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

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Arash Partow
2013-03-15 08:38:09 +11:00
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readme.txt
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@ -13,32 +13,32 @@ extendible.
The ExprTk evaluator supports the following fundamental mathematical
operations, functions and processes:
(1) Basic operators: +, -, *, /, %, ^
(0) Basic operators: +, -, *, /, %, ^
(2) Functions: min, max, avg, sum, abs, ceil, floor, round,
(1) Functions: min, max, avg, sum, abs, ceil, floor, round,
roundn, exp, log, log10, logn, log1p, root,
sqrt, clamp, inrange, sgn, erf, erfc, frac,
trunc
(3) Trigonometry: sin, cos, tan, acos, asin, atan, atan2, cosh,
(2) Trigonometry: sin, cos, tan, acos, asin, atan, atan2, cosh,
cot, csc, sec, sinh, tanh, rad2deg, deg2rad,
deg2grad, grad2deg, hypot
(4) Equalities &
(3) Equalities &
Inequalities: =, ==, <>, !=, <, <=, >, >=
(5) Boolean logic: and, or, xor, not, nand, nor, shr, shl, true,
false
(4) Boolean logic: and, or, xor, xnor, not, nand, nor, shr, shl,
true, false
(6) Conditional &
(5) Conditional &
Loop statement: if-then-else, while
(7) Assignment: :=
(6) Assignment: :=
(8) String
(7) String
processing: in, like, ilike
(9) Calculus: numerical integration and differentiation
(8) Calculus: numerical integration and differentiation
@ -106,6 +106,7 @@ Expression Library can be found at:
(*) PGI C++ (10.x+)
(*) Microsoft Visual Studio C++ Compiler (8.1+)
(*) Comeau C++ Compiler (4.3+)
(*) IBM XL C/C++ (10.x+)
@ -135,7 +136,7 @@ Expression Library can be found at:
+-----------+--------------------------------------------------------+
| OPERATOR | DEFINITION |
+-----------+--------------------------------------------------------+
| == or = | True only if x is strictly equal to y. (eg: x == y) |
| == 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) |
+-----------+--------------------------------------------------------+
@ -170,9 +171,12 @@ Expression Library can be found at:
+-----------+--------------------------------------------------------+
| or | Logical OR, True if either x or y is true. (eg: x or y)|
+-----------+--------------------------------------------------------+
| xor | Local XOR, True only if the logical states of x and 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) |
+-----------+--------------------------------------------------------+
| if | If x is true then return y else return z. |
| | (eg: if(x, y, z) or if((x + 1) > 2y, z + 1, w / v)) |
+-----------+--------------------------------------------------------+
@ -183,7 +187,7 @@ Expression Library can be found at:
+-----------+--------------------------------------------------------+
| abs | Absolute value of x. |
+-----------+--------------------------------------------------------+
| avg | The average of all the inputs. |
| avg | Average of all the inputs. |
| | (eg: avg(x,y,z,w) == (x+y+z+w)/4) |
+-----------+--------------------------------------------------------+
| ceil | Smallest integer that is greater than or equal to x. |
@ -203,18 +207,18 @@ Expression Library can be found at:
+-----------+--------------------------------------------------------+
| frac | Fractional portion of x |
+-----------+--------------------------------------------------------+
| hypot | Hypotenuse of x and y (eg: hypot(x,y)) |
| hypot | Hypotenuse of x and y (eg: hypot(x,y) = sqrt(x*x +y*y))|
+-----------+--------------------------------------------------------+
| log | Natural logarithm of x |
+-----------+--------------------------------------------------------+
| log10 | Base 10 logarithm of x |
+-----------+--------------------------------------------------------+
| log1p | Natural logarithm of 1 + x, where x is very small. |
| | (eg: log1p(x)) |
+-----------+--------------------------------------------------------+
| logn | Base N logarithm of x (eg: logn(1235,8)) |
| | where n > 0 and is an integer. |
+-----------+--------------------------------------------------------+
| log1p | Natural logarithm of 1 + x (eg: log1p(x)) |
| | where x is very small. |
+-----------+--------------------------------------------------------+
| nequal | Not-equal test between x and y using normalized epsilon|
