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Removed vectorclass library [#METR-20000].

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Alexey Milovidov 2016-03-30 23:27:50 +03:00
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110
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change log for vectorclass.zip
------------------------------
2015-10-24 version 1.16
* workaround for problem in Clang compiler extended to version 3.09 because not fixed yet by Clang
(vectorf128.h line 134)
* recognize problem with Apple version of Clang reporting wrong version number
* remove various minor problems with Clang
* function pow(vector, int) modified to strengthen type checking and avoid compiler warnings
* manual discusses dynamic allocation of arrays of vectors
* various minor changes
2015-10-17 version 1.15
* added files ranvec1.h and ranvec1.cpp for random number generator
* constructors to make boolean vectors from their elements
* constructors and = operators to broadcast boolean scalar into boolean vectors
* various lookup functions improved
* operators &, |, ^, ~, etc. defined for various boolean vectors to avoid converson
to integer vectors
* nmul_add functions
* mul_add etc. moved to main header files
* explicit fused multiply-and-add used in math functions to improve performance
on compilers that don't automatically insert FMA
2014-07-24 version 1.14
* support for AVX-512f instruction set and 512-bit vectors:
Vec16i, Vec16ui, Vec8q, Vec8uq, Vec16f, Vec8d, and corresponding boolean vectors
* new define MAX_VECTOR_SIZE, valid values are 128, 256 and 512
* added hyperbolic functions sinh, cosh, tanh, asinh, acosh, atanh
* size() member function on all vector classes returns the number of elements
* functions for conversion between boolean vectors and integer bitfields
* extracting an element from a boolean vector now returns a bool, not an int
* improved precision in exp2 and exp10 functions
* various bug fixes
2014-05-11 version 1.13
* pow function improved
* mul_add, mul_sub, mul_sub_x functions
* propagation of error codes through nan_code function
* "denormal" renamed to "subnormal" everywhere, in accordance with IEEE 754-2008 standard
2014-04-20 version 1.12
* inline implementation of mathematical functions added (vectormath_exp.h vectormath_trig.h vectormath_common.h)
* vectormath.h renamed to vectormath_lib.h because a new alternative is added
* gather functions with constant indexes
* function sign_combine
* function pow_const(vector, const int)
* function pow_ratio(vector, const int, const int)
* functions horizontal_find_first, horizontal_count
* function recipr_sqrt removed
* functions round_to_int64_limited, truncate_to_int64_limited, to_double_limited
* function cubic_root renamed to cbrt
* function atan(vector,vector) renamed to atan2
* function if_mul
* function Vec4i round_to_int(Vec2d)
* operator & (float vector, boolean vector)
* operator &= (int vector, int vector)
* removed constructor Vec128b(int) and Vec256b(int) to avoid implicit conversion
* removed signalling nan function
* minor improvements in various blend and lookup functions
2014-03-01 version 1.11
* fixed missing unsigned operators >>= in vectori256.h
2013-10-04 version 1.10
* clear distinction between boolean vectors and integer vectors for the sake of
compatibility with mask registers in forthcoming AVX512 instruction set
* added function if_add
* tentative support for clang version 3.3 with workaround for bugs
* remove ambiguity for builtin m128i operator == in clang compiler.
* problems in clang compiler, bug reports filed at clang
(http://llvm.org/bugs/show_bug.cgi?id=17164, 17312)
* instrset.h fixes problem with macros named min and max in MS windows.h
* workaround problem in MS Visual Studio 11.0. Bug report 735861 and 804274
* minor bug fixes
2013-03-31 version 1.03 beta
* bug fix for Vec2d cos (Vec2d const & x), VECTORMATH = 1
2012-08-01 version 1.02 beta
* added file vector3d.h for 3-dimensional vectors
* added file complexvec.h for complex numbers and complex vectors
* added file quaternion.h for quaternions
* added function change_sign for floating point vectors
* added operators +, -, *, / between floating point vectors and scalars to remove overloading ambiguity
2012-07-08 version 1.01 beta
* added file decimal.h with Number <-> string conversion functions:
bin2bcd, bin2ascii, bin2hex_ascii, ascii2bin
* added andnot function for boolean vectors
* added functions shift_bytes_up and shift_bytes_down
* added operators for unsigned integer vector classes: >>=, &, &&, |, ||, ^, ~
* inteldispatchpatch.cpp removed. Use asmlib instead (www.agner.org/optimize/#asmlib)
* prefix ++ and -- operators now return a reference, postfix operators return a value
* various improvements in permute and blend functions
* minor improvement in abs function
* added version number to VECTORCLASS_H
2012-05-30 version 1.00 beta
* first public release

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/************************* dispatch_example.cpp ****************************
| Author: Agner Fog
| Date created: 2012-05-30
| Last modified: 2014-07-23
| Version: 1.14
| Project: vector classes
| Description:
| Example of CPU dispatching.
|
| # Example of compiling this with GCC compiler:
| # Compile dispatch_example.cpp five times for different instruction sets:
| g++ -O3 -msse2 -c dispatch_example.cpp -od2.o
| g++ -O3 -msse4.1 -c dispatch_example.cpp -od5.o
| g++ -O3 -mavx -c dispatch_example.cpp -od7.o
| g++ -O3 -mavx2 -c dispatch_example.cpp -od8.o
| g++ -O3 -mavx512f -c dispatch_example.cpp -od9.o
| g++ -O3 -msse2 -otest instrset_detect.cpp d2.o d5.o d7.o d8.o d9.o
| ./test
|
| (c) Copyright 2012 - 2014 GNU General Public License http://www.gnu.org/licenses
\*****************************************************************************/
#include <stdio.h>
#define MAX_VECTOR_SIZE 512
#include "vectorclass.h"
// define function type (change this to fit your purpose. Should not contain vector types)
typedef float MyFuncType(float*);
// function prototypes for each version
MyFuncType myfunc, myfunc_SSE2, myfunc_SSE41, myfunc_AVX, myfunc_AVX2, myfunc_AVX512, myfunc_dispatch;
// Define function name depending on which instruction set we compile for
#if INSTRSET == 2 // SSE2
#define FUNCNAME myfunc_SSE2
#elif INSTRSET == 5 // SSE4.1
#define FUNCNAME myfunc_SSE41
#elif INSTRSET == 7 // AVX
#define FUNCNAME myfunc_AVX
#elif INSTRSET == 8 // AVX2
#define FUNCNAME myfunc_AVX2
#elif INSTRSET == 9 // AVX512
#define FUNCNAME myfunc_AVX512
#endif
// specific version of the function. Compile once for each version
float FUNCNAME (float * f) {
Vec16f a; // vector of 16 floats
a.load(f); // load array into vector
return horizontal_add(a); // return sum of 16 elements
}
#if INSTRSET == 2
// make dispatcher in only the lowest of the compiled versions
// Function pointer initially points to the dispatcher.
