binned.h File Reference

binned.h defines the binned types and the lower level functions associated with their use. More...

#include <stddef.h>
#include <stdlib.h>
#include <float.h>

Go to the source code of this file.

Macros
#define	DBWIDTH   40
	Binned double precision bin width. More...
#define	SBWIDTH   13
	Binned single precision bin width. More...
#define	binned_DBMAXINDEX   (((DBL_MAX_EXP - DBL_MIN_EXP + DBL_MANT_DIG - 1)/DBWIDTH) - 1)
	Binned double precision maximum index. More...
#define	binned_SBMAXINDEX   (((FLT_MAX_EXP - FLT_MIN_EXP + FLT_MANT_DIG - 1)/SBWIDTH) - 1)
	Binned single precision maximum index. More...
#define	binned_DBMAXFOLD   (binned_DBMAXINDEX + 1)
	The maximum double precision fold supported by the library. More...
#define	binned_SBMAXFOLD   (binned_SBMAXINDEX + 1)
	The maximum single precision fold supported by the library. More...
#define	binned_DBENDURANCE   (1 << (DBL_MANT_DIG - DBWIDTH - 2))
	Binned double precision deposit endurance. More...
#define	binned_SBENDURANCE   (1 << (FLT_MANT_DIG - SBWIDTH - 2))
	Binned single precision deposit endurance. More...
#define	binned_DBCAPACITY   (binned_DBENDURANCE*(1.0/DBL_EPSILON - 1.0))
	Binned double precision capacity. More...
#define	binned_SBCAPACITY   (binned_SBENDURANCE*(1.0/FLT_EPSILON - 1.0))
	Binned single precision capacity. More...
#define	binned_DMCOMPRESSION   (1.0/(1 << (DBL_MANT_DIG - DBWIDTH + 1)))
	Binned double precision compression factor. More...
#define	binned_SMCOMPRESSION   (1.0/(1 << (FLT_MANT_DIG - SBWIDTH + 1)))
	Binned single precision compression factor. More...
#define	binned_DMEXPANSION   (1.0*(1 << (DBL_MANT_DIG - DBWIDTH + 1)))
	Binned double precision expansion factor. More...
#define	binned_SMEXPANSION   (1.0*(1 << (FLT_MANT_DIG - SBWIDTH + 1)))
	Binned single precision expansion factor. More...

Typedefs
typedef double	double_binned
	The binned double datatype. More...
typedef double	double_complex_binned
	The binned complex double datatype. More...
typedef float	float_binned
	The binned float datatype. More...
typedef float	float_complex_binned
	The binned complex float datatype. More...

