# Exponential Functions

Many routines in the Intel® Math Library are more optimized for Intel® microprocessors than for non-Intel microprocessors.

The mathimf.h header file includes prototypes for Intel® Math Library functions.

The Intel® Math Library supports the following exponential functions:

## cbrt

Description: The cbrt function returns the cube root of `x`.

Calling interface:
`double cbrt(double x);`
`long double cbrtl(long double x);`
`float cbrtf(float x);`

## exp

Description: The exp function returns `e` raised to the `x` power, `e`x.

errno: ERANGE, for underflow and overflow conditions

Calling interface:
`double exp(double x);`
`long double expl(long double x);`
`float expf(float x);`

## exp10

Description: The exp10 function returns 10 raised to the `x` power, 10x.

errno: ERANGE, for underflow and overflow conditions

Calling interface:
`double exp10(double x);`
`long double exp10l(long double x);`
`float exp10f(float x);`

## exp2

Description: The exp2 function returns 2 raised to the `x` power, 2x.

errno: ERANGE, for underflow and overflow conditions

Calling interface:
`double exp2(double x);`
`long double exp2l(long double x);`
`float exp2f(float x);`

## expm1

Description: The expm1 function returns `e` raised to the `x` power, minus 1, `ex -1`.

errno: ERANGE, for overflow conditions

Calling interface:
`double expm1(double x);`
`long double expm1l(long double x);`
`float expm1f(float x);`

## frexp

Description: The frexp function converts a floating-point number `x` into signed normalized fraction in [1/2, 1) multiplied by an integral power of two. The signed normalized fraction is returned, and the integer exponent stored at location `exp`.

Calling interface:
`double frexp(double x, int *exp);`
`long double frexpl(long double x, int *exp);`
`float frexpf(float x, int *exp);`

## hypot

Description: The hypot function returns the square root of `(x2 + y2)`.

errno: ERANGE, for overflow conditions

Calling interface:
`double hypot(double x, double y);`
`long double hypotl(long double x, long double y);`
`float hypotf(float x, float y);`

## ilogb

Description: The ilogb function returns the exponent of `x` base two as a `signed int` value.

errno: ERANGE, for x = 0

Calling interface:
`int ilogb(double x);`
`int ilogbl(long double x);`
`int ilogbf(float x);`

## invsqrt

Description: The invsqrt function returns the inverse square root.

Calling interface:
`double invsqrt(double x);`
`long double invsqrtl(long double x);`
`float invsqrtf(float x);`

## ldexp

Description: The ldexp function returns `x*2exp`, where `exp` is an integer value.

errno: ERANGE, for underflow and overflow conditions

Calling interface:
`double ldexp(double x, int exp);`
`long double ldexpl(long double x, int exp);`
`float ldexpf(float x, int exp);`

## log

Description: The log function returns the natural log of `x`, ln(`x`).

errno: EDOM, for x < 0
errno: ERANGE, for x = 0

Calling interface:
`double log(double x);`
`long double logl(long double x);`
`float logf(float x);`

## log10

Description: The log10 function returns the base-10 log of `x`, log10(`x`).

errno: EDOM, for x < 0
errno: ERANGE, for x = 0

Calling interface:
`double log10(double x);`
`long double log10l(long double x);`
`float log10f(float x);`

## log1p

Description: The log1p function returns the natural log of `(x+1), ln(x + 1)`.

errno: EDOM, for x < -1
errno: ERANGE, for x = -1

Calling interface:
`double log1p(double x);`
`long double log1pl(long double x);`
`float log1pf(float x);`

## log2

Description: The log2 function returns the base-2 log of `x`, log2(`x`).

errno: EDOM, for x < 0
errno: ERANGE, for x = 0

Calling interface:
`double log2(double x);`
`long double log2l(long double x);`
`float log2f(float x);`

## logb

Description: The logb function returns the signed exponent of `x`.

errno: EDOM, for x = 0

Calling interface:
`double logb(double x);`
`long double logbl(long double x);`
`float logbf(float x);`

## pow

Description: The pow function returns `x` raised to the power of `y`, `xy`.

errno: EDOM, for x = 0 and y < 0
errno: EDOM, for x < 0 and y is a non-integer
errno: ERANGE, for overflow and underflow conditions

Calling interface:
`double pow(double x, double y);`
`long double powl(double x, double y);`
`float powf(float x, float y);`

## pow2o3

Description: The pow2o3 function returns the cube root of `x` squared, `cbrt(x2)`.

Calling interface:
`double pow2o3(double x);`
`float pow2o3f(float x);`

## pow3o2

Description: The pow3o2 function returns the square root of the cube of `x`, `sqrt(x3)`.

errno: EDOM, for x < 0
errno: ERANGE, for overflow and underflow conditions

Calling interface:
`double pow3o2(double x);`
`float pow3o2f(float x);`

## powr

Description: The powr function returns `x` raised to the power of `y`, `xy`, where x ≥ 0.

errno: EDOM, for x < 0
errno: ERANGE, for overflow and underflow conditions

Calling interface:
`double powr(double x, double y);`
`float powrf(float x, float y);`

## scalb

Description: The scalb function returns `x*2y`, where `y` is a floating-point value.

errno: ERANGE, for underflow and overflow conditions

Calling interface:
`double scalb(double x, double y);`
`long double scalbl(long double x, long double y);`
`float scalbf(float x, float y);`

## scalbn

Description: The scalbn function returns `x*2n`, where `n` is an integer value.

errno: ERANGE, for underflow and overflow conditions

Calling interface:
`double scalbn(double x, int n);`
`long double scalbnl (long double x, int n);`
`float scalbnf(float x, int n);`

## scalbln

Description: The scalbln function returns `x*2n`, where `n` is a long integer value.

errno: ERANGE, for underflow and overflow conditions

Calling interface:
`double scalbln(double x, long int n);`
`long double scalblnl (long double x, long int n);`
`float scalblnf(float x, long int n);`

## sqrt

Description: The sqrt function returns the correctly rounded square root.

errno: EDOM, for x < 0

Calling interface:
`double sqrt(double x);`
`long double sqrtl(long double x);`
`float sqrtf(float x);`

Parent topic: Math Functions