math.absf - floating point absolute-value operation

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The absf operation computes the absolute value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type.

Example:

// Scalar absolute value.
%a = math.absf %b : f64

math.absi - integer absolute-value operation

This op has support for result type inference.

Operands

• operand - Single, SignlessIntegerOrIndexLike, signless-integer-like

Results

• result - Single, SignlessIntegerOrIndexLike, signless-integer-like

Description

The absi operation computes the absolute value. It takes one operand of integer type (i.e., scalar, tensor or vector) and returns one result of the same type.

Example:

// Scalar absolute value.
%a = math.absi %b : i64

math.acos - arcus cosine of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The acos operation computes the arcus cosine of a given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar arcus cosine value.
%a = math.acos %b : f64

math.acosh - Hyperbolic arcus cosine of the given value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

Syntax:

operation ::= ssa-id `=` `math.acosh` ssa-use `:` type

The acosh operation computes the arcus cosine of a given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Hyperbolic arcus cosine of scalar value.
%a = math.acosh %b : f64

math.asin - arcus sine of the given value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

Syntax:

operation ::= ssa-id `=` `math.asin` ssa-use `:` type

The asin operation computes the arcus sine of a given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Arcus sine of scalar value.
%a = math.asin %b : f64

math.asinh - hyperbolic arcus sine of the given value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

Syntax:

operation ::= ssa-id `=` `math.asinh` ssa-use `:` type

The asinh operation computes the hyperbolic arcus sine of a given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Hyperbolic arcus sine of scalar value.
%a = math.asinh %b : f64

math.atan2 - 2-argument arcus tangent of the given values

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• lhs - Single, FloatLike, floating-point-like
• rhs - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The atan2 operation takes two operands and returns one result, all of which must be of the same type. The operands must be of floating point type (i.e., scalar, tensor or vector).

The 2-argument arcus tangent atan2(y, x) returns the angle in the Euclidian plane between the positive x-axis and the ray through the point (x, y). It is a generalization of the 1-argument arcus tangent which returns the angle on the basis of the ratio y/x.

See also https://en.wikipedia.org/wiki/Atan2

Example:

// Scalar variant.
%a = math.atan2 %b, %c : f32

math.atan - arcus tangent of the given value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The atan operation computes the arcus tangent of a given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Arcus tangent of scalar value.
%a = math.atan %b : f64

math.atanh - hyperbolic arcus tangent of the given value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

Syntax:

operation ::= ssa-id `=` `math.atanh` ssa-use `:` type

The atanh operation computes the hyperbolic arcus tangent of a given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Hyperbolic arcus tangent of scalar value.
%a = math.atanh %b : f64

math.cbrt - cube root of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The cbrt operation computes the cube root. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar cube root value.
%a = math.cbrt %b : f64

Note: This op is not equivalent to powf(..., 1/3.0).

math.ceil - ceiling of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The ceil operation computes the ceiling of a given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar ceiling value.
%a = math.ceil %b : f64

math.clampf - floating point clamping operation

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• value - Single, FloatLike, floating-point-like
• min - Single, FloatLike, floating-point-like
• max - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The clampf operation takes three operands and returns one result, each of these is required to be the same type. Operands must be of floating point type (i.e., scalar, tensor or vector).

The semantics of the operation are described by:

  clampf(value, min, max) = maxf(minf(value, min), max)

Example:

%d = math.clampf %value to [%min, %max] : f64

math.copysign - A copysign operation

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• lhs - Single, FloatLike, floating-point-like
• rhs - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The copysign returns a value with the magnitude of the first operand and the sign of the second operand. It takes two operands and returns one result of the same type. The operands must be of floating point type (i.e., scalar, tensor or vector). It has no standard attributes.

Example:

// Scalar copysign value.
%a = math.copysign %b, %c : f64

math.cos - cosine of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The cos operation computes the cosine of a given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar cosine value.
%a = math.cos %b : f64

math.cosh - hyperbolic cosine of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The cosh operation computes the hyperbolic cosine. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar hyperbolic cosine value.
%a = math.cosh %b : f64

math.ctlz - counts the leading zeros an integer value

This op has support for result type inference.

Operands

• operand - Single, SignlessIntegerOrIndexLike, signless-integer-like

Results

• result - Single, SignlessIntegerOrIndexLike, signless-integer-like

Description

The ctlz operation computes the number of leading zeros of an integer value. It operates on scalar, tensor or vector.

