binnedBLAS.h defines BLAS Methods that operate on binned types. More...

#include "binned.h"
#include "reproBLAS.h"

Functions
float	binnedBLAS_samax (const int N, const float *X, const int incX)
	Find maximum absolute value in vector of single precision. More...

double	binnedBLAS_damax (const int N, const double *X, const int incX)
	Find maximum absolute value in vector of double precision. More...

void	binnedBLAS_camax_sub (const int N, const void X, const int incX, void amax)
	Find maximum magnitude in vector of complex single precision. More...

void	binnedBLAS_zamax_sub (const int N, const void X, const int incX, void amax)
	Find maximum magnitude in vector of complex double precision. More...

float	binnedBLAS_samaxm (const int N, const float X, const int incX, const float Y, const int incY)
	Find maximum absolute value pairwise product between vectors of single precision. More...

double	binnedBLAS_damaxm (const int N, const double X, const int incX, const double Y, const int incY)
	Find maximum absolute value pairwise product between vectors of double precision. More...

void	binnedBLAS_camaxm_sub (const int N, const void X, const int incX, const void Y, const int incY, void *amaxm)
	Find maximum magnitude pairwise product between vectors of complex single precision. More...

void	binnedBLAS_zamaxm_sub (const int N, const void X, const int incX, const void Y, const int incY, void *amaxm)
	Find maximum magnitude pairwise product between vectors of complex double precision. More...

void	binnedBLAS_dbdsum (const int fold, const int N, const double X, const int incX, double_binned Y)
	Add to binned double precision Y the sum of double precision vector X. More...

void	binnedBLAS_dmdsum (const int fold, const int N, const double X, const int incX, double priY, const int incpriY, double *carY, const int inccarY)
	Add to manually specified binned double precision Y the sum of double precision vector X. More...

void	binnedBLAS_dbdasum (const int fold, const int N, const double X, const int incX, double_binned Y)
	Add to binned double precision Y the absolute sum of double precision vector X. More...

void	binnedBLAS_dmdasum (const int fold, const int N, const double X, const int incX, double priY, const int incpriY, double *carY, const int inccarY)
	Add to manually specified binned double precision Y the absolute sum of double precision vector X. More...

double	binnedBLAS_dbdssq (const int fold, const int N, const double X, const int incX, const double scaleY, double_binned Y)
	Add to scaled binned double precision Y the scaled sum of squares of elements of double precision vector X. More...

double	binnedBLAS_dmdssq (const int fold, const int N, const double X, const int incX, const double scaleY, double priY, const int incpriY, double *carY, const int inccarY)
	Add to scaled manually specified binned double precision Y the scaled sum of squares of elements of double precision vector X. More...

void	binnedBLAS_dbddot (const int fold, const int N, const double X, const int incX, const double Y, const int incY, double_binned *Z)
	Add to binned double precision Z the dot product of double precision vectors X and Y. More...

void	binnedBLAS_dmddot (const int fold, const int N, const double X, const int incX, const double Y, const int incY, double manZ, const int incmanZ, double carZ, const int inccarZ)
	Add to manually specified binned double precision Z the dot product of double precision vectors X and Y. More...

void	binnedBLAS_zbzsum (const int fold, const int N, const void X, const int incX, double_binned Y)
	Add to binned complex double precision Y the sum of complex double precision vector X. More...

void	binnedBLAS_zmzsum (const int fold, const int N, const void X, const int incX, double priY, const int incpriY, double *carY, const int inccarY)
	Add to manually specified binned complex double precision Y the sum of complex double precision vector X. More...

void	binnedBLAS_dbzasum (const int fold, const int N, const void X, const int incX, double_binned Y)
	Add to binned double precision Y the absolute sum of complex double precision vector X. More...

void	binnedBLAS_dmzasum (const int fold, const int N, const void X, const int incX, double priY, const int incpriY, double *carY, const int inccarY)
	Add to manually specified binned double precision Y the absolute sum of complex double precision vector X. More...

double	binnedBLAS_dbzssq (const int fold, const int N, const void X, const int incX, const double scaleY, double_binned Y)
	Add to scaled binned double precision Y the scaled sum of squares of elements of complex double precision vector X. More...

double	binnedBLAS_dmzssq (const int fold, const int N, const void X, const int incX, const double scaleY, double priY, const int incpriY, double *carY, const int inccarY)
	Add to scaled manually specified binned double precision Y the scaled sum of squares of elements of complex double precision vector X. More...

void	binnedBLAS_zbzdotu (const int fold, const int N, const void X, const int incX, const void Y, const int incY, double_binned *Z)
	Add to binned complex double precision Z the unconjugated dot product of complex double precision vectors X and Y. More...

void	binnedBLAS_zmzdotu (const int fold, const int N, const void X, const int incX, const void Y, const int incY, double manZ, const int incmanZ, double carZ, const int inccarZ)
	Add to manually specified binned complex double precision Z the unconjugated dot product of complex double precision vectors X and Y. More...

void	binnedBLAS_zbzdotc (const int fold, const int N, const void X, const int incX, const void Y, const int incY, double_binned *Z)
	Add to binned complex double precision Z the conjugated dot product of complex double precision vectors X and Y. More...

