VM Mathematical Functions

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Date 6/24/2024

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VM Mathematical Functions

This section describes VM functions that compute values of mathematical functions on real and complex vector arguments.

Each function is introduced by its short name, a brief description of its purpose, and the calling sequence for each type of data, as well as a description of the input/output arguments.

The input range of parameters is equal to the mathematical range of the input data type, unless the function description specifies input threshold values, which mark off the precision overflow, as follows:

FLT16_MAX denotes the maximum number representable in half precision real data type
FLT_MAX denotes the maximum number representable in single precision real data type
DBL_MAX denotes the maximum number representable in double precision real data type

The following table lists available mathematical functions and associated data types.

Function	Data Types	Description
Arithmetic Functions
add	h, s, d, c, z	Adds vector elements
sub	h, s, d, c, z	Subtracts vector elements
sqr	h, s, d	Squares vector elements
mul	h, s, d, c, z	Multiplies vector elements
mulbyconj	c, z	Multiplies elements of one vector by conjugated elements of the second vector
conj	c, z	Conjugates vector elements
abs	h, s, d, c, z	Computes the absolute value of vector elements
arg	c, z	Computes the argument of vector elements
linearfrac	h, s, d	Performs linear fraction transformation of vectors
fmod	h, s, d	Performs element by element computation of the modulus function of vector `a` with respect to vector `b`
remainder	h, s, d	Performs element by element computation of the remainder function on the elements of vector `a` and the corresponding elements of vector `b`
Power and Root Functions
inv	h, s, d	Inverts vector elements
div	h, s, d, c, z	Divides elements of one vector by elements of the second vector
sqrt	h, s, d, c, z	Computes the square root of vector elements
invsqrt	h, s, d	Computes the inverse square root of vector elements
cbrt	h, s, d	Computes the cube root of vector elements
invcbrt	h, s, d	Computes the inverse cube root of vector elements
pow2o3	h, s, d	Computes the cube root of the square of each vector element
pow3o2	h, s, d	Computes the square root of the cube of each vector element
pow	h, s, d, c, z	Raises each vector element to the specified power
powx	h, s, d, c, z	Raises each vector element to the constant power
powr	h, s, d	Computes `a` to the power `b` for elements of two vectors, where the elements of vector argument `a` are all non-negative
hypot	h, s, d	Computes the square root of sum of squares
Exponential and Logarithmic Functions
exp	h, s, d, c, z	Computes the base `e` exponential of vector elements
exp2	h, s, d	Computes the base 2 exponential of vector elements
exp10	h, s, d	Computes the base 10 exponential of vector elements
expm1	h, s, d	Computes the base `e` exponential of vector elements decreased by 1
ln	h, s, d, c, z	Computes the natural logarithm of vector elements
log2	h, s, d	Computes the base 2 logarithm of vector elements
log10	h, s, d, c, z	Computes the base 10 logarithm of vector elements
log1p	h, s, d	Computes the natural logarithm of vector elements that are increased by 1
logb	h, s, d	Computes the exponents of the elements of input vector `a`
Trigonometric Functions
cos	h, s, d, c, z	Computes the cosine of vector elements
sin	h, s, d, c, z	Computes the sine of vector elements
sincos	h, s, d	Computes the sine and cosine of vector elements
cis	c, z	Computes the complex exponent of vector elements (cosine and sine combined to complex value)
tan	h, s, d, c, z	Computes the tangent of vector elements
acos	h, s, d, c, z	Computes the inverse cosine of vector elements
asin	h, s, d, c, z	Computes the inverse sine of vector elements
atan	h, s, d, c, z	Computes the inverse tangent of vector elements
atan2	h, s, d	Computes the four-quadrant inverse tangent of ratios of the elements of two vectors
cospi	h, s, d	Computes the cosine of vector elements multiplied by
sinpi	h, s, d	Computes the sine of vector elements multiplied by
tanpi	h, s, d	Computes the tangent of vector elements multiplied by
acospi	h, s, d	Computes the inverse cosine of vector elements divided by
asinpi	h, s, d	Computes the inverse sine of vector elements divided by
atanpi	h, s, d	Computes the inverse tangent of vector elements divided by
atan2pi	h, s, d	Computes the four-quadrant inverse tangent of the ratios of the corresponding elementss of two vectors divided by
cosd	h, s, d	Computes the cosine of vector elements multiplied by /180
sin	h, s, d	Computes the sine of vector elements multiplied by /180
tand	h, s, d	Computes the tangent of vector elements multiplied by /180
Hyperbolic Functions
cosh	h, s, d, c, z	Computes the hyperbolic cosine of vector elements
sinh	h, s, d, c, z	Computes the hyperbolic sine of vector elements
tanh	h, s, d, c, z	Computes the hyperbolic tangent of vector elements
acosh	h, s, d, c, z	Computes the inverse hyperbolic cosine of vector elements
asinh	h, s, d, c, z	Computes the inverse hyperbolic sine of vector elements
atanh	h, s, d, c, z	Computes the inverse hyperbolic tangent of vector elements.
Special Functions
erf	h, s, d	Computes the error function value of vector elements
erfc	h, s, d	Computes the complementary error function value of vector elements
erfcx	h, s, d	Computes the scaled complementary error function value of vector elements
cdfnorm	h, s, d	Computes the cumulative normal distribution function value of vector elements
erfinv	h, s, d	Computes the inverse error function value of vector elements
erfcinv	h, s, d	Computes the inverse complementary error function value of vector elements
cdfnorminv	h, s, d	Computes the inverse cumulative normal distribution function value of vector elements
lgamma	h, s, d	Computes the natural logarithm for the absolute value of the gamma function of vector elements
tgamma	h, s, d	Computes the gamma function of vector elements
expint1	h, s, d	Computes the exponential integral of vector elements
i0	h, s, d	Computes the regular modified cylindrical Bessel function of order 0
i1	h, s, d	Computes the regular modified cylindrical Bessel function of order 1
j0	h, s, d	Computes the Bessel function of the first kind of order 0
j1	h, s, d	Computes the Bessel function of the first kind of order 1
jn	h, s, d	Computes the Bessel function of the first kind of a given order
y0	h, s, d	Computes the Bessel function of the second kind of order 0
y1	h, s, d	Computes the Bessel function of the second kind of order 1
yn	h, s, d	Computes the Bessel function of the second kind of a given order
Rounding Functions
floor	h, s, d	Rounds towards minus infinity
ceil	h, s, d	Rounds towards plus infinity
trunc	h, s, d	Rounds towards zero infinity
round	h, s, d	Rounds to nearest integer
nearbyint	h, s, d	Rounds according to current mode
rint	h, s, d	Rounds according to current mode and raising inexact result exception
modf	h, s, d	Computes the integer and fractional parts
frac	h, s, d	Computes the fractional part
Miscellaneous Functions
copysign	h, s, d	Returns vector of elements of one argument with signs changed to match other argument elements
nextafter	h, s, d	Returns vector of elements containing the next representable floating-point values following the values from the elements of one vector in the direction of the corresponding elements of another vector
fdim	h, s, d	Returns vector containing the differences of the corresponding elements of the vector arguments if the first is larger and +0 otherwise
fmax	h, s, d	Returns the larger of each pair of elements of the two vector arguments
fmin	h, s, d	Returns the smaller of each pair of elements of the two vector arguments
maxmag	h, s, d	Returns the element with the larger magnitude between each pair of elements of the two vector arguments
minmag	h, s, d	Returns the element with the smaller magnitude between each pair of elements of the two vector arguments

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oneMKL - Data Parallel C++ Developer Reference

VM Mathematical Functions