forked from ArashPartow/exprtk
-
Notifications
You must be signed in to change notification settings - Fork 0
C++ Mathematical Expression Parsing And Evaluation Library
gussenov/exprtk
Folders and files
| Name | Name | Last commit message | Last commit date | |
|---|---|---|---|---|
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
 |  | |||
Repository files navigation
C++ Mathematical Expression Toolkit Library
[00 - INTRODUCTION]
The C++ Mathematical Expression Toolkit Library (ExprTk) is a simple
to use, easy to integrate and extremely efficient mathematical
expression parsing and evaluation engine. The parsing engine supports
numerous forms of functional and logic processing semantics and is
easily extendible.
[01 - CAPABILITIES]
The ExprTk expression evaluator supports the following fundamental
arithmetic operations, functions and processes:
(00) Basic operators: +, -, *, /, %, ^
(01) Functions: abs, avg, ceil, clamp, equal, erf, erfc, exp,
expm1, floor, frac, log, log10, log1p, log2,
logn, max, min, mul, ncdf, nequal, root, round,
roundn, sgn, sqrt, sum, swap, trunc
(02) Trigonometry: acos, acosh, asin, asinh, atan, atanh, atan2,
cos, cosh, cot, csc, sec, sin, sinc, sinh,
tan, tanh, hypot, rad2deg, deg2grad, deg2rad,
grad2deg
(03) Equalities &
Inequalities: =, ==, <>, !=, <, <=, >, >=
(04) Boolean logic: and, mand, mor, nand, nor, not, or, shl, shr,
xnor, xor, true, false
(05) Control
structures: if-then-else, ternary conditional, switch-case
(06) Loop statements: while, for, repeat-until, break, continue
(07) Assignment: :=, +=, -=, *=, /=, %=
(08) String
processing: in, like, ilike
(09) Optimisations: constant-folding and simple strength reduction
(10) Calculus: numerical integration and differentiation
[02 - EXAMPLE EXPRESSIONS]
The following is a short listing of the types of mathematical
expressions that can be parsed and evaluated using the ExprTk library.
(01) sqrt(1 - (3 / x^2))
(02) clamp(-1, sin(2 * pi * x) + cos(y / 2 * pi), +1)
(03) sin(2.34e-3 * x)
(04) if(((x[2] + 2) == 3) and ((y + 5) <= 9),1 + w, 2 / z)
(05) inrange(-2,m,+2) == if(({-2 <= m} and [m <= +2]),1,0)
(06) ({1/1}*[1/2]+(1/3))-{1/4}^[1/5]+(1/6)-({1/7}+[1/8]*(1/9))
(07) a * exp(2.2 / 3.3 * t) + c
(08) z := x + sin(2.567 * pi / y)
(09) u := 2.123 * {pi * z} / (w := x + cos(y / pi))
(10) 2x + 3y + 4z + 5w == 2 * x + 3 * y + 4 * z + 5 * w
(11) 3(x + y) / 2.9 + 1.234e+12 == 3 * (x + y) / 2.9 + 1.234e+12
(12) (x + y)3.3 + 1 / 4.5 == [x + y] * 3.3 + 1 / 4.5
(13) (x + y[i])z + 1.1 / 2.7 == (x + y[i]) * z + 1.1 / 2.7
(14) (sin(x / pi) cos(2y) + 1) == (sin(x / pi) * cos(2 * y) + 1)
(15) 75x^17 + 25.1x^5 - 35x^4 - 15.2x^3 + 40x^2 - 15.3x + 1
(16) (avg(x,y) <= x + y ? x - y : x * y) + 2.345 * pi / x
(17) fib_i := fib_i + (x := y + 0 * (fib_i := x + (y := fib_i)))
(18) while (x <= 100) { x -= 1; }
(19) x <= 'abc123' and (y in 'AString') or ('1x2y3z' != z)
(20) (x like '*123*') or ('a123b' ilike y)
[03 - COPYRIGHT NOTICE]
Free use of the C++ Mathematical Expression Toolkit Library is
permitted under the guidelines and in accordance with the most current
version of the Common Public License.
http://www.opensource.org/licenses/cpl1.0.php
[04 - DOWNLOADS & UPDATES]
The most recent version of the C++ Mathematical Expression Toolkit
Library including all updates and tests can be found at the following
locations:
(1) Download: http://www.partow.net/programming/exprtk/index.html
(2) Repository: https://exprtk.googlecode.com/svn/
[05 - INSTALLATION]
The header file exprtk.hpp should be placed in a project or system
include path (e.g: /usr/include/).
[06 - COMPILATION]
(a) For a complete build: make clean all
(b) For a PGO build: make clean pgo
(c) To strip executables: make strip_bin
(d) Execute valgrind check: make valgrind_check
[07 - COMPILER COMPATIBILITY]
ExprTk has been built error and warning free using the following set
of C++ compilers:
(*) GNU Compiler Collection (3.3+)
(*) Intel C++ Compiler (8.x+)
(*) Clang/LLVM (1.1+)
(*) PGI C++ (10.x+)
(*) Microsoft Visual Studio C++ Compiler (8.1+)
(*) Comeau C++ Compiler (4.3+)
(*) IBM XL C/C++ (9.x+)
(*) C++ Builder (XE4+)
[08 - BUILT-IN OPERATIONS & FUNCTIONS]
(0) Arithmetic & Assignment Operators
+----------+---------------------------------------------------------+
| OPERATOR | DEFINITION |
+----------+---------------------------------------------------------+
| + | Addition between x and y. (eg: x + y) |
+----------+---------------------------------------------------------+
| - | Subtraction between x and y. (eg: x - y) |
+----------+---------------------------------------------------------+
| * | Multiplication between x and y. (eg: x * y) |
+----------+---------------------------------------------------------+
| / | Division between x and y. (eg: x / y) |
+----------+---------------------------------------------------------+
| % | Modulus of x with respect to y. (eg: x % y) |
+----------+---------------------------------------------------------+
| ^ | x to the power of y. (eg: x ^ y) |
+----------+---------------------------------------------------------+
| := | Assign the value of x to y. Where y is either a variable|
| | or vector type. (eg: y := x) |
+----------+---------------------------------------------------------+
| += | Increment x to by the value of the expression on the |
| | right-hand side. Where x is either a variable or vector |
| | type. (eg: x += abs(y - z)) |
+----------+---------------------------------------------------------+
| -= | Decrement x to by the value of the expression on the |
| | right-hand side. Where x is either a variable or vector |
| | type. (eg: x[i] -= abs(y + z)) |
+----------+---------------------------------------------------------+
| *= | Assign the multiplication of x by the value of the |
| | expression on the righthand side to x. Where x is either|
| | a variable or vector type. |
| | (eg: x *= abs(y / z)) |
+----------+---------------------------------------------------------+
| /= | Assign the division of x by the value of the expression |
| | on the right-hand side to x. Where x is either a |
| | variable or vector type. (eg: x[i+j] /= abs(y * z)) |
+----------+---------------------------------------------------------+
| %= | Assign x modulo the value of the expression on the right|
| | hand side to x. Where x is either a variable or vector |
| | type. (eg: x[2] %= y ^ 2) |
+----------+---------------------------------------------------------+
(1) Equalities & Inequalities
+----------+---------------------------------------------------------+
| OPERATOR | DEFINITION |
+----------+---------------------------------------------------------+
| == or = | True only if x is strictly equal to y. (eg: x == y) |
+----------+---------------------------------------------------------+
| <> or != | True only if x does not equal y. (eg: x <> y or x != y) |
+----------+---------------------------------------------------------+
| < | True only if x is less than y. (eg: x < y) |
+----------+---------------------------------------------------------+
| <= | True only if x is less than or equal to y. (eg: x <= y) |
+----------+---------------------------------------------------------+
