math

Module

Defines math utilities.

You can import these APIs from the math package. For example:

from math import mul

mod

mod[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise modulo operation of two SIMD vectors.

Parameters:

• type (DType): DType of the input SIMD vectors.
• simd_width (Int): Width of the input SIMD vectors.

Args:

• x (SIMD[type, simd_width]): The numerator of the operation.
• y (SIMD[type, simd_width]): The denominator of the operation.

Returns:

The remainder of x divided by y.

mul

mul[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise multiplication of two SIMD vectors.

Parameters:

• type (DType): DType of the input SIMD vectors.
• simd_width (Int): Width of the input SIMD vectors.

Args:

• x (SIMD[type, simd_width]): First SIMD vector to multiply.
• y (SIMD[type, simd_width]): Second SIMD vector to multiply.

Returns:

Elementwise multiplication of x and y.

sub

sub[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise subtraction of two SIMD vectors.

Parameters:

• type (DType): DType of the input SIMD vectors.
• simd_width (Int): Width of the input SIMD vectors.

Args:

• x (SIMD[type, simd_width]): SIMD vector which y will be subtracted from.
• y (SIMD[type, simd_width]): SIMD vector to subtract from x.

Returns:

Elementwise subtraction of SIMD vector y x - y).

add

add[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise addition of two SIMD vectors.

Parameters:

• type (DType): DType of the input SIMD vectors.
• simd_width (Int): Width of the input SIMD vectors.

Args:

• x (SIMD[type, simd_width]): First SIMD vector to add.
• y (SIMD[type, simd_width]): Second SIMD vector to add.

Returns:

Elementwise addition of x and y.

div

div[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise division of two SIMD vectors.

Parameters:

• type (DType): DType of the input SIMD vectors.
• simd_width (Int): Width of the input SIMD vectors.

Args:

• x (SIMD[type, simd_width]): SIMD vector containing the dividends.
• y (SIMD[type, simd_width]): SIMD vector containing the quotients.

Returns:

Elementwise division of SIMD vector x by SIMD vector y (this is x / y).

clamp

clamp[type: DType, simd_width: Int](x: SIMD[type, simd_width], lower_bound: SIMD[type, simd_width], upper_bound: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Clamps the values in a SIMD vector to be in a certain range.

Clamp cuts values in the input SIMD vector off at the upper bound and lower bound values. For example, SIMD vector [0, 1, 2, 3] clamped to a lower bound of 1 and an upper bound of 2 would return [1, 1, 2, 2].

Parameters:

• type (DType): DType of the input SIMD vectors.
• simd_width (Int): Width of the input SIMD vectors.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform the clamp operation on.
• lower_bound (SIMD[type, simd_width]): Minimum of the range to clamp to.
• upper_bound (SIMD[type, simd_width]): Maximum of the range to clamp to.

Returns:

A new SIMD vector containing x clamped to be within lower_bound and upper_bound.

abs

abs(x: Int) -> Int

Gets the absolute value of an integer.

Args:

• x (Int): Value to take the absolute value of.

Returns:

The absolute value of x.

abs[type: DType, simd_width: Int](x: ComplexSIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise abs (norm) on each element of the complex value.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (ComplexSIMD[type, simd_width]): The complex vector to perform absolute value on.

Returns:

The elementwise abs of x.

abs[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise absolute value on the elements of a SIMD vector.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform absolute value on.

Returns:

The elementwise absolute value of x.

rotate_bits_left

rotate_bits_left[shift: Int](x: Int) -> Int

Shifts the bits of a input to the left by shift bits (with wrap-around).

Constraints:

-size <= shift < size

Parameters:

• shift (Int): The number of bit positions by which to rotate the bits of the integer to the left (with wrap-around).

Args:

• x (Int): The input value.

Returns:

The input rotated to the left by shift elements (with wrap-around).

rotate_bits_left[shift: Int, type: DType, width: Int](x: SIMD[type, width]) -> SIMD[type, width]

Shifts bits to the left by shift positions (with wrap-around) for each element of a SIMD vector.

Constraints:

0 <= shift < size Only unsigned types can be rotated.

