Mathematical Functions
Mathematical Functions are used to modify data with the Data Tools  Data  Transform command in the worksheet or create function plots in the plot window.
Data Types
The expression evaluator supports 32bit signed integer numbers, doubleprecision floatingpoint numbers, a Boolean value, a text string of 0 to 256 characters, and time stamp values.
Variable Names
Variable names must begin with a column letter (i.e. A), row number (i.e. _1), or cell location (i.e. A2), which may be followed by other letters, numbers, or underscores (_), up to a maximum of 256 characters per variable name.
The variable names are not case sensitive. For example, sum(a..z), sum(A..z), and sum(A..Z) all refer to the same variable.
Precedence
The mathematical expression can consist of constants, variables (such as column letters), or functions (outlined below). The formulas follow standard precedence rules. Spaces are used in the equation for clarity.
Operators of equal precedence are evaluated from left to right within the equation. Parentheses are used to override precedence, and expressions within parentheses are performed first.
Operators, in order of decreasing precedence are:
( ) 
parentheses 
 
minus (or negative sign) 
^ 
exponentiation (raisetothepowerof) 
* / 
multiplication and division 
+  
addition and subtraction 
The expression evaluator treats operators with the following precedence:
Builtin Functions
The following builtin functions are supported:
Trigonometric Functions
All trigonometric functions are carried out in radians. If the data are in degrees, use the d2r(x) conversion function (in the Miscellaneous Functions section below) to convert degree data to radians and then use the trigonometric functions.
sin(x) 
sine of angle x 
cosine of angle x 

tan(x) 
tangent of angle x, the value of x must not be an odd multiple of P/2. 
asin(x) 
Arcsine in the range P /2 to P/2, x must be between 1 and 1 
acos(x) 
Arccosine in the range 0 to P, x must be between 1 and 1 
atan(x) 
Arctangent in the range P/2 to P/2 
atan2(y,x) 
Arctangent in the range P to P 
Bessel Functions
j0(x) j1(x) jn(n,x) 
Bessel functions of the first kind at x of orders 0, 1, and n, respectively 
y0(x) y1(x) yn(n,x) 
Return the Bessel functions of the second kind at x, of orders 0, 1, and n, respectively. For y0, y1, and yn, the value of x must not be negative. 
Exponential Functions
exp(x) 
exponential function of x (e to the x) 
sinh(x) 
hyperbolic sine of angle x 
cosh(x) 
hyperbolic cosine of angle x 
tanh(x) 
hyperbolic tangent of angle x 
natural logarithm of x, x must be positive 

