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}
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// Assignment operator to convert from type Vec8ib used as Boolean for integer vectors
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Vec8fb & operator = (Vec8ib const & x) {
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y0 = _mm_castsi128_ps(Vec8i(x).get_low());
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y1 = _mm_castsi128_ps(Vec8i(x).get_high());
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return *this;
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}
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// Constructor to broadcast the same value into all elements:
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Vec8fb(bool b) {
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y1 = y0 = Vec4fb(b);
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}
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// Assignment operator to broadcast scalar value:
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Vec8fb & operator = (bool b) {
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y0 = y1 = Vec4fb(b);
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return *this;
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}
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private: // Prevent constructing from int, etc.
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Vec8fb(int b);
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Vec8fb & operator = (int x);
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public:
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// Type cast operator to convert to type Vec8ib used as Boolean for integer vectors
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operator Vec8ib() const {
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return Vec8i(_mm_castps_si128(y0), _mm_castps_si128(y1));
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}
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#endif // VECTORI256_H
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// Member function to change a single element in vector
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// Note: This function is inefficient. Use load function if changing more than one element
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Vec8fb const & insert(uint32_t index, bool value) {
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if (index < 4) {
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y0 = Vec4fb(y0).insert(index, value);
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}
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else {
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y1 = Vec4fb(y1).insert(index-4, value);
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}
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return *this;
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}
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// Member function extract a single element from vector
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// Note: This function is inefficient. Use store function if extracting more than one element
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bool extract(uint32_t index) const {
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if (index < 4) {
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return Vec4fb(y0).extract(index);
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}
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else {
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return Vec4fb(y1).extract(index-4);
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}
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}
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// Extract a single element. Operator [] can only read an element, not write.
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bool operator [] (uint32_t index) const {
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return extract(index);
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}
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// Member functions to split into two Vec4fb:
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Vec4fb get_low() const {
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return y0;
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}
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Vec4fb get_high() const {
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return y1;
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}
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static int size () {
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return 8;
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}
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};
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/*****************************************************************************
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*
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* Operators for Vec8fb
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*
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*****************************************************************************/
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// vector operator & : bitwise and
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static inline Vec8fb operator & (Vec8fb const & a, Vec8fb const & b) {
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return Vec8fb(a.get_low() & b.get_low(), a.get_high() & b.get_high());
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}
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static inline Vec8fb operator && (Vec8fb const & a, Vec8fb const & b) {
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return a & b;
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}
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// vector operator &= : bitwise and
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static inline Vec8fb & operator &= (Vec8fb & a, Vec8fb const & b) {
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a = a & b;
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return a;
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}
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// vector operator | : bitwise or
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static inline Vec8fb operator | (Vec8fb const & a, Vec8fb const & b) {
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return Vec8fb(a.get_low() | b.get_low(), a.get_high() | b.get_high());
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}
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static inline Vec8fb operator || (Vec8fb const & a, Vec8fb const & b) {
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return a | b;
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}
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// vector operator |= : bitwise or
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static inline Vec8fb & operator |= (Vec8fb & a, Vec8fb const & b) {
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a = a | b;
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return a;
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}
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// vector operator ^ : bitwise xor
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static inline Vec8fb operator ^ (Vec8fb const & a, Vec8fb const & b) {
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return Vec8fb(a.get_low() ^ b.get_low(), a.get_high() ^ b.get_high());
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}
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// vector operator ^= : bitwise xor
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static inline Vec8fb & operator ^= (Vec8fb & a, Vec8fb const & b) {
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a = a ^ b;
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return a;
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}
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// vector operator ~ : bitwise not
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static inline Vec8fb operator ~ (Vec8fb const & a) {
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return Vec8fb(~a.get_low(), ~a.get_high());
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}
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// vector operator ! : logical not
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// (operator ! is less efficient than operator ~. Use only where not
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// all bits in an element are the same)
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static inline Vec8fb operator ! (Vec8fb const & a) {
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return Vec8fb(!a.get_low(), !a.get_high());
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}
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// Functions for Vec8fb
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// andnot: a & ~ b
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static inline Vec8fb andnot(Vec8fb const & a, Vec8fb const & b) {
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return Vec8fb(andnot(a.get_low(), b.get_low()), andnot(a.get_high(), b.get_high()));
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}
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/*****************************************************************************
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*
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* Horizontal Boolean functions
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*
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*****************************************************************************/
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// horizontal_and. Returns true if all bits are 1
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static inline bool horizontal_and (Vec8fb const & a) {
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return horizontal_and(a.get_low() & a.get_high());
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}
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// horizontal_or. Returns true if at least one bit is 1
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static inline bool horizontal_or (Vec8fb const & a) {
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return horizontal_or(a.get_low() | a.get_high());
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}
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/*****************************************************************************
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*
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* Vec4db: Vector of 4 Booleans for use with Vec4d
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*
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*****************************************************************************/
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class Vec4db : public Vec256de {
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public:
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// Default constructor:
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Vec4db() {
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}
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// Constructor to build from all elements:
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Vec4db(bool b0, bool b1, bool b2, bool b3) {
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y0 = Vec2db(b0, b1);
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y1 = Vec2db(b2, b3);
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}
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// Constructor to build from two Vec2db:
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Vec4db(Vec2db const & a0, Vec2db const & a1) {
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y0 = a0; y1 = a1;
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}
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// Constructor to convert from type Vec256de
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Vec4db(Vec256de const & x) {
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y0 = x.get_low(); y1 = x.get_high();
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}
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// Assignment operator to convert from type Vec256de
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Vec4db & operator = (Vec256de const & x) {
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y0 = x.get_low(); y1 = x.get_high();
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return *this;
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}
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#ifdef VECTORI256_H // 256 bit integer vectors are available
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// Constructor to convert from type Vec4qb used as Boolean for integer vectors
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Vec4db(Vec4qb const & x) {
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y0 = _mm_castsi128_pd(Vec4q(x).get_low());
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y1 = _mm_castsi128_pd(Vec4q(x).get_high());
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}
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// Assignment operator to convert from type Vec4qb used as Boolean for integer vectors
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Vec4db & operator = (Vec4qb const & x) {
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y0 = _mm_castsi128_pd(Vec4q(x).get_low());
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y1 = _mm_castsi128_pd(Vec4q(x).get_high());
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return *this;
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}
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// Constructor to broadcast the same value into all elements:
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Vec4db(bool b) {
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y1 = y0 = Vec2db(b);
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}
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// Assignment operator to broadcast scalar value:
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Vec4db & operator = (bool b) {
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y0 = y1 = Vec2db(b);
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return *this;
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}
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private: // Prevent constructing from int, etc.
