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ClickHouse/libs/libvectorclass/vectorf128.h
Andrey Mironov 682bfb46a5 dbms: vectorize math functions. [#METR-13613]
2014-12-02 20:25:10 +03:00

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/**************************** vectorf128.h *******************************
* Author: Agner Fog
* Date created: 2012-05-30
* Last modified: 2014-10-24
* Version: 1.16
* Project: vector classes
* Description:
* Header file defining floating point vector classes as interface to
* intrinsic functions in x86 microprocessors with SSE2 and later instruction
* sets up to AVX.
*
* Instructions:
* Use Gnu, Intel or Microsoft C++ compiler. Compile for the desired
* instruction set, which must be at least SSE2. Specify the supported
* instruction set by a command line define, e.g. __SSE4_1__ if the
* compiler does not automatically do so.
*
* The following vector classes are defined here:
* Vec4f Vector of 4 single precision floating point numbers
* Vec4fb Vector of 4 Booleans for use with Vec4f
* Vec2d Vector of 2 double precision floating point numbers
* Vec2db Vector of 2 Booleans for use with Vec2d
*
* Each vector object is represented internally in the CPU as a 128-bit register.
* This header file defines operators and functions for these vectors.
*
* For example:
* Vec2d a(1.0, 2.0), b(3.0, 4.0), c;
* c = a + b; // now c contains (4.0, 6.0)
*
* For detailed instructions, see VectorClass.pdf
*
* (c) Copyright 2012 - 2014 GNU General Public License http://www.gnu.org/licenses
*****************************************************************************/
#ifndef VECTORF128_H
#define VECTORF128_H
#include "vectori128.h" // Define integer vectors
/*****************************************************************************
*
* select functions
*
*****************************************************************************/
// Select between two __m128 sources, element by element. Used in various functions
// and operators. Corresponds to this pseudocode:
// for (int i = 0; i < 4; i++) result[i] = s[i] ? a[i] : b[i];
// Each element in s must be either 0 (false) or 0xFFFFFFFF (true). No other values are
// allowed. The implementation depends on the instruction set:
// If SSE4.1 is supported then only bit 31 in each dword of s is checked,
// otherwise all bits in s are used.
static inline __m128 selectf (__m128 const & s, __m128 const & a, __m128 const & b) {
#if INSTRSET >= 5 // SSE4.1 supported
return _mm_blendv_ps (b, a, s);
#else
return _mm_or_ps(
_mm_and_ps(s,a),
_mm_andnot_ps(s,b));
#endif
}
// Same, with two __m128d sources.
// and operators. Corresponds to this pseudocode:
// for (int i = 0; i < 2; i++) result[i] = s[i] ? a[i] : b[i];
// Each element in s must be either 0 (false) or 0xFFFFFFFFFFFFFFFF (true). No other
// values are allowed. The implementation depends on the instruction set:
// If SSE4.1 is supported then only bit 63 in each dword of s is checked,
// otherwise all bits in s are used.
static inline __m128d selectd (__m128d const & s, __m128d const & a, __m128d const & b) {
#if INSTRSET >= 5 // SSE4.1 supported
return _mm_blendv_pd (b, a, s);
#else
return _mm_or_pd(
_mm_and_pd(s,a),
_mm_andnot_pd(s,b));
#endif
}
/*****************************************************************************
*
* Vec4fb: Vector of 4 Booleans for use with Vec4f
*
*****************************************************************************/
class Vec4fb {
protected:
__m128 xmm; // Float vector
public:
// Default constructor:
Vec4fb() {
}
// Constructor to build from all elements:
Vec4fb(bool b0, bool b1, bool b2, bool b3) {
xmm = _mm_castsi128_ps(_mm_setr_epi32(-(int)b0, -(int)b1, -(int)b2, -(int)b3));
}
// Constructor to convert from type __m128 used in intrinsics:
Vec4fb(__m128 const & x) {
xmm = x;
}
// Assignment operator to convert from type __m128 used in intrinsics:
Vec4fb & operator = (__m128 const & x) {
xmm = x;
return *this;
}
// Constructor to broadcast scalar value:
Vec4fb(bool b) {
xmm = _mm_castsi128_ps(_mm_set1_epi32(-int32_t(b)));
}
// Assignment operator to broadcast scalar value:
Vec4fb & operator = (bool b) {
*this = Vec4fb(b);
return *this;
}
private: // Prevent constructing from int, etc.
Vec4fb(int b);
Vec4fb & operator = (int x);
public:
// Constructor to convert from type Vec4ib used as Boolean for integer vectors
Vec4fb(Vec4ib const & x) {
xmm = _mm_castsi128_ps(x);
}
// Assignment operator to convert from type Vec4ib used as Boolean for integer vectors
Vec4fb & operator = (Vec4ib const & x) {
xmm = _mm_castsi128_ps(x);
return *this;
}
// Type cast operator to convert to __m128 used in intrinsics
operator __m128() const {
return xmm;
}
#if defined (__clang__) && CLANG_VERSION < 30900 || defined(__apple_build_version__)
#define FIX_CLANG_VECTOR_ALIAS_AMBIGUITY // clang 3.3 - 3.5 has silent conversion between intrinsic vector types.
// I expected this to be fixed in version 3.4 but it still exists!
// http://llvm.org/bugs/show_bug.cgi?id=17164
// Problem: The version number is not consistent across platforms
// The Apple build has different version numbers. Too bad!
// http://llvm.org/bugs/show_bug.cgi?id=12643
#else
// Type cast operator to convert to type Vec4ib used as Boolean for integer vectors
operator Vec4ib() const {
return _mm_castps_si128(xmm);
}
#endif
// Member function to change a single element in vector
// Note: This function is inefficient. Use load function if changing more than one element
Vec4fb const & insert(uint32_t index, bool value) {
static const int32_t maskl[8] = {0,0,0,0,-1,0,0,0};
__m128 mask = _mm_loadu_ps((float const*)(maskl+4-(index & 3))); // mask with FFFFFFFF at index position
if (value) {
xmm = _mm_or_ps(xmm,mask);
}
else {
xmm = _mm_andnot_ps(mask,xmm);
}
return *this;
}
// Member function extract a single element from vector
bool extract(uint32_t index) const {
//return Vec4ib(*this).extract(index);
return Vec4ib(_mm_castps_si128(xmm)).extract(index);
}
// Extract a single element. Operator [] can only read an element, not write.
bool operator [] (uint32_t index) const {
return extract(index);
}
static int size() {
return 4;
}
};
/*****************************************************************************
*
* Operators for Vec4fb
*
*****************************************************************************/
// vector operator & : bitwise and
static inline Vec4fb operator & (Vec4fb const & a, Vec4fb const & b) {
return _mm_and_ps(a, b);
}
static inline Vec4fb operator && (Vec4fb const & a, Vec4fb const & b) {
return a & b;
}
// vector operator &= : bitwise and
static inline Vec4fb & operator &= (Vec4fb & a, Vec4fb const & b) {
a = a & b;
return a;
}
// vector operator | : bitwise or
static inline Vec4fb operator | (Vec4fb const & a, Vec4fb const & b) {
return _mm_or_ps(a, b);
}
static inline Vec4fb operator || (Vec4fb const & a, Vec4fb const & b) {
return a | b;
}
// vector operator |= : bitwise or
static inline Vec4fb & operator |= (Vec4fb & a, Vec4fb const & b) {
a = a | b;
return a;
}
// vector operator ^ : bitwise xor
static inline Vec4fb operator ^ (Vec4fb const & a, Vec4fb const & b) {
return _mm_xor_ps(a, b);
}
// vector operator ^= : bitwise xor
static inline Vec4fb & operator ^= (Vec4fb & a, Vec4fb const & b) {
a = a ^ b;
return a;
}
// vector operator ~ : bitwise not
static inline Vec4fb operator ~ (Vec4fb const & a) {
return _mm_xor_ps(a, _mm_castsi128_ps(_mm_set1_epi32(-1)));
}
// vector operator ! : logical not
// (operator ! is less efficient than operator ~. Use only where not
// all bits in an element are the same)
static inline Vec4fb operator ! (Vec4fb const & a) {
return Vec4fb( ! Vec4ib(a));
}
// Functions for Vec4fb
// andnot: a & ~ b
static inline Vec4fb andnot(Vec4fb const & a, Vec4fb const & b) {
return _mm_andnot_ps(b, a);
}
/*****************************************************************************
*
* Horizontal Boolean functions
*
*****************************************************************************/
// horizontal_and. Returns true if all bits are 1
static inline bool horizontal_and (Vec4fb const & a) {
return horizontal_and(Vec128b(_mm_castps_si128(a)));
}
// horizontal_or. Returns true if at least one bit is 1
static inline bool horizontal_or (Vec4fb const & a) {
return horizontal_or(Vec128b(_mm_castps_si128(a)));
}
/*****************************************************************************
*
* Vec2db: Vector of 2 Booleans for use with Vec2d
*
*****************************************************************************/
class Vec2db {
protected:
__m128d xmm; // Double vector
public:
// Default constructor:
Vec2db() {
}
// Constructor to broadcast the same value into all elements:
// Constructor to build from all elements:
Vec2db(bool b0, bool b1) {
xmm = _mm_castsi128_pd(_mm_setr_epi32(-(int)b0, -(int)b0, -(int)b1, -(int)b1));
}
// Constructor to convert from type __m128d used in intrinsics:
Vec2db(__m128d const & x) {
xmm = x;
}
// Assignment operator to convert from type __m128d used in intrinsics:
Vec2db & operator = (__m128d const & x) {
xmm = x;
return *this;
}
// Constructor to broadcast scalar value:
Vec2db(bool b) {
xmm = _mm_castsi128_pd(_mm_set1_epi32(-int32_t(b)));
}
// Assignment operator to broadcast scalar value:
Vec2db & operator = (bool b) {
*this = Vec2db(b);
return *this;
}
private: // Prevent constructing from int, etc.