Example:

// Scalar ctlz function value.
%a = math.ctlz %b : i32

math.ctpop - counts the number of set bits of an integer value

This op has support for result type inference.

Operands

• operand - Single, SignlessIntegerOrIndexLike, signless-integer-like

Results

• result - Single, SignlessIntegerOrIndexLike, signless-integer-like

Description

The ctpop operation computes the number of set bits of an integer value. It operates on scalar, tensor or vector.

Example:

// Scalar ctpop function value.
%a = math.ctpop %b : i32

math.cttz - counts the trailing zeros an integer value

This op has support for result type inference.

Operands

• operand - Single, SignlessIntegerOrIndexLike, signless-integer-like

Results

• result - Single, SignlessIntegerOrIndexLike, signless-integer-like

Description

The cttz operation computes the number of trailing zeros of an integer value. It operates on scalar, tensor or vector.

Example:

// Scalar cttz function value.
%a = math.cttz %b : i32

math.erf - error function of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The erf operation computes the error function. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar error function value.
%a = math.erf %b : f64

math.erfc - complementary error function of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The erfc operation computes the complementary error function, defined as 1-erf(x). This function is part of libm and is needed for accuracy, since simply calculating 1-erf(x) when x is close to 1 will give inaccurate results. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar error function value.
%a = math.erfc %b : f64

math.exp2 - base-2 exponential of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The exp operation takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar natural exponential.
%a = math.exp2 %b : f64

math.exp - base-e exponential of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The exp operation takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar natural exponential.
%a = math.exp %b : f64

math.expm1 - base-e exponential of the specified value minus 1

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

expm1(x) := exp(x) - 1

The expm1 operation takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar natural exponential minus 1.
%a = math.expm1 %b : f64

math.floor - floor of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The floor operation computes the floor of a given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar floor value.
%a = math.floor %b : f64

math.fma - floating point fused multipy-add operation

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• a - Single, FloatLike, floating-point-like
• b - Single, FloatLike, floating-point-like
• c - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The fma operation takes three operands and returns one result, each of these is required to be the same type. Operands must be of floating point type (i.e., scalar, tensor or vector).

Example:

// Scalar fused multiply-add: d = a*b + c
%d = math.fma %a, %b, %c : f64

The semantics of the operation correspond to those of the llvm.fma intrinsic. In the particular case of lowering to LLVM, this is guaranteed to lower to the llvm.fma.* intrinsic.

math.fpowi - floating point raised to the signed integer power

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• lhs - Single, FloatLike, floating-point-like
• rhs - Single, SignlessIntegerOrIndexLike, signless-integer-like

Results

• result - Single, FloatLike, floating-point-like

Description

The fpowi operation takes a base operand of floating point type (i.e. scalar, tensor or vector) and a power operand of integer type (also scalar, tensor or vector) and returns one result of the same type as base. The result is base raised to the power of power. The operation is elementwise for non-scalars, e.g.:

%v = math.fpowi %base, %power : vector<2xf32>, vector<2xi32

The result is a vector of:

[<math.fpowi %base[0], %power[0]>, <math.fpowi %base[1], %power[1]>]

Example:

// Scalar exponentiation.
%a = math.fpowi %base, %power : f64, i32

math.ipowi - signed integer raised to the power of operation

This op has support for result type inference.

Operands

• lhs - Single, SignlessIntegerOrIndexLike, signless-integer-like
• rhs - Single, SignlessIntegerOrIndexLike, signless-integer-like

Results

• result - Single, SignlessIntegerOrIndexLike, signless-integer-like

Description

The ipowi operation takes two operands of integer type (i.e., scalar, tensor or vector) and returns one result of the same type. Operands must have the same type.

Example:

// Scalar signed integer exponentiation.
%a = math.ipowi %b, %c : i32

math.isfinite - returns true if the operand classifies as finite

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, BoolLike, bool-like

Description

Determines if the given floating-point number has finite value i.e. it is normal, subnormal or zero, but not infinite or NaN.

Example:

%f = math.isfinite %a : f32

math.isinf - returns true if the operand classifies as infinite

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, BoolLike, bool-like

Description

Determines if the given floating-point number is positive or negative infinity.