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Vec4db(int b);
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Vec4db & operator = (int x);
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public:
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// Type cast operator to convert to type Vec4qb used as Boolean for integer vectors
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operator Vec4qb() const {
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return Vec4q(_mm_castpd_si128(y0), _mm_castpd_si128(y1));
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}
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#endif // VECTORI256_H
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// Member function to change a single element in vector
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// Note: This function is inefficient. Use load function if changing more than one element
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Vec4db const & insert(uint32_t index, bool value) {
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if (index < 2) {
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y0 = Vec2db(y0).insert(index, value);
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}
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else {
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y1 = Vec2db(y1).insert(index - 2, value);
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}
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return *this;
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}
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// Member function extract a single element from vector
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// Note: This function is inefficient. Use store function if extracting more than one element
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bool extract(uint32_t index) const {
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if (index < 2) {
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return Vec2db(y0).extract(index);
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}
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else {
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return Vec2db(y1).extract(index - 2);
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}
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}
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// Extract a single element. Operator [] can only read an element, not write.
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bool operator [] (uint32_t index) const {
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return extract(index);
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}
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// Member functions to split into two Vec4fb:
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Vec2db get_low() const {
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return y0;
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}
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Vec2db get_high() const {
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return y1;
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}
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static int size () {
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return 4;
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}
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};
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/*****************************************************************************
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*
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* Operators for Vec4db
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*
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*****************************************************************************/
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// vector operator & : bitwise and
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static inline Vec4db operator & (Vec4db const & a, Vec4db const & b) {
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return Vec4db(a.get_low() & b.get_low(), a.get_high() & b.get_high());
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}
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static inline Vec4db operator && (Vec4db const & a, Vec4db const & b) {
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return a & b;
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}
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// vector operator &= : bitwise and
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static inline Vec4db & operator &= (Vec4db & a, Vec4db const & b) {
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a = a & b;
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return a;
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}
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// vector operator | : bitwise or
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static inline Vec4db operator | (Vec4db const & a, Vec4db const & b) {
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return Vec4db(a.get_low() | b.get_low(), a.get_high() | b.get_high());
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}
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static inline Vec4db operator || (Vec4db const & a, Vec4db const & b) {
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return a | b;
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}
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// vector operator |= : bitwise or
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static inline Vec4db & operator |= (Vec4db & a, Vec4db const & b) {
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a = a | b;
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return a;
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}
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// vector operator ^ : bitwise xor
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static inline Vec4db operator ^ (Vec4db const & a, Vec4db const & b) {
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return Vec4db(a.get_low() ^ b.get_low(), a.get_high() ^ b.get_high());
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}
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// vector operator ^= : bitwise xor
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static inline Vec4db & operator ^= (Vec4db & a, Vec4db const & b) {
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a = a ^ b;
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return a;
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}
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// vector operator ~ : bitwise not
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static inline Vec4db operator ~ (Vec4db const & a) {
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return Vec4db(~a.get_low(), ~a.get_high());
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}
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// vector operator ! : logical not
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// (operator ! is less efficient than operator ~. Use only where not
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// all bits in an element are the same)
