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

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Arash Partow
2013-03-05 00:21:28 +11:00
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@ -36,7 +36,8 @@ operations, functions and processes:
(8) Calculus: numerical integration and differentiation
Note: The trigonometry functions assume radians as input.
Note 1: Normal mathematical operator precedence is applied (BEDMAS).
Note 2: The trigonometry functions assume radians as input.
@ -119,127 +120,62 @@ form by reducing the total number of nodes in the evaluation tree of
an expression and by also leveraging the compiler's ability to
correctly optimize such expressions for a given architecture.
3-Parameter 4-Parameter
+-------------+-------------+ +--------------+------------------+
| Prototype | Operation | | Prototype | Operation |
+-------------+-------------+ +--------------+------------------+
sf00(x,y,z) | (x + y) / z sf35(x,y,z,w) | x + ((y + z) / w)
sf01(x,y,z) | (x + y) * z sf36(x,y,z,w) | x + ((y + z) * w)
sf02(x,y,z) | (x - y) / z sf37(x,y,z,w) | x + ((y - z) / w)
sf03(x,y,z) | (x - y) * z sf38(x,y,z,w) | x + ((y - z) * w)
sf04(x,y,z) | (x * y) + z sf39(x,y,z,w) | x + ((y * z) / w)
sf05(x,y,z) | (x * y) - z sf40(x,y,z,w) | x + ((y * z) * w)
sf06(x,y,z) | (x * y) / z sf41(x,y,z,w) | x + ((y / z) + w)
sf07(x,y,z) | (x * y) * z sf42(x,y,z,w) | x + ((y / z) / w)
sf08(x,y,z) | (x / y) + z sf43(x,y,z,w) | x + ((y / z) * w)
sf09(x,y,z) | (x / y) - z sf44(x,y,z,w) | x - ((y + z) / w)
sf10(x,y,z) | (x / y) / z sf45(x,y,z,w) | x - ((y + z) * w)
sf11(x,y,z) | (x / y) * z sf46(x,y,z,w) | x - ((y - z) / w)
sf12(x,y,z) | x / (y + z) sf47(x,y,z,w) | x - ((y - z) * w)
sf13(x,y,z) | x / (y - z) sf48(x,y,z,w) | x - ((y * z) / w)
sf14(x,y,z) | x / (y * z) sf49(x,y,z,w) | x - ((y * z) * w)
sf15(x,y,z) | x / (y / z) sf50(x,y,z,w) | x - ((y / z) / w)
sf16(x,y,z) | x - (y / z) sf51(x,y,z,w) | x - ((y / z) * w)
sf17(x,y,z) | x - (y / z) sf52(x,y,z,w) | ((x + y) * z) - w
sf18(x,y,z) | x * y^2 + z sf53(x,y,z,w) | ((x - y) * z) - w
sf19(x,y,z) | x * y^3 + z sf54(x,y,z,w) | ((x * y) * z) - w
sf20(x,y,z) | x * y^4 + z sf55(x,y,z,w) | ((x / y) * z) - w
sf21(x,y,z) | x * y^5 + z sf56(x,y,z,w) | ((x + y) / z) - w
sf22(x,y,z) | x * y^6 + z sf57(x,y,z,w) | ((x - y) / z) - w
sf23(x,y,z) | x * y^7 + z sf58(x,y,z,w) | ((x * y) / z) - w
sf24(x,y,z) | x * y^8 + z sf59(x,y,z,w) | ((x / y) / z) - w
sf25(x,y,z) | x * y^9 + z sf60(x,y,z,w) | (x * y) + (z * w)
sf26(x,y,z) | x * log(y)+z sf61(x,y,z,w) | (x * y) - (z * w)
sf27(x,y,z) | x * log(y)-z sf62(x,y,z,w) | (x * y) + (z / w)
sf28(x,y,z) | x * log10(y)+z sf63(x,y,z,w) | (x * y) - (z / w)
sf29(x,y,z) | x * log10(y)-z sf64(x,y,z,w) | (x / y) + (z / w)
sf30(x,y,z) | x * sin(y)+z sf65(x,y,z,w) | (x / y) - (z / w)
sf31(x,y,z) | x * sin(y)-z sf66(x,y,z,w) | (x / y) - (z * w)
sf32(x,y,z) | x * cos(y)+z sf67(x,y,z,w) | x * y^2 + z * w^2
sf33(x,y,z) | x * cos(y)-z sf68(x,y,z,w) | x * y^3 + z * w^3
sf34(x,y,z) | x ? y : z sf69(x,y,z,w) | x * y^4 + z * w^4
sf70(x,y,z,w) | x * y^5 + z * w^5
sf71(x,y,z,w) | x * y^6 + z * w^6
sf72(x,y,z,w) | x * y^7 + z * w^7
sf73(x,y,z,w) | x * y^8 + z * w^8
sf74(x,y,z,w) | x * y^9 + z * w^9
sf75(x,y,z,w) | (x and y) ? z : w
sf76(x,y,z,w) | (x or y) ? z : w
sf77(x,y,z,w) | (x < y) ? z : w
sf78(x,y,z,w) | (x <= y) ? z : w
sf79(x,y,z,w) | (x > y) ? z : w
sf80(x,y,z,w) | (x >= y) ? z : w
sf81(x,y,z,w) | (x == y) ? z : w
sf82(x,y,z,w) | x*sin(y) + z*cos(w)
[MACROS]
ExprTk utilizes certain macros to modify the underlying behaviour of
the parser and the evaluation engine. The following macros are used to
switch off certain capabilities within the ExprTk evaluation engine.