Functions
size_t	binned_dbsize (const int fold)
	binned double precision size More...
size_t	binned_zbsize (const int fold)
	binned complex double precision size More...
size_t	binned_sbsbze (const int fold)
	binned single precision size More...
size_t	binned_cbsize (const int fold)
	binned complex single precision size More...
double_binned *	binned_dballoc (const int fold)
	binned double precision allocation More...
double_complex_binned *	binned_zballoc (const int fold)
	binned complex double precision allocation More...
float_binned *	binned_sballoc (const int fold)
	binned single precision allocation More...
float_complex_binned *	binned_cballoc (const int fold)
	binned complex single precision allocation More...
int	binned_dbnum (const int fold)
	binned double precision size More...
int	binned_zbnum (const int fold)
	binned complex double precision size More...
int	binned_sbnum (const int fold)
	binned single precision size More...
int	binned_cbnum (const int fold)
	binned complex single precision size More...
double	binned_dbbound (const int fold, const int N, const double X, const double S)
	Get binned double precision summation error bound. More...
float	binned_sbbound (const int fold, const int N, const float X, const float S)
	Get binned single precision summation error bound. More...
const double *	binned_dmbins (const int X)
	Get binned double precision reference bins. More...
const float *	binned_smbins (const int X)
	Get binned single precision reference bins. More...
int	binned_dindex (const double X)
	Get index of double precision. More...
int	binned_dmindex (const double *priX)
	Get index of manually specified binned double precision. More...
int	binned_dmindex0 (const double *priX)
	Check if index of manually specified binned double precision is 0. More...
int	binned_sindex (const float X)
	Get index of single precision. More...
int	binned_smindex (const float *priX)
	Get index of manually specified binned single precision. More...
int	binned_smindex0 (const float *priX)
	Check if index of manually specified binned single precision is 0. More...
int	binned_dmdenorm (const int fold, const double *priX)
	Check if binned type has denormal bits. More...
int	binned_zmdenorm (const int fold, const double *priX)
	Check if binned type has denormal bits. More...
int	binned_smdenorm (const int fold, const float *priX)
	Check if binned type has denormal bits. More...
int	binned_cmdenorm (const int fold, const float *priX)
	Check if binned type has denormal bits. More...
void	binned_dbprint (const int fold, const double_binned *X)
	Print binned double precision. More...
void	binned_dmprint (const int fold, const double *priX, const int incpriX, const double *carX, const int inccarX)
	Print manually specified binned double precision. More...
void	binned_zbprint (const int fold, const double_complex_binned *X)
	Print binned complex double precision. More...
void	binned_zmprint (const int fold, const double *priX, const int incpriX, const double *carX, const int inccarX)
	Print manually specified binned complex double precision. More...
void	binned_sbprint (const int fold, const float_binned *X)
	Print binned single precision. More...
void	binned_smprint (const int fold, const float *priX, const int incpriX, const float *carX, const int inccarX)
	Print manually specified binned single precision. More...
void	binned_cbprint (const int fold, const float_complex_binned *X)
	Print binned complex single precision. More...
void	binned_cmprint (const int fold, const float *priX, const int incpriX, const float *carX, const int inccarX)
	Print manually specified binned complex single precision. More...
void	binned_dbdbset (const int fold, const double_binned *X, double_binned *Y)
	Set binned double precision (Y = X) More...
void	binned_dmdmset (const int fold, const double *priX, const int incpriX, const double *carX, const int inccarX, double *priY, const int incpriY, double *carY, const int inccarY)
	Set manually specified binned double precision (Y = X) More...
void	binned_zbzbset (const int fold, const double_complex_binned *X, double_complex_binned *Y)
	Set binned complex double precision (Y = X) More...
void	binned_zmzmset (const int fold, const double *priX, const int incpriX, const double *carX, const int inccarX, double *priY, const int incpriY, double *carY, const int inccarY)
	Set manually specified binned complex double precision (Y = X) More...
void	binned_zbdbset (const int fold, const double_binned *X, double_complex_binned *Y)
	Set binned complex double precision to binned double precision (Y = X) More...
void	binned_zmdmset (const int fold, const double *priX, const int incpriX, const double *carX, const int inccarX, double *priY, const int incpriY, double *carY, const int inccarY)
	Set manually specified binned complex double precision to manually specified binned double precision (Y = X) More...
void	binned_sbsbset (const int fold, const float_binned *X, float_binned *Y)
	Set binned single precision (Y = X) More...
void	binned_smsmset (const int fold, const float *priX, const int incpriX, const float *carX, const int inccarX, float *priY, const int incpriY, float *carY, const int inccarY)
	Set manually specified binned single precision (Y = X) More...
void	binned_cbcbset (const int fold, const float_complex_binned *X, float_complex_binned *Y)
	Set binned complex single precision (Y = X) More...
void	binned_cmcmset (const int fold, const float *priX, const int incpriX, const float *carX, const int inccarX, float *priY, const int incpriY, float *carY, const int inccarY)
	Set manually specified binned complex single precision (Y = X) More...
void	binned_cbsbset (const int fold, const float_binned *X, float_complex_binned *Y)
	Set binned complex single precision to binned single precision (Y = X) More...
void	binned_cmsmset (const int fold, const float *priX, const int incpriX, const float *carX, const int inccarX, float *priY, const int incpriY, float *carY, const int inccarY)
	Set manually specified binned complex single precision to manually specified binned single precision (Y = X) More...
void	binned_dbsetzero (const int fold, double_binned *X)
	Set binned double precision to 0 (X = 0) More...
void	binned_dmsetzero (const int fold, double *priX, const int incpriX, double *carX, const int inccarX)
	Set manually specified binned double precision to 0 (X = 0) More...
void	binned_zbsetzero (const int fold, double_complex_binned *X)
	Set binned double precision to 0 (X = 0) More...
void	binned_zmsetzero (const int fold, double *priX, const int incpriX, double *carX, const int inccarX)
	Set manually specified binned complex double precision to 0 (X = 0) More...
void	binned_sbsetzero (const int fold, float_binned *X)
	Set binned single precision to 0 (X = 0) More...
void	binned_smsetzero (const int fold, float *priX, const int incpriX, float *carX, const int inccarX)
	Set manually specified binned single precision to 0 (X = 0) More...
void	binned_cbsetzero (const int fold, float_complex_binned *X)
	Set binned single precision to 0 (X = 0) More...
void	binned_cmsetzero (const int fold, float *priX, const int incpriX, float *carX, const int inccarX)
	Set manually specified binned complex single precision to 0 (X = 0) More...
void	binned_dbdbadd (const int fold, const double_binned *X, double_binned *Y)
	Add binned double precision (Y += X) More...
void	binned_dmdmadd (const int fold, const double *priX, const int incpriX, const double *carX, const int inccarX, double *priY, const int incpriY, double *carY, const int inccarY)
	Add manually specified binned double precision (Y += X) More...
void	binned_zbzbadd (const int fold, const double_complex_binned *X, double_complex_binned *Y)
	Add binned complex double precision (Y += X) More...
void	binned_zmzmadd (const int fold, const double *priX, const int incpriX, const double *carX, const int inccarX, double *priY, const int incpriY, double *carY, const int inccarY)
	Add manually specified binned complex double precision (Y += X) More...
void	binned_sbsbadd (const int fold, const float_binned *X, float_binned *Y)
	Add binned single precision (Y += X) More...
void	binned_smsmadd (const int fold, const float *priX, const int incpriX, const float *carX, const int inccarX, float *priY, const int incpriY, float *carY, const int inccarY)
	Add manually specified binned single precision (Y += X) More...
void	binned_cbcbadd (const int fold, const float_complex_binned *X, float_complex_binned *Y)
	Add binned complex single precision (Y += X) More...
void	binned_cmcmadd (const int fold, const float *priX, const int incpriX, const float *carX, const int inccarX, float *priY, const int incpriY, float *carY, const int inccarY)
	Add manually specified binned complex single precision (Y += X) More...
void	binned_dbdbaddv (const int fold, const int N, const double_binned *X, const int incX, double_binned *Y, const int incY)
	Add binned double precision vectors (Y += X) More...
void	binned_zbzbaddv (const int fold, const int N, const double_complex_binned *X, const int incX, double_complex_binned *Y, const int incY)
	Add binned complex double precision vectors (Y += X) More...
void	binned_sbsbaddv (const int fold, const int N, const float_binned *X, const int incX, float_binned *Y, const int incY)
	Add binned single precision vectors (Y += X) More...
void	binned_cbcbaddv (const int fold, const int N, const float_complex_binned *X, const int incX, float_complex_binned *Y, const int incY)
	Add binned complex single precision vectors (Y += X) More...
void	binned_dbdadd (const int fold, const double X, double_binned *Y)
	Add double precision to binned double precision (Y += X) More...
void	binned_dmdadd (const int fold, const double X, double *priY, const int incpriY, double *carY, const int inccarY)
	Add double precision to manually specified binned double precision (Y += X) More...
void	binned_zbzadd (const int fold, const void *X, double_complex_binned *Y)
	Add complex double precision to binned complex double precision (Y += X) More...
void	binned_zmzadd (const int fold, const void *X, double *priY, const int incpriY, double *carY, const int inccarY)
	Add complex double precision to manually specified binned complex double precision (Y += X) More...
void	binned_sbsadd (const int fold, const float X, float_binned *Y)
	Add single precision to binned single precision (Y += X) More...
void	binned_smsadd (const int fold, const float X, float *priY, const int incpriY, float *carY, const int inccarY)
	Add single precision to manually specified binned single precision (Y += X) More...
void	binned_cbcadd (const int fold, const void *X, float_complex_binned *Y)
	Add complex single precision to binned complex single precision (Y += X) More...
void	binned_cmcadd (const int fold, const void *X, float *priY, const int incpriY, float *carY, const int inccarY)
	Add complex single precision to manually specified binned complex single precision (Y += X) More...
void	binned_dbdupdate (const int fold, const double X, double_binned *Y)
	Update binned double precision with double precision (X -> Y) More...
void	binned_dmdupdate (const int fold, const double X, double *priY, const int incpriY, double *carY, const int inccarY)
	Update manually specified binned double precision with double precision (X -> Y) More...
void	binned_zbzupdate (const int fold, const void *X, double_complex_binned *Y)
	Update binned complex double precision with complex double precision (X -> Y) More...
void	binned_zmzupdate (const int fold, const void *X, double *priY, const int incpriY, double *carY, const int inccarY)
	Update manually specified binned complex double precision with complex double precision (X -> Y) More...
void	binned_zbdupdate (const int fold, const double X, double_complex_binned *Y)
	Update binned complex double precision with double precision (X -> Y) More...
void	binned_zmdupdate (const int fold, const double X, double *priY, const int incpriY, double *carY, const int inccarY)
	Update manually specified binned complex double precision with double precision (X -> Y) More...
void	binned_sbsupdate (const int fold, const float X, float_binned *Y)
	Update binned single precision with single precision (X -> Y) More...
void	binned_smsupdate (const int fold, const float X, float *priY, const int incpriY, float *carY, const int inccarY)
	Update manually specified binned single precision with single precision (X -> Y) More...
void	binned_cbcupdate (const int fold, const void *X, float_complex_binned *Y)
	Update binned complex single precision with complex single precision (X -> Y) More...
void	binned_cmcupdate (const int fold, const void *X, float *priY, const int incpriY, float *carY, const int inccarY)
	Update manually specified binned complex single precision with complex single precision (X -> Y) More...
void	binned_cbsupdate (const int fold, const float X, float_complex_binned *Y)
	Update binned complex single precision with single precision (X -> Y) More...
void	binned_cmsupdate (const int fold, const float X, float *priY, const int incpriY, float *carY, const int inccarY)
	Update manually specified binned complex single precision with single precision (X -> Y) More...
void	binned_dbddeposit (const int fold, const double X, double_binned *Y)
	Add double precision to suitably binned binned double precision (Y += X) More...
void	binned_dmddeposit (const int fold, const double X, double *priY, const int incpriY)
	Add double precision to suitably binned manually specified binned double precision (Y += X) More...
void	binned_zbzdeposit (const int fold, const void *X, double_complex_binned *Y)
	Add complex double precision to suitably binned binned complex double precision (Y += X) More...
void	binned_zmzdeposit (const int fold, const void *X, double *priY, const int incpriY)
	Add complex double precision to suitably binned manually specified binned complex double precision (Y += X) More...
void	binned_sbsdeposit (const int fold, const float X, float_binned *Y)
	Add single precision to suitably binned binned single precision (Y += X) More...
void	binned_smsdeposit (const int fold, const float X, float *priY, const int incpriY)
	Add single precision to suitably binned manually specified binned single precision (Y += X) More...
void	binned_cbcdeposit (const int fold, const void *X, float_complex_binned *Y)
	Add complex single precision to suitably binned binned complex single precision (Y += X) More...
void	binned_cmcdeposit (const int fold, const void *X, float *priY, const int incpriY)
	Add complex single precision to suitably binned manually specified binned complex single precision (Y += X) More...
void	binned_dbrenorm (const int fold, double_binned *X)
	Renormalize binned double precision. More...
void	binned_dmrenorm (const int fold, double *priX, const int incpriX, double *carX, const int inccarX)
	Renormalize manually specified binned double precision. More...
void	binned_zbrenorm (const int fold, double_complex_binned *X)
	Renormalize binned complex double precision. More...
void	binned_zmrenorm (const int fold, double *priX, const int incpriX, double *carX, const int inccarX)
	Renormalize manually specified binned complex double precision. More...
void	binned_sbrenorm (const int fold, float_binned *X)
	Renormalize binned single precision. More...
void	binned_smrenorm (const int fold, float *priX, const int incpriX, float *carX, const int inccarX)
	Renormalize manually specified binned single precision. More...
void	binned_cbrenorm (const int fold, float_complex_binned *X)
	Renormalize binned complex single precision. More...
void	binned_cmrenorm (const int fold, float *priX, const int incpriX, float *carX, const int inccarX)
	Renormalize manually specified binned complex single precision. More...
void	binned_dbdconv (const int fold, const double X, double_binned *Y)
	Convert double precision to binned double precision (X -> Y) More...
void	binned_dmdconv (const int fold, const double X, double *priY, const int incpriY, double *carY, const int inccarY)
	Convert double precision to manually specified binned double precision (X -> Y) More...
void	binned_zbzconv (const int fold, const void *X, double_complex_binned *Y)
	Convert complex double precision to binned complex double precision (X -> Y) More...
void	binned_zmzconv (const int fold, const void *X, double *priY, const int incpriY, double *carY, const int inccarY)
	Convert complex double precision to manually specified binned complex double precision (X -> Y) More...
void	binned_sbsconv (const int fold, const float X, float_binned *Y)
	Convert single precision to binned single precision (X -> Y) More...
void	binned_smsconv (const int fold, const float X, float *priY, const int incpriY, float *carY, const int inccarY)
	Convert single precision to manually specified binned single precision (X -> Y) More...
void	binned_cbcconv (const int fold, const void *X, float_complex_binned *Y)
	Convert complex single precision to binned complex single precision (X -> Y) More...
void	binned_cmcconv (const int fold, const void *X, float *priY, const int incpriY, float *carY, const int inccarY)
	Convert complex single precision to manually specified binned complex single precision (X -> Y) More...
double	binned_ddbconv (const int fold, const double_binned *X)
	Convert binned double precision to double precision (X -> Y) More...
double	binned_ddmconv (const int fold, const double *priX, const int incpriX, const double *carX, const int inccarX)
	Convert manually specified binned double precision to double precision (X -> Y) More...
void	binned_zzbconv_sub (const int fold, const double_complex_binned *X, void *conv)
	Convert binned complex double precision to complex double precision (X -> Y) More...
void	binned_zzmconv_sub (const int fold, const double *priX, const int incpriX, const double *carX, const int inccarX, void *conv)
	Convert manually specified binned complex double precision to complex double precision (X -> Y) More...
float	binned_ssbconv (const int fold, const float_binned *X)
	Convert binned single precision to single precision (X -> Y) More...
float	binned_ssmconv (const int fold, const float *priX, const int incpriX, const float *carX, const int inccarX)
	Convert manually specified binned single precision to single precision (X -> Y) More...
void	binned_ccbconv_sub (const int fold, const float_complex_binned *X, void *conv)
	Convert binned complex single precision to complex single precision (X -> Y) More...
void	binned_ccmconv_sub (const int fold, const float *priX, const int incpriX, const float *carX, const int inccarX, void *conv)
	Convert manually specified binned complex single precision to complex single precision (X -> Y) More...
void	binned_dbnegate (const int fold, double_binned *X)
	Negate binned double precision (X = -X) More...
void	binned_dmnegate (const int fold, double *priX, const int incpriX, double *carX, const int inccarX)
	Negate manually specified binned double precision (X = -X) More...
void	binned_zbnegate (const int fold, double_complex_binned *X)
	Negate binned complex double precision (X = -X) More...
void	binned_zmnegate (const int fold, double *priX, const int incpriX, double *carX, const int inccarX)
	Negate manually specified binned complex double precision (X = -X) More...
void	binned_sbnegate (const int fold, float_binned *X)
	Negate binned single precision (X = -X) More...
void	binned_smnegate (const int fold, float *priX, const int incpriX, float *carX, const int inccarX)
	Negate manually specified binned single precision (X = -X) More...
void	binned_cbnegate (const int fold, float_complex_binned *X)
	Negate binned complex single precision (X = -X) More...
void	binned_cmnegate (const int fold, float *priX, const int incpriX, float *carX, const int inccarX)
	Negate manually specified binned complex single precision (X = -X) More...
double	binned_dscale (const double X)
	Get a reproducible double precision scale. More...
float	binned_sscale (const float X)
	Get a reproducible single precision scale. More...
void	binned_dmdrescale (const int fold, const double X, const double scaleY, double *priY, const int incpriY, double *carY, const int inccarY)
	rescale manually specified binned double precision sum of squares More...
void	binned_zmdrescale (const int fold, const double X, const double scaleY, double *priY, const int incpriY, double *carY, const int inccarY)
	rescale manually specified binned complex double precision sum of squares More...
void	binned_smsrescale (const int fold, const float X, const float scaleY, float *priY, const int incpriY, float *carY, const int inccarY)
	rescale manually specified binned single precision sum of squares More...
void	binned_cmsrescale (const int fold, const float X, const float scaleY, float *priY, const int incpriY, float *carY, const int inccarY)
	rescale manually specified binned complex single precision sum of squares More...
double	binned_dmdmaddsq (const int fold, const double scaleX, const double *priX, const int incpriX, const double *carX, const int inccarX, const double scaleY, double *priY, const int incpriY, double *carY, const int inccarY)
	Add manually specified binned double precision scaled sums of squares (Y += X) More...
double	binned_dbdbaddsq (const int fold, const double scaleX, const double_binned *X, const double scaleY, double_binned *Y)
	Add binned double precision scaled sums of squares (Y += X) More...
float	binned_smsmaddsq (const int fold, const float scaleX, const float *priX, const int incpriX, const float *carX, const int inccarX, const float scaleY, float *priY, const int incpriY, float *carY, const int inccarY)
	Add manually specified binned single precision scaled sums of squares (Y += X) More...
float	binned_sbsbaddsq (const int fold, const float scaleX, const float_binned *X, const float scaleY, float_binned *Y)
	Add binned single precision scaled sums of squares (Y += X) More...
double	binned_ufp (const double X)
	unit in the first place More...
float	binned_ufpf (const float X)
	unit in the first place More...