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static inline Vec4db operator ! (Vec4db const & a) {
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return Vec4db(!a.get_low(), !a.get_high());
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}
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// Functions for Vec4db
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// andnot: a & ~ b
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static inline Vec4db andnot(Vec4db const & a, Vec4db const & b) {
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return Vec4db(andnot(a.get_low(), b.get_low()), andnot(a.get_high(), b.get_high()));
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}
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/*****************************************************************************
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*
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* Horizontal Boolean functions
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*
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*****************************************************************************/
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// horizontal_and. Returns true if all bits are 1
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static inline bool horizontal_and (Vec4db const & a) {
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return horizontal_and(a.get_low() & a.get_high());
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}
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// horizontal_or. Returns true if at least one bit is 1
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static inline bool horizontal_or (Vec4db const & a) {
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return horizontal_or(a.get_low() | a.get_high());
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}
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/*****************************************************************************
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*
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* Vec8f: Vector of 8 single precision floating point values
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*
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*****************************************************************************/
|
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|
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class Vec8f : public Vec256fe {
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public:
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// Default constructor:
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Vec8f() {
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}
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// Constructor to broadcast the same value into all elements:
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Vec8f(float f) {
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y1 = y0 = _mm_set1_ps(f);
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}
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// Constructor to build from all elements:
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Vec8f(float f0, float f1, float f2, float f3, float f4, float f5, float f6, float f7) {
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y0 = _mm_setr_ps(f0, f1, f2, f3);
|
|
y1 = _mm_setr_ps(f4, f5, f6, f7);
|
|
}
|
|
// Constructor to build from two Vec4f:
|
|
Vec8f(Vec4f const & a0, Vec4f const & a1) {
|
|
y0 = a0; y1 = a1;
|
|
}
|
|
// Constructor to convert from type Vec256fe
|
|
Vec8f(Vec256fe const & x) {
|
|
y0 = x.get_low(); y1 = x.get_high();
|
|
}
|
|
// Assignment operator to convert from type Vec256fe
|
|
Vec8f & operator = (Vec256fe const & x) {
|
|
y0 = x.get_low(); y1 = x.get_high();
|
|
return *this;
|
|
}
|
|
// Member function to load from array (unaligned)
|
|
Vec8f & load(float const * p) {
|
|
y0 = _mm_loadu_ps(p);
|
|
y1 = _mm_loadu_ps(p+4);
|
|
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) {
|
|
y0 = _mm_load_ps(p);
|
|
y1 = _mm_load_ps(p+4);
|
|
return *this;
|
|
}
|
|
// Member function to store into array (unaligned)
|
|
void store(float * p) const {
|
|
_mm_storeu_ps(p, y0);
|
|
_mm_storeu_ps(p+4, y1);
|
|
}
|
|
// 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 {
|
|
_mm_store_ps(p, y0);
|
|
_mm_store_ps(p+4, y1);
|
|
}
|
|
// 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());
|
|
}
|
|
else if (n > 4 && n <= 8) {
|
|
*this = Vec8f(Vec4f().load(p), Vec4f().load_partial(n - 4, p + 4));
|
|
}
|
|
else {
|
|
y1 = y0 = _mm_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;
|
|
else if (n >= 4) {
|
|
y1 = Vec4f(y1).cutoff(n - 4);
|
|
}
|
|
else {
|
|
y0 = Vec4f(y0).cutoff(n);
|
|
y1 = Vec4f(0.0f);
|
|
}
|
|
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) {
|
|
if (index < 4) {
|
|
y0 = Vec4f(y0).insert(index, value);
|
|
}
|
|
else {
|
|
y1 = Vec4f(y1).insert(index - 4, value);
|
|
}
|
|
return *this;
|
|
}
|
|
// Member function extract a single element from vector
|
|
// Note: This function is inefficient. Use store function if extracting more than one element
|
|
float extract(uint32_t index) const {
|
|
if (index < 4) {
|
|
return Vec4f(y0).extract(index);
|
|
}
|
|
else {
|
|
return Vec4f(y1).extract(index - 4);
|
|
}
|
|
}
|
|
// 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 y0;
|
|
}
|
|
Vec4f get_high() const {
|
|
return y1;
|
|
}
|
|
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 Vec8f(a.get_low() + b.get_low(), a.get_high() + b.get_high());
|
|
}
|
|
|
|
// 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 Vec8f(a.get_low() - b.get_low(), a.get_high() - b.get_high());
|
|
}
|
|
|
|
// 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 Vec8f(-a.get_low(), -a.get_high());
|
|
}
|
|
|
|
// 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 Vec8f(a.get_low() * b.get_low(), a.get_high() * b.get_high());
|
|
}
|
|
|
|
// 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 Vec8f(a.get_low() / b.get_low(), a.get_high() / b.get_high());
|
|
}
|
|
|
|
// 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 Vec8fb(a.get_low() == b.get_low(), a.get_high() == b.get_high());
|
|
}
|
|
|
|
// vector operator != : returns true for elements for which a != b
|
|
static inline Vec8fb operator != (Vec8f const & a, Vec8f const & b) {
|
|
return Vec8fb(a.get_low() != b.get_low(), a.get_high() != b.get_high());
|
|
}
|
|
|
|
// vector operator < : returns true for elements for which a < b
|
|
static inline Vec8fb operator < (Vec8f const & a, Vec8f const & b) {
|
|
return Vec8fb(a.get_low() < b.get_low(), a.get_high() < b.get_high());
|
|
}
|
|
|
|
// vector operator <= : returns true for elements for which a <= b
|
|
static inline Vec8fb operator <= (Vec8f const & a, Vec8f const & b) {
|
|
return Vec8fb(a.get_low() <= b.get_low(), a.get_high() <= b.get_high());
|
|
}
|
|
|
|
// vector operator > : returns true for elements for which a > b
|
|
static inline Vec8fb operator > (Vec8f const & a, Vec8f const & b) {
|
|
return Vec8fb(a.get_low() > b.get_low(), a.get_high() > b.get_high());
|
|
}
|
|
|
|
// vector operator >= : returns true for elements for which a >= b
|
|
static inline Vec8fb operator >= (Vec8f const & a, Vec8f const & b) {
|
|
return Vec8fb(a.get_low() >= b.get_low(), a.get_high() >= b.get_high());
