Evaluation of mathematical expressions given as strings in the case file. More...

Data Types
type	expression_t
	A compiled mathematical expression. More...

type	parser_t
	State of the recursive descent parser. More...

type	token_t
	A single token of an expression. More...

Functions/Subroutines
subroutine	expression_init (this, str)
	Compile an expression.

subroutine	parser_free (p)
	Release the memory held by the parser state.

subroutine	expression_free (this)
	Destructor.

subroutine	expression_eval (this, res, n, x, y, z, t, dt)
	Evaluate the expression in `n` points.

subroutine, public	expression_eval_static (str, res, n, x, y, z, usage)
	Compile an expression and evaluate it in a set of points, in a context where there is no time state.

subroutine, public	expression_check_finite (str, res, n, usage)
	Abort if an expression did not evaluate to a finite value everywhere.

subroutine	expr_tokenize (p)
	Split the source string into a stream of tokens.

subroutine	push_token (p, kind, pos)
	Append a token to the token stream.

recursive subroutine	parse_expr (p)
	Parse an additive expression.

recursive subroutine	parse_term (p)
	Parse a multiplicative expression.

recursive subroutine	parse_factor (p)
	Parse a possibly signed factor. Unary minus binds looser than `^`, so `-x^2` is `-(x^2)`, as in Fortran.

recursive subroutine	parse_power (p)
	Parse an exponentiation. Right associative, so `2^3^2` is `2^(3^2)`.

recursive subroutine	parse_primary (p)
	Parse a literal, a symbol, a function call or a parenthesised expression.

subroutine	parse_symbol (p, k)
	Resolve a bare identifier into either a variable opcode or a literal.

integer function	func_op (name, nargs)
	Look up the opcode of a function.

subroutine	emit (p, op, val)
	Append an opcode, keeping track of how deep the evaluation stack gets.

subroutine	expr_error (p, msg, pos)
	Abort with a message pointing at the offending part of the expression.

pure logical function	is_digit (c)
	True if `c` is a decimal digit.

pure logical function	is_alpha (c)
	True if `c` is a letter.

Variables
integer, parameter, public	neko_expr_len = 256
	Maximum length of an expression string read from the case file.

integer, parameter	expr_max_ident = 64
	Maximum length of an identifier appearing in an expression.

integer, parameter	expr_chunk = 1024
	Number of points evaluated per pass over the opcode stream. Chosen so that the evaluation stack stays in cache irrespective of how many points the caller hands over in one go.

integer, parameter	op_lit = 1

integer, parameter	op_x = 2

integer, parameter	op_y = 3

integer, parameter	op_z = 4

integer, parameter	op_t = 5

integer, parameter	op_dt = 6

integer, parameter	op_unary = 20

integer, parameter	op_neg = 20

integer, parameter	op_sin = 21

integer, parameter	op_cos = 22

integer, parameter	op_tan = 23

integer, parameter	op_asin = 24

integer, parameter	op_acos = 25

integer, parameter	op_atan = 26

integer, parameter	op_sinh = 27

integer, parameter	op_cosh = 28

integer, parameter	op_tanh = 29

integer, parameter	op_exp = 30

integer, parameter	op_log = 31

integer, parameter	op_log10 = 32

integer, parameter	op_sqrt = 33

integer, parameter	op_abs = 34

integer, parameter	op_erf = 35

integer, parameter	op_erfc = 36

integer, parameter	op_step = 37

integer, parameter	op_ipow = 38

integer, parameter	op_binary = 60

integer, parameter	op_add = 60

integer, parameter	op_sub = 61

integer, parameter	op_mul = 62

integer, parameter	op_div = 63

integer, parameter	op_pow = 64

integer, parameter	op_atan2 = 65

integer, parameter	op_min = 66

integer, parameter	op_max = 67

integer, parameter	op_mod = 68

integer, parameter	tk_end = 0

integer, parameter	tk_num = 1

integer, parameter	tk_ident = 2

integer, parameter	tk_plus = 3

integer, parameter	tk_minus = 4

integer, parameter	tk_star = 5

integer, parameter	tk_slash = 6

integer, parameter	tk_pow = 7

integer, parameter	tk_lpar = 8

integer, parameter	tk_rpar = 9

integer, parameter	tk_comma = 10

Detailed Description

An expression_t is compiled once, from a string such as "6*U_b*y*(H - y)/H^2", into a stream of stack machine opcodes. It can then be evaluated over an arbitrary set of points, with x, y and z bound to the point coordinates and t, dt bound to the time state.

Any identifier which is not a coordinate, a time variable or the constant pi is looked up in the neko_const_registry when the expression is compiled, and folded into a literal. This is the same mechanism as the one used by json_get_or_lookup, so constants declared under case.constants in the case file can be used directly in the expressions.

