C++ Mathematical Expression Library (ExprTk) http://www.partow.net/programming/exprtk/index.html
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Arash Partow
parent
d5ae48c109
commit
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1388
exprtk.hpp
1388
exprtk.hpp
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@ -1384,6 +1384,42 @@ inline bool run_test01()
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test_xy<T>("((x / 2) * (3 / y))",T(7.0),T(9.0),T(((7.0 / 2.0) * (3.0 / 9.0)))),
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test_xy<T>("((x * 2) / (3 / y))",T(7.0),T(9.0),T(((7.0 * 2.0) / (3.0 / 9.0)))),
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test_xy<T>("((x / 2) / (3 * y))",T(7.0),T(9.0),T(((7.0 / 2.0) / (3.0 * 9.0)))),
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test_xy<T>("([(min(x,8) + y) + 3] - 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) + 3.0) - 4.0))),
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test_xy<T>("([(min(x,8) + y) + 3] + 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) + 3.0) + 4.0))),
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test_xy<T>("([(min(x,8) + y) + 3] * 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) + 3.0) * 4.0))),
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test_xy<T>("([(min(x,8) + y) + 3] / 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) + 3.0) / 4.0))),
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test_xy<T>("([(min(x,8) + y) - 3] - 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) - 3.0) - 4.0))),
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test_xy<T>("([(min(x,8) + y) - 3] + 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) - 3.0) + 4.0))),
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test_xy<T>("([(min(x,8) + y) - 3] * 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) - 3.0) * 4.0))),
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test_xy<T>("([(min(x,8) + y) - 3] / 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) - 3.0) / 4.0))),
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test_xy<T>("([(min(x,8) + y) * 3] - 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) * 3.0) - 4.0))),
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test_xy<T>("([(min(x,8) + y) * 3] + 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) * 3.0) + 4.0))),
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test_xy<T>("([(min(x,8) + y) * 3] * 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) * 3.0) * 4.0))),
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test_xy<T>("([(min(x,8) + y) * 3] / 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) * 3.0) / 4.0))),
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test_xy<T>("([(min(x,8) + y) / 3] - 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) / 3.0) - 4.0))),
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test_xy<T>("([(min(x,8) + y) / 3] + 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) / 3.0) + 4.0))),
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test_xy<T>("([(min(x,8) + y) / 3] * 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) / 3.0) * 4.0))),
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test_xy<T>("([(min(x,8) + y) / 3] / 4)",T(7.0),T(9.0),T((((std::min(7.0,8.0) + 9.0) / 3.0) / 4.0))),
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test_xy<T>("(4 - [3 + (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 - (3.0 + (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 + [3 + (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 + (3.0 + (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 * [3 + (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 * (3.0 + (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 / [3 + (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 / (3.0 + (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 - [3 - (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 - (3.0 - (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 + [3 - (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 + (3.0 - (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 * [3 - (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 * (3.0 - (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 / [3 - (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 / (3.0 - (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 - [3 * (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 - (3.0 * (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 + [3 * (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 + (3.0 * (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 * [3 * (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 * (3.0 * (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 / [3 * (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 / (3.0 * (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 - [3 / (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 - (3.0 / (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 + [3 / (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 + (3.0 / (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 * [3 / (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 * (3.0 / (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("(4 / [3 / (min(x,8) + y)])",T(7.0),T(9.0),T((4.0 / (3.0 / (std::min(7.0,8.0) + 9.0))))),
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test_xy<T>("((2 * x) + (2 * y))",T(7.0),T(9.0),T(((2.0 * 7.0) + (2.0 * 9.0)))),
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test_xy<T>("((2 * x) - (2 * y))",T(7.0),T(9.0),T(((2.0 * 7.0) - (2.0 * 9.0)))),
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test_xy<T>("((2 * x) + (y * 2))",T(7.0),T(9.0),T(((2.0 * 7.0) + (9.0 * 2.0)))),
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test_xy<T>("((x * 2) - (y * 2))",T(7.0),T(9.0),T(((7.0 * 2.0) - (9.0 * 2.0)))),
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test_xy<T>("0 * (abs (x) + acos (y) + asin (x) + atan (y))",T(1.0),T(1.0),T(0.0)),
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test_xy<T>("0 * (ceil (x) + cos (y) + cosh (x) + exp (y))",T(1.0),T(1.0),T(0.0)),
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test_xy<T>("0 * (floor(x) + log (y) + log10(x) + round(y))",T(1.0),T(1.0),T(0.0)),
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@ -1468,7 +1504,39 @@ inline bool run_test01()
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test_xyz<T>("( x / (y / z))",T(7.0),T(9.0),T(3.0),T(( 7.0 / (9.0 / 3.0)))),
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test_xyz<T>("( x / (y / 2))",T(7.0),T(9.0),T(3.0),T(( 7.0 / (9.0 / 2.0)))),
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test_xyz<T>("( x / (2 / y))",T(7.0),T(9.0),T(3.0),T(( 7.0 / (2.0 / 9.0)))),
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test_xyz<T>("( 2 / (x / y))",T(7.0),T(9.0),T(3.0),T(( 2.0 / (7.0 / 9.0))))
