Clamp

Constrains x to the range [lower, upper].

WikipediaClamp (function)WikidataQ5125465

Clamp(x, lower, upper)x if it's already in

[\mathrm{lower}, \mathrm{upper}]

, else the nearer bound.

Clamp(x)x clamped to the default range

[-1, 1]

, Wolfram's Clip[x].

Clamp(x, lower, upper, vLower, vUpper)Wolfram's Clip[x, {lower, upper}, {vLower, vUpper}]: a replacement value outside the range, rather than the nearer bound.

Typed signatures

Type	Package	Applies
`(real \| signed_infinity, real \| signed_infinity, real \| signed_infinity) -> real \| signed_infinity`	`compute-engine`	always
`(any, any?, any?, any?, any?) -> any`	`combinatorics`replaces `compute-engine`	always
`(any, any?, any?, any?, any?) -> any`	`structures`replaces `combinatorics`	always

Domain: Arithmetic

Details

Constrains a value to $[\mathrm{lower}, \mathrm{upper}]$ : below lower it returns lower, above upper it returns upper, otherwise x unchanged.
A 1-argument $\mathrm{Clamp}(x)$ defaults to $[-1, 1]$ , matching Wolfram's Clip[x].
Idempotent: clamping an already-clamped value changes nothing.
Doesn't validate that lower $\le$ upper; with the bounds swapped it just falls through whichever comparison fires first.

Examples

3 more kept as data, checked against the oracles

Basic #

In

\mathrm{Clamp}(5, 0, 3)

Out

3

In

\mathrm{Clamp}(-1, 0, 3)

Out

0

Values already inside the range pass through unchanged

In

\mathrm{Clamp}(2, 0, 3)

Out

2

In

\mathrm{Clamp}(2, 0, 3, -1, 10)

Out

2

Scope #

A 1-argument $\mathrm{Clamp}(x)$ clamps to the default range $[-1, 1]$

In

\mathrm{Clamp}(1.5)

Out

1

Threads element-wise over a list

In

\mathrm{Clamp}(\bigl\lbrack-2, 0.5, 3\bigr\rbrack, 0, 1)

Out

\bigl\lbrack0, 0.5, 1\bigr\rbrack

Exact numeric constants are compared numerically

In

\mathrm{Clamp}(π, 0, 3)

Out

3

In

\mathrm{Clamp}(\frac{7}{2}, 1, 3)

Out

3

Infinities clamp to the nearer bound

In

\mathrm{Clamp}(∞, 0, 3)

Out

3

Wolfram's $\mathrm{Clip}[x, \{min, max\}, \{v_{min}, v_{max}\}]$ returns replacement values outside the range -- here 10 above it

In

\mathrm{Clamp}(5, 0, 3, -1, 10)

Out

10

Applications #

Capping a percentage-like value at 100

In

\mathrm{Clamp}(112, 0, 100)

Out

100

Properties #

Idempotent: clamping an already-clamped value changes nothing

In

\mathrm{Clamp}(\mathrm{Clamp}(5, 0, 3), 0, 3)=\mathrm{Clamp}(5, 0, 3)

Out

\mathrm{True}

Possible issues #

No validation that lower ≤ upper -- with the bounds swapped, this just falls through the upper-bound check

In

\mathrm{Clamp}(5, 3, 0)

Out

0

A symbolic value is left unevaluated rather than assumed to already lie in range

In

\mathrm{Clamp}(x, 0, 3)

Out

\mathrm{Clamp}(x, 0, 3)

About

Examples	17
Checked against	Wolfram Language 17 agree
Crosswalk	Wikipedia Wikidata

See also: Min, Max