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Anonymous committed 0432681

v2014-May-11

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Files changed (20)

+# This code depends on make tool being used
+DEPFILES=$(wildcard $(addsuffix .d, ${OBJECTFILES}))
+ifneq (${DEPFILES},)
+include ${DEPFILES}
+endif
+syntax: glob
+build/*
+nbproject/*
+dist/*
+#
+#  There exist several targets which are by default empty and which can be 
+#  used for execution of your targets. These targets are usually executed 
+#  before and after some main targets. They are: 
+#
+#     .build-pre:              called before 'build' target
+#     .build-post:             called after 'build' target
+#     .clean-pre:              called before 'clean' target
+#     .clean-post:             called after 'clean' target
+#     .clobber-pre:            called before 'clobber' target
+#     .clobber-post:           called after 'clobber' target
+#     .all-pre:                called before 'all' target
+#     .all-post:               called after 'all' target
+#     .help-pre:               called before 'help' target
+#     .help-post:              called after 'help' target
+#
+#  Targets beginning with '.' are not intended to be called on their own.
+#
+#  Main targets can be executed directly, and they are:
+#  
+#     build                    build a specific configuration
+#     clean                    remove built files from a configuration
+#     clobber                  remove all built files
+#     all                      build all configurations
+#     help                     print help mesage
+#  
+#  Targets .build-impl, .clean-impl, .clobber-impl, .all-impl, and
+#  .help-impl are implemented in nbproject/makefile-impl.mk.
+#
+#  Available make variables:
+#
+#     CND_BASEDIR                base directory for relative paths
+#     CND_DISTDIR                default top distribution directory (build artifacts)
+#     CND_BUILDDIR               default top build directory (object files, ...)
+#     CONF                       name of current configuration
+#     CND_PLATFORM_${CONF}       platform name (current configuration)
+#     CND_ARTIFACT_DIR_${CONF}   directory of build artifact (current configuration)
+#     CND_ARTIFACT_NAME_${CONF}  name of build artifact (current configuration)
+#     CND_ARTIFACT_PATH_${CONF}  path to build artifact (current configuration)
+#     CND_PACKAGE_DIR_${CONF}    directory of package (current configuration)
+#     CND_PACKAGE_NAME_${CONF}   name of package (current configuration)
+#     CND_PACKAGE_PATH_${CONF}   path to package (current configuration)
+#
+# NOCDDL
+
+
+# Environment 
+MKDIR=mkdir
+CP=cp
+CCADMIN=CCadmin
+
+
+# build
+build: .build-post
+
+.build-pre:
+# Add your pre 'build' code here...
+
+.build-post: .build-impl
+# Add your post 'build' code here...
+
+
+# clean
+clean: .clean-post
+
+.clean-pre:
+# Add your pre 'clean' code here...
+
+.clean-post: .clean-impl
+# Add your post 'clean' code here...
+
+
+# clobber
+clobber: .clobber-post
+
+.clobber-pre:
+# Add your pre 'clobber' code here...
+
+.clobber-post: .clobber-impl
+# Add your post 'clobber' code here...
+
+
+# all
+all: .all-post
+
+.all-pre:
+# Add your pre 'all' code here...
+
+.all-post: .all-impl
+# Add your post 'all' code here...
+
+
+# build tests
+build-tests: .build-tests-post
+
+.build-tests-pre:
+# Add your pre 'build-tests' code here...
+
+.build-tests-post: .build-tests-impl
+# Add your post 'build-tests' code here...
+
+
+# run tests
+test: .test-post
+
+.test-pre: build-tests
+# Add your pre 'test' code here...
+
+.test-post: .test-impl
+# Add your post 'test' code here...
+
+
+# help
+help: .help-post
+
+.help-pre:
+# Add your pre 'help' code here...
+
+.help-post: .help-impl
+# Add your post 'help' code here...
+
+
+
+# include project implementation makefile
+include nbproject/Makefile-impl.mk
+
+# include project make variables
+include nbproject/Makefile-variables.mk
+change log for vectorclass.zip
+------------------------------
+
+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
+
+
+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
+/****************************  instrset.h   **********************************
+* Author:        Agner Fog
+* Date created:  2012-05-30
+* Last modified: 2014-05-11
+* Version:       1.13
+* 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 112
+
+// 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 ( __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
+#ifdef __GNUC__
+#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
+#define __FMA__  1
+#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__))
+#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__))
+#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