void	binnedBLAS_zmzdotc (const int fold, const int N, const void X, const int incX, const void Y, const int incY, double manZ, const int incmanZ, double carZ, const int inccarZ)
	Add to manually specified binned complex double precision Z the conjugated dot product of complex double precision vectors X and Y. More...

void	binnedBLAS_sbssum (const int fold, const int N, const float X, const int incX, float_binned Y)
	Add to binned single precision Y the sum of single precision vector X. More...

void	binnedBLAS_smssum (const int fold, const int N, const float X, const int incX, float priY, const int incpriY, float *carY, const int inccarY)
	Add to manually specified binned single precision Y the sum of single precision vector X. More...

void	binnedBLAS_sbsasum (const int fold, const int N, const float X, const int incX, float_binned Y)
	Add to binned single precision Y the absolute sum of single precision vector X. More...

void	binnedBLAS_smsasum (const int fold, const int N, const float X, const int incX, float priY, const int incpriY, float *carY, const int inccarY)
	Add to manually specified binned single precision Y the absolute sum of double precision vector X. More...

float	binnedBLAS_sbsssq (const int fold, const int N, const float X, const int incX, const float scaleY, float_binned Y)
	Add to scaled binned single precision Y the scaled sum of squares of elements of single precision vector X. More...

float	binnedBLAS_smsssq (const int fold, const int N, const float X, const int incX, const float scaleY, float priY, const int incpriY, float *carY, const int inccarY)
	Add to scaled manually specified binned single precision Y the scaled sum of squares of elements of single precision vector X. More...

void	binnedBLAS_sbsdot (const int fold, const int N, const float X, const int incX, const float Y, const int incY, float_binned *Z)
	Add to binned single precision Z the dot product of single precision vectors X and Y. More...

void	binnedBLAS_smsdot (const int fold, const int N, const float X, const int incX, const float Y, const int incY, float manZ, const int incmanZ, float carZ, const int inccarZ)
	Add to manually specified binned single precision Z the dot product of single precision vectors X and Y. More...

void	binnedBLAS_cbcsum (const int fold, const int N, const void X, const int incX, float_binned Y)
	Add to binned complex single precision Y the sum of complex single precision vector X. More...

void	binnedBLAS_cmcsum (const int fold, const int N, const void X, const int incX, float priY, const int incpriY, float *carY, const int inccarY)
	Add to manually specified binned complex single precision Y the sum of complex single precision vector X. More...

void	binnedBLAS_sbcasum (const int fold, const int N, const void X, const int incX, float_binned Y)
	Add to binned single precision Y the absolute sum of complex single precision vector X. More...

void	binnedBLAS_smcasum (const int fold, const int N, const void X, const int incX, float priY, const int incpriY, float *carY, const int inccarY)
	Add to manually specified binned single precision Y the absolute sum of complex single precision vector X. More...

float	binnedBLAS_sbcssq (const int fold, const int N, const void X, const int incX, const float scaleY, float_binned Y)
	Add to scaled binned single precision Y the scaled sum of squares of elements of complex single precision vector X. More...

float	binnedBLAS_smcssq (const int fold, const int N, const void X, const int incX, const float scaleY, float priY, const int incpriY, float *carY, const int inccarY)
	Add to scaled manually specified binned single precision Y the scaled sum of squares of elements of complex single precision vector X. More...

void	binnedBLAS_cbcdotu (const int fold, const int N, const void X, const int incX, const void Y, const int incY, float_binned *Z)
	Add to binned complex single precision Z the unconjugated dot product of complex single precision vectors X and Y. More...

void	binnedBLAS_cmcdotu (const int fold, const int N, const void X, const int incX, const void Y, const int incY, float manZ, const int incmanZ, float carZ, const int inccarZ)
	Add to manually specified binned complex single precision Z the unconjugated dot product of complex single precision vectors X and Y. More...

void	binnedBLAS_cbcdotc (const int fold, const int N, const void X, const int incX, const void Y, const int incY, float_binned *Z)
	Add to binned complex single precision Z the conjugated dot product of complex single precision vectors X and Y. More...

void	binnedBLAS_cmcdotc (const int fold, const int N, const void X, const int incX, const void Y, const int incY, float manZ, const int incmanZ, float carZ, const int inccarZ)
	Add to manually specified binned complex single precision Z the conjugated dot product of complex single precision vectors X and Y. More...

void	binnedBLAS_dbdgemv (const int fold, const char Order, const char TransA, const int M, const int N, const double alpha, const double A, const int lda, const double X, const int incX, double_binned *Y, const int incY)
	Add to binned double precision vector Y the matrix-vector product of double precision matrix A and double precision vector X. More...

void	binnedBLAS_dbdgemm (const int fold, const char Order, const char TransA, const char TransB, const int M, const int N, const int K, const double alpha, const double A, const int lda, const double B, const int ldb, double_binned *C, const int ldc)
	Add to binned double precision matrix C the matrix-matrix product of double precision matrices A and B. More...

void	binnedBLAS_sbsgemv (const int fold, const char Order, const char TransA, const int M, const int N, const float alpha, const float A, const int lda, const float X, const int incX, float_binned *Y, const int incY)
	Add to binned single precision vector Y the matrix-vector product of single precision matrix A and single precision vector X. More...