Vec2db(int b);
Vec2db & operator = (int x);
public:
// Constructor to convert from type Vec2qb used as Boolean for integer vectors
Vec2db(Vec2qb const & x) {
xmm = _mm_castsi128_pd(x);
}
// Assignment operator to convert from type Vec2qb used as Boolean for integer vectors
Vec2db & operator = (Vec2qb const & x) {
xmm = _mm_castsi128_pd(x);
return *this;
}
// Type cast operator to convert to __m128d used in intrinsics
operator __m128d() const {
return xmm;
}
#ifndef FIX_CLANG_VECTOR_ALIAS_AMBIGUITY
// Type cast operator to convert to type Vec2qb used as Boolean for integer vectors
operator Vec2qb() const {
return _mm_castpd_si128(xmm);
}
#endif
// Member function to change a single element in vector
// Note: This function is inefficient. Use load function if changing more than one element
Vec2db const & insert(uint32_t index, bool value) {
static const int32_t maskl[8] = {0,0,0,0,-1,-1,0,0};
__m128 mask = _mm_loadu_ps((float const*)(maskl+4-(index&1)*2)); // mask with FFFFFFFFFFFFFFFF at index position
if (value) {
xmm = _mm_or_pd(xmm,_mm_castps_pd(mask));
}
else {
xmm = _mm_andnot_pd(_mm_castps_pd(mask),xmm);
}
return *this;
}
// Member function extract a single element from vector
bool extract(uint32_t index) const {
return Vec2qb(*this).extract(index);
}
// Extract a single element. Operator [] can only read an element, not write.
bool operator [] (uint32_t index) const {
return extract(index);
}
static int size() {
return 2;
}
};
/*****************************************************************************
*
* Operators for Vec2db
*
*****************************************************************************/
// vector operator & : bitwise and
static inline Vec2db operator & (Vec2db const & a, Vec2db const & b) {
return _mm_and_pd(a, b);
}
static inline Vec2db operator && (Vec2db const & a, Vec2db const & b) {
return a & b;
}
// vector operator &= : bitwise and
static inline Vec2db & operator &= (Vec2db & a, Vec2db const & b) {
a = a & b;
return a;
}
// vector operator | : bitwise or
static inline Vec2db operator | (Vec2db const & a, Vec2db const & b) {
return _mm_or_pd(a, b);
}
static inline Vec2db operator || (Vec2db const & a, Vec2db const & b) {
return a | b;
}
// vector operator |= : bitwise or
static inline Vec2db & operator |= (Vec2db & a, Vec2db const & b) {
a = a | b;
return a;
}
// vector operator ^ : bitwise xor
static inline Vec2db operator ^ (Vec2db const & a, Vec2db const & b) {
return _mm_xor_pd(a, b);
}
// vector operator ^= : bitwise xor
static inline Vec2db & operator ^= (Vec2db & a, Vec2db const & b) {
a = a ^ b;
return a;
}
// vector operator ~ : bitwise not
static inline Vec2db operator ~ (Vec2db const & a) {
return _mm_xor_pd(a, _mm_castsi128_pd(_mm_set1_epi32(-1)));
}
// vector operator ! : logical not
// (operator ! is less efficient than operator ~. Use only where not
// all bits in an element are the same)
static inline Vec2db operator ! (Vec2db const & a) {
return Vec2db (! Vec2qb(a));
}
// Functions for Vec2db
// andnot: a & ~ b
static inline Vec2db andnot(Vec2db const & a, Vec2db const & b) {
return _mm_andnot_pd(b, a);
}
/*****************************************************************************
*
* Horizontal Boolean functions
*
*****************************************************************************/
// horizontal_and. Returns true if all bits are 1
static inline bool horizontal_and (Vec2db const & a) {
return horizontal_and(Vec128b(_mm_castpd_si128(a)));
}
// horizontal_or. Returns true if at least one bit is 1
static inline bool horizontal_or (Vec2db const & a) {
return horizontal_or(Vec128b(_mm_castpd_si128(a)));
}
/*****************************************************************************
*
* Vec4f: Vector of 4 single precision floating point values
*
*****************************************************************************/
class Vec4f {
protected:
__m128 xmm; // Float vector
public:
// Default constructor:
Vec4f() {
}
// Constructor to broadcast the same value into all elements:
Vec4f(float f) {
xmm = _mm_set1_ps(f);
}
// Constructor to build from all elements:
Vec4f(float f0, float f1, float f2, float f3) {
xmm = _mm_setr_ps(f0, f1, f2, f3);
}
// Constructor to convert from type __m128 used in intrinsics:
Vec4f(__m128 const & x) {
xmm = x;
}
// Assignment operator to convert from type __m128 used in intrinsics:
Vec4f & operator = (__m128 const & x) {
xmm = x;
return *this;
}
// Type cast operator to convert to __m128 used in intrinsics
operator __m128() const {
return xmm;
}
// Member function to load from array (unaligned)
Vec4f & load(float const * p) {
xmm = _mm_loadu_ps(p);
return *this;
}
// Member function to load from array, aligned by 16
// "load_a" is faster than "load" on older Intel processors (Pentium 4, Pentium M, Core 1,
// Merom, Wolfdale) and Atom, but not on other processors from Intel, AMD or VIA.
// You may use load_a instead of load if you are certain that p points to an address
// divisible by 16.
Vec4f & load_a(float const * p) {
xmm = _mm_load_ps(p);
return *this;
}
// Member function to store into array (unaligned)
void store(float * p) const {
_mm_storeu_ps(p, xmm);
}
// Member function to store into array, aligned by 16
// "store_a" is faster than "store" on older Intel processors (Pentium 4, Pentium M, Core 1,
// Merom, Wolfdale) and Atom, but not on other processors from Intel, AMD or VIA.
// You may use store_a instead of store if you are certain that p points to an address
// divisible by 16.
void store_a(float * p) const {
_mm_store_ps(p, xmm);
}
// Partial load. Load n elements and set the rest to 0
Vec4f & load_partial(int n, float const * p) {
__m128 t1, t2;
switch (n) {
case 1:
xmm = _mm_load_ss(p); break;
case 2:
xmm = _mm_castpd_ps(_mm_load_sd((double*)p)); break;
case 3:
t1 = _mm_castpd_ps(_mm_load_sd((double*)p));
t2 = _mm_load_ss(p + 2);
xmm = _mm_movelh_ps(t1, t2); break;
case 4:
load(p); break;
default:
xmm = _mm_setzero_ps();
}
return *this;
}
// Partial store. Store n elements
void store_partial(int n, float * p) const {
__m128 t1;
switch (n) {
case 1:
_mm_store_ss(p, xmm); break;
case 2:
_mm_store_sd((double*)p, _mm_castps_pd(xmm)); break;
case 3:
_mm_store_sd((double*)p, _mm_castps_pd(xmm));
t1 = _mm_movehl_ps(xmm,xmm);
_mm_store_ss(p + 2, t1); break;
case 4:
store(p); break;
default:;
}
}
// cut off vector to n elements. The last 4-n elements are set to zero
Vec4f & cutoff(int n) {
if (uint32_t(n) >= 4) return *this;
static const union {
int32_t i[8];
float f[8];
} mask = {{1,-1,-1,-1,0,0,0,0}};
xmm = _mm_and_ps(xmm, Vec4f().load(mask.f + 4 - n));
return *this;
}
// Member function to change a single element in vector
// Note: This function is inefficient. Use load function if changing more than one element
Vec4f const & insert(uint32_t index, float value) {
#if INSTRSET >= 5 // SSE4.1 supported
switch (index & 3) {
case 0:
xmm = _mm_insert_ps(xmm, _mm_set_ss(value), 0 << 4); break;
case 1:
xmm = _mm_insert_ps(xmm, _mm_set_ss(value), 1 << 4); break;
case 2:
xmm = _mm_insert_ps(xmm, _mm_set_ss(value), 2 << 4); break;
default:
xmm = _mm_insert_ps(xmm, _mm_set_ss(value), 3 << 4); break;
}
#else
static const int32_t maskl[8] = {0,0,0,0,-1,0,0,0};
__m128 broad = _mm_set1_ps(value); // broadcast value into all elements
__m128 mask = _mm_loadu_ps((float const*)(maskl+4-(index & 3))); // mask with FFFFFFFF at index position
xmm = selectf(mask,broad,xmm);
#endif
return *this;
};
// Member function extract a single element from vector
float extract(uint32_t index) const {
float x[4];
store(x);
return x[index & 3];
}
// Extract a single element. Use store function if extracting more than one element.
// Operator [] can only read an element, not write.
float operator [] (uint32_t index) const {
return extract(index);
}
static int size() {
return 4;
}
};
/*****************************************************************************
*
* Operators for Vec4f
*
*****************************************************************************/
// vector operator + : add element by element
static inline Vec4f operator + (Vec4f const & a, Vec4f const & b) {
return _mm_add_ps(a, b);
}
// vector operator + : add vector and scalar
static inline Vec4f operator + (Vec4f const & a, float b) {
return a + Vec4f(b);
}
static inline Vec4f operator + (float a, Vec4f const & b) {
return Vec4f(a) + b;
}
// vector operator += : add
static inline Vec4f & operator += (Vec4f & a, Vec4f const & b) {
a = a + b;
return a;
}
// postfix operator ++
static inline Vec4f operator ++ (Vec4f & a, int) {
Vec4f a0 = a;
a = a + 1.0f;
return a0;
}
// prefix operator ++
static inline Vec4f & operator ++ (Vec4f & a) {
a = a + 1.0f;
return a;
}
// vector operator - : subtract element by element
static inline Vec4f operator - (Vec4f const & a, Vec4f const & b) {
return _mm_sub_ps(a, b);
}
// vector operator - : subtract vector and scalar
static inline Vec4f operator - (Vec4f const & a, float b) {
return a - Vec4f(b);
}
static inline Vec4f operator - (float a, Vec4f const & b) {
return Vec4f(a) - b;
}
// vector operator - : unary minus
// Change sign bit, even for 0, INF and NAN
static inline Vec4f operator - (Vec4f const & a) {
return _mm_xor_ps(a, _mm_castsi128_ps(_mm_set1_epi32(0x80000000)));
}
// vector operator -= : subtract
static inline Vec4f & operator -= (Vec4f & a, Vec4f const & b) {
a = a - b;
return a;
}
// postfix operator --
static inline Vec4f operator -- (Vec4f & a, int) {
Vec4f a0 = a;
a = a - 1.0f;
return a0;
}
// prefix operator --
static inline Vec4f & operator -- (Vec4f & a) {
a = a - 1.0f;
return a;
}
// vector operator * : multiply element by element
static inline Vec4f operator * (Vec4f const & a, Vec4f const & b) {
return _mm_mul_ps(a, b);
}
// vector operator * : multiply vector and scalar
static inline Vec4f operator * (Vec4f const & a, float b) {
return a * Vec4f(b);
}
static inline Vec4f operator * (float a, Vec4f const & b) {
return Vec4f(a) * b;
}
// vector operator *= : multiply
static inline Vec4f & operator *= (Vec4f & a, Vec4f const & b) {
a = a * b;
return a;
}
// vector operator / : divide all elements by same integer
static inline Vec4f operator / (Vec4f const & a, Vec4f const & b) {
return _mm_div_ps(a, b);
}
// vector operator / : divide vector and scalar
static inline Vec4f operator / (Vec4f const & a, float b) {
return a / Vec4f(b);
}
static inline Vec4f operator / (float a, Vec4f const & b) {
return Vec4f(a) / b;
}
// vector operator /= : divide
static inline Vec4f & operator /= (Vec4f & a, Vec4f const & b) {
a = a / b;
return a;
}
// vector operator == : returns true for elements for which a == b
static inline Vec4fb operator == (Vec4f const & a, Vec4f const & b) {
return _mm_cmpeq_ps(a, b);
}
// vector operator != : returns true for elements for which a != b
static inline Vec4fb operator != (Vec4f const & a, Vec4f const & b) {
return _mm_cmpneq_ps(a, b);
}
// vector operator < : returns true for elements for which a < b
static inline Vec4fb operator < (Vec4f const & a, Vec4f const & b) {
return _mm_cmplt_ps(a, b);
}
// vector operator <= : returns true for elements for which a <= b
static inline Vec4fb operator <= (Vec4f const & a, Vec4f const & b) {
return _mm_cmple_ps(a, b);
}
// vector operator > : returns true for elements for which a > b
static inline Vec4fb operator > (Vec4f const & a, Vec4f const & b) {
return b < a;
}
// vector operator >= : returns true for elements for which a >= b
static inline Vec4fb operator >= (Vec4f const & a, Vec4f const & b) {
return b <= a;
}
// Bitwise logical operators
// vector operator & : bitwise and
static inline Vec4f operator & (Vec4f const & a, Vec4f const & b) {
return _mm_and_ps(a, b);
}
// vector operator &= : bitwise and
static inline Vec4f & operator &= (Vec4f & a, Vec4f const & b) {
a = a & b;
return a;
}
// vector operator & : bitwise and of Vec4f and Vec4fb
static inline Vec4f operator & (Vec4f const & a, Vec4fb const & b) {
return _mm_and_ps(a, b);
}
static inline Vec4f operator & (Vec4fb const & a, Vec4f const & b) {
return _mm_and_ps(a, b);
}
// vector operator | : bitwise or
static inline Vec4f operator | (Vec4f const & a, Vec4f const & b) {
return _mm_or_ps(a, b);
}
// vector operator |= : bitwise or
static inline Vec4f & operator |= (Vec4f & a, Vec4f const & b) {
a = a | b;
return a;
}
// vector operator ^ : bitwise xor
static inline Vec4f operator ^ (Vec4f const & a, Vec4f const & b) {
return _mm_xor_ps(a, b);
}
// vector operator ^= : bitwise xor
static inline Vec4f & operator ^= (Vec4f & a, Vec4f const & b) {
a = a ^ b;
return a;
}
// vector operator ! : logical not. Returns Boolean vector
static inline Vec4fb operator ! (Vec4f const & a) {
return a == Vec4f(0.0f);
}
/*****************************************************************************
*
* Functions for Vec4f
*
*****************************************************************************/
// Select between two operands. Corresponds to this pseudocode:
// for (int i = 0; i < 4; 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 Vec4f select (Vec4fb const & s, Vec4f const & a, Vec4f const & b) {
return selectf(s,a,b);
}
// Conditional add: For all vector elements i: result[i] = f[i] ? (a[i] + b[i]) : a[i]
static inline Vec4f if_add (Vec4fb const & f, Vec4f const & a, Vec4f const & b) {
return a + (Vec4f(f) & b);
}
// Conditional multiply: For all vector elements i: result[i] = f[i] ? (a[i] * b[i]) : a[i]
static inline Vec4f if_mul (Vec4fb const & f, Vec4f const & a, Vec4f 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 (Vec4f const & a) {
#if INSTRSET >= 3 // SSE3
__m128 t1 = _mm_hadd_ps(a,a);
__m128 t2 = _mm_hadd_ps(t1,t1);
return _mm_cvtss_f32(t2);
#else
__m128 t1 = _mm_movehl_ps(a,a);
__m128 t2 = _mm_add_ps(a,t1);
__m128 t3 = _mm_shuffle_ps(t2,t2,1);
__m128 t4 = _mm_add_ss(t2,t3);
return _mm_cvtss_f32(t4);
#endif
}
// function max: a > b ? a : b
static inline Vec4f max(Vec4f const & a, Vec4f const & b) {
return _mm_max_ps(a,b);
}
// function min: a < b ? a : b
static inline Vec4f min(Vec4f const & a, Vec4f const & b) {
return _mm_min_ps(a,b);
}
// function abs: absolute value
// Removes sign bit, even for -0.0f, -INF and -NAN
static inline Vec4f abs(Vec4f const & a) {
__m128 mask = _mm_castsi128_ps(_mm_set1_epi32(0x7FFFFFFF));
return _mm_and_ps(a,mask);
}
// function sqrt: square root
static inline Vec4f sqrt(Vec4f const & a) {
return _mm_sqrt_ps(a);
}
// function square: a * a
static inline Vec4f square(Vec4f const & a) {
return a * a;
}
// pow(vector,int) function template
template <typename VTYPE>
static inline VTYPE pow_template_i(VTYPE const & x0, int n) {
VTYPE x = x0; // a^(2^i)
VTYPE y(1.0f); // accumulator
if (n >= 0) { // make sure n is not negative
while (true) { // loop for each bit in n
if (n & 1) y *= x; // multiply if bit = 1
n >>= 1; // get next bit of n
if (n == 0) return y; // finished
x *= x; // x = a^2, a^4, a^8, etc.