+-----------+--------------------------------------------------------+
| root | Nth-Root of x (eg: root(x,3)) |
@ -229,7 +233,7 @@ Expression Library can be found at:
+-----------+--------------------------------------------------------+
| sqrt | Square root of x, where x > 0 |
+-----------+--------------------------------------------------------+
| sum | The sum of all the inputs. |
| sum | Sum of all the inputs. |
| | (eg: sum(x,y,z,w,v) == (x+y+z+w+v)) |
+-----------+--------------------------------------------------------+
| trunc | Integer portion of x |
@ -265,12 +269,12 @@ Expression Library can be found at:
+-----------+--------------------------------------------------------+
| tanh | Hyperbolic tangent of x |
+-----------+--------------------------------------------------------+
| rad2deg | Convert x from radians to degrees |
+-----------+--------------------------------------------------------+
| deg2rad | Convert x from degrees to radians |
+-----------+--------------------------------------------------------+
| deg2grad | Convert x from degrees to gradians |
+-----------+--------------------------------------------------------+
| rad2deg | Convert x from radians to degrees |
+-----------+--------------------------------------------------------+
| grad2deg | Convert x from gradians to degrees |
+-----------+--------------------------------------------------------+
@ -284,25 +288,25 @@ Expression Library can be found at:
| 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*') |
| | (eg: x like y or 'abcdefgh' like 'a?d*h') |
+-----------+--------------------------------------------------------+
| like | 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 'abcdefgh' like 'a?d*') |
| | (eg: x ilike y or 'a1B2c3D4e5F6g7H' like 'a?d*h') |
+-----------+--------------------------------------------------------+
[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
$f24(x,y,z,w)). Where possible, for sub-expressions that are comprised
of combinations of variables and literal values the ExprTk compiler
will perform a best effort attempt to replace such expressions with
special functions.
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 C++ compiler's ability to
select an appropriate set of instructions for the given expression and
architecture so as to provide the most optimal and precision sensitive
result.
Special functions dramatically decrease the total evaluation time of
expressions which would otherwise have been written using the common
@ -370,27 +374,42 @@ correctly optimize such expressions for a given architecture.
[EXPRTK NOTES]
(0) Supported types are float, double and long double.
(00) Supported types are float, double and long double.
(1) Standard mathematical operator precedence is applied (BEDMAS).
(01) Standard mathematical operator precedence is applied (BEDMAS).
(2) All variables and functions are case-insensitive
(02) Supported user defined types are numeric and string variables
and functions.
(3) Expression lengths are limited only by storage capacity.
(03) All variable and function names are case-insensitive
(4) Equal/Nequal routines use epsilons of 0.00000000001 and 0.000001
for double and float types respectively.
(04) 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)
(5) All trigonometric functions assume radian input unless
stated otherwise.
(05) Expression lengths are limited only by storage capacity.
(6) Expressions can contain white-space characters such as
space, tabs, new-lines, control-feed et al.
('\n', '\r', '\t', '\b', '\v', '\f')
(06) Equal/Nequal routines use epsilons of 0.0000000001 and 0.000001
for double and float types respectively.
(7) User defined functions can have up to 20 parameters.
(07) All trigonometric functions assume radian input unless
stated otherwise.
(8) Polynomial functions can be at most of degree 10.
(08) Expressions may contain white-space characters such as
space, tabs, new-lines, control-feed et al.
('\n', '\r', '\t', '\b', '\v', '\f')
(09) 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 don't give a damn!'
(10) User defined functions can have up to 20 parameters.
(11) Polynomial functions can be at most of degree 10.
(12) Where appropriate constant folding optimisations will be
applied. (eg: The expression '2+(3-(x/y))' becomes '5-(x/y)')