void	binnedBLAS_sbsgemm (const int fold, const char Order, const char TransA, const char TransB, const int M, const int N, const int K, const float alpha, const float A, const int lda, const float B, const int ldb, float_binned *C, const int ldc)
	Add to binned single precision matrix C the matrix-matrix product of single precision matrices A and B. More...

void	binnedBLAS_zbzgemv (const int fold, const char Order, const char TransA, const int M, const int N, const void alpha, const void A, const int lda, const void X, const int incX, double_complex_binned Y, const int incY)
	Add to binned complex double precision vector Y the matrix-vector product of complex double precision matrix A and complex double precision vector X. More...

void	binnedBLAS_zbzgemm (const int fold, const char Order, const char TransA, const char TransB, const int M, const int N, const int K, const void alpha, const void A, const int lda, const void B, const int ldb, double_complex_binned C, const int ldc)
	Add to binned complex double precision matrix C the matrix-matrix product of complex double precision matrices A and B. More...

void	binnedBLAS_cbcgemv (const int fold, const char Order, const char TransA, const int M, const int N, const void alpha, const void A, const int lda, const void X, const int incX, float_complex_binned Y, const int incY)
	Add to binned complex single precision vector Y the matrix-vector product of complex single precision matrix A and complex single precision vector X. More...

void	binnedBLAS_cbcgemm (const int fold, const char Order, const char TransA, const char TransB, const int M, const int N, const int K, const void alpha, const void A, const int lda, const void B, const int ldb, float_complex_binned C, const int ldc)
	Add to binned complex single precision matrix C the matrix-matrix product of complex single precision matrices A and B. More...

Detailed Description

binnedBLAS.h defines BLAS Methods that operate on binned types.

This header is modeled after cblas.h, and as such functions are prefixed with character sets describing the data types they operate upon. For example, the function dfoo would perform the function foo on double possibly returning a double.

If two character sets are prefixed, the first set of characters describes the output and the second the input type. For example, the function dzbar would perform the function bar on double complex and return a double.

Such character sets are listed as follows:

d - double (double)
z - complex double (*void)
s - float (float)
c - complex float (*void)
db - binned double (double_binned)
zb - binned complex double (double_complex_binned)
sb - binned float (float_binned)
cb - binned complex float (float_complex_binned)
dm - manually specified binned double (double, double)
zm - manually specified binned complex double (double, double)
sm - manually specified binned float (float, float)
cm - manually specified binned complex float (float, float)

Throughout the library, complex types are specified via *void pointers. These routines will sometimes be suffixed by sub, to represent that a function has been made into a subroutine. This allows programmers to use whatever complex types they are already using, as long as the memory pointed to is of the form of two adjacent floating point types, the first and second representing real and imaginary components of the complex number.

The goal of using binned types is to obtain either more accurate or reproducible summation of floating point numbers. In reproducible summation, floating point numbers are split into several slices along predefined boundaries in the exponent range. The space between two boundaries is called a bin. Binned types are composed of several accumulators, each accumulating the slices in a particular bin. The accumulators correspond to the largest consecutive nonzero bins seen so far.

The parameter fold describes how many accumulators are used in the binned types supplied to a subroutine (an binned type with k accumulators is k-fold). The default value for this parameter can be set in config.h. If you are unsure of what value to use for fold, we recommend 3. Note that the fold of binned types must be the same for all binned types that interact with each other. Operations on more than one binned type assume all binned types being operated upon have the same fold. Note that the fold of an binned type may not be changed once the type has been allocated. A common use case would be to set the value of fold as a global macro in your code and supply it to all binned functions that you use.

Power users of the library may find themselves wanting to manually specify the underlying primary and carry vectors of an binned type themselves. If you do not know what these are, don't worry about the manually specified binned types.

Function Documentation

void binnedBLAS_camax_sub	(	const int	N,
		const void *	X,
		const int	incX,
		void *	amax
	)

Find maximum magnitude in vector of complex single precision.

Returns the magnitude of the element of maximum magnitude in an array.

Parameters

N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
amax	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_camaxm_sub	(	const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		void *	amaxm
	)

Find maximum magnitude pairwise product between vectors of complex single precision.

Returns the magnitude of the pairwise product of maximum magnitude between X and Y.

Parameters

N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
Y	complex single precision vector
incY	Y vector stride (use every incY'th element)
amaxm	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_cbcdotc	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		float_complex_binned *	Z
	)

Add to binned complex single precision Z the conjugated dot product of complex single precision vectors X and Y.

Add to Z the binned sum of the pairwise products of X and conjugated Y.

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
Y	complex single precision vector
incY	Y vector stride (use every incY'th element)
Z	binned scalar Z

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_cbcdotu	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		float_complex_binned *	Z
	)

Add to binned complex single precision Z the unconjugated dot product of complex single precision vectors X and Y.

Add to Z the binned sum of the pairwise products of X and Y.