Parameters:

• shift (Int): The number of positions by which to shift left the bits for each element of a SIMD vector to the left (with wrap-around).
• type (DType): The dtype of the input and output SIMD vector.
• width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, width]): SIMD vector to perform the operation on.

Returns:

The SIMD vector with each element’s bits shifted to the left by shift bits (with wrap-around).

rotate_bits_right

rotate_bits_right[shift: Int](x: Int) -> Int

Shifts the bits of a input to the left by shift bits (with wrap-around).

Constraints:

-size <= shift < size

Parameters:

• shift (Int): The number of bit positions by which to rotate the bits of the integer to the left (with wrap-around).

Args:

• x (Int): The input value.

Returns:

The input rotated to the left by shift elements (with wrap-around).

rotate_bits_right[shift: Int, type: DType, width: Int](x: SIMD[type, width]) -> SIMD[type, width]

Shifts bits to the right by shift positions (with wrap-around) for each element of a SIMD vector.

Constraints:

0 <= shift < size Only unsigned types can be rotated.

Parameters:

• shift (Int): The number of positions by which to shift right the bits for each element of a SIMD vector to the left (with wrap-around).
• type (DType): The dtype of the input and output SIMD vector.
• width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, width]): SIMD vector to perform the operation on.

Returns:

The SIMD vector with each element’s bits shifted to the right by shift bits (with wrap-around).

rotate_left

rotate_left[shift: Int](x: Int) -> Int

Shifts the bits of a input to the left by shift bits (with wrap-around).

Constraints:

-size <= shift < size

Parameters:

• shift (Int): The number of bit positions by which to rotate the bits of the integer to the left (with wrap-around).

Args:

• x (Int): The input value.

Returns:

The input rotated to the left by shift elements (with wrap-around).

rotate_left[shift: Int, type: DType, size: Int](x: SIMD[type, size]) -> SIMD[type, size]

Shifts the elements of a SIMD vector to the left by shift elements (with wrap-around).

Constraints:

-size <= shift < size

Parameters:

• shift (Int): The number of positions by which to rotate the elements of SIMD vector to the left (with wrap-around).
• type (DType): The DType of the input and output SIMD vector.
• size (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, size]): The input value.

Returns:

The SIMD vector rotated to the left by shift elements (with wrap-around).

rotate_right

rotate_right[shift: Int](x: Int) -> Int

Shifts the bits of a input to the right by shift bits (with wrap-around).

Constraints:

-size <= shift < size

Parameters:

• shift (Int): The number of bit positions by which to rotate the bits of the integer to the right (with wrap-around).

Args:

• x (Int): The input value.

Returns:

The input rotated to the right by shift elements (with wrap-around).

rotate_right[shift: Int, type: DType, size: Int](x: SIMD[type, size]) -> SIMD[type, size]

Shifts the elements of a SIMD vector to the right by shift elements (with wrap-around).

Constraints:

-size < shift <= size

Parameters:

• shift (Int): The number of positions by which to rotate the elements of SIMD vector to the right (with wrap-around).
• type (DType): The DType of the input and output SIMD vector.
• size (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, size]): The input value.

Returns:

The SIMD vector rotated to the right by shift elements (with wrap-around).

floor

floor[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise floor on the elements of a SIMD vector.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform floor on.

Returns:

The elementwise floor of x.

ceil

ceil[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise ceiling on the elements of a SIMD vector.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform ceiling on.

Returns:

The elementwise ceiling of x.

ceildiv

ceildiv(x: Int, y: Int) -> Int

Return the rounded-up result of dividing x by y.

Args:

• x (Int): The numerator.
• y (Int): The denominator.

Returns:

The ceiling of dividing x by y.

trunc

trunc[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise truncation on the elements of a SIMD vector.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform trunc on.

Returns:

The elementwise truncation of x.

round

round[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise rounding on the elements of a SIMD vector.

This rounding goes to the nearest integer with ties away from zero.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform rounding on.

Returns:

The elementwise rounding of x.

roundeven

roundeven[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise banker’s rounding on the elements of a SIMD vector.

This rounding goes to the nearest integer with ties toward the nearest even integer.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform rounding on.

Returns:

The elementwise banker’s rounding of x.

round_half_down

round_half_down[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Rounds ties towards the smaller integer”.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform rounding on.

