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Fundamentals of AVX Programming

Data Types

Data Type Description
__m128 128-bit vector containing 4 floats
__m128d 128-bit vector containing 2 doubles
__m128i 128-bit vector containing integers
__m256 256-bit vector containing 8 floats
__m256d 256-bit vector containing 4 doubles
__m256i 256-bit vector containing integers
  • Each type starts with two underscores, an m, and the width of the vector in bits.
  • If a vector type ends in d, it contains doubles, and if it doesn't have a suffix, it contains floats.
  • An integer vector type can contain any type of integer, from chars to shorts to unsigned long longs. That is, an _m256i may contain 32 chars, 16 shorts, 8 ints, or 4 longs. These integers can be signed or unsigned.

Function Naming Conventions

_mm<bit_width>_<name>_<data_type>

  • <bit_width> identifies the size of the vector returned by the function. For 128-bit vectors, this is empty. For 256-bit vectors, this is set to 256.
  • <name> describes the operation performed by the intrinsic
  • <data_type> identifies the data type of the function's primary arguments
    > - ps - vectors contain floats (ps stands for packed single-precision)
    > - pd - vectors contain doubles (pd stands for packed double-precision)
    > - epi8/epi16/epi32/epi64 - vectors contain 8-bit/16-bit/32-bit/64-bit signed integers
    > - epu8/epu16/epu32/epu64 - vectors contain 8-bit/16-bit/32-bit/64-bit unsigned integers
    > - si128/si256 - unspecified 128-bit vector or 256-bit vector
    > - m128/m128i/m128d/m256/m256i/m256d - identifies input vector types when they're different than the type of the returned vector

A data type represents memory and a function represents a multimedia operation, so the AVX data types start with two underscores with an m, AVX functions start with an underscore with two ms .

Initialization Intrinsics

Initialization with Scalar Values

Function Description
_mm256_setzero_ps/pd Returns a floating-point vector filled with zeros
_mm256_setzero_si256 Returns an integer vector whose bytes are set to zero
_mm256_set1_ps/pd Fill a vector with a floating-point value
_mm256_set1_epi8/epi16/epi32/epi64x Fill a vector with an integer
_mm256_set_ps/pd Initialize a vector with eight floats (ps)or four doubles (pd)
_mm256_set_epi8/epi16/epi32/epi64x Initialize a vector with integers
_mm256_set_m128/m128d/m128i Initialize a 256-bit vector with two 128-bit vectors
_mm256_setr_ps/pd Initialize a vector with eight floats (ps) or four doubles (pd) in reverse order
_mm256_setr_epi8/epi16/epi32/epi64x Initialize a vector with integers in reverse order

Loading Data from Memory

Data Type Description
_mm256_load_ps/pd Loads a floating-point vector from an aligned memory address
_mm256_load_si256 Loads an integer vector from an aligned memory address
_mm256_loadu_ps/pd Loads a floating-point vector from an unaligned memory address
_mm256_loadu_si256 Loads an integer vector from an unalignedmemory address
_mm_maskload_ps/pd _mm256_maskload_ps/pd Load portions of a 128-bit/256-bitfloating-point vector according to a mask
(2)_mm_maskload_epi32/64 (2)_mm256_maskload_epi32/64 Load portions of a 128-bit/256-bitinteger vector according to a mask

The last two functions are preceded with (2) because they're provided by AVX2, not AVX.

Each _mm256_load_*intrinsic accepts a memory address that must be aligned on a 32-byte boundary.

Arithmetic Intrinsics

Addition and Subtraction

Data Type Description
_mm256_add_ps/pd Add two floating-point vectors
_mm256_sub_ps/pd Subtract two floating-point vectors
(2)_mm256_add_epi8/16/32/64 Add two integer vectors
(2)_mm236_sub_epi8/16/32/64 Subtract two integer vectors
(2)_mm256_adds_epi8/16 (2)_mm256_adds_epu8/16 Add two integer vectors with saturation
(2)_mm256_subs_epi8/16 (2)_mm256_subs_epu8/16 Subtract two integer vectors with saturation
_mm256_hadd_ps/pd Add two floating-point vectors horizontally
_mm256_hsub_ps/pd Subtract two floating-point vectors horizontally
(2)_mm256_hadd_epi16/32 Add two integer vectors horizontally
(2)_mm256_hsub_epi16/32 Subtract two integer vectors horizontally
(2)_mm256_hadds_epi16 Add two vectors containing shorts horizontally with saturation
(2)_mm256_hsubs_epi16 Subtract two vectors containing shorts horizontally with saturation
_mm256_addsub_ps/pd Add and subtract two floating-point vectors

Functions that take saturation into account clamp the result to the minimum/maximum value that can be stored. Functions without saturation ignore the memory issue when saturation occurs.