}
}
else { // n < 0
return VTYPE(1.0f)/pow_template_i<VTYPE>(x0,-n); // reciprocal
}
}
// pow(Vec4f, int):
// The purpose of this template is to prevent implicit conversion of a float
// exponent to int when calling pow(vector, float) and vectormath_exp.h is
// not included
template <typename TT> static Vec4f pow(Vec4f const & a, TT n);
// Raise floating point numbers to integer power n
template <>
inline Vec4f pow<int>(Vec4f const & x0, int n) {
return pow_template_i<Vec4f>(x0, n);
}
// allow conversion from unsigned int
template <>
inline Vec4f pow<uint32_t>(Vec4f const & x0, uint32_t n) {
return pow_template_i<Vec4f>(x0, (int)n);
}
// Raise floating point numbers to integer power n, where n is a compile-time constant
template <int n>
static inline Vec4f pow_n(Vec4f const & a) {
if (n < 0) return Vec4f(1.0f) / pow_n<-n>(a);
if (n == 0) return Vec4f(1.0f);
if (n >= 256) return pow(a, n);
Vec4f x = a; // a^(2^i)
Vec4f y; // accumulator
const int lowest = n - (n & (n-1));// lowest set bit in n
if (n & 1) y = x;
if (n < 2) return y;
x = x*x; // x^2
if (n & 2) {
if (lowest == 2) y = x; else y *= x;
}
if (n < 4) return y;
x = x*x; // x^4
if (n & 4) {
if (lowest == 4) y = x; else y *= x;
}
if (n < 8) return y;
x = x*x; // x^8
if (n & 8) {
if (lowest == 8) y = x; else y *= x;
}
if (n < 16) return y;
x = x*x; // x^16
if (n & 16) {
if (lowest == 16) y = x; else y *= x;
}
if (n < 32) return y;
x = x*x; // x^32
if (n & 32) {
if (lowest == 32) y = x; else y *= x;
}
if (n < 64) return y;
x = x*x; // x^64
if (n & 64) {
if (lowest == 64) y = x; else y *= x;
}
if (n < 128) return y;
x = x*x; // x^128
if (n & 128) {
if (lowest == 128) y = x; else y *= x;
}
return y;
}
// implement as function pow(vector, const_int)
template <int n>
static inline Vec4f pow(Vec4f const & a, Const_int_t<n>) {
return pow_n<n>(a);
}
// implement the same as macro pow_const(vector, int)
#define pow_const(x,n) pow_n<n>(x)
// avoid unsafe optimization in function round
#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__) && INSTRSET < 5
static inline Vec4f round(Vec4f const & a) __attribute__ ((optimize("-fno-unsafe-math-optimizations")));
#elif defined(__clang__) && INSTRSET < 5
// static inline Vec4f round(Vec4f const & a) __attribute__ ((optnone));
// This doesn't work, but current versions of Clang (3.5) don't optimize away signedmagic, even with -funsafe-math-optimizations
// Add volatile to b if future versions fail
#elif defined (_MSC_VER) || defined(__INTEL_COMPILER) && INSTRSET < 5
#pragma float_control(push)
#pragma float_control(precise,on)
#define FLOAT_CONTROL_PRECISE_FOR_ROUND
#endif
// function round: round to nearest integer (even). (result as float vector)
static inline Vec4f round(Vec4f const & a) {
#if INSTRSET >= 5 // SSE4.1 supported
return _mm_round_ps(a, 0);
#else // SSE2. Use magic number method
// Note: assume MXCSR control register is set to rounding
// (don't use conversion to int, it will limit the value to +/- 2^31)
Vec4f signmask = _mm_castsi128_ps(constant4i<(int)0x80000000,(int)0x80000000,(int)0x80000000,(int)0x80000000>()); // -0.0
Vec4f magic = _mm_castsi128_ps(constant4i<0x4B000000,0x4B000000,0x4B000000,0x4B000000>()); // magic number = 2^23
Vec4f sign = _mm_and_ps(a, signmask); // signbit of a
Vec4f signedmagic = _mm_or_ps(magic, sign); // magic number with sign of a
// volatile
Vec4f b = a + signedmagic; // round by adding magic number
return b - signedmagic; // .. and subtracting it again
#endif
}
#ifdef FLOAT_CONTROL_PRECISE_FOR_ROUND
#pragma float_control(pop)
#endif
// function truncate: round towards zero. (result as float vector)
static inline Vec4f truncate(Vec4f const & a) {
#if INSTRSET >= 5 // SSE4.1 supported
return _mm_round_ps(a, 3);
#else // SSE2. Use magic number method (conversion to int would limit the value to 2^31)
uint32_t t1 = _mm_getcsr(); // MXCSR
uint32_t t2 = t1 | (3 << 13); // bit 13-14 = 11
_mm_setcsr(t2); // change MXCSR
Vec4f r = round(a); // use magic number method
_mm_setcsr(t1); // restore MXCSR
return r;
#endif
}
// function floor: round towards minus infinity. (result as float vector)
static inline Vec4f floor(Vec4f const & a) {
#if INSTRSET >= 5 // SSE4.1 supported
return _mm_round_ps(a, 1);
#else // SSE2. Use magic number method (conversion to int would limit the value to 2^31)
uint32_t t1 = _mm_getcsr(); // MXCSR
uint32_t t2 = t1 | (1 << 13); // bit 13-14 = 01
_mm_setcsr(t2); // change MXCSR
Vec4f r = round(a); // use magic number method
_mm_setcsr(t1); // restore MXCSR
return r;
#endif
}
// function ceil: round towards plus infinity. (result as float vector)
static inline Vec4f ceil(Vec4f const & a) {
#if INSTRSET >= 5 // SSE4.1 supported
return _mm_round_ps(a, 2);
#else // SSE2. Use magic number method (conversion to int would limit the value to 2^31)
uint32_t t1 = _mm_getcsr(); // MXCSR
uint32_t t2 = t1 | (2 << 13); // bit 13-14 = 10
_mm_setcsr(t2); // change MXCSR
Vec4f r = round(a); // use magic number method
_mm_setcsr(t1); // restore MXCSR
return r;
#endif
}
// function round_to_int: round to nearest integer (even). (result as integer vector)
static inline Vec4i round_to_int(Vec4f const & a) {
// Note: assume MXCSR control register is set to rounding
return _mm_cvtps_epi32(a);
}
// function truncate_to_int: round towards zero. (result as integer vector)
static inline Vec4i truncate_to_int(Vec4f const & a) {
return _mm_cvttps_epi32(a);
}
// function to_float: convert integer vector to float vector
static inline Vec4f to_float(Vec4i const & a) {
return _mm_cvtepi32_ps(a);
}
// Approximate math functions
// approximate reciprocal (Faster than 1.f / a. relative accuracy better than 2^-11)
static inline Vec4f approx_recipr(Vec4f const & a) {
return _mm_rcp_ps(a);
}
// approximate reciprocal squareroot (Faster than 1.f / sqrt(a). Relative accuracy better than 2^-11)
static inline Vec4f approx_rsqrt(Vec4f const & a) {
return _mm_rsqrt_ps(a);
}
// Fused multiply and add functions
// Multiply and add
static inline Vec4f mul_add(Vec4f const & a, Vec4f const & b, Vec4f const & c) {
#ifdef __FMA__
return _mm_fmadd_ps(a, b, c);
#elif defined (__FMA4__)
return _mm_macc_ps(a, b, c);
#else
return a * b + c;
#endif
}
// Multiply and subtract
static inline Vec4f mul_sub(Vec4f const & a, Vec4f const & b, Vec4f const & c) {
#ifdef __FMA__
return _mm_fmsub_ps(a, b, c);
#elif defined (__FMA4__)
return _mm_msub_ps(a, b, c);
#else
return a * b - c;
#endif
}
// Multiply and inverse subtract
static inline Vec4f nmul_add(Vec4f const & a, Vec4f const & b, Vec4f const & c) {
#ifdef __FMA__
return _mm_fnmadd_ps(a, b, c);
#elif defined (__FMA4__)
return _mm_nmacc_ps(a, b, c);
#else
return c - a * b;
#endif
}
// Multiply and subtract with extra precision on the intermediate calculations,
// even if FMA instructions not supported, using Veltkamp-Dekker split
static inline Vec4f mul_sub_x(Vec4f const & a, Vec4f const & b, Vec4f const & c) {
#ifdef __FMA__
return _mm_fmsub_ps(a, b, c);
#elif defined (__FMA4__)
return _mm_msub_ps(a, b, c);
#else
// calculate a * b - c with extra precision
Vec4i upper_mask = -(1 << 12); // mask to remove lower 12 bits
Vec4f a_high = a & Vec4f(_mm_castsi128_ps(upper_mask));// split into high and low parts
Vec4f b_high = b & Vec4f(_mm_castsi128_ps(upper_mask));
Vec4f a_low = a - a_high;
Vec4f b_low = b - b_high;
Vec4f r1 = a_high * b_high; // this product is exact
Vec4f r2 = r1 - c; // subtract c from high product
Vec4f r3 = r2 + (a_high * b_low + b_high * a_low) + a_low * b_low; // add rest of product
return r3; // + ((r2 - r1) + c);
#endif
}
// Math functions using fast bit manipulation
// 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 Vec4i exponent(Vec4f const & a) {
Vec4ui t1 = _mm_castps_si128(a); // reinterpret as 32-bit integer
Vec4ui t2 = t1 << 1; // shift out sign bit
Vec4ui t3 = t2 >> 24; // shift down logical to position 0
Vec4i t4 = Vec4i(t3) - 0x7F; // subtract bias from exponent
return t4;
}
// 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 Vec4f fraction(Vec4f const & a) {
Vec4ui t1 = _mm_castps_si128(a); // reinterpret as 32-bit integer
Vec4ui t2 = Vec4ui((t1 & 0x007FFFFF) | 0x3F800000); // set exponent to 0 + bias
return _mm_castsi128_ps(t2);
}
// 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 Vec4f exp2(Vec4i const & n) {
Vec4i t1 = max(n, -0x7F); // limit to allowed range
Vec4i t2 = min(t1, 0x80);
Vec4i t3 = t2 + 0x7F; // add bias
Vec4i t4 = t3 << 23; // put exponent into position 23
return _mm_castsi128_ps(t4); // reinterpret as float
}
//static Vec4f exp2(Vec4f const & x); // defined in vectormath_exp.h
// Control word manipulaton
// ------------------------
// The MXCSR control word has the following bits:
// 0: Invalid Operation Flag
// 1: Denormal Flag (=subnormal)
// 2: Divide-by-Zero Flag
// 3: Overflow Flag
// 4: Underflow Flag
// 5: Precision Flag
// 6: Denormals Are Zeros (=subnormals)
// 7: Invalid Operation Mask
// 8: Denormal Operation Mask (=subnormal)
// 9: Divide-by-Zero Mask
// 10: Overflow Mask
// 11: Underflow Mask
// 12: Precision Mask
// 13-14: Rounding control
// 00: round to nearest or even
// 01: round down towards -infinity
// 10: round up towards +infinity
// 11: round towards zero (truncate)
// 15: Flush to Zero
// Function get_control_word:
// Read the MXCSR control word
static inline uint32_t get_control_word() {
return _mm_getcsr();
}
// Function set_control_word:
// Write the MXCSR control word
static inline void set_control_word(uint32_t w) {
_mm_setcsr(w);
}
// Function no_subnormals:
// Set "Denormals Are Zeros" and "Flush to Zero" mode to avoid the extremely
// time-consuming denormals in case of underflow
static inline void no_subnormals() {
uint32_t t1 = get_control_word();
t1 |= (1 << 6) | (1 << 15); // set bit 6 and 15 in MXCSR
set_control_word(t1);
}
// Function reset_control_word:
// Set the MXCSR control word to the default value 0x1F80.
// This will mask floating point exceptions, set rounding mode to nearest (or even),
// and allow denormals.
static inline void reset_control_word() {
set_control_word(0x1F80);
}
// 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(Vec4f(-0.0f)) gives true, while Vec4f(-0.0f) < Vec4f(0.0f) gives false
// (the underscore in the name avoids a conflict with a macro in Intel's mathimf.h)
static inline Vec4fb sign_bit(Vec4f const & a) {
Vec4i t1 = _mm_castps_si128(a); // reinterpret as 32-bit integer
Vec4i t2 = t1 >> 31; // extend sign bit
return _mm_castsi128_ps(t2); // reinterpret as 32-bit Boolean
}
// 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 Vec4f sign_combine(Vec4f const & a, Vec4f const & b) {
Vec4f signmask = _mm_castsi128_ps(constant4i<(int)0x80000000,(int)0x80000000,(int)0x80000000,(int)0x80000000>()); // -0.0
return a ^ (b & signmask);
}
// Function is_finite: gives true for elements that are normal, denormal or zero,
// false for INF and NAN
// (the underscore in the name avoids a conflict with a macro in Intel's mathimf.h)
static inline Vec4fb is_finite(Vec4f const & a) {
Vec4i t1 = _mm_castps_si128(a); // reinterpret as 32-bit integer
Vec4i t2 = t1 << 1; // shift out sign bit
Vec4i t3 = Vec4i(t2 & 0xFF000000) != 0xFF000000; // exponent field is not all 1s
return Vec4ib(t3);
}
// 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 Vec4fb is_inf(Vec4f const & a) {
Vec4i t1 = _mm_castps_si128(a); // reinterpret as 32-bit integer
Vec4i t2 = t1 << 1; // shift out sign bit
return t2 == Vec4i(0xFF000000); // exponent is all 1s, fraction is 0
}
// 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 Vec4fb is_nan(Vec4f const & a) {
Vec4i t1 = _mm_castps_si128(a); // reinterpret as 32-bit integer
Vec4i t2 = t1 << 1; // shift out sign bit
Vec4i t3 = 0xFF000000; // exponent mask
Vec4i t4 = t2 & t3; // exponent
Vec4i t5 = _mm_andnot_si128(t3,t2);// fraction
return Vec4ib((t4 == t3) & (t5 != 0));// exponent = all 1s and fraction != 0
}
// Function is_subnormal: gives true for elements that are denormal (subnormal)
// false for finite numbers, zero, NAN and INF
static inline Vec4fb is_subnormal(Vec4f const & a) {
Vec4i t1 = _mm_castps_si128(a); // reinterpret as 32-bit integer
Vec4i t2 = t1 << 1; // shift out sign bit
Vec4i t3 = 0xFF000000; // exponent mask
Vec4i t4 = t2 & t3; // exponent
Vec4i t5 = _mm_andnot_si128(t3,t2);// fraction
return Vec4ib((t4 == 0) & (t5 != 0));// exponent = 0 and fraction != 0
}
// Function is_zero_or_subnormal: gives true for elements that are zero or subnormal (denormal)
// false for finite numbers, NAN and INF
static inline Vec4fb is_zero_or_subnormal(Vec4f const & a) {
Vec4i t = _mm_castps_si128(a); // reinterpret as 32-bit integer
t &= 0x7F800000; // isolate exponent
return t == 0; // exponent = 0
}
// Function infinite4f: returns a vector where all elements are +INF
static inline Vec4f infinite4f() {
return _mm_castsi128_ps(_mm_set1_epi32(0x7F800000));
}
// Function nan4f: returns a vector where all elements are NAN (quiet)
static inline Vec4f nan4f(int n = 0x10) {
return _mm_castsi128_ps(_mm_set1_epi32(0x7FC00000 + n));
}
/*****************************************************************************
*
* Vector Vec4f 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. A negative index will generate zero.
*
* Example:
* Vec4f a(10.f,11.f,12.f,13.f); // a is (10,11,12,13)
* Vec4f b, c;
* b = permute4f<0,0,2,2>(a); // b is (10,10,12,12)
* c = permute4f<3,2,-1,-1>(a); // c is (13,12, 0, 0)
*
*
* 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:
* Vec4f a(10.f,11.f,12.f,13.f); // a is (10, 11, 12, 13)
* Vec4f b(20.f,21.f,22.f,23.f); // b is (20, 21, 22, 23)
* Vec4f c;
* c = blend4f<1,4,-1,7> (a,b); // c is (11, 20, 0, 23)
*
* Don't worry about the complicated code for these functions. Most of the
* code is resolved at compile time to generate only a few instructions.
