memoize-raw.lisp

; ACL2 Version 8.1 -- A Computational Logic for Applicative Common Lisp
; Copyright (C) 2018, Regents of the University of Texas

; This version of ACL2 is a descendent of ACL2 Version 1.9, Copyright
; (C) 1997 Computational Logic, Inc.  See the documentation topic NOTE-2-0.

; This program is free software; you can redistribute it and/or modify
; it under the terms of the LICENSE file distributed with ACL2.

; This program is distributed in the hope that it will be useful,
; but WITHOUT ANY WARRANTY; without even the implied warranty of
; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
; LICENSE for more details.

; Written by:  Matt Kaufmann               and J Strother Moore
; email:       Kaufmann@cs.utexas.edu      and Moore@cs.utexas.edu
; Department of Computer Science
; University of Texas at Austin
; Austin, TX 78712 U.S.A.

; memoize-raw.lisp -- Raw lisp definitions for memoization functions, only to
; be included in the hons-enabled ACL2 executables (which is all ACL2
; executables starting with Version_7.2).

; The original version of this file was contributed by Bob Boyer and Warren
; A. Hunt, Jr.  The design of this system of Hash CONS, function memoization,
; and fast association lists (applicative hash tables) was initially
; implemented by Boyer and Hunt.  Contributions have been made since then by
; Jared Davis, Matt Kaufmann, J Moore, and Sol Swords.

(in-package "ACL2")

; SECTION: To do, near-term

; - Incorporate some Lisp comments into the :doc.  In particular, probably the
;   *record-xxx* and *report-xxx* should be incorporated into the :doc.  In
;   general, add/improve documentation, including for the following.
;   - *memoize-summary-order-list*
;   - *sort-to-from-by-calls*
;   - memoize (e.g., clarify/emphasize that :recursive actually avoids inlining
;     and :recursive nil avoids counting recursive calls in (memsum)); maybe
;     explain how fns like LEN with special raw-Lisp code can thus be memoized
;     only with :recursive nil; perhaps move some things from the Lisp comment
;     to the :doc
;   - Memoize-summary and memsum.  Incorporate long comment in memoize-summary.
;     Update :doc (maybe other topics too) to clarify that we stop at
;     most-positive-mfixnum [see safe-incf].  Alternatively, memsum could just
;     print a message if we ever hit that limit, and require an optional
;     argument if one wants the results anyhow.
;   - Update :doc for the pons/hons-wash soundness fix checked into git,
;     especially for hons-wash.

; - Consider counting pons calls even when a number is returned; else make sure
;   the :doc is clear about this.  (See the definition of pons.)

; - Perhaps write an essay summarizing how memoization works, including
;   discussion of *memoize-call-array* (or at least pointing to the comment
;   there).

; - Add interface functions, perhaps including the following.  I can imagine a
;   single macro or function that takes, say, a keyword argument in order to
;   print (to the comment window, or to state perhaps using the oracle) what's
;   desired.  OR -- maybe suitable utilities can go into books, if we make
;   enough interface functions available.

;   o *Memoize-summary-order-list* (as a state global perhaps)

;   o Profile, unmemoize-profiled; maybe even profile-all and profile-acl2, but
;     maybe keep those instead in books/centaur/memoize/old/profile*, or maybe
;     both, with a sort of autoloading as is done for WET.

;   o And so on -- see in particular function with this comment: "Note: This
;     function should probably either be made available in the loop or else
;     eliminated."

; - If we want to be able to memoize n functions, then it looks like the number
;   of (virtual) columns of *memoize-call-array* need only be something like
;   n+5.  So perhaps that array need not be a square array -- it can have fewer
;   columns than rows -- in which case we can save close to a factor of two on
;   space.  But that might well require considerable code re-work; for example,
;   memoize-call-array-grow computes (/ *2max-memoize-fns* 2), but surely that
;   would have to change.  It's not clear that it's worth saving a factor of
;   roughly two on something whose default is of size 10^6 and might not need
;   to grow.

; - We have calls like (make-symbol "BODY-NAME") and bindings like
;   (,*mf-old-caller* *caller*) -- the former interns a new symbol each time
;   (though with the same, EQ result each time) while the latter saves a symbol
;   using a defconstant form in file acl2.lisp.  Consider making this all more
;   consistent in style.

; SECTION: To do, longer-term

; - Consider eliminating the function memoized-values (and memstat) or, perhaps
;   better yet, have it return a data structure rather than printing individual
;   values.