// After first call it points to the selected version
MyFuncType * myfunc_pointer = &myfunc_dispatch; // function pointer
// Dispatcher
float myfunc_dispatch(float * f) {
int iset = instrset_detect(); // Detect supported instruction set
if (iset >= 9) myfunc_pointer = &myfunc_AVX512; // AVX512 version
else if (iset >= 8) myfunc_pointer = &myfunc_AVX2; // AVX2 version
else if (iset >= 7) myfunc_pointer = &myfunc_AVX; // AVX version
else if (iset >= 5) myfunc_pointer = &myfunc_SSE41; // SSE4.1 version
else if (iset >= 2) myfunc_pointer = &myfunc_SSE2; // SSE2 version
else {
// Error: lowest instruction set not supported (put your own error message here:)
fprintf(stderr, "\nError: Instruction set SSE2 not supported on this computer");
return 0.f;
}
// continue in dispatched version
return (*myfunc_pointer)(f);
}
// Entry to dispatched function call
inline float myfunc(float * f) {
return (*myfunc_pointer)(f); // go to dispatched version
}
// Example: main calls myfunc
int main(int argc, char* argv[])
{
float a[16]={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}; // array of 16 floats
float sum = myfunc(a); // call function with dispatching
printf("\nsum = %8.3f \n", sum); // print result
return 0;
}
#endif // INSTRSET == 2

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/**************************** instrset.h **********************************
* Author: Agner Fog
* Date created: 2012-05-30
* Last modified: 2014-10-22
* Version: 1.16
* Project: vector classes
* Description:
* Header file for various compiler-specific tasks and other common tasks to
* vector class library:
* > selects the supported instruction set
* > defines integer types
* > defines compiler version macros
* > undefines certain macros that prevent function overloading
* > defines template class to represent compile-time integer constant
* > defines template for compile-time error messages
*
* (c) Copyright 2012 - 2014 GNU General Public License www.gnu.org/licenses
******************************************************************************/
#ifndef INSTRSET_H
#define INSTRSET_H 116
// Detect 64 bit mode
#if (defined(_M_AMD64) || defined(_M_X64) || defined(__amd64) ) && ! defined(__x86_64__)
#define __x86_64__ 1 // There are many different macros for this, decide on only one
#endif
// Find instruction set from compiler macros if INSTRSET not defined
// Note: Microsoft compilers do not define these macros automatically
#ifndef INSTRSET
#if defined ( __AVX512F__ ) || defined ( __AVX512__ ) // || defined ( __AVX512ER__ )
#define INSTRSET 9
#elif defined ( __AVX2__ )
#define INSTRSET 8
#elif defined ( __AVX__ )
#define INSTRSET 7
#elif defined ( __SSE4_2__ )
#define INSTRSET 6
#elif defined ( __SSE4_1__ )
#define INSTRSET 5
#elif defined ( __SSSE3__ )
#define INSTRSET 4
#elif defined ( __SSE3__ )
#define INSTRSET 3
#elif defined ( __SSE2__ ) || defined ( __x86_64__ )
#define INSTRSET 2
#elif defined ( __SSE__ )
#define INSTRSET 1
#elif defined ( _M_IX86_FP ) // Defined in MS compiler. 1: SSE, 2: SSE2
#define INSTRSET _M_IX86_FP
#else
#define INSTRSET 0
#endif // instruction set defines
#endif // INSTRSET
// Include the appropriate header file for intrinsic functions
#if INSTRSET > 7 // AVX2 and later
#if defined (__GNUC__) && ! defined (__INTEL_COMPILER)
#include <x86intrin.h> // x86intrin.h includes header files for whatever instruction
// sets are specified on the compiler command line, such as:
// xopintrin.h, fma4intrin.h
#else
#include <immintrin.h> // MS version of immintrin.h covers AVX, AVX2 and FMA3
#endif // __GNUC__
#elif INSTRSET == 7
#include <immintrin.h> // AVX
#elif INSTRSET == 6
#include <nmmintrin.h> // SSE4.2
#elif INSTRSET == 5
#include <smmintrin.h> // SSE4.1
#elif INSTRSET == 4
#include <tmmintrin.h> // SSSE3
#elif INSTRSET == 3
#include <pmmintrin.h> // SSE3
#elif INSTRSET == 2
#include <emmintrin.h> // SSE2
#elif INSTRSET == 1
#include <xmmintrin.h> // SSE
#endif // INSTRSET
#if INSTRSET >= 8 && !defined(__FMA__)
// Assume that all processors that have AVX2 also have FMA3
#if defined (__GNUC__) && ! defined (__INTEL_COMPILER) && ! defined (__clang__)
// Prevent error message in g++ when using FMA intrinsics with avx2:
#pragma message "It is recommended to specify also option -mfma when using -mavx2 or higher"
#else
#define __FMA__ 1
#endif
#endif
// AMD instruction sets
#if defined (__XOP__) || defined (__FMA4__)
#ifdef __GNUC__
#include <x86intrin.h> // AMD XOP (Gnu)
#else
#include <ammintrin.h> // AMD XOP (Microsoft)
#endif // __GNUC__
#elif defined (__SSE4A__) // AMD SSE4A
#include <ammintrin.h>
#endif // __XOP__
// FMA3 instruction set
#if defined (__FMA__) && (defined(__GNUC__) || defined(__clang__)) && ! defined (__INTEL_COMPILER)
#include <fmaintrin.h>
#endif // __FMA__
// FMA4 instruction set
#if defined (__FMA4__) && (defined(__GNUC__) || defined(__clang__))
#include <fma4intrin.h> // must have both x86intrin.h and fma4intrin.h, don't know why
#endif // __FMA4__
// Define integer types with known size
#if defined(__GNUC__) || defined(__clang__) || (defined(_MSC_VER) && _MSC_VER >= 1600)
// Compilers supporting C99 or C++0x have stdint.h defining these integer types
#include <stdint.h>
#elif defined(_MSC_VER)
// Older Microsoft compilers have their own definitions
typedef signed __int8 int8_t;
typedef unsigned __int8 uint8_t;
typedef signed __int16 int16_t;
typedef unsigned __int16 uint16_t;
typedef signed __int32 int32_t;
typedef unsigned __int32 uint32_t;
typedef signed __int64 int64_t;
typedef unsigned __int64 uint64_t;
#ifndef _INTPTR_T_DEFINED
#define _INTPTR_T_DEFINED
#ifdef __x86_64__
typedef int64_t intptr_t;
#else
typedef int32_t intptr_t;
#endif
#endif
#else
// This works with most compilers
typedef signed char int8_t;
typedef unsigned char uint8_t;
typedef signed short int int16_t;
typedef unsigned short int uint16_t;
typedef signed int int32_t;
typedef unsigned int uint32_t;
typedef long long int64_t;
typedef unsigned long long uint64_t;
#ifdef __x86_64__
typedef int64_t intptr_t;
#else
typedef int32_t intptr_t;
#endif
#endif
#include <stdlib.h> // define abs(int)
#ifdef _MSC_VER // Microsoft compiler or compatible Intel compiler
#include <intrin.h> // define _BitScanReverse(int), __cpuid(int[4],int), _xgetbv(int)
#endif // _MSC_VER
// functions in instrset_detect.cpp
int instrset_detect(void); // tells which instruction sets are supported
bool hasFMA3(void); // true if FMA3 instructions supported
bool hasFMA4(void); // true if FMA4 instructions supported
bool hasXOP (void); // true if XOP instructions supported
// GCC version
#if defined(__GNUC__) && !defined (GCC_VERSION) && !defined (__clang__)
#define GCC_VERSION ((__GNUC__) * 10000 + (__GNUC_MINOR__) * 100 + (__GNUC_PATCHLEVEL__))
#endif
// Clang version
#if defined (__clang__)
#define CLANG_VERSION ((__clang_major__) * 10000 + (__clang_minor__) * 100 + (__clang_patchlevel__))
// Problem: The version number is not consistent across platforms
// http://llvm.org/bugs/show_bug.cgi?id=12643
// Apple bug 18746972
#endif
// Fix problem with macros named min and max in WinDef.h
#ifdef _MSC_VER
#if defined (_WINDEF_) && defined(min) && defined(max)
#undef min
#undef max
#endif
#ifndef NOMINMAX
#define NOMINMAX
#endif
#endif
// Template class to represent compile-time integer constant
template <int32_t n> class Const_int_t {}; // represent compile-time signed integer constant
template <uint32_t n> class Const_uint_t {}; // represent compile-time unsigned integer constant
#define const_int(n) (Const_int_t <n>()) // n must be compile-time integer constant
#define const_uint(n) (Const_uint_t<n>()) // n must be compile-time unsigned integer constant
// Template for compile-time error messages
template <bool> class Static_error_check {
public: Static_error_check(){};
};
template <> class Static_error_check<false> { // generate compile-time error if false
private: Static_error_check(){};
};
#endif // INSTRSET_H

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/************************** instrset_detect.cpp ****************************
| Author: Agner Fog
| Date created: 2012-05-30
| Last modified: 2014-07-23
| Version: 1.14
| Project: vector classes
| Description:
| Functions for checking which instruction sets are supported.
|
| (c) Copyright 2012 - 2014 GNU General Public License http://www.gnu.org/licenses
\*****************************************************************************/
#include "instrset.h"
// Define interface to cpuid instruction.