| > | True only if x is greater than y. (eg: x > y) |
+----------+---------------------------------------------------------+
| >= | True only if x greater than or equal to y. (eg: x >= y) |
+----------+---------------------------------------------------------+
(2) Boolean Operations
+----------+---------------------------------------------------------+
| OPERATOR | DEFINITION |
+----------+---------------------------------------------------------+
| true | True state or any value other than zero (typically 1). |
+----------+---------------------------------------------------------+
| false | False state, value of zero. |
+----------+---------------------------------------------------------+
| and | Logical AND, True only if x and y are both true. |
| | (eg: x and y) |
+----------+---------------------------------------------------------+
| mand | Multi-input logical AND, True only if all inputs are |
| | true. Left to right short-circuiting of expressions. |
| | (eg: mand(x > y, z < w, u or v, w and x)) |
+----------+---------------------------------------------------------+
| mor | Multi-input logical OR, True if at least one of the |
| | inputs are true. Left to right short-circuiting of |
| | expressions. (eg: mor(x > y, z < w, u or v, w and x)) |
+----------+---------------------------------------------------------+
| nand | Logical NAND, True only if either x or y is false. |
| | (eg: x nand y) |
+----------+---------------------------------------------------------+
| nor | Logical NOR, True only if the result of x or y is false |
| | (eg: x nor y) |
+----------+---------------------------------------------------------+
| not | Logical NOT, Negate the logical sense of the input. |
| | (eg: not(x and y) == x nand y) |
+----------+---------------------------------------------------------+
| or | Logical OR, True if either x or y is true. (eg: x or y) |
+----------+---------------------------------------------------------+
| xor | Logical XOR, True only if the logical states of x and y |
| | differ. (eg: x xor y) |
+----------+---------------------------------------------------------+
| xnor | Logical XNOR, True iff the biconditional of x and y is |
| | satisfied. (eg: x xnor y) |
+----------+---------------------------------------------------------+
| & | Similar to AND but with left to right expression short |
| | circuiting optimisation. (eg: (x & y) == (y and x)) |
+----------+---------------------------------------------------------+
| | | Similar to OR but with left to right expression short |
| | circuiting optimisation. (eg: (x | y) == (y or x)) |
+----------+---------------------------------------------------------+
(3) General Purpose Functions
+----------+---------------------------------------------------------+
| FUNCTION | DEFINITION |
+----------+---------------------------------------------------------+
| abs | Absolute value of x. (eg: abs(x)) |
+----------+---------------------------------------------------------+
| avg | Average of all the inputs. |
| | (eg: avg(x,y,z,w,u,v) == (x + y + z + w + u + v) / 6) |
+----------+---------------------------------------------------------+
| ceil | Smallest integer that is greater than or equal to x. |
+----------+---------------------------------------------------------+
| clamp | Clamp x in range between r0 and r1, where r0 < r1. |
| | (eg: clamp(r0,x,r1) |
+----------+---------------------------------------------------------+
| equal | Equality test between x and y using normalized epsilon |
+----------+---------------------------------------------------------+
| erf | Error function of x. (eg: erf(x)) |
+----------+---------------------------------------------------------+
| erfc | Complimentary error function of x. (eg: erfc(x)) |
+----------+---------------------------------------------------------+
| exp | e to the power of x. (eg: exp(x)) |
+----------+---------------------------------------------------------+
| expm1 | e to the power of x minus 1, where x is very small. |
| | (eg: expm1(x)) |
+----------+---------------------------------------------------------+
| floor | Largest integer that is less than or equal to x. |
| | (eg: floor(x)) |
+----------+---------------------------------------------------------+
| frac | Fractional portion of x. (eg: frac(x)) |
+----------+---------------------------------------------------------+
| hypot | Hypotenuse of x and y (eg: hypot(x,y) = sqrt(x*x + y*y))|
+----------+---------------------------------------------------------+
| iclamp | Inverse-clamp x outside of the range r0 and r1. Where |
| | r0 < r1. If x is within the range it will snap to the |
| | closest bound. (eg: iclamp(r0,x,r1) |
+----------+---------------------------------------------------------+
| inrange | In-range returns 'true' when x is within the range r0 |
| | and r1. Where r0 < r1. (eg: inrange(r0,x,r1) |
+----------+---------------------------------------------------------+
| log | Natural logarithm of x. (eg: log(x)) |
+----------+---------------------------------------------------------+
| log10 | Base 10 logarithm of x. (eg: log10(x)) |
+----------+---------------------------------------------------------+
| log1p | Natural logarithm of 1 + x, where x is very small. |
| | (eg: log1p(x)) |
+----------+---------------------------------------------------------+
| log2 | Base 2 logarithm of x. (eg: log2(x)) |
+----------+---------------------------------------------------------+
| logn | Base N logarithm of x. where n is a positive integer. |
| | (eg: logn(x,8)) |
+----------+---------------------------------------------------------+
| max | Largest value of all the inputs. (eg: max(x,y,z,w,u,v)) |
+----------+---------------------------------------------------------+
| min | Smallest value of all the inputs. (eg: min(x,y,z,w,u)) |
+----------+---------------------------------------------------------+
| mul | Product of all the inputs. |
| | (eg: mul(x,y,z,w,u,v,t) == (x * y * z * w * u * v * t)) |
+----------+---------------------------------------------------------+
| ncdf | Normal cumulative distribution function. (eg: ncdf(x)) |
+----------+---------------------------------------------------------+
| nequal | Not-equal test between x and y using normalized epsilon |
+----------+---------------------------------------------------------+
| root | Nth-Root of x. where n is a positive integer. |
| | (eg: root(x,3)) |
+----------+---------------------------------------------------------+
| round | Round x to the nearest integer. (eg: round(x)) |
+----------+---------------------------------------------------------+
| roundn | Round x to n decimal places (eg: roundn(x,3)) |
| | where n > 0 and is an integer. |
| | (eg: roundn(1.2345678,4) == 1.2346) |
+----------+---------------------------------------------------------+
| sgn | Sign of x, -1 where x < 0, +1 where x > 0, else zero. |
| | (eg: sgn(x)) |
+----------+---------------------------------------------------------+
| sqrt | Square root of x, where x > 0. (eg: sqrt(x)) |
+----------+---------------------------------------------------------+
| sum | Sum of all the inputs. |
| | (eg: sum(x,y,z,w,u,v,t) == (x + y + z + w + u + v + t)) |
