Math

The firmware supports extensive mathematical operations in G-code using expressions enclosed in square brackets []. These expressions can be used in G-code parameters and with the M118.1 P# command to evaluate and print results. Note that all functions using letters are lowercase and are case sensitive.

Basic Arithmetic Operations

Operators

• +: Addition

• -: Subtraction

• *: Multiplication

• /: Division

• ^: Exponentiation (power)

• mod: Modulo (remainder)

Examples

M118.1 P[1+1]        ; Returns result = 2.000
M118.1 P[5-3]        ; Returns result = 2.000
M118.1 P[4*3]        ; Returns result = 12.000
M118.1 P[10/2]       ; Returns result = 5.000
M118.1 P[2^3]        ; Returns result = 8.000
M118.1 P[7mod3]      ; Returns result = 1.000
G01 X[#103+2*#107]

Mathematical Functions

Trigonometric Functions (angles in degrees)

• sin[x]: Sine of x degrees

• cos[x]: Cosine of x degrees

• tan[x]: Tangent of x degrees

• asin[x]: Arcsine of x (returns degrees)

• acos[x]: Arccosine of x (returns degrees)

• atan[x]: Arctangent of x (returns degrees)

Examples

M118.1 P[sin[45]]    ; Returns result = 0.707
M118.1 P[cos[0]]     ; Returns result = 1
M118.1 P[tan[90]]    ; Returns result = nan
M118.1 P[asin[0.5]]  ; Returns result = 30
M118.1 P[acos[0]]    ; Returns result = 90

Other Mathematical Functions

• sqrt[x]: Square root of x

• abs[x]: Absolute value of x

• round[x]: Round x to nearest integer

• fix[x]: Floor function (truncate to integer)

• fup[x]: Ceiling function (round up to integer)

• ln[x]: Natural logarithm of x

• exp[x]: Exponential function (e^x)

Examples

M118.1 P[sqrt[16]]   ; Returns result = 4.000
M118.1 P[abs[-5]]    ; Returns result = 5.000
M118.1 P[round[3.7]] ; Returns result = 4.000
M118.1 P[fix[3.7]]   ; Returns result = 3.000
M118.1 P[fup[3.2]]   ; Returns result = 4.000
M118.1 P[ln[2.718]]  ; Returns result = 1.000
M118.1 P[exp[2]]     ; Returns result = 7.389

Comparison Operators

Boolean comparisons can be used and will evaluate to 1 (true) or 0 (false):

Boolean Comparisons

• eq: Equal (with tolerance)

• ne: Not equal

• gt: Greater than

• ge: Greater than or equal

• lt: Less than

• le: Less than or equal

Examples

M118.1 P[5eq5]       ; Returns result = 1.000 (true)
M118.1 P[3gt2]       ; Returns result = 1.000 (true)
M118.1 P[2lt5]       ; Returns result = 1.000 (true)
M118.1 P[4le4]       ; Returns result = 1.000 (true)

Logical Operators

Logical Operators can be used and will evaluate to 1 (true) or 0 (false):

Boolean Logic

• and: Logical AND (both values must be non-zero)

• or: Logical OR (at least one value must be non-zero)

• xor: Logical XOR (exactly one value must be non-zero)

• nor: Logical NOR (both values must be zero)

Examples

M118.1 P[1and1]      ; Returns result = 1.000 (true)
M118.1 P[0or1]       ; Returns result = 1.000 (true)
M118.1 P[1xor0]      ; Returns result = 1.000 (true)
M118.1 P[0nor0]      ; Returns result = 1.000 (true)

Complex Expressions

Complex expressions can be used and will be evaluated per normal PEMDAS order of operations.

Order of Operations (PEMDAS)

1. Parentheses/Brackets

2. Exponentiation

3. Multiplication/Division/Modulo

4. Addition/Subtraction

5. Comparison operators

6. Logical operators

Examples

M118.1 P[1+2*[5-2*2]+2^2+sin[45]]   ; Returns result = 7.707

Error Handling

The follow are the expected behaviors when errors are encountered:

• Division by zero: Halts with error

• Modulo by zero: Halts with error

• Undefined functions: Returns nan

• Invalid variables: Halts with error

• Mismatched brackets: Halts with error

Further Reading

GCodeTutor.com has a good article describing how variables and math can be used in GCode.