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C++ Mathematical Expression Library (ExprTk) http://www.partow.net/programming/exprtk/index.html

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Arash Partow
2014-10-14 22:06:52 +11:00
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@ -706,17 +706,19 @@ 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)
(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)
(k) '%' '=' ---> '%=' (modulo assignment)
(l) '<=' '>' ---> '<=>' (swap)
An example of the transformation that takes place is as follows:
@ -917,6 +919,25 @@ will be returned. Where as for vectors, the value of the first element
(eg: v[0]) will be returned.
(4) Variable/Vector Assignment
The value of a variable can be assigned to a vector and a vector or a
vector expression can be assigned to a variable.
(a) Variable To Vector:
Every element of the vector is assigned the value of the variable
or expression.
var x := 3;
var y[3] := {1,2,3};
y := x + 1;
(b) Vector To Variable:
The variable is assigned the value of the first element of the
vector (aka vec[0])
var x := 3;
var y[3] := {1,2,3};
x := y + 1;
[13 - VECTOR PROCESSING]
ExprTk provides support for various forms of vector oriented
@ -932,14 +953,15 @@ with vectors:
(a) Arithmetic: +, -, *, /, %
(b) Exponentiation: vector ^ scalar
(c) Assignment: :=, +=, -=, *=, /=, %=
(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
abs, acos, acosh, asin, asinh, atan, atanh, ceil, cos, cosh,
cot, csc, deg2grad, deg2rad, erf, erfc, exp, expm1, floor,
frac, grad2deg, log, log10, log1p, log2, rad2deg, round, sec,
sgn, sin, sinc, sinh, sqrt, swap, tan, tanh, trunc
(f) Aggregate and Reduce operations:
avg, max, min, mul, sum
Note: When one of the above described operations is being performed
between two vectors, the operation will only span the size of the
@ -968,6 +990,27 @@ the previously mentioned dot-product computation expression:
}
Note: In the scenario of inequalities between two vectors, the result
is not a vector but rather a singular variable denoting a boolean
state of either 'true' or 'false' depending on the nature of the
inequality.
var x[3] := {1,1,1};
var y[3] := {3,2,1};
y > x == false
Note: When the aggregate operations denoted above are used in
conjunction with a vector or vector expression, the return value is
not a vector but rather a single value.
var x[3] := {1,2,3};
sum(1 + 2x) == 15
7 == avg(3x + 1)
[14 - USER DEFINED FUNCTIONS]
ExprTk provides a means whereby custom functions can be defined and
@ -1057,13 +1100,10 @@ demonstrates how all the pieces are put together:
(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.
All function calls are assumed to have side-effects by default. This
assumption implicitly disables constant folding optimisations when all
parameters being passed to the function are deduced as being constants
at compile time.
If it is certain that the function being registered does not have any
side effects and can be correctly constant folded where appropriate,
@ -1102,7 +1142,7 @@ into account when using Exprtk:
(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.
(02) Supported types are float, double, long double and MPFR/GMP.
(03) Standard mathematical operator precedence is applied (BEDMAS).
@ -1113,9 +1153,10 @@ into account when using Exprtk:
(05) Supported user defined types are numeric and string variables
and functions.
(06) All variable and function names are case-insensitive.
(06) All reserved and key words, variable, vector and function names
are case-insensitive.
(07) Variable and function names must begin with a letter
(07) Variable, vector 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)
@ -1139,10 +1180,10 @@ into account when using Exprtk:
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 (~!@#$%^&*()[]|=+ ,./?<>;:"`~_), and must
be enclosed with single-quotes.
eg: 'Frankly my dear, I do not give a damn!'
(13) Strings may be comprised of any combination of letters, digits
or special characters including (~!@#$%^&*()[]|=+ ,./?<>;:"`~_),
and must be enclosed with single-quotes.
eg: 'Frankly my dear, 1 do n0t give a damn!'
(14) User defined normal functions can have up to 20 parameters,
where as user defined vararg-functions can have an unlimited
@ -1175,9 +1216,9 @@ into account when using Exprtk:
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.
is one-to-many. Hence the intended use case where possible 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
@ -1197,6 +1238,28 @@ into account when using Exprtk:
2. # .... \n
3. /* .... */
(26) Every ExprTk statement is a "value returning" expression. Unlike
some languages that limit the types of expressions that can be
performed in certain situations, in ExprTk any valid expression
can be used in any "value consuming" context. Eg:
var y := 3;
for (var x := switch
{
case 1 : 7;
case 2 : -1 + ~{var x{};};
default: y > 2 ? 3 : 4;
};
x != while (y > 0) { y -= 1; };
x -= {if(min(x,y) < 2 * max(x,y))
x + 2;
else
x + y - 3;}
)
{
(x + y) / (x - y);
}
[16 - SIMPLE EXPRTK EXAMPLE]
@ -1294,8 +1357,8 @@ 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.
This define will enable printing of debug information to stdout during
the compilation process.
(2) exprtk_disable_comments
This define will disable the ability for expressions to have comments.