Function/Subroutine Documentation

◆ emit()

subroutine expression::emit	(	type(parser_t), intent(inout)	p,
		integer, intent(in)	op,
		real(kind=rp), intent(in), optional	val
	)

private

Parameters

[in,out]	p	The parser state.
[in]	op	The opcode to append.
[in]	val	The literal operand, only meaningful for `OP_LIT`.

Definition at line 943 of file expression.f90.

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◆ expr_error()

subroutine expression::expr_error	(	type(parser_t), intent(in)	p,
		character(len=*), intent(in)	msg,
		integer, intent(in)	pos
	)

private

Parameters

[in]	p	The parser state.
[in]	msg	What is wrong with the expression.
[in]	pos	Position in the source string to point at.

Definition at line 973 of file expression.f90.

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◆ expr_tokenize()

subroutine expression::expr_tokenize ( type(parser_t), intent(inout) p )

private

Parameters

[in,out] p The parser state, whose src holds the expression.

Definition at line 514 of file expression.f90.

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◆ expression_check_finite()

subroutine, public expression::expression_check_finite	(	character(len=*), intent(in)	str,
		real(kind=rp), dimension(n), intent(in)	res,
		integer, intent(in)	n,
		character(len=*), intent(in)	usage
	)

Split out of expression_eval_static so that the boundary conditions, which compile and evaluate their expressions themselves, can apply the same check. A non-finite value typically means a division by zero or the square root of a negative number somewhere.

Parameters

[in]	str	The expression, used in the error message.
[in]	res	The values to check.
[in]	n	The number of values.
[in]	usage	What the expression configures, used in error messages.

Definition at line 492 of file expression.f90.

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◆ expression_eval()

subroutine expression::expression_eval	(	class(expression_t), intent(inout)	this,
		real(kind=rp), dimension(n), intent(inout)	res,
		integer, intent(in)	n,
		real(kind=rp), dimension(n), intent(in)	x,
		real(kind=rp), dimension(n), intent(in)	y,
		real(kind=rp), dimension(n), intent(in)	z,
		real(kind=rp), intent(in), optional	t,
		real(kind=rp), intent(in), optional	dt
	)

private

Not thread safe. The evaluation stack is a component of the expression, so two concurrent calls on the same object corrupt each other's intermediate values. A caller inside an OpenMP parallel region must evaluate on one thread only.

Parameters

[in,out]	res	The result, one value per point.
[in]	n	The number of points.
[in]	x	The x-coordinates of the points.
[in]	y	The y-coordinates of the points.
[in]	z	The z-coordinates of the points.
[in]	t	The current time, required if the expression uses `t`.
[in]	dt	The current timestep, required if the expression uses `dt`.

Definition at line 226 of file expression.f90.

◆ expression_eval_static()

subroutine, public expression::expression_eval_static	(	character(len=*), intent(in)	str,
		real(kind=rp), dimension(n), intent(inout)	res,
		integer, intent(in)	n,
		real(kind=rp), dimension(n), intent(in)	x,
		real(kind=rp), dimension(n), intent(in)	y,
		real(kind=rp), dimension(n), intent(in)	z,
		character(len=*), intent(in)	usage
	)

Convenience routine for initial conditions and other setup-time uses of an expression. The expression is rejected if it is empty, if it depends on time, or if it does not evaluate to a finite value in every point, the latter typically meaning a division by zero or the square root of a negative number somewhere in the domain.

Parameters

[in]	str	The expression.
[in,out]	res	The result, one value per point.
[in]	n	The number of points.
[in]	x	The x-coordinates of the points.
[in]	y	The y-coordinates of the points.
[in]	z	The z-coordinates of the points.
[in]	usage	What the expression configures, used in error messages.

Definition at line 455 of file expression.f90.

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◆ expression_free()

subroutine expression::expression_free ( class(expression_t), intent(inout) this )

private

Definition at line 201 of file expression.f90.

◆ expression_init()

subroutine expression::expression_init	(	class(expression_t), intent(inout)	this,
		character(len=*), intent(in)	str
	)

Parameters

[in] str The expression, e.g. "6*U_b*y*(H - y)/H^2".

Definition at line 146 of file expression.f90.

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◆ func_op()

integer function expression::func_op	(	character(len=*), intent(in)	name,
		integer, intent(in)	nargs
	)

private

Parameters

[in]	name	The name of the function.
[in]	nargs	The number of arguments it was called with.

Returns: The opcode, -1 if the name is unknown and -2 if the name is known but the number of arguments is wrong.

Definition at line 877 of file expression.f90.

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◆ is_alpha()

pure logical function expression::is_alpha ( character(len=1), intent(in) c )

private

Parameters

[in] c The character to test.