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
Y	complex single precision vector
incY	Y vector stride (use every incY'th element)
Z	binned scalar Z

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_cbcgemm	(	const int	fold,
		const char	Order,
		const char	TransA,
		const char	TransB,
		const int	M,
		const int	N,
		const int	K,
		const void *	alpha,
		const void *	A,
		const int	lda,
		const void *	B,
		const int	ldb,
		float_complex_binned *	C,
		const int	ldc
	)

Add to binned complex single precision matrix C the matrix-matrix product of complex single precision matrices A and B.

Performs one of the matrix-matrix operations

C := alpha*op(A)*op(B) + C,

where op(X) is one of

op(X) = X or op(X) = X**T or op(X) = X**H,

alpha is a scalar, A and B are matrices with op(A) an M by K matrix and op(B) a K by N matrix, and C is an binned M by N matrix.

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
TransB	a character specifying whether or not to transpose B before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
M	number of rows of matrix op(A) and of the matrix C.
N	number of columns of matrix op(B) and of the matrix C.
K	number of columns of matrix op(A) and columns of the matrix op(B).
alpha	scalar alpha
A	complex single precision matrix of dimension (ma, lda) in row-major or (lda, na) in column-major. (ma, na) is (M, K) if A is not transposed and (K, M) otherwise.
lda	the first dimension of A as declared in the calling program. lda must be at least na in row major or ma in column major.
B	complex single precision matrix of dimension (mb, ldb) in row-major or (ldb, nb) in column-major. (mb, nb) is (K, N) if B is not transposed and (N, K) otherwise.
ldb	the first dimension of B as declared in the calling program. ldb must be at least nb in row major or mb in column major.
C	binned complex single precision matrix of dimension (M, ldc) in row-major or (ldc, N) in column-major.
ldc	the first dimension of C as declared in the calling program. ldc must be at least N in row major or M in column major.

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_cbcgemv	(	const int	fold,
		const char	Order,
		const char	TransA,
		const int	M,
		const int	N,
		const void *	alpha,
		const void *	A,
		const int	lda,
		const void *	X,
		const int	incX,
		float_complex_binned *	Y,
		const int	incY
	)

Add to binned complex single precision vector Y the matrix-vector product of complex single precision matrix A and complex single precision vector X.

Performs one of the matrix-vector operations

y := alpha*A*x + y or y := alpha*A**T*x + y or y := alpha*A**H*x + y,

where alpha is a scalar, x is a vector, y is an binned vector, and A is an M by N matrix.

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-vector product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
M	number of rows of matrix A
N	number of columns of matrix A
alpha	scalar alpha
A	complex single precision matrix of dimension (M, lda) in row-major or (lda, N) in column-major
lda	the first dimension of A as declared in the calling program
X	complex single precision vector of at least size N if not transposed or size M otherwise
incX	X vector stride (use every incX'th element)
Y	binned complex single precision vector Y of at least size M if not transposed or size N otherwise
incY	Y vector stride (use every incY'th element)

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_cbcsum	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		float_complex_binned *	Y
	)

Add to binned complex single precision Y the sum of complex single precision vector X.

Add to Y the binned sum of X.

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
Y	binned scalar Y

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_cmcdotc	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		float *	priZ,
		const int	incpriZ,
		float *	carZ,
		const int	inccarZ
	)

Add to manually specified binned complex single precision Z the conjugated dot product of complex single precision vectors X and Y.

Add to Z the binned sum of the pairwise products of X and conjugated Y.

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
Y	complex single precision vector
incY	Y vector stride (use every incY'th element)
priZ	Z's primary vector
incpriZ	stride within Z's primary vector (use every incpriZ'th element)
carZ	Z's carry vector
inccarZ	stride within Z's carry vector (use every inccarZ'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_cmcdotu	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		float *	priZ,
		const int	incpriZ,
		float *	carZ,
		const int	inccarZ
	)

Add to manually specified binned complex single precision Z the unconjugated dot product of complex single precision vectors X and Y.

Add to Z the binned sum of the pairwise products of X and Y.

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
Y	complex single precision vector
incY	Y vector stride (use every incY'th element)
priZ	Z's primary vector
incpriZ	stride within Z's primary vector (use every incpriZ'th element)
carZ	Z's carry vector
inccarZ	stride within Z's carry vector (use every inccarZ'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_cmcsum	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Add to manually specified binned complex single precision Y the sum of complex single precision vector X.

Add to Y the binned sum of X.

Parameters

fold	the fold of the binned types
fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

double binnedBLAS_damax	(	const int	N,
		const double *	X,
		const int	incX
	)

Find maximum absolute value in vector of double precision.

Returns the absolute value of the element of maximum absolute value in an array.

Parameters

N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)

Returns: absolute maximum value of X

Author: Peter Ahrens

Date: 15 Jan 2016

double binnedBLAS_damaxm	(	const int	N,
		const double *	X,
		const int	incX,
		const double *	Y,
		const int	incY
	)

Find maximum absolute value pairwise product between vectors of double precision.

Returns the absolute value of the pairwise product of maximum absolute value between X and Y.

Parameters

N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)
Y	double precision vector
incY	Y vector stride (use every incY'th element)

Returns: absolute maximum value multiple of X and Y

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_dbdasum	(	const int	fold,
		const int	N,
		const double *	X,
		const int	incX,
		double_binned *	Y
	)

Add to binned double precision Y the absolute sum of double precision vector X.

