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

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Arash Partow
2013-03-12 00:29:59 +11:00
parent 73a594675e
commit 7ead3055af
4 changed files with 647 additions and 708 deletions
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1116
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", "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)", "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))", "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); 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) 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("log(2.7182818284590451)",1.0),
test_t("log10(10.0)",1.0), test_t("log10(10.0)",1.0),
test_t("frac(12.34) + trunc(12.34)",12.34), test_t("frac(12.34) + trunc(12.34)",12.34),
test_t("hyp(3.0,4.0)",5.0), test_t("hypot(3.0,4.0)",5.0),
test_t("hyp(1.0,sqrt(3.0))",2.0), test_t("hypot(1.0,sqrt(3.0))",2.0),
test_t("if(1 < 2, 3, 4)",3.0), 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(1.1 < 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), 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: +, -, *, /, %, ^ (1) Basic operators: +, -, *, /, %, ^
(2) Functions: min, max, avg, sum, abs, ceil, floor, round, (2) Functions: min, max, avg, sum, abs, ceil, floor, round,
roundn, exp, log, log10, logn, root, sqrt, roundn, exp, log, log10, logn, log1p, root,
clamp, inrange, sgn, erf, erfc, frac, trunc sqrt, clamp, inrange, sgn, erf, erfc, frac,
trunc
(3) Trigonometry: sin, cos, tan, acos, asin, atan, atan2, cosh, (3) Trigonometry: sin, cos, tan, acos, asin, atan, atan2, cosh,
cot, csc, sec, sinh, tanh, rad2deg, deg2rad, cot, csc, sec, sinh, tanh, rad2deg, deg2rad,
deg2grad, grad2deg, hyp deg2grad, grad2deg, hypot
(4) Equalities & (4) Equalities &
Inequalities: =, ==, <>, !=, <, <=, >, >= Inequalities: =, ==, <>, !=, <, <=, >, >=
@ -34,10 +35,10 @@ operations, functions and processes:
(7) Assignment: := (7) Assignment: :=
(8) Calculus: numerical integration and differentiation (8) String
processing: in, like, ilike
Note 1: Normal mathematical operator precedence is applied (BEDMAS). (9) Calculus: numerical integration and differentiation
Note 2: The trigonometry functions assume radians as input.
@ -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] [SPECIAL FUNCTIONS]
The purpose of special functions in ExprTk is to provide compiler The purpose of special functions in ExprTk is to provide compiler
generated equivalents of common mathematical expressions which can be generated equivalents of common mathematical expressions which can be
invoked by using the 'special function' syntax (eg: $f12(x,y,z) or 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 Special functions dramatically decrease the total evaluation time of
expressions which would otherwise have been written using the common 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 --- --- snip ---
#include <cstdio> #include <cstdio>
#include <string> #include <string>