Returns:

The elementwise rounding of x evaluating ties towards the smaller integer.

round_half_up

round_half_up[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Rounds ties towards the larger integer”.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform rounding on.

Returns:

The elementwise rounding of x evaluating ties towards the larger integer.

sqrt

sqrt[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise square root on the elements of a SIMD vector.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform square root on.

Returns:

The elementwise square root of x.

rsqrt

rsqrt[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise reciprocal square root on the elements of a SIMD vector.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform reciprocal square root on.

Returns:

The elementwise reciprocal square root of x.

exp2

exp2[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes elementwise 2 raised to the power of n, where n is an element of the input SIMD vector.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform exp2 on.

Returns:

Vector containing \(2^n\) computed elementwise, where n is an element in the input SIMD vector.

ldexp

ldexp[type: DType, simd_width: Int](x: SIMD[type, simd_width], exp: SIMD[si32, simd_width]) -> SIMD[type, simd_width]

Computes elementwise ldexp function.

The ldexp function multiplies a floating point value x by the number 2 raised to the exp power. I.e. \(ldexp(x,exp)\) calculate the value of \(x * 2^{exp}\) and is used within the \(erf\) function.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector of floating point values.
• exp (SIMD[si32, simd_width]): SIMD vector containing the exponents.

Returns:

Vector containing elementwise result of ldexp on x and exp.

exp

exp[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Calculates elementwise e^{X_i}, where X_i is an element in the input SIMD vector at position i.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): The input SIMD vector.

Returns:

A SIMD vector containing e raised to the power Xi where Xi is an element in the input SIMD vector.

frexp

frexp[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> StaticTuple[2, SIMD[type, simd_width]]

Breaks floating point values into a fractional part and an exponent part.

Constraints:

type must be a floating point value.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): The input values.

Returns:

A tuple of two SIMD vectors containing the fractional and exponent parts of the input floating point values.

log

log[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise natural log (base E) of a SIMD vector.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): Vector to perform logarithm operation on.

Returns:

Vector containing result of performing natural log base E on x.

log2

log2[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise log (base 2) of a SIMD vector.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): Vector to perform logarithm operation on.

Returns:

Vector containing result of performing log base 2 on x.

copysign

copysign[type: DType, simd_width: Int](magnitude: SIMD[type, simd_width], sign: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Returns a value with the magnitude of the first operand and the sign of the second operand.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• magnitude (SIMD[type, simd_width]): The magnitude to use.
• sign (SIMD[type, simd_width]): The sign to copy.

Returns:

Copies the sign from sign to magnitude.

erf

erf[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs the elementwise Erf on a SIMD vector.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): SIMD vector to perform elementwise Erf on.

Returns:

The result of the elementwise Erf operation.

tanh

tanh[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise evaluation of the tanh function.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): The vector to perform the elementwise tanh on.

Returns:

The result of the elementwise tanh operation.

isclose

isclose[type: DType, simd_width: Int](a: SIMD[type, simd_width], b: SIMD[type, simd_width], absolute_tolerance: SIMD[type, 1], relative_tolerance: SIMD[type, 1]) -> SIMD[bool, simd_width]

Checks if the two input values are numerically within a tolerance.

When the type is integral, then equality is checked. When the type is floating point, then this checks if the two input values are numerically the close using the \(abs(a - b) <= max(rtol * max(abs(a), abs(b)), atol)\) formula.

Unlike Pythons’s math.isclose, this implementation is symmetric. I.e. isclose(a,b) == isclose(b,a).

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• a (SIMD[type, simd_width]): The first value to compare.
• b (SIMD[type, simd_width]): The second value to compare.
• absolute_tolerance (SIMD[type, 1]): The absolute tolerance.
• relative_tolerance (SIMD[type, 1]): The relative tolerance.

Returns:

A boolean vector where a and b are equal within the specified tolerance.

isclose[type: DType, simd_width: Int](a: SIMD[type, simd_width], b: SIMD[type, simd_width]) -> SIMD[bool, simd_width]

Checks if the two input values are numerically within tolerance, with atol=1e-08 and rtol=1e-05.

