.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation .. .. SPDX-License-Identifier: CC-BY-4.0 .. _onemath_vm_mathematical_functions: VM Mathematical Functions ========================= .. container:: This section describes VM functions that compute values of mathematical functions on real and complex vector arguments with unit increment. 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: - ``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 tables list the available mathematical functions grouped by category. .. container:: tablenoborder .. tabularcolumns:: |p{0.4\textwidth}|p{0.6\textwidth}| .. list-table:: :header-rows: 1 :class: longtable * - Arithmetic Routines - Description * - :ref:`onemath_vm_add` - Adds vector elements * - :ref:`onemath_vm_sub` - Subtracts vector elements * - :ref:`onemath_vm_sqr` - Squares vector elements * - :ref:`onemath_vm_mul` - Multiplies vector elements * - :ref:`onemath_vm_mulbyconj` - Multiplies elements of one vector by conjugated elements of the second vector * - :ref:`onemath_vm_conj` - Conjugates vector elements * - :ref:`onemath_vm_abs` - Computes the absolute value of vector elements * - :ref:`onemath_vm_arg` - Computes the argument of vector elements * - :ref:`onemath_vm_linearfrac` - Performs linear fraction transformation of vectors * - :ref:`onemath_vm_fmod` - Performs element by element computation of the modulus function of vector ``a`` with respect to vector ``b`` * - :ref:`onemath_vm_remainder` - Performs element by element computation of the remainder function on the elements of vector ``a`` and the corresponding elements of vector ``b`` .. tabularcolumns:: |p{0.4\textwidth}|p{0.6\textwidth}| .. list-table:: :header-rows: 1 :class: longtable * - Power and Root Routines - Description * - :ref:`onemath_vm_inv` - Inverts vector elements * - :ref:`onemath_vm_div` - Divides elements of one vector by elements of the second vector * - :ref:`onemath_vm_sqrt` - Computes the square root of vector elements * - :ref:`onemath_vm_invsqrt` - Computes the inverse square root of vector elements * - :ref:`onemath_vm_cbrt` - Computes the cube root of vector elements * - :ref:`onemath_vm_invcbrt` - Computes the inverse cube root of vector elements * - :ref:`onemath_vm_pow2o3` - Computes the cube root of the square of each vector element * - :ref:`onemath_vm_pow3o2` - Computes the square root of the cube of each vector element * - :ref:`onemath_vm_pow` - Raises each vector element to the specified power * - :ref:`onemath_vm_powx` - Raises each vector element to the constant power * - :ref:`onemath_vm_powr` - Computes ``a`` to the power ``b`` for elements of two vectors, where the elements of vector argument ``a`` are all non-negative * - :ref:`onemath_vm_hypot` - Computes the square root of sum of squares .. tabularcolumns:: |p{0.4\textwidth}|p{0.6\textwidth}| .. list-table:: :header-rows: 1 :class: longtable * - Exponential and Logarithmic Routines - Description * - :ref:`onemath_vm_exp` - Computes the base ``e`` exponential of vector elements * - :ref:`onemath_vm_exp2` - Computes the base 2 exponential of vector elements * - :ref:`onemath_vm_exp10` - Computes the base 10 exponential of vector elements * - :ref:`onemath_vm_expm1` - Computes the base ``e`` exponential of vector elements decreased by 1 * - :ref:`onemath_vm_ln` - Computes the natural logarithm of vector elements * - :ref:`onemath_vm_log2` - Computes the base 2 logarithm of vector elements * - :ref:`onemath_vm_log10` - Computes the base 10 logarithm of vector elements * - :ref:`onemath_vm_log1p` - Computes the natural logarithm of vector elements that are increased by 1 * - :ref:`onemath_vm_logb` - Computes the exponents of the elements of input vector ``a`` .. tabularcolumns:: |p{0.4\textwidth}|p{0.6\textwidth}| .. list-table:: :header-rows: 1 :class: longtable * - Trigonometric Routines - Description * - :ref:`onemath_vm_cos` - Computes the cosine of vector elements * - :ref:`onemath_vm_sin` - Computes the sine of vector elements * - :ref:`onemath_vm_sincos` - Computes the sine and cosine of vector elements * - :ref:`onemath_vm_cis` - Computes the complex exponent of vector elements (cosine and sine combined to complex value) * - :ref:`onemath_vm_tan` - Computes the tangent of vector elements * - :ref:`onemath_vm_acos` - Computes the inverse cosine of vector elements * - :ref:`onemath_vm_asin` - Computes the inverse sine of vector elements * - :ref:`onemath_vm_atan` - Computes the inverse tangent of vector elements * - :ref:`onemath_vm_atan2` - Computes the four-quadrant inverse tangent of ratios of the elements of two vectors * - :ref:`onemath_vm_cospi` - Computes the cosine of vector elements multiplied by ``π`` * - :ref:`onemath_vm_sinpi` - Computes