+----------+---------------------------------------------------------+
| swap | Swap the values of the variables x and y and return the |
| <=> | current value of y. (eg: swap(x,y) or x <=> y) |
+----------+---------------------------------------------------------+
| trunc | Integer portion of x. (eg: trunc(x)) |
+----------+---------------------------------------------------------+
(4) Trigonometry Functions
+----------+---------------------------------------------------------+
| FUNCTION | DEFINITION |
+----------+---------------------------------------------------------+
| acos | Arc cosine of x expressed in radians. Interval [-1,+1] |
| | (eg: acos(x)) |
+----------+---------------------------------------------------------+
| acosh | Inverse hyperbolic cosine of x expressed in radians. |
| | (eg: acosh(x)) |
+----------+---------------------------------------------------------+
| asin | Arc sine of x expressed in radians. Interval [-1,+1] |
| | (eg: asin(x)) |
+----------+---------------------------------------------------------+
| asinh | Inverse hyperbolic sine of x expressed in radians. |
| | (eg: asinh(x)) |
+----------+---------------------------------------------------------+
| atan | Arc tangent of x expressed in radians. Interval [-1,+1] |
| | (eg: atan(x)) |
+----------+---------------------------------------------------------+
| atan2 | Arc tangent of (x / y) expressed in radians. [-pi,+pi] |
| | eg: atan2(x,y) |
+----------+---------------------------------------------------------+
| atanh | Inverse hyperbolic tangent of x expressed in radians. |
| | (eg: atanh(x)) |
+----------+---------------------------------------------------------+
| cos | Cosine of x. (eg: cos(x)) |
+----------+---------------------------------------------------------+
| cosh | Hyperbolic cosine of x. (eg: cosh(x)) |
+----------+---------------------------------------------------------+
| cot | Cotangent of x. (eg: cot(x)) |
+----------+---------------------------------------------------------+
| csc | Cosecant of x. (eg: csc(x)) |
+----------+---------------------------------------------------------+
| sec | Secant of x. (eg: sec(x)) |
+----------+---------------------------------------------------------+
| sin | Sine of x. (eg: sin(x)) |
+----------+---------------------------------------------------------+
| sinc | Sine cardinal of x. (eg: sinc(x)) |
+----------+---------------------------------------------------------+
| sinh | Hyperbolic sine of x. (eg: sinh(x)) |
+----------+---------------------------------------------------------+
| tan | Tangent of x. (eg: tan(x)) |
+----------+---------------------------------------------------------+
| tanh | Hyperbolic tangent of x. (eg: tanh(x)) |
+----------+---------------------------------------------------------+
| deg2rad | Convert x from degrees to radians. (eg: deg2rad(x)) |
+----------+---------------------------------------------------------+
| deg2grad | Convert x from degrees to gradians. (eg: deg2grad(x)) |
+----------+---------------------------------------------------------+
| rad2deg | Convert x from radians to degrees. (eg: rad2deg(x)) |
+----------+---------------------------------------------------------+
| grad2deg | Convert x from gradians to degrees. (eg: grad2deg(x)) |
+----------+---------------------------------------------------------+
(5) String Processing
+----------+---------------------------------------------------------+
| FUNCTION | DEFINITION |
+----------+---------------------------------------------------------+
| = , == | All common equality/inequality operators are applicable |
| !=, <> | to strings and are applied in a case sensitive manner. |
| <=, >= | In the following example x, y and z are of type string. |
| < , > | (eg: not((x <= 'AbC') and ('1x2y3z' <> y)) or (z == x) |
+----------+---------------------------------------------------------+
| in | True only if x is a substring of y. |
| | (eg: x in y or 'abc' in 'abcdefgh') |
+----------+---------------------------------------------------------+
| like | True only if the string x matches the pattern y. |
| | Available wildcard characters are '*' and '?' denoting |
| | zero or more and zero or one matches respectively. |
| | (eg: x like y or 'abcdefgh' like 'a?d*h') |
+----------+---------------------------------------------------------+
| ilike | True only if the string x matches the pattern y in a |
| | case insensitive manner. Available wildcard characters |
| | are '*' and '?' denoting zero or more and zero or one |
| | matches respectively. |
| | (eg: x ilike y or 'a1B2c3D4e5F6g7H' ilike 'a?d*h') |
+----------+---------------------------------------------------------+
| [r0:r1] | The closed interval [r0,r1] of the specified string. |
| | eg: Given a string x with a value of 'abcdefgh' then: |
| | 1. x[1:4] == 'bcde' |
| | 2. x[ :5] == x[:5] == 'abcdef' |
| | 3. x[3: ] == x[3:] =='cdefgh' |
| | 4. x[ : ] == x[:] == 'abcdefgh' |
| | 5. x[4/2:3+2] == x[2:5] == 'cdef' |
| | |
| | Note: Both r0 and r1 are assumed to be integers, where |
| | r0 <= r1. They may also be the result of an expression, |
| | in the event they have fractional components truncation |
| | will be performed. (eg: 1.67 --> 1) |
+----------+---------------------------------------------------------+
| [] | The string size operator returns the size of the string |
| | being actioned. |
| | eg: |
| | 1. 'abc'[] == 3 |
| | 2. var max_str_length := max(s0[],s1[],s2[],s3[]) |
+----------+---------------------------------------------------------+
(6) Control Structures
+----------+---------------------------------------------------------+
|STRUCTURE | DEFINITION |
+----------+---------------------------------------------------------+
| if | If x is true then return y else return z. |
| | eg: |
| | 1. if(x, y, z) |
| | 2. if((x + 1) > 2y, z + 1, w / v) |
+----------+---------------------------------------------------------+
| if-else | The if-else/else-if statement. Subject to the condition |
| | branch the statement will return either the value of the|
| | consequent or the alternative branch. |
| | eg: |
| | 1. if (x > y) z; else w; |
| | 2. if (x > y) z; else if (w != u) v; |
| | 3. if (x < y) {z; w+1;} else u; |
| | 4. if ((x != y) and (z > w)) |
| | { |
| | y := sin(x) / u; |
| | z := w+1; |
| | } |
| | else if (x > (z + 1)) |
| | { |
| | w := abs (x - y) + z; |
| | u := (x + 1) > 2y ? 2u : 3u; |
| | } |
+----------+---------------------------------------------------------+
| switch | The first true case condition that is encountered will |
| | determine the result of the switch. If none of the case |
| | conditions hold true, the default action is assumed as |
| | the final return value. This is sometimes also known as |
| | a multi-way branch mechanism. |
| | eg: |
| | switch |
| | { |
| | case x > (y + z) : 2 * x / abs(y - z); |
| | case x < 3 : sin(x + y); |
| | default : 1 + x; |
| | } |
+----------+---------------------------------------------------------+
| while | The structure will repeatedly evaluate the internal |
| | statement(s) 'while' the condition is true. The final |
| | statement in the final iteration will be used as the |