*****************************************************************************/
// permute vector Vec4f
template <int i0, int i1, int i2, int i3>
static inline Vec4f permute4f(Vec4f const & a) {
// is shuffling needed
const bool do_shuffle = (i0 > 0) || (i1 != 1 && i1 >= 0) || (i2 != 2 && i2 >= 0) || (i3 != 3 && i3 >= 0);
// is zeroing needed
const bool do_zero = (i0 | i1 | i2 | i3) < 0 && ((i0 | i1 | i2 | i3) & 0x80);
if (!do_shuffle && !do_zero) {
return a; // trivial case: do nothing
}
if (do_zero && !do_shuffle) { // zeroing, not shuffling
if ((i0 & i1 & i2 & i3) < 0) return _mm_setzero_ps(); // zero everything
// zero some elements
__m128i mask1 = constant4i< -int(i0>=0), -int(i1>=0), -int(i2>=0), -int(i3>=0) >();
return _mm_and_ps(a,_mm_castsi128_ps(mask1)); // zero with AND mask
}
if (do_shuffle && !do_zero) { // shuffling, not zeroing
return _mm_shuffle_ps(a, a, (i0&3) | (i1&3)<<2 | (i2&3)<<4 | (i3&3)<<6);
}
// both shuffle and zero
if ((i0 & i1) < 0 && (i2 | i3) >= 0) { // zero low half, shuffle high half
return _mm_shuffle_ps(_mm_setzero_ps(), a, (i2&3)<<4 | (i3&3)<<6);
}
if ((i0 | i1) >= 0 && (i2 & i3) < 0) { // shuffle low half, zero high half
return _mm_shuffle_ps(a, _mm_setzero_ps(), (i0&3) | (i1&3)<<2);
}
#if INSTRSET >= 4 // SSSE3
// With SSSE3 we can do both with the PSHUFB instruction
const int j0 = (i0 & 3) << 2;
const int j1 = (i1 & 3) << 2;
const int j2 = (i2 & 3) << 2;
const int j3 = (i3 & 3) << 2;
__m128i mask2 = constant4i <
i0 < 0 ? -1 : j0 | (j0+1)<<8 | (j0+2)<<16 | (j0+3) << 24,
i1 < 0 ? -1 : j1 | (j1+1)<<8 | (j1+2)<<16 | (j1+3) << 24,
i2 < 0 ? -1 : j2 | (j2+1)<<8 | (j2+2)<<16 | (j2+3) << 24,
i3 < 0 ? -1 : j3 | (j3+1)<<8 | (j3+2)<<16 | (j3+3) << 24 > ();
return _mm_castsi128_ps(_mm_shuffle_epi8(_mm_castps_si128(a),mask2));
#else
__m128 t1 = _mm_shuffle_ps(a, a, (i0&3) | (i1&3)<<2 | (i2&3)<<4 | (i3&3)<<6); // shuffle
__m128i mask3 = constant4i< -int(i0>=0), -int(i1>=0), -int(i2>=0), -int(i3>=0) >();
return _mm_and_ps(t1,_mm_castsi128_ps(mask3)); // zero with AND mask
#endif
}
// blend vectors Vec4f
template <int i0, int i1, int i2, int i3>
static inline Vec4f blend4f(Vec4f const & a, Vec4f const & b) {
// Combine all the indexes into a single bitfield, with 8 bits for each
const int m1 = (i0&7) | (i1&7)<<8 | (i2&7)<<16 | (i3&7)<<24;
// Mask to zero out negative indexes
const int m2 = (i0<0?0:0xFF) | (i1<0?0:0xFF)<<8 | (i2<0?0:0xFF)<<16 | (i3<0?0:0xFF)<<24;
if ((m1 & 0x04040404 & m2) == 0) {
// no elements from b
return permute4f<i0,i1,i2,i3>(a);
}
if (((m1^0x04040404) & 0x04040404 & m2) == 0) {
// no elements from a
return permute4f<i0&~4, i1&~4, i2&~4, i3&~4>(b);
}
if (((m1 & ~0x04040404) ^ 0x03020100) == 0 && m2 == -1) {
// selecting without shuffling or zeroing
__m128i sel = constant4i <i0 & 4 ? 0 : -1, i1 & 4 ? 0 : -1, i2 & 4 ? 0 : -1, i3 & 4 ? 0 : -1> ();
return selectf(_mm_castsi128_ps(sel), a, b);
}
#ifdef __XOP__ // Use AMD XOP instruction PPERM
__m128i maska = constant4i <
i0 < 0 ? 0x80808080 : (i0*4 & 31) + (((i0*4 & 31) + 1) << 8) + (((i0*4 & 31) + 2) << 16) + (((i0*4 & 31) + 3) << 24),
i1 < 0 ? 0x80808080 : (i1*4 & 31) + (((i1*4 & 31) + 1) << 8) + (((i1*4 & 31) + 2) << 16) + (((i1*4 & 31) + 3) << 24),
i2 < 0 ? 0x80808080 : (i2*4 & 31) + (((i2*4 & 31) + 1) << 8) + (((i2*4 & 31) + 2) << 16) + (((i2*4 & 31) + 3) << 24),
i3 < 0 ? 0x80808080 : (i3*4 & 31) + (((i3*4 & 31) + 1) << 8) + (((i3*4 & 31) + 2) << 16) + (((i3*4 & 31) + 3) << 24) > ();
return _mm_castsi128_ps(_mm_perm_epi8(_mm_castps_si128(a), _mm_castps_si128(b), maska));
#else
if ((((m1 & ~0x04040404) ^ 0x03020100) & m2) == 0) {
// selecting and zeroing, not shuffling
__m128i sel1 = constant4i <i0 & 4 ? 0 : -1, i1 & 4 ? 0 : -1, i2 & 4 ? 0 : -1, i3 & 4 ? 0 : -1> ();
__m128i mask1 = constant4i< -int(i0>=0), -int(i1>=0), -int(i2>=0), -int(i3>=0) >();
__m128 t1 = selectf(_mm_castsi128_ps(sel1), a, b); // select
return _mm_and_ps(t1, _mm_castsi128_ps(mask1)); // zero
}
// special cases unpckhps, unpcklps, shufps
Vec4f t;
if (((m1 ^ 0x05010400) & m2) == 0) {
t = _mm_unpacklo_ps(a, b);
goto DOZERO;
}
if (((m1 ^ 0x01050004) & m2) == 0) {
t = _mm_unpacklo_ps(b, a);
goto DOZERO;
}
if (((m1 ^ 0x07030602) & m2) == 0) {
t = _mm_unpackhi_ps(a, b);
goto DOZERO;
}
if (((m1 ^ 0x03070206) & m2) == 0) {
t = _mm_unpackhi_ps(b, a);
goto DOZERO;
}
// first two elements from a, last two from b
if (((m1^0x04040000) & 0x04040404 & m2) == 0) {
t = _mm_shuffle_ps(a, b, (i0&3) + ((i1&3)<<2) + ((i2&3)<<4) + ((i3&3)<<6));
goto DOZERO;
}
// first two elements from b, last two from a
if (((m1^0x00000404) & 0x04040404 & m2) == 0) {
t = _mm_shuffle_ps(b, a, (i0&3) + ((i1&3)<<2) + ((i2&3)<<4) + ((i3&3)<<6));
goto DOZERO;
}
{ // general case. combine two permutes
__m128 a1 = permute4f <
(uint32_t)i0 < 4 ? i0 : -1,
(uint32_t)i1 < 4 ? i1 : -1,
(uint32_t)i2 < 4 ? i2 : -1,
(uint32_t)i3 < 4 ? i3 : -1 > (a);
__m128 b1 = permute4f <
(uint32_t)(i0^4) < 4 ? (i0^4) : -1,
(uint32_t)(i1^4) < 4 ? (i1^4) : -1,
(uint32_t)(i2^4) < 4 ? (i2^4) : -1,
(uint32_t)(i3^4) < 4 ? (i3^4) : -1 > (b);
return _mm_or_ps(a1,b1);
}
DOZERO:
if ((i0|i1|i2|i3) & 0x80) {
// zero some elements
__m128i mask1 = constant4i< -int(i0>=0), -int(i1>=0), -int(i2>=0), -int(i3>=0) >();
t = _mm_and_ps(t,_mm_castsi128_ps(mask1)); // zero with AND mask
}
return t;
#endif // __XOP__
}
// change signs on vectors Vec4f
// 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 Vec4f change_sign(Vec4f const & a) {
if ((i0 | i1 | i2 | i3) == 0) return a;
__m128i mask = constant4i<i0 ? 0x80000000 : 0, i1 ? 0x80000000 : 0, i2 ? 0x80000000 : 0, i3 ? 0x80000000 : 0>();
return _mm_xor_ps(a, _mm_castsi128_ps(mask)); // flip sign bits
}
/*****************************************************************************
*
* Vec2d: Vector of 2 double precision floating point values
*
*****************************************************************************/
class Vec2d {
protected:
__m128d xmm; // double vector
public:
// Default constructor:
Vec2d() {
}
// Constructor to broadcast the same value into all elements:
Vec2d(double d) {
xmm = _mm_set1_pd(d);
}
// Constructor to build from all elements:
Vec2d(double d0, double d1) {
xmm = _mm_setr_pd(d0, d1);
}
// Constructor to convert from type __m128d used in intrinsics:
Vec2d(__m128d const & x) {
xmm = x;
}
// Assignment operator to convert from type __m128d used in intrinsics:
Vec2d & operator = (__m128d const & x) {
xmm = x;
return *this;
}
// Type cast operator to convert to __m128d used in intrinsics
operator __m128d() const {
return xmm;
}
// Member function to load from array (unaligned)
Vec2d & load(double const * p) {
xmm = _mm_loadu_pd(p);
return *this;
}
// Member function to load from array, aligned by 16
// "load_a" is faster than "load" on older Intel processors (Pentium 4, Pentium M, Core 1,
// Merom, Wolfdale) and Atom, but not on other processors from Intel, AMD or VIA.
// You may use load_a instead of load if you are certain that p points to an address
// divisible by 16.
Vec2d const & load_a(double const * p) {
xmm = _mm_load_pd(p);
return *this;
}
// Member function to store into array (unaligned)
void store(double * p) const {
_mm_storeu_pd(p, xmm);
}
