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

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2013-07-09 08:32:08 +10:00
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@ -31,7 +31,7 @@ operations, functions and processes:
(5) Conditional,
Switch &
Loop statements: if-then-else, switch-case, while
Loop statements: if-then-else, switch-case, while, repeat-until
(6) Assignment: :=
@ -43,7 +43,7 @@ operations, functions and processes:
[02 - EXAMPLE EXPRESSIONS]
The following is a short sample of the types of mathematical
The following is a short listing of the types of mathematical
expressions that can be parsed and evaluated using the ExprTk library.
(01) sqrt(1 - (x^2))
@ -102,7 +102,7 @@ include path (e.g: /usr/include/).
[07 - COMPILER COMPATIBILITY]
(*) GNU Compiler Collection (4.3+)
(*) GNU Compiler Collection (4.1+)
(*) Intel<65> C++ Compiler (9.x+)
(*) Clang/LLVM (1.1+)
(*) PGI C++ (10.x+)
@ -115,266 +115,276 @@ include path (e.g: /usr/include/).
[08 - BUILT-IN OPERATIONS & FUNCTIONS]
(0) Arithmetic 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. |
+-----------+--------------------------------------------------------+
+----------+---------------------------------------------------------+
| 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. |
+----------+---------------------------------------------------------+
| <=> | Swap the values of x and y. (eg: x <=> y) |
| | Where both x and y are variables. |
+----------+---------------------------------------------------------+
(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 is less than y. (eg: x < y) |
+-----------+--------------------------------------------------------+
| <= | True only if x is less than or equal to y. (eg: x <= y)|
+-----------+--------------------------------------------------------+
| > | True only if x is greater than y. (eg: x > y) |
+-----------+--------------------------------------------------------+
| >= | True only if x greater than or equal to y (eg: x >= y) |
+-----------+--------------------------------------------------------+
+----------+---------------------------------------------------------+
| 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 is less than y. (eg: x < y) |
+----------+---------------------------------------------------------+
| <= | True only if x is less than or equal to y. (eg: x <= y) |
+----------+---------------------------------------------------------+
| > | True only if x is 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) |
+-----------+--------------------------------------------------------+
| mand | Multi-input logical AND, True only if all inputs are |
| | true. Left to right short-circuiting of expressions. |
| | (eg: mand(x > y,z < w,u or v,w and x)) |
+-----------+--------------------------------------------------------+
| mor | Multi-input logical OR, True if at least one of the |
| | inputs are true. Left to right short-circuiting of |
| | expressions. (eg: mand(x > y,z < w,u or v,w and x)) |
+-----------+--------------------------------------------------------+
| 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 | Logical XOR, True only if the logical states of x and y|
| | differ. (eg: x xor y) |
+-----------+--------------------------------------------------------+
| xnor | Logical XNOR, True iff the biconditional of x and y is |
| | satisfied. (eg: x xnor y) |
+-----------+--------------------------------------------------------+
| & | Similar to AND but with left to right expression short |
| | circuiting optimisation. (eg: (x & y) == (y and x)) |
+-----------+--------------------------------------------------------+
| | | Similar to OR but with left to right expression short |
| | circuiting optimisation. (eg: (x | y) == (y or x)) |
+-----------+--------------------------------------------------------+
+----------+---------------------------------------------------------+
| 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) |
+----------+---------------------------------------------------------+
| mand | Multi-input logical AND, True only if all inputs are |
| | true. Left to right short-circuiting of expressions. |
| | (eg: mand(x > y,z < w,u or v,w and x)) |
+----------+---------------------------------------------------------+
| mor | Multi-input logical OR, True if at least one of the |
| | inputs are true. Left to right short-circuiting of |
| | expressions. (eg: mand(x > y,z < w,u or v,w and x)) |
+----------+---------------------------------------------------------+