| | return value of the loop. |
| | eg: |
| | while ((x -= 1) > 0) |
| | { |
| | y := x + z; |
| | w := u + y; |
| | } |
+----------+---------------------------------------------------------+
| repeat/ | The structure will repeatedly evaluate the internal |
| until | statement(s) 'until' the condition is true. The final |
| | statement in the final iteration will be used as the |
| | return value of the loop. |
| | eg: |
| | repeat |
| | y := x + z; |
| | w := u + y; |
| | until ((x += 1) > 100) |
+----------+---------------------------------------------------------+
| for | The structure will repeatedly evaluate the internal |
| | statement(s) while the condition is true. On each loop |
| | iteration, an 'incrementing' expression is evaluated. |
| | The conditional is mandatory whereas the initializer |
| | and incrementing expressions are optional. |
| | eg: |
| | for (var x := 0; (x < n) and (x != y); x += 1) |
| | { |
| | y := y + x / 2 - z; |
| | w := u + y; |
| | } |
+----------+---------------------------------------------------------+
| break | Break terminates the execution of the nearest enclosed |
| break[] | loop, allowing for the execution to continue on external|
| | to the loop. The default break statement will set the |
| | return value of the loop to NaN, where as the return |
| | based form will set the value to that of the break |
| | expression. |
| | eg: |
| | while ((i += 1) < 10) |
| | { |
| | if (i < 5) |
| | j -= i + 2; |
| | else if (i % 2 == 0) |
| | break; |
| | else |
| | break[2i + 3]; |
| | } |
+----------+---------------------------------------------------------+
| continue | Continue results in the remaining portion of the nearest|
| | enclosing loop body to be skipped. |
| | eg: |
| | for (var i := 0; i < 10; i += 1) |
| | { |
| | if (i < 5) |
| | continue; |
| | j -= i + 2; |
| | } |
+----------+---------------------------------------------------------+
| ?: | Ternary conditional statement, similar to that of the |
| | above denoted if-statement. |
| | eg: |
| | 1. x ? y : z |
| | 2. x + 1 > 2y ? z + 1 : (w / v) |
| | 3. min(x,y) > z ? (x < y + 1) ? x : y : (w * v) |
+----------+---------------------------------------------------------+
| ~ | Evaluate each sub-expression, then return as the result |
| | the value of the last sub-expression. This is sometimes |
| | known as multiple sequence point evaluation. |
| | eg: |
| | ~(i := x + 1, j := y / z, k := sin(w/u)) == (sin(w/u))) |
| | ~{i := x + 1; j := y / z; k := sin(w/u)} == (sin(w/u))) |
+----------+---------------------------------------------------------+
| [*] | Evaluate any consequent for which its case statement is |
| | true. The return value will be either zero or the result|
| | of the last consequent to have been evaluated. |
| | eg: |
| | [*] |
| | { |
| | case (x + 1) > (y - 2) : x := z / 2 + sin(y / pi); |
| | case (x + 2) < abs(y + 3): w / 4 + min(5y,9); |
| | case (x + 3) = (y * 4) : y := abs(z / 6) + 7y; |
| | } |
+----------+---------------------------------------------------------+
| [] | The vector size operator returns the size of the vector |
| | being actioned. |
| | eg: |
| | 1. v[] |
| | 2. max_size := max(v0[],v1[],v2[],v3[]) |
+----------+---------------------------------------------------------+
Note: In the above tables, the symbols x, y, z, w, u and v where
appropriate may represent any of one the following:
1. Literal numeric/string value
2. A variable
3. A vector element
4. A vector
5. An expression comprised of [1], [2] or [3] (eg: 2 + x / vec[3])
[09 - COMPONENTS]
There are three primary components, that are specialized upon a given
numeric type, which make up the core of ExprTk. The components are as
follows:
1. Symbol Table exprtk::symbol_table<NumericType>
2. Expression exprtk::expression<NumericType>
3. Parser exprtk::parser<NumericType>
(1) Symbol Table
A structure that is used to store references to variables, constants
and functions that are to be used within expressions. Furthermore in
the context of composited recursive functions the symbol table can
also be thought of as a simple representation of a stack specific for
the expression(s) that reference it. The following is a list of the
types a symbol table can handle:
(a) Numeric variables
(b) Numeric constants
(c) Numeric vector elements
(d) String variables
(e) String constants
(f) Functions
(g) Vararg functions
During the compilation process if an expression is found to require
any of the elements noted above, the expression's associated
symbol_table will be queried for the element and if present a
reference to the element will be embedded within the expression's AST.
This allows for the original element to be modified independently of
the expression instance and to also allow the expression to be
evaluated using the current value of the element.
The example below demonstrates the relationship between variables,
symbol_table and expression. Note the variables are modified as they
normally would in a program, and when the expression is evaluated the
current values assigned to the variables will be used.
typedef exprtk::symbol_table<double> symbol_table_t;
typedef exprtk::expression<double> expression_t;
typedef exprtk::parser<double> parser_t;
symbol_table_t symbol_table;
expression_t expression;
parser_t parser;
double x = 0;
double y = 0;
std::string expression_string = "x * y + 3";
symbol_table.add_variable("x",x);
symbol_table.add_variable("y",y);
expression.register_symbol_table(symbol_table);
parser.compile(expression_string,expression);
x = 1.0;
y = 2.0;
expression.value(); // 1 * 2 + 3
x = 3.7;
expression.value(); // 3.7 * 2 + 3
y = -9.0;
expression.value(); // 3.7 * -9 + 3
// 'x * -9 + 3' for x in range of [0,100] in steps of 0.0001
for (var x = 0; x < 100; x += 0.0001)
{
expression.value(); // x * -9 + 3
}
(2) Expression
A structure that holds an AST for a specified expression and is used
to evaluate said expression. If a compiled Expression uses variables
or user defined functions, it will then also have an associated Symbol
Table, which will contain references to said variables, functions et
al. An example AST structure for the denoted expression is as follows:
Expression: z := (x + y^-2.345) * sin(pi / min(w - 7.3,v))
[Root]
|
[Assignment]
________/ \_____
/ \
Variable(z) [Multiplication]
____________/ \___________
/ \
/ [Unary-Func(sin)]
[Addition] |
____/ \____ [Division]
/ \ ___/ \___
Variable(x) [Exponentiation] / \
______/ \______ Constant(pi) [Binary-Func(min)]
/ \ ____/ \____
Variable(y) [Negation] / \
| / Variable(v)
Constant(2.345) /
/
[Subtraction]
____/ \____
/ \
Variable(w) Constant(7.3)
(3) Parser
A structure which takes as input a string representation of an
expression and attempts to compile said input with the result being an
instance of Expression. If an error is encountered during the
compilation process, the parser will stop compiling and return an
error status code, with a more detailed description of the error(s)
and its location within the input provided by the 'get_error'
interface.
[10 - COMPILATION OPTIONS]
The exprtk::parser when being instantiated takes as input a set of
options to be used during the compilation process of expressions.
