Update readme
| author |
Steve Losh <steve@stevelosh.com> |
| date |
Thu, 06 Apr 2017 20:07:56 +0000 |
| parents |
a4f701ecf78c |
| children |
8ac3147a3182 |
(in-package :pcg)
;;;; Constants ----------------------------------------------------------------
(defconstant +multiplier+ 6364136223846793005)
(defconstant +modulus+ (expt 2 64))
(defconstant +limit+ (1- (expt 2 64)))
;;;; Utils ---------------------------------------------------------------------
(defmacro defun-inline (name &body body)
"Like `defun`, but declaims `name` to be `inline`."
`(progn
(declaim (inline ,name))
(defun ,name ,@body)
',name))
(defmacro check-types (&rest place-type-pairs)
`(progn ,@(loop :for (place type . nil) :on place-type-pairs :by #'cddr
:collect `(check-type ,place ,type))))
(defun rotate-byte (count bytespec integer)
"Rotates a field of bits within INTEGER; specifically, returns an
integer that contains the bits of INTEGER rotated COUNT times
leftwards within the byte specified by BYTESPEC, and elsewhere
contains the bits of INTEGER. See http://www.cliki.net/ROTATE-BYTE"
(declare (optimize (speed 3) (safety 0) (space 0) (debug 1)))
(let ((size (byte-size bytespec)))
(when (= size 0)
(return-from rotate-byte integer))
(let ((count (mod count size)))
(flet ((rotate-byte-from-0 (count size integer)
(let ((bytespec (byte size 0)))
(if (> count 0)
(logior (ldb bytespec (ash integer count))
(ldb bytespec (ash integer (- count size))))
(logior (ldb bytespec (ash integer count))
(ldb bytespec (ash integer (+ count size))))))))
(dpb (rotate-byte-from-0 count size (ldb bytespec integer))
bytespec
integer)))))
(defun-inline % (n)
(mod n +modulus+))
(defun-inline *+ (a b increment)
(+ (* a b) increment))
(deftype u64 ()
'(unsigned-byte 64))
(deftype u32 ()
'(unsigned-byte 32))
;;;; Data ---------------------------------------------------------------------
(defstruct (pcg (:constructor actually-make-pcg))
(state 0 :type u64)
(increment 0 :type u64))
(defun-inline compute-increment (stream-id)
(logior 1 (ash stream-id 1)))
;;;; Permutations -------------------------------------------------------------
(defun-inline permute-xor-shift (data)
(declare (optimize speed)
(type (unsigned-byte 37) data))
;; The reference implementation does this:
;;
;; uint32_t xorshifted = ((oldstate >> 18u) ^ oldstate) >> 27u;
;;
;; Which is a bunch of shit packed into one line because C programmers don't
;; like typing or something.
;;
;; oldstate starts as a 64-bit value, which looks roughly like this:
;;
;; SSSSSbbb bbbbbbbb bbbbbbbb bbbbbbbb bbbbbxxx xxxxxxxx xxxxxxxx xxxxxxxx
;;
;; * S - 5 "selector" bits for the permutation. Confusingly the xorshift
;; permutation doesn't use these to SELECT anything, but instead mixes
;; them into the other random bits. The next permutation uses them to
;; decide how far to rotate.
;; * b - 32 decently random bits, which are going to be permuted and used for
;; the output value.
;; * x - 27 not-very-random garbage low-order bits that we throw away.
;;
;; What this permutation does is xor the top half of the good bits into the
;; bottom half of the good bits to mix them up a bit:
;;
;; oldstate: SSSSSbbb bbbbbbbb bbbbbbbb bbbbbbbb bbbbbxxx xxxxxxxx xxxxxxxx xxxxxxxx
;; oldstate >> 18: 00000000 00000000 00SSSSSb bbbbbbbb bbbbbbbb bbbbbbbb bbbbbbxx xxxxxxxx ...lost...
;; result: SSSSSbbb bbbbbbbb bbBBBBBB BBBBBBBB BBBBBxxx xxxxxxxx xxxxxxxx xxxxxxxx
;;
;; Then it shifts by 27 to drop the garbage bits:
;;
;; SSSSS bbbbbbbb bbbbbBBB BBBBBBBB BBBBBBBB
;;
;; And finally it assigns the resulting 37-bit value to a uint32_t which
;; clears out the 5 remaining high-order selector bits.