; - Replace (COND (T <code>)) by <code> in what is generated by
;   memoize-fn-def.  (For an example, look just below memoize-fn-def.)

; - Perhaps think about this comment in the definition of pons:

; It might be tempting to think about creating a static cons here.

; - Consider using memo-max-sizes-entry records not only to guess good sizes,
;   but also to guess good rehash sizes.

; - Tests such as (< (* 100 local-tt) tt) and (> (* 10000 local-tt) tt) in
;   function memoize-summary-after-compute-calls-and-times restrict reporting
;   to cases where the time is at least 1% of the time taken by the main
;   function.  We might want to make this customizable.

; - Consider finer-grained way to make memoization thread-safe.

; - Consider eliminating defun-one-output in most cases, simply for the sake of
;   elegance.

; - Consider eliminating some uses of our-syntax, instead relying on normal
;   ACL2 printing.

; - Consider printing sufficiently small floats without E notation.

; - Think about when to use defv vs. defg; maybe pick one and stick with it?
;   Or perhaps better yet, this question might be moot after considering the
;   next item.

; - Perhaps bundle up user-settable variables (see "User-settable variables for
;   recording" below) into a single defrec stored in a state global, and
;   provide suitable interface functions.  Careful though -- some books may
;   bind current such variables, so we'd probably want to provide a convenient
;   mechanism for doing such bindings.  As Jared notes, if such records are
;   stored in ordinary special variables -- i.e., not introduced with defg or
;   defv -- then although some performance advantage of defg/defv might be
;   lost, it can be easier to support multi-threading by taking advantage of
;   the fact that bindings of specials are thread-local.  He also reminds us of
;   the ability to use local variables [see for example mf-shorten and the use
;   of physical-memory-cached-answer in the defun of physical-memory], and
;   tells us that these can give similar efficiency to defv/defg with the
;   similar drawback of not being thread-local, but with the advantage that the
;   locality can ease not only ACL2 source code maintenance, but also avoid
;   problems for other people's code (because it can't access such globals
;   directly).

; - Document user-settable variables (or if the item just above is implemented
;   with a record stored in a state global, document the fields and/or their
;   readers and setters).

; - Try turning egc on in CCL.  (See function acl2h-init.)  Jared says (9/2014)
;   that "leaving on EGC could really reduce the memory requirements of 95+% of
;   the ACL2 jobs in the community books, and could be really good."

; - Consider moving set-gc-strategy (note that set-gc-strategy-builtin-delay
;   was formerly called start-sol-gc) and supporting functions out of the ACL2
;   code base, quite possibly into community books directory
;   books/centaur/misc/memory-mgmt/.  But if so, perhaps retain some way (an
;   interface of some sort) to get the effect of set-gc-strategy when
;   desirable, without the need for trust tags.  Perhaps consider the effect on
;   ACL2(hp).  Jared thinks that removing memory management responsibility out
;   of the ACL2 sources "might be especially useful if you are going to turn
;   EGC back on by default."

; - In pons-addr-of-argument, (+ hl-dynamic-base-addr (hl-staticp x)) is
;   probably a fixnum.  Especially for GCL, maybe wrap (the fixnum ...) around
;   it.  Also maybe declaim a return type of (values (or null fixnum)), in case
;   that helps GCL in particular; or maybe make this a macro (or at least
;   inline it, but then maybe we still want the declaim form).

; - Revisit the comment in mf-index about how we use hl-staticp without
;   checking that the argument is as normally expected.

; - Consider this suggestion from Jared, quoting a comment in memoize:

; Jared Davis suggests that we consider bundling up these 13 parameters, for
; example into an alist.  He says: "Various subsets of these arguments occur in
; spaghetti fashion throughout the code for memoize, add-trip, the
; memoize-table stuff, etc."

; - Investigate odd behavior of with-lower-overhead for LispWorks, as explained
;   in a comment there.

; SECTION: Preliminaries

;; One may comment out the following PUSHNEW and rebuild to get profiling
;; times not based upon the curious and wondrous RDTSC instruction of some x86
;; processors.  On a machine with several cores, the RDTSC values returned by
;; different cores may be slightly different, which could lead one into such
;; nonsense as instructions apparently executing in negative time, when timing
;; starts on one core and finishes on another.  To some extent we ignore such
;; RDTSC nonsense, but we still can report mysterious results since we have no
;; clue about which core we are running on in CCL (or, presumably, SBCL).

