MyIntrinsics++ (MIPP)

Purpose

MIPP is a portable and Open-source wrapper (MIT license) for vector intrinsic functions (SIMD) written in C++11. It works for SSE, AVX, AVX-512 and ARM NEON (32-bit and 64-bit) instructions. MIPP wrapper supports simple/double precision floating-point numbers and also signed integer arithmetic (64-bit, 32-bit, 16-bit and 8-bit).

With the MIPP wrapper you do not need to write a specific intrinsic code anymore. Just use provided functions and the wrapper will automatically generates the right intrisic calls for your specific architecture.

Miscellaneous

Scientific publications

Adrien Cassagne, Olivier Aumage, Denis Barthou, Camille Leroux and Christophe Jégo,
MIPP: a Portable C++ SIMD Wrapper and its use for Error Correction Coding in 5G Standard,
The 5th International Workshop on Programming Models for SIMD/Vector Processing (WPMVP 2018), February 2018.

Adrien Cassagne, Olivier Hartmann, Mathieu Léonardon, Kun He, Camille Leroux, Romain Tajan, Olivier Aumage, Denis Barthou, Thibaud Tonnellier, Vincent Pignoly, Bertrand Le Gal and Christophe Jégo,
AFF3CT: A Fast Forward Error Correction Toolbox!,
Elsevier SoftwareX, October 2019.

Mathieu Léonardon, Adrien Cassagne, Camille Leroux, Christophe Jégo, Louis-Philippe Hamelin and Yvon Savaria,
Fast and Flexible Software Polar List Decoders,
Springer Journal of Signal Processing Systems (JSPS), January 2019.

Alireza Ghaffari, Mathieu Leonardon, Adrien Cassagne, Camille Leroux, Yvon Savaria,
Toward High-Performance Implementation of 5G SCMA Algorithms,
IEEE Acces, January 2019.

Adrien Cassagne, Thibaud Tonnellier, Camille Leroux, Bertrand Le Gal, Olivier Aumage and Denis Barthou,
Beyond Gbps Turbo Decoder on Multi-Core CPUs,
The 10th International Symposium on Turbo Codes and Iterative Information Processing (ISTC 2016), September 2016.

Adrien Cassagne, Olivier Aumage, Camille Leroux, Denis Barthou and Bertrand Le Gal,
Energy Consumption Analysis of Software Polar Decoders on Low Power Processors,
The 24nd European Signal Processing Conference (EUSIPCO 2016), September 2016.

Adrien Cassagne, Bertrand Le Gal, Camille Leroux, Olivier Aumage and Denis Barthou,
An Efficient, Portable and Generic Library for Successive Cancellation Decoding of Polar Codes,
The 28th International Workshop on Languages and Compilers for Parallel Computing (LCPC 2015), September 2015.

Open-source projects in which MIPP is used

• AFF3CT: A Fast Forward Error Correction Toolbox!
• MUrB: a N-body problem simulator with various implementations (multi-threaded, MPI, SIMD, etc.).
• mandelbrot: the Mandelbrot fractal, sequential and SIMD implementations.

Short documentation

Supported compilers

At this time, MIPP has been tested on the following compilers:

• Intel: icpc >= 16,
• GNU: g++ >= 4.8,
• Clang: clang++ >= 3.6,
• Microsoft: msvc >= 14.

On msvc 14.10 (Microsoft Visual Studio 2017), the performances are reduced compared to the other compilers, the compiler is not able to fully inline all the MIPP methods. This has been fixed on msvc 14.21 (Microsoft Visual Studio 2019) and now you can expect high performances.

Install and configure your code

You don't have to install MIPP because it is a simple C++ header file. Just include the header into your source files when the wrapper is needed.

#include "mipp.h"

mipp.h use a C++ namespace: mipp, if you do not want to prefix all the MIPP calls by mipp:: you can do that:

#include "mipp.h"
using namespace mipp;

Before trying to compile, think to tell the compiler what kind of vector instructions you want to use. For instance, if you are using GNU compiler (g++) you simply have to add the -march=native option for SSE and AVX CPUs compatible. For ARM CPUs with NEON instructions you have to add the -mfpu=neon option (since most of current NEON instructions are not IEEE-754 compatible). MIPP also use some nice features provided by the C++11 and so we have to add the -std=c++11 flag to compile the code. Your are now ready to run your code with the mipp.h wrapper.

