ceiling

1. Description

The ceiling operator pops a number from the operand stack and pushes the smallest integer that is greater than or equal to that number. The type of the result is the same as the type of the operand - if the input is an integer, it returns an integer; if the input is a real, it returns a real with no fractional part.

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

2. Syntax

num1 ceiling num2

2.1. Stack Effect

Table 1. Before Execution
Position	Content
Top	`num1` (integer or real) - Number to round up

Table 2. After Execution
Position	Content
Top	`num2` (integer or real) - Ceiling of num1 (same type as num1)

3. Parameters

num1: Any number (integer or real)

4. Return Values

num2

The ceiling of num1 (type matches num1):

For integers: returns the same value
For reals: returns real with no fractional part, rounded up

5. Examples

5.1. Basic Usage

% Positive reals round up
3.2 ceiling    % → 4.0
3.9 ceiling    % → 4.0
4.0 ceiling    % → 4.0 (already integer value)

% Negative reals round toward zero (less negative)
-4.8 ceiling   % → -4.0 (rounds toward zero)
-4.1 ceiling   % → -4.0
-4.0 ceiling   % → -4.0

% Integers unchanged
99 ceiling     % → 99
-50 ceiling    % → -50

5.2. Rounding Behavior

% ceiling always rounds up (toward positive infinity)
0.1 ceiling    % → 1.0
0.9 ceiling    % → 1.0
1.0 ceiling    % → 1.0

% For negative numbers, "up" means toward zero
-0.1 ceiling   % → -0.0 (or 0.0)
-0.9 ceiling   % → -0.0 (or 0.0)
-1.0 ceiling   % → -1.0
-1.1 ceiling   % → -1.0 (rounded toward zero/up)

5.3. Round Up for Allocation

% Calculate pages needed
/pagesNeeded {  % items itemsPerPage -> pages
    div ceiling cvi
} def

100 30.0 pagesNeeded  % → 4 (need 4 pages for 100 items at 30/page)
90 30.0 pagesNeeded   % → 3

5.4. Grid Cell Calculation

% Calculate grid dimensions needed
/gridCells {  % totalItems cellsPerRow -> rows
    div ceiling cvi
} def

25 7.0 gridCells  % → 4 (need 4 rows)

6. Advanced Examples

6.1. Round Up to Multiple

% Round up to nearest multiple
/roundUpToMultiple {  % value multiple -> rounded
    div ceiling
    1 index mul
    exch pop
} def

23 5.0 roundUpToMultiple  % → 25.0 (next multiple of 5)
100 64.0 roundUpToMultiple % → 128.0 (next multiple of 64)

6.2. Buffer Size Calculation

% Calculate buffer size needed
/bufferSize {  % dataSize blockSize -> numBlocks
    exch dup 0 eq {
        pop pop 0
    } {
        exch div ceiling cvi
    } ifelse
} def

1000 256 bufferSize  % → 4 (need 4 blocks of 256)

6.3. Price Rounding

% Round price up to next cent
/roundUpToCent {  % price -> roundedPrice
    100 mul ceiling 100 div
} def

1.234 roundUpToCent  % → 1.24
1.231 roundUpToCent  % → 1.24 (rounds up)

6.4. Convert to Integer (Round Up)

% Get integer ceiling
/iceil {  % num -> int
    ceiling cvi
} def

3.1 iceil      % → 4
-2.8 iceil     % → -2

7. Edge Cases and Common Pitfalls

Type is preserved - real input gives real output.

7.1. Type Preservation

% Type matches input type
3.5 ceiling    % → 4.0 (real)
3 ceiling      % → 3 (integer)

% To get integer result from real
3.5 ceiling cvi % → 4 (converted to integer)

7.2. Already an Integer Value

% Integer values unchanged
5.0 ceiling    % → 5.0 (no change, but still real)
-3.0 ceiling   % → -3.0

% Actual integers
5 ceiling      % → 5

7.3. Negative Number Behavior

% ceiling rounds toward positive infinity
% For negative numbers, this means toward zero

-3.2 ceiling   % → -3.0 (toward zero, less negative)
-3.9 ceiling   % → -3.0 (not -4.0!)

% Compare with floor
-3.2 floor     % → -4.0 (away from zero, more negative)
-3.2 ceiling   % → -3.0 (toward zero, less negative)

7.4. Fractional Part Exactly Zero

% No change if already integer value
4.0 ceiling    % → 4.0
-7.0 ceiling   % → -7.0
0.0 ceiling    % → 0.0

8. Type Requirements

The operand must be numeric (integer or real). Other types will cause a typecheck error:

% BAD: Non-numeric operands
(hello) ceiling    % ERROR: typecheck
[1 2] ceiling      % ERROR: typecheck
true ceiling       % ERROR: typecheck

floor - Round down to integer
round - Round to nearest integer
truncate - Truncate toward zero
abs - Absolute value

10. PostScript Level

Available in: PostScript Level 1 and higher

This is a fundamental arithmetic operator available in all PostScript implementations.

11. Error Conditions

stackunderflow

The operand stack is empty.

ceiling        % ERROR: stackunderflow (need 1 operand)

typecheck

The operand is not a number.

(text) ceiling % ERROR: typecheck

12. Performance Considerations

The ceiling operator is fast:

Simple comparison and rounding operation
O(1) constant time complexity
Efficient for allocation calculations

13. Best Practices

Use for allocation and capacity calculations
Convert with cvi if integer needed - ceiling preserves type
Understand negative behavior - rounds toward zero
Use for "round up" logic - next page, next block, etc.

13.1. Common Patterns

% Round up for resources
/resourcesNeeded {  % demand capacity -> units
    div ceiling cvi
} def

% Ensure positive ceiling
/posCeiling {  % num -> ceil
    dup 0 ge {
        ceiling
    } {
        truncate
    } ifelse
} def

% Pages needed (rounds up)
/calculatePages {  % items perPage -> pages
    div dup
    dup truncate eq {
        % Exact division
        truncate
    } {
        % Round up
        ceiling
    } ifelse
    cvi
} def

14. See Also

Arithmetic and Math - All arithmetic operators
PostScript Language Levels