|
|
}
|
|
|
|
// Bitwise logical operators
|
|
|
|
// vector operator & : bitwise and
|
|
static inline Vec8f operator & (Vec8f const & a, Vec8f const & b) {
|
|
return Vec8f(a.get_low() & b.get_low(), a.get_high() & b.get_high());
|
|
}
|
|
|
|
// 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 Vec8f(a.get_low() & b.get_low(), a.get_high() & b.get_high());
|
|
}
|
|
static inline Vec8f operator & (Vec8fb const & a, Vec8f const & b) {
|
|
return Vec8f(a.get_low() & b.get_low(), a.get_high() & b.get_high());
|
|
}
|
|
|
|
// vector operator | : bitwise or
|
|
static inline Vec8f operator | (Vec8f const & a, Vec8f const & b) {
|
|
return Vec8f(a.get_low() | b.get_low(), a.get_high() | b.get_high());
|
|
}
|
|
|
|
// 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 Vec8f(a.get_low() ^ b.get_low(), a.get_high() ^ b.get_high());
|
|
}
|
|
|
|
// 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 Vec8fb(!a.get_low(), !a.get_high());
|
|
}
|
|
|
|
|
|
/*****************************************************************************
|
|
*
|
|
* 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 Vec8f(select(s.get_low(),a.get_low(),b.get_low()), select(s.get_high(),a.get_high(),b.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return horizontal_add(a.get_low() + a.get_high());
|
|
}
|
|
|
|
// function max: a > b ? a : b
|
|
static inline Vec8f max(Vec8f const & a, Vec8f const & b) {
|
|
return Vec8f(max(a.get_low(),b.get_low()), max(a.get_high(),b.get_high()));
|
|
}
|
|
|
|
// function min: a < b ? a : b
|
|
static inline Vec8f min(Vec8f const & a, Vec8f const & b) {
|
|
return Vec8f(min(a.get_low(),b.get_low()), min(a.get_high(),b.get_high()));
|
|
}
|
|
|
|
// function abs: absolute value
|
|
// Removes sign bit, even for -0.0f, -INF and -NAN
|
|
static inline Vec8f abs(Vec8f const & a) {
|
|
return Vec8f(abs(a.get_low()), abs(a.get_high()));
|
|
}
|
|
|
|
// function sqrt: square root
|
|
static inline Vec8f sqrt(Vec8f const & a) {
|
|
return Vec8f(sqrt(a.get_low()), sqrt(a.get_high()));
|
|
}
|
|
|
|
// function square: a * a
|
|
static inline Vec8f square(Vec8f const & a) {
|
|
return Vec8f(square(a.get_low()), square(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec8f(pow_n<n>(a.get_low()), pow_n<n>(a.get_high()));
|
|
}
|
|
|
|
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 Vec8f(round(a.get_low()), round(a.get_high()));
|
|
}
|
|
|
|
// function truncate: round towards zero. (result as float vector)
|
|
static inline Vec8f truncate(Vec8f const & a) {
|
|
return Vec8f(truncate(a.get_low()), truncate(a.get_high()));
|
|
}
|
|
|
|
// function floor: round towards minus infinity. (result as float vector)
|
|
static inline Vec8f floor(Vec8f const & a) {
|
|
return Vec8f(floor(a.get_low()), floor(a.get_high()));
|
|
}
|
|
|
|
// function ceil: round towards plus infinity. (result as float vector)
|
|
static inline Vec8f ceil(Vec8f const & a) {
|
|
return Vec8f(ceil(a.get_low()), ceil(a.get_high()));
|
|
}
|
|
|
|
#ifdef VECTORI256_H // 256 bit integer vectors are available
|
|
// 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(round_to_int(a.get_low()), round_to_int(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(truncate_to_int(a.get_low()), truncate_to_int(a.get_high()));
|
|
}
|
|
|
|
// function to_float: convert integer vector to float vector
|
|
static inline Vec8f to_float(Vec8i const & a) {
|
|
return Vec8f(to_float(a.get_low()), to_float(a.get_high()));
|
|
}
|
|
#endif // VECTORI256_H
|
|
|
|
|
|
// 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 Vec8f(approx_recipr(a.get_low()), approx_recipr(a.get_high()));
|
|
}
|
|
|
|
// approximate reciprocal squareroot (Faster than 1.f / sqrt(a). Relative accuracy better than 2^-11)
|
|
static inline Vec8f approx_rsqrt(Vec8f const & a) {
|
|
return Vec8f(approx_rsqrt(a.get_low()), approx_rsqrt(a.get_high()));
|
|
}
|
|
|
|
// Fused multiply and add functions
|
|
|
|
// Multiply and add
|
|
static inline Vec8f mul_add(Vec8f const & a, Vec8f const & b, Vec8f const & c) {
|
|
return Vec8f(mul_add(a.get_low(),b.get_low(),c.get_low()), mul_add(a.get_high(),b.get_high(),c.get_high()));
|
|
}
|
|
|
|
// Multiply and subtract
|
|
static inline Vec8f mul_sub(Vec8f const & a, Vec8f const & b, Vec8f const & c) {
|
|
return Vec8f(mul_sub(a.get_low(),b.get_low(),c.get_low()), mul_sub(a.get_high(),b.get_high(),c.get_high()));
|
|
}
|
|
|
|
// Multiply and inverse subtract
|
|
static inline Vec8f nmul_add(Vec8f const & a, Vec8f const & b, Vec8f const & c) {
|
|
return Vec8f(nmul_add(a.get_low(),b.get_low(),c.get_low()), nmul_add(a.get_high(),b.get_high(),c.get_high()));
|
|
}
|
|
|
|
|
|
// 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) {
|
|
return Vec8f(mul_sub_x(a.get_low(),b.get_low(),c.get_low()), mul_sub_x(a.get_high(),b.get_high(),c.get_high()));
|
|
}
|
|
|
|
|
|
// 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(1.0f) = 0, exponent(0.0f) = -127, exponent(INF) = +128, exponent(NAN) = +128
|
|
static inline Vec8i exponent(Vec8f const & a) {
|
|
return Vec8i(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(1.0f) = 1.0f, fraction(5.0f) = 1.25f
|
|
static inline Vec8f fraction(Vec8f const & a) {
|
|
return Vec8f(fraction(a.get_low()), fraction(a.get_high()));
|
|
}
|
|
|
|
#ifdef VECTORI256_H // 256 bit integer vectors are available
|
|
// 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 & a) {
|
|
return Vec8f(exp2(a.get_low()), exp2(a.get_high()));
|
|
}
|
|
//static 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) {
|
|
return Vec8fb(sign_bit(a.get_low()), sign_bit(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec8f(sign_combine(a.get_low(), b.get_low()), sign_combine(a.get_high(), b.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec8fb(is_finite(a.get_low()), is_finite(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec8fb(is_inf(a.get_low()), is_inf(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec8fb(is_nan(a.get_low()), is_nan(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec8fb(is_subnormal(a.get_low()), is_subnormal(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec8fb(is_zero_or_subnormal(a.get_low()), is_zero_or_subnormal(a.get_high()));
|
|
}
|
|
|
|
// 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 Vec8f(nan4f(n), nan4f(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;
|
|
Vec4f lo = change_sign<i0,i1,i2,i3>(a.get_low());
|
|
Vec4f hi = change_sign<i4,i5,i6,i7>(a.get_high());
|
|
return Vec8f(lo, hi);
|
|
}
|
|
|
|
|
|
/*****************************************************************************
|
|
*
|
|
* Vec2d: Vector of 2 double precision floating point values
|
|
*
|
|
*****************************************************************************/
|
|
|
|
class Vec4d : public Vec256de {
|
|
public:
|
|
// Default constructor:
|
|
Vec4d() {
|
|
}
|
|
// Constructor to broadcast the same value into all elements:
|
|
Vec4d(double d) {
|
|
y1 = y0 = _mm_set1_pd(d);
|
|
}
|
|
// Constructor to build from all elements:
|
|
Vec4d(double d0, double d1, double d2, double d3) {
|
|
y0 = _mm_setr_pd(d0, d1);
|
|
y1 = _mm_setr_pd(d2, d3);
|
|
}
|
|
// Constructor to build from two Vec4f:
|
|
Vec4d(Vec2d const & a0, Vec2d const & a1) {
|
|
y0 = a0; y1 = a1;
|
|
}
|
|
// Constructor to convert from type Vec256de
|
|
Vec4d(Vec256de const & x) {
|
|
y0 = x.get_low();
|
|
y1 = x.get_high();