The capabilities are predominantly related to expression optimisations
and the ability to evaluate strings within expressions.
(1) exprtk_disable_string_capabilities
(2) exprtk_disable_cardinal_pow_optimisation
(3) exprtk_disable_extended_optimisations
(4) exprtk_disable_extended_operator_optimizations
(5) exprtk_lean_and_mean
(6) exprtk_lean_and_mean_numeric_only
(7) exprtk_enable_all_optimizations
(1) "exprtk_disable_string_capabilities"
If defined, the macro will disable all string processing capabilities.
When defined, if an expression containing a string or string related
action is encountered, a compilation error will be raised by the
parser.
(2) "exprtk_disable_cardinal_pow_optimisation"
If defined, the macro will disable the special case regarding
exponentiation of a variable to an integer constant (where the
constant is <= 60). Defining this variable may be desirable if the
error magnitude of the results using this special case are intolerable
with regards to the precision required. When defined, the pow function
used for all other powers will be invoked.
(3) "exprtk_disable_extended_optimisations"
If defined, the macro will disable the third tier optimisations. This
group of optimisations creates roughly 4K type instantiations. This
large number of type and branch instantiations in one translation unit
may cause some older compilers to crash or not be able to properly
compile ExprTk. If such compiler problems are encountered it is
recommended to test having this particular macro defined. It should
also be noted that some of the third tier optimisations are also
available through the predefined 'special functions', however these
require that expressions utilize them explicitly.
(4) "exprtk_disable_extended_operator_optimizations"
By default most of the mathematical operators are included as part of
the optimisation process. However if this macro is defined, then only
the basic mathematical operators (+,-,*,/,^) will be included.
(5) "exprtk_lean_and_mean"
The default mode of ExprTk is lean and mean. This macro encompasses
both modes [3] and [4].
(6) "exprtk_lean_and_mean_numeric_only"
The mode when this macro is defined, is 'lean and mean' coupled with
all string capabilities disabled [1].
(7) "exprtk_enable_all_optimizations"
When defined all optimization mechanisms are turned on, including all
string processing related optimizations. In short nothing is disabled.
This mode will cause older C++ compilers and or compilers running on
slower machines with limited RAM to nearly come to a grinding halt as
per (3). This mode will however produce the most efficient and high
performance expression evaluation results. It is advised to have this
mode turned on for final builds and not to be used during the
development cycle.
Note: Foregoing a few extra clock cycles during compilation in
exchange for a dramatic increase in performance during run-time is
always a worthy undertaking.
