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

This commit is contained in:
Arash Partow 2013-03-12 00:29:59 +11:00
parent 73a594675e
commit 7ead3055af
4 changed files with 647 additions and 708 deletions
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1102
exprtk.hpp
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File diff suppressed because it is too large Load Diff

4
exprtk_benchmark.cpp
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@ -40,7 +40,7 @@ const std::string expression_list[] = {
"x + (cos(y - sin(2 / x * pi)) - sin(x - cos(2 * y / pi))) - y",
"clamp(-1.0, sin(2 * pi * x) + cos(y / 2 * pi), +1.0)",
"max(3.33, min(sqrt(1 - sin(2 * x) + cos(pi / y) / 3), 1.11))",
"if(avg(x,y) <= x + y, x - y, x * y) + 2 * pi / x"
"if((y + (x * 2.2)) <= (x + y + 1.1), x - y, x * y) + 2 * pi / x"
};
const std::size_t expression_list_size = sizeof(expression_list) / sizeof(std::string);
@ -257,7 +257,7 @@ struct native
static inline T func15(Type x, Type y)
{
return ((avg(x,y) <= x + y) ? x - y : x * y) + T(2.0) * pi / x;
return (((y + (x * 2.2)) <= (x + y + 1.1)) ? x - y : x * y) + T(2.0) * pi / x;
}
};

4
exprtk_test.cpp
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@ -600,8 +600,8 @@ static const test_t test_list[] =
test_t("log(2.7182818284590451)",1.0),
test_t("log10(10.0)",1.0),
test_t("frac(12.34) + trunc(12.34)",12.34),
test_t("hyp(3.0,4.0)",5.0),
test_t("hyp(1.0,sqrt(3.0))",2.0),
test_t("hypot(3.0,4.0)",5.0),
test_t("hypot(1.0,sqrt(3.0))",2.0),
test_t("if(1 < 2, 3, 4)",3.0),
test_t("if(1.1 < 2.2, 3.3, 4.4)",3.3),
test_t("if((1.0+1.1) < (2.0+1.2), 3.3, 4.4)",3.3),

