Expression Help

Expression Syntax

Expressions have pretty much the same syntax as they would have on paper, with the following exceptions:

Each expression must end with a semicolon. This is because the expression string can actually contain multiple expressions. The semicolon is used to mark the end of the expression.
Examples:

4*x+5;

y=5+2;g=4+6;

y=r*sin(a);x=r*cos(a);

The asterisk '*' must be used to multiply.
Examples:

y=5*6; Valid

g=(x+1)*(x-1); Valid

g=(x+1)(x-1); Invalid

More than one expression may be contained within an expression string. As shown above, each expression must end with a semicolon, even if only one expression is in the string. The value of an expression string is the value of the last expression in the string.
Examlples:

g=7; Value: 7

k=z+1; Value: z+1

r=4;k=6;o=9+r-k; Value: 9+r-k

Some functions may take reference parameters. These parameters are references to other variables. You can mix reference parameters with normal parameters. The order of the normal parameters must remain the same and the order of the reference parameters must remain the same.
Examples:

min(1,2,3,4,&mval); &mval is a reference to a variable mval

min(1,2,&mval,3,4); You may mix them inside like this.

min(1,2,(&mval),3,4); You may not nest reference parameters in any way

Expressions may also be nested with parenthesis.
Examples:

y=sin(x-cos(5+max(4,5,6*x)));

6+(5-2*(x+y));

Expressions may also have whitespace characters and comments. Whitespace characters such as newlines, linefeeds, carriage returns, spaces, and tabs are ignored. Comments begin with the pound sign '#' and end at the end of the line.
Example:
#Set the x value
x = d * cos(r);

#Set the y value
y = d * sin(r);
                
If a variable is used in an expression, but that variable does not exist, it is considered zero. If it does exist then its value is used instead.

Notice: An expression can NOT assign to a constant and an expression can NOT use a constant as a reference parameter.

Order of operators.

The order of operators are processed correctly in ExprEval. The parameters to functions may be evaluated out of order, depending on the function itself.
The following illustrates the order of operators:

Operator Direction Example

Functions and Parenthesis N/A (x + 5) * sin(d);

Negation Right to Left y = -2;

Exponents Left to Right y = x ^ 2;

Multiplication and Division Left to Right x * 5 / y;

Addition and Subtraction Left to Right 4 + 5 - 3;

Assignment Right to Left x = y = z = 0;

ExprEval Internal Functions

The following functions are provided with ExprEval:

Function Min. Args Max. Args Min. Ref Args Max. Ref Args Result/Comment

abs(v) 1 1 0 0 Absolute value of v.
abs(-4.3) returns 4.3

mod(v,d) 2 2 0 0 Remainder of v/d.
mod(5.2,2.5) return 0.2

ipart(v) 1 1 0 0 The integer part of v.
ipart(3.2) returns 3

fpart(v) 1 1 0 0 The fractional part of v.
fpart(3.2) returns 0.2

min(v,...) 1 None 0 0 The minimum number passed.
min(3,2,-5,-2,7) returns -5

max(v,...) 1 None 0 0 The maximum number passed.
max(3,2,-5,-2,7) returns 7

pow(a,b) 2 2 0 0 The value a raised to the power b.
pow(3.2,1.7) returns 3.2^1.7

sqrt(a) 1 1 0 0 The square root of a.
sqrt(16) returns 4

sin(a) 1 1 0 0 The sine of a radians.
sin(1.5) returns around 0.997

sinh(a) 1 1 0 0 The hyperbolic sine of a.
sinh(1.5) returns around 2.129

asin(a) 1 1 0 0 The arc-sine of a in radians.
asin(0.5) returns around 0.524

cos(a) 1 1 0 0 The cosine of a radians.
cos(1.5) returns around 0.0707

cosh(a) 1 1 0 0 The hyperbolic cosine of a.
cosh(1.5) returns around 2.352

acos(a) 1 1 0 0 The arc-cosine of a in radians.
acos(0.5) returns around 1.047

tan(a) 1 1 0 0 The tangent of a radians.
tan(1.5) returns around 14.101

tanh(a) 1 1 0 0 The hyperbolic tangent of a.
tanh(1.5) returns around 0.905

atan(a) 1 1 0 0 The arc-tangent of a in radians.
atan(0.3) returns about 0.291

atan2(y,x) 2 2 0 0 The arc-tangent of y/x, with quadrant correction.
atan2(4,3) returns about 0.927

log(a) 1 1 0 0 The base 10 logarithm of a.
log(100) returns 2

pow10(a) 1 1 0 0 10 raised to the power of a.
pow10(2) returns 100

ln(a) 1 1 0 0 The base e logarithm of a.
ln(2.8) returns around 1.030

exp(a) 1 1 0 0 e raised to the power of a.
exp(2) returns around 7.389

logn(a,b) 2 2 0 0 The base b logarithm of a.
logn(16,2) returns 4

ceil(a) 1 1 0 0 Rounds a up to the nearest integer.
ceil(3.2) returns 4

floor(a) 1 1 0 0 Rounds a down to the nearest integer.
floor(3.2) returns 3

rand(&seed) 0 0 1 1 Returns a number between 0 up to but not including 1.