Detailed Description

binned.h defines the binned types and the lower level functions associated with their use.

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.

Macro Definition Documentation

#define binned_DBCAPACITY   (binned_DBENDURANCE*(1.0/DBL_EPSILON - 1.0))

Binned double precision capacity.

The maximum number of double precision numbers that can be summed using binned double precision. Applies also to binned complex double precision.

Author

Peter Ahrens

Date

27 Apr 2015

#define binned_DBENDURANCE   (1 << (DBL_MANT_DIG - DBWIDTH - 2))

Binned double precision deposit endurance.

The number of deposits that can be performed before a renorm is necessary. Applies also to binned complex double precision.

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

#define binned_DBMAXFOLD   (binned_DBMAXINDEX + 1)

The maximum double precision fold supported by the library.

Author

Peter Ahrens

Date

14 Jan 2016

#define binned_DBMAXINDEX   (((DBL_MAX_EXP - DBL_MIN_EXP + DBL_MANT_DIG - 1)/DBWIDTH) - 1)

Binned double precision maximum index.

maximum index (inclusive)

Author

Peter Ahrens

Date

24 Jun 2015

#define binned_DMCOMPRESSION   (1.0/(1 << (DBL_MANT_DIG - DBWIDTH + 1)))

Binned double precision compression factor.

This factor is used to scale down inputs before deposition into the bin of highest index

Author

Peter Ahrens

Date

19 May 2015

#define binned_DMEXPANSION   (1.0*(1 << (DBL_MANT_DIG - DBWIDTH + 1)))

Binned double precision expansion factor.

This factor is used to scale up inputs after deposition into the bin of highest index

Author

Peter Ahrens

Date

19 May 2015

#define binned_SBCAPACITY   (binned_SBENDURANCE*(1.0/FLT_EPSILON - 1.0))

Binned single precision capacity.

The maximum number of single precision numbers that can be summed using binned single precision. Applies also to binned complex double precision.

Author

Peter Ahrens

Date

27 Apr 2015

#define binned_SBENDURANCE   (1 << (FLT_MANT_DIG - SBWIDTH - 2))

Binned single precision deposit endurance.

The number of deposits that can be performed before a renorm is necessary. Applies also to binned complex single precision.

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

#define binned_SBMAXFOLD   (binned_SBMAXINDEX + 1)

The maximum single precision fold supported by the library.

