Prototypes for portable math library (ported from C Toolkit) More...

#include <algo/blast/core/ncbi_std.h>
#include <algo/blast/core/blast_export.h>

Include dependency graph for ncbi_math.h:

This graph shows which files directly or indirectly include this file:

Macros
#define	LOGDERIV_ORDER_MAX 4
	Number of derivatives of log(x) to carry in gamma-related computations. More...

#define	POLYGAMMA_ORDER_MAX LOGDERIV_ORDER_MAX
	Number of derivatives of polygamma(x) to carry in gamma-related computations for non-integral values of x. More...

#define	NCBIMATH_PI 3.1415926535897932384626433832795
	value of pi is only used in gamma-related computations More...

#define	NCBIMATH_LN2 0.69314718055994530941723212145818
	Natural log(2) More...

#define	NCBIMATH_LNPI 1.1447298858494001741434273513531
	Natural log(PI) More...

Functions
double	BLAST_Log1p (double x)
	Natural logarithm with shifted input. More...

double	BLAST_Expm1 (double x)
	Exponentional with base e. More...

double	BLAST_Factorial (Int4 n)
	Factorial function. More...

double	BLAST_LnFactorial (double x)
	Logarithm of the factorial. More...

double	BLAST_LnGammaInt (Int4 n)
	log(gamma(n)), integral n More...

double	BLAST_RombergIntegrate (double(f)(double, void ), void *fargs, double p, double q, double eps, Int4 epsit, Int4 itmin)
	Romberg numerical integrator. More...

Int4	BLAST_Gcd (Int4 a, Int4 b)
	Greatest common divisor. More...

Int4	BLAST_Gdb3 (Int4 a, Int4 b, Int4 *c)
	Divide 3 numbers by their greatest common divisor. More...

long	BLAST_Nint (double x)
	Nearest integer. More...

double	BLAST_Powi (double x, Int4 n)
	Integral power of x. More...

double	BLAST_Erf (double x)
	The error function of x: the integral from 0 to x of e(-t*t) dt, scaled by 2/sqrt(pi) to fall within the range (-1,1). More...

double	BLAST_ErfC (double x)
	The complementary error function of x: 1 - erf(x), but calculated more accurately for large x (where erf(x) approaches unity). More...

Detailed Description

Prototypes for portable math library (ported from C Toolkit)

Definition in file ncbi_math.h.

Macro Definition Documentation

◆ LOGDERIV_ORDER_MAX

#define LOGDERIV_ORDER_MAX 4

Number of derivatives of log(x) to carry in gamma-related computations.

Definition at line 152 of file ncbi_math.h.

◆ NCBIMATH_LN2

#define NCBIMATH_LN2 0.69314718055994530941723212145818

Natural log(2)

Definition at line 161 of file ncbi_math.h.

◆ NCBIMATH_LNPI

#define NCBIMATH_LNPI 1.1447298858494001741434273513531

Natural log(PI)

Definition at line 163 of file ncbi_math.h.

◆ NCBIMATH_PI

#define NCBIMATH_PI 3.1415926535897932384626433832795

value of pi is only used in gamma-related computations

Definition at line 158 of file ncbi_math.h.

◆ POLYGAMMA_ORDER_MAX

#define POLYGAMMA_ORDER_MAX LOGDERIV_ORDER_MAX

Number of derivatives of polygamma(x) to carry in gamma-related computations for non-integral values of x.

Definition at line 155 of file ncbi_math.h.

Function Documentation

◆ BLAST_Erf()

double BLAST_Erf ( double x )

The error function of x: the integral from 0 to x of e(-t*t) dt, scaled by 2/sqrt(pi) to fall within the range (-1,1).

◆ BLAST_ErfC()

double BLAST_ErfC ( double x )

The complementary error function of x: 1 - erf(x), but calculated more accurately for large x (where erf(x) approaches unity).

◆ BLAST_Expm1()

double BLAST_Expm1 ( double x )

Exponentional with base e.

Parameters

x	input operand

Returns: exp(x) - 1

Definition at line 33 of file ncbi_math.c.

References ABS.

Referenced by BLAST_KarlinEtoP(), BlastKarlinLHtoK(), s_BlastSumP(), and s_BlastSumPCalc().

◆ BLAST_Factorial()

double BLAST_Factorial ( Int4 n )

Factorial function.

Parameters

n	input operand

Returns: (double)(1 * 2 * 3 * ... * n)

Definition at line 312 of file ncbi_math.c.

References DIM, kPrecomputedFactorial, n, and s_LnGamma().

Referenced by s_GeneralLnGamma(), and s_PolyGamma().

◆ BLAST_Gcd()

Int4 BLAST_Gcd	(	Int4	a,
		Int4	b
	)

Greatest common divisor.

Parameters

a	First operand (any integer)
b	Second operand (any integer)

Returns: The largest integer that evenly divides a and b

Definition at line 405 of file ncbi_math.c.

References a, ABS, and b.

Referenced by BLAST_Gdb3(), Blast_KarlinLambdaNR(), BlastKarlinLHtoK(), and s_GetNuclValuesArray().