Add to Y the binned sum of absolute values of elements in X.

Parameters

fold	the fold of the binned types
N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)
Y	binned scalar Y

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_dbddot	(	const int	fold,
		const int	N,
		const double *	X,
		const int	incX,
		const double *	Y,
		const int	incY,
		double_binned *	Z
	)

Add to binned double precision Z the dot product of double precision vectors X and Y.

Add to Z the binned sum of the pairwise products of X and Y.

Parameters

fold	the fold of the binned types
N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)
Y	double precision vector
incY	Y vector stride (use every incY'th element)
Z	binned scalar Z

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_dbdgemm	(	const int	fold,
		const char	Order,
		const char	TransA,
		const char	TransB,
		const int	M,
		const int	N,
		const int	K,
		const double	alpha,
		const double *	A,
		const int	lda,
		const double *	B,
		const int	ldb,
		double_binned *	C,
		const int	ldc
	)

Add to binned double precision matrix C the matrix-matrix product of double precision matrices A and B.

Performs one of the matrix-matrix operations

C := alpha*op(A)*op(B) + C,

where op(X) is one of

op(X) = X or op(X) = X**T,

alpha is a scalar, A and B are matrices with op(A) an M by K matrix and op(B) a K by N matrix, and C is an binned M by N matrix.

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
TransB	a character specifying whether or not to transpose B before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
M	number of rows of matrix op(A) and of the matrix C.
N	number of columns of matrix op(B) and of the matrix C.
K	number of columns of matrix op(A) and columns of the matrix op(B).
alpha	scalar alpha
A	double precision matrix of dimension (ma, lda) in row-major or (lda, na) in column-major. (ma, na) is (M, K) if A is not transposed and (K, M) otherwise.
lda	the first dimension of A as declared in the calling program. lda must be at least na in row major or ma in column major.
B	double precision matrix of dimension (mb, ldb) in row-major or (ldb, nb) in column-major. (mb, nb) is (K, N) if B is not transposed and (N, K) otherwise.
ldb	the first dimension of B as declared in the calling program. ldb must be at least nb in row major or mb in column major.
C	binned double precision matrix of dimension (M, ldc) in row-major or (ldc, N) in column-major.
ldc	the first dimension of C as declared in the calling program. ldc must be at least N in row major or M in column major.

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_dbdgemv	(	const int	fold,
		const char	Order,
		const char	TransA,
		const int	M,
		const int	N,
		const double	alpha,
		const double *	A,
		const int	lda,
		const double *	X,
		const int	incX,
		double_binned *	Y,
		const int	incY
	)

Add to binned double precision vector Y the matrix-vector product of double precision matrix A and double precision vector X.

Performs one of the matrix-vector operations

y := alpha*A*x + y or y := alpha*A**T*x + y,

where alpha is a scalar, x is a vector, y is an binned vector, and A is an M by N matrix.

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-vector product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
M	number of rows of matrix A
N	number of columns of matrix A
alpha	scalar alpha
A	double precision matrix of dimension (M, lda) in row-major or (lda, N) in column-major
lda	the first dimension of A as declared in the calling program
X	double precision vector of at least size N if not transposed or size M otherwise
incX	X vector stride (use every incX'th element)
Y	binned double precision vector Y of at least size M if not transposed or size N otherwise
incY	Y vector stride (use every incY'th element)

Author: Peter Ahrens

Date: 18 Jan 2016

double binnedBLAS_dbdssq	(	const int	fold,
		const int	N,
		const double *	X,
		const int	incX,
		const double	scaleY,
		double_binned *	Y
	)

Add to scaled binned double precision Y the scaled sum of squares of elements of double precision vector X.

Add to Y the scaled binned sum of the squares of each element of X. The scaling of each square is performed using binned_dscale()

Parameters

fold	the fold of the binned types
N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)
scaleY	the scaling factor of Y
Y	binned scalar Y

Returns: the new scaling factor of Y

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_dbdsum	(	const int	fold,
		const int	N,
		const double *	X,
		const int	incX,
		double_binned *	Y
	)

Add to binned double precision Y the sum of double precision vector X.

Add to Y the binned sum of X.

Parameters

fold	the fold of the binned types
N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)
Y	binned scalar Y

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_dbzasum	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		double_binned *	Y
	)

Add to binned double precision Y the absolute sum of complex double precision vector X.

Add to Y the binned sum of magnitudes of elements of X.

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
Y	binned scalar Y

Author: Peter Ahrens

Date: 15 Jan 2016

double binnedBLAS_dbzssq	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const double	scaleY,
		double_binned *	Y
	)

Add to scaled binned double precision Y the scaled sum of squares of elements of complex double precision vector X.

Add to Y the scaled binned sum of the squares of each element of X. The scaling of each square is performed using binned_dscale()

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
scaleY	the scaling factor of Y
Y	binned scalar Y

Returns: the new scaling factor of Y

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_dmdasum	(	const int	fold,
		const int	N,
		const double *	X,
		const int	incX,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Add to manually specified binned double precision Y the absolute sum of double precision vector X.