|
|
}
|
|
// Assignment operator to convert from type Vec256de
|
|
Vec4d & operator = (Vec256de const & x) {
|
|
y0 = x.get_low();
|
|
y1 = x.get_high();
|
|
return *this;
|
|
}
|
|
// Member function to load from array (unaligned)
|
|
Vec4d & load(double const * p) {
|
|
y0 = _mm_loadu_pd(p);
|
|
y1 = _mm_loadu_pd(p+2);
|
|
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) {
|
|
y0 = _mm_load_pd(p);
|
|
y1 = _mm_load_pd(p+2);
|
|
return *this;
|
|
}
|
|
// Member function to store into array (unaligned)
|
|
void store(double * p) const {
|
|
_mm_storeu_pd(p, y0);
|
|
_mm_storeu_pd(p+2, y1);
|
|
}
|
|
// 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 {
|
|
_mm_store_pd(p, y0);
|
|
_mm_store_pd(p+2, y1);
|
|
}
|
|
// 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 {
|
|
y1 = y0 = _mm_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);
|
|
}
|
|
}
|
|
Vec4d & cutoff(int n) {
|
|
if (uint32_t(n) >= 4) return *this;
|
|
else if (n >= 2) {
|
|
y1 = Vec2d(y1).cutoff(n - 2);
|
|
}
|
|
else {
|
|
y0 = Vec2d(y0).cutoff(n);
|
|
y1 = Vec2d(0.0);
|
|
}
|
|
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) {
|
|
if (index < 2) {
|
|
y0 = Vec2d(y0).insert(index, value);
|
|
}
|
|
else {
|
|
y1 = Vec2d(y1).insert(index-2, value);
|
|
}
|
|
return *this;
|
|
}
|
|
// Member function extract a single element from vector
|
|
// Note: This function is inefficient. Use store function if extracting more than one element
|
|
double extract(uint32_t index) const {
|
|
if (index < 2) {
|
|
return Vec2d(y0).extract(index);
|
|
}
|
|
else {
|
|
return Vec2d(y1).extract(index-2);
|
|
}
|
|
}
|
|
// 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 y0;
|
|
}
|
|
Vec2d get_high() const {
|
|
return y1;
|
|
}
|
|
static int size () {
|
|
return 2;
|
|
}
|
|
};
|
|
|
|
|
|
|
|
/*****************************************************************************
|
|
*
|
|
* Operators for Vec4d
|
|
*
|
|
*****************************************************************************/
|
|
|
|
// vector operator + : add element by element
|
|
static inline Vec4d operator + (Vec4d const & a, Vec4d const & b) {
|
|
return Vec4d(a.get_low() + b.get_low(), a.get_high() + b.get_high());
|
|
}
|
|
|
|
// 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 Vec4d(a.get_low() - b.get_low(), a.get_high() - b.get_high());
|
|
}
|
|
|
|
// 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 Vec4d(-a.get_low(), -a.get_high());
|
|
}
|
|
|
|
// 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 Vec4d(a.get_low() * b.get_low(), a.get_high() * b.get_high());
|
|
}
|
|
|
|
// 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 Vec4d(a.get_low() / b.get_low(), a.get_high() / b.get_high());
|
|
}
|
|
|
|
// 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 Vec4db(a.get_low() == b.get_low(), a.get_high() == b.get_high());
|
|
}
|
|
|
|
// vector operator != : returns true for elements for which a != b
|
|
static inline Vec4db operator != (Vec4d const & a, Vec4d const & b) {
|
|
return Vec4db(a.get_low() != b.get_low(), a.get_high() != b.get_high());
|
|
}
|
|
|
|
// vector operator < : returns true for elements for which a < b
|
|
static inline Vec4db operator < (Vec4d const & a, Vec4d const & b) {
|
|
return Vec4db(a.get_low() < b.get_low(), a.get_high() < b.get_high());
|
|
}
|
|
|
|
// vector operator <= : returns true for elements for which a <= b
|
|
static inline Vec4db operator <= (Vec4d const & a, Vec4d const & b) {
|
|
return Vec4db(a.get_low() <= b.get_low(), a.get_high() <= b.get_high());
|
|
}
|
|
|
|
// vector operator > : returns true for elements for which a > b
|
|
static inline Vec4db operator > (Vec4d const & a, Vec4d const & b) {
|
|
return Vec4db(a.get_low() > b.get_low(), a.get_high() > b.get_high());
|
|
}
|
|
|
|
// vector operator >= : returns true for elements for which a >= b
|
|
static inline Vec4db operator >= (Vec4d const & a, Vec4d const & b) {
|
|
return Vec4db(a.get_low() >= b.get_low(), a.get_high() >= b.get_high());
|
|
}
|
|
|
|
// Bitwise logical operators
|
|
|
|
// vector operator & : bitwise and
|
|
static inline Vec4d operator & (Vec4d const & a, Vec4d const & b) {
|
|
return Vec4d(a.get_low() & b.get_low(), a.get_high() & b.get_high());
|
|
}
|
|
|
|
// 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 Vec4d(a.get_low() & b.get_low(), a.get_high() & b.get_high());
|
|
}
|
|
static inline Vec4d operator & (Vec4db const & a, Vec4d const & b) {
|
|
return Vec4d(a.get_low() & b.get_low(), a.get_high() & b.get_high());
|
|
}
|
|
|
|
// vector operator | : bitwise or
|
|
static inline Vec4d operator | (Vec4d const & a, Vec4d const & b) {
|
|
return Vec4d(a.get_low() | b.get_low(), a.get_high() | b.get_high());
|
|
}
|
|
|
|
// 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 Vec4d(a.get_low() ^ b.get_low(), a.get_high() ^ b.get_high());
|
|
}
|
|
|
|
// 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 Vec4db(!a.get_low(), !a.get_high());
|
|
}
|
|
|
|
|
|
/*****************************************************************************
|
|
*
|
|
* 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 Vec4d(select(s.get_low(), a.get_low(), b.get_low()), select(s.get_high(), a.get_high(), b.get_high()));
|
|
}
|
|
|
|
// 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.f);
|
|
}
|
|
|
|
// General arithmetic functions, etc.
|
|
|
|
// Horizontal add: Calculates the sum of all vector elements.
|
|
static inline double horizontal_add (Vec4d const & a) {
|
|
return horizontal_add(a.get_low() + a.get_high());
|
|
}
|
|
|
|
// function max: a > b ? a : b
|
|
static inline Vec4d max(Vec4d const & a, Vec4d const & b) {
|
|
return Vec4d(max(a.get_low(),b.get_low()), max(a.get_high(),b.get_high()));
|
|
}
|
|
|
|
// function min: a < b ? a : b
|
|
static inline Vec4d min(Vec4d const & a, Vec4d const & b) {
|
|
return Vec4d(min(a.get_low(),b.get_low()), min(a.get_high(),b.get_high()));
|
|
}
|
|
|
|
// function abs: absolute value
|
|
// Removes sign bit, even for -0.0f, -INF and -NAN
|
|
static inline Vec4d abs(Vec4d const & a) {
|
|
return Vec4d(abs(a.get_low()), abs(a.get_high()));
|
|
}
|
|
|
|
// function sqrt: square root
|
|
static inline Vec4d sqrt(Vec4d const & a) {
|
|
return Vec4d(sqrt(a.get_low()), sqrt(a.get_high()));
|
|
}
|
|
|
|
// function square: a * a
|
|
static inline Vec4d square(Vec4d const & a) {
|
|
return Vec4d(square(a.get_low()), square(a.get_high()));
|
|
}
|
|
|
|
// pow(Vec4d, int):
|
|
// Raise floating point numbers to integer power n
|
|
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) {
|
|
return Vec4d(pow_n<n>(a.get_low()), pow_n<n>(a.get_high()));
|
|
}
|
|
|
|
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 Vec4d(round(a.get_low()), round(a.get_high()));
|
|
}
|
|
|
|
// function truncate: round towards zero. (result as double vector)
|
|
static inline Vec4d truncate(Vec4d const & a) {
|
|
return Vec4d(truncate(a.get_low()), truncate(a.get_high()));
|
|
}
|
|
|
|
// function floor: round towards minus infinity. (result as double vector)
|
|
static inline Vec4d floor(Vec4d const & a) {
|
|
return Vec4d(floor(a.get_low()), floor(a.get_high()));
|
|
}
|
|
|
|
// function ceil: round towards plus infinity. (result as double vector)
|
|
static inline Vec4d ceil(Vec4d const & a) {
|
|
return Vec4d(ceil(a.get_low()), ceil(a.get_high()));
|
|
}
|
|
|
|
// 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 round_to_int(a.get_low(), a.get_high());