When the type is integral, then equality is checked. When the type is floating point, then this checks if the two input values are numerically the close using the abs(a - b) <= max(rtol * max(abs(a), abs(b)), atol) formula. The default absolute and relative tolerances are picked from the numpy default values.

Parameters:

• type (DType): The dtype of the input SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• a (SIMD[type, simd_width]): The first value to compare.
• b (SIMD[type, simd_width]): The second value to compare.

Returns:

A boolean vector where a and b are equal within tolerance, with atol=1e-08 and rtol=1e-05.

all_true

all_true[simd_width: Int](val: SIMD[bool, simd_width]) -> Bool

Returns True if all elements in the SIMD vector are True and False otherwise.

Parameters:

• simd_width (Int): The width of the input and output SIMD vector.

Args:

• val (SIMD[bool, simd_width]): The SIMD vector to reduce.

Returns:

True if all values in the SIMD vector are True and False otherwise.

any_true

any_true[simd_width: Int](val: SIMD[bool, simd_width]) -> Bool

Returns True if any elements in the SIMD vector is True and False otherwise.

Parameters:

• simd_width (Int): The width of the input and output SIMD vector.

Args:

• val (SIMD[bool, simd_width]): The SIMD vector to reduce.

Returns:

True if any values in the SIMD vector is True and False otherwise.

none_true

none_true[simd_width: Int](val: SIMD[bool, simd_width]) -> Bool

Returns True if all element in the SIMD vector are False and False otherwise.

Parameters:

• simd_width (Int): The width of the input and output SIMD vector.

Args:

• val (SIMD[bool, simd_width]): The SIMD vector to reduce.

Returns:

True if all values in the SIMD vector are False and False otherwise.

reduce_bit_count

reduce_bit_count[type: DType, simd_width: Int](val: SIMD[type, simd_width]) -> Int

Returns a scalar containing total number of bits set in given vector.

Constraints:

The input must be either integral or boolean type.

Parameters:

• type (DType): The dtype of the input SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• val (SIMD[type, simd_width]): The SIMD vector to reduce.

Returns:

Count of set bits across all elements of the vector.

iota

iota[type: DType, simd_width: Int]() -> SIMD[type, simd_width]

Creates a SIMD vector containing an increasing sequence, starting from 0.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Returns:

An increasing sequence of values, starting from 0.

iota[type: DType, simd_width: Int](offset: SIMD[type, 1]) -> SIMD[type, simd_width]

Creates a SIMD vector containing an increasing sequence, starting from offset.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• offset (SIMD[type, 1]): The value to start the sequence at. Default is zero.

Returns:

An increasing sequence of values, starting from offset.

iota[type: DType](inout buff: DTypePointer[type], len: Int, offset: Int)

Fill the buffer with numbers ranging from offset to offset + len - 1, spaced by 1.

The function doesn’t return anything, the buffer is updated inplace.

Parameters:

• type (DType): DType of the underlying data.

Args:

• buff (DTypePointer[type]): The buffer to fill.
• len (Int): The length of the buffer to fill.
• offset (Int): The value to fill at index 0.

iota[type: DType](inout v: DynamicVector[SIMD[type, 1]], offset: Int)

Fill the vector with numbers ranging from offset to offset + len - 1, spaced by 1.

The function doesn’t return anything, the vector is updated inplace.

Parameters:

• type (DType): DType of the underlying data.

Args:

• v (DynamicVector[SIMD[type, 1]]): The vector to fill.
• offset (Int): The value to fill at index 0.

iota(inout v: DynamicVector[Int], offset: Int)

Fill the vector with numbers ranging from offset to offset + len - 1, spaced by 1.

The function doesn’t return anything, the vector is updated inplace.

Args:

• v (DynamicVector[Int]): The vector to fill.
• offset (Int): The value to fill at index 0.

is_power_of_2

is_power_of_2[type: DType, simd_width: Int](val: SIMD[type, simd_width]) -> SIMD[bool, simd_width]

Performs elementwise check of whether SIMD vector contains integer powers of two.

An element of the result SIMD vector will be True if the value is an integer power of two, and False otherwise.

Parameters:

• type (DType): The dtype of the input SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• val (SIMD[type, simd_width]): The SIMD vector to perform is_power_of_2 on.