#+(or ccl sbcl)
(eval-when
 (:execute :compile-toplevel :load-toplevel)
 (when #+ccl (fboundp 'ccl::rdtsc)
       #+sbcl

; In SBCL 1.4.7, function sb-impl::read-cycle-counter is no longer defined, as
; it was in older versions (at least as recently as 1.4.2).  With (apropos
; "READ-CYCLE-COUNTER") we found sb-vm::%read-cycle-counter; actually, Keshav
; Kini first pointed us to sb-vm::%read-cycle-counter.  Oddly, fboundp returns
; nil on this symbol, and it cannot be called as the top-level function symbol
; in the read-eval-print loop.  But it seems to work fine here, and it seems to
; be equivalent to sb-impl::read-cycle-counter in older versions.  We completed
; a successful build and used it for (profile 'rewrite) followed by
; :mini-proveall and then (memsum), on top of both SBCL 1.1.11 and SBCL 1.4.7.

       (not (ignore-errors (sb-vm::%read-cycle-counter)))
   (pushnew :RDTSC *features*)))

#+rdtsc
(defconstant *2^30-1-for-rdtsc*
  (1- (ash 1 30)))

#+rdtsc
(defmacro rdtsc ()

; rdtsc always returns a fixnum, by zeroing out the top two bits of the real
; rdtsc value.  We add with the possibly slightly faster logior.

  #+ccl
  '(ccl::rdtsc)
  #+sbcl
  '(multiple-value-bind
       (t1 t2)
       (sb-vm::%read-cycle-counter)
     (declare (fixnum t1 t2))
     (the fixnum (logior (the fixnum (ash (logand t1 *2^30-1-for-rdtsc*)
                                          32))
                         t2))))

#+rdtsc
(defmacro rdtsc64 ()

; Rdtsc64 may return a bignum, but it returns all 64 bits of the real rdtsc
; value.

  #+ccl
  '(ccl::rdtsc64)
  #+sbcl
  '(multiple-value-bind
       (t1 t2)
       (sb-vm::%read-cycle-counter)
     (declare (fixnum t1 t2))
     (+ (ash t1 32) t2)))

; SECTION: Multithreaded Memoization

; This section was initially contributed by Jared Davis, who contributed the
; following comment (indented and re-filled here).

;   The implementation is in many ways suboptimal because, for the most part, I
;   just want to get something working.  To keep things simple, I have added a
;   single, global memoize lock.  This lock needs to be acquired whenever a
;   thread needs to do something that could mutate soundness-related memoize
;   state.  This is straightforward, but could (obviously) lead to a lot of
;   lock contention if you write multithreaded code that is using memoization
;   heavily.  It could also slow down single threaded code because of the
;   overhead of acquiring and releasing locks all the time.
;
;   In the future it would probably be worth reworking things so that, e.g.,
;   each memo table has its own separate lock.  On the other hand, that makes
;   things like deadlock a lot trickier.  That sounds pretty horrifying, so I'm
;   going to stick with the simple but possibly slow implementation for now.

(defg *enable-multithreaded-memoization*
  ;; By default set up multithreaded memoization only if we are running on
  ;; ACL2(p).  However, nothing here is really ACL2(p) specific, and users of
  ;; plain ACL2(h) can change this in raw Lisp if they know what they're doing.
  ;;
  ;; Note for raw Lisp hackers.  We ordinarily consult this variable
  ;; dynamically.  However, to make memoized functions execute more
  ;; efficiently, we only consult its value AT MEMOIZE TIME when creating the
  ;; memoized definitions.  Consequences of this:
  ;;
  ;;   - If you ever want to change this, e.g., because you are using ordinary
  ;;     ACL2(h) instead of ACL2(hp), but you want to do something with raw
  ;;     Lisp threads, then you really need to do something like this:
  ;;
  ;;        (setq *enable-multithreaded-memoization* t)
  ;;        (rememoize-all t)
  ;;
  ;;   - You need to be careful to do the rememoize-all AFTER you have already
  ;;     loaded any books that might contain memoized functions.  For instance,
  ;;     if you do the above and then include a book with a memoized F, then
  ;;     the definition of F will not do appropriate locking until you again do
  ;;     a rememoize-all.
  #+acl2-par t
  #-acl2-par nil)

; Historical Note: Many function names below are prefixed with ``mf-''.  This
; was a convention followed by Bob and Warren in their original prototype of
; this code, and preserved (and possibly followed) by Jared.  We have continued
; to follow the convention but we confess we don't know why ``mf-'' was used or
; what it stood for!  Our best guess is ``memoize function.''  The prefix
; ``ma-'' stood for ``memoize call array.''