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This may seem strange to add and subtract elements horizontally, but these operations are helpful when multiplying complex numbers.

_mm256_addsub_ps/pd, alternately subtracts and adds elements of two floating-point vectors. That is, even elements are subtracted and odd elements are added .

Multiplication and Division

Data Type Description
_mm256_mul_ps/pd Multiply two floating-point vectors
(2)_mm256_mul_epi32 (2)_mm256_mul_epu32 Multiply the lowest four elements of vectors containing 32-bit integers
(2)_mm256_mullo_epi16/32 Multiply integers and store low halves
(2)_mm256_mulhi_epi16 (2)_mm256_mulhi_epu16 Multiply integers and store high halves
(2)_mm256_mulhrs_epi16 Multiply 16-bit elements to form 32-bit elements
_mm256_div_ps/pd Divide two floating-point vectors

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This image is WRONG !!!

Please read the reference from this manual.

Only the four low elements of the _mm256_mul_epi32 and _mm256_mul_epu32 intrinsics are multiplied together, and the result is a vector containing four long integers.

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They multiply every element of both vectors store only the low half of each product

Fused Multiply and Add (FMA)

Data Type Description
(2)_mm_fmadd_ps/pd/ (2)_mm256_fmadd_ps/pd Multiply two vectors and add the product to a third (res = a * b + c)
(2)_mm_fmsub_ps/pd/ (2)_mm256_fmsub_ps/pd Multiply two vectors and subtract a vector from the product (res = a * b - c)
(2)_mm_fmadd_ss/sd Multiply and add the lowest element in the vectors (res[0] = a[0] * b[0] + c[0])
(2)_mm_fmsub_ss/sd Multiply and subtract the lowest element in the vectors (res[0] = a[0] * b[0] - c[0])
(2)_mm_fnmadd_ps/pd (2)_mm256_fnmadd_ps/pd Multiply two vectors and add the negated product to a third (res = -(a * b) + c)
(2)_mm_fnmsub_ps/pd/ (2)_mm256_fnmsub_ps/pd Multiply two vectors and add the negated product to a third (res = -(a * b) - c)
(2)_mm_fnmadd_ss/sd Multiply the two lowest elements and add the negated product to the lowest element of the third vector (res[0] = -(a[0] * b[0]) + c[0])
(2)_mm_fnmsub_ss/sd Multiply the lowest elements and subtract the lowest element of the third vector from the negated product (res[0] = -(a[0] * b[0]) - c[0])
(2)_mm_fmaddsub_ps/pd/ (2)_mm256_fmaddsub_ps/pd Multiply two vectors and alternately add and subtract from the product (res = a * b +/- c) (Odd add, even sub)
(2)_mm_fmsubadd_ps/pd/ (2)_mmf256_fmsubadd_ps/pd Multiply two vectors and alternately subtract and add from the product (res = a * b -/+ c) (Odd sub, even add)

Permuting and Shuffling

Permuting

Data Type Description
_mm_permute_ps/pd _mm256_permute_ps/pd Select elements from the input vector based on an 8-bit control value
(2)_mm256_permute4x64_pd/ (2)_mm256_permute4x64_epi64 Select 64-bit elements from the input vector based on an 8-bit control value
_mm256_permute2f128_ps/pd Select 128-bit chunks from two input vectors based on an 8-bit control value
_mm256_permute2f128_si256 Select 128-bit chunks from two input vectors based on an 8-bit control value
_mm_permutevar_ps/pd _mm256_permutevar_ps/pd Select elements from the input vector based on bits in an integer vector
(2)_mm256_permutevar8x32_ps (2)_mm256_permutevar8x32_epi32 Select 32-bit elements (floats and ints) using indices in an integer vector

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Shuffling

Data Type Description
_mm256_shuffle_ps/pd Select floating-point elements according to an 8-bit value
_mm256_shuffle_epi8/ _mm256_shuffle_epi32 Select integer elements according to an8-bit value
(2)_mm256_shufflelo_epi16/ (2)_mm256_shufflehi_epi16 Select 128-bit chunks from two input vectors based on an 8-bit control value

For _mm256_shuffle_pd, only the high four bits of the control value are used. If the input vectors contain ints or floats, all the control bits are used. For _mm256_shuffle_ps, the first two pairs of bits select elements from the first vector and the second two pairs of bits select elements from the second vector.

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