An example instantiation of exprtk::parser where only the joiner,
commutative and strength reduction options are enabled is as follows:
typedef exprtk::parser<NumericType> parser_t;
std::size_t compile_options = parser_t::e_joiner +
parser_t::e_commutative_check +
parser_t::e_strength_reduction;
parser_t parser(compile_options);
Currently seven types of compile time options are supported, and
enabled by default. The options and their explanations are as follows:
(1) Replacer (e_replacer)
Enable replacement of specific tokens with other tokens. For example
the token "true" of type symbol will be replaced with the numeric
token of value one.
(a) (x < y) == true ---> (x < y) == 1
(b) false == (x > y) ---> 0 == (x > y)
(2) Joiner (e_joiner)
Enable joining of multi-character operators that may have been
incorrectly disjoint in the string representation of the specified
expression. For example the consecutive tokens of ">" "=" will become
">=" representing the "greater than or equal to" operator. If not
properly resolved the original form will cause a compilation error.
The following is a listing of the scenarios that the joiner can
handle:
(a) '>' '=' ---> '>=' (gte)
(b) '<' '=' ---> '<=' (lte)
(c) '=' '=' ---> '==' (equal)
(d) '!' '=' ---> '!=' (not-equal)
(e) '<' '>' ---> '<>' (not-equal)
(f) ':' '=' ---> ':=' (assignment)
(g) '+' '=' ---> '+=' (addition assignment)
(h) '-' '=' ---> '-=' (subtraction assignment)
(i) '*' '=' ---> '*=' (multiplication assignment)
(j) '/' '=' ---> '/=' (division assignment)
(j) '%' '=' ---> '%=' (modulo assignment)
An example of the transformation that takes place is as follows:
(a) (x > = y) and (z ! = w) ---> (x >= y) and (z != w)
(3) Numeric Check (e_numeric_check)
Enable validation of tokens representing numeric types so as to catch
any errors prior to the costly process of the main compilation step
commencing.
(4) Bracket Check (e_bracket_check)
Enable the check for validating the ordering of brackets in the
specified expression.
(5) Sequence Check (e_sequence_check)
Enable the check for validating that sequences of either pairs or
triplets of tokens make sense. For example the following sequence of
tokens when encountered will raise an error:
(a) (x + * 3) ---> sequence error
(6) Commutative Check (e_commutative_check)
Enable the check that will transform sequences of pairs of tokens that
imply a multiplication operation. The following are some examples of
such transformations:
(a) 2x ---> 2 * x
(b) 25x^3 ---> 25 * x^3
(c) 3(x + 1) ---> 3 * (x + 1)
(d) (x + 1)4 ---> (x + 1) * 4
(e) 5foo(x,y) ---> 5 * foo(x,y)
(f) foo(x,y)6 + 1 ---> foo(x,y) * 6 + 1
(g) (4((2x)3)) ---> 4 * ((2 * x) * 3)
(7) Strength Reduction Check (e_strength_reduction)
Enable the use of strength reduction optimisations during the
compilation process. In ExprTk strength reduction optimisations
predominantly involve transforming sub-expressions into other forms
that are algebraically equivalent yet less costly to compute. The
following are examples of the various transformations that can occur:
(a) (x / y) / z ---> x / (y * z)
(b) (x / y) / (z / w) ---> (x * w) / (y * z)
(c) (2 * x) - (2 * y) ---> 2 * (x - y)
(d) (2 / x) / (3 / y) ---> (2 / 3) / (x * y)
(e) (2 * x) * (3 * y) ---> (2 * 3) * (x * y)
Note:
When using strength reduction in conjunction with expressions whose
inputs or sub-expressions may result in values nearing either of the
bounds of the underlying numeric type (eg: double), there may be the
possibility of a decrease in the precision of results.
In the following example the given expression which represents an
attempt at computing the average between x and y will be transformed
as follows:
(x * 0.5) + (y * 0.5) ---> 0.5 * (x + y)
There may be situations where the above transformation will cause
numerical overflows and that the original form of the expression is
desired over the strength reduced form. In these situations it is best
to turn off strength reduction optimisations or to use a type with a
larger numerical bound.
[11 - SPECIAL FUNCTIONS]
The purpose of special functions in ExprTk is to provide compiler
generated equivalents of common mathematical expressions which can be
invoked by using the 'special function' syntax (eg: $f12(x,y,z) or
$f82(x,y,z,w)).
Special functions dramatically decrease the total evaluation time of
expressions which would otherwise have been written using the common
form by reducing the total number of nodes in the evaluation tree of
an expression and by also leveraging the compiler's ability to
correctly optimize such expressions for a given architecture.
3-Parameter 4-Parameter
+-------------+-------------+ +--------------+------------------+
| Prototype | Operation | | Prototype | Operation |
+-------------+-------------+ +--------------+------------------+
$f00(x,y,z) | (x + y) / z $f48(x,y,z,w) | x + ((y + z) / w)
$f01(x,y,z) | (x + y) * z $f49(x,y,z,w) | x + ((y + z) * w)
$f02(x,y,z) | (x + y) - z $f50(x,y,z,w) | x + ((y - z) / w)
$f03(x,y,z) | (x + y) + z $f51(x,y,z,w) | x + ((y - z) * w)
$f04(x,y,z) | (x - y) + z $f52(x,y,z,w) | x + ((y * z) / w)
$f05(x,y,z) | (x - y) / z $f53(x,y,z,w) | x + ((y * z) * w)
$f06(x,y,z) | (x - y) * z $f54(x,y,z,w) | x + ((y / z) + w)
$f07(x,y,z) | (x * y) + z $f55(x,y,z,w) | x + ((y / z) / w)
$f08(x,y,z) | (x * y) - z $f56(x,y,z,w) | x + ((y / z) * w)
$f09(x,y,z) | (x * y) / z $f57(x,y,z,w) | x - ((y + z) / w)
$f10(x,y,z) | (x * y) * z $f58(x,y,z,w) | x - ((y + z) * w)
$f11(x,y,z) | (x / y) + z $f59(x,y,z,w) | x - ((y - z) / w)
$f12(x,y,z) | (x / y) - z $f60(x,y,z,w) | x - ((y - z) * w)
$f13(x,y,z) | (x / y) / z $f61(x,y,z,w) | x - ((y * z) / w)
$f14(x,y,z) | (x / y) * z $f62(x,y,z,w) | x - ((y * z) * w)
$f15(x,y,z) | x / (y + z) $f63(x,y,z,w) | x - ((y / z) / w)
$f16(x,y,z) | x / (y - z) $f64(x,y,z,w) | x - ((y / z) * w)
$f17(x,y,z) | x / (y * z) $f65(x,y,z,w) | ((x + y) * z) - w
