Contents

# Exponential 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 exponential functions:
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.

## 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);
_Float16 cbrtf16(_Float16 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);
_Float16 expf16(_Float16 x);

## exp10

Description:
The
exp10
function returns 10 raised to the
x
power, 10
x
.
errno
: ERANGE, for underflow and overflow conditions
Calling interface:
double exp10(double x);
long double exp10l(long double x);
float exp10f(float x);
_Float16 exp10f16(_Float16 x);

## exp2

Description:
The
exp2
function returns 2 raised to the
x
power, 2
x
.
errno
: ERANGE, for underflow and overflow conditions
Calling interface:
double exp2(double x);
long double exp2l(long double x);
float exp2f(float x);
_Float16 exp2f16(_Float16 x);

## expm1

Description:
The
expm1
function returns
e
raised to the
x
power, minus 1,
e
x
-1
.
errno
: ERANGE, for overflow conditions
Calling interface:
double expm1(double x);
long double expm1l(long double x);
float expm1f(float x);
_Float16 expm1f16(_Float16 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);
_Float16 frexpf16(_Float16 x, int *exp);

## hypot

Description:
The
hypot
function returns the square root of
(x
2
+ y
2
)
.
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);
_Float16 hypotf16(_Float16 x, _Float16 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);
int ilogbf16(_Float16 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);
_Float16 invsqrtf16(_Float16 x);

## ldexp

Description:
The
ldexp
function returns
x*2
exp
, 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);
_Float16 ldexpf16(_Float16 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);
_Float16 logf16(_Float16 x);

## log10

Description:
The
log10
function returns the base-10 log of
x
, log
10
(
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);
_Float16 log10f16(_Float16 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);
_Float16 log1pf16(_Float16 x);

## log2

Description:
The
log2
function returns the base-2 log of
x
, log
2
(
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);
_Float16 log2f16(_Float16 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);
_Float16 logbf16(_Float16 x);

## pow

Description:
The
pow
function returns
x
raised to the power of
y
,
x
y
.
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);
_Float16 powf16(_Float16 x, _Float16 y);

## pow2o3

Description:
The
pow2o3
function returns the cube root of
x
squared,
cbrt(x
2
)
.
Calling interface:
double pow2o3(double x);
float pow2o3f(float x);
_Float16 pow2o3f16(_Float16 x);

## pow3o2

Description:
The
pow3o2
function returns the square root of the cube of
x
,
sqrt(x
3
)
.
errno
: EDOM, for x < 0
errno
: ERANGE, for overflow and underflow conditions
Calling interface:
double pow3o2(double x);
float pow3o2f(float x);
_Float16 pow3o2f16(_Float16 x);

## powr

Description:
The
powr
function returns
x
raised to the power of
y
,
x
y
, 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);
_Float16 powrf16(_Float16 x, _Float16 y);

## scalb

Description:
The
scalb
function returns
x*2
y
, 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);
_Float16 scalbf16(_Float16 x, _Float16 y);

## scalbn

Description:
The
scalbn
function returns
x*2
n
, 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);
_Float16 scalbnf16(_Float16 x, int n);

## scalbln

Description:
The
scalbln
function returns
x*2
n
, 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);
_Float16 scalblnf16(_Float16 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);
_Float16 sqrtf16(_Float16 x);

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.