Returns:

A SIMD vector containing True if the corresponding element in val is a power of two, otherwise False.

is_power_of_2(val: Int) -> Bool

Checks whether an integer is a power of two.

Args:

• val (Int): The integer to check.

Returns:

True if val is a power of two, otherwise False.

is_odd

is_odd(val: Int) -> Bool

Performs elementwise check of whether an integer value is odd.

Args:

• val (Int): The int value to check.

Returns:

True if the input is odd and False otherwise.

is_odd[type: DType, simd_width: Int](val: SIMD[type, simd_width]) -> SIMD[bool, simd_width]

Performs elementwise check of whether SIMD vector contains odd values.

An element of the result SIMD vector will be True if the value is odd, and False otherwise.

Parameters:

• type (DType): The dtype of the input SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• val (SIMD[type, simd_width]): The SIMD vector to check.

Returns:

A SIMD vector containing True if the corresponding element in val is odd, otherwise False.

is_even

is_even(val: Int) -> Bool

Performs elementwise check of whether an integer value is even.

Args:

• val (Int): The int value to check.

Returns:

True if the input is even and False otherwise.

is_even[type: DType, simd_width: Int](val: SIMD[type, simd_width]) -> SIMD[bool, simd_width]

Performs elementwise check of whether SIMD vector contains even values.

An element of the result SIMD vector will be True if the value is even, and False otherwise.

Parameters:

• type (DType): The dtype of the input SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• val (SIMD[type, simd_width]): The SIMD vector to check.

Returns:

A SIMD vector containing True if the corresponding element in val is even, otherwise False.

fma

fma(a: Int, b: Int, c: Int) -> Int

Performs fma (fused multiply-add) on the inputs.

The result is (a * b) + c.

Args:

• a (Int): The first input.
• b (Int): The second input.
• c (Int): The third input.

Returns:

(a * b) + c.

fma[type: DType, simd_width: Int](a: SIMD[type, simd_width], b: SIMD[type, simd_width], c: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise fma (fused multiply-add) on the inputs.

Each element in the result SIMD vector is \((A_i * B_i) + C_i\), where \(A_i\), \(B_i\) and \(C_i\) are elements at index \(i\) in a, b, and c respectively.

Parameters:

• type (DType): The dtype of the input SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• a (SIMD[type, simd_width]): The first vector of inputs.
• b (SIMD[type, simd_width]): The second vector of inputs.
• c (SIMD[type, simd_width]): The third vector of inputs.

Returns:

Elementwise fma of a, b and c.

reciprocal

reciprocal[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Takes the elementwise reciprocal of a SIMD vector.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): The SIMD vector to perform elementwise reciprocal on.

Returns:

A SIMD vector the elementwise reciprocal of x.

identity

identity[type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Gets the identity of a SIMD vector.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): The SIMD vector to take identity of.

Returns:

Identity of x, which is x.

greater

greater[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[bool, simd_width]

Performs elementwise check of whether values in x are greater than values in y.

An element of the result SIMD vector will be True if the corresponding element in x is greater than the corresponding element in y, and False otherwise.

Parameters:

• type (DType): The dtype of the input SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): First SIMD vector to compare.
• y (SIMD[type, simd_width]): Second SIMD vector to compare.

Returns:

A SIMD vector containing True if the corresponding element in x is greater than the corresponding element in y, otherwise False.

greater_equal

greater_equal[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[bool, simd_width]

Performs elementwise check of whether values in x are greater than or equal to values in y.

An element of the result SIMD vector will be True if the corresponding element in x is greater than or equal to the corresponding element in y, and False otherwise.

Parameters:

• type (DType): The dtype of the input SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): First SIMD vector to compare.
• y (SIMD[type, simd_width]): Second SIMD vector to compare.

Returns:

A SIMD vector containing True if the corresponding element in x is greater than or equal to the corresponding element in y, otherwise False.

less

less[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[bool, simd_width]

Performs elementwise check of whether values in x are less than values in y.

An element of the result SIMD vector will be True if the corresponding element in x is less than the corresponding element in y, and False otherwise.

Parameters:

• type (DType): The dtype of the input SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): First SIMD vector to compare.
• y (SIMD[type, simd_width]): Second SIMD vector to compare.