// input: eax = functionnumber, ecx = 0
// output: eax = output[0], ebx = output[1], ecx = output[2], edx = output[3]
static inline void cpuid (int output[4], int functionnumber) {
#if defined (_MSC_VER) || defined (__INTEL_COMPILER) // Microsoft or Intel compiler, intrin.h included
__cpuidex(output, functionnumber, 0); // intrinsic function for CPUID
#elif defined(__GNUC__) || defined(__clang__) // use inline assembly, Gnu/AT&T syntax
int a, b, c, d;
__asm("cpuid" : "=a"(a),"=b"(b),"=c"(c),"=d"(d) : "a"(functionnumber),"c"(0) : );
output[0] = a;
output[1] = b;
output[2] = c;
output[3] = d;
#else // unknown platform. try inline assembly with masm/intel syntax
__asm {
mov eax, functionnumber
xor ecx, ecx
cpuid;
mov esi, output
mov [esi], eax
mov [esi+4], ebx
mov [esi+8], ecx
mov [esi+12], edx
}
#endif
}
// Define interface to xgetbv instruction
static inline int64_t xgetbv (int ctr) {
#if (defined (_MSC_FULL_VER) && _MSC_FULL_VER >= 160040000) || (defined (__INTEL_COMPILER) && __INTEL_COMPILER >= 1200) // Microsoft or Intel compiler supporting _xgetbv intrinsic
return _xgetbv(ctr); // intrinsic function for XGETBV
#elif defined(__GNUC__) // use inline assembly, Gnu/AT&T syntax
uint32_t a, d;
__asm("xgetbv" : "=a"(a),"=d"(d) : "c"(ctr) : );
return a | (uint64_t(d) << 32);
#else // #elif defined (_WIN32) // other compiler. try inline assembly with masm/intel/MS syntax
uint32_t a, d;
__asm {
mov ecx, ctr
_emit 0x0f
_emit 0x01
_emit 0xd0 ; // xgetbv
mov a, eax
mov d, edx
}
return a | (uint64_t(d) << 32);
#endif
}
/* find supported instruction set
return value:
0 = 80386 instruction set
1 or above = SSE (XMM) supported by CPU (not testing for O.S. support)
2 or above = SSE2
3 or above = SSE3
4 or above = Supplementary SSE3 (SSSE3)
5 or above = SSE4.1
6 or above = SSE4.2
7 or above = AVX supported by CPU and operating system
8 or above = AVX2
9 or above = AVX512F
*/
int instrset_detect(void) {
static int iset = -1; // remember value for next call
if (iset >= 0) {
return iset; // called before
}
iset = 0; // default value
int abcd[4] = {0,0,0,0}; // cpuid results
cpuid(abcd, 0); // call cpuid function 0
if (abcd[0] == 0) return iset; // no further cpuid function supported
cpuid(abcd, 1); // call cpuid function 1 for feature flags
if ((abcd[3] & (1 << 0)) == 0) return iset; // no floating point
if ((abcd[3] & (1 << 23)) == 0) return iset; // no MMX
if ((abcd[3] & (1 << 15)) == 0) return iset; // no conditional move
if ((abcd[3] & (1 << 24)) == 0) return iset; // no FXSAVE
if ((abcd[3] & (1 << 25)) == 0) return iset; // no SSE
iset = 1; // 1: SSE supported
if ((abcd[3] & (1 << 26)) == 0) return iset; // no SSE2
iset = 2; // 2: SSE2 supported
if ((abcd[2] & (1 << 0)) == 0) return iset; // no SSE3
iset = 3; // 3: SSE3 supported
if ((abcd[2] & (1 << 9)) == 0) return iset; // no SSSE3
iset = 4; // 4: SSSE3 supported
if ((abcd[2] & (1 << 19)) == 0) return iset; // no SSE4.1
iset = 5; // 5: SSE4.1 supported
if ((abcd[2] & (1 << 23)) == 0) return iset; // no POPCNT
if ((abcd[2] & (1 << 20)) == 0) return iset; // no SSE4.2
iset = 6; // 6: SSE4.2 supported
if ((abcd[2] & (1 << 27)) == 0) return iset; // no OSXSAVE
if ((xgetbv(0) & 6) != 6) return iset; // AVX not enabled in O.S.
if ((abcd[2] & (1 << 28)) == 0) return iset; // no AVX
iset = 7; // 7: AVX supported
cpuid(abcd, 7); // call cpuid leaf 7 for feature flags
if ((abcd[1] & (1 << 5)) == 0) return iset; // no AVX2
iset = 8; // 8: AVX2 supported
cpuid(abcd, 0xD); // call cpuid leaf 0xD for feature flags
if ((abcd[0] & 0x60) != 0x60) return iset; // no AVX512
iset = 9; // 8: AVX512F supported
return iset;
}
// detect if CPU supports the FMA3 instruction set
bool hasFMA3(void) {
if (instrset_detect() < 7) return false; // must have AVX
int abcd[4]; // cpuid results
cpuid(abcd, 1); // call cpuid function 1
return ((abcd[2] & (1 << 12)) != 0); // ecx bit 12 indicates FMA3
}
// detect if CPU supports the FMA4 instruction set
bool hasFMA4(void) {
if (instrset_detect() < 7) return false; // must have AVX
int abcd[4]; // cpuid results
cpuid(abcd, 0x80000001); // call cpuid function 0x80000001
return ((abcd[2] & (1 << 16)) != 0); // ecx bit 16 indicates FMA4
}
// detect if CPU supports the XOP instruction set
bool hasXOP(void) {
if (instrset_detect() < 7) return false; // must have AVX
int abcd[4]; // cpuid results
cpuid(abcd, 0x80000001); // call cpuid function 0x80000001
return ((abcd[2] & (1 << 11)) != 0); // ecx bit 11 indicates XOP
}

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GNU GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
Preamble
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The licenses for most software and other practical works are designed
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Developers that use the GNU GPL protect your rights with two steps:
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/**************************** vectorclass.h ********************************
* Author: Agner Fog
* Date created: 2012-05-30
* Last modified: 2014-10-24
* Version: 1.16
* Project: vector classes
* Description:
* Header file defining vector classes as interface to intrinsic functions
* in x86 microprocessors with SSE2 and later instruction sets up to AVX512.
*
* Instructions:
* Use Gnu, Clang, 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.
*
* Each vector object is represented internally in the CPU as a vector
* register with 128, 256 or 512 bits.