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test_xyz<T>("( 2 / (x / y))",T(7.0),T(9.0),T(3.0),T(( 2.0 / (7.0 / 9.0)))),
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test_xyz<T>("([(min(x,y) + z) + 3] - 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) + 3.0) - 4.0))),
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test_xyz<T>("([(min(x,y) + z) + 3] + 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) + 3.0) + 4.0))),
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test_xyz<T>("([(min(x,y) + z) + 3] * 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) + 3.0) * 4.0))),
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test_xyz<T>("([(min(x,y) + z) + 3] / 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) + 3.0) / 4.0))),
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test_xyz<T>("([(min(x,y) + z) - 3] - 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) - 3.0) - 4.0))),
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test_xyz<T>("([(min(x,y) + z) - 3] + 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) - 3.0) + 4.0))),
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test_xyz<T>("([(min(x,y) + z) - 3] * 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) - 3.0) * 4.0))),
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test_xyz<T>("([(min(x,y) + z) - 3] / 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) - 3.0) / 4.0))),
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test_xyz<T>("([(min(x,y) + z) * 3] - 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) * 3.0) - 4.0))),
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test_xyz<T>("([(min(x,y) + z) * 3] + 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) * 3.0) + 4.0))),
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test_xyz<T>("([(min(x,y) + z) * 3] * 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) * 3.0) * 4.0))),
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test_xyz<T>("([(min(x,y) + z) * 3] / 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) * 3.0) / 4.0))),
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test_xyz<T>("([(min(x,y) + z) / 3] - 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) / 3.0) - 4.0))),
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test_xyz<T>("([(min(x,y) + z) / 3] + 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) / 3.0) + 4.0))),
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test_xyz<T>("([(min(x,y) + z) / 3] * 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) / 3.0) * 4.0))),
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test_xyz<T>("([(min(x,y) + z) / 3] / 4)",T(5.0),T(7.0),T(9.0),T((((std::min(5.0,7.0) + 9.0) / 3.0) / 4.0))),
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test_xyz<T>("(4 - [3 + (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 - (3.0 + (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 + [3 + (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 + (3.0 + (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 * [3 + (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 * (3.0 + (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 / [3 + (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 / (3.0 + (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 - [3 - (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 - (3.0 - (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 + [3 - (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 + (3.0 - (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 * [3 - (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 * (3.0 - (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 / [3 - (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 / (3.0 - (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 - [3 * (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 - (3.0 * (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 + [3 * (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 + (3.0 * (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 * [3 * (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 * (3.0 * (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 / [3 * (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 / (3.0 * (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 - [3 / (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 - (3.0 / (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 + [3 / (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 + (3.0 / (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 * [3 / (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 * (3.0 / (std::min(5.0,7.0) + 9.0))))),
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test_xyz<T>("(4 / [3 / (min(x,y) + z)])",T(5.0),T(7.0),T(9.0),T((4.0 / (3.0 / (std::min(5.0,7.0) + 9.0))))),
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};
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static const std::size_t test_list_size = sizeof(test_list) / sizeof(test_xyz<T>);
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@ -3854,6 +3922,12 @@ inline bool run_test19()
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// gof(x) = g(f(x))
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compositor.add("gof","g(f(x))","x");
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// fogof(x) = f(g(f(x)))
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compositor.add("fogof","f(g(f(x)))","x");
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// gofog(x) = g(f(g(x)))
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compositor.add("gofog","g(f(g(x)))","x");
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symbol_table_t& symbol_table = compositor.symbol_table();
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symbol_table.add_constants();
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symbol_table.add_variable("x",x);
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@ -3866,6 +3940,8 @@ inline bool run_test19()
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"equal(gog(x),(x^4 - 6x^2 + 6))",
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"equal(fog(x),(x^2 - 1))",
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"equal(gof(x),(x^2 + 4x + 1))",
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"equal(fogof(x),(x^2 + 4x + 3))",
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"equal(gofog(x),(x^4 - 2x^2 - 2))"
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};
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static const std::size_t expr_str_list_size = sizeof(expr_str_list) / sizeof(std::string);
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211
readme.txt
211
readme.txt
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@ -49,26 +49,26 @@ operations, functions and processes:
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The following is a short listing of the types of mathematical
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expressions that can be parsed and evaluated using the ExprTk library.