random(a,b,&seed) 2 2 1 1 Returns a number between a up to and including b.

randomize(&seed) 0 0 1 1 Seed the random number generator with a value based on the current time.
Return value is unknown

deg(a) 1 1 0 0 Returns a radians converted to degrees.
deg(3.14) returns around 179.909

rad(a) 1 1 0 0 Returns a degrees converted to radians.
rad(180) returns around 3.142

recttopolr(x,y) 2 2 0 0 Returns the polar radius of the rectangular co-ordinates.
recttopolr(2,3) returns around 3.606

recttopola(x,y) 2 2 0 0 Returns the polar angle (0...2PI) in radians of the rectangular co-ordinates.
recttopola(2,3) returns around 0.588

poltorectx(r,a) 2 2 0 0 Returns the x rectangular co-ordinate of the polar co-ordinates.
poltorectx(3,1.5) returns around 0.212

poltorecty(r,a) 2 2 0 0 Returns the y rectangular co-ordinate of the polar co-ordinates.
poltorecty(3,1.5) returns around 2.992

if(c,t,f) 3 3 0 0 Evaluates and returns t if c is not 0.0. Else evaluates and returns f.
if(0.1,2.1,3.9) returns 2.1

select(c,n,z[,p]) 3 4 0 0 Returns n if c is less than 0.0. Returns z if c is 0.0. If c is greater than 0.0 and only three arguments were passed, returns z. If c is greater than 0.0 and four arguments were passed, return p.
select(3,1,4,5) returns 5

equal(a,b) 2 2 0 0 Returns 1.0 if a is equal to b. Else returns 0.0
equal(3,2) returns 0.0

above(a,b) 2 2 0 0 Returns 1.0 if a is above b. Else returns 0.0
above(3,2) returns 1.0

below(a,b) 2 2 0 0 Returns 1.0 if a is below b. Else returns 0.0
below(3,2) returns 0.0

avg(a,...) 1 None 0 0 Returns the average of the values passed.
avg(3,3,6) returns 4

clip(v,min,max) 3 3 0 0 Clips v to the range from min to max. If v is less than min, it returns min. If v is greater than max it returns max. Otherwise it returns v.
clip(3,1,2) returns 2

clamp(v,min,max) 3 3 0 0 Clamps v to the range from min to max, looping if needed.
clamp(8.2,1.3,4.7) returns 1.4

pntchange(side1old, side2old, side1new, side2new, oldpnt) 5 5 0 0 This is used to translate points from different scale. It works no matter the orientation as long as the sides are lined up correctly.
pntchange(-1,1,0,480,-0.5) returns 120 (x example)
pntchange(-1,1,480,0,-0.5) returns 360 (y example)

poly(x,c1,...) 2 None 0 0 This function calculates the polynomial. x is the value to use in the polynomial. c1 and on are the coefficients.
poly(4,6,9,3,1,4) returns 2168
same as 6*4⁴ + 9*4³ + 3*4² + 1*4¹ + 4*4⁰

and(a,b) 2 2 0 0 Returns 0.0 if either a or b are 0.0 Else returns 1.0
and(2.1,0.0) returns 0.0

or(a,b) 2 2 0 0 Returns 0.0 if both a and b are 0.0 Else returns 1.0
or(2.1,0.0) returns 1.0

not(a) 1 1 0 0 Returns 1.0 if a is 0.0 Else returns 0.0
not(0.3) returns 0.0

for(init,test,inc,a1,...) 4 None 0 0 This function acts like a for loop in C. First init is evaluated. Then test is evaluated. As long as the test is not 0.0, the action statements (a1 to an) are evaluated, the inc statement is evaluated, and the test is evaluated again. The result is the result of the final action statement.
for(x=0,below(x,11),x=x+1,y=y+x) returns 55.0 (if y was initially 0.0)

many(expr,...) 1 None 0 0 This function treats many subexpressions as a single object (function). It is mainly for the 'for' function.
for(many(j=5,k=1),above(j*k,0.001),many(j=j+5,k=k/2),0)

ExprEval Internal Constants

The following constants are provided with ExprEval:

Constant Math Form Value

M_E e 2.7182818284590452354

M_LOG2E log₂(e) 1.4426950408889634074

M_LOG10E log₁₀(e) 0.43429448190325182765

M_LN2 ln(2) 0.69314718055994530942

M_LN10 ln(10) 2.30258509299404568402

M_PI π 3.14159265358979323846

M_PI_2 π/2 1.57079632679489661923

M_PI_4 π/4 0.78539816339744830962

M_1_PI 1/π 0.31830988618379067154

M_2_PI 2/π 0.63661977236758134308

M_1_SQRTPI 1/√(π) 0.56418958354776

M_2_SQRTPI 2/√(π) 1.12837916709551257390

M_SQRT2 √(2) 1.41421356237309504880

M_1_SQRT2 1/√(2) 0.70710678118654752440

Application Internal Functions

Application defined expression functions go here.

Function Min. Args Max. Args Min. Ref Args Max. Ref Args Result/Comment

Application Internal Constants

Application defined expression constants go here.

Constant Math Form Value

Application Internal Variables

Application defined expression variables go here.

Variable Math Form Value

Expression Help

Contents

Expression Syntax

Order of Operators

ExprEval Internal Functions

ExprEval Internal Constants

Application Internal Functions

Application Internal Constants

Application Internal Variables

Expression Syntax

Order of operators.

ExprEval Internal Functions

ExprEval Internal Constants

Application Internal Functions

Application Internal Constants

Application Internal Variables

Operator	Direction	Example
Functions and Parenthesis	N/A	(x + 5) * sin(d);
Negation	Right to Left	y = -2;
Exponents	Left to Right	y = x ^ 2;
Multiplication and Division	Left to Right	x * 5 / y;
Addition and Subtraction	Left to Right	4 + 5 - 3;
Assignment	Right to Left	x = y = z = 0;