Returns:

A SIMD vector containing True if the corresponding element in x is less than the corresponding element in y, otherwise False.

less_equal

less_equal[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[bool, simd_width]

Performs elementwise check of whether values in x are less than or equal to values in y.

An element of the result SIMD vector will be True if the corresponding element in x is less than or equal to the corresponding element in y, and False otherwise.

Parameters:

• type (DType): The dtype of the input SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): First SIMD vector to compare.
• y (SIMD[type, simd_width]): Second SIMD vector to compare.

Returns:

A SIMD vector containing True if the corresponding element in x is less than or equal to the corresponding element in y, otherwise False.

equal

equal[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[bool, simd_width]

Performs elementwise check of whether values in x are equal to values in y.

An element of the result SIMD vector will be True if the corresponding element in x is equal to the corresponding element in y, and False otherwise.

Parameters:

• type (DType): The dtype of the input SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): First SIMD vector to compare.
• y (SIMD[type, simd_width]): Second SIMD vector to compare.

Returns:

A SIMD vector containing True if the corresponding element in x is equal to the corresponding element in y, otherwise False.

logical_and

logical_and[simd_width: Int](x: SIMD[bool, simd_width], y: SIMD[bool, simd_width]) -> SIMD[bool, simd_width]

Performs elementwise logical And operation.

An element of the result SIMD vector will be True if the corresponding elements in x and y are both True, and False otherwise.

Parameters:

• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[bool, simd_width]): First SIMD vector to perform the And operation.
• y (SIMD[bool, simd_width]): Second SIMD vector to perform the And operation.

Returns:

A SIMD vector containing True if the corresponding elements in x and y are both True, otherwise False.

logical_not

logical_not[simd_width: Int](x: SIMD[bool, simd_width]) -> SIMD[bool, simd_width]

Performs elementwise logical Not operation.

An element of the result SIMD vector will be True if the corresponding element in x is True, and False otherwise.

Parameters:

• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[bool, simd_width]): SIMD vector to perform the Not operation.

Returns:

A SIMD vector containing True if the corresponding element in x is True, otherwise False.

logical_xor

logical_xor[simd_width: Int](x: SIMD[bool, simd_width], y: SIMD[bool, simd_width]) -> SIMD[bool, simd_width]

Performs elementwise logical Xor operation.

An element of the result SIMD vector will be True if only one of the corresponding elements in x and y is True, and False otherwise.

Parameters:

• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[bool, simd_width]): First SIMD vector to perform the Xor operation.
• y (SIMD[bool, simd_width]): Second SIMD vector to perform the Xor operation.

Returns:

A SIMD vector containing True if only one of the corresponding elements in x and y is True, otherwise False.

not_equal

not_equal[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[bool, simd_width]

Performs elementwise check of whether values in x are not equal to values in y.

An element of the result SIMD vector will be True if the corresponding element in x is not equal to the corresponding element in y, and False otherwise.

Parameters:

• type (DType): The dtype of the input SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): First SIMD vector to compare.
• y (SIMD[type, simd_width]): Second SIMD vector to compare.

Returns:

A SIMD vector containing True if the corresponding element in x is not equal to the corresponding element in y, otherwise False.

select

select[type: DType, simd_width: Int](cond: SIMD[bool, simd_width], true_case: SIMD[type, simd_width], false_case: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Selects the values of the true_case or the false_case based on the input boolean values of the given SIMD vector.

Parameters:

• type (DType): The element type of the input and output SIMD vectors.
• simd_width (Int): Width of the SIMD vectors we are comparing.

Args:

• cond (SIMD[bool, simd_width]): The vector of bools to check.
• true_case (SIMD[type, simd_width]): The values selected if the positional value is True.
• false_case (SIMD[type, simd_width]): The values selected if the positional value is False.

Returns:

A new vector of the form [true_case[i] if cond[i] else false_case[i] in enumerate(self)].

max

max(x: Int, y: Int) -> Int

Gets the maximum of two integers.

Args:

• x (Int): Integer input to max.
• y (Int): Integer input to max.

Returns:

Maximum of x and y.

max[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Performs elementwise maximum of x and y.

An element of the result SIMD vector will be the maximum of the corresponding elements in x and y.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): First SIMD vector.
• y (SIMD[type, simd_width]): Second SIMD vector.