|
|
}
|
|
|
|
// function truncate_to_int: round towards zero. (result as integer vector)
|
|
static inline Vec4i truncate_to_int(Vec4d const & a) {
|
|
return truncate_to_int(a.get_low(), a.get_high());
|
|
}
|
|
|
|
#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) {
|
|
return Vec4q(truncate_to_int64_limited(a.get_low()), truncate_to_int64_limited(a.get_high()));
|
|
}
|
|
|
|
// 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
|
|
// result as 64-bit integer vector, but with limited range
|
|
static inline Vec4q round_to_int64_limited(Vec4d const & a) {
|
|
return Vec4q(round_to_int64_limited(a.get_low()), round_to_int64_limited(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec4d(to_double_limited(x.get_low()),to_double_limited(x.get_high()));
|
|
}
|
|
|
|
#endif // VECTORI256_H
|
|
|
|
// function to_double: convert integer vector to double vector
|
|
static inline Vec4d to_double(Vec4i const & a) {
|
|
return Vec4d(to_double_low(a), to_double_high(a));
|
|
}
|
|
|
|
// function compress: convert two Vec4d to one Vec8f
|
|
static inline Vec8f compress (Vec4d const & low, Vec4d const & high) {
|
|
return Vec8f(compress(low.get_low(), low.get_high()), compress(high.get_low(), high.get_high()));
|
|
}
|
|
|
|
// Function extend_low : convert Vec8f vector elements 0 - 3 to Vec4d
|
|
static inline Vec4d extend_low (Vec8f const & a) {
|
|
return Vec4d(extend_low(a.get_low()), extend_high(a.get_low()));
|
|
}
|
|
|
|
// Function extend_high : convert Vec8f vector elements 4 - 7 to Vec4d
|
|
static inline Vec4d extend_high (Vec8f const & a) {
|
|
return Vec4d(extend_low(a.get_high()), extend_high(a.get_high()));
|
|
}
|
|
|
|
|
|
// Fused multiply and add functions
|
|
|
|
// Multiply and add
|
|
static inline Vec4d mul_add(Vec4d const & a, Vec4d const & b, Vec4d const & c) {
|
|
return Vec4d(mul_add(a.get_low(),b.get_low(),c.get_low()), mul_add(a.get_high(),b.get_high(),c.get_high()));
|
|
}
|
|
|
|
// Multiply and subtract
|
|
static inline Vec4d mul_sub(Vec4d const & a, Vec4d const & b, Vec4d const & c) {
|
|
return Vec4d(mul_sub(a.get_low(),b.get_low(),c.get_low()), mul_sub(a.get_high(),b.get_high(),c.get_high()));
|
|
}
|
|
|
|
// Multiply and inverse subtract
|
|
static inline Vec4d nmul_add(Vec4d const & a, Vec4d const & b, Vec4d const & c) {
|
|
return Vec4d(nmul_add(a.get_low(),b.get_low(),c.get_low()), nmul_add(a.get_high(),b.get_high(),c.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec4d(mul_sub_x(a.get_low(),b.get_low(),c.get_low()), mul_sub_x(a.get_high(),b.get_high(),c.get_high()));
|
|
}
|
|
|
|
|
|
// 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(1.0) = 0, exponent(0.0) = -1023, exponent(INF) = +1024, exponent(NAN) = +1024
|
|
static inline Vec4q exponent(Vec4d const & a) {
|
|
return Vec4q(exponent(a.get_low()), exponent(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec4d(fraction(a.get_low()), fraction(a.get_high()));
|
|
}
|
|
|
|
// 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 & a) {
|
|
return Vec4d(exp2(a.get_low()), exp2(a.get_high()));
|
|
}
|
|
//static 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) {
|
|
return Vec4db(sign_bit(a.get_low()), sign_bit(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec4d(sign_combine(a.get_low(), b.get_low()), sign_combine(a.get_high(), b.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec4db(is_finite(a.get_low()), is_finite(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec4db(is_inf(a.get_low()), is_inf(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec4db(is_nan(a.get_low()), is_nan(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec4db(is_subnormal(a.get_low()), is_subnormal(a.get_high()));
|
|
}
|
|
|
|
// 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) {
|
|
return Vec4db(is_zero_or_subnormal(a.get_low()),is_zero_or_subnormal(a.get_high()));
|
|
}
|
|
|
|
// Function infinite2d: returns a vector where all elements are +INF
|
|
static inline Vec4d infinite4d() {
|
|
return Vec4d(infinite2d(), infinite2d());
|
|
}
|
|
|
|
// Function nan2d: returns a vector where all elements are +NAN (quiet)
|
|
static inline Vec4d nan4d(int n = 0x10) {
|
|
return Vec4d(nan2d(n), nan2d(n));
|
|
}
|
|
|
|
// 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;
|
|
Vec2d lo = change_sign<i0,i1>(a.get_low());
|
|
Vec2d hi = change_sign<i2,i3>(a.get_high());
|
|
return Vec4d(lo, hi);
|
|
}
|
|
|
|
|
|
/*****************************************************************************
|
|
*
|
|
* Functions for reinterpretation between vector types
|
|
*
|
|
*****************************************************************************/
|
|
|
|
static inline Vec256ie reinterpret_i (Vec256ie const & x) {
|
|
return x;
|
|
}
|
|
|
|
static inline Vec256ie reinterpret_i (Vec256fe const & x) {
|
|
return Vec256ie(reinterpret_i(x.get_low()), reinterpret_i(x.get_high()));
|
|
}
|
|
|
|
static inline Vec256ie reinterpret_i (Vec256de const & x) {
|
|
return Vec256ie(reinterpret_i(x.get_low()), reinterpret_i(x.get_high()));
|
|
}
|
|
|
|
static inline Vec256fe reinterpret_f (Vec256ie const & x) {
|
|
return Vec256fe(reinterpret_f(x.get_low()), reinterpret_f(x.get_high()));
|
|
}
|
|
|
|
static inline Vec256fe reinterpret_f (Vec256fe const & x) {
|
|
return x;
|
|
}
|
|
|
|
static inline Vec256fe reinterpret_f (Vec256de const & x) {
|
|
return Vec256fe(reinterpret_f(x.get_low()), reinterpret_f(x.get_high()));
|
|
}
|
|
|
|
static inline Vec256de reinterpret_d (Vec256ie const & x) {
|
|
return Vec256de(reinterpret_d(x.get_low()), reinterpret_d(x.get_high()));
|
|
}
|
|
|
|
static inline Vec256de reinterpret_d (Vec256fe const & x) {
|
|
return Vec256de(reinterpret_d(x.get_low()), reinterpret_d(x.get_high()));
|
|
}
|
|
|
|
static inline Vec256de reinterpret_d (Vec256de const & x) {
|
|
return x;
|
|
}
|
|
|
|
|
|
/*****************************************************************************
|
|
*
|
|
* 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)
|
|
*****************************************************************************/
|
|
|
|
// permute vector Vec4d
|
|
template <int i0, int i1, int i2, int i3>
|
|
static inline Vec4d permute4d(Vec4d const & a) {
|
|
return Vec4d(blend2d<i0,i1> (a.get_low(), a.get_high()),
|
|
blend2d<i2,i3> (a.get_low(), a.get_high()));
|
|
}
|
|
|
|
// helper function used below
|
|
template <int n>
|
|
static inline Vec2d select4(Vec4d const & a, Vec4d const & b) {
|
|
switch (n) {
|
|
case 0:
|
|
return a.get_low();
|
|
case 1:
|
|
return a.get_high();
|
|
case 2:
|
|
return b.get_low();
|
|
case 3:
|
|
return b.get_high();
|
|
}
|
|
return _mm_setzero_pd();
|
|
}
|
|
|
|
// blend vectors Vec4d
|
|
template <int i0, int i1, int i2, int i3>
|
|
static inline Vec4d blend4d(Vec4d const & a, Vec4d const & b) {
|
|
const int j0 = i0 >= 0 ? i0/2 : i0;
|
|
const int j1 = i1 >= 0 ? i1/2 : i1;
|
|
const int j2 = i2 >= 0 ? i2/2 : i2;
|
|
const int j3 = i3 >= 0 ? i3/2 : i3;
|
|
Vec2d x0, x1;
|
|
|
|
if (j0 == j1 || i0 < 0 || i1 < 0) { // both from same
|
|
const int k0 = j0 >= 0 ? j0 : j1;
|
|
x0 = permute2d<i0 & -7, i1 & -7> (select4<k0> (a,b));
|
|
}
|
|
else {
|
|
x0 = blend2d<i0 & -7, (i1 & -7) | 2> (select4<j0>(a,b), select4<j1>(a,b));
|
|
}
|
|
if (j2 == j3 || i2 < 0 || i3 < 0) { // both from same
|
|
const int k1 = j2 >= 0 ? j2 : j3;
|
|
x1 = permute2d<i2 & -7, i3 & -7> (select4<k1> (a,b));
|
|
}
|
|
