rnd31
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## rnd31

rnd31 — 31-bit bipolar random opcodes with controllable distribution.

## Description

31-bit bipolar random opcodes with controllable distribution. These units are portable, i.e. using the same seed value will generate the same random sequence on all systems. The distribution of generated random numbers can be varied at k-rate.

## Syntax

    ax rnd31 kscl, krpow [, iseed]

    ix rnd31 iscl, irpow [, iseed]

    kx rnd31 kscl, krpow [, iseed]

## Initialization

ix -- i-rate output value.

iscl -- output scale. The generated random numbers are in the range -iscl to iscl.

irpow -- controls the distribution of random numbers. If irpow is positive, the random distribution (x is in the range -1 to 1) is abs(x) ^ ((1 / irpow) - 1); for negative irpow values, it is (1 - abs(x)) ^ ((-1 / irpow) - 1). Setting irpow to -1, 0, or 1 will result in uniform distribution (this is also faster to calculate).

A graph of distributions for different values of irpow.

iseed (optional, default=0) -- seed value for random number generator (positive integer in the range 1 to 2147483646 (2 ^ 31 - 2)). Zero or negative value seeds from current time (this is also the default). Seeding from current time is guaranteed to generate different random sequences, even if multiple random opcodes are called in a very short time.

In the a- and k-rate version the seed is set at opcode initialization. With i-rate output, if iseed is zero or negative, it will seed from current time in the first call, and return the next value from the random sequence in successive calls; positive seed values are set at all i-rate calls. The seed is local for a- and k-rate, and global for i-rate units.

| Notes
although seed values up to 2147483646 are allowed, it is recommended to use smaller numbers (< 1000000) for portability, as large integers may be rounded to a different value if 32-bit floats are used. i-rate rnd31 with a positive seed will always produce the same output value (this is not a bug). To get different values, set seed to 0 in successive calls, which will return the next value from the random sequence.

## Performance

ax -- a-rate output value.

kx -- k-rate output value.

kscl -- output scale. The generated random numbers are in the range -kscl to kscl. It is the same as iscl, but can be varied at k-rate.

krpow -- controls the distribution of random numbers. It is the same as irpow, but can be varied at k-rate.

## Examples

Here is an example of the rnd31 opcode at a-rate. It uses the file rnd31.csd.

Example 904. An example of the rnd31 opcode at a-rate.

See the sections Real-time Audio and Command Line Flags for more information on using command line flags.

    <CsoundSynthesizer>
    <CsOptions>
    ; Select audio/midi flags here according to platform
    ; Audio out   Audio in
    -odac           -iadc    ;;;RT audio I/O
    ; For Non-realtime ouput leave only the line below:
    ; -o rnd31.wav -W ;;; for file output any platform
    </CsOptions>
    <CsInstruments>

    ; Initialize the global variables.
    sr = 44100
    kr = 4410
    ksmps = 10
    nchnls = 1

    ; Instrument #1.
    instr 1
      ; Create random numbers at a-rate in the range -2 to 2 with
      ; a triangular distribution, seed from the current time.
      a31 rnd31 2, -0.5

      ; Use the random numbers to choose a frequency.
      afreq = a31 * 500 + 100

      a1 oscil 30000, afreq, 1
      out a1
    endin

    </CsInstruments>
    <CsScore>

    ; Table #1, a sine wave.
    f 1 0 16384 10 1

    ; Play Instrument #1 for one second.
    i 1 0 1
    e

    </CsScore>
    </CsoundSynthesizer>

Here is an example of the rnd31 opcode at k-rate. It uses the file rnd31_krate.csd.

Example 905. An example of the rnd31 opcode at k-rate.

    <CsoundSynthesizer>
    <CsOptions>
    ; Select audio/midi flags here according to platform
    ; Audio out   Audio in
    -odac           -iadc    ;;;RT audio I/O
    ; For Non-realtime ouput leave only the line below:
    ; -o rnd31_krate.wav -W ;;; for file output any platform
    </CsOptions>
    <CsInstruments>

    ; Initialize the global variables.
    sr = 44100
    kr = 4410
    ksmps = 10
    nchnls = 1

    ; Instrument #1.
    instr 1
      ; Create random numbers at k-rate in the range -1 to 1
      ; with a uniform distribution, seed=10.
      k1 rnd31 1, 0, 10

      printks "k1=%f\\n", 0.1, k1
    endin

    </CsInstruments>
    <CsScore>

    ; Play Instrument #1 for one second.
    i 1 0 1
    e

    </CsScore>
    </CsoundSynthesizer>

Its output should include lines like this:

    k1=0.112106
    k1=-0.274665
    k1=0.403933

Here is an example of the rnd31 opcode that uses the number 7 as a seed value. It uses the file rnd31_seed7.csd.

Example 906. An example of the rnd31 opcode that uses the number 7 as a seed value.

    <CsoundSynthesizer>
    <CsOptions>
    ; Select audio/midi flags here according to platform
    ; Audio out   Audio in
    -odac           -iadc    ;;;RT audio I/O
    ; For Non-realtime ouput leave only the line below:
    ; -o rnd31_seed7.wav -W ;;; for file output any platform
    </CsOptions>
    <CsInstruments>

    ; Initialize the global variables.
    sr = 44100
    kr = 4410
    ksmps = 10
    nchnls = 1

    ; Instrument #1.
    instr 1
      ; i-rate random numbers with linear distribution, seed=7.
      ; (Note that the seed was used only in the first call.)
      i1 rnd31 1, 0.5, 7
      i2 rnd31 1, 0.5
      i3 rnd31 1, 0.5

      print i1
      print i2
      print i3
    endin

    </CsInstruments>
    <CsScore>

    ; Play Instrument #1 for one second.
    i 1 0 1
    e

    </CsScore>
    </CsoundSynthesizer>

Its output should include lines like this:

    instr 1:  i1 = -0.649
    instr 1:  i2 = -0.761
    instr 1:  i3 = 0.677

Here is an example of the rnd31 opcode that uses the current time as a seed value. It uses the file rnd31_time.csd.

Example 907. An example of the rnd31 opcode that uses the current time as a seed value.

See the sections Real-time Audio and Command Line Flags for more information on using command line flags.

    <CsoundSynthesizer>
    <CsOptions>
    ; Select audio/midi flags here according to platform
    ; Audio out   Audio in
    -odac           -iadc    ;;;RT audio I/O
    ; For Non-realtime ouput leave only the line below:
    ; -o rnd31_time.wav -W ;;; for file output any platform
    </CsOptions>
    <CsInstruments>

    ; Initialize the global variables.
    sr = 44100
    kr = 4410
    ksmps = 10
    nchnls = 1

    ; Instrument #1.
    instr 1
      ; i-rate random numbers with linear distribution,
      ; seeding from the current time. (Note that the seed
      ; was used only in the first call.)
      i1 rnd31 1, 0.5, 0
      i2 rnd31 1, 0.5
      i3 rnd31 1, 0.5

      print i1
      print i2
      print i3
    endin

    </CsInstruments>
    <CsScore>

    ; Play Instrument #1 for one second.
    i 1 0 1
    e

    </CsScore>
    </CsoundSynthesizer>

Its output should include lines like this:

    instr 1:  i1 = -0.691
    instr 1:  i2 = -0.686
    instr 1:  i3 = -0.358

## Credits

Author: Istvan Varga

New in version 4.16

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