Sequential mode

By default, MIPP try to recognize the instruction set from the preprocessor definitions. If MIPP can't match the instruction set (for instance when MIPP does not support the targeted instruction set), MIPP fall back on standard sequential instructions. In this mode, the vectorization is not guarantee anymore but the compiler can still perform auto-vectorization.

It is possible to force MIPP to use the sequential mode with the following compiler definition: -DMIPP_NO_INTRINSICS. Sometime it can be useful for debugging or to bench a code.

If you want to check the MIPP mode configuration, you can print the following global variable: mipp::InstructionFullType (std::string).

Vector register declaration

Just use the mipp::Reg<T> type.

mipp::Reg<T> r1, r2, r3; // we have declared 3 vector registers

But we do not know the number of elements per registers here. This number of elements can be obtained by calling the mipp::N<T>() function (T is a template parameter, it can be double, float, int64_t, int32_t, int16_t or int8_t type).

for(int i = 0; i < n; i += mipp::N<float>()) {
	// ...
}

The register size directly depends on the precision of the data we are working on.

Register load and store instructions

Loading memory from a vector into a register:

int n = mipp::N<float>() * 10;
std::vector<float> myVector(n);
int i = 0;
mipp::Reg<float> r1 = &myVector[i*mipp::N<float>()];

Store can be done with the store(...) method:

int n = mipp::N<float>() * 10;
std::vector<float> myVector(n);
int i = 0;
mipp::Reg<float> r1 = &myVector[i*mipp::N<float>()];

// do something with r1

r1.store(&myVector[(i+1)*mipp::N<float>()]);

By default the loads and stores work on unaligned memory. It is possible to control this behavior with the -DMIPP_ALIGNED_LOADS definition: when specified, the loads and stores work on aligned memory by default. In the aligned memory mode, it is still possible to perform unaligned memory operations with the mipp::loadu and mipp::storeu functions. However, it is not possible to perform aligned loads and stores in the unaligned memory mode.

To allocate aligned data you can use the MIPP aligned memory allocator wrapped into the mipp::vector class. mipp::vector is fully retro-compatible with the standard std::vector class and it can be use everywhere you can use std::vector.

mipp::vector<float> myVector(n);

Register initialization

You can initialize a vector register from a scalar value:

mipp::Reg<float> r1; // r1 = | unknown | unknown | unknown | unknown |
r1 = 1.0;            // r1 = |    +1.0 |    +1.0 |    +1.0 |    +1.0 |

Or from an initializer list (std::initializer_list):

mipp::Reg<float> r1;       // r1 = | unknown | unknown | unknown | unknown |
r1 = {1.0, 2.0, 3.0, 4.0}; // r1 = |    +1.0 |    +2.0 |    +3.0 |    +4.0 |

Computational instructions

Add two vector registers:

mipp::Reg<float> r1, r2, r3;

r1 = 1.0;     // r1 = | +1.0 | +1.0 | +1.0 | +1.0 |
r2 = 2.0;     // r2 = | +2.0 | +2.0 | +2.0 | +2.0 |

r3 = r1 + r2; // r3 = | +3.0 | +3.0 | +3.0 | +3.0 |

Subtract two vector registers:

mipp::Reg<float> r1, r2, r3;

r1 = 1.0;     // r1 = | +1.0 | +1.0 | +1.0 | +1.0 |
r2 = 2.0;     // r2 = | +2.0 | +2.0 | +2.0 | +2.0 |

r3 = r1 - r2; // r3 = | -1.0 | -1.0 | -1.0 | -1.0 |

Multiply two vector registers:

mipp::Reg<float> r1, r2, r3;

r1 = 1.0;     // r1 = | +1.0 | +1.0 | +1.0 | +1.0 |
r2 = 2.0;     // r2 = | +2.0 | +2.0 | +2.0 | +2.0 |

r3 = r1 * r2; // r3 = | +2.0 | +2.0 | +2.0 | +2.0 |

Divide two vector registers:

mipp::Reg<float> r1, r2, r3;

r1 = 1.0;     // r1 = | +1.0 | +1.0 | +1.0 | +1.0 |
r2 = 2.0;     // r2 = | +2.0 | +2.0 | +2.0 | +2.0 |

r3 = r1 / r2; // r3 = | +0.5 | +0.5 | +0.5 | +0.5 |

Fused multiply and add of three vector registers:

mipp::Reg<float> r1, r2, r3, r4;

r1 = 2.0;                     // r1 = | +2.0 | +2.0 | +2.0 | +2.0 |
r2 = 3.0;                     // r2 = | +3.0 | +3.0 | +3.0 | +3.0 |
r2 = 1.0;                     // r3 = | +1.0 | +1.0 | +1.0 | +1.0 |

