# CyclicValue

Command: CyclicValue

Description

For a given value and a given norm interval "CyclicValue" returns
the value's norm equivalent. This is useful for all values with a
cyclic definition such as angles.
The output is always of type double regardless of the input type.

Alternatives: Function CyclicValue_d_d_d if you use it with three doubles
(interval = double1 - double2) CyclicValue_d_a if you use it with
double and array (both undocumented) -> behaviour and synopsis are the same.

Parameters

In : value: value in (-oo oo)

b1 b2: norm interval.
This interval is half-open: [.) or (.] depending on
the following rules:

b1 must not equal b2.
b1 always denotes the closed end of the interval.
b2 always denotes the open end of the interval.
If b1 If b1>b2 the norm interval used is (b2 b1].

See below for examples.

Out: The value's norm equivalent in the interval [b1 b2).
The output is always of type double regardless of the input
type.

Author
Ruediger Kupper

Synopsis

value [b1 b2] CyclicValue -> normvalue
value b1 b2 CyclicValue -> normvalue

See below for the meaning of b1 b2!

Examples

%% project angle in degrees onto [0 360):
-3601 [0 360] CyclicValue -> 359.0

%% project angle in radians onto [-pi pi):
23.0 [Pi -1 mul Pi] CyclicValue -> -2.13274

%% this demonstrates the handling of open/closed interval ends:
%% project number onto [1 4):
1 [1 4] CyclicValue -> 1
2 [1 4] CyclicValue -> 2
3 [1 4] CyclicValue -> 3
4 [1 4] CyclicValue -> 1
%% project number onto (1 4]:
1 [4 1] CyclicValue -> 4
2 [4 1] CyclicValue -> 2
3 [4 1] CyclicValue -> 3
4 [4 1] CyclicValue -> 4

File
lib/sli/misc_helpers.sli
Diagnostics

b1 must not equal b2. This is not checked for efficency reasons!
If b1=b2 code will break with /DivisionByZero during execution.

Remarks

Variant *_d_d_d is fastest. Prefer this variant over *_d_a in time
critical applications.

Inspired by IDL/NASE commandfunction cyclic_value().

FirstVersion
13.3.2003