the sine of vector elements multiplied by ``π`` * - :ref:`onemath_vm_tanpi` - Computes the tangent of vector elements multiplied by ``π`` * - :ref:`onemath_vm_acospi` - Computes the inverse cosine of vector elements divided by ``π`` * - :ref:`onemath_vm_asinpi` - Computes the inverse sine of vector elements divided by ``π`` * - :ref:`onemath_vm_atanpi` - Computes the inverse tangent of vector elements divided by ``π`` * - :ref:`onemath_vm_atan2pi` - Computes the four-quadrant inverse tangent of the ratios of the corresponding elements of two vectors divided by ``π`` * - :ref:`onemath_vm_cosd` - Computes the cosine of vector elements multiplied by ``π``/180 * - :ref:`onemath_vm_sind` - Computes the sine of vector elements multiplied by ``π``/180 * - :ref:`onemath_vm_tand` - Computes the tangent of vector elements multiplied by ``π``/180 .. tabularcolumns:: |p{0.4\textwidth}|p{0.6\textwidth}| .. list-table:: :header-rows: 1 :class: longtable * - Hyperbolic Routines - Description * - :ref:`onemath_vm_cosh` - Computes the hyperbolic cosine of vector elements * - :ref:`onemath_vm_sinh` - Computes the hyperbolic sine of vector elements * - :ref:`onemath_vm_tanh` - Computes the hyperbolic tangent of vector elements * - :ref:`onemath_vm_acosh` - Computes the inverse hyperbolic cosine of vector elements * - :ref:`onemath_vm_asinh` - Computes the inverse hyperbolic sine of vector elements * - :ref:`onemath_vm_atanh` - Computes the inverse hyperbolic tangent of vector elements. .. tabularcolumns:: |p{0.4\textwidth}|p{0.6\textwidth}| .. list-table:: :header-rows: 1 :class: longtable * - Special Routines - Description * - :ref:`onemath_vm_erf` - Computes the error function value of vector elements * - :ref:`onemath_vm_erfc` - Computes the complementary error function value of vector elements * - :ref:`onemath_vm_cdfnorm` - Computes the cumulative normal distribution function value of vector elements * - :ref:`onemath_vm_erfinv` - Computes the inverse error function value of vector elements * - :ref:`onemath_vm_erfcinv` - Computes the inverse complementary error function value of vector elements * - :ref:`onemath_vm_cdfnorminv` - Computes the inverse cumulative normal distribution function value of vector elements * - :ref:`onemath_vm_lgamma` - Computes the natural logarithm for the absolute value of the gamma function of vector elements * - :ref:`onemath_vm_tgamma` - Computes the gamma function of vector elements * - :ref:`onemath_vm_expint1` - Computes the exponential integral of vector elements .. tabularcolumns:: |p{0.4\textwidth}|p{0.6\textwidth}| .. list-table:: :header-rows: 1 :class: longtable * - Rounding Routines - Description * - :ref:`onemath_vm_floor` - Rounds towards minus infinity * - :ref:`onemath_vm_ceil` - Rounds towards plus infinity * - :ref:`onemath_vm_trunc` - Rounds towards zero infinity * - :ref:`onemath_vm_round` - Rounds to nearest integer * - :ref:`onemath_vm_nearbyint` - Rounds according to current mode * - :ref:`onemath_vm_rint` - Rounds according to current mode and reports inexact result status * - :ref:`onemath_vm_modf` - Computes the integer and fractional parts * - :ref:`onemath_vm_frac` - Computes the fractional part .. tabularcolumns:: |p{0.4\textwidth}|p{0.6\textwidth}| .. list-table:: :header-rows: 1 :class: longtable * - Miscellaneous Routines - Description * - :ref:`onemath_vm_copysign` - Returns vector of elements of one argument with signs changed to match other argument elements * - :ref:`onemath_vm_nextafter` - 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 * - :ref:`onemath_vm_fdim` - Returns vector containing the differences of the corresponding elements of the vector arguments if the first is larger and +0 otherwise * - :ref:`onemath_vm_fmax` - Returns the larger of each pair of elements of the two vector arguments * - :ref:`onemath_vm_fmin` - Returns the smaller of each pair of elements of the two vector arguments * - :ref:`onemath_vm_maxmag` - Returns the element with the larger magnitude between each pair of elements of the two vector arguments * - :ref:`onemath_vm_minmag` - Returns the element with the smaller magnitude between each pair of elements of the two vector arguments **Parent topic:** :ref:`onemath_vm` .. toctree:: :hidden: abs acos acosh acospi add arg asin asinh asinpi atan atan2 atan2pi atanh atanpi cbrt cdfnorm cdfnorminv ceil cis conj copysign cos cosd cosh cospi div erf erfc erfcinv erfinv exp exp10 exp2 expint1 expm1 fdim floor fmax fmin fmod frac hypot inv invcbrt invsqrt lgamma linearfrac ln log10 log1p log2 logb maxmag minmag modf mul mulbyconj nearbyint nextafter pow pow2o3 pow3o2 powr powx remainder rint round sin sincos sind sinh sinpi sqr sqrt sub tan tand tanh tanpi tgamma trunc