else {
|
|
x1 = blend2d<i2 & -7, (i3 & -7) | 2> (select4<j2>(a,b), select4<j3>(a,b));
|
|
}
|
|
return Vec4d(x0,x1);
|
|
}
|
|
|
|
/*****************************************************************************
|
|
*
|
|
* 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) {
|
|
return Vec8f(blend4f<i0,i1,i2,i3> (a.get_low(), a.get_high()),
|
|
blend4f<i4,i5,i6,i7> (a.get_low(), a.get_high()));
|
|
}
|
|
|
|
// helper function used below
|
|
template <int n>
|
|
static inline Vec4f select4(Vec8f const & a, Vec8f const & b) {
|
|
switch (n) {
|
|
case 0:
|
|
return a.get_low();
|
|
case 1:
|
|
return a.get_high();
|
|
case 2:
|
|
return b.get_low();
|
|
case 3:
|
|
return b.get_high();
|
|
}
|
|
return _mm_setzero_ps();
|
|
}
|
|
|
|
// blend vectors Vec8f
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template <int i0, int i1, int i2, int i3, int i4, int i5, int i6, int i7>
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static inline Vec8f blend8f(Vec8f const & a, Vec8f const & b) {
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const int j0 = i0 >= 0 ? i0/4 : i0;
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const int j1 = i1 >= 0 ? i1/4 : i1;
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const int j2 = i2 >= 0 ? i2/4 : i2;
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const int j3 = i3 >= 0 ? i3/4 : i3;
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const int j4 = i4 >= 0 ? i4/4 : i4;
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const int j5 = i5 >= 0 ? i5/4 : i5;
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const int j6 = i6 >= 0 ? i6/4 : i6;
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const int j7 = i7 >= 0 ? i7/4 : i7;
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Vec4f x0, x1;
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const int r0 = j0 >= 0 ? j0 : j1 >= 0 ? j1 : j2 >= 0 ? j2 : j3;
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const int r1 = j4 >= 0 ? j4 : j5 >= 0 ? j5 : j6 >= 0 ? j6 : j7;
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const int s0 = (j1 >= 0 && j1 != r0) ? j1 : (j2 >= 0 && j2 != r0) ? j2 : j3;
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const int s1 = (j5 >= 0 && j5 != r1) ? j5 : (j6 >= 0 && j6 != r1) ? j6 : j7;
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// Combine all the indexes into a single bitfield, with 4 bits for each
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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;
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// Mask to zero out negative indexes
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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;
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if (r0 < 0) {
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x0 = _mm_setzero_ps();
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}
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else if (((m1 ^ r0*0x4444) & 0xCCCC & mz) == 0) {
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// i0 - i3 all from same source
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x0 = permute4f<i0 & -13, i1 & -13, i2 & -13, i3 & -13> (select4<r0> (a,b));
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}
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else if ((j2 < 0 || j2 == r0 || j2 == s0) && (j3 < 0 || j3 == r0 || j3 == s0)) {
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// i0 - i3 all from two sources
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const int k0 = i0 >= 0 ? i0 & 3 : i0;
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const int k1 = (i1 >= 0 ? i1 & 3 : i1) | (j1 == s0 ? 4 : 0);
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const int k2 = (i2 >= 0 ? i2 & 3 : i2) | (j2 == s0 ? 4 : 0);
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const int k3 = (i3 >= 0 ? i3 & 3 : i3) | (j3 == s0 ? 4 : 0);
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x0 = blend4f<k0,k1,k2,k3> (select4<r0>(a,b), select4<s0>(a,b));
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}
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else {
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// i0 - i3 from three or four different sources
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x0 = blend4f<0,1,6,7> (
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blend4f<i0 & -13, (i1 & -13) | 4, -0x100, -0x100> (select4<j0>(a,b), select4<j1>(a,b)),
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blend4f<-0x100, -0x100, i2 & -13, (i3 & -13) | 4> (select4<j2>(a,b), select4<j3>(a,b)));
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}
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if (r1 < 0) {
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x1 = _mm_setzero_ps();
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}
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else if (((m1 ^ r1*0x44440000u) & 0xCCCC0000 & mz) == 0) {
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// i4 - i7 all from same source
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x1 = permute4f<i4 & -13, i5 & -13, i6 & -13, i7 & -13> (select4<r1> (a,b));
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}
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else if ((j6 < 0 || j6 == r1 || j6 == s1) && (j7 < 0 || j7 == r1 || j7 == s1)) {
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// i4 - i7 all from two sources
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const int k4 = i4 >= 0 ? i4 & 3 : i4;
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const int k5 = (i5 >= 0 ? i5 & 3 : i5) | (j5 == s1 ? 4 : 0);
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const int k6 = (i6 >= 0 ? i6 & 3 : i6) | (j6 == s1 ? 4 : 0);
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const int k7 = (i7 >= 0 ? i7 & 3 : i7) | (j7 == s1 ? 4 : 0);
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x1 = blend4f<k4,k5,k6,k7> (select4<r1>(a,b), select4<s1>(a,b));
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}
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else {
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// i4 - i7 from three or four different sources
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x1 = blend4f<0,1,6,7> (
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blend4f<i4 & -13, (i5 & -13) | 4, -0x100, -0x100> (select4<j4>(a,b), select4<j5>(a,b)),
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blend4f<-0x100, -0x100, i6 & -13, (i7 & -13) | 4> (select4<j6>(a,b), select4<j7>(a,b)));
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}
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return Vec8f(x0,x1);
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}
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/*****************************************************************************
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*
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* Vector lookup functions
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*
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******************************************************************************
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*
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* These functions use vector elements as indexes into a table.
