SawtoothWave

The sawtooth wave: x - floor(x), period 1, range [0, 1).

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SawtoothWave(x)x - floor(x), unit period, range [0, 1).

SawtoothWave({min, max}, x)the sawtooth rescaled to vary from min to max, unit period.

Typed signatures

Type	Package	Applies
(real | vector<real^2>, real?) -> number	analytic	always

Domain: Elementary functions

Details

• Unlike FractionalPart, which keeps the sign of x, SawtoothWave(x) is always in [0, 1) -- SawtoothWave(-1/4) is 3/4, not -1/4.
• The range form takes the range FIRST, x second -- SawtoothWave({min, max}, x) -- matching Wolfram's own argument order for this family.

Examples

Basic #

live ↗

In$\mathrm{SawtoothWave}(0)$Out$0$

live ↗

In$\mathrm{SawtoothWave}(\frac{1}{3})$Out$\frac{1}{3}$

Scope #

Always nonnegative, unlike FractionalPart

live ↗

In$\mathrm{SawtoothWave}(-\frac{1}{4})$Out$\frac{3}{4}$

Rescaled to a {min, max} range

live ↗

In$\mathrm{SawtoothWave}(\bigl\lbrack0, 10\bigr\rbrack, \frac{1}{2})$Out$5$

An exact irrational input: the branch is decided numerically, but the result stays exact

live ↗

In$\mathrm{SawtoothWave}(-π)$Out$4-π$

Known value · Frac(x) = x - Floor(x); Floor(-π) = -4, so Frac(-π) = 4 - π

A huge exact argument stays unevaluated: a double can't resolve 10^20·π's fractional part to certify a branch, so this declines rather than risk a wrong one

live ↗

In$\mathrm{SawtoothWave}(10^{20}π)$Out$\mathrm{SawtoothWave}(100\,000\,000\,000\,000\,000\,000π)$

Properties #

Period 1

live ↗

In$\mathrm{SawtoothWave}(\frac{1}{3})=\mathrm{SawtoothWave}(5\frac{1}{3})$Out$\mathrm{True}$

About

Examples	7
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