Intel® oneAPI DPC++/C++ Compiler Developer Guide and Reference

ID 767253
Date 3/22/2024
Public

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Document Table of Contents

Special Functions

Many routines in the Intel® oneAPI DPC++/C++ Compiler Math Library are more optimized for Intel® microprocessors than for non-Intel microprocessors.

The mathimf.h header file includes prototypes for Intel® oneAPI DPC++/C++ Compiler Math Library functions.

The math library supports the following special functions:

NOTE:

FP16 Math Functions have the following requirements:

  • Version 2021.4 or higher of the Intel® oneAPI DPC++/C++ Compiler.

  • A next-generation Intel® Xeon® Scalable processor, code name Sapphire Rapids.

annuity

Description: The annuity function computes the present value factor for an annuity, (1 - (1+x)(-y) ) / x, where x is a rate and y is a period.

errno: ERANGE, for underflow and overflow conditions

Calling interface:
double annuity(double x, double y);
long double annuityl(long double x, long double y);
float annuityf(float x, float y);
_Float16 annuityf16(_Float16 x, _Float16 y);

cdfnorm

Description: The cdfnorm function returns the cumulative normal distribution function value.

Calling interface:
double cdfnorm(double x);
float cdfnormf(float x);
_Float16 cdfnormf16 (_Float16 x);

cdfnorminv

Description: The cdfnorminv function returns the inverse cumulative normal distribution function value.

errno:
EDOM, for finite or infinite (x > 1) || (x < 0)
ERANGE, for x = 0 or x = 1

Calling interface:
double cdfnorminv(double x);
float cdfnorminvf (float x);
_Float16 cdfnorminvf16 (_Float16 x);

compound

Description: The compound function computes the compound interest factor, (1+x)y, where x is a rate and y is a period.

errno: ERANGE, for underflow and overflow conditions

Calling interface:
double compound(double x, double y);
long double compoundl(long double x, long double y);
float compoundf(float x, float y);
_Float16 compoundf16(_Float16 x, _Float16 y);

erf

Description: The erf function returns the error function value.

Calling interface:
double erf(double x);
long double erfl(long double x);
float erff(float x);
_Float16 erff16(_Float16 x);

erfc

Description: The erfc function returns the complementary error function value.

errno: ERANGE, for underflow conditions

Calling interface:
double erfc(double x);
long double erfcl(long double x);
float erfcf(float x);
_Float16 erfcf16(_Float16 x);

erfcx

Description: The erfcx function returns the scaled complementary error function value.

errno: ERANGE, for overflow conditions

Calling interface:
double erfcx(double x);
float erfcxf(float x);

erfcinv

Description: The erfcinv function returns the value of the inverse complementary error function of x.

errno: EDOM, for finite or infinite (x > 2) || (x < 0)

Calling interface:
double erfcinv(double x);
float erfcinvf(float x);
_Float16 erfcinvf16(_Float16 x);

erfinv

Description: The erfinv function returns the value of the inverse error function of x.

errno: EDOM, for finite or infinite |x| > 1

Calling interface:
double erfinv(double x);
long double erfinvl(long double x);
float erfinvf(float x);
_Float16 erfinvf16(_Float16 x);

gamma

Description: The gamma function returns the value of the logarithm of the absolute value of gamma.

errno: ERANGE, for overflow conditions when x is a negative integer.

Calling interface:
double gamma(double x);
long double gammal(long double x);
float gammaf(float x);
_Float16 gammaf16(_Float16 x);

gamma_r

Description: The gamma_r function returns the value of the logarithm of the absolute value of gamma. The sign of the gamma function is returned in the integer signgam.

Calling interface:
double gamma_r(double x, int *signgam);
long double gammal_r(long double x, int *signgam);
float gammaf_r(float x, int *signgam);
_Float16 gammaf16_r(_Float16 x, int *signgam);

j0

Description: Computes the Bessel function (of the first kind) of x with order 0.

Calling interface:
double j0(double x);
long double j0l(long double x);
float j0f(float x);
_Float16 j0f16(_Float16 x);

j1

Description: Computes the Bessel function (of the first kind) of x with order 1.

Calling interface:
double j1(double x);
long double j1l(long double x);
float j1f(float x);
_Float16 j1f16(_Float16 x);

jn

Description: Computes the Bessel function (of the first kind) of x with order n.

Calling interface:
double jn(int n, double x);
long double jnl(int n, long double x);
float jnf(int n, float x);
_Float16 jnf16(int n, _Float16 x);

lgamma

Description: The lgamma function returns the value of the logarithm of the absolute value of gamma.

errno: ERANGE, for overflow conditions, x=0 or negative integers.

Calling interface:
double lgamma(double x);
long double lgammal(long double x);
float lgammaf(float x);
_Float16 lgammaf16(_Float16 x);

lgamma_r

Description: The lgamma_r function returns the value of the logarithm of the absolute value of gamma. The sign of the gamma function is returned in the integer signgam.

errno: ERANGE, for overflow conditions, x=0 or negative integers.

Calling interface:
double lgamma_r(double x, int *signgam);
long double lgammal_r(long double x, int *signgam);
float lgammaf_r(float x, int *signgam);
_Float16 lgammaf16_r(_Float16 x, int *signgam);

tgamma

Description: The tgamma function computes the gamma function of x.

errno:

EDOM, for x=0 or negative integers.

ERANGE, for overflow conditions.

Calling interface:
double tgamma(double x);
long double tgammal(long double x);
float tgammaf(float x);
_Float16 tgammaf16(_Float16 x);

y0

Description: Computes the Bessel function (of the second kind) of x with order 0.

errno: EDOM, for x <= 0

Calling interface:
double y0(double x);
long double y0l(long double x);
float y0f(float x);
_Float16 y0f16(_Float16 x);

y1

Description: Computes the Bessel function (of the second kind) of x with order 1.

errno: EDOM, for x <= 0

Calling interface:
double y1(double x);
long double y1l(long double x);
float y1f(float x);
_Float16 y1f16(_Float16 x);

yn

Description: Computes the Bessel function (of the second kind) of x with order n.

errno: EDOM, for x <= 0

Calling interface:
double yn(int n, double x);
long double ynl(int n, long double x);
float ynf(int n, float x);
_Float16 ynf16(int n, _Float16 x);