// r4 = (r1 * r2) + r3
r4 = mipp::fmadd(r1, r2, r3); // r4 = | +7.0 | +7.0 | +7.0 | +7.0 |

Fused negative multiply and add of three vector registers:

mipp::Reg<float> r1, r2, r3, r4;

r1 = 2.0;                      // r1 = | +2.0 | +2.0 | +2.0 | +2.0 |
r2 = 3.0;                      // r2 = | +3.0 | +3.0 | +3.0 | +3.0 |
r2 = 1.0;                      // r3 = | +1.0 | +1.0 | +1.0 | +1.0 |

// r4 = -((r1 * r2) + r3)
r4 = mipp::fnmadd(r1, r2, r3); // r4 = | -7.0 | -7.0 | -7.0 | -7.0 |

Square root of a vector register:

mipp::Reg<float> r1, r2;

r1 = 9.0;             // r1 = | +9.0 | +9.0 | +9.0 | +9.0 |

r2 = mipp::sqrt(r1);  // r2 = | +3.0 | +3.0 | +3.0 | +3.0 |

Reciprocal square root of a vector register (be careful: this intrinsic exists only for simple precision floating-point numbers):

mipp::Reg<float> r1, r2;

r1 = 9.0;             // r1 = | +9.0 | +9.0 | +9.0 | +9.0 |

r2 = mipp::rsqrt(r1); // r2 = | +0.3 | +0.3 | +0.3 | +0.3 |

Selections

Select the minimum between two vector registers:

mipp::Reg<float> r1, r2, r3;

r1 = 2.0;               // r1 = | +2.0 | +2.0 | +2.0 | +2.0 |
r2 = 3.0;               // r2 = | +3.0 | +3.0 | +3.0 | +3.0 |

r3 = mipp::min(r1, r2); // r3 = | +2.0 | +2.0 | +2.0 | +2.0 |

Select the maximum between two vector registers:

mipp::Reg<float> r1, r2, r3;

r1 = 2.0;               // r1 = | +2.0 | +2.0 | +2.0 | +2.0 |
r2 = 3.0;               // r2 = | +3.0 | +3.0 | +3.0 | +3.0 |

r3 = mipp::max(r1, r2); // r3 = | +3.0 | +3.0 | +3.0 | +3.0 |

Permutations

The rrot(...) method allows you to perform a right rotation (a cyclic permutation) of the elements inside the register:

mipp::Reg<float> r1, r2;
r1 = {3.0, 2.0, 1.0, 0.0}  // r1 = | +3.0 | +2.0 | +1.0 | +0.0 |

r2 = mipp::rrot(r1);       // r2 = | +0.0 | +3.0 | +2.0 | +1.0 |
r1 = mipp::rrot(r2);       // r1 = | +1.0 | +0.0 | +3.0 | +2.0 |
r2 = mipp::rrot(r1);       // r2 = | +2.0 | +1.0 | +0.0 | +3.0 |
r1 = mipp::rrot(r2);       // r1 = | +3.0 | +2.0 | +1.0 | +0.0 |

Of course there are many more available instructions in the MIPP wrapper and you can find these instructions at the end of this page.

Addition of two vectors

#include <cstdlib> // rand()
#include "mipp.h"

int main()
{
	// data allocation
	const int n = 32000; // size of the vectors vA, vB, vC
	mipp::vector<float> vA(n); // in
	mipp::vector<float> vB(n); // in
	mipp::vector<float> vC(n); // out

	// data initialization
	for (int i = 0; i < n; i++) vA[i] = rand() % 10;
	for (int i = 0; i < n; i++) vB[i] = rand() % 10;

	// declare 3 vector registers
	mipp::Reg<float> rA, rB, rC;

	// compute rC with the MIPP vectorized functions
	for (int i = 0; i < n; i += mipp::N<float>()) {
		rA.load(&vA[i]); // Unaligned load by default (use the -DMIPP_ALIGNED_LOADS
		rB.load(&vB[i]); // macro definition to force aligned loads and stores).
		rC = rA + rB;
		rC.store(&vC[i]);
	}

	return 0;
}

Vectorizing an existing code

Scalar code

// ...
for (int i = 0; i < n; i++) {
	out[i] = 0.75f * in1[i] * std::exp(in2[i]);
}
// ...

