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

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Arash Partow
2014-01-22 08:13:37 +11:00
parent e3d51a3222
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readme.txt
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@ -415,9 +415,9 @@ There are three primary components, that are specialized upon a given
numeric type, which make up the core of ExprTk. The components are as
follows:
1. Symbol Table exprtk::symbol_table<T>
2. Expression exprtk::expression<T>
3. Parser exprtk::parser<T>
1. Symbol Table exprtk::symbol_table<NumericType>
2. Expression exprtk::expression<NumericType>
3. Parser exprtk::parser<NumericType>
(1) Symbol Table
@ -447,15 +447,15 @@ Expression: z := (x + y^-2.345) * sin(pi / min(w - 7.3,v))
/ \ ___/ \___
Variable(x) [Power] / \
______/ \______ Constant(pi) [Binary-Func(min)]
/ \ ___/ \___
Variable(y) [Negate] / \
| / Variable(v)
Constant(2.345) /
/
[Subtract]
____/ \___
/ \
Variable(w) Constant(7.3)
/ \ ____/ \____
Variable(y) [Negate] / \
| / Variable(v)
Constant(2.345) /
/
[Subtract]
____/ \____
/ \
Variable(w) Constant(7.3)
(3) Parser
A structure which takes as input a string representation of an
@ -484,58 +484,58 @@ correctly optimize such expressions for a given architecture.
+-------------+-------------+ +--------------+------------------+
| Prototype | Operation | | Prototype | Operation |
+-------------+-------------+ +--------------+------------------+
$f00(x,y,z) | (x + y) / z $f47(x,y,z,w) | x + ((y + z) / w)
$f01(x,y,z) | (x + y) * z $f48(x,y,z,w) | x + ((y + z) * w)
$f02(x,y,z) | (x + y) - z $f49(x,y,z,w) | x + ((y - z) / w)
$f03(x,y,z) | (x + y) + z $f50(x,y,z,w) | x + ((y - z) * w)
$f04(x,y,z) | (x - y) / z $f51(x,y,z,w) | x + ((y * z) / w)
$f05(x,y,z) | (x - y) * z $f52(x,y,z,w) | x + ((y * z) * w)
$f06(x,y,z) | (x * y) + z $f53(x,y,z,w) | x + ((y / z) + w)
$f07(x,y,z) | (x * y) - z $f54(x,y,z,w) | x + ((y / z) / w)
$f08(x,y,z) | (x * y) / z $f55(x,y,z,w) | x + ((y / z) * w)
$f09(x,y,z) | (x * y) * z $f56(x,y,z,w) | x - ((y + z) / w)
$f10(x,y,z) | (x / y) + z $f57(x,y,z,w) | x - ((y + z) * w)
$f11(x,y,z) | (x / y) - z $f58(x,y,z,w) | x - ((y - z) / w)
$f12(x,y,z) | (x / y) / z $f59(x,y,z,w) | x - ((y - z) * w)
$f13(x,y,z) | (x / y) * z $f60(x,y,z,w) | x - ((y * z) / w)
$f14(x,y,z) | x / (y + z) $f61(x,y,z,w) | x - ((y * z) * w)
$f15(x,y,z) | x / (y - z) $f62(x,y,z,w) | x - ((y / z) / w)
$f16(x,y,z) | x / (y * z) $f63(x,y,z,w) | x - ((y / z) * w)
$f17(x,y,z) | x / (y / z) $f64(x,y,z,w) | ((x + y) * z) - w
$f18(x,y,z) | x * (y + z) $f65(x,y,z,w) | ((x - y) * z) - w
$f19(x,y,z) | x * (y - z) $f66(x,y,z,w) | ((x * y) * z) - w
$f20(x,y,z) | x * (y * z) $f67(x,y,z,w) | ((x / y) * z) - w
$f21(x,y,z) | x * (y / z) $f68(x,y,z,w) | ((x + y) / z) - w
$f22(x,y,z) | x - (y + z) $f69(x,y,z,w) | ((x - y) / z) - w