Author

Peter Ahrens

Date

14 Jan 2016

#define binned_SBMAXINDEX   (((FLT_MAX_EXP - FLT_MIN_EXP + FLT_MANT_DIG - 1)/SBWIDTH) - 1)

Binned single precision maximum index.

maximum index (inclusive)

Author

Peter Ahrens

Date

24 Jun 2015

#define binned_SMCOMPRESSION   (1.0/(1 << (FLT_MANT_DIG - SBWIDTH + 1)))

Binned single precision compression factor.

This factor is used to scale down inputs before deposition into the bin of highest index

Author

Peter Ahrens

Date

19 May 2015

#define binned_SMEXPANSION   (1.0*(1 << (FLT_MANT_DIG - SBWIDTH + 1)))

Binned single precision expansion factor.

This factor is used to scale up inputs after deposition into the bin of highest index

Author

Peter Ahrens

Date

19 May 2015

#define DBWIDTH   40

Binned double precision bin width.

bin width (in bits)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

#define SBWIDTH   13

Binned single precision bin width.

bin width (in bits)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

Typedef Documentation

typedef double double_binned

The binned double datatype.

To allocate a double_binned, call binned_dballoc()

Warning

A double_binned is, under the hood, an array of double. Therefore, if you have defined an array of double_binned, you must index it by multiplying the index into the array by the number of underlying double that make up the double_binned. This number can be obtained by a call to binned_dbnum()

typedef double double_complex_binned

The binned complex double datatype.

To allocate a double_complex_binned, call binned_zballoc()

Warning

A double_complex_binned is, under the hood, an array of double. Therefore, if you have defined an array of double_complex_binned, you must index it by multiplying the index into the array by the number of underlying double that make up the double_complex_binned. This number can be obtained by a call to binned_zbnum()

typedef float float_binned

The binned float datatype.

To allocate a float_binned, call binned_sballoc()

Warning

A float_binned is, under the hood, an array of float. Therefore, if you have defined an array of float_binned, you must index it by multiplying the index into the array by the number of underlying float that make up the float_binned. This number can be obtained by a call to binned_sbnum()

typedef float float_complex_binned

The binned complex float datatype.

To allocate a float_complex_binned, call binned_cballoc()

Warning

A float_complex_binned is, under the hood, an array of float. Therefore, if you have defined an array of float_complex_binned, you must index it by multiplying the index into the array by the number of underlying float that make up the float_complex_binned. This number can be obtained by a call to binned_cbnum()

Function Documentation

float_complex_binned* binned_cballoc

(

const int

fold

)

binned complex single precision allocation

Parameters

fold	the fold of the binned type

Returns

a freshly allocated binned type. (free with free())

Author

Peter Ahrens

Date

27 Apr 2015

void binned_cbcadd	(	const int	fold,
		const void *	X,
		float_complex_binned *	Y
	)

Add complex single precision to binned complex single precision (Y += X)

Performs the operation Y += X on an binned type Y

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cbcbadd	(	const int	fold,
		const float_complex_binned *	X,
		float_complex_binned *	Y
	)

Add binned complex single precision (Y += X)

Performs the operation Y += X

Parameters

fold	the fold of the binned types
X	binned scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

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

Add binned complex single precision vectors (Y += X)

Performs the operation Y += X

Parameters

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

Author

Peter Ahrens

Date

25 Jun 2015

void binned_cbcbset	(	const int	fold,
		const float_complex_binned *	X,
		float_complex_binned *	Y
	)

Set binned complex single precision (Y = X)

Performs the operation Y = X

Parameters

fold	the fold of the binned types
X	binned scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cbcconv	(	const int	fold,
		const void *	X,
		float_complex_binned *	Y
	)

Convert complex single precision to binned complex single precision (X -> Y)

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cbcdeposit	(	const int	fold,
		const void *	X,
		float_complex_binned *	Y
	)

Add complex single precision to suitably binned binned complex single precision (Y += X)

Performs the operation Y += X on an binned type Y where the index of Y is larger than the index of X

Note

This routine was provided as a means of allowing the you to optimize your code. After you have called binned_cbcupdate() on Y with the maximum absolute value of all future elements you wish to deposit in Y, you can call binned_cbcdeposit() to deposit a maximum of binned_SBENDURANCE elements into Y before renormalizing Y with binned_cbrenorm(). After any number of successive calls of binned_cbcdeposit() on Y, you must renormalize Y with binned_cbrenorm() before using any other function on Y.

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

10 Jun 2015

void binned_cbcupdate	(	const int	fold,
		const void *	X,
		float_complex_binned *	Y
	)

Update binned complex single precision with complex single precision (X -> Y)

This method updates Y to an index suitable for adding numbers with absolute value of real and imaginary components less than absolute value of real and imaginary components of X respectively.

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cbnegate	(	const int	fold,
		float_complex_binned *	X
	)

Negate binned complex single precision (X = -X)

Performs the operation X = -X

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

int binned_cbnum

(

const int

fold

)

binned complex single precision size

Parameters

fold	the fold of the binned type

Returns

the size (in float) of the binned type

Author

Peter Ahrens

Date

27 Apr 2015

void binned_cbprint	(	const int	fold,
		const float_complex_binned *	X
	)

Print binned complex single precision.

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cbrenorm	(	const int	fold,
		float_complex_binned *	X
	)

Renormalize binned complex single precision.

Renormalization keeps the primary vector within the necessary bins by shifting over to the carry vector

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cbsbset	(	const int	fold,
		const float_binned *	X,
		float_complex_binned *	Y
	)

Set binned complex single precision to binned single precision (Y = X)

Performs the operation Y = X

Parameters

fold	the fold of the binned types
X	binned scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cbsetzero	(	const int	fold,
		float_complex_binned *	X
	)

Set binned single precision to 0 (X = 0)

Performs the operation X = 0

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

size_t binned_cbsize

(

const int

fold

)

binned complex single precision size

Parameters

fold	the fold of the binned type

Returns

the size (in bytes) of the binned type

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cbsupdate	(	const int	fold,
		const float	X,
		float_complex_binned *	Y
	)

Update binned complex single precision with single precision (X -> Y)

This method updates Y to an index suitable for adding numbers with absolute value less than X

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_ccbconv_sub	(	const int	fold,
		const float_complex_binned *	X,
		void *	conv
	)

Convert binned complex single precision to complex single precision (X -> Y)

Parameters

fold	the fold of the binned types
X	binned scalar X
conv	scalar return

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_ccmconv_sub	(	const int	fold,
		const float *	priX,
		const int	incpriX,
		const float *	carX,
		const int	inccarX,
		void *	conv
	)

Convert manually specified binned complex single precision to complex single precision (X -> Y)

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)
conv	scalar return

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cmcadd	(	const int	fold,
		const void *	X,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Add complex single precision to manually specified binned complex single precision (Y += X)

Performs the operation Y += X on an binned type Y

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cmcconv	(	const int	fold,
		const void *	X,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Convert complex single precision to manually specified binned complex single precision (X -> Y)

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cmcdeposit	(	const int	fold,
		const void *	X,
		float *	priY,
		const int	incpriY
	)

Add complex single precision to suitably binned manually specified binned complex single precision (Y += X)

Performs the operation Y += X on an binned type Y where the index of Y is larger than the index of X

Note

This routine was provided as a means of allowing the you to optimize your code. After you have called binned_cmcupdate() on Y with the maximum absolute value of all future elements you wish to deposit in Y, you can call binned_cmcdeposit() to deposit a maximum of binned_SBENDURANCE elements into Y before renormalizing Y with binned_cmrenorm(). After any number of successive calls of binned_cmcdeposit() on Y, you must renormalize Y with binned_cmrenorm() before using any other function on Y.

Parameters

fold	the fold of the binned types
X	scalar X
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

10 Jun 2015

void binned_cmcmadd	(	const int	fold,
		const float *	priX,
		const int	incpriX,
		const float *	carX,
		const int	inccarX,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Add manually specified binned complex single precision (Y += X)

Performs the operation Y += X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cmcmset	(	const int	fold,
		const float *	priX,
		const int	incpriX,
		const float *	carX,
		const int	inccarX,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Set manually specified binned complex single precision (Y = X)

Performs the operation Y = X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cmcupdate	(	const int	fold,
		const void *	X,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Update manually specified binned complex single precision with complex single precision (X -> Y)

This method updates Y to an index suitable for adding numbers with absolute value of real and imaginary components less than absolute value of real and imaginary components of X respectively.

