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Arithmetic Operators

General

Arithmetic operators perform mathematical calculations on numbers from the operand stack. They consume their operands and push the result back onto the stack.

PostScript supports both integer and real (floating-point) arithmetic, with automatic type promotion when mixing types.

add

General

The add operator adds two numbers.

Syntax

num1 num2 add (1) (2) (3)

  1. First number

  2. Second number

  3. Operator that adds them

Where,

num1, num2

Numbers to add

Stack effect: num1 num2 — sum

Examples

5 3 add                % 8
2.5 1.5 add            % 4.0

sub

General

The sub operator subtracts the second number from the first.

Syntax

num1 num2 sub (1) (2) (3)

  1. Minuend

  2. Subtrahend

  3. Operator that subtracts

Where,

num1

Number to subtract from

num2

Number to subtract

Stack effect: num1 num2 — difference

Examples

10 3 sub               % 7 (10 - 3)
5 8 sub                % -3 (5 - 8)

mul

General

The mul operator multiplies two numbers.

Syntax

num1 num2 mul (1) (2) (3)

  1. First factor

  2. Second factor

  3. Operator that multiplies

Where,

num1, num2

Numbers to multiply

Stack effect: num1 num2 — product

Examples

6 7 mul                % 42
2.5 4 mul              % 10.0

div

General

The div operator divides two numbers, always producing a real result.

Syntax

num1 num2 div (1) (2) (3)

  1. Dividend

  2. Divisor

  3. Operator that divides

Where,

num1

Number to divide

num2

Divisor (must not be zero)

Stack effect: num1 num2 — quotient

Examples

10 4 div               % 2.5
15 3 div               % 5.0

Always returns a real number.

idiv

General

The idiv operator performs integer division, truncating toward zero.

Syntax

int1 int2 idiv (1) (2) (3)

  1. Dividend (integer)

  2. Divisor (integer)

  3. Operator for integer division

Where,

int1, int2

Integer operands

Stack effect: int1 int2 — quotient

Examples

10 3 idiv              % 3 (truncated)
-10 3 idiv             % -3 (toward zero)

mod

General

The mod operator returns the remainder after integer division.

Syntax

int1 int2 mod (1) (2) (3)

  1. Dividend

  2. Divisor

  3. Operator for modulo

Where,

int1, int2

Integer operands

Stack effect: int1 int2 — remainder

Examples

10 3 mod               % 1 (10 = 3×3 + 1)
17 5 mod               % 2

abs

General

The abs operator returns the absolute value of a number.

Syntax

num abs (1) (2)

  1. Number

  2. Operator for absolute value

Where,

num

Any number

Stack effect: num — |num|

Examples

-5 abs                 % 5
3.14 abs               % 3.14

neg

General

The neg operator negates a number (multiplies by -1).

Syntax

num neg (1) (2)

  1. Number to negate

  2. Operator that negates

Where,

num

Any number

Stack effect: num — -num

Examples

5 neg                  % -5
-3 neg                 % 3

sqrt

General

The sqrt operator returns the square root of a number.

Syntax

num sqrt (1) (2)

  1. Number (non-negative)

  2. Operator for square root

Where,

num

Non-negative number

Stack effect: num — √num

Examples

16 sqrt                % 4.0
2 sqrt                 % 1.41421...

sin

General

The sin operator returns the sine of an angle in degrees.

Syntax

angle sin (1) (2)

  1. Angle in degrees

  2. Operator for sine

Where,

angle

Angle in degrees (number)

Stack effect: angle — sine

Examples

0 sin                  % 0.0
90 sin                 % 1.0
30 sin                 % 0.5

cos

General

The cos operator returns the cosine of an angle in degrees.

Syntax

angle cos (1) (2)

  1. Angle in degrees

  2. Operator for cosine

Where,

angle

Angle in degrees (number)

Stack effect: angle — cosine

Examples

0 cos                  % 1.0
90 cos                 % 0.0
60 cos                 % 0.5

atan

General

The atan operator returns the arctangent of num1/num2 in degrees, with proper handling of the quadrant.

Syntax

num1 num2 atan (1) (2) (3)

  1. Numerator (Y value)

  2. Denominator (X value)

  3. Operator for arctangent

Where,

num1, num2

Numbers (num2 cannot be zero unless num1 is also zero)

Stack effect: num1 num2 — angle

Examples

1 1 atan               % 45.0 (first quadrant)
1 -1 atan              % 135.0 (second quadrant)

Arithmetic Patterns

Calculating distances

% Distance between (x1,y1) and (x2,y2)
/x1 10 def /y1 20 def
/x2 40 def /y2 60 def

x2 x1 sub dup mul      % (x2-x1)²
y2 y1 sub dup mul      % (y2-y1)²
add sqrt               % √((x2-x1)² + (y2-y1)²)
% Result: 50.0

Pythagorean theorem for distance.

Converting units

% Inches to points (72 points per inch)
2.5 72 mul             % 180.0 points

% Degrees to radians (approximately)
90 3.14159 mul 180 div % π/2 radians