*
* This header file includes the appropriate header files depending on the
* supported instruction set
*
* For detailed instructions, see VectorClass.pdf
*
* (c) Copyright 2012 - 2014 GNU General Public License www.gnu.org/licenses
******************************************************************************/
#ifndef VECTORCLASS_H
#define VECTORCLASS_H 116
// Maximum vector size, bits. Allowed values are 128, 256, 512
#ifndef MAX_VECTOR_SIZE
#define MAX_VECTOR_SIZE 256
#endif
#include "instrset.h" // Select supported instruction set
#if INSTRSET < 2 // SSE2 required
#error Please compile for the SSE2 instruction set or higher
#else
#include "vectori128.h" // 128-bit integer vectors
#include "vectorf128.h" // 128-bit floating point vectors
#if MAX_VECTOR_SIZE >= 256
#if INSTRSET >= 8
#include "vectori256.h" // 256-bit integer vectors, requires AVX2 instruction set
#else
#include "vectori256e.h" // 256-bit integer vectors, emulated
#endif // INSTRSET >= 8
#if INSTRSET >= 7
#include "vectorf256.h" // 256-bit floating point vectors, requires AVX instruction set
#else
#include "vectorf256e.h" // 256-bit floating point vectors, emulated
#endif // INSTRSET >= 7
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
#if INSTRSET >= 9
#include "vectori512.h" // 512-bit integer vectors, requires AVX512 instruction set
#include "vectorf512.h" // 512-bit floating point vectors, requires AVX512 instruction set
#else
#include "vectori512e.h" // 512-bit integer vectors, emulated
#include "vectorf512e.h" // 512-bit floating point vectors, emulated
#endif // INSTRSET >= 9
#endif // MAX_VECTOR_SIZE >= 512
#endif // INSTRSET < 2
#endif // VECTORCLASS_H

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/*************************** vectormath_common.h ****************************
* Author: Agner Fog
* Date created: 2014-04-18
* Last modified: 2014-10-16
* Version: 1.16
* Project: vector classes
* Description:
* Header file containing common code for inline version of mathematical functions.
*
* Theory, methods and inspiration based partially on these sources:
* > Moshier, Stephen Lloyd Baluk: Methods and programs for mathematical functions.
* Ellis Horwood, 1989.
* > VDT library developed on CERN by Danilo Piparo, Thomas Hauth and
* Vincenzo Innocente, 2012, https://svnweb.cern.ch/trac/vdt
* > Cephes math library by Stephen L. Moshier 1992,
* http://www.netlib.org/cephes/
*
* Calculation methods:
* Some functions are using Padé approximations f(x) = P(x)/Q(x)
* Most single precision functions are using Taylor expansions
*
* For detailed instructions, see VectorClass.pdf
*
* (c) Copyright 2014 GNU General Public License http://www.gnu.org/licenses
******************************************************************************/
#ifndef VECTORMATH_COMMON_H
#define VECTORMATH_COMMON_H 1
#ifdef VECTORMATH_LIB_H
#error conflicting header files: vectormath_lib.h for external math functions, other vectormath_xxx.h for inline math functions
#endif
#include <math.h>
#include "vectorclass.h"
/******************************************************************************
define mathematical constants
******************************************************************************/
#define VM_PI 3.14159265358979323846 // pi
#define VM_PI_2 1.57079632679489661923 // pi / 2
#define VM_PI_4 0.785398163397448309616 // pi / 4
#define VM_SQRT2 1.41421356237309504880 // sqrt(2)
#define VM_LOG2E 1.44269504088896340736 // 1/log(2)
#define VM_LOG10E 0.434294481903251827651 // 1/log(10)
#define VM_LN2 0.693147180559945309417 // log(2)
#define VM_LN10 2.30258509299404568402 // log(10)
#define VM_SMALLEST_NORMAL 2.2250738585072014E-308 // smallest normal number, double
#define VM_SMALLEST_NORMALF 1.17549435E-38f // smallest normal number, float
/******************************************************************************
templates for producing infinite and nan in desired vector type
******************************************************************************/
template <class VTYPE>
static inline VTYPE infinite_vec();
template <>
inline Vec2d infinite_vec<Vec2d>() {
return infinite2d();
}
template <>
inline Vec4f infinite_vec<Vec4f>() {
return infinite4f();
}
#if MAX_VECTOR_SIZE >= 256
template <>
inline Vec4d infinite_vec<Vec4d>() {
return infinite4d();
}
template <>
inline Vec8f infinite_vec<Vec8f>() {
return infinite8f();
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
template <>
inline Vec8d infinite_vec<Vec8d>() {
return infinite8d();
}
template <>
inline Vec16f infinite_vec<Vec16f>() {
return infinite16f();
}
#endif // MAX_VECTOR_SIZE >= 512
// template for producing quiet NAN
template <class VTYPE>
static inline VTYPE nan_vec(int n = 0x100);
template <>
inline Vec2d nan_vec<Vec2d>(int n) {
return nan2d(n);
}
template <>
inline Vec4f nan_vec<Vec4f>(int n) {
return nan4f(n);
}
#if MAX_VECTOR_SIZE >= 256
template <>
inline Vec4d nan_vec<Vec4d>(int n) {
return nan4d(n);
}
template <>
inline Vec8f nan_vec<Vec8f>(int n) {
return nan8f(n);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
template <>
inline Vec8d nan_vec<Vec8d>(int n) {
return nan8d(n);
}
template <>
inline Vec16f nan_vec<Vec16f>(int n) {
return nan16f(n);
}
#endif // MAX_VECTOR_SIZE >= 512
// Define NAN trace values
#define NAN_LOG 0x101 // logarithm for x<0
#define NAN_POW 0x102 // negative number raised to non-integer power
#define NAN_HYP 0x104 // acosh for x<1 and atanh for abs(x)>1
/******************************************************************************
templates for polynomials
Using Estrin's scheme to make shorter dependency chains and use FMA, starting
longest dependency chains first.
******************************************************************************/
// template <typedef VECTYPE, typedef CTYPE>
template <class VTYPE, class CTYPE>
static inline VTYPE polynomial_2(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2) {
// calculates polynomial c2*x^2 + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
//return = x2 * c2 + (x * c1 + c0);
return mul_add(x2, c2, mul_add(x, c1, c0));
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_3(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2, CTYPE c3) {
// calculates polynomial c3*x^3 + c2*x^2 + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
//return (c2 + c3*x)*x2 + (c1*x + c0);
return mul_add(mul_add(c3,x,c2), x2, mul_add(c1,x,c0));
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_4(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2, CTYPE c3, CTYPE c4) {
// calculates polynomial c4*x^4 + c3*x^3 + c2*x^2 + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
VTYPE x4 = x2 * x2;
//return (c2+c3*x)*x2 + ((c0+c1*x) + c4*x4);
return mul_add(mul_add(c3,x,c2), x2, mul_add(c1,x,c0) + c4*x4);
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_4n(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2, CTYPE c3) {
// calculates polynomial 1*x^4 + c3*x^3 + c2*x^2 + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
VTYPE x4 = x2 * x2;
//return (c2+c3*x)*x2 + ((c0+c1*x) + x4);
return mul_add(mul_add(c3,x,c2), x2, mul_add(c1,x,c0) + x4);
