Table of Contents

• 1. Description
• 2. Syntax
  • 2.1. Stack Effect
• 3. Parameters
• 4. Return Values
• 5. Examples
  • 5.1. Basic Usage
  • 5.2. Distance Calculation
  • 5.3. Vector Magnitude
• 6. Advanced Examples
  • 6.1. Normalize Vector
  • 6.2. Quadratic Formula
• 7. Edge Cases
  • 7.1. Domain Restriction
  • 7.2. Zero and Small Numbers
• 8. Related Commands
• 9. PostScript Level
• 10. Error Conditions
• 11. See Also

Returns the square root of a number.

1. Description

The sqrt operator pops a non-negative number from the operand stack and pushes its square root. The operand must be non-negative; negative values cause a rangecheck error. The result is always a real number.

This is a Level 1 operator, available in all PostScript implementations.

2. Syntax

num sqrt real

2.1. Stack Effect

Table 1. Before Execution

Position	Content
Top	num (integer or real) - Non-negative number

Table 2. After Execution

Position	Content
Top	real (real) - Square root of num

3. Parameters

num

A non-negative number (integer or real, must be ≥ 0)

4. Return Values

real

The square root of num (always a real number)

5. Examples

5.1. Basic Usage

% Perfect squares
4 sqrt         % → 2.0
9 sqrt         % → 3.0
16 sqrt        % → 4.0
25 sqrt        % → 5.0

% Non-perfect squares
2 sqrt         % → 1.41421...
10 sqrt        % → 3.16228...

5.2. Distance Calculation

% Pythagorean theorem: distance between points
/distance2D {  % x1 y1 x2 y2 -> dist
    3 -1 roll sub  % x1 y1 (y2-y1)
    dup mul        % x1 y1 dy²
    3 1 roll       % dy² x1 y1
    exch sub       % dy² (x1-x2)
    dup mul add    % dx² + dy²
    sqrt           % √(dx² + dy²)
} def

0 0 3 4 distance2D  % → 5.0

5.3. Vector Magnitude

/magnitude {  % [x y] -> mag
    aload pop dup mul exch dup mul add sqrt
} def

[3 4] magnitude  % → 5.0

6. Advanced Examples

6.1. Normalize Vector

/normalize {  % [x y] -> [nx ny]
    dup magnitude    % [x y] mag
    dup 0 eq {
        pop pop [0 0]
    } {
        exch aload pop  % mag x y
        2 index div     % mag x (y/mag)
        3 1 roll div    % (y/mag) (x/mag)
        exch 2 array astore
    } ifelse
} def

[3 4] normalize  % → [0.6 0.8]

6.2. Quadratic Formula

/quadratic {  % a b c -> root1 root2 or null
    % Solve ax² + bx + c = 0
    3 copy             % a b c a b c
    pop dup mul        % a b c b²
    4 4 index mul      % a b c b² 4a
    5 -1 roll mul sub  % a b (b²-4ac)
    dup 0 lt {
        % No real roots
        pop pop pop null
    } {
        sqrt           % a b √(b²-4ac)
        1 index neg    % a b √d (-b)
        1 index add    % a b √d (-b+√d)
        3 index 2 mul div  % a b √d root1
        4 1 roll       % root1 a b √d
        neg add        % root1 a (-b-√d)
        exch 2 mul div % root1 root2
    } ifelse
} def

7. Edge Cases

Negative arguments cause rangecheck error.

7.1. Domain Restriction

% WRONG: Negative argument
-4 sqrt        % ERROR: rangecheck

% CORRECT: Validate input
/safeSqrt {  % num -> sqrt|0
    dup 0 lt {
        pop 0
    } {
        sqrt
    } ifelse
} def

-4 safeSqrt    % → 0 (safe fallback)
4 safeSqrt     % → 2.0

7.2. Zero and Small Numbers

% Zero is valid
0 sqrt         % → 0.0

% Very small numbers
0.0001 sqrt    % → 0.01
1.0e-10 sqrt   % → 1.0e-5

8. Related Commands

• exp - Exponentiation

• mul - Multiplication

9. PostScript Level

Available in: PostScript Level 1 and higher

10. Error Conditions

stackunderflow

The operand stack is empty.

typecheck

The operand is not a number.

rangecheck

The operand is negative.

-4 sqrt        % ERROR: rangecheck

11. See Also

• Arithmetic and Math - All arithmetic operators