| 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 | Logical XOR, True only if the logical states of x and y |
| | differ. (eg: x xor y) |
+----------+---------------------------------------------------------+
| xnor | Logical XNOR, True iff the biconditional of x and y is |
| | satisfied. (eg: x xnor y) |
+----------+---------------------------------------------------------+
| & | Similar to AND but with left to right expression short |
| | circuiting optimisation. (eg: (x & y) == (y and x)) |
+----------+---------------------------------------------------------+
| | | Similar to OR but with left to right expression short |
| | circuiting optimisation. (eg: (x | y) == (y or x)) |
+----------+---------------------------------------------------------+
(3) General Purpose Functions
+-----------+--------------------------------------------------------+
| FUNCTION | DEFINITION |
+-----------+--------------------------------------------------------+
| abs | Absolute value of x. |
+-----------+--------------------------------------------------------+
| avg | Average of all the inputs. |
| | (eg: avg(x,y,z,w,u,v) == (x + y + z + w + u + v) / 6) |
+-----------+--------------------------------------------------------+
| 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) = sqrt(x*x +y*y))|
+-----------+--------------------------------------------------------+
| log | Natural logarithm of x |
+-----------+--------------------------------------------------------+
| log10 | Base 10 logarithm of x |
+-----------+--------------------------------------------------------+
| log1p | Natural logarithm of 1 + x, where x is very small. |
| | (eg: log1p(x)) |
+-----------+--------------------------------------------------------+
| log2 | Base 2 logarithm of x |
+-----------+--------------------------------------------------------+
| logn | Base N logarithm of x (eg: logn(1235,8)) |
| | where n > 0 and is an integer. |
+-----------+--------------------------------------------------------+
| max | Largest value of all the inputs. (eg: max(x,y,z,w,u,v))|
+-----------+--------------------------------------------------------+
| min | Smallest value of all the inputs. (eg: min(x,y,z,w,u)) |
+-----------+--------------------------------------------------------+
| mul | Product of all the inputs. |
| | (eg: mul(x,y,z,w,u,v,t) == (x * y * z * w * u * v * t))|
+-----------+--------------------------------------------------------+
| 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 | Sum of all the inputs. |
| | (eg: sum(x,y,z,w,u,v,t) == (x + y + z + w + u + v + t))|
+-----------+--------------------------------------------------------+
| trunc | Integer portion of x |
+-----------+--------------------------------------------------------+
+----------+---------------------------------------------------------+
| FUNCTION | DEFINITION |
+----------+---------------------------------------------------------+
| abs | Absolute value of x. |
+----------+---------------------------------------------------------+
| avg | Average of all the inputs. |
| | (eg: avg(x,y,z,w,u,v) == (x + y + z + w + u + v) / 6) |
+----------+---------------------------------------------------------+
| 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) = sqrt(x*x + y*y))|
+----------+---------------------------------------------------------+
| log | Natural logarithm of x |
+----------+---------------------------------------------------------+
| log10 | Base 10 logarithm of x |
+----------+---------------------------------------------------------+
| log1p | Natural logarithm of 1 + x, where x is very small. |
| | (eg: log1p(x)) |
+----------+---------------------------------------------------------+
| log2 | Base 2 logarithm of x |
+----------+---------------------------------------------------------+
| logn | Base N logarithm of x (eg: logn(1235,8)) |
| | where n > 0 and is an integer. |
+----------+---------------------------------------------------------+
| max | Largest value of all the inputs. (eg: max(x,y,z,w,u,v)) |
+----------+---------------------------------------------------------+
| min | Smallest value of all the inputs. (eg: min(x,y,z,w,u)) |
+----------+---------------------------------------------------------+
| mul | Product of all the inputs. |
| | (eg: mul(x,y,z,w,u,v,t) == (x * y * z * w * u * v * t)) |
+----------+---------------------------------------------------------+
| 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 n decimal places (eg: roundn(x,3)) |
| | where n > 0 and is an integer. |