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_5(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2, CTYPE c3, CTYPE c4, CTYPE c5) {
// calculates polynomial c5*x^5 + c4*x^4 + c3*x^3 + c2*x^2 + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
VTYPE x4 = x2 * x2;
//return (c2+c3*x)*x2 + ((c4+c5*x)*x4 + (c0+c1*x));
return mul_add(mul_add(c3,x,c2), x2, mul_add(mul_add(c5,x,c4), x4, mul_add(c1,x,c0)));
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_5n(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2, CTYPE c3, CTYPE c4) {
// calculates polynomial 1*x^5 + c4*x^4 + c3*x^3 + c2*x^2 + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
VTYPE x4 = x2 * x2;
//return (c2+c3*x)*x2 + ((c4+x)*x4 + (c0+c1*x));
return mul_add( mul_add(c3,x,c2), x2, mul_add(c4+x,x4,mul_add(c1,x,c0)) );
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_6(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2, CTYPE c3, CTYPE c4, CTYPE c5, CTYPE c6) {
// calculates polynomial c6*x^6 + c5*x^5 + c4*x^4 + c3*x^3 + c2*x^2 + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
VTYPE x4 = x2 * x2;
//return (c4+c5*x+c6*x2)*x4 + ((c2+c3*x)*x2 + (c0+c1*x));
return mul_add(mul_add(c6,x2,mul_add(c5,x,c4)), x4, mul_add(mul_add(c3,x,c2), x2, mul_add(c1,x,c0)));
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_6n(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2, CTYPE c3, CTYPE c4, CTYPE c5) {
// calculates polynomial 1*x^6 + c5*x^5 + c4*x^4 + c3*x^3 + c2*x^2 + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
VTYPE x4 = x2 * x2;
//return (c4+c5*x+x2)*x4 + ((c2+c3*x)*x2 + (c0+c1*x));
return mul_add(mul_add(c5,x,c4+x2), x4, mul_add(mul_add(c3,x,c2), x2, mul_add(c1,x,c0)));
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_7(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2, CTYPE c3, CTYPE c4, CTYPE c5, CTYPE c6, CTYPE c7) {
// calculates polynomial c7*x^7 + c6*x^6 + c5*x^5 + c4*x^4 + c3*x^3 + c2*x^2 + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
VTYPE x4 = x2 * x2;
//return ((c6+c7*x)*x2 + (c4+c5*x))*x4 + ((c2+c3*x)*x2 + (c0+c1*x));
return mul_add(mul_add(mul_add(c7,x,c6), x2, mul_add(c5,x,c4)), x4, mul_add(mul_add(c3,x,c2), x2, mul_add(c1,x,c0)));
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_8(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2, CTYPE c3, CTYPE c4, CTYPE c5, CTYPE c6, CTYPE c7, CTYPE c8) {
// calculates polynomial c8*x^8 + c7*x^7 + c6*x^6 + c5*x^5 + c4*x^4 + c3*x^3 + c2*x^2 + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
VTYPE x4 = x2 * x2;
VTYPE x8 = x4 * x4;
//return ((c6+c7*x)*x2 + (c4+c5*x))*x4 + (c8*x8 + (c2+c3*x)*x2 + (c0+c1*x));
return mul_add(mul_add(mul_add(c7,x,c6), x2, mul_add(c5,x,c4)), x4,
mul_add(mul_add(c3,x,c2), x2, mul_add(c1,x,c0)+c8*x8));
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_9(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2, CTYPE c3, CTYPE c4, CTYPE c5, CTYPE c6, CTYPE c7, CTYPE c8, CTYPE c9) {
// calculates polynomial c9*x^9 + c8*x^8 + c7*x^7 + c6*x^6 + c5*x^5 + c4*x^4 + c3*x^3 + c2*x^2 + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
VTYPE x4 = x2 * x2;
VTYPE x8 = x4 * x4;
//return (((c6+c7*x)*x2 + (c4+c5*x))*x4 + (c8+c9*x)*x8) + ((c2+c3*x)*x2 + (c0+c1*x));
return mul_add(mul_add(c9,x,c8), x8, mul_add(
mul_add(mul_add(c7,x,c6), x2, mul_add(c5,x,c4)), x4,
mul_add(mul_add(c3,x,c2), x2, mul_add(c1,x,c0))));
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_10(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2, CTYPE c3, CTYPE c4, CTYPE c5, CTYPE c6, CTYPE c7, CTYPE c8, CTYPE c9, CTYPE c10) {
// calculates polynomial c10*x^10 + c9*x^9 + c8*x^8 + c7*x^7 + c6*x^6 + c5*x^5 + c4*x^4 + c3*x^3 + c2*x^2 + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
VTYPE x4 = x2 * x2;
VTYPE x8 = x4 * x4;
//return (((c6+c7*x)*x2 + (c4+c5*x))*x4 + (c8+c9*x+c10*x2)*x8) + ((c2+c3*x)*x2 + (c0+c1*x));
return mul_add(mul_add(x2,c10,mul_add(c9,x,c8)), x8,
mul_add(mul_add(mul_add(c7,x,c6),x2,mul_add(c5,x,c4)), x4,
mul_add(mul_add(c3,x,c2),x2,mul_add(c1,x,c0))));
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_13(VTYPE const & x, CTYPE c0, CTYPE c1, CTYPE c2, CTYPE c3, CTYPE c4, CTYPE c5, CTYPE c6, CTYPE c7, CTYPE c8, CTYPE c9, CTYPE c10, CTYPE c11, CTYPE c12, CTYPE c13) {
// calculates polynomial c13*x^13 + c12*x^12 + ... + c1*x + c0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
VTYPE x4 = x2 * x2;
VTYPE x8 = x4 * x4;
return mul_add(
mul_add(
mul_add(c13,x,c12), x4,
mul_add(mul_add(c11,x,c10), x2, mul_add(c9,x,c8))), x8,
mul_add(
mul_add(mul_add(c7,x,c6), x2, mul_add(c5,x,c4)), x4,
mul_add(mul_add(c3,x,c2), x2, mul_add(c1,x,c0))));
}
template<class VTYPE, class CTYPE>
static inline VTYPE polynomial_13m(VTYPE const & x, CTYPE c2, CTYPE c3, CTYPE c4, CTYPE c5, CTYPE c6, CTYPE c7, CTYPE c8, CTYPE c9, CTYPE c10, CTYPE c11, CTYPE c12, CTYPE c13) {
// calculates polynomial c13*x^13 + c12*x^12 + ... + x + 0
// VTYPE may be a vector type, CTYPE is a scalar type
VTYPE x2 = x * x;
VTYPE x4 = x2 * x2;
VTYPE x8 = x4 * x4;
// return ((c8+c9*x) + (c10+c11*x)*x2 + (c12+c13*x)*x4)*x8 + (((c6+c7*x)*x2 + (c4+c5*x))*x4 + ((c2+c3*x)*x2 + x));
return mul_add(
mul_add(mul_add(c13,x,c12), x4, mul_add(mul_add(c11,x,c10), x2, mul_add(c9,x,c8))), x8,
mul_add( mul_add(mul_add(c7,x,c6), x2, mul_add(c5,x,c4)), x4, mul_add(mul_add(c3,x,c2),x2,x)));
}
#endif

1995
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/**************************** vectormath_hyp.h ******************************
* Author: Agner Fog
* Date created: 2014-07-09
* Last modified: 2014-10-16
* Version: 1.16
* Project: vector classes
* Description:
* Header file containing inline vector functions of hyperbolic and inverse
* hyperbolic functions:
* sinh hyperbolic sine
* cosh hyperbolic cosine
* tanh hyperbolic tangent
* asinh inverse hyperbolic sine
* acosh inverse hyperbolic cosine
* atanh inverse hyperbolic tangent
*
* Theory, methods and inspiration based partially on these sources:
* > Moshier, Stephen Lloyd Baluk: Methods and programs for mathematical functions.
* Ellis Horwood, 1989.
* > VDT library developed on CERN by Danilo Piparo, Thomas Hauth and
* Vincenzo Innocente, 2012, https://svnweb.cern.ch/trac/vdt
* > Cephes math library by Stephen L. Moshier 1992,
* http://www.netlib.org/cephes/
*
* For detailed instructions, see vectormath_common.h and VectorClass.pdf
*
* (c) Copyright 2014 GNU General Public License http://www.gnu.org/licenses
******************************************************************************/
#ifndef VECTORMATH_HYP_H
#define VECTORMATH_HYP_H 1
#include "vectormath_exp.h"
/******************************************************************************
* Hyperbolic functions
******************************************************************************/
// Template for sinh function, double precision
// This function does not produce denormals
// Template parameters:
// VTYPE: double vector type
// BTYPE: boolean vector type
template<class VTYPE, class BTYPE>
static inline VTYPE sinh_d(VTYPE const & x0) {
// The limit of abs(x) is 709.7, as defined by max_x in vectormath_exp.h for 0.5*exp(x).