Add to Y the binned sum of absolute values of elements in X.

Parameters

fold	the fold of the binned types
N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_dmddot	(	const int	fold,
		const int	N,
		const double *	X,
		const int	incX,
		const double *	Y,
		const int	incY,
		double *	priZ,
		const int	incpriZ,
		double *	carZ,
		const int	inccarZ
	)

Add to manually specified binned double precision Z the dot product of double precision vectors X and Y.

Add to Z the binned sum of the pairwise products of X and Y.

Parameters

fold	the fold of the binned types
N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)
Y	double precision vector
incY	Y vector stride (use every incY'th element)
priZ	Z's primary vector
incpriZ	stride within Z's primary vector (use every incpriZ'th element)
carZ	Z's carry vector
inccarZ	stride within Z's carry vector (use every inccarZ'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

double binnedBLAS_dmdssq	(	const int	fold,
		const int	N,
		const double *	X,
		const int	incX,
		const double	scaleY,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Add to scaled manually specified binned double precision Y the scaled sum of squares of elements of double precision vector X.

Add to Y the scaled binned sum of the squares of each element of X. The scaling of each square is performed using binned_dscale()

Parameters

fold	the fold of the binned types
N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)
scaleY	the scaling factor of Y
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Returns: the new scaling factor of Y

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_dmdsum	(	const int	fold,
		const int	N,
		const double *	X,
		const int	incX,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Add to manually specified binned double precision Y the sum of double precision vector X.

Set Y to the binned sum of X.

Parameters

fold	the fold of the binned types
N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_dmzasum	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Add to manually specified binned double precision Y the absolute sum of complex double precision vector X.

Add to Y the binned sum of magnitudes of elements of X.

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

double binnedBLAS_dmzssq	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const double	scaleY,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Add to scaled manually specified binned double precision Y the scaled sum of squares of elements of complex double precision vector X.

Add to Y the scaled binned sum of the squares of each element of X. The scaling of each square is performed using binned_dscale()

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
scaleY	the scaling factor of Y
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Returns: the new scaling factor of Y

Author: Peter Ahrens

Date: 18 Jan 2016

float binnedBLAS_samax	(	const int	N,
		const float *	X,
		const int	incX
	)

Find maximum absolute value in vector of single precision.

Returns the absolute value of the element of maximum absolute value in an array.

Parameters

N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)

Returns: absolute maximum value of X

Author: Peter Ahrens

Date: 15 Jan 2016

float binnedBLAS_samaxm	(	const int	N,
		const float *	X,
		const int	incX,
		const float *	Y,
		const int	incY
	)

Find maximum absolute value pairwise product between vectors of single precision.

Returns the absolute value of the pairwise product of maximum absolute value between X and Y.

Parameters

N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
Y	single precision vector
incY	Y vector stride (use every incY'th element)

Returns: absolute maximum value multiple of X and Y

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_sbcasum	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		float_binned *	Y
	)

Add to binned single precision Y the absolute sum of complex single precision vector X.

Add to Y the binned sum of magnitudes of elements of X.

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
Y	binned scalar Y

Author: Peter Ahrens

Date: 15 Jan 2016

float binnedBLAS_sbcssq	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const float	scaleY,
		float_binned *	Y
	)

Add to scaled binned single precision Y the scaled sum of squares of elements of complex single precision vector X.

Add to Y the scaled binned sum of the squares of each element of X. The scaling of each square is performed using binned_sscale()

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
scaleY	the scaling factor of Y
Y	binned scalar Y

Returns: the new scaling factor of Y

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_sbsasum	(	const int	fold,
		const int	N,
		const float *	X,
		const int	incX,
		float_binned *	Y
	)

Add to binned single precision Y the absolute sum of single precision vector X.

Add to Y the binned sum of absolute values of elements in X.

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
Y	binned scalar Y

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_sbsdot	(	const int	fold,
		const int	N,
		const float *	X,
		const int	incX,
		const float *	Y,
		const int	incY,
		float_binned *	Z
	)

Add to binned single precision Z the dot product of single precision vectors X and Y.

Add to Z the binned sum of the pairwise products of X and Y.

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
Y	single precision vector
incY	Y vector stride (use every incY'th element)
Z	binned scalar Z

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_sbsgemm	(	const int	fold,
		const char	Order,
		const char	TransA,
		const char	TransB,
		const int	M,
		const int	N,
		const int	K,
		const float	alpha,
		const float *	A,
		const int	lda,
		const float *	B,
		const int	ldb,
		float_binned *	C,
		const int	ldc
	)

Add to binned single precision matrix C the matrix-matrix product of single precision matrices A and B.

Performs one of the matrix-matrix operations

C := alpha*op(A)*op(B) + C,

where op(X) is one of

op(X) = X or op(X) = X**T,

alpha is a scalar, A and B are matrices with op(A) an M by K matrix and op(B) a K by N matrix, and C is an binned M by N matrix.

