# DGEMM

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In this article, we have covered DGEMM (**Double** Precision General Matrix Multiplication) which is a standard library function for Matrix Multiplication and a variant of GEMM.

Table of contents:

- Introduction to DGEMM
- Use of DGEMM
- Difference between DGEMM and other GEMM functions

## Introduction to DGEMM

DGEMM stands for "**Double Precision General Matrix Multiplication**".

It is a standard gemm routine in BLAS and BLIS libraries like OpenBLAS and is used to do Matrix Multiplication. It performs the standard GEMM operation that is Matrix Matrix multiplication with the matrices being of datatype **Double 64 bits**.

The API of DGEMM is as follows:

```
status dgemm(
char transa,
char transb,
dim_t M,
dim_t N,
dim_t K,
double alpha,
const double* A,
dim_t lda,
const double* B,
dim_t ldb,
double beta,
double* C,
dim_t ldc
)
```

Note:

- The 3 matrices A, B and C are in double datatype (64 bits).

DGEMM operation is defined as follows:

```
C = alpha * op(A) * op(B) + beta * C
```

where

- op(X) = X or X
^{T}depending on transa and related values. X is a matrix. - alpha and beta are scalars
- A, B, and C are matrices
- op(A) is an MxK matrix
- op(B) is an KxN matrix
- C is an MxN matrix (output)

The parameters are as follows:

- transa: Transposition flag for matrix A. If it is set to 0, op(A) = A and if it is set to 1, op(A) = A
^{T}. - transb: Transposition flag for matrix B. If it is set to 0, op(B) = B and if it is set to 1, op(B) = B
^{T}. - M, N, K: dimensions
- alpha: parameter that is used to scale the product of matrices A and B.
- A: Input matrix of size MxK
- lda: Leading dimension for matrix A
- B: Input matrix of size KxN
- ldb: Leading dimension for matrix B
- beta: Beta parameter that is used to scale matrix C
- C: Output matrix
- ldc: Leading dimension for matrix C

The different combinations in DGEMM will be:

- C = alpha * A * B + beta * C
- C = alpha * A
^{T}* B + beta * C - C = alpha * A * B
^{T}+ beta * C - C = alpha * A
^{T}* B^{T}+ beta * C

The GEMM operations like DGEMM from any library are highly optimized for specific applications and platforms.

## Use of DGEMM

DGEMM is used in different operations in Scientific calculations where the precision is expected to be maximum possible.

DGEMM functions are **not used** in Machine Learning models. These operations include MatMul, Convolution and others. This is because single precision (float, 32 bits) is enough for Machine Learning calculations. Moreover, the research is towards lower precision like INT8, INT4, FP16. Hence, SGEMM is used in this case instead of DGEMM.

DGEMM calls are available in different libraries like:

- BLAS like OpenBLAS
- BLIS like FLAME BLIS
- FBGEMM
- OneDNN

and others.

## Difference between dgemm and other gemm functions

**SGEMM vs DGEMM**

The major difference is that SGEMM deals with **single precision (float 32 bits)** data while DGEMM deals with **double precision (double 64 bits)** data.

The float datatype in SGEMM has 7 decimal digits reserved for precision and the toal size is 32 bits . On the other hand, the double datatype used in DGEMM has a total size of 64 bits and is a standard: "*IEEE 754 double-precision floating point number*".

**DGEMM vs GEMM**

The main difference is that GEMM is the generalized function. DGEMM is a specific implementation of GEMM.

The general GEMM functions have different variations with different datatypes for the 3 matrices involved like:

- gemm_u8s8s32: GEMM with A of datatype unsigned INT8, B of datatype signed INT8 and output as signed INT32.
- gemm_s8s8s32: GEMM with A of datatype signed INT8, B of datatype signed INT8 and output as signed INT32.

and much more.

The datatype is DGEMM is fixed that is **DOUBLE 64 bits**.

- dgemm vs (cgemm and zgemm)

cgemm and zgemm deal with matrices of Complex datatype (that is a real and imaginary part). DGEMM deals with only real numbers of double datatype.

With this article at OpenGenus, you must have the complete idea of DGEMM.