(defun mf-multiprocessing (flg &optional quiet)
  (cond ((iff *enable-multithreaded-memoization* flg)
         (when (not quiet)
           (format *standard-output*
                   "~%; Note: Multiprocessing is already ~a.~%"
                   (if *enable-multithreaded-memoization* "on" "off"))))
        (t
         (unwind-protect ; make sure we finish!
             (setq *enable-multithreaded-memoization* flg)
           (rememoize-all t))))
  flg)

(defg *global-memoize-lock*
  (make-lock "*GLOBAL-MEMOIZE-LOCK*"))

(defmacro with-global-memoize-lock (&rest forms)

; We consult *enable-multithreaded-memoization* at runtime; compare with macro
; with-global-memoize-lock-static.

  #-(or ccl sb-thread lispworks) ; with-lock-raw is just progn
  `(progn ,@forms)
  #+(or ccl sb-thread lispworks)

; We tried the following alternative to the code below, in order to avoid
; duplicating code during macroexpansion.  But for ACL2(h) (in its normal mode
; -- that is without *enable-multithreaded-memoization*, hence not ACL2(hp))
; this seemed to slow down the regression slightly.  This macro is only used in
; this file so we're not too concerned about the compiled code duplication.

; (let ((body (gensym)))
;   ;; Avoid duplication of ,forms to avoid code blowup
;   `(flet ((,body () ,@forms))
;      (if *enable-multithreaded-memoization*
;          (with-lock-raw *global-memoize-lock* (,body))
;        (,body))))

  `(if *enable-multithreaded-memoization*
       (with-lock-raw *global-memoize-lock* ,@forms)
     (progn ,@forms)))

(defmacro with-global-memoize-lock-static (&rest forms)
  ;; Faster but less safe way to grab the lock, i.e., this version consults
  ;; *enable-multithreaded-memoization* at macroexpansion time instead of at
  ;; run time.  This is nothing more than a progn in the single-threaded case.
  ;;
  ;; NOTE: ONLY USE THIS WHEN CREATING MEMOIZED DEFINITIONS.  For everything
  ;; else, the safer version should be plenty fast.
  #-(or ccl sb-thread lispworks) ; with-lock-raw is just progn
  `(progn ,@forms)
  #+(or ccl sb-thread lispworks)
  (if *enable-multithreaded-memoization*
      `(with-lock-raw *global-memoize-lock* . ,forms)
    `(progn . ,forms)))

(defmacro mf-mht (&rest args)

; Call this macro with :shared :default unless we know that the call
; (mf-multiprocessing t) will blow away the hash table (and reconstitute it as
; a :shared table).

; We believe that at least one of :lock-free or :shared must be t in order to
; avoid "not owner of hash table" errors, and the following experiments support
; that belief.

; (defparameter *ht* (make-hash-table :lock-free nil :shared t))
; ; ok:
; (ccl:process-run-function "t1" (lambda () (setf (gethash 'my-key *ht*) 17)))
; (defparameter *ht* (make-hash-table :lock-free t :shared nil))
; ; ok:
; (ccl:process-run-function "t2" (lambda () (setf (gethash 'my-key *ht*) 17)))
; (defparameter *ht* (make-hash-table :lock-free nil :shared nil))
; ; error:
; (ccl:process-run-function "t3" (lambda () (setf (gethash 'my-key *ht*) 17)))

; The following experiment suggests that we get better performance with :shared
; t than with :lock-free t.  In fact :shared t may rival performance with
; :shared nil.

;   cd books/centaur/tutorial/
;   (include-book "alu16-book")
;   (time$ (def-gl-thm foo
;            :hyp (and (alu16-test-vector-autohyps)
;                      (equal op *op-mult*)
;                      (< a (expt 2 12))
;                      (< b (expt 2 12)))
;            :concl (equal (alu16-basic-result)
;                          (mod (* a b) (expt 2 24)))
;            :g-bindings (alu16-default-bindings)))

; :lock-free nil :shared nil
; 48.42 seconds realtime, 48.29 seconds runtime
; (4,169,078,496 bytes allocated).

; :lock-free t :shared nil
; 54.33 seconds realtime, 54.19 seconds runtime
; (4,528,524,384 bytes allocated).

; :lock-free nil :shared t
; 48.35 seconds realtime, 48.23 seconds runtime
; (4,169,087,440 bytes allocated).