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(01) sqrt(1 - (x^2))
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(02) clamp(-1, sin(2 * pi * x) + cos(y / 2 * pi), +1)
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(03) sin(2.34e-3 * x)
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(04) if(((x + 2) == 3) and ((y + 5) <= 9),1 + w, 2 / z)
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(05) inrange(-2,m,+2) == if(({-2 <= m} and [m <= +2]),1,0)
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(06) ({1/1}*[1/2]+(1/3))-{1/4}^[1/5]+(1/6)-({1/7}+[1/8]*(1/9))
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(07) a * exp(2.2 / 3.3 * t) + c
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(08) z := x + sin(2.567 * pi / y)
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(09) u := 2.123 * (pi * z) / (w := x + cos(y / pi))
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(10) 2x + 3y + 4z + 5w == 2 * x + 3 * y + 4 * z + 5 * w
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(11) 3(x + y) / 2.9 + 1.234e+12 == 3 * (x + y) / 2.9 + 1.234e+12
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(12) (x + y)3.3 + 1 / 4.5 == (x + y) * 3.3 + 1 / 4.5
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(13) (x + y)z + 1.1 / 2.7 == (x + y) * z + 1.1 / 2.7
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(14) (sin(x / pi) cos(2y) + 1) == (sin(x / pi) * cos(2 * y) + 1)
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(15) 75x^17 + 25.1x^5 - 35x^4 - 15.2x^3 + 40x^2 - 15.3x + 1
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(16) if (avg(x,y) <= x + y, x - y, x * y) + 2.345 * pi / x
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(17) fib_i := fib_i + (x := y + 0 * (fib_i := x + (y := fib_i)))
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(18) while (x <= 100) { x := x + 1 }
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(19) x <= 'abc123' and (y in 'AString') or ('1x2y3z' != z)
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(20) (x like '*123*') or ('a123b' ilike y)
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(01) sqrt(1 - (x^2))
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(02) clamp(-1, sin(2 * pi * x) + cos(y / 2 * pi), +1)
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(03) sin(2.34e-3 * x)
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(04) if(((x + 2) == 3) and ((y + 5) <= 9),1 + w, 2 / z)
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(05) inrange(-2,m,+2) == if(({-2 <= m} and [m <= +2]),1,0)
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(06) ({1/1}*[1/2]+(1/3))-{1/4}^[1/5]+(1/6)-({1/7}+[1/8]*(1/9))
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(07) a * exp(2.2 / 3.3 * t) + c
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(08) z := x + sin(2.567 * pi / y)
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(09) u := 2.123 * (pi * z) / (w := x + cos(y / pi))
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(10) 2x + 3y + 4z + 5w == 2 * x + 3 * y + 4 * z + 5 * w
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(11) 3(x + y) / 2.9 + 1.234e+12 == 3 * (x + y) / 2.9 + 1.234e+12
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(12) (x + y)3.3 + 1 / 4.5 == (x + y) * 3.3 + 1 / 4.5
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(13) (x + y)z + 1.1 / 2.7 == (x + y) * z + 1.1 / 2.7