$f18(x,y,z) | x / (y / z) $f66(x,y,z,w) | ((x - y) * z) - w
$f19(x,y,z) | x * (y + z) $f67(x,y,z,w) | ((x * y) * z) - w
$f20(x,y,z) | x * (y - z) $f68(x,y,z,w) | ((x / y) * z) - w
$f21(x,y,z) | x * (y * z) $f69(x,y,z,w) | ((x + y) / z) - w
$f22(x,y,z) | x * (y / z) $f70(x,y,z,w) | ((x - y) / z) - w
$f23(x,y,z) | x - (y + z) $f71(x,y,z,w) | ((x * y) / z) - w
$f24(x,y,z) | x - (y - z) $f72(x,y,z,w) | ((x / y) / z) - w
$f25(x,y,z) | x - (y / z) $f73(x,y,z,w) | (x * y) + (z * w)
$f26(x,y,z) | x - (y * z) $f74(x,y,z,w) | (x * y) - (z * w)
$f27(x,y,z) | x + (y * z) $f75(x,y,z,w) | (x * y) + (z / w)
$f28(x,y,z) | x + (y / z) $f76(x,y,z,w) | (x * y) - (z / w)
$f29(x,y,z) | x + (y + z) $f77(x,y,z,w) | (x / y) + (z / w)
$f30(x,y,z) | x + (y - z) $f78(x,y,z,w) | (x / y) - (z / w)
$f31(x,y,z) | x * y^2 + z $f79(x,y,z,w) | (x / y) - (z * w)
$f32(x,y,z) | x * y^3 + z $f80(x,y,z,w) | x / (y + (z * w))
$f33(x,y,z) | x * y^4 + z $f81(x,y,z,w) | x / (y - (z * w))
$f34(x,y,z) | x * y^5 + z $f82(x,y,z,w) | x * (y + (z * w))
$f35(x,y,z) | x * y^6 + z $f83(x,y,z,w) | x * (y - (z * w))
$f36(x,y,z) | x * y^7 + z $f84(x,y,z,w) | x*y^2 + z*w^2
$f37(x,y,z) | x * y^8 + z $f85(x,y,z,w) | x*y^3 + z*w^3
$f38(x,y,z) | x * y^9 + z $f86(x,y,z,w) | x*y^4 + z*w^4
$f39(x,y,z) | x * log(y)+z $f87(x,y,z,w) | x*y^5 + z*w^5
$f40(x,y,z) | x * log(y)-z $f88(x,y,z,w) | x*y^6 + z*w^6
$f41(x,y,z) | x * log10(y)+z $f89(x,y,z,w) | x*y^7 + z*w^7
$f42(x,y,z) | x * log10(y)-z $f90(x,y,z,w) | x*y^8 + z*w^8
$f43(x,y,z) | x * sin(y)+z $f91(x,y,z,w) | x*y^9 + z*w^9
$f44(x,y,z) | x * sin(y)-z $f92(x,y,z,w) | (x and y) ? z : w
$f45(x,y,z) | x * cos(y)+z $f93(x,y,z,w) | (x or y) ? z : w
$f46(x,y,z) | x * cos(y)-z $f94(x,y,z,w) | (x < y) ? z : w
$f47(x,y,z) | x ? y : z $f95(x,y,z,w) | (x <= y) ? z : w
$f96(x,y,z,w) | (x > y) ? z : w
$f97(x,y,z,w) | (x >= y) ? z : w
$f98(x,y,z,w) | (x == y) ? z : w
$f99(x,y,z,w) | x*sin(y)+z*cos(w)
[12 - VARIABLE & VECTOR DEFINITION]
ExprTk supports the definition of expression local variables and
vectors. The definitions must be unique as shadowing is not allowed
and object life-times are based on scope. Definitions use the
following general form:
var <name> := <initializer>;
(1) Variable Definition
Variables are of numeric type denoting a single value. They can be
explicitly initialised to a value, otherwise they will be defaulted to
zero. The following are examples of variable definitions:
(a) Initialise x to zero
var x;
(b) Initialise y to three
var y := 3;
(c) Initialise z to the expression
var z := if(max(1,x + y) > 2,w,v);
(2) Vector Definition
Vectors are arrays of a common numeric type. The elements in a vector
can be explicitly initialised, otherwise they will all be defaulted to
zero. The following are examples of vector definitions:
(a) Initialise all values to zero
var x[3];
(b) Initialise all values to zero
var x[3] := {};
(c) Initialise all values to given expression
var x[3] := [123 + 3y + sin(w/z)];
(d) Initialise the first two values, other elements to zero
var x[3] := {1 + x[2], sin(y[0] / x[]) + 3};
(e) Initialise the first three (all) values
var x[3] := {1,2,3};
(f) Error as there are too many initializers
var x[3] := {1,2,3,4};
(g) Error as a vector of size zero is not allowed.
var x[0];
(3) Return Value
Variable and vector definitions have a return value. In the case of
variable definitions, the value to which the variable is initialized
will be returned. Where as for vectors, the value of the first element
(eg: v[0]) will be returned.
[13 - VECTOR PROCESSING]
ExprTk provides support for various forms of vector oriented
arithmetic, inequalities and processing. The various supported pairs
are as follows:
(a) vector and vector (eg: v0 + v1)
(b) vector and scalar (eg: v + 33)
(c) scalar and vector (eg: 22 * v)
The following is a list of operations that can be used in conjunction
with vectors:
(a) Arithmetic: +, -, *, /, %
(b) Exponentiation: vector ^ scalar
(c) Assignment: :=, +=, -=, *=, /=, %=
(d) Inequalities: <, <=, >, >=, ==, =
(e) Unary operations:
abs, acos, acosh, asin, asinh, atan, atanh, avg, ceil,
cos, cosh, cot, csc, deg2grad, deg2rad, erf, erfc, exp,
expm1, floor, frac, grad2deg, log, log10, log1p, log2,
max, min, mul, rad2deg, round, sec, sgn, sin, sinc, sinh,
sqrt, sum, tan, tanh, trunc
Note: When one of the above described operations is being performed
between two vectors, the operation will only span the size of the
smallest vector. The elements of the larger vector outside of the
range will not be included.
The following simple example demonstrates the vector processing
capabilities by computing the dot-product of the vectors v0 and v1 and
then assigning it to the variable v0dotv1:
var v0[3] := {1,2,3};
var v1[3] := {4,5,6};
var v0dotv1 := sum(v0 * v1);
The following is a for-loop based implementation that is equivalent to
the previously mentioned dot-product computation expression:
var v0[3] := {1,2,3};
var v1[3] := {4,5,6};
var v0dotv1;
for (var i := 0; i < min(v0[],v1[]); i += 1)
{
v0dotv1 += (v0[i] * v1[i]);
}
[14 - USER DEFINED FUNCTIONS]
ExprTk provides a means whereby custom functions can be defined and
utilized within expressions. The concept requires the user to
provide a reference to the function coupled with an associated name
that will be invoked within expressions. Function can take in numerous
inputs but will always return one value.
During expression compilation when required the reference to the
function will be obtained from the associated symbol_table and be
embedded into the expression.
There are two types of function interface:
(1) ifunction
(2) ivararg_function
(1) ifunction
This interface supports zero to 20 input parameters. The usage
requires a custom function be derived from ifunction and to override
one of the 21 function operators. As part of the constructor the
custom function will define how many parameters it expects to handle.
