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

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Arash Partow 2016-12-18 15:34:51 +11:00
parent 71bba0b6fa
commit 65c09ad7f8
2 changed files with 140 additions and 11 deletions
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3
Makefile
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@ -21,6 +21,9 @@ OPTIMIZATION_OPT = -O1
BASE_OPTIONS = -pedantic-errors -Wall -Wextra -Werror -Wno-long-long
OPTIONS = $(BASE_OPTIONS) $(OPTIMIZATION_OPT)
LINKER_OPT = -L/usr/lib -lstdc++ -lm
ASAN_OPT = -g -fsanitize=address -fno-omit-frame-pointer
MSAN_OPT = -g -fsanitize=memory -fno-omit-frame-pointer
LSAN_OPT = -g -fsanitize=leak -fno-omit-frame-pointer
BUILD_LIST+=exprtk_test
BUILD_LIST+=exprtk_benchmark

148
readme.txt
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@ -24,11 +24,12 @@ C++ Mathematical Expression Toolkit Library Documentation
Section 21 - Compilation Errors
Section 22 - Runtime Library Packages
Section 23 - Helpers & Utils
Section 24 - Exprtk Notes
Section 25 - Simple Exprtk Example
Section 26 - Build Options
Section 27 - Files
Section 28 - Language Structure
Section 24 - Benchmarking
Section 25 - Exprtk Notes
Section 26 - Simple Exprtk Example
Section 27 - Build Options
Section 28 - Files
Section 29 - Language Structure
[00 - INTRODUCTION]
@ -2489,7 +2490,7 @@ which obviously is not the intended outcome by the user. A possible
solution to this problem is for one to implement their own specific
USR that will perform a user defined business logic in determining if
an encountered unknown symbol should be treated as a variable or if it
should raise a compilation error. The following example demonstrated a
should raise a compilation error. The following example demonstrates a
simple user defined USR:
typedef exprtk::symbol_table<T> symbol_table_t;
@ -3438,7 +3439,132 @@ a name in string form. Example usage of the function is as follows:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[24 - EXPRTK NOTES]
[24 - BENCHMARKING]
As part of the ExprTk package there is an expression benchmark utility
named 'exprtk_benchmark'. The utility attempts to determine expression
evaluation speed (or rate of evaluations - evals per second), by
evaluating each expression numerous times and mutating the underlying
variables of the expression between each evaluation. The utility
assumes any valid ExprTk expression (containing conditionals, loops
etc), however it will only make use of a predefined set of scalar
variables, namely: a, b, c, x, y, z, w. That being said expressions
themselves can contain any number of local variables, vectors or
strings. There are two modes of operation:
(1) Default
(2) User Specified Expressions
(1) Default
The default mode is enabled simply by executing the exprtk_benchmark
binary with no command line parameters. In this mode a predefined set
of expressions will be evaluated in three phases:
(a) ExprTk evaluation
(b) Native evaluation
(c) ExprTk parse
In the first two phases (a and b) a list of predefined (hard-coded)
expressions will be evaluated using both ExprTk and native mode
implementations. This is done so as to compare evaluation times
between ExprTk and native implementations. The set of expressions used
are as follows:
(01) (y + x)
(02) 2 * (y + x)
(03) (2 * y + 2 * x)
(04) ((1.23 * x^2) / y) - 123.123
(05) (y + x / y) * (x - y / x)
(06) x / ((x + y) + (x - y)) / y
(07) 1 - ((x * y) + (y / x)) - 3
(08) (5.5 + x) + (2 * x - 2 / 3 * y) * (x / 3 + y / 4) + (y + 7.7)
(09) 1.1x^1 + 2.2y^2 - 3.3x^3 + 4.4y^15 - 5.5x^23 + 6.6y^55
(10) sin(2 * x) + cos(pi / y)
(11) 1 - sin(2 * x) + cos(pi / y)
(12) sqrt(111.111 - sin(2 * x) + cos(pi / y) / 333.333)
(13) (x^2 / sin(2 * pi / y)) - x / 2
(14) x + (cos(y - sin(2 / x * pi)) - sin(x - cos(2 * y / pi))) - y
(15) clamp(-1.0, sin(2 * pi * x) + cos(y / 2 * pi), +1.0)
(16) max(3.33, min(sqrt(1 - sin(2 * x) + cos(pi / y) / 3), 1.11))
(17) if((y + (x * 2.2)) <= (x + y + 1.1), x - y, x*y) + 2 * pi / x
The third and final phase (c), is used to determine average
compilation rates (compiles per second) for expressions of varying
complexity. Each expression is compiled 100K times and the average for
each expression is output.