Vectorized code

// ...
// Compute the vectorized loop size which is a multiple of 'mipp::N<float>()'.
auto vecLoopSize = (n / mipp::N<float>()) * mipp::N<float>();
mipp::Reg<float> rout, rin1, rin2;
for (int i = 0; i < vecLoopSize; i += mipp::N<float>()) {
	rin1.load(&in1[i]); // Unaligned load by default (use the -DMIPP_ALIGNED_LOADS
	rin2.load(&in2[i]); // macro definition to force aligned loads and stores).
	// The '0.75f' constant will be broadcast in a vector but it has to be at
	// the right of a 'mipp::Reg<T>', this is why it has been moved at the right
	// of the 'rin1' register. Notice that 'std::exp' has been replaced by
	// 'mipp::exp'.
	rout = rin1 * 0.75f * mipp::exp(rin2);
	rout.store(&out[i]);
}

// Scalar tail loop: compute the remaining elements that can't be vectorized.
for (int i = vecLoopSize; i < n; i++) {
	out[i] = 0.75f * in1[i] * std::exp(in2[i]);
}
// ...

Masked instructions

MIPP comes with two generic and templatized masked functions (mask and maskz). Those functions allow you to benefit from the AVX-512 masked instructions. mask and maskz functions are retro compatible with older instruction sets.

mipp::Reg<        float   > ZMM1 = {   40,  -30,    60,    80};
mipp::Reg<        float   > ZMM2 = 0.1; // broadcast
mipp::Msk<mipp::N<float>()> k1   = {false, true, false, false};

// ZMM3 = k1 ? ZMM1 * ZMM2 : ZMM1;
auto ZMM3 = mipp::mask<float, mipp::mul>(k1, ZMM1, ZMM1, ZMM2);
std::cout << ZMM3 << std::endl; // output: "[40, -3, 60, 80]"

// ZMM4 = k1 ? ZMM1 * ZMM2 : 0;
auto ZMM4 = mipp::maskz<float, mipp::mul>(k1, ZMM1, ZMM2);
std::cout << ZMM4 << std::endl; // output: "[0, -3, 0, 0]"

List of MIPP functions

This section presents an exhaustive list of all the available functions in MIPP. Of course the MIPP wrapper does not cover all the possible intrinsics of each instruction set but it tries to give you the most important and useful ones.

In the following tables, T, T1 and T2 stand for data types (double, float, int64_t, int32_t, int16_t or int8_t). N stands for the number or elements in a mask or in a register. N is a strictly positive integer and can easily be deduced from the data type: constexpr int N = mipp::N<T>(). When T and N are mixed in a prototype, N has to satisfy the previous constraint (N = mipp::N<T>()).

In the documentation there are some terms that requires to be clarified:

• register element: a SIMD register is composed by multiple scalar elements, those elements are built-in data types (double, float, int64_t, ...),
• register lane: modern instruction sets can have multiple implicit sub parts in an entire SIMD register, those sub parts are called lanes (SSE has one lane of 128 bits, AVX has two lanes of 128 bits, AVX-512 has four lanes of 128 bits).

Memory operations

Bitwise operations

The pipe keyword stands for the "|" binary operator.

Logical comparisons

Conversions and packing

Arithmetic operations

Arithmetic operations on complex numbers

The complex operations are exclusively performed on Regx2<T> objects (one Regx2<T> object contains two Reg<T> hardware registers). Each Regx2<T> object contains mipp::N<T>() complex number. If we declare a Regx2<T> cmplx object, the cmplx[0] register will contain the real part of the complex numbers and cmplx[1] will contain the imaginary part. Depending on how you stored your complex numbers in memory you can need to use reordering before calling a complex operation. For instance, if you choose to store the complex numbers in a mixed format like this: r0, i0, r1, i1, r2, i2, ..., rn, in you will need to call the mipp::deinterleave operation before and the mipp::interleave operation after the complex operation.

Reductions (horizontal functions)

Math functions