The following example defines a 3 parameter function called 'foo':
template <typename T>
struct foo : public exprtk::ifunction<T>
{
foo() : exprtk::ifunction<T>(3)
{}
T operator()(const T& v1, const T& v2, const T& v3)
{
return T(1) + (v1 * v2) / T(v3);
}
};
(2) ivararg_function
This interface supports a variable number of arguments as input into
the function. The function operator interface uses a std::vector
specialized upon type T to facilitate parameter passing. The following
example defines a vararg function called 'boo':
template <typename T>
struct boo : public exprtk::ivararg_function<T>
{
inline T operator()(const std::vector<T>& arglist)
{
T result = T(0);
for (std::size_t i = 0; i < arglist.size(); ++i)
{
result += arglist[i] / arglist[i > 0 ? (i - 1) : 0];
}
return result;
}
};
(3) Using Functions In Expressions
For the above denoted custom functions to be used in an expression, an
instance of each function needs to be registered with a symbol_table
that has been associated with the expression instance. The following
demonstrates how all the pieces are put together:
typedef exprtk::symbol_table<double> symbol_table_t;
typedef exprtk::expression<double> expression_t;
typedef exprtk::parser<double> parser_t;
foo<double> f;
boo<double> b;
symbol_table_t symbol_table;
symbol_table.add_function("foo",f);
symbol_table.add_vararg_function("boo",b);
expression_t expression;
expression.register_symbol_table(symbol_table);
std::string expression_str =
"foo(1,2,3) + boo(1) / boo(1/2,2/3,3/4,4/5,5/6)";
parser_t parser;
parser.compile(expression_str,expression);
expression.value();
(4) Function Side-Effects
All function calls are assumed to have side-effects by default. What
that means is that a certain type of optimisation will not be carried
out when the function is being called. The optimisation in question
is: constant folding. Normally during compilation this optimisation
would be invoked when all the parameters being passed into the
function are literals, the function will be evaluated at that point
and a new literal will replace the function call node in the AST.
If it is certain that the function being registered does not have any
side effects and can be correctly constant folded where appropriate,
then during the construction of the function a 'false' can be passed
to the constructor to denote the lack of side-effects.
template <typename T>
struct foo : public exprtk::ifunction<T>
{
foo() : exprtk::ifunction<T>(3,false)
{}
T operator()(const T& v1, const T& v2, const T& v3)
{ ... }
};
(5) Zero Parameter Functions
When either an ifunction or ivararg_function derived type is defined
with zero number of parameters, there are two calling conventions
within expressions that are allowed. For a function named 'foo' with
zero input parameters the calling styles are as follows:
(1) x + sin(foo()- 2) / y
(2) x + sin(foo - 2) / y
[15 - EXPRTK NOTES]
The following is a list of facts and suggestions one may want to take
into account when using Exprtk:
(00) Precision and performance of expression evaluations are the
dominant principles of the ExprTk library.
(01) ExprTk uses a rudimentary imperative programming model with
syntax based on languages such as Pascal and C.
(02) Supported types are float, double and long double.
(03) Standard mathematical operator precedence is applied (BEDMAS).
(04) Results of expressions that are deemed as being 'valid' are to
exist within the set of Real numbers. All other results will be
of the value: Not-A-Number (NaN).
(05) Supported user defined types are numeric and string variables
and functions.
(06) All variable and function names are case-insensitive.
(07) Variable and function names must begin with a letter
(A-Z or a-z), then can be comprised of any combination of
letters, digits and underscores. (eg: x, var1 or power_func99)
(08) Expression lengths and sub-expression lists are limited only by
storage capacity.
(09) The life-time of objects registered with or created from a
specific symbol-table must span at least the life-time of the
compiled expressions which utilize objects, such as variables,
of that symbol-table, otherwise the result will be undefined
behavior.
(10) Equal/Nequal are normalized equality routines, which use
epsilons of 0.0000000001 and 0.000001 for double and float
types respectively.
(11) All trigonometric functions assume radian input unless
stated otherwise.
(12) Expressions may contain white-space characters such as
space, tabs, new-lines, control-feed et al.
('\n', '\r', '\t', '\b', '\v', '\f')
(13) Strings may be constructed from any letters, digits or special
characters such as (~!@#$%^&*()[]|=+ ,./?<>;:"`~_), and must
be enclosed with single-quotes.
eg: 'Frankly my dear, I do not give a damn!'
(14) User defined normal functions can have up to 20 parameters,
where as user defined vararg-functions can have an unlimited
number of parameters.
(15) The inbuilt polynomial functions can be at most of degree 12.
(16) Where appropriate constant folding optimisations may be
applied. (eg: The expression '2+(3-(x/y))' becomes '5-(x/y)')
(17) If the strength reduction compilation option has been enabled,
then where applicable strength reduction optimisations may be
applied.
(18) String processing capabilities are available by default.
To turn them off, the following needs to be defined at
compile time: exprtk_disable_string_capabilities
(19) Composited functions can call themselves or any other functions
that have been defined prior to their own definition.
(20) Recursive calls made from within composited functions will have
a stack size bound by the stack of the executing architecture.
(21) User defined functions by default are assumed to have side
effects. As such an "all constant parameter" invocation of such
functions wont result in constant folding. If the function has
no side effects then that can be noted during the constructor
of the ifunction allowing it to be constant folded where
appropriate.
(22) The entity relationship between symbol_table and an expression
is one-to-many. Hence the intended use case is to have a single
symbol table manage the variable and function requirements of
multiple expressions.
(23) The common use-case for an expression is to have it compiled
only ONCE and then subsequently have it evaluated multiple
times. An extremely inefficient and suboptimal approach would
be to recompile an expression from its string form every time
it requires evaluating.
(24) The following are examples of compliant floating point value
representations:
(a) 12345 (e) -123.456
(b) +123.456e+12 (f) 123.456E-12
(c) +012.045e+07 (g) .1234
(d) 123.456f (h) -321.654E+3L
(25) Expressions may contain any of the following comment styles:
1. // .... \n
2. # .... \n
3. /* .... */
[16 - SIMPLE EXPRTK EXAMPLE]
--- snip ---
#include <cstdio>
#include <string>
#include "exprtk.hpp"
template <typename T>
struct myfunc : public exprtk::ifunction<T>
{
myfunc() : exprtk::ifunction<T>(2) {}
T operator()(const T& v1, const T& v2)
{
return T(1) + (v1 * v2) / T(3);
}
};
int main()
{
typedef exprtk::symbol_table<double> symbol_table_t;
typedef exprtk::expression<double> expression_t;
typedef exprtk::parser<double> parser_t;
typedef exprtk::parser_error::type error_t;
std::string expression_str =
"z := 2 myfunc([4 + sin(x / pi)^3],y ^ 2)";
double x = 1.1;
double y = 2.2;
double z = 3.3;
myfunc<double> mf;
symbol_table_t symbol_table;
symbol_table.add_constants();
symbol_table.add_variable("x",x);
symbol_table.add_variable("y",y);
symbol_table.add_variable("z",z);
symbol_table.add_function("myfunc",mf);
expression_t expression;
expression.register_symbol_table(symbol_table);
parser_t parser;
if (!parser.compile(expression_str,expression))
{
// A compilation error has occurred. Attempt to
// print all errors to stdout.
printf("Error: %s\tExpression: %s\n",
parser.error().c_str(),
expression_str.c_str());
for (std::size_t i = 0; i < parser.error_count(); ++i)
{
// Include the specific nature of each error
// and its position in the expression string.
error_t error = parser.get_error(i);
printf("Error: %02d Position: %02d "
"Type: [%s] "
"Message: %s "
"Expression: %s\n",
static_cast<int>(i),
static_cast<int>(error.token.position),
exprtk::parser_error::to_str(error.mode).c_str(),
error.diagnostic.c_str(),
expression_str.c_str());
}
return 1;
}
// Evaluate the expression and obtain its result.
double result = expression.value();
printf("Result: %10.5f\n",result);
return 0;
}
--- snip ---
[17 - BUILD OPTIONS]
When building ExprTk there are a number of defines that will enable or
disable certain features and capabilities. The defines can either be
part of a compiler command line switch or scoped around the include to
the ExprTk header.