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

int binned_cmdenorm	(	const int	fold,
		const float *	priX
	)

Check if binned type has denormal bits.

A quick check to determine if calculations involving X cannot be performed with "denormals are zero"

Parameters

fold	the fold of the binned type
priX	X's primary vector

Returns

>0 if x has denormal bits, 0 otherwise.

Author

Peter Ahrens

Date

23 Jun 2015

void binned_cmnegate	(	const int	fold,
		float *	priX,
		const int	incpriX,
		float *	carX,
		const int	inccarX
	)

Negate manually specified binned complex single precision (X = -X)

Performs the operation X = -X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cmprint	(	const int	fold,
		const float *	priX,
		const int	incpriX,
		const float *	carX,
		const int	inccarX
	)

Print manually specified binned complex single precision.

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cmrenorm	(	const int	fold,
		float *	priX,
		const int	incpriX,
		float *	carX,
		const int	inccarX
	)

Renormalize manually specified binned complex single precision.

Renormalization keeps the primary vector within the necessary bins by shifting over to the carry vector

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cmsetzero	(	const int	fold,
		float *	priX,
		const int	incpriX,
		float *	carX,
		const int	inccarX
	)

Set manually specified binned complex single precision to 0 (X = 0)

Performs the operation X = 0

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cmsmset	(	const int	fold,
		const float *	priX,
		const int	incpriX,
		const float *	carX,
		const int	inccarX,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Set manually specified binned complex single precision to manually specified binned single precision (Y = X)

Performs the operation Y = X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_cmsrescale	(	const int	fold,
		const float	X,
		const float	scaleY,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

rescale manually specified binned complex single precision sum of squares

Rescale an binned complex single precision sum of squares Y

Parameters

fold	the fold of the binned types
X	Y's new scaleY (X == binned_sscale (f) for some float f) (X >= scaleY)
scaleY	Y's current scaleY (scaleY == binned_sscale (f) for some float f) (X >= scaleY)
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

19 Jun 2015

void binned_cmsupdate	(	const int	fold,
		const float	X,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Update manually specified binned complex single precision with single precision (X -> Y)

This method updates Y to an index suitable for adding numbers with absolute value less than X

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

double_binned* binned_dballoc

(

const int

fold

)

binned double precision allocation

Parameters

fold	the fold of the binned type

Returns

a freshly allocated binned type. (free with free())

Author

Peter Ahrens

Date

27 Apr 2015

double binned_dbbound	(	const int	fold,
		const int	N,
		const double	X,
		const double	S
	)

Get binned double precision summation error bound.

This is a bound on the absolute error of a summation using binned types

Parameters

fold	the fold of the binned types
N	the number of double precision floating point summands
X	the summand of maximum absolute value
S	the value of the sum computed using binned types

Returns

error bound

Author

Peter Ahrens

Date

31 Jul 2015

void binned_dbdadd	(	const int	fold,
		const double	X,
		double_binned *	Y
	)

Add double precision to binned double precision (Y += X)

Performs the operation Y += X on an binned type Y

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_dbdbadd	(	const int	fold,
		const double_binned *	X,
		double_binned *	Y
	)

Add binned double precision (Y += X)

Performs the operation Y += X

Parameters

fold	the fold of the binned types
X	binned scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

double binned_dbdbaddsq	(	const int	fold,
		const double	scaleX,
		const double_binned *	X,
		const double	scaleY,
		double_binned *	Y
	)

Add binned double precision scaled sums of squares (Y += X)

Performs the operation Y += X, where X and Y represent scaled sums of squares.

Parameters

fold	the fold of the binned types
scaleX	scale of X (scaleX == binned_dscale (Z) for some double Z)
X	binned scalar X
scaleY	scale of Y (scaleY == binned_dscale (Z) for some double Z)
Y	binned scalar Y

Returns

updated scale of Y

Author

Peter Ahrens

Date

2 Dec 2015

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

Add binned double precision vectors (Y += X)

Performs the operation Y += X

Parameters

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

Author

Peter Ahrens

Date

25 Jun 2015

void binned_dbdbset	(	const int	fold,
		const double_binned *	X,
		double_binned *	Y
	)

Set binned double precision (Y = X)

Performs the operation Y = X

Parameters

fold	the fold of the binned types
X	binned scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_dbdconv	(	const int	fold,
		const double	X,
		double_binned *	Y
	)

Convert double precision to binned double precision (X -> Y)

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_dbddeposit	(	const int	fold,
		const double	X,
		double_binned *	Y
	)

Add double precision to suitably binned binned double precision (Y += X)

Performs the operation Y += X on an binned type Y where the index of Y is larger than the index of X

Note

This routine was provided as a means of allowing the you to optimize your code. After you have called binned_dbdupdate() on Y with the maximum absolute value of all future elements you wish to deposit in Y, you can call binned_dbddeposit() to deposit a maximum of binned_DBENDURANCE elements into Y before renormalizing Y with binned_dbrenorm(). After any number of successive calls of binned_dbddeposit() on Y, you must renormalize Y with binned_dbrenorm() before using any other function on Y.

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

10 Jun 2015

void binned_dbdupdate	(	const int	fold,
		const double	X,
		double_binned *	Y
	)

Update binned double precision with double precision (X -> Y)

This method updates Y to an index suitable for adding numbers with absolute value less than X

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_dbnegate	(	const int	fold,
		double_binned *	X
	)

Negate binned double precision (X = -X)

Performs the operation X = -X

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

int binned_dbnum

(

const int

fold

)

binned double precision size

Parameters

fold	the fold of the binned type

Returns

the size (in double) of the binned type

Author

Peter Ahrens

Date

27 Apr 2015

void binned_dbprint	(	const int	fold,
		const double_binned *	X
	)

Print binned double precision.

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_dbrenorm	(	const int	fold,
		double_binned *	X
	)

Renormalize binned double precision.

Renormalization keeps the primary vector within the necessary bins by shifting over to the carry vector

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_dbsetzero	(	const int	fold,
		double_binned *	X
	)

Set binned double precision to 0 (X = 0)

Performs the operation X = 0

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

size_t binned_dbsize

(

const int

fold

)

binned double precision size

Parameters

fold	the fold of the binned type

Returns

the size (in bytes) of the binned type

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

double binned_ddbconv	(	const int	fold,
		const double_binned *	X
	)

Convert binned double precision to double precision (X -> Y)

Parameters

fold	the fold of the binned types
X	binned scalar X

Returns

scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

double binned_ddmconv	(	const int	fold,
		const double *	priX,
		const int	incpriX,
		const double *	carX,
		const int	inccarX
	)

Convert manually specified binned double precision to double precision (X -> Y)

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Returns

scalar Y

Author

Peter Ahrens

Date

31 Jul 2015

int binned_dindex

(

const double

X

)

Get index of double precision.

The index of a non-binned type is the smallest index an binned type would need to have to sum it reproducibly. Higher indicies correspond to smaller bins.

Parameters

X

scalar X

Returns

X's index

Author

Peter Ahrens

Hong Diep Nguyen

Date

19 Jun 2015

const double* binned_dmbins

(

const int

X

)

Get binned double precision reference bins.

returns a pointer to the bins corresponding to the given index

Parameters

X

index

Returns

pointer to constant double precision bins of index X

Author

Peter Ahrens

Hong Diep Nguyen

Date

19 Jun 2015

void binned_dmdadd	(	const int	fold,
		const double	X,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Add double precision to manually specified binned double precision (Y += X)

Performs the operation Y += X on an binned type Y

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_dmdconv	(	const int	fold,
		const double	X,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Convert double precision to manually specified binned double precision (X -> Y)

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

30 Apr 2015

void binned_dmddeposit	(	const int	fold,
		const double	X,
		double *	priY,
		const int	incpriY
	)

Add double precision to suitably binned manually specified binned double precision (Y += X)

Performs the operation Y += X on an binned type Y where the index of Y is larger than the index of X

Note

This routine was provided as a means of allowing the you to optimize your code. After you have called binned_dmdupdate() on Y with the maximum absolute value of all future elements you wish to deposit in Y, you can call binned_dmddeposit() to deposit a maximum of binned_DBENDURANCE elements into Y before renormalizing Y with binned_dmrenorm(). After any number of successive calls of binned_dmddeposit() on Y, you must renormalize Y with binned_dmrenorm() before using any other function on Y.