; To access or update tables created by mf-mht, we use mf-gethash and
; mf-sethash.  Of course, :shared t is not sufficient to avoid the use of locks
; when performing atomic operations.  Moreover, as of this writing only CCL,
; among the supported host Lisps, pays attention to :shared (or :lock-free).

; Pons tables contain flex-alists, which can contain hash-tables.  Since
; hons-raw.lisp is loaded before memoize-raw.lisp, we define our own interface
; with hl-flex-acons; see mf-flex-acons.  See "SECTION: Ponsing: Creating keys
; ("ponses") for memoization tables".

  (if (assoc-keyword :shared args) ; then use :shared as supplied
      `(hl-mht ,@args)
    `(if *enable-multithreaded-memoization*
         (hl-mht :shared :default ,@args)
       (hl-mht ,@args))))

(defmacro mf-gethash (key ht)

; Ht was created by mf-mht.  See mf-mht.

  `(gethash ,key (the hash-table ,ht)))

(defmacro mf-sethash (key val ht)

; Ht was created by mf-mht.  See mf-mht.

  `(setf (gethash ,key (the hash-table ,ht)) ,val))

(defmacro mf-flex-acons (elem al)
  `(hl-flex-acons ,elem ,al *enable-multithreaded-memoization*))

(defmacro mf-hash-table-count (ht)

; Ht was created by mf-mht.  See mf-mht.

  `(hash-table-count (the hash-table ,ht)))

(defmacro mf-hash-table-size (ht)

; Ht was created by mf-mht.  See mf-mht.

  `(hash-table-size (the hash-table ,ht)))

(defmacro mf-maphash (lam ht)

; Ht was created by mf-mht.  See mf-mht.

  `(maphash ,lam (the hash-table ,ht)))

; SECTION: Constants and globals

; This section contains most of the constants and globals in this file,
; including all globals that might be modified (for example, directly by the
; user, or during initialization).

; NOTE: It might be best to skip this section on a first reading, or at most
; browse it lightly, returning to look at specific constants and globals when
; they are encountered later.

; Subsection: User-settable variables for recording

; To minimize metering overhead costs, one may set the "*RECORD-" variables
; below to NIL before memoizing.

; *RECORD-BYTES* and other *RECORD-...* variables are bound in
; REMEMOIZE-ALL, so we use DEFPARAMETER rather than DEFG.

; Warning: Keep the following set of globals in sync with memoize-info, as
; described there.

(defparameter *record-bytes*

; If *record-bytes* is not NIL at the time a function is memoized, we attempt
; to count all heap bytes allocated during calls of that function.

; It is quite possibly fine to replace the following form by T.  However, we
; leave this restriction, which produces nil in 32-bit CCL, because it has
; probably been here for many versions through 6.5 and at this point (August
; 2014) we don't expect much use of 32-bit CCL when doing memoization.

  (and (or (member :ccl *features*) ; most Lisps don't report bytes
           (member :sbcl *features*))
       (> most-positive-fixnum (expt 2 32))))

(defparameter *record-calls*

; If *RECORD-CALLS* is not NIL at the time a function is memoized, we count all
; calls of the function.

  t)

(defparameter *record-hits*

; If *RECORD-HITS* is not NIL at the time a function is memoized, we count the
; number of times that a previously computed answer is used again.

  t)

(defparameter *record-mht-calls*

; If *RECORD-MHT-CALLS* is not NIL at the time a function is memoized, we
; record the number of times that a memoize hash-table is created for the
; function.  See *report-mht-calls* below for an explanation of why we
; might create many hash-tables for a function.

  t)

(defparameter *record-pons-calls*

; If *RECORD-PONS-CALLS* is not NIL at the time a function is memoized, pons
; calls are counted.

  t)

(defparameter *record-time*

; If *RECORD-TIME* is not NIL the time a function is memoized, we record the
; elapsed time for each outermost call of the function.

  t)

; Subsection: User-settable variables for reporting

(defg *mf-print-right-margin* ; rather arbitrary default; seems to work well
  79)

(defv *report-bytes*

; When memoize-summary is invoked, print the number of bytes allocated on the
; heap, if this variable is not nil at that time and the host Lisp supports
; providing that information.