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* The table is given as one or more vectors or as an array.
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*
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* This can be used for several purposes:
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* - table lookup
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* - permute or blend with variable indexes
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* - blend from more than two sources
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* - gather non-contiguous data
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*
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* An index out of range may produce any value - the actual value produced is
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* implementation dependent and may be different for different instruction
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* sets. An index out of range does not produce an error message or exception.
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*
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* Example:
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* Vec4i a(2,0,0,3); // index a is ( 2, 0, 0, 3)
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* Vec4f b(1.0f,1.1f,1.2f,1.3f); // table b is (1.0, 1.1, 1.2, 1.3)
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* Vec4f c;
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* c = lookup4 (a,b); // result c is (1.2, 1.0, 1.0, 1.3)
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*
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*****************************************************************************/
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#ifdef VECTORI256_H // Vec8i and Vec4q must be defined
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static inline Vec8f lookup8(Vec8i const & index, Vec8f const & table) {
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Vec4f r0 = lookup8(index.get_low() , table.get_low(), table.get_high());
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Vec4f r1 = lookup8(index.get_high(), table.get_low(), table.get_high());
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return Vec8f(r0, r1);
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}
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template <int n>
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static inline Vec8f lookup(Vec8i const & index, float const * table) {
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if (n <= 0) return 0;
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if (n <= 4) {
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Vec4f table1 = Vec4f().load(table);
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return Vec8f(
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lookup4 (index.get_low(), table1),
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lookup4 (index.get_high(), table1));
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}
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if (n <= 8) {
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return lookup8(index, Vec8f().load(table));
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}
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// Limit index
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Vec8ui index1;
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if ((n & (n-1)) == 0) {
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// n is a power of 2, make index modulo n
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index1 = Vec8ui(index) & (n-1);
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}
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else {
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// n is not a power of 2, limit to n-1
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index1 = min(Vec8ui(index), n-1);
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}
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return Vec8f(table[index1[0]],table[index1[1]],table[index1[2]],table[index1[3]],
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table[index1[4]],table[index1[5]],table[index1[6]],table[index1[7]]);
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}
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static inline Vec4d lookup4(Vec4q const & index, Vec4d const & table) {
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Vec2d r0 = lookup4(index.get_low() , table.get_low(), table.get_high());
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Vec2d r1 = lookup4(index.get_high(), table.get_low(), table.get_high());
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return Vec4d(r0, r1);
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}
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template <int n>
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static inline Vec4d lookup(Vec4q const & index, double const * table) {
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if (n <= 0) return 0;
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if (n <= 2) {
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Vec2d table1 = Vec2d().load(table);
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return Vec4d(
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lookup2 (index.get_low(), table1),
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lookup2 (index.get_high(), table1));
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}
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// Limit index
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Vec8ui index1;
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if ((n & (n-1)) == 0) {
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// n is a power of 2, make index modulo n
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index1 = Vec8ui(index) & constant8i<n-1, 0, n-1, 0, n-1, 0, n-1, 0>();
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}
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else {
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// n is not a power of 2, limit to n-1
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index1 = min(Vec8ui(index), constant8i<n-1, 0, n-1, 0, n-1, 0, n-1, 0>() );
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}
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Vec4q index2 = Vec4q(index1);
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return Vec4d(table[index2[0]],table[index2[1]],table[index2[2]],table[index2[3]]);
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}
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#endif // VECTORI256_H
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/*****************************************************************************
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*
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* Horizontal scan functions
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*
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*****************************************************************************/
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// Get index to the first element that is true. Return -1 if all are false
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static inline int horizontal_find_first(Vec8fb const & x) {
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return horizontal_find_first(Vec8ib(x));
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}
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static inline int horizontal_find_first(Vec4db const & x) {
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return horizontal_find_first(Vec4qb(x));
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}
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// Count the number of elements that are true
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static inline uint32_t horizontal_count(Vec8fb const & x) {
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return horizontal_count(Vec8ib(x));
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}
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static inline uint32_t horizontal_count(Vec4db const & x) {
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return horizontal_count(Vec4qb(x));
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}
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/*****************************************************************************
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*
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* Boolean <-> bitfield conversion functions
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*
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*****************************************************************************/
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// to_bits: convert boolean vector to integer bitfield
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static inline uint8_t to_bits(Vec8fb const & x) {
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return to_bits(Vec8ib(x));
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}
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// to_Vec8fb: convert integer bitfield to boolean vector
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static inline Vec8fb to_Vec8fb(uint8_t x) {
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return Vec8fb(to_Vec8ib(x));
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}
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// to_bits: convert boolean vector to integer bitfield
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static inline uint8_t to_bits(Vec4db const & x) {
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return to_bits(Vec4qb(x));
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}
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// to_Vec4db: convert integer bitfield to boolean vector
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static inline Vec4db to_Vec4db(uint8_t x) {
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return Vec4db(to_Vec4qb(x));
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}
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#endif // VECTORF256_H
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