Example:

%f = math.isinf %a : f32

math.isnan - returns true if the operand classifies as NaN

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, BoolLike, bool-like

Description

Determines if the given floating-point number is a not-a-number (NaN) value.

Example:

%f = math.isnan %a : f32

math.isnormal - returns true if the operand classifies as normal

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, BoolLike, bool-like

Description

Determines if the given floating-point number is normal, i.e. is neither zero, subnormal, infinite, nor NaN.

Example:

%f = math.isnormal %a : f32

math.log1p - Computes the natural logarithm of one plus the given value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

Computes the base-e logarithm of one plus the given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type.

log1p(x) := log(1 + x)

Example:

// Scalar log1p operation.
%y = math.log1p %x : f64

math.log2 - base-2 logarithm of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

Computes the base-2 logarithm of the given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type.

Example:

// Scalar log2 operation.
%y = math.log2 %x : f64

math.log10 - base-10 logarithm of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

Computes the base-10 logarithm of the given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type.

Example:

// Scalar log10 operation.
%y = math.log10 %x : f64

math.log - base-e logarithm of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

Computes the base-e logarithm of the given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type.

Example:

// Scalar log operation.
%y = math.log %x : f64

math.powf - floating point raised to the power of operation

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• lhs - Single, FloatLike, floating-point-like
• rhs - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The powf operation takes two operands of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. Operands must have the same type.

Example:

// Scalar exponentiation.
%a = math.powf %b, %c : f64

math.round - round of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The round operation returns the operand rounded to the nearest integer value in floating-point format. It takes one operand of floating point type (i.e., scalar, tensor or vector) and produces one result of the same type. The operation rounds the argument to the nearest integer value in floating-point format, rounding halfway cases away from zero, regardless of the current rounding direction.

Example:

// Scalar round operation.
%a = math.round %b : f64

math.roundeven - round of the specified value with halfway cases to even

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The roundeven operation returns the operand rounded to the nearest integer value in floating-point format. It takes one operand of floating point type (i.e., scalar, tensor or vector) and produces one result of the same type. The operation rounds the argument to the nearest integer value in floating-point format, rounding halfway cases to even, regardless of the current rounding direction.

Example:

// Scalar round operation.
%a = math.roundeven %b : f64

math.rsqrt - reciprocal of sqrt (1 / sqrt of the specified value)

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The rsqrt operation computes the reciprocal of the square root. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar reciprocal square root value.
%a = math.rsqrt %b : f64

math.sin - sine of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The sin operation computes the sine of a given value. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar sine value.
%a = math.sin %b : f64

math.sincos - sine and cosine of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• sin - Single, FloatLike, floating-point-like
• cos - Single, FloatLike, floating-point-like

Description

The sincos operation computes both the sine and cosine of a given value simultaneously. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns two results of the same type. This operation can be more efficient than computing sine and cosine separately when both values are needed.

Example:

// Scalar sine and cosine values.
%sin, %cos = math.sincos %input : f64

math.sinh - hyperbolic sine of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The sinh operation computes the hyperbolic sine. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar hyperbolic sine value.
%a = math.sinh %b : f64

math.sqrt - sqrt of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The sqrt operation computes the square root. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar square root value.
%a = math.sqrt %b : f64

math.tan - tangent of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The tan operation computes the tangent. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar tangent value.
%a = math.tan %b : f64

math.tanh - hyperbolic tangent of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The tanh operation computes the hyperbolic tangent. It takes one operand of floating point type (i.e., scalar, tensor or vector) and returns one result of the same type. It has no standard attributes.

Example:

// Scalar hyperbolic tangent value.
%a = math.tanh %b : f64

math.trunc - trunc of the specified value

This op has support for result type inference.

Attributes

• fastmath - Single, Arith_FastMathAttr, Floating point fast math flags

Operands

• operand - Single, FloatLike, floating-point-like

Results

• result - Single, FloatLike, floating-point-like

Description

The trunc operation returns the operand rounded to the nearest integer value in floating-point format. It takes one operand of floating point type (i.e., scalar, tensor or vector) and produces one result of the same type. The operation always rounds to the nearest integer not larger in magnitude than the operand, regardless of the current rounding direction.

Example:

// Scalar trunc operation.
%a = math.trunc %b : f64