// Coefficients
const double p0 = -3.51754964808151394800E5;
const double p1 = -1.15614435765005216044E4;
const double p2 = -1.63725857525983828727E2;
const double p3 = -7.89474443963537015605E-1;
const double q0 = -2.11052978884890840399E6;
const double q1 = 3.61578279834431989373E4;
const double q2 = -2.77711081420602794433E2;
const double q3 = 1.0;
// data vectors
VTYPE x, x2, y1, y2;
BTYPE x_small; // boolean vector
x = abs(x0);
x_small = x <= 1.0; // use Pade approximation if abs(x) <= 1
if (horizontal_or(x_small)) {
// At least one element needs small method
x2 = x*x;
y1 = polynomial_3(x2, p0, p1, p2, p3) / polynomial_3(x2, q0, q1, q2, q3);
y1 = mul_add(y1, x*x2, x); // y1 = x + x2*(x*y1);
}
if (!horizontal_and(x_small)) {
// At least one element needs big method
y2 = exp_d<VTYPE, BTYPE, 0, 1>(x); // 0.5 * exp(x)
y2 -= 0.25 / y2; // - 0.5 * exp(-x)
}
y1 = select(x_small, y1, y2); // choose method
y1 = sign_combine(y1, x0); // get original sign
return y1;
}
// instances of sinh_d template
static inline Vec2d sinh(Vec2d const & x) {
return sinh_d<Vec2d, Vec2db>(x);
}
#if MAX_VECTOR_SIZE >= 256
static inline Vec4d sinh(Vec4d const & x) {
return sinh_d<Vec4d, Vec4db>(x);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
static inline Vec8d sinh(Vec8d const & x) {
return sinh_d<Vec8d, Vec8db>(x);
}
#endif // MAX_VECTOR_SIZE >= 512
// Template for sinh function, single precision
// This function does not produce denormals
// Template parameters:
// VTYPE: double vector type
// BTYPE: boolean vector type
template<class VTYPE, class BTYPE>
static inline VTYPE sinh_f(VTYPE const & x0) {
// The limit of abs(x) is 89.0, as defined by max_x in vectormath_exp.h for 0.5*exp(x).
// Coefficients
const float r0 = 1.66667160211E-1f;
const float r1 = 8.33028376239E-3f;
const float r2 = 2.03721912945E-4f;
// data vectors
VTYPE x, x2, y1, y2;
BTYPE x_small; // boolean vector
x = abs(x0);
x_small = x <= 1.0f; // use polynomial approximation if abs(x) <= 1
if (horizontal_or(x_small)) {
// At least one element needs small method
x2 = x*x;
y1 = polynomial_2(x2, r0, r1, r2);
y1 = mul_add(y1, x2*x, x); // y1 = x + x2*(x*y1);
}
if (!horizontal_and(x_small)) {
// At least one element needs big method
y2 = exp_f<VTYPE, BTYPE, 0, 1>(x); // 0.5 * exp(x)
y2 -= 0.25f / y2; // - 0.5 * exp(-x)
}
y1 = select(x_small, y1, y2); // choose method
y1 = sign_combine(y1, x0); // get original sign
return y1;
}
// instances of sinh_f template
static inline Vec4f sinh(Vec4f const & x) {
return sinh_f<Vec4f, Vec4fb>(x);
}
#if MAX_VECTOR_SIZE >= 256
static inline Vec8f sinh(Vec8f const & x) {
return sinh_f<Vec8f, Vec8fb>(x);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
static inline Vec16f sinh(Vec16f const & x) {
return sinh_f<Vec16f, Vec16fb>(x);
}
#endif // MAX_VECTOR_SIZE >= 512
// Template for cosh function, double precision
// This function does not produce denormals
// Template parameters:
// VTYPE: double vector type
// BTYPE: boolean vector type
template<class VTYPE, class BTYPE>
static inline VTYPE cosh_d(VTYPE const & x0) {
// The limit of abs(x) is 709.7, as defined by max_x in vectormath_exp.h for 0.5*exp(x).
// data vectors
VTYPE x, y;
x = abs(x0);
y = exp_d<VTYPE, BTYPE, 0, 1>(x); // 0.5 * exp(x)
y += 0.25 / y; // + 0.5 * exp(-x)
return y;
}
// instances of sinh_d template
static inline Vec2d cosh(Vec2d const & x) {
return cosh_d<Vec2d, Vec2db>(x);
}
#if MAX_VECTOR_SIZE >= 256
static inline Vec4d cosh(Vec4d const & x) {
return cosh_d<Vec4d, Vec4db>(x);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
static inline Vec8d cosh(Vec8d const & x) {
return cosh_d<Vec8d, Vec8db>(x);
}
#endif // MAX_VECTOR_SIZE >= 512
// Template for cosh function, single precision
// This function does not produce denormals
// Template parameters:
// VTYPE: double vector type
// BTYPE: boolean vector type
template<class VTYPE, class BTYPE>
static inline VTYPE cosh_f(VTYPE const & x0) {
// The limit of abs(x) is 89.0, as defined by max_x in vectormath_exp.h for 0.5*exp(x).
// data vectors
VTYPE x, y;
x = abs(x0);
y = exp_f<VTYPE, BTYPE, 0, 1>(x); // 0.5 * exp(x)
y += 0.25f / y; // + 0.5 * exp(-x)
return y;
}
// instances of sinh_d template
static inline Vec4f cosh(Vec4f const & x) {
return cosh_f<Vec4f, Vec4fb>(x);
}
#if MAX_VECTOR_SIZE >= 256
static inline Vec8f cosh(Vec8f const & x) {
return cosh_f<Vec8f, Vec8fb>(x);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
static inline Vec16f cosh(Vec16f const & x) {
return cosh_f<Vec16f, Vec16fb>(x);
}
#endif // MAX_VECTOR_SIZE >= 512
// Template for tanh function, double precision
// This function does not produce denormals
// Template parameters:
// VTYPE: double vector type
// BTYPE: boolean vector type
template<class VTYPE, class BTYPE>
static inline VTYPE tanh_d(VTYPE const & x0) {
// Coefficients
const double p0 = -1.61468768441708447952E3;
const double p1 = -9.92877231001918586564E1;
const double p2 = -9.64399179425052238628E-1;
const double q0 = 4.84406305325125486048E3;
const double q1 = 2.23548839060100448583E3;
const double q2 = 1.12811678491632931402E2;
const double q3 = 1.0;
// data vectors
VTYPE x, x2, y1, y2;
BTYPE x_small, x_big; // boolean vectors
x = abs(x0);
x_small = x <= 0.625; // use Pade approximation if abs(x) <= 5/8
if (horizontal_or(x_small)) {
// At least one element needs small method
x2 = x*x;
y1 = polynomial_2(x2, p0, p1, p2) / polynomial_3(x2, q0, q1, q2, q3);
y1 = mul_add(y1, x2*x, x); // y1 = x + x2*(x*y1);
}
if (!horizontal_and(x_small)) {
// At least one element needs big method
y2 = exp(x+x); // exp(2*x)
y2 = 1.0 - 2.0 / (y2 + 1.0); // tanh(x)
}
x_big = x > 350.;
y1 = select(x_small, y1, y2); // choose method
y1 = select(x_big, 1.0, y1); // avoid overflow
y1 = sign_combine(y1, x0); // get original sign
return y1;
}
// instances of tanh_d template
static inline Vec2d tanh(Vec2d const & x) {
return tanh_d<Vec2d, Vec2db>(x);
}
#if MAX_VECTOR_SIZE >= 256
static inline Vec4d tanh(Vec4d const & x) {
return tanh_d<Vec4d, Vec4db>(x);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
static inline Vec8d tanh(Vec8d const & x) {
return tanh_d<Vec8d, Vec8db>(x);
}
#endif // MAX_VECTOR_SIZE >= 512
// Template for tanh function, single precision
// This function does not produce denormals
// Template parameters:
// VTYPE: double vector type
// BTYPE: boolean vector type
template<class VTYPE, class BTYPE>
static inline VTYPE tanh_f(VTYPE const & x0) {
// The limit of abs(x) is 89.0, as defined by max_x in vectormath_exp.h for 0.5*exp(x).