$f23(x,y,z) | x - (y - z) $f70(x,y,z,w) | ((x * y) / z) - w
$f24(x,y,z) | x - (y / z) $f71(x,y,z,w) | ((x / y) / z) - w
$f25(x,y,z) | x - (y * z) $f72(x,y,z,w) | (x * y) + (z * w)
$f26(x,y,z) | x + (y * z) $f73(x,y,z,w) | (x * y) - (z * w)
$f27(x,y,z) | x + (y / z) $f74(x,y,z,w) | (x * y) + (z / w)
$f28(x,y,z) | x + (y + z) $f75(x,y,z,w) | (x * y) - (z / w)
$f29(x,y,z) | x + (y - z) $f76(x,y,z,w) | (x / y) + (z / w)
$f30(x,y,z) | x * y^2 + z $f77(x,y,z,w) | (x / y) - (z / w)
$f31(x,y,z) | x * y^3 + z $f78(x,y,z,w) | (x / y) - (z * w)
$f32(x,y,z) | x * y^4 + z $f79(x,y,z,w) | x / (y + (z * w))
$f33(x,y,z) | x * y^5 + z $f80(x,y,z,w) | x / (y - (z * w))
$f34(x,y,z) | x * y^6 + z $f81(x,y,z,w) | x * (y + (z * w))
$f35(x,y,z) | x * y^7 + z $f82(x,y,z,w) | x * (y - (z * w))
$f36(x,y,z) | x * y^8 + z $f83(x,y,z,w) | x*y^2 + z*w^2
$f37(x,y,z) | x * y^9 + z $f84(x,y,z,w) | x*y^3 + z*w^3
$f38(x,y,z) | x * log(y)+z $f85(x,y,z,w) | x*y^4 + z*w^4
$f39(x,y,z) | x * log(y)-z $f86(x,y,z,w) | x*y^5 + z*w^5
$f40(x,y,z) | x * log10(y)+z $f87(x,y,z,w) | x*y^6 + z*w^6
$f41(x,y,z) | x * log10(y)-z $f88(x,y,z,w) | x*y^7 + z*w^7
$f42(x,y,z) | x * sin(y)+z $f89(x,y,z,w) | x*y^8 + z*w^8
$f43(x,y,z) | x * sin(y)-z $f90(x,y,z,w) | x*y^9 + z*w^9
$f44(x,y,z) | x * cos(y)+z $f91(x,y,z,w) | (x and y) ? z : w
$f45(x,y,z) | x * cos(y)-z $f92(x,y,z,w) | (x or y) ? z : w
$f46(x,y,z) | x ? y : z $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 == y) ? z : w
$f98(x,y,z,w) | x * sin(y) + z * cos(w)
$f00(x,y,z) | (x + y) / z $f48(x,y,z,w) | x + ((y + z) / w)
$f01(x,y,z) | (x + y) * z $f49(x,y,z,w) | x + ((y + z) * w)
$f02(x,y,z) | (x + y) - z $f50(x,y,z,w) | x + ((y - z) / w)
$f03(x,y,z) | (x + y) + z $f51(x,y,z,w) | x + ((y - z) * w)
$f04(x,y,z) | (x - y) + z $f52(x,y,z,w) | x + ((y * z) / w)
$f05(x,y,z) | (x - y) / z $f53(x,y,z,w) | x + ((y * z) * w)
$f06(x,y,z) | (x - y) * z $f54(x,y,z,w) | x + ((y / z) + w)
$f07(x,y,z) | (x * y) + z $f55(x,y,z,w) | x + ((y / z) / w)
$f08(x,y,z) | (x * y) - z $f56(x,y,z,w) | x + ((y / z) * w)
$f09(x,y,z) | (x * y) / z $f57(x,y,z,w) | x - ((y + z) / w)
$f10(x,y,z) | (x * y) * z $f58(x,y,z,w) | x - ((y + z) * w)
$f11(x,y,z) | (x / y) + z $f59(x,y,z,w) | x - ((y - z) / w)
$f12(x,y,z) | (x / y) - z $f60(x,y,z,w) | x - ((y - z) * w)
$f13(x,y,z) | (x / y) / z $f61(x,y,z,w) | x - ((y * z) / w)
$f14(x,y,z) | (x / y) * z $f62(x,y,z,w) | x - ((y * z) * w)
$f15(x,y,z) | x / (y + z) $f63(x,y,z,w) | x - ((y / z) / w)
$f16(x,y,z) | x / (y - z) $f64(x,y,z,w) | x - ((y / z) * w)
$f17(x,y,z) | x / (y * z) $f65(x,y,z,w) | ((x + y) * z) - w
$f18(x,y,z) | x / (y / z) $f66(x,y,z,w) | ((x - y) * z) - w
$f19(x,y,z) | x * (y + z) $f67(x,y,z,w) | ((x * y) * z) - w
$f20(x,y,z) | x * (y - z) $f68(x,y,z,w) | ((x / y) * z) - w
$f21(x,y,z) | x * (y * z) $f69(x,y,z,w) | ((x + y) / z) - w
$f22(x,y,z) | x * (y / z) $f70(x,y,z,w) | ((x - y) / z) - w