// Member function to store into array, aligned by 16
// "store_a" is faster than "store" on older Intel processors (Pentium 4, Pentium M, Core 1,
// Merom, Wolfdale) and Atom, but not on other processors from Intel, AMD or VIA.
// You may use store_a instead of store if you are certain that p points to an address
// divisible by 16.
void store_a(double * p) const {
_mm_store_pd(p, xmm);
}
// Partial load. Load n elements and set the rest to 0
Vec2d & load_partial(int n, double const * p) {
if (n == 1) {
xmm = _mm_load_sd(p);
}
else if (n == 2) {
load(p);
}
else {
xmm = _mm_setzero_pd();
}
return *this;
}
// Partial store. Store n elements
void store_partial(int n, double * p) const {
if (n == 1) {
_mm_store_sd(p, xmm);
}
else if (n == 2) {
store(p);
}
}
// cut off vector to n elements. The last 4-n elements are set to zero
Vec2d & cutoff(int n) {
xmm = _mm_castps_pd(Vec4f(_mm_castpd_ps(xmm)).cutoff(n*2));
return *this;
}
// Member function to change a single element in vector
// Note: This function is inefficient. Use load function if changing more than one element
Vec2d const & insert(uint32_t index, double value) {
__m128d v2 = _mm_set_sd(value);
if (index == 0) {
xmm = _mm_shuffle_pd(v2,xmm,2);
}
else {
xmm = _mm_shuffle_pd(xmm,v2,0);
}
return *this;
};
// Member function extract a single element from vector
double extract(uint32_t index) const {
double x[2];
store(x);
return x[index & 1];
}
// 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);
}
static int size() {
return 2;
}
};
/*****************************************************************************
*
* Operators for Vec2d
*
*****************************************************************************/
// vector operator + : add element by element
static inline Vec2d operator + (Vec2d const & a, Vec2d const & b) {
return _mm_add_pd(a, b);
}
// vector operator + : add vector and scalar
static inline Vec2d operator + (Vec2d const & a, double b) {
return a + Vec2d(b);
}
static inline Vec2d operator + (double a, Vec2d const & b) {
return Vec2d(a) + b;
}
// vector operator += : add
static inline Vec2d & operator += (Vec2d & a, Vec2d const & b) {
a = a + b;
return a;
}
// postfix operator ++
static inline Vec2d operator ++ (Vec2d & a, int) {
Vec2d a0 = a;
a = a + 1.0;
return a0;
}
// prefix operator ++
static inline Vec2d & operator ++ (Vec2d & a) {
a = a + 1.0;
return a;
}
// vector operator - : subtract element by element
static inline Vec2d operator - (Vec2d const & a, Vec2d const & b) {
return _mm_sub_pd(a, b);
}
// vector operator - : subtract vector and scalar
static inline Vec2d operator - (Vec2d const & a, double b) {
return a - Vec2d(b);
}
static inline Vec2d operator - (double a, Vec2d const & b) {
return Vec2d(a) - b;
}
// vector operator - : unary minus
// Change sign bit, even for 0, INF and NAN
static inline Vec2d operator - (Vec2d const & a) {
return _mm_xor_pd(a, _mm_castsi128_pd(_mm_setr_epi32(0,0x80000000,0,0x80000000)));
}
// vector operator -= : subtract
static inline Vec2d & operator -= (Vec2d & a, Vec2d const & b) {
a = a - b;
return a;
}
// postfix operator --
static inline Vec2d operator -- (Vec2d & a, int) {
Vec2d a0 = a;
a = a - 1.0;
return a0;
}
// prefix operator --
static inline Vec2d & operator -- (Vec2d & a) {
a = a - 1.0;
return a;
}
// vector operator * : multiply element by element
static inline Vec2d operator * (Vec2d const & a, Vec2d const & b) {
return _mm_mul_pd(a, b);
}
// vector operator * : multiply vector and scalar
static inline Vec2d operator * (Vec2d const & a, double b) {
return a * Vec2d(b);
}
static inline Vec2d operator * (double a, Vec2d const & b) {
return Vec2d(a) * b;
}
// vector operator *= : multiply
static inline Vec2d & operator *= (Vec2d & a, Vec2d const & b) {
a = a * b;
return a;
}
// vector operator / : divide all elements by same integer
static inline Vec2d operator / (Vec2d const & a, Vec2d const & b) {
return _mm_div_pd(a, b);
}
// vector operator / : divide vector and scalar
static inline Vec2d operator / (Vec2d const & a, double b) {
return a / Vec2d(b);
}
static inline Vec2d operator / (double a, Vec2d const & b) {
return Vec2d(a) / b;
}
// vector operator /= : divide
static inline Vec2d & operator /= (Vec2d & a, Vec2d const & b) {
a = a / b;
return a;
}
// vector operator == : returns true for elements for which a == b
static inline Vec2db operator == (Vec2d const & a, Vec2d const & b) {
return _mm_cmpeq_pd(a, b);
}
// vector operator != : returns true for elements for which a != b
static inline Vec2db operator != (Vec2d const & a, Vec2d const & b) {
return _mm_cmpneq_pd(a, b);
}
// vector operator < : returns true for elements for which a < b
static inline Vec2db operator < (Vec2d const & a, Vec2d const & b) {
return _mm_cmplt_pd(a, b);
}
// vector operator <= : returns true for elements for which a <= b
static inline Vec2db operator <= (Vec2d const & a, Vec2d const & b) {
return _mm_cmple_pd(a, b);
}
// vector operator > : returns true for elements for which a > b
static inline Vec2db operator > (Vec2d const & a, Vec2d const & b) {
return b < a;
}
// vector operator >= : returns true for elements for which a >= b
static inline Vec2db operator >= (Vec2d const & a, Vec2d const & b) {
return b <= a;
}
// Bitwise logical operators
// vector operator & : bitwise and
static inline Vec2d operator & (Vec2d const & a, Vec2d const & b) {
return _mm_and_pd(a, b);
}
// vector operator &= : bitwise and
static inline Vec2d & operator &= (Vec2d & a, Vec2d const & b) {
a = a & b;
return a;
}
// vector operator & : bitwise and of Vec2d and Vec2db
static inline Vec2d operator & (Vec2d const & a, Vec2db const & b) {
return _mm_and_pd(a, b);
}
static inline Vec2d operator & (Vec2db const & a, Vec2d const & b) {
return _mm_and_pd(a, b);
}
// vector operator | : bitwise or
static inline Vec2d operator | (Vec2d const & a, Vec2d const & b) {
return _mm_or_pd(a, b);
}
// vector operator |= : bitwise or
static inline Vec2d & operator |= (Vec2d & a, Vec2d const & b) {
a = a | b;
return a;
}
// vector operator ^ : bitwise xor
static inline Vec2d operator ^ (Vec2d const & a, Vec2d const & b) {
return _mm_xor_pd(a, b);
}
// vector operator ^= : bitwise xor
static inline Vec2d & operator ^= (Vec2d & a, Vec2d const & b) {
a = a ^ b;
return a;
}
// vector operator ! : logical not. Returns Boolean vector
static inline Vec2db operator ! (Vec2d const & a) {
return a == Vec2d(0.0);
}
/*****************************************************************************
*
* Functions for Vec2d
*
*****************************************************************************/
// 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 Vec2d select (Vec2db const & s, Vec2d const & a, Vec2d const & b) {
return selectd(s,a,b);
}
// Conditional add: For all vector elements i: result[i] = f[i] ? (a[i] + b[i]) : a[i]
static inline Vec2d if_add (Vec2db const & f, Vec2d const & a, Vec2d const & b) {
return a + (Vec2d(f) & b);
}
// Conditional multiply: For all vector elements i: result[i] = f[i] ? (a[i] * b[i]) : a[i]
static inline Vec2d if_mul (Vec2db const & f, Vec2d const & a, Vec2d const & b) {
return a * select(f, b, 1.);
}
// General arithmetic functions, etc.