Parameters

fold	the fold of the binned types
X	scalar X
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

10 Jun 2015

int binned_dmdenorm	(	const int	fold,
		const double *	priX
	)

Check if binned type has denormal bits.

A quick check to determine if calculations involving X cannot be performed with "denormals are zero"

Parameters

fold	the fold of the binned type
priX	X's primary vector

Returns

>0 if x has denormal bits, 0 otherwise.

Author

Peter Ahrens

Date

23 Jun 2015

void binned_dmdmadd	(	const int	fold,
		const double *	priX,
		const int	incpriX,
		const double *	carX,
		const int	inccarX,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Add manually specified binned double precision (Y += X)

Performs the operation Y += X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

double binned_dmdmaddsq	(	const int	fold,
		const double	scaleX,
		const double *	priX,
		const int	incpriX,
		const double *	carX,
		const int	inccarX,
		const double	scaleY,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Add manually specified binned double precision scaled sums of squares (Y += X)

Performs the operation Y += X, where X and Y represent scaled sums of squares.

Parameters

fold	the fold of the binned types
scaleX	scale of X (scaleX == binned_dscale (Z) for some double Z)
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)
scaleY	scale of Y (scaleY == binned_dscale (Z) for some double Z)
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

updated scale of Y

Author

Peter Ahrens

Date

1 Jun 2015

void binned_dmdmset	(	const int	fold,
		const double *	priX,
		const int	incpriX,
		const double *	carX,
		const int	inccarX,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Set manually specified binned double precision (Y = X)

Performs the operation Y = X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_dmdrescale	(	const int	fold,
		const double	X,
		const double	scaleY,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

rescale manually specified binned double precision sum of squares

Rescale an binned double precision sum of squares Y

Parameters

fold	the fold of the binned types
X	Y's new scaleY (X == binned_dscale (f) for some double f) (X >= scaleY)
scaleY	Y's current scaleY (scaleY == binned_dscale (f) for some double f) (X >= scaleY)
priY	Y's primary vector
incpriY	stride within Y's primary vector
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Author

Peter Ahrens

Date

19 Jun 2015

void binned_dmdupdate	(	const int	fold,
		const double	X,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Update manually specified binned double precision with double precision (X -> Y)

This method updates Y to an index suitable for adding numbers with absolute value less than X

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

5 May 2015

int binned_dmindex

(

const double *

priX

)

Get index of manually specified binned double precision.

The index of an binned type is the bin that it corresponds to. Higher indicies correspond to smaller bins.

Parameters

priX	X's primary vector

Returns

X's index

Author

Peter Ahrens

Hong Diep Nguyen

Date

23 Sep 2015

int binned_dmindex0

(

const double *

priX

)

Check if index of manually specified binned double precision is 0.

A quick check to determine if the index is 0

Parameters

priX	X's primary vector

Returns

>0 if x has index 0, 0 otherwise.

Author

Peter Ahrens

Date

19 May 2015

void binned_dmnegate	(	const int	fold,
		double *	priX,
		const int	incpriX,
		double *	carX,
		const int	inccarX
	)

Negate manually specified binned double precision (X = -X)

Performs the operation X = -X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_dmprint	(	const int	fold,
		const double *	priX,
		const int	incpriX,
		const double *	carX,
		const int	inccarX
	)

Print manually specified binned double precision.

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_dmrenorm	(	const int	fold,
		double *	priX,
		const int	incpriX,
		double *	carX,
		const int	inccarX
	)

Renormalize manually specified binned double precision.

Renormalization keeps the primary vector within the necessary bins by shifting over to the carry vector

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

23 Sep 2015

void binned_dmsetzero	(	const int	fold,
		double *	priX,
		const int	incpriX,
		double *	carX,
		const int	inccarX
	)

Set manually specified binned double precision to 0 (X = 0)

Performs the operation X = 0

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

double binned_dscale

(

const double

X

)

Get a reproducible double precision scale.

For any given X, return a reproducible scaling factor Y of the form

2^(DBWIDTH * z) where z is an integer

such that

Y * 2^(-DBL_MANT_DIG - DBWIDTH - 1) < X < Y * 2\^(DBWIDTH + 2)

Parameters

X	double precision number to be scaled

Returns

reproducible scaling factor

Author

Peter Ahrens

Date

19 Jun 2015

float_binned* binned_sballoc

(

const int

fold

)

binned single precision allocation

Parameters

fold	the fold of the binned type

Returns

a freshly allocated binned type. (free with free())

Author

Peter Ahrens

Date

27 Apr 2015

float binned_sbbound	(	const int	fold,
		const int	N,
		const float	X,
		const float	S
	)

Get binned single precision summation error bound.

This is a bound on the absolute error of a summation using binned types

Parameters

fold	the fold of the binned types
N	the number of single precision floating point summands
X	the summand of maximum absolute value
S	the value of the sum computed using binned types

Returns

error bound

Author

Peter Ahrens

Date

31 Jul 2015

Author

Peter Ahrens

Hong Diep Nguyen

Date

21 May 2015

void binned_sbnegate	(	const int	fold,
		float_binned *	X
	)

Negate binned single precision (X = -X)

Performs the operation X = -X

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

int binned_sbnum

(

const int

fold

)

binned single precision size

Parameters

fold	the fold of the binned type

Returns

the size (in float) of the binned type

Author

Peter Ahrens

Date

27 Apr 2015

void binned_sbprint	(	const int	fold,
		const float_binned *	X
	)

Print binned single precision.

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_sbrenorm	(	const int	fold,
		float_binned *	X
	)

Renormalize binned single precision.

Renormalization keeps the primary vector within the necessary bins by shifting over to the carry vector

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_sbsadd	(	const int	fold,
		const float	X,
		float_binned *	Y
	)

Add single precision to binned single precision (Y += X)

Performs the operation Y += X on an binned type Y

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_sbsbadd	(	const int	fold,
		const float_binned *	X,
		float_binned *	Y
	)

Add binned single precision (Y += X)

Performs the operation Y += X

Parameters

fold	the fold of the binned types
X	binned scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

float binned_sbsbaddsq	(	const int	fold,
		const float	scaleX,
		const float_binned *	X,
		const float	scaleY,
		float_binned *	Y
	)

Add binned single precision scaled sums of squares (Y += X)

Performs the operation Y += X, where X and Y represent scaled sums of squares.

Parameters

fold	the fold of the binned types
scaleX	scale of X (scaleX == binned_sscale (Z) for some float Z)
X	binned scalar X
scaleY	scale of Y (scaleY == binned_sscale (Z) for some float Z)
Y	binned scalar Y

Returns

updated scale of Y

Author

Peter Ahrens

Date

2 Dec 2015

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

Add binned single precision vectors (Y += X)

Performs the operation Y += X

Parameters

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

Author

Peter Ahrens

Date

25 Jun 2015

void binned_sbsbset	(	const int	fold,
		const float_binned *	X,
		float_binned *	Y
	)

Set binned single precision (Y = X)

Performs the operation Y = X

Parameters

fold	the fold of the binned types
X	binned scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

size_t binned_sbsbze

(

const int

fold

)

binned single precision size

Parameters

fold	the fold of the binned type

Returns

the size (in bytes) of the binned type

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_sbsconv	(	const int	fold,
		const float	X,
		float_binned *	Y
	)

Convert single precision to binned single precision (X -> Y)

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_sbsdeposit	(	const int	fold,
		const float	X,
		float_binned *	Y
	)

Add single precision to suitably binned binned single precision (Y += X)

Performs the operation Y += X on an binned type Y where the index of Y is larger than the index of X

Note

This routine was provided as a means of allowing the you to optimize your code. After you have called binned_sbsupdate() on Y with the maximum absolute value of all future elements you wish to deposit in Y, you can call binned_sbsdeposit() to deposit a maximum of binned_SBENDURANCE elements into Y before renormalizing Y with binned_sbrenorm(). After any number of successive calls of binned_sbsdeposit() on Y, you must renormalize Y with binned_sbrenorm() before using any other function on Y.