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(14) (sin(x / pi) cos(2y) + 1) == (sin(x / pi) * cos(2 * y) + 1)
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(15) 75x^17 + 25.1x^5 - 35x^4 - 15.2x^3 + 40x^2 - 15.3x + 1
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(16) if (avg(x,y) <= x + y, x - y, x * y) + 2.345 * pi / x
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(17) fib_i := fib_i + (x := y + 0 * (fib_i := x + (y := fib_i)))
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(18) while (x <= 100) { x := x + 1 }
|
||||
(19) x <= 'abc123' and (y in 'AString') or ('1x2y3z' != z)
|
||||
(20) (x like '*123*') or ('a123b' ilike y)
|
||||
|
||||
|
||||
|
||||
|
|
@ -86,8 +86,8 @@ The most recent version of the C++ Mathematical Expression Toolkit
|
|||
Library including all updates and tests can be found at the following
|
||||
locations:
|
||||
|
||||
(1) http://www.partow.net/programming/exprtk/index.html
|
||||
(2) svn checkout http://exprtk.googlecode.com/svn/ exprtk
|
||||
(1) http://www.partow.net/programming/exprtk/index.html
|
||||
(2) svn checkout http://exprtk.googlecode.com/svn/ exprtk
|
||||
|
||||
|
||||
|
||||
|
|
@ -98,20 +98,21 @@ include path (e.g: /usr/include/).
|
|||
|
||||
|
||||
[06 - COMPILATION]
|
||||
(1) For a complete build: make clean all
|
||||
(2) For a PGO build: make clean pgo
|
||||
(3) To strip executables: make strip_bin
|
||||
(1) For a complete build: make clean all
|
||||
(2) For a PGO build: make clean pgo
|
||||
(3) To strip executables: make strip_bin
|
||||
(5) Execute valgrind check: make valgrind_check
|
||||
|
||||
|
||||
|
||||
[07 - COMPILER COMPATIBILITY]
|
||||
(*) GNU Compiler Collection (4.1+)
|
||||
(*) Intel C++ Compiler (9.x+)
|
||||
(*) Clang/LLVM (1.1+)
|
||||
(*) PGI C++ (10.x+)
|
||||
(*) Microsoft Visual Studio C++ Compiler (8.1+)
|
||||
(*) Comeau C++ Compiler (4.3+)
|
||||
(*) IBM XL C/C++ (10.x+)
|
||||
(*) GNU Compiler Collection (4.1+)
|
||||
(*) Intel C++ Compiler (9.x+)
|
||||
(*) Clang/LLVM (1.1+)
|
||||
(*) PGI C++ (10.x+)
|
||||
(*) Microsoft Visual Studio C++ Compiler (8.1+)
|
||||
(*) Comeau C++ Compiler (4.3+)
|
||||
(*) IBM XL C/C++ (10.x+)
|
||||
|
||||
|
||||
|
||||
|
|
@ -424,7 +425,11 @@ follows:
|
|||
|
||||
(1) Symbol Table
|
||||
A structure that is used to store references to variables, constants
|
||||
and functions that are to be used within expressions.
|
||||
and functions that are to be used within expressions. Furthermore in
|
||||
the context of composited recursive functions the symbol table can
|
||||
also be thought of as a simple representation of a stack specific for
|
||||
the expression(s) that reference it.
|
||||
|
||||
|
||||
(2) Expression
|
||||
A structure that holds an AST for a specified expression and is used
|
||||
|
|
@ -459,6 +464,7 @@ Expression: z := (x + y^-2.345) * sin(pi / min(w - 7.3,v))
|
|||
/ \
|
||||
Variable(w) Constant(7.3)
|
||||
|
||||
|
||||
(3) Parser
|
||||
A structure which takes as input a string representation of an
|
||||
expression and attempts to compile said input with the result being an
|
||||
|
|
@ -470,7 +476,118 @@ interface.
|
|||
|
||||
|
||||
|
||||
[10 - SPECIAL FUNCTIONS]
|
||||
[10 - COMPILATION OPTIONS]
|
||||
The exprtk::parser when being instantiated takes as input a set of
|
||||
options to be used during the compilation process of expressions.