(ldb (byte 32 0)
(logxor data (ash data -18))))
(defun-inline permute-rotate (data selector)
(declare (optimize speed)
(type (unsigned-byte 32) data)
(type (unsigned-byte 5) selector))
#+sbcl (sb-rotate-byte:rotate-byte selector (byte 32 0) data)
#-sbcl (rotate-byte selector (byte 32 0) data))
;;;; State Advancement --------------------------------------------------------
(defun-inline advance-state (pcg)
(declare (optimize speed)
(type pcg pcg))
(setf (pcg-state pcg)
(% (*+ (pcg-state pcg) +multiplier+ (pcg-increment pcg))))
nil)
;;;; Low-Level API ------------------------------------------------------------
(declaim
(ftype (function (pcg) u32) pcg-random%)
;; 2^32 streams ought to be enough for anybody
(ftype (function (u64 u32)
pcg)
make-pcg%)
(ftype (function (pcg (and u32 (integer 1))) u32)
pcg-random-bounded%)
(ftype (function (pcg (signed-byte 32) (signed-byte 32))
(signed-byte 32))
pcg-random-range%)
(ftype (function (pcg u64)) pcg-advance% pcg-rewind%)
(ftype (function (pcg) single-float) pcg-random-float%))
(defun-inline pcg-random% (pcg)
"Return a random `(unsigned-byte 32)`.
As a side effect, the state of `pcg` will be advanced.
This is a low-level function that assumes you are passing in the correct types.
"
(declare (optimize speed))
(let* ((state (pcg-state pcg))
(data (ldb (byte 37 (- 64 37)) state))
(selector (ldb (byte 5 (- 64 5)) state)))
(advance-state pcg)
(permute-rotate (permute-xor-shift data)
selector)))
(defun-inline make-pcg% (seed stream-id)
"Create and return a new `pcg` for the given `seed` and `stream-id`.
This is a low-level function that assumes you are passing in the correct types.
"
(declare (optimize speed))
(let* ((increment (compute-increment stream-id))
(pcg (actually-make-pcg :state 0 :increment increment)))
(pcg-random% pcg)
(setf (pcg-state pcg)
(% (+ (pcg-state pcg) seed)))
(pcg-random% pcg)
pcg))
(defun-inline pcg-random-bounded% (pcg bound)
"Return a random integer between `0` (inclusive) and `bound` (exclusive).
As a side effect, the state of `pcg` will be advanced.
This is a low-level function that assumes you are passing in the correct types.
"
(declare (optimize speed))
(loop :with threshold = (mod (expt 2 32) bound)
:for n = (pcg-random% pcg)
:when (>= n threshold)
:do (return (values (mod n bound)))))
(defun-inline pcg-random-range% (pcg min max)
(declare (optimize speed))
(+ min (pcg-random-bounded% pcg (- max min))))
(defun-inline pcg-random-float% (pcg)
"Return a random `single-float` between `0.0` and `1.0`.
As a side effect, the state of `pcg` will be advanced.
This is a low-level function that assumes you are passing in the correct types.
"
(declare (optimize speed))
(/ (pcg-random% pcg)
(coerce (expt 2 32) 'single-float)))
(defun-inline pcg-advance% (pcg steps)
"Advance the state of `pcg` by `steps` steps.
This function returns `nil` and is only useful for its side effects.
This is a low-level function that assumes you are passing in the correct types.
"
(declare (optimize speed))
;; See "Random Number Generation with Arbitrary Strides", Forrest B. Brown:
;; https://laws.lanl.gov/vhosts/mcnp.lanl.gov/pdf_files/anl-rn-arb-stride.pdf
;;
;; The original paper uses single-letter names like G, C, i, f, h because
;; math, but we're all literate here so let's use words instead.
(loop
:with increment = (pcg-increment pcg)
:with multiplier-accumulator :of-type u64 = 1 ; G
:with increment-accumulator :of-type u64 = 0 ; C
:for i :of-type u64 = steps :then (ash i -1) ; i
:for inc :of-type u64 = increment :then (% (* inc (1+ mul))) ; f
:for mul :of-type u64 = +multiplier+ :then (% (expt mul 2)) ; h
:while (plusp i)
:when (oddp i)
:do (setf multiplier-accumulator (% (* multiplier-accumulator mul))
increment-accumulator (% (*+ increment-accumulator mul inc)))
:finally
(setf (pcg-state pcg)
(% (*+ (pcg-state pcg) multiplier-accumulator increment-accumulator)))))
(defun-inline pcg-rewind% (pcg steps)
"Rewind the state of `pcg` by `steps` steps.