// Horizontal add: Calculates the sum of all vector elements.
static inline double horizontal_add (Vec2d const & a) {
#if INSTRSET >= 3 // SSE3
__m128d t1 = _mm_hadd_pd(a,a);
return _mm_cvtsd_f64(t1);
#else
__m128 t0 = _mm_castpd_ps(a);
__m128d t1 = _mm_castps_pd(_mm_movehl_ps(t0,t0));
__m128d t2 = _mm_add_sd(a,t1);
return _mm_cvtsd_f64(t2);
#endif
}
// function max: a > b ? a : b
static inline Vec2d max(Vec2d const & a, Vec2d const & b) {
return _mm_max_pd(a,b);
}
// function min: a < b ? a : b
static inline Vec2d min(Vec2d const & a, Vec2d const & b) {
return _mm_min_pd(a,b);
}
// function abs: absolute value
// Removes sign bit, even for -0.0f, -INF and -NAN
static inline Vec2d abs(Vec2d const & a) {
__m128d mask = _mm_castsi128_pd(_mm_setr_epi32(-1,0x7FFFFFFF,-1,0x7FFFFFFF));
return _mm_and_pd(a,mask);
}
// function sqrt: square root
static inline Vec2d sqrt(Vec2d const & a) {
return _mm_sqrt_pd(a);
}
// function square: a * a
static inline Vec2d square(Vec2d const & a) {
return a * a;
}
// pow(Vec2d, int):
// The purpose of this template is to prevent implicit conversion of a float
// exponent to int when calling pow(vector, float) and vectormath_exp.h is
// not included
template <typename TT> static Vec2d pow(Vec2d const & a, TT n);
// Raise floating point numbers to integer power n
template <>
inline Vec2d pow<int>(Vec2d const & x0, int n) {
return pow_template_i<Vec2d>(x0, n);
}
// allow conversion from unsigned int
template <>
inline Vec2d pow<uint32_t>(Vec2d const & x0, uint32_t n) {
return pow_template_i<Vec2d>(x0, (int)n);
}
// Raise floating point numbers to integer power n, where n is a compile-time constant
template <int n>
static inline Vec2d pow_n(Vec2d const & a) {
if (n < 0) return Vec2d(1.0) / pow_n<-n>(a);
if (n == 0) return Vec2d(1.0);
if (n >= 256) return pow(a, n);
Vec2d x = a; // a^(2^i)
Vec2d y; // accumulator
const int lowest = n - (n & (n-1));// lowest set bit in n
if (n & 1) y = x;
if (n < 2) return y;
x = x*x; // x^2
if (n & 2) {
if (lowest == 2) y = x; else y *= x;
}
if (n < 4) return y;
x = x*x; // x^4
if (n & 4) {
if (lowest == 4) y = x; else y *= x;
}
if (n < 8) return y;
x = x*x; // x^8
if (n & 8) {
if (lowest == 8) y = x; else y *= x;
}
if (n < 16) return y;
x = x*x; // x^16
if (n & 16) {
if (lowest == 16) y = x; else y *= x;
}
if (n < 32) return y;
x = x*x; // x^32
if (n & 32) {
if (lowest == 32) y = x; else y *= x;
}
if (n < 64) return y;
x = x*x; // x^64
if (n & 64) {
if (lowest == 64) y = x; else y *= x;
}
if (n < 128) return y;
x = x*x; // x^128
if (n & 128) {
if (lowest == 128) y = x; else y *= x;
}
return y;
}
template <int n>
static inline Vec2d pow(Vec2d const & a, Const_int_t<n>) {
return pow_n<n>(a);
}
// avoid unsafe optimization in function round
#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__) && INSTRSET < 5
static inline Vec4f round(Vec4f const & a) __attribute__ ((optimize("-fno-unsafe-math-optimizations")));
#elif defined (FLOAT_CONTROL_PRECISE_FOR_ROUND)
#pragma float_control(push)
#pragma float_control(precise,on)
#endif
// function round: round to nearest integer (even). (result as double vector)
static inline Vec2d round(Vec2d const & a) {
#if INSTRSET >= 5 // SSE4.1 supported
return _mm_round_pd(a, 0);
#else // SSE2. Use magic number method
// Note: assume MXCSR control register is set to rounding
// (don't use conversion to int, it will limit the value to +/- 2^31)
Vec2d signmask = _mm_castsi128_pd(constant4i<0,(int)0x80000000,0,(int)0x80000000>()); // -0.0
Vec2d magic = _mm_castsi128_pd(constant4i<0,0x43300000,0,0x43300000>()); // magic number = 2^52
Vec2d sign = _mm_and_pd(a, signmask); // signbit of a
Vec2d signedmagic = _mm_or_pd(magic, sign); // magic number with sign of a
return a + signedmagic - signedmagic; // round by adding magic number
#endif
}
#if defined (FLOAT_CONTROL_PRECISE_FOR_ROUND)
#pragma float_control(pop)
#endif
// function truncate: round towards zero. (result as double vector)
static inline Vec2d truncate(Vec2d const & a) {
// (note: may fail on MS Visual Studio 2008, works in later versions)
#if INSTRSET >= 5 // SSE4.1 supported
return _mm_round_pd(a, 3);
#else // SSE2. Use magic number method (conversion to int would limit the value to 2^31)
uint32_t t1 = _mm_getcsr(); // MXCSR
uint32_t t2 = t1 | (3 << 13); // bit 13-14 = 11
_mm_setcsr(t2); // change MXCSR
Vec2d r = round(a); // use magic number method
_mm_setcsr(t1); // restore MXCSR
return r;
#endif
}
// function floor: round towards minus infinity. (result as double vector)
// (note: may fail on MS Visual Studio 2008, works in later versions)
static inline Vec2d floor(Vec2d const & a) {
#if INSTRSET >= 5 // SSE4.1 supported
return _mm_round_pd(a, 1);
#else // SSE2. Use magic number method (conversion to int would limit the value to 2^31)
uint32_t t1 = _mm_getcsr(); // MXCSR
uint32_t t2 = t1 | (1 << 13); // bit 13-14 = 01
_mm_setcsr(t2); // change MXCSR
Vec2d r = round(a); // use magic number method
_mm_setcsr(t1); // restore MXCSR
return r;
#endif
}
// function ceil: round towards plus infinity. (result as double vector)
static inline Vec2d ceil(Vec2d const & a) {
#if INSTRSET >= 5 // SSE4.1 supported
return _mm_round_pd(a, 2);
#else // SSE2. Use magic number method (conversion to int would limit the value to 2^31)
uint32_t t1 = _mm_getcsr(); // MXCSR
uint32_t t2 = t1 | (2 << 13); // bit 13-14 = 10
_mm_setcsr(t2); // change MXCSR
Vec2d r = round(a); // use magic number method
_mm_setcsr(t1); // restore MXCSR
return r;
#endif
}
// function truncate_to_int: round towards zero.
static inline Vec4i truncate_to_int(Vec2d const & a, Vec2d const & b) {
Vec4i t1 = _mm_cvttpd_epi32(a);
Vec4i t2 = _mm_cvttpd_epi32(b);
return blend4i<0,1,4,5> (t1, t2);
}
// function truncate_to_int64: round towards zero. (inefficient)
static inline Vec2q truncate_to_int64(Vec2d const & a) {
double aa[2];
a.store(aa);
return Vec2q(int64_t(aa[0]), int64_t(aa[1]));
}
// function truncate_to_int64_limited: round towards zero. (inefficient)
// result as 64-bit integer vector, but with limited range
static inline Vec2q truncate_to_int64_limited(Vec2d const & a) {
// Note: assume MXCSR control register is set to rounding
Vec4i t1 = _mm_cvttpd_epi32(a);
return extend_low(t1);
}
// function round_to_int: round to nearest integer (even).
// result as 32-bit integer vector
static inline Vec4i round_to_int(Vec2d const & a, Vec2d const & b) {
// Note: assume MXCSR control register is set to rounding
Vec4i t1 = _mm_cvtpd_epi32(a);
Vec4i t2 = _mm_cvtpd_epi32(b);
return blend4i<0,1,4,5> (t1, t2);
}
// function round_to_int: round to nearest integer (even).
