# Command: CyclicValue

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Name:

    CyclicValue - project a cyclic value onto it's norm interval (e.g. angle on [0,360))

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

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.

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().

Author:

    Ruediger Kupper

FirstVersion:

    13.3.2003

SeeAlso:

- mod
- floor

Source:

    /opt/conda/conda-bld/nest_1512418852064/work/nest-2.12.0/lib/sli/misc_helpers.sli

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