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\
\ noise.4th
\
\ Pseudo-random noise generation routines:
\
\ ran0 generates a random number between 0e and 1e with a
\ uniform distribution. Translated from Numerical Recipes
\ in C, by Press, et. al.
\
\ gauss generates statistical noise with a normal distribution
\ having mean of 0e and variance of 1e. Uses the output
\ of ran0 to generate a uniform deviate and
\ transforms this number into a normally distributed
\ deviate.
\
\ Notes:
\
\ The formula for the inverse cumulative distribution function (CDF)
\ of a normal distribution is taken from Abramowitz and Stegun, p. 933.
\
variable idum
16807 constant IA
2147483647 constant IM
1e IM s>f f/ fconstant AM
127773 constant IQ
2836 constant IR
123459876 constant MASK
\ The word ran0 returns an observation from a uniform distribution
\ between 0. and 1.
\
\ Initialize the variable idum to any integer value prior to calling
\ ran0. Do not alter idum between calls for successive deviates in
\ a sequence.
: ran0 ( -- f )
idum @ MASK xor dup idum !
IQ /
dup IR * swap
IQ * idum @ swap - IA *
swap - idum !
idum @ 0< if
IM idum +!
then
idum @ s>f AM f*
idum @ MASK xor idum !
;
variable iflag
2.515517e fconstant C0
.802853e fconstant C1
.010328e fconstant C2
1.432788e fconstant D1
.189269e fconstant D2
.001308e fconstant D3
: gauss ( -- f | generate a pseudo-random number with a Gaussian distribution )
false iflag !
begin
ran0
fdup
f0=
while
fdrop
repeat
fdup 0.5e f> dup iflag !
if 1e fswap f- then \ compute X
\ Compute the inverse of the CDF
fdup f* 1e fswap f/ flog fsqrt \ compute T
fdup 3e f** D3 f*
fover fdup f* D2 f* f+
fover D1 f* f+ 1e f+ \ compute 1+D1*T+D2*T^2+D3*T^3
>r >r
fdup fdup f* C2 f*
fover C1 f* f+ C0 f+ \ compute C0+C1*T+C2*T^2
r> r>
f/ f-
iflag @ if fnegate then
\ T = SQRT(LOG(1./X**2.))
\ XP = T - (C0+C1*T+C2*T**2.)/(1.+D1*T+D2*T**2.+D3*T**3.)
\ IF (IFLAG) XP = -XP
;
|