// result as 32-bit integer vector. Upper two values of result are 0
static inline Vec4i round_to_int(Vec2d const & a) {
Vec4i t1 = _mm_cvtpd_epi32(a);
return t1;
}
// function round_to_int64: round to nearest or even. (inefficient)
static inline Vec2q round_to_int64(Vec2d const & a) {
return truncate_to_int64(round(a));
}
// function round_to_int: round to nearest integer (even)
// result as 64-bit integer vector, but with limited range
static inline Vec2q round_to_int64_limited(Vec2d const & a) {
// Note: assume MXCSR control register is set to rounding
Vec4i t1 = _mm_cvtpd_epi32(a);
return extend_low(t1);
}
// function to_double: convert integer vector elements to double vector (inefficient)
static inline Vec2d to_double(Vec2q const & a) {
int64_t aa[2];
a.store(aa);
return Vec2d(double(aa[0]), double(aa[1]));
}
// function to_double_limited: convert integer vector elements to double vector
// limited to abs(x) < 2^31
static inline Vec2d to_double_limited(Vec2q const & x) {
Vec4i compressed = permute4i<0,2,-256,-256>(Vec4i(x));
return _mm_cvtepi32_pd(compressed);
}
// function to_double_low: convert integer vector elements [0] and [1] to double vector
static inline Vec2d to_double_low(Vec4i const & a) {
return _mm_cvtepi32_pd(a);
}
// function to_double_high: convert integer vector elements [2] and [3] to double vector
static inline Vec2d to_double_high(Vec4i const & a) {
return to_double_low(_mm_srli_si128(a,8));
}
// function compress: convert two Vec2d to one Vec4f
static inline Vec4f compress (Vec2d const & low, Vec2d const & high) {
Vec4f t1 = _mm_cvtpd_ps(low);
Vec4f t2 = _mm_cvtpd_ps(high);
return blend4f<0,1,4,5> (t1, t2);
}
// Function extend_low : convert Vec4f vector elements [0] and [1] to Vec2d
static inline Vec2d extend_low (Vec4f const & a) {
return _mm_cvtps_pd(a);
}
// Function extend_high : convert Vec4f vector elements [2] and [3] to Vec2d
static inline Vec2d extend_high (Vec4f const & a) {
return _mm_cvtps_pd(_mm_movehl_ps(a,a));
}
// Fused multiply and add functions
// Multiply and add
static inline Vec2d mul_add(Vec2d const & a, Vec2d const & b, Vec2d const & c) {
#ifdef __FMA__
return _mm_fmadd_pd(a, b, c);
#elif defined (__FMA4__)
return _mm_macc_pd(a, b, c);
#else
return a * b + c;
#endif
}
// Multiply and subtract
static inline Vec2d mul_sub(Vec2d const & a, Vec2d const & b, Vec2d const & c) {
#ifdef __FMA__
return _mm_fmsub_pd(a, b, c);
#elif defined (__FMA4__)
return _mm_msub_pd(a, b, c);
#else
return a * b - c;
#endif
}
// Multiply and inverse subtract
static inline Vec2d nmul_add(Vec2d const & a, Vec2d const & b, Vec2d const & c) {
#ifdef __FMA__
return _mm_fnmadd_pd(a, b, c);
#elif defined (__FMA4__)
return _mm_nmacc_pd(a, b, c);
#else
return c - a * b;
#endif
}
// Multiply and subtract with extra precision on the intermediate calculations,
// even if FMA instructions not supported, using Veltkamp-Dekker split
static inline Vec2d mul_sub_x(Vec2d const & a, Vec2d const & b, Vec2d const & c) {
#ifdef __FMA__
return _mm_fmsub_pd(a, b, c);
#elif defined (__FMA4__)
return _mm_msub_pd(a, b, c);
#else
// calculate a * b - c with extra precision
Vec2q upper_mask = -(1LL << 27); // mask to remove lower 27 bits
Vec2d a_high = a & Vec2d(_mm_castsi128_pd(upper_mask));// split into high and low parts
Vec2d b_high = b & Vec2d(_mm_castsi128_pd(upper_mask));
Vec2d a_low = a - a_high;
Vec2d b_low = b - b_high;
Vec2d r1 = a_high * b_high; // this product is exact
Vec2d r2 = r1 - c; // subtract c from high product
Vec2d r3 = r2 + (a_high * b_low + b_high * a_low) + a_low * b_low; // add rest of product
return r3; // + ((r2 - r1) + c);
#endif
}
// Math functions using fast bit manipulation
// 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 Vec2q exponent(Vec2d const & a) {
Vec2uq t1 = _mm_castpd_si128(a); // reinterpret as 64-bit integer
Vec2uq t2 = t1 << 1; // shift out sign bit
Vec2uq t3 = t2 >> 53; // shift down logical to position 0
Vec2q t4 = Vec2q(t3) - 0x3FF; // subtract bias from exponent
return t4;
}
// 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 Vec2d fraction(Vec2d const & a) {
Vec2uq t1 = _mm_castpd_si128(a); // reinterpret as 64-bit integer
Vec2uq t2 = Vec2uq((t1 & 0x000FFFFFFFFFFFFFll) | 0x3FF0000000000000ll); // set exponent to 0 + bias
return _mm_castsi128_pd(t2);
}
// 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 Vec2d exp2(Vec2q const & n) {
Vec2q t1 = max(n, -0x3FF); // limit to allowed range
Vec2q t2 = min(t1, 0x400);
Vec2q t3 = t2 + 0x3FF; // add bias
Vec2q t4 = t3 << 52; // put exponent into position 52
return _mm_castsi128_pd(t4); // reinterpret as double
}
//static Vec2d exp2(Vec2d const & x); // defined in vectormath_exp.h
// 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(Vec2d(-0.0)) gives true, while Vec2d(-0.0) < Vec2d(0.0) gives false
static inline Vec2db sign_bit(Vec2d const & a) {
Vec2q t1 = _mm_castpd_si128(a); // reinterpret as 64-bit integer
Vec2q t2 = t1 >> 63; // extend sign bit
return _mm_castsi128_pd(t2); // reinterpret as 64-bit Boolean
}
// 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 Vec2d sign_combine(Vec2d const & a, Vec2d const & b) {
Vec2d signmask = _mm_castsi128_pd(constant4i<0,(int)0x80000000,0,(int)0x80000000>()); // -0.0
return a ^ (b & signmask);
}
// Function is_finite: gives true for elements that are normal, denormal or zero,
// false for INF and NAN
static inline Vec2db is_finite(Vec2d const & a) {
Vec2q t1 = _mm_castpd_si128(a); // reinterpret as integer
Vec2q t2 = t1 << 1; // shift out sign bit
Vec2q t3 = 0xFFE0000000000000ll; // exponent mask
Vec2qb t4 = Vec2q(t2 & t3) != t3; // exponent field is not all 1s
return t4;
}
// Function is_inf: gives true for elements that are +INF or -INF
// false for finite numbers and NAN
static inline Vec2db is_inf(Vec2d const & a) {
Vec2q t1 = _mm_castpd_si128(a); // reinterpret as integer
Vec2q t2 = t1 << 1; // shift out sign bit
return t2 == 0xFFE0000000000000ll; // exponent is all 1s, fraction is 0
}
// Function is_nan: gives true for elements that are +NAN or -NAN
// false for finite numbers and +/-INF
static inline Vec2db is_nan(Vec2d const & a) {
Vec2q t1 = _mm_castpd_si128(a); // reinterpret as integer
Vec2q t2 = t1 << 1; // shift out sign bit
Vec2q t3 = 0xFFE0000000000000ll; // exponent mask
Vec2q t4 = t2 & t3; // exponent
Vec2q t5 = _mm_andnot_si128(t3,t2);// fraction
return Vec2qb((t4==t3) & (t5!=0)); // exponent = all 1s and fraction != 0
}
// Function is_subnormal: gives true for elements that are subnormal (denormal)
// false for finite numbers, zero, NAN and INF
static inline Vec2db is_subnormal(Vec2d const & a) {
Vec2q t1 = _mm_castpd_si128(a); // reinterpret as 32-bit integer
Vec2q t2 = t1 << 1; // shift out sign bit
Vec2q t3 = 0xFFE0000000000000ll; // exponent mask
Vec2q t4 = t2 & t3; // exponent
Vec2q t5 = _mm_andnot_si128(t3,t2);// fraction
return Vec2qb((t4==0) & (t5!=0)); // exponent = 0 and fraction != 0
}
// Function is_zero_or_subnormal: gives true for elements that are zero or subnormal (denormal)
// false for finite numbers, NAN and INF
static inline Vec2db is_zero_or_subnormal(Vec2d const & a) {
Vec2q t = _mm_castpd_si128(a); // reinterpret as 32-bit integer
t &= 0x7FF0000000000000ll; // isolate exponent
return t == 0; // exponent = 0
}
// Function infinite2d: returns a vector where all elements are +INF
static inline Vec2d infinite2d() {
return _mm_castsi128_pd(_mm_setr_epi32(0,0x7FF00000,0,0x7FF00000));
}
// Function nan2d: returns a vector where all elements are +NAN (quiet)
static inline Vec2d nan2d(int n = 0x10) {
return _mm_castsi128_pd(_mm_setr_epi32(n, 0x7FF80000, n, 0x7FF80000));
}
/*****************************************************************************
*
* Functions for reinterpretation between vector types
*
*****************************************************************************/
static inline __m128i reinterpret_i (__m128i const & x) {
return x;
}
static inline __m128i reinterpret_i (__m128 const & x) {
return _mm_castps_si128(x);
}
static inline __m128i reinterpret_i (__m128d const & x) {
return _mm_castpd_si128(x);
}
static inline __m128 reinterpret_f (__m128i const & x) {
return _mm_castsi128_ps(x);
}
static inline __m128 reinterpret_f (__m128 const & x) {
return x;
}
static inline __m128 reinterpret_f (__m128d const & x) {
return _mm_castpd_ps(x);
}
static inline __m128d reinterpret_d (__m128i const & x) {
return _mm_castsi128_pd(x);
}
static inline __m128d reinterpret_d (__m128 const & x) {
return _mm_castps_pd(x);
}
static inline __m128d reinterpret_d (__m128d 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:
* Vec2d a(10., 11.); // a is (10, 11)
* Vec2d b, c;
* b = permute2d<1,1>(a); // b is (11, 11)
* c = permute2d<-1,0>(a); // c is ( 0, 10)
*
*
* 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 - 1 indicate an element from the first source
* vector and indexes 2 - 3 indicate an element from the second source vector.
* An index of -1 will generate zero.
*
*
* Example:
* Vec2d a(10., 11.); // a is (10, 11)
* Vec2d b(20., 21.); // b is (20, 21)
* Vec2d c;
* c = blend2d<0,3> (a,b); // c is (10, 21)
*
* A lot of the code here is metaprogramming aiming to find the instructions
* that best fit the template parameters and instruction set. The metacode
* will be reduced out to leave only a few vector instructions in release
* mode with optimization on.