Function	Min. Args	Max. Args	Min. Ref Args	Max. Ref Args	Result/Comment
abs(v)	1	1	0	0	Absolute value of v. abs(-4.3) returns 4.3
mod(v,d)	2	2	0	0	Remainder of v/d. mod(5.2,2.5) return 0.2
ipart(v)	1	1	0	0	The integer part of v. ipart(3.2) returns 3
fpart(v)	1	1	0	0	The fractional part of v. fpart(3.2) returns 0.2
min(v,...)	1	None	0	0	The minimum number passed. min(3,2,-5,-2,7) returns -5
max(v,...)	1	None	0	0	The maximum number passed. max(3,2,-5,-2,7) returns 7
pow(a,b)	2	2	0	0	The value a raised to the power b. pow(3.2,1.7) returns 3.2^1.7
sqrt(a)	1	1	0	0	The square root of a. sqrt(16) returns 4
sin(a)	1	1	0	0	The sine of a radians. sin(1.5) returns around 0.997
sinh(a)	1	1	0	0	The hyperbolic sine of a. sinh(1.5) returns around 2.129
asin(a)	1	1	0	0	The arc-sine of a in radians. asin(0.5) returns around 0.524
cos(a)	1	1	0	0	The cosine of a radians. cos(1.5) returns around 0.0707
cosh(a)	1	1	0	0	The hyperbolic cosine of a. cosh(1.5) returns around 2.352
acos(a)	1	1	0	0	The arc-cosine of a in radians. acos(0.5) returns around 1.047
tan(a)	1	1	0	0	The tangent of a radians. tan(1.5) returns around 14.101
tanh(a)	1	1	0	0	The hyperbolic tangent of a. tanh(1.5) returns around 0.905
atan(a)	1	1	0	0	The arc-tangent of a in radians. atan(0.3) returns about 0.291
atan2(y,x)	2	2	0	0	The arc-tangent of y/x, with quadrant correction. atan2(4,3) returns about 0.927
log(a)	1	1	0	0	The base 10 logarithm of a. log(100) returns 2
pow10(a)	1	1	0	0	10 raised to the power of a. pow10(2) returns 100
ln(a)	1	1	0	0	The base e logarithm of a. ln(2.8) returns around 1.030
exp(a)	1	1	0	0	e raised to the power of a. exp(2) returns around 7.389
logn(a,b)	2	2	0	0	The base b logarithm of a. logn(16,2) returns 4
ceil(a)	1	1	0	0	Rounds a up to the nearest integer. ceil(3.2) returns 4
floor(a)	1	1	0	0	Rounds a down to the nearest integer. floor(3.2) returns 3
rand(&seed)	0	0	1	1	Returns a number between 0 up to but not including 1.
random(a,b,&seed)	2	2	1	1	Returns a number between a up to and including b.
randomize(&seed)	0	0	1	1	Seed the random number generator with a value based on the current time. Return value is unknown
deg(a)	1	1	0	0	Returns a radians converted to degrees. deg(3.14) returns around 179.909
rad(a)	1	1	0	0	Returns a degrees converted to radians. rad(180) returns around 3.142
recttopolr(x,y)	2	2	0	0	Returns the polar radius of the rectangular co-ordinates. recttopolr(2,3) returns around 3.606
recttopola(x,y)	2	2	0	0	Returns the polar angle (0...2PI) in radians of the rectangular co-ordinates. recttopola(2,3) returns around 0.588
poltorectx(r,a)	2	2	0	0	Returns the x rectangular co-ordinate of the polar co-ordinates. poltorectx(3,1.5) returns around 0.212
poltorecty(r,a)	2	2	0	0	Returns the y rectangular co-ordinate of the polar co-ordinates. poltorecty(3,1.5) returns around 2.992
if(c,t,f)	3	3	0	0	Evaluates and returns t if c is not 0.0. Else evaluates and returns f. if(0.1,2.1,3.9) returns 2.1
select(c,n,z[,p])	3	4	0	0	Returns n if c is less than 0.0. Returns z if c is 0.0. If c is greater than 0.0 and only three arguments were passed, returns z. If c is greater than 0.0 and four arguments were passed, return p. select(3,1,4,5) returns 5
equal(a,b)	2	2	0	0	Returns 1.0 if a is equal to b. Else returns 0.0 equal(3,2) returns 0.0
above(a,b)	2	2	0	0	Returns 1.0 if a is above b. Else returns 0.0 above(3,2) returns 1.0
below(a,b)	2	2	0	0	Returns 1.0 if a is below b. Else returns 0.0 below(3,2) returns 0.0
avg(a,...)	1	None	0	0	Returns the average of the values passed. avg(3,3,6) returns 4
clip(v,min,max)	3	3	0	0	Clips v to the range from min to max. If v is less than min, it returns min. If v is greater than max it returns max. Otherwise it returns v. clip(3,1,2) returns 2
clamp(v,min,max)	3	3	0	0	Clamps v to the range from min to max, looping if needed. clamp(8.2,1.3,4.7) returns 1.4
pntchange(side1old, side2old, side1new, side2new, oldpnt)	5	5	0	0	This is used to translate points from different scale. It works no matter the orientation as long as the sides are lined up correctly. pntchange(-1,1,0,480,-0.5) returns 120 (x example) pntchange(-1,1,480,0,-0.5) returns 360 (y example)
poly(x,c1,...)	2	None	0	0	This function calculates the polynomial. x is the value to use in the polynomial. c1 and on are the coefficients. poly(4,6,9,3,1,4) returns 2168 same as 64⁴ + 94³ + 34² + 14¹ + 4*4⁰
and(a,b)	2	2	0	0	Returns 0.0 if either a or b are 0.0 Else returns 1.0 and(2.1,0.0) returns 0.0
or(a,b)	2	2	0	0	Returns 0.0 if both a and b are 0.0 Else returns 1.0 or(2.1,0.0) returns 1.0
not(a)	1	1	0	0	Returns 1.0 if a is 0.0 Else returns 0.0 not(0.3) returns 0.0
for(init,test,inc,a1,...)	4	None	0	0	This function acts like a for loop in C. First init is evaluated. Then test is evaluated. As long as the test is not 0.0, the action statements (a1 to an) are evaluated, the inc statement is evaluated, and the test is evaluated again. The result is the result of the final action statement. for(x=0,below(x,11),x=x+1,y=y+x) returns 55.0 (if y was initially 0.0)
many(expr,...)	1	None	0	0	This function treats many subexpressions as a single object (function). It is mainly for the 'for' function. for(many(j=5,k=1),above(j*k,0.001),many(j=j+5,k=k/2),0)

Constant	Math Form	Value
M_E	e	2.7182818284590452354
M_LOG2E	log₂(e)	1.4426950408889634074
M_LOG10E	log₁₀(e)	0.43429448190325182765
M_LN2	ln(2)	0.69314718055994530942
M_LN10	ln(10)	2.30258509299404568402
M_PI	π	3.14159265358979323846
M_PI_2	π/2	1.57079632679489661923
M_PI_4	π/4	0.78539816339744830962
M_1_PI	1/π	0.31830988618379067154
M_2_PI	2/π	0.63661977236758134308
M_1_SQRTPI	1/√(π)	0.56418958354776
M_2_SQRTPI	2/√(π)	1.12837916709551257390
M_SQRT2	√(2)	1.41421356237309504880
M_1_SQRT2	1/√(2)	0.70710678118654752440