Definition at line 997 of file expression.f90.

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◆ is_digit()

pure logical function expression::is_digit ( character(len=1), intent(in) c )

private

Parameters

[in] c The character to test.

Definition at line 987 of file expression.f90.

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◆ parse_expr()

recursive subroutine expression::parse_expr ( type(parser_t), intent(inout) p )

private

Parameters

[in,out] p The parser state.

Definition at line 665 of file expression.f90.

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◆ parse_factor()

recursive subroutine expression::parse_factor ( type(parser_t), intent(inout) p )

private

Parameters

[in,out] p The parser state.

Definition at line 710 of file expression.f90.

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◆ parse_power()

recursive subroutine expression::parse_power ( type(parser_t), intent(inout) p )

private

Parameters

[in,out] p The parser state.

Definition at line 736 of file expression.f90.

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◆ parse_primary()

recursive subroutine expression::parse_primary ( type(parser_t), intent(inout) p )

private

Parameters

[in,out] p The parser state.

Definition at line 769 of file expression.f90.

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◆ parse_symbol()

subroutine expression::parse_symbol	(	type(parser_t), intent(inout)	p,
		integer, intent(in)	k
	)

private

Coordinates and time variables take precedence over anything else. Everything that is left is looked up in the neko_const_registry and folded into a literal, so the value it had when the expression was compiled is the value that is used.

Parameters

[in,out]	p	The parser state.
[in]	k	Index of the identifier token to resolve.

Definition at line 830 of file expression.f90.

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◆ parse_term()

recursive subroutine expression::parse_term ( type(parser_t), intent(inout) p )

private

Parameters

[in,out] p The parser state.

Definition at line 687 of file expression.f90.

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◆ parser_free()

subroutine expression::parser_free ( type(parser_t), intent(inout) p )

private

Parameters

[in,out] p The parser state.

Definition at line 183 of file expression.f90.

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◆ push_token()

subroutine expression::push_token	(	type(parser_t), intent(inout)	p,
		integer, intent(in)	kind,
		integer, intent(in)	pos
	)

private

Parameters

[in,out]	p	The parser state.
[in]	kind	The kind of the token, one of the `TK_` constants.
[in]	pos	Position of the token in the source string.

Definition at line 642 of file expression.f90.

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Variable Documentation

◆ expr_chunk

integer, parameter expression::expr_chunk = 1024

private

Definition at line 63 of file expression.f90.

◆ expr_max_ident

integer, parameter expression::expr_max_ident = 64

private

Definition at line 58 of file expression.f90.

◆ neko_expr_len

integer, parameter, public expression::neko_expr_len = 256

Definition at line 55 of file expression.f90.

◆ op_abs

integer, parameter expression::op_abs = 34

private

Definition at line 74 of file expression.f90.

◆ op_acos

integer, parameter expression::op_acos = 25

private

Definition at line 74 of file expression.f90.

◆ op_add

integer, parameter expression::op_add = 60

private

Definition at line 81 of file expression.f90.

◆ op_asin

integer, parameter expression::op_asin = 24

private

Definition at line 74 of file expression.f90.

◆ op_atan

integer, parameter expression::op_atan = 26

private

Definition at line 74 of file expression.f90.

◆ op_atan2

integer, parameter expression::op_atan2 = 65

private

Definition at line 81 of file expression.f90.

◆ op_binary

integer, parameter expression::op_binary = 60

private

Definition at line 80 of file expression.f90.

◆ op_cos

integer, parameter expression::op_cos = 22

private

Definition at line 74 of file expression.f90.

◆ op_cosh

integer, parameter expression::op_cosh = 28

private

Definition at line 74 of file expression.f90.

◆ op_div

integer, parameter expression::op_div = 63

private

Definition at line 81 of file expression.f90.

◆ op_dt

integer, parameter expression::op_dt = 6

private

Definition at line 70 of file expression.f90.

◆ op_erf

integer, parameter expression::op_erf = 35

private

Definition at line 74 of file expression.f90.

◆ op_erfc

integer, parameter expression::op_erfc = 36

private

Definition at line 74 of file expression.f90.

◆ op_exp

integer, parameter expression::op_exp = 30

private

Definition at line 74 of file expression.f90.

◆ op_ipow

integer, parameter expression::op_ipow = 38

private

Definition at line 74 of file expression.f90.

◆ op_lit

integer, parameter expression::op_lit = 1

private

Definition at line 70 of file expression.f90.

◆ op_log

integer, parameter expression::op_log = 31

private

Definition at line 74 of file expression.f90.

◆ op_log10

integer, parameter expression::op_log10 = 32

private

Definition at line 74 of file expression.f90.