*****************************************************************************/
// permute vector Vec2d
template <int i0, int i1>
static inline Vec2d permute2d(Vec2d const & a) {
// is shuffling needed
const bool do_shuffle = (i0 > 0) || (i1 != 1 && i1 >= 0);
// is zeroing needed
const bool do_zero = ((i0 | i1) < 0 && (i0 | i1) & 0x80);
if (do_zero && !do_shuffle) { // zeroing, not shuffling
if ((i0 & i1) < 0) return _mm_setzero_pd(); // zero everything
// zero some elements
__m128i mask1 = constant4i< -int(i0>=0), -int(i0>=0), -int(i1>=0), -int(i1>=0) >();
return _mm_and_pd(a,_mm_castsi128_pd(mask1)); // zero with AND mask
}
else if (do_shuffle && !do_zero) { // shuffling, not zeroing
return _mm_shuffle_pd(a, a, (i0&1) | (i1&1)<<1);
}
else if (do_shuffle && do_zero) { // shuffling and zeroing
// both shuffle and zero
if (i0 < 0 && i1 >= 0) { // zero low half, shuffle high half
return _mm_shuffle_pd(_mm_setzero_pd(), a, (i1 & 1) << 1);
}
if (i0 >= 0 && i1 < 0) { // shuffle low half, zero high half
return _mm_shuffle_pd(a, _mm_setzero_pd(), i0 & 1);
}
}
return a; // trivial case: do nothing
}
// blend vectors Vec2d
template <int i0, int i1>
static inline Vec2d blend2d(Vec2d const & a, Vec2d const & b) {
// Combine all the indexes into a single bitfield, with 8 bits for each
const int m1 = (i0 & 3) | (i1 & 3) << 8;
// Mask to zero out negative indexes
const int m2 = (i0 < 0 ? 0 : 0xFF) | (i1 < 0 ? 0 : 0xFF) << 8;
if ((m1 & 0x0202 & m2) == 0) {
// no elements from b, only elements from a and possibly zero
return permute2d <i0, i1> (a);
}
if (((m1^0x0202) & 0x0202 & m2) == 0) {
// no elements from a, only elements from b and possibly zero
return permute2d <i0 & ~2, i1 & ~2> (b);
}
// selecting from both a and b without zeroing
if ((i0 & 2) == 0) { // first element from a, second element from b
return _mm_shuffle_pd(a, b, (i0 & 1) | (i1 & 1) << 1);
}
else { // first element from b, second element from a
return _mm_shuffle_pd(b, a, (i0 & 1) | (i1 & 1) << 1);
}
}
// change signs on vectors Vec4f
// Each index i0 - i1 is 1 for changing sign on the corresponding element, 0 for no change
template <int i0, int i1>
static inline Vec2d change_sign(Vec2d const & a) {
if ((i0 | i1) == 0) return a;
__m128i mask = constant4i<0, i0 ? 0x80000000 : 0, 0, i1 ? 0x80000000 : 0> ();
return _mm_xor_pd(a, _mm_castsi128_pd(mask)); // flip sign bits
}
/*****************************************************************************
*
* Vector lookup functions
*
******************************************************************************
*
* These functions use vector elements as indexes into a table.
* The table is given as one or more vectors or as an array.
*
* This can be used for several purposes:
* - table lookup
* - permute or blend with variable indexes
* - blend from more than two sources
* - gather non-contiguous data
*
* An index out of range may produce any value - the actual value produced is
* implementation dependent and may be different for different instruction
* sets. An index out of range does not produce an error message or exception.
*
* Example:
* Vec4i a(2,0,0,3); // index a is ( 2, 0, 0, 3)
* Vec4f b(1.0f,1.1f,1.2f,1.3f); // table b is (1.0, 1.1, 1.2, 1.3)
* Vec4f c;
* c = lookup4 (a,b); // result c is (1.2, 1.0, 1.0, 1.3)
*
*****************************************************************************/
static inline Vec4f lookup4(Vec4i const & index, Vec4f const & table) {
#if INSTRSET >= 7 // AVX
return _mm_permutevar_ps(table, index);
#else
int32_t ii[4];
float tt[6];
table.store(tt); (index & 3).store(ii);
__m128 r01 = _mm_loadh_pi(_mm_load_ss(&tt[ii[0]]), (const __m64 *)&tt[ii[1]]);
__m128 r23 = _mm_loadh_pi(_mm_load_ss(&tt[ii[2]]), (const __m64 *)&tt[ii[3]]);
return _mm_shuffle_ps(r01, r23, 0x88);
#endif
}
static inline Vec4f lookup8(Vec4i const & index, Vec4f const & table0, Vec4f const & table1) {
#if INSTRSET >= 8 // AVX2
__m256 tt = _mm256_insertf128_ps(_mm256_castps128_ps256(table0), table1, 1); // combine tables
#if defined (_MSC_VER) && _MSC_VER < 1700 && ! defined(__INTEL_COMPILER)
// bug in MS VS 11 beta: operands in wrong order
__m128 r = _mm256_castps256_ps128(_mm256_permutevar8x32_ps(_mm256_castsi256_ps(_mm256_castsi128_si256(index)), _mm256_castps_si256(tt)));
r = _mm_and_ps(r,r); // fix another bug in VS 11 beta (would store r as 256 bits aligned by 16)
#elif defined (GCC_VERSION) && GCC_VERSION <= 40700 && !defined(__INTEL_COMPILER) && !defined(__clang__)
// Gcc 4.7.0 has wrong parameter type and operands in wrong order
__m128 r = _mm256_castps256_ps128(_mm256_permutevar8x32_ps(_mm256_castsi256_ps(_mm256_castsi128_si256(index)), tt));
#else
// no bug version
__m128 r = _mm256_castps256_ps128(_mm256_permutevar8x32_ps(tt, _mm256_castsi128_si256(index)));
#endif
return r;
#elif INSTRSET >= 7 // AVX
__m128 r0 = _mm_permutevar_ps(table0, index);
__m128 r1 = _mm_permutevar_ps(table1, index);
__m128i i4 = _mm_slli_epi32(index, 29);
return _mm_blendv_ps(r0, r1, _mm_castsi128_ps(i4));
#elif INSTRSET >= 5 // SSE4.1
Vec4f r0 = lookup4(index, table0);
Vec4f r1 = lookup4(index, table1);
__m128i i4 = _mm_slli_epi32(index, 29);
return _mm_blendv_ps(r0, r1, _mm_castsi128_ps(i4));
#else // SSE2
Vec4f r0 = lookup4(index, table0);
Vec4f r1 = lookup4(index, table1);
__m128i i4 = _mm_srai_epi32(_mm_slli_epi32(index, 29), 31);
return selectf(_mm_castsi128_ps(i4), r1, r0);
#endif
}
template <int n>
static inline Vec4f lookup(Vec4i const & index, float const * table) {
if (n <= 0) return 0.0f;
if (n <= 4) return lookup4(index, Vec4f().load(table));
if (n <= 8) {
#if INSTRSET >= 8 // AVX2
__m256 tt = _mm256_loadu_ps(table);
#if defined (_MSC_VER) && _MSC_VER < 1700 && ! defined(__INTEL_COMPILER)
// bug in MS VS 11 beta: operands in wrong order
__m128 r = _mm256_castps256_ps128(_mm256_permutevar8x32_ps(_mm256_castsi256_ps(_mm256_castsi128_si256(index)), _mm256_castps_si256(tt)));
r = _mm_and_ps(r,r); // fix another bug in VS 11 beta (would store r as 256 bits aligned by 16)
#elif defined (GCC_VERSION) && GCC_VERSION <= 40700 && !defined(__INTEL_COMPILER) && !defined(__clang__)
// Gcc 4.7.0 has wrong parameter type and operands in wrong order
__m128 r = _mm256_castps256_ps128(_mm256_permutevar8x32_ps(_mm256_castsi256_ps(_mm256_castsi128_si256(index)), tt));
#else
// no bug version
__m128 r = _mm256_castps256_ps128(_mm256_permutevar8x32_ps(tt, _mm256_castsi128_si256(index)));
#endif
return r;
#else // not AVX2
return lookup8(index, Vec4f().load(table), Vec4f().load(table+4));
#endif // INSTRSET
}
// n > 8. Limit index
Vec4ui index1;
if ((n & (n-1)) == 0) {
// n is a power of 2, make index modulo n
index1 = Vec4ui(index) & (n-1);
}
else {
// n is not a power of 2, limit to n-1
index1 = min(Vec4ui(index), n-1);
}
#if INSTRSET >= 8 // AVX2
return _mm_i32gather_ps(table, index1, 4);
#else
uint32_t ii[4]; index1.store(ii);
return Vec4f(table[ii[0]], table[ii[1]], table[ii[2]], table[ii[3]]);
#endif
}
static inline Vec2d lookup2(Vec2q const & index, Vec2d const & table) {
#if INSTRSET >= 7 // AVX
return _mm_permutevar_pd(table, index + index);
#else
int32_t ii[4];
double tt[2];
table.store(tt); (index & 1).store(ii);
return Vec2d(tt[ii[0]], tt[ii[2]]);
#endif
}
static inline Vec2d lookup4(Vec2q const & index, Vec2d const & table0, Vec2d const & table1) {
#if INSTRSET >= 7 // AVX
Vec2q index2 = index + index; // index << 1
__m128d r0 = _mm_permutevar_pd(table0, index2);
__m128d r1 = _mm_permutevar_pd(table1, index2);
__m128i i4 = _mm_slli_epi64(index, 62);
return _mm_blendv_pd(r0, r1, _mm_castsi128_pd(i4));
#else
int32_t ii[4];
double tt[4];
table0.store(tt); table1.store(tt + 2);
(index & 3).store(ii);
return Vec2d(tt[ii[0]], tt[ii[2]]);
#endif
}
template <int n>
static inline Vec2d lookup(Vec2q const & index, double const * table) {
if (n <= 0) return 0.0;
if (n <= 2) return lookup2(index, Vec2d().load(table));
#if INSTRSET < 8 // not AVX2
if (n <= 4) return lookup4(index, Vec2d().load(table), Vec2d().load(table + 2));
#endif
// Limit index
Vec2uq index1;
if ((n & (n-1)) == 0) {
// n is a power of 2, make index modulo n
index1 = Vec2uq(index) & (n-1);
}
else {
// n is not a power of 2, limit to n-1
index1 = min(Vec2uq(index), n-1);
}
#if INSTRSET >= 8 // AVX2
return _mm_i64gather_pd(table, index1, 8);
#else
uint32_t ii[4]; index1.store(ii);
return Vec2d(table[ii[0]], table[ii[2]]);
#endif
}
/*****************************************************************************
*
* Gather functions with fixed indexes
*
*****************************************************************************/
// Load elements from array a with indices i0, i1, i2, i3
template <int i0, int i1, int i2, int i3>
static inline Vec4f gather4f(void const * a) {
return reinterpret_f(gather4i<i0, i1, i2, i3>(a));
}
// Load elements from array a with indices i0, i1
template <int i0, int i1>
static inline Vec2d gather2d(void const * a) {
return reinterpret_d(gather2q<i0, i1>(a));
}
/*****************************************************************************
*
* Horizontal scan functions
*
*****************************************************************************/
// Get index to the first element that is true. Return -1 if all are false
static inline int horizontal_find_first(Vec4fb const & x) {
return horizontal_find_first(Vec4ib(x));
}
static inline int horizontal_find_first(Vec2db const & x) {
return horizontal_find_first(Vec2qb(x));
}
// Count the number of elements that are true
static inline uint32_t horizontal_count(Vec4fb const & x) {
return horizontal_count(Vec4ib(x));
}
static inline uint32_t horizontal_count(Vec2db const & x) {
return horizontal_count(Vec2qb(x));
}
/*****************************************************************************
*
* Boolean <-> bitfield conversion functions
*
*****************************************************************************/
// to_bits: convert boolean vector to integer bitfield
static inline uint8_t to_bits(Vec4fb const & x) {
return to_bits(Vec4ib(x));
}
// to_Vec4fb: convert integer bitfield to boolean vector
static inline Vec4fb to_Vec4fb(uint8_t x) {
return Vec4fb(to_Vec4ib(x));
}
// to_bits: convert boolean vector to integer bitfield
static inline uint8_t to_bits(Vec2db const & x) {
return to_bits(Vec2qb(x));
}
// to_Vec2db: convert integer bitfield to boolean vector
static inline Vec2db to_Vec2db(uint8_t x) {
return Vec2db(to_Vec2qb(x));
}
#endif // VECTORF128_H
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