// Coefficients
const float r0 = -3.33332819422E-1f;
const float r1 = 1.33314422036E-1f;
const float r2 = -5.37397155531E-2f;
const float r3 = 2.06390887954E-2f;
const float r4 = -5.70498872745E-3f;
// data vectors
VTYPE x, x2, y1, y2;
BTYPE x_small, x_big; // boolean vectors
x = abs(x0);
x_small = x <= 0.625f; // use polynomial approximation if abs(x) <= 5/8
if (horizontal_or(x_small)) {
// At least one element needs small method
x2 = x*x;
y1 = polynomial_4(x2, r0, r1, r2, r3, r4);
y1 = mul_add(y1, x2*x, x); // y1 = x + (x2*x)*y1;
}
if (!horizontal_and(x_small)) {
// At least one element needs big method
y2 = exp(x+x); // exp(2*x)
y2 = 1.0f - 2.0f / (y2 + 1.0f); // tanh(x)
}
x_big = x > 44.4f;
y1 = select(x_small, y1, y2); // choose method
y1 = select(x_big, 1.0f, y1); // avoid overflow
y1 = sign_combine(y1, x0); // get original sign
return y1;
}
// instances of tanh_f template
static inline Vec4f tanh(Vec4f const & x) {
return tanh_f<Vec4f, Vec4fb>(x);
}
#if MAX_VECTOR_SIZE >= 256
static inline Vec8f tanh(Vec8f const & x) {
return tanh_f<Vec8f, Vec8fb>(x);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
static inline Vec16f tanh(Vec16f const & x) {
return tanh_f<Vec16f, Vec16fb>(x);
}
#endif // MAX_VECTOR_SIZE >= 512
/******************************************************************************
* Inverse hyperbolic functions
******************************************************************************/
// Template for asinh function, double precision
// This function does not produce denormals
// Template parameters:
// VTYPE: double vector type
// BTYPE: boolean vector type
template<class VTYPE, class BTYPE>
static inline VTYPE asinh_d(VTYPE const & x0) {
// Coefficients
const double p0 = -5.56682227230859640450E0;
const double p1 = -9.09030533308377316566E0;
const double p2 = -4.37390226194356683570E0;
const double p3 = -5.91750212056387121207E-1;
const double p4 = -4.33231683752342103572E-3;
const double q0 = 3.34009336338516356383E1;
const double q1 = 6.95722521337257608734E1;
const double q2 = 4.86042483805291788324E1;
const double q3 = 1.28757002067426453537E1;
const double q4 = 1.0;
// data vectors
VTYPE x, x2, y1, y2;
BTYPE x_small, x_huge; // boolean vectors
x2 = x0 * x0;
x = abs(x0);
x_small = x <= 0.533; // use Pade approximation if abs(x) <= 0.5
// both methods give the highest error close to 0.5. this limit is adjusted for minimum error
x_huge = x > 1.E20; // simple approximation, avoid overflow
if (horizontal_or(x_small)) {
// At least one element needs small method
y1 = polynomial_4(x2, p0, p1, p2, p3, p4) / polynomial_4(x2, q0, q1, q2, q3, q4);
y1 = mul_add(y1, x2*x, x); // y1 = x + (x2*x)*y1;
}
if (!horizontal_and(x_small)) {
// At least one element needs big method
y2 = log(x + sqrt(x2 + 1.0));
if (horizontal_or(x_huge)) {
// At least one element needs huge method to avoid overflow
y2 = select(x_huge, log(x) + VM_LN2, y2);
}
}
y1 = select(x_small, y1, y2); // choose method
y1 = sign_combine(y1, x0); // get original sign
return y1;
}
// instances of asinh_d template
static inline Vec2d asinh(Vec2d const & x) {
return asinh_d<Vec2d, Vec2db>(x);
}
#if MAX_VECTOR_SIZE >= 256
static inline Vec4d asinh(Vec4d const & x) {
return asinh_d<Vec4d, Vec4db>(x);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
static inline Vec8d asinh(Vec8d const & x) {
return asinh_d<Vec8d, Vec8db>(x);
}
#endif // MAX_VECTOR_SIZE >= 512
// Template for asinh function, single precision
// This function does not produce denormals
// Template parameters:
// VTYPE: double vector type
// BTYPE: boolean vector type
template<class VTYPE, class BTYPE>
static inline VTYPE asinh_f(VTYPE const & x0) {
// Coefficients
const float r0 = -1.6666288134E-1f;
const float r1 = 7.4847586088E-2f;
const float r2 = -4.2699340972E-2f;
const float r3 = 2.0122003309E-2f;
// data vectors
VTYPE x, x2, y1, y2;
BTYPE x_small, x_huge; // boolean vectors
x2 = x0 * x0;
x = abs(x0);
x_small = x <= 0.51f; // use polynomial approximation if abs(x) <= 0.5
x_huge = x > 1.E10f; // simple approximation, avoid overflow
if (horizontal_or(x_small)) {
// At least one element needs small method
y1 = polynomial_3(x2, r0, r1, r2, r3);
y1 = mul_add(y1, x2*x, x); // y1 = x + (x2*x)*y1;
}
if (!horizontal_and(x_small)) {
// At least one element needs big method
y2 = log(x + sqrt(x2 + 1.0f));
if (horizontal_or(x_huge)) {
// At least one element needs huge method to avoid overflow
y2 = select(x_huge, log(x) + (float)VM_LN2, y2);
}
}
y1 = select(x_small, y1, y2); // choose method
y1 = sign_combine(y1, x0); // get original sign
return y1;
}
// instances of asinh_f template
static inline Vec4f asinh(Vec4f const & x) {
return asinh_f<Vec4f, Vec4fb>(x);
}
#if MAX_VECTOR_SIZE >= 256
static inline Vec8f asinh(Vec8f const & x) {
return asinh_f<Vec8f, Vec8fb>(x);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
static inline Vec16f asinh(Vec16f const & x) {
return asinh_f<Vec16f, Vec16fb>(x);
}
#endif // MAX_VECTOR_SIZE >= 512
// Template for acosh function, double precision
// This function does not produce denormals
// Template parameters:
// VTYPE: double vector type
// BTYPE: boolean vector type
template<class VTYPE, class BTYPE>
static inline VTYPE acosh_d(VTYPE const & x0) {
// Coefficients
const double p0 = 1.10855947270161294369E5;
const double p1 = 1.08102874834699867335E5;
const double p2 = 3.43989375926195455866E4;
const double p3 = 3.94726656571334401102E3;
const double p4 = 1.18801130533544501356E2;
const double q0 = 7.83869920495893927727E4;
const double q1 = 8.29725251988426222434E4;
const double q2 = 2.97683430363289370382E4;
const double q3 = 4.15352677227719831579E3;
const double q4 = 1.86145380837903397292E2;
const double q5 = 1.0;
// data vectors
VTYPE x1, y1, y2;
BTYPE x_small, x_huge, undef; // boolean vectors
x1 = x0 - 1.0;
undef = x0 < 1.0; // result is NAN
x_small = x1 < 0.49; // use Pade approximation if abs(x-1) < 0.5
x_huge = x1 > 1.E20; // simple approximation, avoid overflow
if (horizontal_or(x_small)) {
// At least one element needs small method