instrset_detect.cpp

+/**************************  instrset_detect.cpp   ****************************
+| Author:        Agner Fog
+| Date created:  2012-05-30
+| Last modified: 2013-10-04
+| Version:       1.10
+| Project:       vector classes
+| Description:
+| Functions for checking which instruction sets are supported.
+|
+| (c) Copyright 2012 - 2013 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
+*/
+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
+    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
+}
+                    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.
+
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+
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+
+  The licenses for most software and other practical works are designed
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special.zip

Binary file added.
+/****************************  vectorclass.h   ********************************
+* Author:        Agner Fog
+* Date created:  2012-05-30
+* Last modified: 2014-05-11
+* Version:       1.13
+* 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 AVX2.
+*
+* 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 128-bit or
+* 256 bit register.
+*
+* 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  112
+
+
+#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 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  // INSTRSET < 2
+
+
+#endif  // VECTORCLASS_H

vectorclass.pdf

Binary file added.
+/****************************  vectorf128.h   *******************************
+* Author:        Agner Fog
+* Date created:  2012-05-30
+* Last modified: 2014-04-22
+* Version:       1.12
+* 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 broadcast the same value into all elements:
+    Vec4fb(bool b) {
+        xmm = _mm_castsi128_ps(_mm_set1_epi32(-(int)b));
+    };
+    // 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;
+    };
+    // Type cast operator to convert to __m128 used in intrinsics
+    operator __m128() const {
+        return xmm;
+    }
+    // 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;
+    };
+#if defined (__clang__) && CLANG_VERSION < 30400
+#define FIX_CLANG_VECTOR_ALIAS_AMBIGUITY  // clang 3.3 has silent conversion between intrinsic vector types. Will probably be fixed in v. 3.4
+#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
+    int extract(uint32_t index) const {
+        return Vec4ib(*this).extract(index);
+    }
+    // Extract a single element. Operator [] can only read an element, not write.
+    int operator [] (uint32_t index) const {
+        return extract(index);
+    }
+};
+
+
+/*****************************************************************************
+*
+*          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:
+    Vec2db(bool b) {
+        xmm = _mm_castsi128_pd(_mm_set1_epi32(-(int)b));
+    };
+    // 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;
+    };
+    // Type cast operator to convert to __m128d used in intrinsics
+    operator __m128d() const {
+        return xmm;
+    }
+    // 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;
+    };
+#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
+    int extract(uint32_t index) const {
+        return int32_t(Vec2q(*this).extract(index));
+    }
+    // Extract a single element. Operator [] can only read an element, not write.
+    int operator [] (uint32_t index) const {
+        return extract(index);
+    }
+};
+
+
+/*****************************************************************************
+*
+*          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);
+    }
+};
+
+
+/*****************************************************************************
+*
+*          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(Vec4f, int):
+// Raise floating point numbers to integer power n
+static inline Vec4f pow(Vec4f const & a, int n) {
+    Vec4f x = a;                       // a^(2^i)
+    Vec4f 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 Vec4f(1.0f)/pow(x,-n);  // reciprocal
+    }
+}
+// prevent implicit conversion of float exponent to int
+static Vec4f pow(Vec4f const & x, float y);
+
+// 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 (_MSC_VER) || defined(__INTEL_COMPILER) || defined(__clang__)) && 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<0x80000000,0x80000000,0x80000000,0x80000000>());  // -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
+    return a + signedmagic - signedmagic;                                           // round by adding magic number
+#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)