Returns:

A SIMD vector containing the elementwise maximum of x and y.

min

min(x: Int, y: Int) -> Int

Gets the minimum of two integers.

Args:

• x (Int): Integer input to max.
• y (Int): Integer input to max.

Returns:

Minimum of x and y.

min[type: DType, simd_width: Int](x: SIMD[type, simd_width], y: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Gets the elementwise minimum of x and y.

An element of the result SIMD vector will be the minimum of the corresponding elements in x and y.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• x (SIMD[type, simd_width]): First SIMD vector.
• y (SIMD[type, simd_width]): Second SIMD vector.

Returns:

A SIMD vector containing the elementwise minimum of x and y.

pow

pow[type: DType, simd_width: Int](lhs: SIMD[type, simd_width], rhs: Int) -> SIMD[type, simd_width]

Computes the pow of the inputs.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• lhs (SIMD[type, simd_width]): The first input argument.
• rhs (Int): The second input argument.

Returns:

The pow of the inputs.

pow[lhs_type: DType, rhs_type: DType, simd_width: Int](lhs: SIMD[lhs_type, simd_width], rhs: SIMD[rhs_type, simd_width]) -> SIMD[lhs_type, simd_width]

Computes elementwise power of a floating point type raised to another floating point type.

An element of the result SIMD vector will be the result of raising the corresponding element of lhs to the corresponding element of rhs.

Constraints:

rhs_type and lhs_type must be the same, and must be floating point types.

Parameters:

• lhs_type (DType): The dtype of the lhs SIMD vector.
• rhs_type (DType): The dtype of the rhs SIMD vector.
• simd_width (Int): The width of the input and output SIMD vectors.

Args:

• lhs (SIMD[lhs_type, simd_width]): Base of the power operation.
• rhs (SIMD[rhs_type, simd_width]): Exponent of the power operation.

Returns:

A SIMD vector containing elementwise lhs raised to the power of rhs.

pow[n: Int, type: DType, simd_width: Int](x: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the elementwise power where the exponent is an integer known at compile time.

Constraints:

n must be a signed si32 type.

Parameters:

• n (Int): Exponent of the power operation.
• type (DType): The dtype of the x SIMD vector.
• simd_width (Int): The width of the input and output SIMD vectors.

Args:

• x (SIMD[type, simd_width]): Base of the power operation.

Returns:

A SIMD vector containing elementwise x raised to the power of n.

div_ceil

div_ceil(numerator: Int, denominator: Int) -> Int

Divides an integer by another integer, and round up to the nearest integer.

Constraints:

Will raise an exception if denominator is zero.

Args:

• numerator (Int): The numerator.
• denominator (Int): The denominator.

Returns:

The ceiling of numerator divided by denominator.

align_down

align_down(value: Int, alignment: Int) -> Int

Returns the closest multiple of alignment that is less than or equal to value.

Constraints:

Will raise an exception if the alignment is zero.

Args:

• value (Int): The value to align.
• alignment (Int): Value to align to.

Returns:

Closest multiple of the alignment that is less than or equal to the input value. In other words, floor(value / alignment) * alignment.

align_up

align_up(value: Int, alignment: Int) -> Int

Returns the closest multiple of alignment that is greater than or equal to value.

Constraints:

Will raise an exception if the alignment is zero.

Args:

• value (Int): The value to align.
• alignment (Int): Value to align to.

Returns:

Closest multiple of the alignment that is greater than or equal to the input value. In other words, ceiling(value / alignment) * alignment.

acos

acos[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the acos of the inputs.

Constraints:

The input must be a floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The acos of the input.

asin

asin[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the asin of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The asin of the input.

atan

atan[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the atan of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The atan of the input.

atan2

atan2[type: DType, simd_width: Int](arg0: SIMD[type, simd_width], arg1: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the atan2 of the inputs.

Constraints:

The inputs must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg0 (SIMD[type, simd_width]): The first input argument.
• arg1 (SIMD[type, simd_width]): The second input argument.