y1 = sqrt(x1) * (polynomial_4(x1, p0, p1, p2, p3, p4) / polynomial_5(x1, q0, q1, q2, q3, q4, q5));
// x < 1 generates NAN
y1 = select(undef, nan_vec<VTYPE>(NAN_HYP), y1);
}
if (!horizontal_and(x_small)) {
// At least one element needs big method
y2 = log(x0 + sqrt(mul_sub(x0,x0,1.0)));
if (horizontal_or(x_huge)) {
// At least one element needs huge method to avoid overflow
y2 = select(x_huge, log(x0) + VM_LN2, y2);
}
}
y1 = select(x_small, y1, y2); // choose method
return y1;
}
// instances of acosh_d template
static inline Vec2d acosh(Vec2d const & x) {
return acosh_d<Vec2d, Vec2db>(x);
}
#if MAX_VECTOR_SIZE >= 256
static inline Vec4d acosh(Vec4d const & x) {
return acosh_d<Vec4d, Vec4db>(x);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
static inline Vec8d acosh(Vec8d const & x) {
return acosh_d<Vec8d, Vec8db>(x);
}
#endif // MAX_VECTOR_SIZE >= 512
// Template for acosh function, single precision
// This function does not produce denormals
// Template parameters:
// VTYPE: double vector type
// BTYPE: boolean vector type
template<class VTYPE, class BTYPE>
static inline VTYPE acosh_f(VTYPE const & x0) {
// Coefficients
const float r0 = 1.4142135263E0f;
const float r1 = -1.1784741703E-1f;
const float r2 = 2.6454905019E-2f;
const float r3 = -7.5272886713E-3f;
const float r4 = 1.7596881071E-3f;
// data vectors
VTYPE x1, y1, y2;
BTYPE x_small, x_huge, undef; // boolean vectors
x1 = x0 - 1.0f;
undef = x0 < 1.0f; // result is NAN
x_small = x1 < 0.49f; // use Pade approximation if abs(x-1) < 0.5
x_huge = x1 > 1.E10f; // simple approximation, avoid overflow
if (horizontal_or(x_small)) {
// At least one element needs small method
y1 = sqrt(x1) * polynomial_4(x1, r0, r1, r2, r3, r4);
// x < 1 generates NAN
y1 = select(undef, nan_vec<VTYPE>(NAN_HYP), y1);
}
if (!horizontal_and(x_small)) {
// At least one element needs big method
y2 = log(x0 + sqrt(mul_sub(x0,x0,1.0)));
if (horizontal_or(x_huge)) {
// At least one element needs huge method to avoid overflow
y2 = select(x_huge, log(x0) + (float)VM_LN2, y2);
}
}
y1 = select(x_small, y1, y2); // choose method
return y1;
}
// instances of acosh_f template
static inline Vec4f acosh(Vec4f const & x) {
return acosh_f<Vec4f, Vec4fb>(x);
}
#if MAX_VECTOR_SIZE >= 256
static inline Vec8f acosh(Vec8f const & x) {
return acosh_f<Vec8f, Vec8fb>(x);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
static inline Vec16f acosh(Vec16f const & x) {
return acosh_f<Vec16f, Vec16fb>(x);
}
#endif // MAX_VECTOR_SIZE >= 512
// Template for atanh function, double precision
// This function does not produce denormals
// Template parameters:
// VTYPE: double vector type
// BTYPE: boolean vector type
template<class VTYPE, class BTYPE>
static inline VTYPE atanh_d(VTYPE const & x0) {
// Coefficients
const double p0 = -3.09092539379866942570E1;
const double p1 = 6.54566728676544377376E1;
const double p2 = -4.61252884198732692637E1;
const double p3 = 1.20426861384072379242E1;
const double p4 = -8.54074331929669305196E-1;
const double q0 = -9.27277618139601130017E1;
const double q1 = 2.52006675691344555838E2;
const double q2 = -2.49839401325893582852E2;
const double q3 = 1.08938092147140262656E2;
const double q4 = -1.95638849376911654834E1;
const double q5 = 1.0;
// data vectors
VTYPE x, x2, y1, y2, y3;
BTYPE x_small; // boolean vector
x = abs(x0);
x_small = x < 0.5; // use Pade approximation if abs(x) < 0.5
if (horizontal_or(x_small)) {
// At least one element needs small method
x2 = x * x;
y1 = polynomial_4(x2, p0, p1, p2, p3, p4) / polynomial_5(x2, q0, q1, q2, q3, q4, q5);
y1 = mul_add(y1, x2*x, x);
}
if (!horizontal_and(x_small)) {
// At least one element needs big method
y2 = log((1.0+x)/(1.0-x)) * 0.5;
// check if out of range
y3 = select(x == 1.0, infinite_vec<VTYPE>(), nan_vec<VTYPE>(NAN_HYP));
y2 = select(x >= 1.0, y3, y2);
}
y1 = select(x_small, y1, y2); // choose method
y1 = sign_combine(y1, x0); // get original sign
return y1;
}
// instances of atanh_d template
static inline Vec2d atanh(Vec2d const & x) {
return atanh_d<Vec2d, Vec2db>(x);
}
#if MAX_VECTOR_SIZE >= 256
static inline Vec4d atanh(Vec4d const & x) {
return atanh_d<Vec4d, Vec4db>(x);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
static inline Vec8d atanh(Vec8d const & x) {
return atanh_d<Vec8d, Vec8db>(x);
}
#endif // MAX_VECTOR_SIZE >= 512
// Template for atanh function, single precision
// This function does not produce denormals
// Template parameters:
// VTYPE: double vector type
// BTYPE: boolean vector type
template<class VTYPE, class BTYPE>
static inline VTYPE atanh_f(VTYPE const & x0) {
// Coefficients
const float r0 = 3.33337300303E-1f;
const float r1 = 1.99782164500E-1f;
const float r2 = 1.46691431730E-1f;
const float r3 = 8.24370301058E-2f;
const float r4 = 1.81740078349E-1f;
// data vectors
VTYPE x, x2, y1, y2, y3;
BTYPE x_small; // boolean vector
x = abs(x0);
x_small = x < 0.5f; // use polynomial approximation if abs(x) < 0.5
if (horizontal_or(x_small)) {
// At least one element needs small method
x2 = x * x;
y1 = polynomial_4(x2, r0, r1, r2, r3, r4);
y1 = mul_add(y1, x2*x, x);
}
if (!horizontal_and(x_small)) {
// At least one element needs big method
y2 = log((1.0f+x)/(1.0f-x)) * 0.5f;
// check if out of range
y3 = select(x == 1.0f, infinite_vec<VTYPE>(), nan_vec<VTYPE>(NAN_HYP));
y2 = select(x >= 1.0f, y3, y2);
}
y1 = select(x_small, y1, y2); // choose method
y1 = sign_combine(y1, x0); // get original sign
return y1;
}
// instances of atanh_f template
static inline Vec4f atanh(Vec4f const & x) {
return atanh_f<Vec4f, Vec4fb>(x);
}
#if MAX_VECTOR_SIZE >= 256
static inline Vec8f atanh(Vec8f const & x) {
return atanh_f<Vec8f, Vec8fb>(x);
}
#endif // MAX_VECTOR_SIZE >= 256
#if MAX_VECTOR_SIZE >= 512
static inline Vec16f atanh(Vec16f const & x) {
return atanh_f<Vec16f, Vec16fb>(x);
}
#endif // MAX_VECTOR_SIZE >= 512
#endif

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contrib/libvectorclass/vectormath_lib.h
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contrib/libvectorclass/vectormath_trig.h
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