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

10 Jun 2015

void binned_sbsetzero	(	const int	fold,
		float_binned *	X
	)

Set binned single precision to 0 (X = 0)

Performs the operation X = 0

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_sbsupdate	(	const int	fold,
		const float	X,
		float_binned *	Y
	)

Update binned single precision with single precision (X -> Y)

This method updates Y to an index suitable for adding numbers with absolute value less than X

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

int binned_sindex

(

const float

X

)

Get index of single precision.

The index of a non-binned type is the smallest index an binned type would need to have to sum it reproducibly. Higher indicies correspond to smaller bins.

Parameters

X

scalar X

Returns

X's index

Author

Peter Ahrens

Hong Diep Nguyen

Date

19 Jun 2015

const float* binned_smbins

(

const int

X

)

Get binned single precision reference bins.

returns a pointer to the bins corresponding to the given index

Parameters

X

index

Returns

pointer to constant single precision bins of index X

Author

Peter Ahrens

Hong Diep Nguyen

Date

19 Jun 2015

int binned_smdenorm	(	const int	fold,
		const float *	priX
	)

Check if binned type has denormal bits.

A quick check to determine if calculations involving X cannot be performed with "denormals are zero"

Parameters

fold	the fold of the binned type
priX	X's primary vector

Returns

>0 if x has denormal bits, 0 otherwise.

Author

Peter Ahrens

Date

23 Jun 2015

int binned_smindex

(

const float *

priX

)

Get index of manually specified binned single precision.

The index of an binned type is the bin that it corresponds to. Higher indicies correspond to smaller bins.

Parameters

priX	X's primary vector

Returns

X's index

Author

Peter Ahrens

Hong Diep Nguyen

Date

23 Sep 2015

int binned_smindex0

(

const float *

priX

)

Check if index of manually specified binned single precision is 0.

A quick check to determine if the index is 0

Parameters

priX	X's primary vector

Returns

>0 if x has index 0, 0 otherwise.

Author

Peter Ahrens

Date

19 May 2015

void binned_smnegate	(	const int	fold,
		float *	priX,
		const int	incpriX,
		float *	carX,
		const int	inccarX
	)

Negate manually specified binned single precision (X = -X)

Performs the operation X = -X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_smprint	(	const int	fold,
		const float *	priX,
		const int	incpriX,
		const float *	carX,
		const int	inccarX
	)

Print manually specified binned single precision.

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_smrenorm	(	const int	fold,
		float *	priX,
		const int	incpriX,
		float *	carX,
		const int	inccarX
	)

Renormalize manually specified binned single precision.

Renormalization keeps the primary vector within the necessary bins by shifting over to the carry vector

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

23 Sep 2015

void binned_smsadd	(	const int	fold,
		const float	X,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Add single precision to manually specified binned single precision (Y += X)

Performs the operation Y += X on an binned type Y

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_smsconv	(	const int	fold,
		const float	X,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Convert single precision to manually specified binned single precision (X -> Y)

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

30 Apr 2015

void binned_smsdeposit	(	const int	fold,
		const float	X,
		float *	priY,
		const int	incpriY
	)

Add single precision to suitably binned manually specified binned single precision (Y += X)

Performs the operation Y += X on an binned type Y where the index of Y is larger than the index of X

Note

This routine was provided as a means of allowing the you to optimize your code. After you have called binned_smsupdate() on Y with the maximum absolute value of all future elements you wish to deposit in Y, you can call binned_smsdeposit() to deposit a maximum of binned_SBENDURANCE elements into Y before renormalizing Y with binned_smrenorm(). After any number of successive calls of binned_smsdeposit() on Y, you must renormalize Y with binned_smrenorm() before using any other function on Y.

Parameters

fold	the fold of the binned types
X	scalar X
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

10 Jun 2015

void binned_smsetzero	(	const int	fold,
		float *	priX,
		const int	incpriX,
		float *	carX,
		const int	inccarX
	)

Set manually specified binned single precision to 0 (X = 0)

Performs the operation X = 0

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_smsmadd	(	const int	fold,
		const float *	priX,
		const int	incpriX,
		const float *	carX,
		const int	inccarX,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Add manually specified binned single precision (Y += X)

Performs the operation Y += X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

float binned_smsmaddsq	(	const int	fold,
		const float	scaleX,
		const float *	priX,
		const int	incpriX,
		const float *	carX,
		const int	inccarX,
		const float	scaleY,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Add manually specified binned single precision scaled sums of squares (Y += X)

Performs the operation Y += X, where X and Y represent scaled sums of squares.

Parameters

fold	the fold of the binned types
scaleX	scale of X (scaleX == binned_sscale (Z) for some float Z)
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)
scaleY	scale of Y (scaleY == binned_sscale (Z) for some double Z)
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

updated scale of Y

Author

Peter Ahrens

Date

1 Jun 2015

void binned_smsmset	(	const int	fold,
		const float *	priX,
		const int	incpriX,
		const float *	carX,
		const int	inccarX,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Set manually specified binned single precision (Y = X)

Performs the operation Y = X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_smsrescale	(	const int	fold,
		const float	X,
		const float	scaleY,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

rescale manually specified binned single precision sum of squares

Rescale an binned single precision sum of squares Y

Parameters

fold	the fold of the binned types
X	Y's new scaleY (X == binned_sscale (f) for some float f) (X >= scaleY)
scaleY	Y's current scaleY (scaleY == binned_sscale (f) for some float f) (X >= scaleY)
priY	Y's primary vector
incpriY	stride within Y's primary vector
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Author

Peter Ahrens

Date

1 Jun 2015

void binned_smsupdate	(	const int	fold,
		const float	X,
		float *	priY,
		const int	incpriY,
		float *	carY,
		const int	inccarY
	)

Update manually specified binned single precision with single precision (X -> Y)

This method updates Y to an index suitable for adding numbers with absolute value less than X

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

5 May 2015

float binned_ssbconv	(	const int	fold,
		const float_binned *	X
	)

Convert binned single precision to single precision (X -> Y)

Parameters

fold	the fold of the binned types
X	binned scalar X

Returns

scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

float binned_sscale

(

const float

X

)

Get a reproducible single precision scale.

For any given X, return a reproducible scaling factor Y of the form

2^(SBWIDTH * z) where z is an integer

such that

Y * 2^(-FLT_MANT_DIG - SBWIDTH - 1) < X < Y * 2\^(SBWIDTH + 2)

Parameters

X	single precision number to be scaled

Returns

reproducible scaling factor

Author

Peter Ahrens

Date

19 Jun 2015

float binned_ssmconv	(	const int	fold,
		const float *	priX,
		const int	incpriX,
		const float *	carX,
		const int	inccarX
	)

Convert manually specified binned single precision to single precision (X -> Y)

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Returns

scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

double binned_ufp

(

double

X

)

unit in the first place

This method returns just the implicit 1 in the mantissa of a double

Parameters

X

scalar X

Returns

unit in the first place

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

float binned_ufpf

(

float

X

)

unit in the first place

This method returns just the implicit 1 in the mantissa of a float

Parameters

X

scalar X

Returns

unit in the first place

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

double_complex_binned* binned_zballoc

(

const int

fold

)

binned complex double precision allocation

Parameters

fold	the fold of the binned type

Returns

a freshly allocated binned type. (free with free())

Author

Peter Ahrens

Date

27 Apr 2015

void binned_zbdbset	(	const int	fold,
		const double_binned *	X,
		double_complex_binned *	Y
	)

Set binned complex double precision to binned double precision (Y = X)

Performs the operation Y = X

Parameters

fold	the fold of the binned types
X	binned scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zbdupdate	(	const int	fold,
		const double	X,
		double_complex_binned *	Y
	)

Update binned complex double precision with double precision (X -> Y)

This method updates Y to an index suitable for adding numbers with absolute value less than X

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zbnegate	(	const int	fold,
		double_complex_binned *	X
	)

Negate binned complex double precision (X = -X)

Performs the operation X = -X

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

int binned_zbnum

(

const int

fold

)

binned complex double precision size

Parameters

fold	the fold of the binned type

Returns

the size (in double) of the binned type

Author

Peter Ahrens

Date

27 Apr 2015

void binned_zbprint	(	const int	fold,
		const double_complex_binned *	X
	)

Print binned complex double precision.

