Arithmetic Operations

Functions for building arithmetic expressions. More...

Classes
class	sdfg::symbolic::IModFunction
	Function class for integer modulo operation. More...
class	sdfg::symbolic::ZExtI64Function
	Function class for zero-extension to 64-bit integer. More...
class	sdfg::symbolic::TruncI32Function
	Function class for truncation to 32-bit integer. More...

Functions
Expression	sdfg::symbolic::add (const Expression lhs, const Expression rhs)
	Addition of two expressions.
Expression	sdfg::symbolic::sub (const Expression lhs, const Expression rhs)
	Subtraction of two expressions.
Expression	sdfg::symbolic::mul (const Expression lhs, const Expression rhs)
	Multiplication of two expressions.
Expression	sdfg::symbolic::div (const Expression lhs, const Expression rhs)
	Integer division idiv(lhs, rhs) with the semantics of signed C/C++ lhs / rhs on int64.
Expression	sdfg::symbolic::floor_div (const Expression lhs, const Expression divisor)
	Exact floor division floor(lhs / divisor) in terms of idiv.
Expression	sdfg::symbolic::ceil_div (const Expression dividend, const Expression divisor)
	Exact ceiling division ceil(dividend / divisor) in terms of idiv.
Expression	sdfg::symbolic::ceil_count (const Expression extent, const Expression chunk)
	Number of chunks of size chunk (positive) covering extent: max(0, ceil(extent / chunk)).
Expression	sdfg::symbolic::min (const Expression lhs, const Expression rhs)
	Minimum of two expressions.
Expression	sdfg::symbolic::max (const Expression lhs, const Expression rhs)
	Maximum of two expressions.
Expression	sdfg::symbolic::abs (const Expression expr)
	Absolute value of an expression.
Expression	sdfg::symbolic::mod (const Expression lhs, const Expression rhs)
	Integer remainder imod(lhs, rhs) with the semantics of signed C/C++ lhs % rhs on int64.
Expression	sdfg::symbolic::bit_xor (const Expression lhs, const Expression rhs)
	Bitwise XOR operation (integer).
Expression	sdfg::symbolic::pow (const Expression base, const Expression exp)
	Power/exponentiation operation.
Expression	sdfg::symbolic::zext_i64 (const Expression expr)
	Zero-extend to 64-bit integer.
Expression	sdfg::symbolic::trunc_i32 (const Expression expr)
	Truncate to 32-bit integer.

Detailed Description

Functions for building arithmetic expressions.

These functions construct symbolic arithmetic expressions representing integer operations. They are used in address calculations (memlets) and loop bounds.

// Example: Compute 2*i + j
auto i = symbolic::symbol("i");
auto j = symbolic::symbol("j");
auto expr = symbolic::add(symbolic::mul(symbolic::integer(2), i), j);

Function Documentation

abs()

Expression sdfg::symbolic::abs

(

const Expression

expr

)

Absolute value of an expression.

Parameters

expr	Expression to take absolute value of

Returns

Expression representing |expr|

add()

Expression sdfg::symbolic::add	(	const Expression	lhs,
		const Expression	rhs )

Addition of two expressions.

Parameters

lhs	Left-hand side expression
rhs	Right-hand side expression

Returns

Expression representing (lhs + rhs)

bit_xor()

Expression sdfg::symbolic::bit_xor	(	const Expression	lhs,
		const Expression	rhs )

Bitwise XOR operation (integer).

Parameters

lhs	Left operand
rhs	Right operand

Returns

Expression representing (lhs ^ rhs); lowered to ^ by codegen. Used by swizzled shared-memory layouts (a bijection on a power-of-two range).

ceil_count()

Expression sdfg::symbolic::ceil_count	(	const Expression	extent,
		const Expression	chunk )

Number of chunks of size chunk (positive) covering extent: max(0, ceil(extent / chunk)).

For trip counts, grid sizes, page counts, etc. Cheaper than max(0, ceil_div(...)): idiv(extent + chunk - 1, chunk) is exact under the clamp.

ceil_div()

Expression sdfg::symbolic::ceil_div	(	const Expression	dividend,
		const Expression	divisor )

Exact ceiling division ceil(dividend / divisor) in terms of idiv.

Integer literals fold for any non-zero divisor. Otherwise the divisor must be positive (a negative integer literal is normalized by negating both operands).

div()

Expression sdfg::symbolic::div	(	const Expression	lhs,
		const Expression	rhs )

Integer division idiv(lhs, rhs) with the semantics of signed C/C++ lhs / rhs on int64.

The quotient is truncated toward zero, e.g. idiv(-7, 2) == -3; codegen emits /. Integer literals are folded unless the result is undefined in C (rhs == 0, INT64_MIN / -1).

floor_div()

Expression sdfg::symbolic::floor_div	(	const Expression	lhs,
		const Expression	divisor )

Exact floor division floor(lhs / divisor) in terms of idiv.

Integer literals fold for any non-zero divisor. Otherwise the divisor must be positive (a negative integer literal is normalized by negating both operands).

max()

Expression sdfg::symbolic::max	(	const Expression	lhs,
		const Expression	rhs )

Maximum of two expressions.

Parameters

lhs	First expression
rhs	Second expression

Returns

Expression representing max(lhs, rhs)

min()

Expression sdfg::symbolic::min	(	const Expression	lhs,
		const Expression	rhs )

Minimum of two expressions.

Parameters

lhs	First expression
rhs	Second expression

Returns

Expression representing min(lhs, rhs)

mod()

Expression sdfg::symbolic::mod	(	const Expression	lhs,
		const Expression	rhs )

Integer remainder imod(lhs, rhs) with the semantics of signed C/C++ lhs % rhs on int64.

The result has the sign of lhs and satisfies lhs == rhs * idiv(lhs, rhs) + imod(lhs, rhs), e.g. imod(-7, 2) == -1; codegen emits %. Folding follows the same rules as div.

mul()

Expression sdfg::symbolic::mul	(	const Expression	lhs,
		const Expression	rhs )

Multiplication of two expressions.

Parameters

lhs	Left-hand side expression
rhs	Right-hand side expression

Returns

Expression representing (lhs * rhs)

pow()

Expression sdfg::symbolic::pow	(	const Expression	base,
		const Expression	exp )

Power/exponentiation operation.

Parameters

base	Base expression
exp	Exponent expression

Returns

Expression representing base^exp

sub()

Expression sdfg::symbolic::sub	(	const Expression	lhs,
		const Expression	rhs )

Subtraction of two expressions.

Parameters

lhs	Left-hand side expression
rhs	Right-hand side expression

Returns

Expression representing (lhs - rhs)

trunc_i32()

Expression sdfg::symbolic::trunc_i32

(

const Expression

expr

)

Truncate to 32-bit integer.

Parameters

expr	Expression to truncate

Returns

Expression representing the truncated value

zext_i64()

Expression sdfg::symbolic::zext_i64

(

const Expression

expr

)

Zero-extend to 64-bit integer.

Parameters

expr	Expression to zero-extend

Returns

Expression representing the zero-extended value