| | (eg: roundn(1.2345678,4) == 1.2346) |
+----------+---------------------------------------------------------+
| sgn | Sign of x, -1 where x < 0, +1 where x > 0, else zero. |
+----------+---------------------------------------------------------+
| sqrt | Square root of x, where x > 0 |
+----------+---------------------------------------------------------+
| sum | Sum of all the inputs. |
| | (eg: sum(x,y,z,w,u,v,t) == (x + y + z + w + u + v + t)) |
+----------+---------------------------------------------------------+
| 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 |
+-----------+--------------------------------------------------------+
| deg2rad | Convert x from degrees to radians |
+-----------+--------------------------------------------------------+
| deg2grad | Convert x from degrees to gradians |
+-----------+--------------------------------------------------------+
| rad2deg | Convert x from radians to degrees |
+-----------+--------------------------------------------------------+
| grad2deg | Convert x from gradians to degrees |
+-----------+--------------------------------------------------------+
+----------+---------------------------------------------------------+
| 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/y) expressed in radians. [-pi,+pi] |
| | eg: atan2(x,y) |
+----------+---------------------------------------------------------+
| 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 |
+----------+---------------------------------------------------------+
| deg2rad | Convert x from degrees to radians |
+----------+---------------------------------------------------------+
| deg2grad | Convert x from degrees to gradians |
+----------+---------------------------------------------------------+
| rad2deg | Convert x from radians to degrees |
+----------+---------------------------------------------------------+
| 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*h') |
+-----------+--------------------------------------------------------+
| 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 'a1B2c3D4e5F6g7H' like 'a?d*h') |
+-----------+--------------------------------------------------------+
| [r0:r1] | The closed interval [r0,r1] of the specified string. |
| | eg: Given a string x with a value of 'abcdefgh' then: |
| | 0. x[1:4] == 'bcde' |
| | 1. x[ :5] == 'abcdef' |
| | 2. x[3: ] == 'cdefgh' |
| | 3. x[ : ] == 'abcdefgh' |
| | 4. x[4/2:3+2] == x[2:5] == 'cdef' |
+-----------+--------------------------------------------------------+
+----------+---------------------------------------------------------+
| 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*h') |
+----------+---------------------------------------------------------+
| ilike | 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 'a1B2c3D4e5F6g7H' ilike 'a?d*h') |
+----------+---------------------------------------------------------+
| [r0:r1] | The closed interval [r0,r1] of the specified string. |
| | eg: Given a string x with a value of 'abcdefgh' then: |
| | 0. x[1:4] == 'bcde' |
| | 1. x[ :5] == 'abcdef' |
| | 2. x[3: ] == 'cdefgh' |
| | 3. x[ : ] == 'abcdefgh' |
| | 4. x[4/2:3+2] == x[2:5] == 'cdef' |
| | |
| | Note: Both r0 and r1 are assumed to be integers. They |
| | may also be the result of an expression, in the event |
| | they have fractional components truncation will be |
| | performed. (eg: 1.67 -> 1) |
+----------+---------------------------------------------------------+
(6) Control Structures
+-----------+--------------------------------------------------------+
| STRUCTURE | DEFINITION |
+-----------+--------------------------------------------------------+
| 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)) |
+-----------+--------------------------------------------------------+
| switch | The first true case condition that is encountered will |
| | determine the result of the switch. If none of the case|
| | conditions hold true, the default action is assumed as |
| | the final return value. This is sometimes also known as|
| | a multi-way branch mechanism. |
| | eg: |
| | switch |
| | { |
| | case x > (y + z) : 2 * x / abs(y - z); |
| | case x < 3 : sin(x + y) |
| | default : 1 + x; |
| | } |
+-----------+--------------------------------------------------------+
| while | The structure will repeatedly evaluate the internal |
| | statement(s) 'while' the condition is true. The final |
| | statement in the final iteration will be used as the |
| | return value of the loop. |
| | eg: |
| | while ((x := (x - 1)) > 0) |