$f23(x,y,z) | x - (y + z) $f71(x,y,z,w) | ((x * y) / z) - w
$f24(x,y,z) | x - (y - z) $f72(x,y,z,w) | ((x / y) / z) - w
$f25(x,y,z) | x - (y / z) $f73(x,y,z,w) | (x * y) + (z * w)
$f26(x,y,z) | x - (y * z) $f74(x,y,z,w) | (x * y) - (z * w)
$f27(x,y,z) | x + (y * z) $f75(x,y,z,w) | (x * y) + (z / w)
$f28(x,y,z) | x + (y / z) $f76(x,y,z,w) | (x * y) - (z / w)
$f29(x,y,z) | x + (y + z) $f77(x,y,z,w) | (x / y) + (z / w)
$f30(x,y,z) | x + (y - z) $f78(x,y,z,w) | (x / y) - (z / w)
$f31(x,y,z) | x * y^2 + z $f79(x,y,z,w) | (x / y) - (z * w)
$f32(x,y,z) | x * y^3 + z $f80(x,y,z,w) | x / (y + (z * w))
$f33(x,y,z) | x * y^4 + z $f81(x,y,z,w) | x / (y - (z * w))
$f34(x,y,z) | x * y^5 + z $f82(x,y,z,w) | x * (y + (z * w))
$f35(x,y,z) | x * y^6 + z $f83(x,y,z,w) | x * (y - (z * w))
$f36(x,y,z) | x * y^7 + z $f84(x,y,z,w) | x*y^2 + z*w^2
$f37(x,y,z) | x * y^8 + z $f85(x,y,z,w) | x*y^3 + z*w^3
$f38(x,y,z) | x * y^9 + z $f86(x,y,z,w) | x*y^4 + z*w^4
$f39(x,y,z) | x * log(y)+z $f87(x,y,z,w) | x*y^5 + z*w^5
$f40(x,y,z) | x * log(y)-z $f88(x,y,z,w) | x*y^6 + z*w^6
$f41(x,y,z) | x * log10(y)+z $f89(x,y,z,w) | x*y^7 + z*w^7
$f42(x,y,z) | x * log10(y)-z $f90(x,y,z,w) | x*y^8 + z*w^8
$f43(x,y,z) | x * sin(y)+z $f91(x,y,z,w) | x*y^9 + z*w^9
$f44(x,y,z) | x * sin(y)-z $f92(x,y,z,w) | (x and y) ? z : w
$f45(x,y,z) | x * cos(y)+z $f93(x,y,z,w) | (x or y) ? z : w
$f46(x,y,z) | x * cos(y)-z $f94(x,y,z,w) | (x < y) ? z : w
$f47(x,y,z) | x ? y : z $f95(x,y,z,w) | (x <= y) ? z : w
$f96(x,y,z,w) | (x > y) ? z : w
$f97(x,y,z,w) | (x >= y) ? z : w
$f98(x,y,z,w) | (x == y) ? z : w
$f99(x,y,z,w) | x * sin(y) + z * cos(w)
@ -604,14 +604,26 @@ correctly optimize such expressions for a given architecture.
(18) Recursive calls made from within composited functions will have
a stack size bound by the stack of the executing architecture.
(19) The following are examples of compliant floating point value
(19) The entity relationship between symbol_table and an expression
is one-to-many. Hence the intended use case is to have a single
symbol table manage the variable and function requirements of
multiple expressions. An inappropriate approach would be to have
a unique symbol table for each unique expression.
(20) The common use-case for an expression is to have it compiled
only once and then subsequently have it evaluated multiple
times. An extremely inefficient approach would be to recompile
an expression from its string form every time it requires
evaluating.
(21) The following are examples of compliant floating point value
representations:
(a) 12345 (b) -123.456
(c) +123.456e+12 (d) 123.456E-12
(e) +012.045e+07 (f) .1234
(g) 123.456f (h) -321.654E+3L
(20) Expressions may contain any of the following comment styles:
(22) Expressions may contain any of the following comment styles:
1. // .... \n
2. # .... \n
3. /* .... */