|
||||
An example instantiation of exprtk::parser where only the joiner,
|
||||
commutative and strength reduction options are enabled is as follows:
|
||||
|
||||
const std::size_t compile_options = e_joiner +
|
||||
e_commutative_check +
|
||||
e_strength_reduction;
|
||||
|
||||
exprtk::parser<NumericType> parser(compile_options);
|
||||
|
||||
|
||||
Currently seven types of options are supported, and enabled by
|
||||
default. The options and their explanations are as follows:
|
||||
|
||||
(1) Replacer (e_replacer)
|
||||
Enable replacement of specific tokens with other tokens. For example
|
||||
the token "true" of type symbol will be replaced with the numeric
|
||||
token of value one.
|
||||
|
||||
(a) (x < y) == true ---> (x < y) == 1
|
||||
(b) false == (x > y) ---> 0 == (x > y)
|
||||
|
||||
|
||||
(2) Joiner (e_joiner)
|
||||
Enable joining of multi-character operators that may have been
|
||||
incorrectly disjoint in the string representation of the specified
|
||||
expression. For example the consecutive tokens of ">" "=" will become
|
||||
">=" representing the "greater than or equal to" operator. If not
|
||||
properly resolved the original form will cause a compilation error.
|
||||
The following is a listing of the scenarios that the joiner can
|
||||
handle:
|
||||
|
||||
(a) ':' '=' ---> ':=' (assignment)
|
||||
(b) '>' '=' ---> '>=' (gte)
|
||||
(c) '<' '=' ---> '<=' (lte)
|
||||
(d) '=' '=' ---> '==' (equal)
|
||||
(e) '!' '=' ---> '!=' (not-equal)
|
||||
(f) '<' '>' ---> '<>' (not-equal)
|
||||
|
||||
An example of the transformation that takes place is as follows:
|
||||
|
||||
(a) (x > = y) and (z ! = w) ---> (x >= y) and (z != w)
|
||||
|
||||
|
||||
(3) Numeric Check (e_numeric_check)
|
||||
Enable validation of tokens representing numeric types so as to catch
|
||||
any errors prior to the costly process of the main compilation step
|
||||
commencing.
|
||||
|
||||
|
||||
(4) Bracket Check (e_bracket_check)
|
||||
Enable the check for validating the ordering of brackets in the
|
||||
specified expression.
|
||||
|
||||
|
||||
(5) Sequence Check (e_sequence_check)
|
||||
Enable the check for validating that sequences of either pairs or
|
||||
triplets of tokens make sense. For example the following sequence of
|
||||
tokens when encountered will raise an error:
|
||||
|
||||
(a) (x + * 3) ---> sequence error
|
||||
|
||||
|
||||
(6) Commutative Check (e_commutative_check)
|
||||
Enable the check that will transform sequences of pairs of tokens that
|
||||
imply a multiplication operation. The following are some examples of
|
||||
such transformations:
|
||||
|
||||
(a) 2x ---> 2 * x
|
||||
(b) 25x^3 ---> 25 * x^3
|
||||
(c) 3(x + 1) ---> 3 * (x + 1)
|
||||
(d) (x + 1)4 ---> (x + 1) * 4
|
||||
(e) 5foo(x,y) ---> 5 * foo(x,y)
|
||||
(f) foo(x,y)6 + 1 ---> foo(x,y) * 6 + 1
|
||||
|
||||
|
||||
(7) Strength Reduction Check (e_strength_reduction)
|
||||
Enable the use of strength reduction optimisations during the
|
||||
compilation process. In ExprTk strength reduction optimisations
|
||||
predominantly involve transforming sub-expressions into other forms
|
||||
that are algebraically equivalent yet less costly to compute. The
|
||||
following are examples of the various transformations that can occur:
|
||||
|
||||
(a) (x / y) / z ---> x / (y * z)
|
||||
(b) (x / y) / (z / w) ---> (x * w) / (y * z)
|
||||
(c) (2 * x) - (2 * y) ---> 2 * (x - y)
|
||||
(d) (2 / x) / (3 / y) ---> (2 / 3) / (x * y)
|
||||
(e) (2 * x) * (3 * y) ---> (2 * 3) * (x * y)
|
||||
|
||||
Note:
|
||||
When using strength reduction in conjunction with expressions whose
|
||||
inputs or sub-expressions may result in values nearing either of the
|
||||
bounds of the underlying numeric type (eg: double), there may be the
|
||||
possibility of a decrease in the precision of results.