◆ op_max

integer, parameter expression::op_max = 67

private

Definition at line 81 of file expression.f90.

◆ op_min

integer, parameter expression::op_min = 66

private

Definition at line 81 of file expression.f90.

◆ op_mod

integer, parameter expression::op_mod = 68

private

Definition at line 81 of file expression.f90.

◆ op_mul

integer, parameter expression::op_mul = 62

private

Definition at line 81 of file expression.f90.

◆ op_neg

integer, parameter expression::op_neg = 20

private

Definition at line 74 of file expression.f90.

◆ op_pow

integer, parameter expression::op_pow = 64

private

Definition at line 81 of file expression.f90.

◆ op_sin

integer, parameter expression::op_sin = 21

private

Definition at line 74 of file expression.f90.

◆ op_sinh

integer, parameter expression::op_sinh = 27

private

Definition at line 74 of file expression.f90.

◆ op_sqrt

integer, parameter expression::op_sqrt = 33

private

Definition at line 74 of file expression.f90.

◆ op_step

integer, parameter expression::op_step = 37

private

Definition at line 74 of file expression.f90.

◆ op_sub

integer, parameter expression::op_sub = 61

private

Definition at line 81 of file expression.f90.

◆ op_t

integer, parameter expression::op_t = 5

private

Definition at line 70 of file expression.f90.

◆ op_tan

integer, parameter expression::op_tan = 23

private

Definition at line 74 of file expression.f90.

◆ op_tanh

integer, parameter expression::op_tanh = 29

private

Definition at line 74 of file expression.f90.

◆ op_unary

integer, parameter expression::op_unary = 20

private

Definition at line 73 of file expression.f90.

◆ op_x

integer, parameter expression::op_x = 2

private

Definition at line 70 of file expression.f90.

◆ op_y

integer, parameter expression::op_y = 3

private

Definition at line 70 of file expression.f90.

◆ op_z

integer, parameter expression::op_z = 4

private

Definition at line 70 of file expression.f90.

◆ tk_comma

integer, parameter expression::tk_comma = 10

private

Definition at line 87 of file expression.f90.

◆ tk_end

integer, parameter expression::tk_end = 0

private

Definition at line 87 of file expression.f90.

◆ tk_ident

integer, parameter expression::tk_ident = 2

private

Definition at line 87 of file expression.f90.

◆ tk_lpar

integer, parameter expression::tk_lpar = 8

private

Definition at line 87 of file expression.f90.

◆ tk_minus

integer, parameter expression::tk_minus = 4

private

Definition at line 87 of file expression.f90.

◆ tk_num

integer, parameter expression::tk_num = 1

private

Definition at line 87 of file expression.f90.

◆ tk_plus

integer, parameter expression::tk_plus = 3

private

Definition at line 87 of file expression.f90.

◆ tk_pow

integer, parameter expression::tk_pow = 7

private

Definition at line 87 of file expression.f90.

◆ tk_rpar

integer, parameter expression::tk_rpar = 9

private

Definition at line 87 of file expression.f90.

◆ tk_slash

integer, parameter expression::tk_slash = 6

private

Definition at line 87 of file expression.f90.

◆ tk_star

integer, parameter expression::tk_star = 5

private

Definition at line 87 of file expression.f90.

Data Types

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ emit()

◆ expr_error()

◆ expr_tokenize()

◆ expression_check_finite()

◆ expression_eval()

◆ expression_eval_static()

◆ expression_free()

◆ expression_init()

◆ func_op()

◆ is_alpha()

◆ is_digit()

◆ parse_expr()

◆ parse_factor()

◆ parse_power()

◆ parse_primary()

◆ parse_symbol()

◆ parse_term()

◆ parser_free()

◆ push_token()

Variable Documentation

◆ expr_chunk

◆ expr_max_ident

◆ neko_expr_len

◆ op_abs

◆ op_acos

◆ op_add

◆ op_asin

◆ op_atan

◆ op_atan2

◆ op_binary

◆ op_cos

◆ op_cosh

◆ op_div

◆ op_dt

◆ op_erf

◆ op_erfc

◆ op_exp

◆ op_ipow

◆ op_lit

◆ op_log

◆ op_log10

◆ op_max

◆ op_min

◆ op_mod

◆ op_mul

◆ op_neg

◆ op_pow

◆ op_sin

◆ op_sinh

◆ op_sqrt

◆ op_step

◆ op_sub

◆ op_t

◆ op_tan

◆ op_tanh

◆ op_unary

◆ op_x

◆ op_y

◆ op_z

◆ tk_comma

◆ tk_end

◆ tk_ident

◆ tk_lpar

◆ tk_minus

◆ tk_num

◆ tk_plus

◆ tk_pow

◆ tk_rpar

◆ tk_slash

◆ tk_star