231
readme.txt
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@ -16,12 +16,13 @@ operations, functions and processes:
(1) Basic operators: +, -, *, /, %, ^
(2) Functions: min, max, avg, sum, abs, ceil, floor, round,
roundn, exp, log, log10, logn, root, sqrt,
clamp, inrange, sgn, erf, erfc, frac, trunc
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,
cot, csc, sec, sinh, tanh, rad2deg, deg2rad,
deg2grad, grad2deg, hyp
deg2grad, grad2deg, hypot
(4) Equalities &
Inequalities: =, ==, <>, !=, <, <=, >, >=
@ -34,10 +35,10 @@ operations, functions and processes:
(7) Assignment: :=
(8) Calculus: numerical integration and differentiation
(8) String
processing: in, like, ilike
Note 1: Normal mathematical operator precedence is applied (BEDMAS).
Note 2: The trigonometry functions assume radians as input.
(9) Calculus: numerical integration and differentiation
@ -108,11 +109,200 @@ Expression Library can be found at:
[BUILT-IN OPERATIONS & FUNCTIONS]
(0) Basic 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. (eg: y := x) |
| | where y is a variable type. |
+-----------+--------------------------------------------------------+
(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 less than y. (eg: x < y) |
+-----------+--------------------------------------------------------+
| <= | True only if x less than or equal to y. (eg: x <= y) |
+-----------+--------------------------------------------------------+
| > | True only if x 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) |
+-----------+--------------------------------------------------------+
| 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 | Local XOR, True only if the logical states of x and y |
| | differ. (eg: x xor 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)) |
+-----------+--------------------------------------------------------+
(3) General Purpose Functions
+-----------+--------------------------------------------------------+
| FUNCTION | DEFINITION |
+-----------+--------------------------------------------------------+
| abs | Absolute value of x. |
+-----------+--------------------------------------------------------+
| avg | The 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. |
+-----------+--------------------------------------------------------+
| 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 |
+-----------+--------------------------------------------------------+
| erfc | Complimentary error function of x |
+-----------+--------------------------------------------------------+
| exp | e to the power of x |
+-----------+--------------------------------------------------------+
| floor | Largest integer that is less than or equal to x. |
+-----------+--------------------------------------------------------+
| frac | Fractional portion of x |
+-----------+--------------------------------------------------------+
| hypot | Hypotenuse of x and y (eg: hypot(x,y)) |
+-----------+--------------------------------------------------------+
| log | Natural logarithm of x |
+-----------+--------------------------------------------------------+
| log10 | Base 10 logarithm of 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)) |
| | where n > 0 and is an integer. |
+-----------+--------------------------------------------------------+
| round | Round x to the nearest integer. |
+-----------+--------------------------------------------------------+
| roundn | Round x to the n decimal places (eg: roundn(x,4)) |
| | where n > 0 and is an integer. |
+-----------+--------------------------------------------------------+
| sgn | Sign of x, -1 where x < 0, +1 where x > 0, else zero. |
+-----------+--------------------------------------------------------+
| sqrt | Square root of x, where x > 0 |
+-----------+--------------------------------------------------------+
| sum | The sum of all the inputs. |
| | (eg: sum(x,y,z,w,v) == (x+y+z+w+v)) |
+-----------+--------------------------------------------------------+
| trunc | Integer portion of x |
+-----------+--------------------------------------------------------+
(4) Trigonometry Functions
+-----------+--------------------------------------------------------+
| FUNCTION | DEFINITION |
+-----------+--------------------------------------------------------+
| acos | Arc cosine of x expressed in radians. Interval [-1,+1] |
+-----------+--------------------------------------------------------+
| asin | Arc sine of x expressed in radians. Interval [-1,+1] |
+-----------+--------------------------------------------------------+
| atan | Arc tangent of x expressed in radians. Interval [-1,+1]|
+-----------+--------------------------------------------------------+
| atan2 | Arc tangent of x expressed in radians. Interval [-1,+1]|
+-----------+--------------------------------------------------------+
| cos | Cosine of x |
+-----------+--------------------------------------------------------+
| cosh | Hyperbolic cosine of x |
+-----------+--------------------------------------------------------+
| cot | Cotangent of x |
+-----------+--------------------------------------------------------+
| csc | Cosecant of x |
+-----------+--------------------------------------------------------+
| sec | Secant of x |
+-----------+--------------------------------------------------------+
| sin | Sine of x |
+-----------+--------------------------------------------------------+
| sinh | Hyperbolic sine of x |
+-----------+--------------------------------------------------------+
| tan | Tangent of x |
+-----------+--------------------------------------------------------+
| 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 |
+-----------+--------------------------------------------------------+
| grad2deg | Convert x from gradians to degrees |
+-----------+--------------------------------------------------------+
(5) String Processing
+-----------+--------------------------------------------------------+
| FUNCTION | DEFINITION |
+-----------+--------------------------------------------------------+
| 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*') |
+-----------+--------------------------------------------------------+
| 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*') |
+-----------+--------------------------------------------------------+
[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)).
$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
@ -179,7 +369,32 @@ correctly optimize such expressions for a given architecture.
[SIMPLE EXAMPLE]
[EXPRTK NOTES]
(0) Supported types are float, double and long double.
(1) Standard mathematical operator precedence is applied (BEDMAS).
(2) All variables and functions are case-insensitive
(3) Expression lengths are limited only by storage capacity.
(4) Equal/Nequal routines use epsilons of 0.00000000001 and 0.000001
for double and float types respectively.
(5) All trigonometric functions assume radian input unless
stated otherwise.
(6) Expressions can contain white-space characters such as
space, tabs, new-lines, control-feed et al.
('\n', '\r', '\t', '\b', '\v', '\f')
(7) User defined functions can have up to 20 parameters.
(8) Polynomial functions can be at most of degree 10.
[SIMPLE EXPRTK EXAMPLE]
--- snip ---
#include <cstdio>
#include <string>