added linear congruential generator for streams and lists

maths.lib

@@ -818,4 +818,80 @@ declare avg_t19 copyright "Copyright (C) 2020 Dario Sanfilippo
       <[email protected]> and
        2003-2020 by Julius O. Smith III <[email protected]>";
 declare avg_t19 license "MIT-style STK-4.3 license";
-avg_t19(period, x) = fi.lpt19(period, x); 
+avg_t19(period, x) = fi.lpt19(period, x);
+
+
+//----------(ma.)lcg------------------------------------------------------------
+// Linear congruential generator for streams of integer values based on
+// the equation: y[n] = (A * y[n - 1] + C) % M.
+// See https://en.wikipedia.org/wiki/Linear_congruential_generator.
+// See also noises.lib for noise generators based on the same mechanism.
+//
+// #### Usage
+//
+// ````
+// lcg(M, A, C, S) : _
+// ````
+//
+// Where:
+//
+// * M is the divisor in the modulo operation.
+// * A is the multiplier.
+// * C is the offset.
+// * S is the seed.
+//
+// #### Reference:
+//
+// L’ecuyer, P. (1999). Tables of linear congruential generators of different 
+// sizes and good lattice structure. Mathematics of Computation, 68(225), 
+// 249-260.
+//
+// Steele, G., & Vigna, S. (2020). Computationally easy, spectrally good 
+// multipliers for congruential pseudorandom number generators. arXiv 
+// preprint arXiv:2001.05304.
+//------------------------------------------------------------------------------
+declare lcg author "Dario Sanfilippo";
+declare lcg copyright "Copyright (C) 2020 Dario Sanfilippo
+      <[email protected]>";
+declare lcg license "GPL v3 license";
+lcg(M, A, C, S) =  ((+ (S - S') * A + C) % M) 
+                   ~ _;
+
+//----------(ma.)lcg_par--------------------------------------------------------
+// Linear congruential generator for lists of integer values based on
+// the equation: y[n] = (A * y[n - 1] + C) % M.
+// See https://en.wikipedia.org/wiki/Linear_congruential_generator.
+// See also noises.lib for noise generators based on the same mechanism.
+//
+// #### Usage
+//
+// ````
+// lcg_par(N, M, A, C, S) : si.bus(N)
+// ````
+//
+// Where:
+//
+// * N is the number of values of the sequence in parallel 
+//    (known at compile-time).
+// * M is the divisor in the modulo operation.
+// * A is the multiplier.
+// * C is the offset.
+// * S is the seed.
+//
+// #### Reference:
+//
+// L’ecuyer, P. (1999). Tables of linear congruential generators of different
+// sizes and good lattice structure. Mathematics of Computation, 68(225),
+// 249-260.
+//
+// Steele, G., & Vigna, S. (2020). Computationally easy, spectrally good
+// multipliers for congruential pseudorandom number generators. arXiv
+// preprint arXiv:2001.05304.
+//------------------------------------------------------------------------------
+declare lcg_par author "Dario Sanfilippo";
+declare lcg_par copyright "Copyright (C) 2020 Dario Sanfilippo
+      <[email protected]>";
+declare lcg_par license "GPL v3 license";
+lcg_par(1, M, A, C, S) = (A * S + C) % M;
+lcg_par(N, M, A, C, S) =   (A * S + C) % M , 
+                           lcg_par(N - 1, M, A, C, (A * S + C) % M);

noises.lib

@@ -49,23 +49,41 @@ to be LGPL or GPL. For example you are free to choose a commercial or
 closed source license or any other license if you decide so.
 ************************************************************************
 ************************************************************************/
+//----------`(no.)noiseed`------------------------------------------------------
+// White noise generator with seed (outputs random numbers between -1 and 1).
+// `Noiseed` is a standard Faust function.
+// See also the lcg and lcg_par functions in maths.lib.
+//
+// #### Usage
+//
+// ```
+// noiseed(S) : _
+// ```
+//
+// Where:
+//
+// * S is the seed of the noise generator.
+//------------------------------------------------------------------------------
+noiseed(S) = random / RANDMAX
+      with {
+           mask = 4294967295; // 2^32-1
+           random =    +(S) 
+                       ~ *(1103515245) & mask; // "linear congruential"
+           RANDMAX = 2147483647.0; // = 2^31-1 = MAX_SIGNED_INT in 32 bits
+      };
 
 //-------`(no.)noise`----------
-// White noise generator (outputs random number between -1 and 1).
+// White noise generator (outputs random numbers between -1 and 1).
 // `Noise` is a standard Faust function.
+// See also the lcg and lcg_par functions in maths.lib.
 //
 // #### Usage
 //
 // ```
 // noise : _
 // ```
 //------------------------
-noise = random / RANDMAX
-with{
-	mask = 4294967295; // 2^32-1
-	random = +(12345) ~ *(1103515245) & mask; // "linear congruential"
-	RANDMAX	= 2147483647.0; // = 2^31-1 = MAX_SIGNED_INT in 32 bits
-};
+noise = noiseed(12345);
 
 //---------------------`(no.)multirandom`--------------------------
 // Generates multiple decorrelated random numbers in parallel.