CEILING.MATH

What it does

CEILING.MATH(number, [significance], [mode])

CEILING.MATH(number,[significance],[mode]) rounds to a multiple of the step’s absolute value, which defaults to one. By default, negative numbers move toward zero and positive numbers away from zero. A nonzero mode reverses the negative-input direction. Significance supplies a multiple, rather than a number of decimal places.

Try it

=CEILING.MATH(-10.3,3) returns -9; =CEILING.MATH(-10.3,3,1) returns -12. The nonzero mode changes negative inputs to rounding away from zero. Both answers are multiples of three.

Quirks

The significance sign is ignored. Mode affects only negative numbers, and the current helper tests zero versus any nonzero mode without truncating the flag. Its zero-significance route returns zero.

The opened Microsoft page’s argument summary calls significance a count of digits, while its remarks and worked examples use a multiple. Use the multiple interpretation shown here. The current wrapper defaults significance to one when the call ends before it; an explicitly empty slot is read as zero instead.

The shared current model rounds the quotient to fifteen significant decimal digits before choosing a count. Recorded scope for the legacy FLOOR rule does not by itself establish every modern variant’s quotient edge or last bit.

How to implement

1. Apply omitted defaults: significance one and mode zero. Coerce numeric arguments, retain the distinction between an omitted tail and an explicitly empty slot, and set s=abs(significance). Return zero if s is zero.
2. For nonnegative input, obtain the current fifteen-digit quotient reading of number/s, then take its ceiling.
3. For negative input, read the positive quotient abs(number)/s. Take its floor when mode is zero, or its ceiling when mode is nonzero; restore the negative sign.
4. The ported modern helper multiplies that count by s with ordinary binary64 arithmetic and normalizes zero. This is distinct from assuming every family spelling uses the native legacy wrapper’s final stored-x87 site. Apply the surrounding number publication rule.

For -10.3 and step three, the positive quotient reads near 3.43333333333333. Default mode chooses three and returns -9; nonzero mode chooses four and returns -12. The current fractional mode 0.5 follows the nonzero branch too.

The quotient helper and branch recipe describe the current implementation. FN-FLOOR-002 explicitly leaves transfer of the isolated legacy quotient rule to modern spellings open. Exact edge behaviour and a whole-domain modern-family identification are not established by the shared code alone.

Rust code

1 ceiling_math "CEILING.MATH" (1, 3) [V "number", V "significance", V "mode"] |s, a, sv| {
    three(s, a, cf::ceiling_math_kernel)
}

No implementation has been published with a Handbook test suite for this function.

Version differences

The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.

The record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.

Recorded environments and comparison details.

Alternatives

For the ordinary input -10.3 on a grid of magnitude three:

CEILING.PRECISE and ISO.CEILING have the fixed upward convention. FLOOR.MATH selects the other directional default. MROUND chooses a nearest multiple.

Named variants

No named variants are recorded yet.