Arithmetic and Math

1.1. Overview

PostScript provides a comprehensive set of arithmetic and mathematical operators for numerical computation. These operators work with both integer and real (floating-point) numbers, with automatic type promotion where appropriate.

1.2. Categories

1.2.1. Basic Arithmetic

The fundamental arithmetic operations:

add - Add two numbers
sub - Subtract two numbers
mul - Multiply two numbers
div - Divide (real result)
idiv - Integer division
mod - Modulo (remainder)

1.2.2. Unary Operations

Operations on a single number:

abs - Absolute value
neg - Negate
ceiling - Round up to integer
floor - Round down to integer
round - Round to nearest integer
truncate - Truncate to integer

1.2.3. Exponential and Logarithmic

Power and logarithm functions:

sqrt - Square root
exp - Exponential (base^exponent)
ln - Natural logarithm (base e)
log - Common logarithm (base 10)

1.2.4. Trigonometric

Trigonometric functions (angles in degrees):

sin - Sine
cos - Cosine
atan - Arctangent

1.2.5. Bitwise Operations

Operations on integer bit patterns:

bitshift - Bitwise shift left or right

1.2.6. Random Numbers

Pseudo-random number generation:

rand - Generate random integer
srand - Seed random generator
rrand - Get/set random seed

1.3. Type Coercion Rules

1.3.1. Integer vs. Real Results

If both operands are integers and the result fits in integer range, the result is an integer
Otherwise, the result is a real number
The div operator always returns a real, even with integer operands
The idiv operator always returns an integer

1.3.2. Examples

3 4 add        % → 7 (integer)
3 4.0 add      % → 7.0 (real)
4 2 div        % → 2.0 (real, always)
4 2 idiv       % → 2 (integer, always)

1.4. Common Pitfalls

Division by Zero

Dividing by zero results in an undefinedresult error:

5 0 div    % Error: undefinedresult

Domain Restrictions

Some operations have restricted domains:

sqrt requires non-negative arguments
ln and log require positive arguments
exp with fractional exponent requires non-negative base

-4 sqrt    % Error: rangecheck
0 ln       % Error: rangecheck
-2 0.5 exp % Error: undefinedresult

Trigonometric Functions Use Degrees

PostScript trigonometric functions work in degrees, not radians:

90 sin     % → 1.0 (90 degrees)
0 cos      % → 1.0 (0 degrees)
1 0 atan   % → 90.0 (returns degrees)

Integer Overflow

When integer operations exceed the maximum integer value, the result becomes a real:

2147483647 1 add  % → 2147483648.0 (real)

1.5. Best Practices

1.5.1. Use Appropriate Division Operator

Use div for mathematical division requiring precise real results
Use idiv when you need integer quotients (truncated toward zero)
Use mod to get the remainder

1.5.2. Check Domain Before Operations

For operations with restricted domains, validate input:

/safesqrt {  % num -> real or error
  dup 0 lt {
    pop
    (sqrt: negative argument) print
    0
  } {
    sqrt
  } ifelse
} def

1.5.3. Be Aware of Precision

Real numbers have finite precision. Avoid comparing reals for exact equality:

% Bad:
0.1 0.2 add 0.3 eq  % May be false due to rounding

% Better:
/nearlyequal {  % num1 num2 tolerance -> bool
  3 1 roll sub abs exch lt
} def

0.1 0.2 add 0.3 0.0001 nearlyequal  % true

1. Arithmetic and Math Operators