3-Parameter 4-Parameter
+-------------+-------------+ +--------------+------------------+
| Prototype | Operation | | Prototype | Operation |
+-------------+-------------+ +--------------+------------------+
$f00(x,y,z) | (x + y) / z $f46(x,y,z,w) | x + ((y + z) / w)
$f01(x,y,z) | (x + y) * z $f47(x,y,z,w) | x + ((y + z) * w)
$f02(x,y,z) | (x + y) - z $f48(x,y,z,w) | x + ((y - z) / w)
$f03(x,y,z) | (x + y) + z $f49(x,y,z,w) | x + ((y - z) * w)
$f04(x,y,z) | (x - y) / z $f50(x,y,z,w) | x + ((y * z) / w)
$f05(x,y,z) | (x - y) * z $f51(x,y,z,w) | x + ((y * z) * w)
$f06(x,y,z) | (x * y) + z $f52(x,y,z,w) | x + ((y / z) + w)
$f07(x,y,z) | (x * y) - z $f53(x,y,z,w) | x + ((y / z) / w)
$f08(x,y,z) | (x * y) / z $f54(x,y,z,w) | x + ((y / z) * w)
$f09(x,y,z) | (x * y) * z $f55(x,y,z,w) | x - ((y + z) / w)
$f10(x,y,z) | (x / y) + z $f56(x,y,z,w) | x - ((y + z) * w)
$f11(x,y,z) | (x / y) - z $f57(x,y,z,w) | x - ((y - z) / w)
$f12(x,y,z) | (x / y) / z $f58(x,y,z,w) | x - ((y - z) * w)
$f13(x,y,z) | (x / y) * z $f59(x,y,z,w) | x - ((y * z) / w)
$f14(x,y,z) | x / (y + z) $f60(x,y,z,w) | x - ((y * z) * w)
$f15(x,y,z) | x / (y - z) $f61(x,y,z,w) | x - ((y / z) / w)
$f16(x,y,z) | x / (y * z) $f62(x,y,z,w) | x - ((y / z) * w)
$f17(x,y,z) | x / (y / z) $f63(x,y,z,w) | ((x + y) * z) - w
$f18(x,y,z) | x * (y + z) $f64(x,y,z,w) | ((x - y) * z) - w
$f19(x,y,z) | x * (y - z) $f65(x,y,z,w) | ((x * y) * z) - w
$f20(x,y,z) | x * (y * z) $f66(x,y,z,w) | ((x / y) * z) - w
$f21(x,y,z) | x * (y / z) $f67(x,y,z,w) | ((x + y) / z) - w
$f22(x,y,z) | x - (y / z) $f68(x,y,z,w) | ((x - y) / z) - w
$f23(x,y,z) | x - (y / z) $f69(x,y,z,w) | ((x * y) / z) - w
$f24(x,y,z) | x - (y * z) $f70(x,y,z,w) | ((x / y) / z) - w
$f25(x,y,z) | x + (y * z) $f71(x,y,z,w) | (x * y) + (z * w)
$f26(x,y,z) | x + (y / z) $f72(x,y,z,w) | (x * y) - (z * w)
$f27(x,y,z) | x + (y + z) $f73(x,y,z,w) | (x * y) + (z / w)
$f28(x,y,z) | x + (y - z) $f74(x,y,z,w) | (x * y) - (z / w)
$f29(x,y,z) | x * y^2 + z $f75(x,y,z,w) | (x / y) + (z / w)
$f30(x,y,z) | x * y^3 + z $f76(x,y,z,w) | (x / y) - (z / w)
$f31(x,y,z) | x * y^4 + z $f77(x,y,z,w) | (x / y) - (z * w)
$f32(x,y,z) | x * y^5 + z $f78(x,y,z,w) | x / (y + (z * w))
$f33(x,y,z) | x * y^6 + z $f79(x,y,z,w) | x / (y - (z * w))
$f34(x,y,z) | x * y^7 + z $f80(x,y,z,w) | x * (y + (z * w))
$f35(x,y,z) | x * y^8 + z $f81(x,y,z,w) | x * (y - (z * w))
$f36(x,y,z) | x * y^9 + z $f82(x,y,z,w) | x * y^2 + z * w^2
$f37(x,y,z) | x * log(y)+z $f83(x,y,z,w) | x * y^3 + z * w^3
$f38(x,y,z) | x * log(y)-z $f84(x,y,z,w) | x * y^4 + z * w^4
$f39(x,y,z) | x * log10(y)+z $f85(x,y,z,w) | x * y^5 + z * w^5
$f40(x,y,z) | x * log10(y)-z $f86(x,y,z,w) | x * y^6 + z * w^6
$f41(x,y,z) | x * sin(y)+z $f87(x,y,z,w) | x * y^7 + z * w^7
$f42(x,y,z) | x * sin(y)-z $f88(x,y,z,w) | x * y^8 + z * w^8
$f43(x,y,z) | x * cos(y)+z $f89(x,y,z,w) | x * y^9 + z * w^9
$f44(x,y,z) | x * cos(y)-z $f90(x,y,z,w) | (x and y) ? z : w
$f45(x,y,z) | x ? y : z $f91(x,y,z,w) | (x or y) ? z : w
$f92(x,y,z,w) | (x < y) ? z : w
$f93(x,y,z,w) | (x <= y) ? z : w
$f94(x,y,z,w) | (x > y) ? z : w
$f95(x,y,z,w) | (x >= y) ? z : w
$f96(x,y,z,w) | (x == y) ? z : w
$f97(x,y,z,w) | x*sin(y) + z*cos(w)