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zbrenorm	(	const int	fold,
		double_complex_binned *	X
	)

Renormalize binned complex double precision.

Renormalization keeps the primary vector within the necessary bins by shifting over to the carry vector

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zbsetzero	(	const int	fold,
		double_complex_binned *	X
	)

Set binned double precision to 0 (X = 0)

Performs the operation X = 0

Parameters

fold	the fold of the binned types
X	binned scalar X

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

size_t binned_zbsize

(

const int

fold

)

binned complex double precision size

Parameters

fold	the fold of the binned type

Returns

the size (in bytes) of the binned type

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zbzadd	(	const int	fold,
		const void *	X,
		double_complex_binned *	Y
	)

Add complex double precision to binned complex double precision (Y += X)

Performs the operation Y += X on an binned type Y

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zbzbadd	(	const int	fold,
		const double_complex_binned *	X,
		double_complex_binned *	Y
	)

Add binned complex double precision (Y += X)

Performs the operation Y += X

Parameters

fold	the fold of the binned types
X	binned scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

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

Add binned complex double precision vectors (Y += X)

Performs the operation Y += X

Parameters

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

Author

Peter Ahrens

Date

25 Jun 2015

void binned_zbzbset	(	const int	fold,
		const double_complex_binned *	X,
		double_complex_binned *	Y
	)

Set binned complex double precision (Y = X)

Performs the operation Y = X

Parameters

fold	the fold of the binned types
X	binned scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zbzconv	(	const int	fold,
		const void *	X,
		double_complex_binned *	Y
	)

Convert complex double precision to binned complex double precision (X -> Y)

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zbzdeposit	(	const int	fold,
		const void *	X,
		double_complex_binned *	Y
	)

Add complex double precision to suitably binned binned complex double precision (Y += X)

Performs the operation Y += X on an binned type Y where the index of Y is larger than the index of X

Note

This routine was provided as a means of allowing the you to optimize your code. After you have called binned_zbzupdate() on Y with the maximum absolute value of all future elements you wish to deposit in Y, you can call binned_zbzdeposit() to deposit a maximum of binned_DBENDURANCE elements into Y before renormalizing Y with binned_zbrenorm(). After any number of successive calls of binned_zbzdeposit() on Y, you must renormalize Y with binned_zbrenorm() before using any other function on Y.

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

10 Jun 2015

void binned_zbzupdate	(	const int	fold,
		const void *	X,
		double_complex_binned *	Y
	)

Update binned complex double precision with complex double precision (X -> Y)

This method updates Y to an index suitable for adding numbers with absolute value of real and imaginary components less than absolute value of real and imaginary components of X respectively.

Parameters

fold	the fold of the binned types
X	scalar X
Y	binned scalar Y

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

int binned_zmdenorm	(	const int	fold,
		const double *	priX
	)

Check if binned type has denormal bits.

A quick check to determine if calculations involving X cannot be performed with "denormals are zero"

Parameters

fold	the fold of the binned type
priX	X's primary vector

Returns

>0 if x has denormal bits, 0 otherwise.

Author

Peter Ahrens

Date

23 Jun 2015

void binned_zmdmset	(	const int	fold,
		const double *	priX,
		const int	incpriX,
		const double *	carX,
		const int	inccarX,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Set manually specified binned complex double precision to manually specified binned double precision (Y = X)

Performs the operation Y = X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zmdrescale	(	const int	fold,
		const double	X,
		const double	scaleY,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

rescale manually specified binned complex double precision sum of squares

Rescale an binned complex double precision sum of squares Y

Parameters

fold	the fold of the binned types
X	Y's new scaleY (X == binned_dscale (f) for some double f) (X >= scaleY)
scaleY	Y's current scaleY (scaleY == binned_dscale (f) for some double f) (X >= scaleY)
priY	Y's primary vector
incpriY	stride within Y's primary vector
carY	Y's carry vector
inccarY	stride within Y's carry vector (use every inccarY'th element)

Author

Peter Ahrens

Date

1 Jun 2015

void binned_zmdupdate	(	const int	fold,
		const double	X,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Update manually specified binned complex double precision with double precision (X -> Y)

This method updates Y to an index suitable for adding numbers with absolute value less than X

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zmnegate	(	const int	fold,
		double *	priX,
		const int	incpriX,
		double *	carX,
		const int	inccarX
	)

Negate manually specified binned complex double precision (X = -X)

Performs the operation X = -X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zmprint	(	const int	fold,
		const double *	priX,
		const int	incpriX,
		const double *	carX,
		const int	inccarX
	)

Print manually specified binned complex double precision.

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zmrenorm	(	const int	fold,
		double *	priX,
		const int	incpriX,
		double *	carX,
		const int	inccarX
	)

Renormalize manually specified binned complex double precision.

Renormalization keeps the primary vector within the necessary bins by shifting over to the carry vector

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zmsetzero	(	const int	fold,
		double *	priX,
		const int	incpriX,
		double *	carX,
		const int	inccarX
	)

Set manually specified binned complex double precision to 0 (X = 0)

Performs the operation X = 0

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zmzadd	(	const int	fold,
		const void *	X,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Add complex double precision to manually specified binned complex double precision (Y += X)

Performs the operation Y += X on an binned type Y

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zmzconv	(	const int	fold,
		const void *	X,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Convert complex double precision to manually specified binned complex double precision (X -> Y)

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zmzdeposit	(	const int	fold,
		const void *	X,
		double *	priY,
		const int	incpriY
	)

Add complex double precision to suitably binned manually specified binned complex double precision (Y += X)

Performs the operation Y += X on an binned type Y where the index of Y is larger than the index of X

Note

This routine was provided as a means of allowing the you to optimize your code. After you have called binned_zmzupdate() on Y with the maximum absolute value of all future elements you wish to deposit in Y, you can call binned_zmzdeposit() to deposit a maximum of binned_DBENDURANCE elements into Y before renormalizing Y with binned_zmrenorm(). After any number of successive calls of binned_zmzdeposit() on Y, you must renormalize Y with binned_zmrenorm() before using any other function on Y.

Parameters

fold	the fold of the binned types
X	scalar X
priY	Y's primary vector
incpriY	stride within Y's primary vector (use every incpriY'th element)

Author

Hong Diep Nguyen

Peter Ahrens

Date

10 Jun 2015

void binned_zmzmadd	(	const int	fold,
		const double *	priX,
		const int	incpriX,
		const double *	carX,
		const int	inccarX,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Add manually specified binned complex double precision (Y += X)

Performs the operation Y += X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zmzmset	(	const int	fold,
		const double *	priX,
		const int	incpriX,
		const double *	carX,
		const int	inccarX,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Set manually specified binned complex double precision (Y = X)

Performs the operation Y = X

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zmzupdate	(	const int	fold,
		const void *	X,
		double *	priY,
		const int	incpriY,
		double *	carY,
		const int	inccarY
	)

Update manually specified binned complex double precision with complex double precision (X -> Y)

This method updates Y to an index suitable for adding numbers with absolute value of real and imaginary components less than absolute value of real and imaginary components of X respectively.

Parameters

fold	the fold of the binned types
X	scalar X
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

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zzbconv_sub	(	const int	fold,
		const double_complex_binned *	X,
		void *	conv
	)

Convert binned complex double precision to complex double precision (X -> Y)

Parameters

fold	the fold of the binned types
X	binned scalar X
conv	scalar return

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015

void binned_zzmconv_sub	(	const int	fold,
		const double *	priX,
		const int	incpriX,
		const double *	carX,
		const int	inccarX,
		void *	conv
	)

Convert manually specified binned complex double precision to complex double precision (X -> Y)

Parameters

fold	the fold of the binned types
priX	X's primary vector
incpriX	stride within X's primary vector (use every incpriX'th element)
carX	X's carry vector
inccarX	stride within X's carry vector (use every inccarX'th element)
conv	scalar return

Author

Hong Diep Nguyen

Peter Ahrens

Date

27 Apr 2015