(2) User Specified Expressions
In this mode two parameters are passed to the utility via the command
line:
(a) A name of a text file containing one expression per line
(b) An integer representing the number of evaluations per expression
An example execution of the benchmark utility in this mode is as
follows:
./exprtk_benchmark my_expressions.txt 1000000
The above invocation will load the expressions from the file
'my_expressions.txt' and will then proceed to evaluate each expression
one million times, varying the above mentioned variables (x, y, z
etc.) between each evaluation, and at the end of each expression round
a print out of running times, result of a single evaluation and total
sum of results is provided as demonstrated below:
Expression 1 of 7 4.770 ns 47700 ns ( 9370368.0) '((((x+y)+z)))'
Expression 2 of 7 4.750 ns 47500 ns ( 1123455.9) '((((x+y)-z)))'
Expression 3 of 7 4.766 ns 47659 ns (21635410.7) '((((x+y)*z)))'
Expression 4 of 7 5.662 ns 56619 ns ( 1272454.9) '((((x+y)/z)))'
Expression 5 of 7 4.950 ns 49500 ns ( 4123455.9) '((((x-y)+z)))'
Expression 6 of 7 7.581 ns 75810 ns (-4123455.9) '((((x-y)-z)))'
Expression 7 of 7 4.801 ns 48010 ns ( 0.0) '((((x-y)*z)))'
The benchmark utility can be very useful when investigating evaluation
efficiency issues with ExprTk or simply during the prototyping of
expressions. As an example, lets take the following expression:
1 / sqrt(2x) * e^(3y)
Let's say we would like to determine which sub-part of the expression
takes the most time to evaluate and perhaps attempt to rework the
expression based on the results. In order to do this we will create a
text file called 'test.txt' and then proceed to make some educated
guesses about how to break the expression up into its more
'interesting' sub-parts which we will then add as one expression per
line to the file. An example breakdown may be as follows:
1 / sqrt(2x) * e^(3y)
1 / sqrt(2x)
e^(3y)
The benchmark with the given file, where each expression will be
evaluated 100K times can be executed as follows:
./exprtk_benchmark test.txt 100000
Expr 1 of 3 90.340 ns 9034000 ns (296417859.3) '1/sqrt(2x)*e^(3y)'
Expr 2 of 3 11.100 ns 1109999 ns ( 44267.3) '1/sqrt(2x)'
Expr 3 of 3 77.830 ns 7783000 ns (615985286.6) 'e^(3y)'
[*] Number Of Evals: 300000
[*] Total Time: 0.018sec
[*] Total Single Eval Time: 0.000ms
From the results above we can see that the third expression (e^(3y))
consumes the largest amount of time and should perhaps be replaced
with the 'exp' function for more efficient evaluation.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[25 - EXPRTK NOTES]
The following is a list of facts and suggestions one may want to take
into account when using ExprTk:
@ -3639,7 +3765,7 @@ into account when using ExprTk:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[25 - SIMPLE EXPRTK EXAMPLE]
[26 - SIMPLE EXPRTK EXAMPLE]
The following is a simple yet complete example demonstrating typical
usage of the ExprTk Library. The example instantiates a symbol table
object, adding to it three variables named x, y and z, and a custom
@ -3744,7 +3870,7 @@ int main()
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[26 - BUILD OPTIONS]
[27 - 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
@ -3811,7 +3937,7 @@ error.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[27 - FILES]
[28 - FILES]
The source distribution of ExprTk is comprised of the following set of
files:
@ -3842,7 +3968,7 @@ files:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[28 - LANGUAGE STRUCTURE]
[29 - LANGUAGE STRUCTURE]
+-------------------------------------------------------------+
|00 - If Statement |
| |