(1) exprtk_enable_debugging
This define will enable printing of debug information during the
compilation process.
(2) exprtk_disable_comments
This define will disable the ability for expressions to have comments.
Expressions that have comments when parsed with a build that has this
option, will result in a compilation failure.
(3) exprtk_disable_break_continue
This define will disable the loop-wise 'break' and 'continue'
capabilities. Any expression that contains those keywords will result
in a compilation failure.
(4) exprtk_disable_sc_andor
This define will disable the short-circuit '&' (and) and '|' (or)
operators
(5) exprtk_disable_enhanced_features
This define will disable all enhanced features such as strength
reduction and special function optimisations and expression specific
type instantiations. This feature will reduce compilation times and
binary sizes but will also result in massive performance degradation
of expression evaluations.
(6) exprtk_disable_string_capabilities
This define will disable all string processing capabilities. Any
expression that contains a string or string related syntax will result
in a compilation failure.
[18 - FILES]
(00) Makefile
(01) readme.txt
(02) exprtk.hpp
(03) exprtk_test.cpp
(04) exprtk_benchmark.cpp
(05) exprtk_simple_example_01.cpp
(06) exprtk_simple_example_02.cpp
(07) exprtk_simple_example_03.cpp
(08) exprtk_simple_example_04.cpp
(09) exprtk_simple_example_05.cpp
(10) exprtk_simple_example_06.cpp
(11) exprtk_simple_example_07.cpp
(12) exprtk_simple_example_08.cpp
(13) exprtk_simple_example_09.cpp
(14) exprtk_simple_example_10.cpp
(15) exprtk_simple_example_11.cpp
(16) exprtk_simple_example_12.cpp
(17) exprtk_simple_example_13.cpp
(18) exprtk_simple_example_14.cpp
(19) exprtk_simple_example_15.cpp
(20) exprtk_simple_example_16.cpp
[19 - LANGUAGE STRUCTURE]
+-------------------------------------------------------------+
|00 - If Statement |
| |
| [if] ---> [(] ---> [condition] -+-> [,] -+ |
| | | |
| +---------------<---------------+ | |
| | | |
| | +------------------<------------------+ |
| | | |
| | +--> [consequent] ---> [,] ---> [alternative] ---> [)] |
| | |
| +--> [)] --+-> [{] ---> [expression*] ---> [}] --+ |
| | | |
| | +---------<----------+ |
| +----<-----+ | |
| | v |
| +--> [consequent] --> [;] -{*}-> [else-statement] |
| |
+-------------------------------------------------------------+
|01 - Else Statement |
| |
| [else] -+-> [alternative] ---> [;] |
| | |
| +--> [{] ---> [expression*] ---> [}] |
| | |
| +--> [if-statement] |
| |
+-------------------------------------------------------------+
|02 - Ternary Statement |
| |
| [condition] ---> [?] ---> [consequent] ---> [:] --+ |
| | |
| +------------------------<------------------------+ |
| | |
| +--> [alternative] --> [;] |
| |
+-------------------------------------------------------------+
|03 - While Loop |
| |
| [while] ---> [(] ---> [condition] ---> [)] ---+ |
| | |
| +----------------------<----------------------+ |
| | |
| +--> [{] ---> [expression*] ---> [}] |
| |
+-------------------------------------------------------------+
|04 - Repeat Until Loop |
| |
| [repeat] ---> [expression*] ---+ |
| | |
| +--------------<---------------+ |
| | |
| +--> [until] ---> [(] ---> [condition] --->[)] |
| |
+-------------------------------------------------------------+
|05 - For Loop |
| |
| [for] ---> [(] -+-> [initialise expression] --+--+ |
| | | | |
| +------------->---------------+ v |
| | |
| +-----------------------<------------------------+ |
| | |
| +--> [;] -+-> [condition] -+-> [;] ---+ |
| | | | |
| +------->--------+ v |
| | |
| +------------------<---------+--------+ |
| | | |
| +--> [increment expression] -+-> [)] --+ |
| | |
| +------------------<-------------------+ |
| | |
| +--> [{] ---> [expression*] ---> [}] |
| |
+-------------------------------------------------------------+
|06 - Switch Statement |
| |
| [switch] ---> [{] ---+ |
| | |
| +---------<----------+-----------<-----------+ |
| | | |
| +--> [case] ---> [condition] ---> [:] ---+ | |
| | | |
| +-------------------<--------------------+ | |
| | | |
| +--> [consequent] ---> [;] --------->--------+ |
| | | |
| | | |
| +--> [default] ---> [consequent] ---> [;] ---+ |
| | | |
| +---------------------<----------------------+ |
| | |
| +--> [}] |
| |
+-------------------------------------------------------------+
|07 - Multi Subexpression Statement |
| |
| +--------------<---------------+ |
| | | |
| [~] ---> [{\(] -+-> [expression] -+-> [;\,] ---+ |
| | |
| +----------------<----------------+ |
| | |
| +--> [}\)] |
| |
+-------------------------------------------------------------+
|08 - Multi Case-Consequent Statement |
| |
| [[*]] ---> [{] ---+ |
| | |
| +--------<--------+--------------<----------+ |
| | | |
| +--> [case] ---> [condition] ---> [:] ---+ | |
| | | |
| +-------------------<--------------------+ | |
| | | |
| +--> [consequent] ---> [;] ---+------>------+ |
| | |
| +--> [}] |
| |
+-------------------------------------------------------------+
|09 - Variable Definition Statement |
| |
| [var] ---> [symbol] -+-> [:=] ---> [expression] -+-> [;] |
| | | |
| +------------->-------------+ |
| |
+-------------------------------------------------------------+
|10 - Vector Definition Statement |
| |
| [var] ---> [symbol] ---> [[] ---> [constant] ---> []] --+ |
| | |
| +---------------------------<---------------------------+ |
| | |
| | +--------->---------+ |
| | | | |
| +--> [:=] ---> [{] -+-+-> [expression] -+-> [}] -+-> [;] |
| | | |
| +--<--- [,] <-----+ |
| |
+-------------------------------------------------------------+
About
C++ Mathematical Expression Parsing And Evaluation Library
Resources
Stars
Watchers
Forks
Releases
No releases published
Packages 0
No packages published
Languages
- C++ 99.9%
- Makefile 0.1%