| | { |
| | y := x + z; |
| | w := z + y; |
| | } |
+-----------+--------------------------------------------------------+
| repeat/ | The structure will repeatedly evaluate the internal |
| until | statement(s) 'until' the condition is true. The final |
| | statement in the final iteration will be used as the |
| | return value of the loop. |
| | eg: |
| | repeat |
| | y := x + z; |
| | w := z + y; |
| | until ((x := (x - 1)) <= 0) |
+-----------+--------------------------------------------------------+
| ~ | Evaluate each sub-expression, then return as the result|
| | the value of the last sub-expression. This is sometimes|
| | known as multiple sequence point evaluation. |
| | eg: |
| | ~(i := x + 1, j := y / z, k := sin(w/u)) == (sin(w/u)))|
| | ~{i := x + 1; j := y / z; k := sin(w/u)} == (sin(w/u)))|
+-----------+--------------------------------------------------------+
+----------+---------------------------------------------------------+
|STRUCTURE | DEFINITION |
+----------+---------------------------------------------------------+
| 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)) |
+----------+---------------------------------------------------------+
| switch | The first true case condition that is encountered will |
| | determine the result of the switch. If none of the case |
| | conditions hold true, the default action is assumed as |
| | the final return value. This is sometimes also known as |
| | a multi-way branch mechanism. |
| | eg: |
| | switch |
| | { |
| | case x > (y + z) : 2 * x / abs(y - z); |
| | case x < 3 : sin(x + y) |
| | default : 1 + x; |
| | } |
+----------+---------------------------------------------------------+
| while | The structure will repeatedly evaluate the internal |
| | statement(s) 'while' the condition is true. The final |
| | statement in the final iteration will be used as the |
| | return value of the loop. |
| | eg: |
| | while ((x := (x - 1)) > 0) |
| | { |
| | y := x + z; |
| | w := z + y; |
| | } |
+----------+---------------------------------------------------------+
| repeat/ | The structure will repeatedly evaluate the internal |
| until | statement(s) 'until' the condition is true. The final |
| | statement in the final iteration will be used as the |
| | return value of the loop. |
| | eg: |
| | repeat |
| | y := x + z; |
| | w := z + y; |
| | until ((x := (x - 1)) <= 0) |
+----------+---------------------------------------------------------+
| ~ | Evaluate each sub-expression, then return as the result |
| | the value of the last sub-expression. This is sometimes |
| | known as multiple sequence point evaluation. |
| | eg: |
| | ~(i := x + 1, j := y / z, k := sin(w/u)) == (sin(w/u))) |
| | ~{i := x + 1; j := y / z; k := sin(w/u)} == (sin(w/u))) |
+----------+---------------------------------------------------------+
@ -382,7 +392,7 @@ include path (e.g: /usr/include/).
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
$f24(x,y,z,w)).
$f82(x,y,z,w)).
Special functions dramatically decrease the total evaluation time of
expressions which would otherwise have been written using the common
@ -466,7 +476,8 @@ correctly optimize such expressions for a given architecture.
(A-Z or a-z), then can be comprised of any combination of
letters, digits and underscores. (eg: x, var1 or power_func99)
(06) Expression lengths are limited only by storage capacity.
(06) Expression lengths and sub-expression lists are limited only by
storage capacity.
(07) The life-time of objects registered with or created from a
specific symbol-table must span at least the life-time of
@ -487,7 +498,7 @@ correctly optimize such expressions for a given architecture.
(11) Strings may be constructed from any letters, digits or special
characters such as (~!@#$%^&*()[]|=+ ,./?<>;:"`~_), and must
be enclosed with single-quotes.
eg: 'Frankly, my dear, I don't give a damn!'
eg: 'Frankly, my dear, I do not give a damn!'
(12) User defined normal functions can have up to 20 parameters,
where as user defined vararg-functions can have an unlimited
@ -505,7 +516,10 @@ correctly optimize such expressions for a given architecture.
(16) Composited functions can call themselves or any other functions
that have been defined prior to their own definition.
(17) Expressions may contain any of the following comment styles:
(17) Recursive calls made from within composited functions will have
a stack size bound by the stack of executing architecture.
(18) Expressions may contain any of the following comment styles:
1. // .... \n
2. # .... \n
3. /* .... */