base 10 logarithm of x, x must be positive 

pow(x,y) 
x raised to the yth power Alternatively use x^y Error conditions result if x is zero and y is negative or zero, x is negative and y is not an integer, an overflow results. 
Miscellaneous Functions
Statistical Functions of an Interval
sum(a..z) 
calculates the sum of a range of columns in a row 
sum(_1.._5) 
calculates the sum of a range of rows in a column 
avg(a..z) 
calculates the average of a range of columns in a row 
avg(_1.._5) 
calculates the average of a range of rows in a column 
std(a..z) 
calculates the (population) standard deviation of a range of columns in a row 
std(_1.._5) 
calculates the (population) standard deviation of a range of rows in a column 
rowmin(a..z) 
finds the minimum value of a range of columns in a row 
rowmin(_1.._5) 
finds the minimum value of a range of rows in a column 
rowmax(a..z) 
finds the maximum value of a range of columns in a row 
rowmax(_1.._5) 
finds the maximum value of a range of rows in a column 
The statistical functions of an interval of columns operate rowwise on an interval of columns. For example, SUM(A..Z) computes the sum of the twentysix columns A, B, C, ..., Z separately for each row. You can replace A..Z with any valid interval of columns, e.g., C..H or W..AC. There must be exactly two periods between the column labels. Columns may be given in reverse order, i.e., SUM(Z..A).
The statistical functions of an interval of rows operate columnwise on an interval of rows. For example, SUM(_1.._5) computes the sum of the 5 rows 1, 2, 3, 4, 5 separately for each column. You can replace _1.._5 with any valid interval of rows, e.g., _3.._12 or _34.._413. There must be exactly two periods between the row labels. Rows may be given in reverse order, i.e., SUM(_5.._1).
String Comparison
atof(x) 
converts string to floatingpoint number 
atoi(x) 
convert a string x to an integer value 
ftoa(x,y) 
convert a floatingpoint number x to a string with y digits after the decimal 
strlen(x) 
length of string x in characters 
strcmp(x,y) 
compare string x with y and return 1 if x>y, 1 if x<y, or 0 if x=y 
stricmp(x,y) 
compare string x with y without regard to the case of any letters in the strings 
strncmp(x,y,z) 
compare the first z character of string x with y 
strnicmp(x,y,z) 
compare the first z characters of string x with y without regard to the case of any letters in the strings 
String comparison functions work with strings, not numbers. Any rows or columns containing numbers result in blanks. In each of the string comparison functions, 1 is returned if string x is greater than string y, 1 is returned if string x is less than string y, and 0 if string x = string y. In the threeparameter comparison functions, the third parameter, z, specifies the number of characters to compare. For example, a z value of 3 compares the x and y strings' first three characters and ignores any characters after the third.
The comparisons are based on the standard ASCII table:
1. numeric values (disregarded in string comparisons as mentioned above)
2. cells starting with a space character
3. common punctuation
4. numeric text (numbers entered as text)
5. less common punctuation
6. uppercase letters
7. even less common punctuation
8. lower case letters
9. uncommon punctuation
10. blank cells (disregarded in string comparisons)
This is the ASCII table order. The table is read left to right, top to
bottom.
Items appearing toward the upper left corner are less than the items
appearing toward the lower left corner.
Boolean Expressions
Boolean expressions, include:
· logical operators (and, or, xor, not)
· comparison operators (=, <>, <, >, <=, >=)
· the IF function, i.e., IF(condition,true_value,false_value)
The words AND, OR, XOR, NOT, and IF are reserved keywords and may not be used as variable names.
Logical Operators (and, or, xor, not)
SYMBOL 
NAME 
DESCRIPTION 
AND 
AND 
The result is true if both operands are true 
&& 
AND 
The result is true if both operands are true 
! 
Logical NOT 
Inverts the Boolean value. True becomes false, false becomes true 
NOT 
Logical NOT 
Inverts the Boolean value. True becomes false, false becomes true 
& 
AND 
The result is true if both operands are true 
 
OR 
The result is true if either of the two operands are true 
XOR 
ExclusiveOR (XOR) 
The result is true only when the two operands are different 
 
OR 
The result is true if either of the two operands are true 
OR 
OR 
The result is true if either of the two operands are true 
Comparison Operators (=, <>, <, >, <=, >=)
SYMBOL 
NAME 
DESCRIPTION 
~ 
Bitwise NOT 
Inverts the bits in an integer 
* 
Multiple 
Multiplies the two operands 
/ 
Divide 
Divides the first operand by the second 
% 
Remainder 
Integer remainder of the first operand divided by the second 
+ 
Add 
Adds the two operands 
 
Subtract 
Subtracts the second operand from the first 
<< 
Shift Left 
Shifts the operand to the left 
>> 
Shift Right 
Shifts the operand to the right 
< 
Less Than 
Result is true if the value of p1 is less than the value of p2 
<= 
Less Than or Equal To 
Result is true if the ordinal value of p1 is less than or equal to p2 
> 
Greater Than 
Result is true if the ordinal value of p1 is greater than p2 
>= 
Greater Than or Equal To 
Result is true if the ordinal value of p1 is greater than or equal to p2 
== 
Equal To 
Result is true if the operands have identical values 
!= 
Not Equal To 
Result is true if the operands do not have identical values 
<> 
Not Equal To 
Result is true if the operands do not have identical values 
IF Function IF(condition, true_value, false_value)
SYMBOL 
NAME 
EXAMPLE 
DESCRIPTION 
IF 
Conditional Evaluation 
IF(p1,p2,p3) 
IF(condition,true_value,false_value) If p1 is true, the result will be p2. If p1 is false, the result will be p3 
IF 
Conditional Evaluation 
p1?p2:p3 
condition?true_value:false_value If p1 is true, the result will be p2. If p1 is false, the result will be p3 
Examples
The following are examples of mathematical function syntax. If you use Transform in the worksheet, replace X, Y, and Z with column letters (A is column A), row numbers (_1 is row 1), or cell locations (A1).
Equation 
Mathematical Function Syntax 

x^2 OR pow(x,2) 

ln(x) 

log10(x) 

(1exp(X)) 

1exp(x^2) 

1(sin(x)/x) 

x^2/(1+x^2) 

(2 * X)pow(x,2) 

(pow(x,2)+pow(y,2))*(sin(8*atan(x*y))) 
See Also