◆ BLAST_Gdb3()

Int4 BLAST_Gdb3	(	Int4 *	a,
		Int4 *	b,
		Int4 *	c
	)

Divide 3 numbers by their greatest common divisor.

Parameters

a	First integer [in] [out]
b	Second integer [in] [out]
c	Third integer [in] [out]

Returns: The greatest common divisor

Definition at line 422 of file ncbi_math.c.

References a, b, BLAST_Gcd(), and g().

Referenced by BLAST_AffineGreedyAlign(), and s_BlastGreedyAlignMemAlloc().

◆ BLAST_LnFactorial()

double BLAST_LnFactorial ( double x )

Logarithm of the factorial.

Parameters

x	input operand

Returns: log(1 * 2 * 3 * ... * x)

Definition at line 473 of file ncbi_math.c.

References s_LnGamma().

Referenced by BLAST_LargeGapSumE(), BLAST_SmallGapSumE(), and BLAST_UnevenGapSumE().

◆ BLAST_LnGammaInt()

double BLAST_LnGammaInt ( Int4 n )

log(gamma(n)), integral n

Parameters

n	input operand

Returns: log(1 * 2 * 3 * ... (n-1))

Definition at line 323 of file ncbi_math.c.

References DIM, kPrecomputedFactorial, log, n, and s_LnGamma().

Referenced by s_BlastSumP(), and s_BlastSumPCalc().

◆ BLAST_Log1p()

double BLAST_Log1p ( double x )

Natural logarithm with shifted input.

Parameters

x	input operand (x > -1)

Returns: log(x+1)

Definition at line 64 of file ncbi_math.c.

References ABS, DBL_EPSILON, i, and log.

Referenced by BLAST_KarlinPtoE().

◆ BLAST_Nint()

long BLAST_Nint ( double x )

Nearest integer.

Parameters

x	Input to round (rounded value must be representable as a 32-bit signed integer)

Returns: floor(x + 0.5);

Definition at line 437 of file ncbi_math.c.

Referenced by _PSIConvertFreqRatiosToPSSM(), _PSIScaleMatrix(), Blast_GumbelBlkLoadFromTables(), Blast_KarlinBlkGappedLoadFromTables(), BLAST_PrintAllowedValues(), BlastKarlinReportAllowedValues(), BlastScoreBlkNuclMatrixCreate(), BOOST_AUTO_TEST_CASE(), CalculateLinkHSPCutoffs(), impalaScaleMatrix(), RPSRescalePssm(), s_BuildCompressedScoreMatrix(), s_HSPListNormalizeScores(), s_RescaleSearch(), and CMakeProfileDBApp::x_UpdateFreqRatios().

◆ BLAST_Powi()

double BLAST_Powi	(	double	x,
		Int4	n
	)

Integral power of x.

Parameters

x	floating-point base of the exponential
n	(integer) exponent

Returns: x multiplied by itself n times

Definition at line 444 of file ncbi_math.c.

References n.

Referenced by BLAST_GapDecayDivisor(), BlastKarlinLtoH(), s_GeneralLnGamma(), and s_PolyGamma().

◆ BLAST_RombergIntegrate()

double BLAST_RombergIntegrate	(	double()(double, void )	f,
		void *	fargs,
		double	p,
		double	q,
		double	eps,
		Int4	epsit,
		Int4	itmin
	)

Romberg numerical integrator.

Parameters

f	Pointer to the function to integrate; the first argument is the variable to integrate over, the second is a pointer to a list of additional arguments that f may need
fargs	Pointer to an array of extra arguments or parameters needed to compute the function to be integrated. None of the items in this list may vary over the region of integration
p	Left-hand endpoint of the integration interval
q	Right-hand endpoint of the integration interval (q is assumed > p)
eps	The relative error tolerance that indicates convergence
epsit	The number of consecutive diagonal entries in the Romberg array whose relative difference must be less than eps before convergence is assumed. This is presently limited to 1, 2, or 3
itmin	The minimum number of diagnonal Romberg entries that will be computed

Returns: The computed integral of f() between p and q

Definition at line 346 of file ncbi_math.c.

References ABS, F, i, MAX, MAX_DIAGS, MIN, and n.

Referenced by s_BlastSumPCalc(), and s_InnerIntegralCback().

Macros

Functions

Detailed Description

Macro Definition Documentation

◆ LOGDERIV_ORDER_MAX

◆ NCBIMATH_LN2

◆ NCBIMATH_LNPI

◆ NCBIMATH_PI

◆ POLYGAMMA_ORDER_MAX

Function Documentation

◆ BLAST_Erf()

◆ BLAST_ErfC()

◆ BLAST_Expm1()

◆ BLAST_Factorial()

◆ BLAST_Gcd()

◆ BLAST_Gdb3()

◆ BLAST_LnFactorial()

◆ BLAST_LnGammaInt()

◆ BLAST_Log1p()

◆ BLAST_Nint()

◆ BLAST_Powi()

◆ BLAST_RombergIntegrate()