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
TransB	a character specifying whether or not to transpose B before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
M	number of rows of matrix op(A) and of the matrix C.
N	number of columns of matrix op(B) and of the matrix C.
K	number of columns of matrix op(A) and columns of the matrix op(B).
alpha	scalar alpha
A	single precision matrix of dimension (ma, lda) in row-major or (lda, na) in column-major. (ma, na) is (M, K) if A is not transposed and (K, M) otherwise.
lda	the first dimension of A as declared in the calling program. lda must be at least na in row major or ma in column major.
B	single precision matrix of dimension (mb, ldb) in row-major or (ldb, nb) in column-major. (mb, nb) is (K, N) if B is not transposed and (N, K) otherwise.
ldb	the first dimension of B as declared in the calling program. ldb must be at least nb in row major or mb in column major.
C	binned single precision matrix of dimension (M, ldc) in row-major or (ldc, N) in column-major.
ldc	the first dimension of C as declared in the calling program. ldc must be at least N in row major or M in column major.

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_sbsgemv	(	const int	fold,
		const char	Order,
		const char	TransA,
		const int	M,
		const int	N,
		const float	alpha,
		const float *	A,
		const int	lda,
		const float *	X,
		const int	incX,
		float_binned *	Y,
		const int	incY
	)

Add to binned single precision vector Y the matrix-vector product of single precision matrix A and single precision vector X.

Performs one of the matrix-vector operations

y := alpha*A*x + y or y := alpha*A**T*x + y,

where alpha is a scalar, x is a vector, y is an binned vector, and A is an M by N matrix.

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-vector product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
M	number of rows of matrix A
N	number of columns of matrix A
alpha	scalar alpha
A	single precision matrix of dimension (M, lda) in row-major or (lda, N) in column-major
lda	the first dimension of A as declared in the calling program
X	single precision vector of at least size N if not transposed or size M otherwise
incX	X vector stride (use every incX'th element)
Y	binned single precision vector Y of at least size M if not transposed or size N otherwise
incY	Y vector stride (use every incY'th element)

Author: Peter Ahrens

Date: 18 Jan 2016

float binnedBLAS_sbsssq	(	const int	fold,
		const int	N,
		const float *	X,
		const int	incX,
		const float	scaleY,
		float_binned *	Y
	)

Add to scaled binned single precision Y the scaled sum of squares of elements of single precision vector X.

Add to Y the scaled binned sum of the squares of each element of X. The scaling of each square is performed using binned_sscale()

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
scaleY	the scaling factor of Y
Y	binned scalar Y

Returns: the new scaling factor of Y

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_sbssum	(	const int	fold,
		const int	N,
		const float *	X,
		const int	incX,
		float_binned *	Y
	)

Add to binned single precision Y the sum of single precision vector X.

Add to Y the binned sum of X.

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
Y	binned scalar Y

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_smcasum	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Add to manually specified binned single precision Y the absolute sum of complex single precision vector X.

Add to Y the binned sum of magnitudes of elements of X.

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

float binnedBLAS_smcssq	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const float	scaleY,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Add to scaled manually specified binned single precision Y the scaled sum of squares of elements of complex single precision vector X.

Add to Y the scaled binned sum of the squares of each element of X. The scaling of each square is performed using binned_sscale()

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
scaleY	the scaling factor of Y
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Returns: the new scaling factor of Y

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_smsasum	(	const int	fold,
		const int	N,
		const float *	X,
		const int	incX,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Add to manually specified binned single precision Y the absolute sum of double precision vector X.

Add to Y to the binned sum of absolute values of elements in X.

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_smsdot	(	const int	fold,
		const int	N,
		const float *	X,
		const int	incX,
		const float *	Y,
		const int	incY,
		float *	priZ,
		const int	incpriZ,
		float *	carZ,
		const int	inccarZ
	)

Add to manually specified binned single precision Z the dot product of single precision vectors X and Y.

Add to Z the binned sum of the pairwise products of X and Y.

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
Y	single precision vector
incY	Y vector stride (use every incY'th element)
priZ	Z's primary vector
incpriZ	stride within Z's primary vector (use every incpriZ'th element)
carZ	Z's carry vector
inccarZ	stride within Z's carry vector (use every inccarZ'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

float binnedBLAS_smsssq	(	const int	fold,
		const int	N,
		const float *	X,
		const int	incX,
		const float	scaleY,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Add to scaled manually specified binned single precision Y the scaled sum of squares of elements of single precision vector X.

Add to Y the scaled binned sum of the squares of each element of X. The scaling of each square is performed using binned_sscale()

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
scaleY	the scaling factor of Y
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Returns: the new scaling factor of Y

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_smssum	(	const int	fold,
		const int	N,
		const float *	X,
		const int	incX,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Add to manually specified binned single precision Y the sum of single precision vector X.

Add to Y the binned sum of X.

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_zamax_sub	(	const int	N,
		const void *	X,
		const int	incX,
		void *	amax
	)

Find maximum magnitude in vector of complex double precision.

Returns the magnitude of the element of maximum magnitude in an array.

Parameters

N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
amax	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_zamaxm_sub	(	const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		void *	amaxm
	)

Find maximum magnitude pairwise product between vectors of complex double precision.

Returns the magnitude of the pairwise product of maximum magnitude between X and Y.