|
||||
|
||||
In the following example the given expression which represents an
|
||||
attempt at computing the average between x and y will be transformed
|
||||
as follows:
|
||||
|
||||
(x * 0.5) + (y * 0.5) ---> 0.5 * (x + y)
|
||||
|
||||
There may be situations where the above transformation will cause
|
||||
numerical overflows and that the original form of the expression is
|
||||
desired over the strength reduced form. In these situations it is best
|
||||
to turn off strength reduction optimisations or to use a type with a
|
||||
larger numerical bound.
|
||||
|
||||
|
||||
|
||||
[11 - 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
|
||||
|
|
@ -537,11 +654,11 @@ correctly optimize such expressions for a given architecture.
|
|||
$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)
|
||||
$f99(x,y,z,w) | x*sin(y)+z*cos(w)
|
||||
|
||||
|
||||
|
||||
[11 - EXPRTK NOTES]
|
||||
[12 - EXPRTK NOTES]
|
||||
(00) Precision and performance of expression evaluations are the
|
||||
dominant principles of the ExprTk library.
|
||||
|
||||
|
|
@ -596,10 +713,9 @@ correctly optimize such expressions for a given architecture.
|
|||
(15) Where appropriate constant folding optimisations may be
|
||||
applied. (eg: The expression '2+(3-(x/y))' becomes '5-(x/y)')
|
||||
|
||||
(16) Where applicable strength reduction optimisations may be
|
||||
applied. The following are example of such optimisations:
|
||||
(a) '(x / y) / z' --> 'x / (y * z)'
|
||||
(b) '(x / 3)' --> 'x * (1 / 3)'
|
||||
(16) If the strength reduction compilation option has been enabled,
|
||||
then where applicable strength reduction optimisations may be
|
||||
applied.
|
||||
|
||||
(17) String processing capabilities are available by default.
|
||||
To turn them off, the following needs to be defined at
|
||||
|
|
@ -614,8 +730,7 @@ correctly optimize such expressions for a given architecture.
|
|||
(20) 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.
|
||||
multiple expressions.
|
||||
|
||||
(21) The common use-case for an expression is to have it compiled
|
||||
only once and then subsequently have it evaluated multiple
|
||||
|
|
@ -637,7 +752,7 @@ correctly optimize such expressions for a given architecture.
|
|||
|
||||
|
||||
|
||||
[12 - SIMPLE EXPRTK EXAMPLE]
|
||||
[13 - SIMPLE EXPRTK EXAMPLE]
|
||||
--- snip ---
|
||||
#include <cstdio>
|
||||
#include <string>
|
||||
|
|
@ -684,12 +799,18 @@ int main()
|
|||
|
||||
if (!parser.compile(expression_str,expression))
|
||||
{
|
||||
// A compilation error has occured. Attempt to
|
||||
// print all errors to the stdout.
|
||||
|
||||
printf("Error: %s\tExpression: %s\n",
|
||||
parser.error().c_str(),
|
||||
expression_str.c_str());
|
||||
|
||||
for (std::size_t i = 0; i < parser.error_count(); ++i)
|
||||
{
|
||||
// Include the specific nature of each error
|
||||
// and its position in the expression string.
|
||||
|
||||
error_t error = parser.get_error(i);
|
||||
printf("Error: %02d Position: %02d "
|
||||
"Type: [%s] "
|
||||
|
|
@ -705,6 +826,8 @@ int main()
|
|||
return 1;
|
||||
}
|
||||
|
||||
// Evaluate the expression and obtain its result.
|
||||
|
||||
double result = expression.value();
|
||||
|
||||
printf("Result: %10.5f\n",result);
|
||||
|
|
@ -715,7 +838,7 @@ int main()
|
|||
|
||||
|
||||
|
||||
[13 - FILES]
|
||||
[14 - FILES]
|
||||
(00) Makefile
|
||||
(01) readme.txt
|
||||
(02) exprtk.hpp
|
||||
|
|
|
|||
Loading…
Reference in New Issue