Returns:

The atan2 of the inputs.

cos

cos[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the cos of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The cos of the input.

sin

sin[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the sin of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The sin of the input.

tan

tan[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the tan of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The tan of the input.

acosh

acosh[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the acosh of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The acosh of the input.

asinh

asinh[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the asinh of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The asinh of the input.

atanh

atanh[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the atanh of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The atanh of the input.

cosh

cosh[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the cosh of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The cosh of the input.

sinh

sinh[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the sinh of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The sinh of the input.

expm1

expm1[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the expm1 of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The expm1 of the input.

log10

log10[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the log10 of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The log10 of the input.

log1p

log1p[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the log1p of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The log1p of the input.

logb

logb[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the logb of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The logb of the input.

cbrt

cbrt[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the cbrt of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The cbrt of the input.

hypot

hypot[type: DType, simd_width: Int](arg0: SIMD[type, simd_width], arg1: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the hypot of the inputs.

Constraints:

The inputs must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg0 (SIMD[type, simd_width]): The first input argument.
• arg1 (SIMD[type, simd_width]): The second input argument.

Returns:

The hypot of the inputs.

erfc

erfc[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the erfc of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The erfc of the input.

lgamma

lgamma[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the lgamma of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The lgamma of the input.

tgamma

tgamma[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the tgamma of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The tgamma of the input.

nearbyint

nearbyint[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the nearbyint of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The nearbyint of the input.

rint

rint[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the rint of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The rint of the input.

remainder

remainder[type: DType, simd_width: Int](arg0: SIMD[type, simd_width], arg1: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the remainder of the inputs.

Constraints:

The inputs must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg0 (SIMD[type, simd_width]): The first input argument.
• arg1 (SIMD[type, simd_width]): The second input argument.

Returns:

The remainder of the inputs.

nextafter

nextafter[type: DType, simd_width: Int](arg0: SIMD[type, simd_width], arg1: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the nextafter of the inputs.

Constraints:

The inputs must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg0 (SIMD[type, simd_width]): The first input argument.
• arg1 (SIMD[type, simd_width]): The second input argument.

Returns:

The nextafter of the inputs.

j0

j0[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the j0 of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The j0 of the input.

j1

j1[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the j1 of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The j1 of the input.

y0

y0[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the y0 of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The y0 of the input.

y1

y1[type: DType, simd_width: Int](arg: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the y1 of the inputs.

Constraints:

The input must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg (SIMD[type, simd_width]): The input argument.

Returns:

The y1 of the input.

scalb

scalb[type: DType, simd_width: Int](arg0: SIMD[type, simd_width], arg1: SIMD[type, simd_width]) -> SIMD[type, simd_width]

Computes the scalb of the inputs.

Constraints:

The inputs must be of floating point type.

Parameters:

• type (DType): The dtype of the input and output SIMD vector.
• simd_width (Int): The width of the input and output SIMD vector.

Args:

• arg0 (SIMD[type, simd_width]): The first input argument.
• arg1 (SIMD[type, simd_width]): The second input argument.

Returns:

The scalb of the inputs.

gcd

gcd(a: Int, b: Int) -> Int

Computes the greatest common divisor of two integers.

Constraints:

The inputs must be non-negative integers.

Args:

• a (Int): The first input argument.
• b (Int): The second input argument.

Returns:

The gcd of the inputs.

lcm

lcm(a: Int, b: Int) -> Int

Computes the least common divisor of two integers.

Constraints:

The inputs must be non-negative integers.

Args:

• a (Int): The first input argument.
• b (Int): The second input argument.

Returns:

The lcm of the inputs.

factorial

factorial(n: Int) -> Int

Computes the factorial of the integer.

Args:

• n (Int): The input value.

Returns:

The factorial of the input.

nan

nan[type: DType]() -> SIMD[type, 1]

Gets a NaN value for the given dtype.

Constraints:

Can only be used for FP dtypes.

Parameters:

• type (DType): The value dtype.

Returns:

The NaN value of the given dtype.

isnan

isnan[type: DType, simd_width: Int](val: SIMD[type, simd_width]) -> SIMD[bool, simd_width]

Checks if the value is Not a Number (NaN).

Parameters:

• type (DType): The value dtype.
• simd_width (Int): The width of the SIMD vector.

Args:

• val (SIMD[type, simd_width]): The value to check.

Returns:

True if val is NaN and False otherwise.