Parameters

N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
Y	complex double precision vector
incY	Y vector stride (use every incY'th element)
amaxm	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_zbzdotc	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		double_complex_binned *	Z
	)

Add to binned complex double precision Z the conjugated dot product of complex double precision vectors X and Y.

Add to Z the binned sum of the pairwise products of X and conjugated Y.

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
Y	complex double precision vector
incY	Y vector stride (use every incY'th element)
Z	scalar return Z

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_zbzdotu	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		double_complex_binned *	Z
	)

Add to binned complex double precision Z the unconjugated dot product of complex double precision vectors X and Y.

Add to Z the binned sum of the pairwise products of X and Y.

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
Y	complex double precision vector
incY	Y vector stride (use every incY'th element)
Z	binned scalar Z

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_zbzgemm	(	const int	fold,
		const char	Order,
		const char	TransA,
		const char	TransB,
		const int	M,
		const int	N,
		const int	K,
		const void *	alpha,
		const void *	A,
		const int	lda,
		const void *	B,
		const int	ldb,
		double_complex_binned *	C,
		const int	ldc
	)

Add to binned complex double precision matrix C the matrix-matrix product of complex double precision matrices A and B.

Performs one of the matrix-matrix operations

C := alpha*op(A)*op(B) + C,

where op(X) is one of

op(X) = X or op(X) = X**T or op(X) = X**H,

alpha is a scalar, A and B are matrices with op(A) an M by K matrix and op(B) a K by N matrix, and C is an binned M by N matrix.

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
TransB	a character specifying whether or not to transpose B before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
M	number of rows of matrix op(A) and of the matrix C.
N	number of columns of matrix op(B) and of the matrix C.
K	number of columns of matrix op(A) and columns of the matrix op(B).
alpha	scalar alpha
A	complex double precision matrix of dimension (ma, lda) in row-major or (lda, na) in column-major. (ma, na) is (M, K) if A is not transposed and (K, M) otherwise.
lda	the first dimension of A as declared in the calling program. lda must be at least na in row major or ma in column major.
B	complex double precision matrix of dimension (mb, ldb) in row-major or (ldb, nb) in column-major. (mb, nb) is (K, N) if B is not transposed and (N, K) otherwise.
ldb	the first dimension of B as declared in the calling program. ldb must be at least nb in row major or mb in column major.
C	binned complex double precision matrix of dimension (M, ldc) in row-major or (ldc, N) in column-major.
ldc	the first dimension of C as declared in the calling program. ldc must be at least N in row major or M in column major.

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_zbzgemv	(	const int	fold,
		const char	Order,
		const char	TransA,
		const int	M,
		const int	N,
		const void *	alpha,
		const void *	A,
		const int	lda,
		const void *	X,
		const int	incX,
		double_complex_binned *	Y,
		const int	incY
	)

Add to binned complex double precision vector Y the matrix-vector product of complex double precision matrix A and complex double precision vector X.

Performs one of the matrix-vector operations

y := alpha*A*x + y or y := alpha*A**T*x + y or y := alpha*A**H*x + y,

where alpha is a scalar, x is a vector, y is an binned vector, and A is an M by N matrix.

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-vector product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
M	number of rows of matrix A
N	number of columns of matrix A
alpha	scalar alpha
A	complex double precision matrix of dimension (M, lda) in row-major or (lda, N) in column-major
lda	the first dimension of A as declared in the calling program
X	complex double precision vector of at least size N if not transposed or size M otherwise
incX	X vector stride (use every incX'th element)
Y	binned complex double precision vector Y of at least size M if not transposed or size N otherwise
incY	Y vector stride (use every incY'th element)

Author: Peter Ahrens

Date: 18 Jan 2016

void binnedBLAS_zbzsum	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		double_complex_binned *	Y
	)

Add to binned complex double precision Y the sum of complex double precision vector X.

Add to Y the binned sum of X.

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
Y	binned scalar Y

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_zmzdotc	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		double *	priZ,
		const int	incpriZ,
		double *	carZ,
		const int	inccarZ
	)

Add to manually specified binned complex double precision Z the conjugated dot product of complex double precision vectors X and Y.

Add to Z the binned sum of the pairwise products of X and conjugated Y.

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
Y	complex double precision vector
incY	Y vector stride (use every incY'th element)
priZ	Z's primary vector
incpriZ	stride within Z's primary vector (use every incpriZ'th element)
carZ	Z's carry vector
inccarZ	stride within Z's carry vector (use every inccarZ'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_zmzdotu	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		double *	priZ,
		const int	incpriZ,
		double *	carZ,
		const int	inccarZ
	)

Add to manually specified binned complex double precision Z the unconjugated dot product of complex double precision vectors X and Y.

Add to Z to the binned sum of the pairwise products of X and Y.

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
Y	complex double precision vector
incY	Y vector stride (use every incY'th element)
priZ	Z's primary vector
incpriZ	stride within Z's primary vector (use every incpriZ'th element)
carZ	Z's carry vector
inccarZ	stride within Z's carry vector (use every inccarZ'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

void binnedBLAS_zmzsum	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Add to manually specified binned complex double precision Y the sum of complex double precision vector X.

Add to Y the binned sum of X.

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Author: Peter Ahrens

Date: 15 Jan 2016

Functions

Detailed Description

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