This function returns `nil` and is only useful for its side effects.
This is a low-level function that assumes you are passing in the correct types.
"
(declare (optimize speed))
(when (plusp steps)
(pcg-advance% pcg (- +limit+ (1- steps)))))
;;;; High-Level API -----------------------------------------------------------
(defun resolve-seed (seed)
(if (null seed)
(random (expt 2 64) (make-random-state t))
seed))
(defun make-pcg (&key (seed nil) (stream-id 0))
"Create and return a new PCG.
If `seed` is `nil`, a fresh random seed will be generated with the
implementation's `cl:random` function, as if by:
(random ... (make-random-state t))
"
(check-types stream-id u32
seed (or null u64))
(make-pcg% (resolve-seed seed) stream-id))
(defparameter *global-pcg* (make-pcg))
(deftype pcg-designator ()
'(or (eql t) pcg))
(defun-inline resolve-pcg (pcg-designator)
(if (eq t pcg-designator)
*global-pcg*
pcg-designator))
(defun pcg-random-integer (pcg min max)
"Return a random integer.
As a side effect, the state of `pcg` will be advanced.
"
(check-types pcg pcg-designator
min integer
max integer)
(+ min (pcg-random-bounded% (resolve-pcg pcg)
(+ (- max min)))))
(defun pcg-random-float (pcg min max)
"Return a random `single-float`.
As a side effect, the state of `pcg` will be advanced.
"
(check-types pcg pcg-designator
min single-float
max single-float)
(+ min (* (- max min)
(pcg-random-float% (resolve-pcg pcg)))))
(defun pcg-random (pcg bound &optional max inclusive?)
"Generate and return a random number in the specified interval.
If `max` is omitted the interval will be `[0, bound)`.
If `max` is given the interval will be `[bound, max)`.
If `inclusive?` is given the interval will be `[bound, max]`.
If either of `bound` or `max` are floats, the result will be a float.
Otherwise the result will be an integer.
As a side effect, the state of `pcg` will be advanced.
"
(let* ((float? (or (floatp bound)
(floatp max)))
(result-type (if float? 'single-float 'integer))
(delta (if (and inclusive? (not float?)) 1 0))
(min (coerce (if (null max) 0 bound) result-type))
(max (coerce (+ (if (null max) bound max) delta) result-type)))
(assert (< min max) ()
"Invalid interval for generating a random number: [~S, ~S~A"
min max (if inclusive? "]" ")"))
(case result-type
(integer (pcg-random-integer pcg min max))
(single-float (pcg-random-float pcg min max)))))
(defun pcg-advance (pcg steps)
"Advance the state of `pcg` by `steps` steps.
This function returns `nil` and is only useful for its side effects.
"
(check-types pcg pcg-designator
steps u64)
(pcg-advance% (resolve-pcg pcg) steps))
(defun pcg-rewind (pcg steps)
"Rewind the state of `pcg` by `steps` steps.
This function returns `nil` and is only useful for its side effects.
"
(check-types pcg pcg-designator
steps u64)
(pcg-rewind% (resolve-pcg pcg) steps))
;;;; Scratch ------------------------------------------------------------------
;; (defparameter *p* (make-pcg))
;; (defun data (n)
;; (loop :repeat n :collect (pcg-random *p* 9.0)))
;; (losh:gnuplot
;; (data 10000)
;; :x #'identity
;; :y (lambda (i) (/ 1.0 10000))
;; :line-width 2
;; :smooth :cumulative)
;; (defun slow-advance (pcg n)
;; (dotimes (_ n) (pcg-random pcg))
;; nil)
;; (defun test (n)
;; (let ((a (make-pcg))
;; (b (make-pcg)))
;; (time (slow-advance a n))
;; (time (pcg-advance% b n))
;; (assert (= (pcg-random a) (pcg-random b)))))
;; (losh:gnuplot
;; (sort (losh:hash-table-contents
;; (losh:proportions
;; (loop :repeat 1000000
;; :collect (pcg-random-range-inclusive *p* -50 200))))
;; #'<
;; :key #'first)
;; :x #'first
;; :y #'second
;; :min-y 0.00
;; :max-y 0.01
;; :style :lines
;; :line-width 1)
;;;; TODO ----------------------------------------------------------------------
;;; https://experilous.com/1/blog/post/perfect-fast-random-floating-point-numbers
;;; as an alternative float generation scheme.