  #+(or ccl sbcl) t #-(or ccl sbcl) nil)

(defv *report-calls*

; When memoize-summary is invoked, print the number of calls, if this variable
; is not nil at that time.

  t)

(defv *report-calls-from*

; When memoize-summary is invoked, print the following if this variable is not
; nil at that time: which functions called the given function, how many times,
; and how long the calls took.

  t)

(defv *report-calls-to*

; When memoize-summary is invoked, print the following if this variable is not
; nil at that time: which functions were called by the given function, how many
; times, and how long the calls took.

  t)

(defv *report-hits*

; When memoize-summary is invoked, print the number of times that a previously
; computed answer was reused, if this variable is not nil at that time.

  t)

(defv *report-mht-calls*

; When memoize-summary is invoked, print the number of times that a memo
; hash-table for the function was created, if this variable is not nil at that
; time.  This may be of interest to those who memoize functions with stobj
; arguments, since when such a stobj changes, the function's memoization hash
; table is deleted, and then later, when necessary, created afresh.

  t)

(defv *report-pons-calls*

; When memoize-summary is invoked, print the number of calls of pons, if this
; variable is not nil at that time.

  t)

(defv *report-time*

; When memoize-summary is invoked, print information about the total time used
; to compute the outermost calls, if this variable is not nil at that time.

  t)

(defv *report-on-memo-tables*

; When memoize-summary is invoked, print information about memo tables, if this
; variable is not nil at that time.

  t)

(defv *report-on-pons-tables*

; When memoize-summary is invoked, print information about pons tables, if this
; variable is not nil at that time.

  t)

(defg *sort-to-from-by-calls* nil)

(defg *memoize-summary-order-reversed*

; When memoize-summary is invoked, report on functions in order from least to
; greatest, if this variable is not nil at that time.

  nil)

(defg *mf-print-alist-width* 45)

(defg *memoize-summary-order-list*

; This is a list of functions that MEMOIZE-SUMMARY uses to sort all functions
; that are currently memoized in preparation for displaying information about
; them.  The order used is lexicographical, with the first order having the
; most weight.  Each order function takes one argument, a symbol, and returns a
; rational.

; The default is '(total-time number-of-calls).

; Options for the functions include the following.

;    bytes-allocated [CCL and SBCL only]
;    bytes-allocated/call [CCL and SBCL only]
;    execution-order
;    hits/calls
;    pons-calls
;    number-of-calls
;    number-of-hits
;    number-of-memoized-entries
;    number-of-mht-calls
;    symbol-name-order
;    time-for-non-hits/call
;    time/call
;    total-time

  '(total-time number-of-calls))

(defg *memoize-summary-limit*

; The value is either nil or the maximum number of functions upon which
; memoize-summary reports.  A nil value means report on all."

  100)

(defg *condition-nil-as-hit*

; Set this variable to a non-nil value if you want the failure of a memoization
; condition to be recorded as a "hit".  That seems counterintuitive, which is
; why the default is nil.  (Note profiling doesn't report misses, so this
; decision doesn't impact profiling reports.)  But if you care a lot about the
; "Time per missed call" reported by memsum, maybe you'll want to set this to
; t.  NOTE that this value is consulted at the time a function is memoized, not
; at call time or memsum time.

  nil)

; Subsection: Miscellaneous user-settable variables

(defvar *never-memoize-ht*

; Function exit-boot-strap-mode further populates this hash table by calling
; function initialize-never-memoize-ht.

; Users can set this with never-memoize.

; Note: Consider locking uses of this global variable.

  (let ((ht (mf-mht :test 'eq :shared :default)))
    (loop for x in *stobjs-out-invalid*
          do (mf-sethash x t ht))
    #+rdtsc (mf-sethash #+ccl 'ccl::rdtsc
                        #+sbcl 'sb-impl::read-cycle-counter
                        t
                        ht) ; used in memoize implementation
    ht))

; Subsection: Variables not user-settable (managed by the implementation)

(defg *float-ticks/second* (float (expt 2 31))) ; 2 GHz
(defg *float-ticks/second-initialized* nil)

(declaim (float *float-ticks/second*))

(defg *pons-call-counter* 0)
(defg *pons-misses-counter* 0)
(declaim (type mfixnum *pons-call-counter*))
(declaim (type mfixnum *pons-misses-counter*))

(defg *mf-shorten-ht*

; This global is used in mf-shorten.  As explained there, no lock is needed.
; Since hons-copy is applied to form the keys, we can use eql as the test.

  (mf-mht :test 'eql :shared :default))

(defun initial-memoize-info-ht ()
  (if *enable-multithreaded-memoization*
      (mf-mht :shared :default)

; This table is essentially blown away and reconstituted by rememoize-all,
; hence by (mf-multiprocessing t).  So we avoid using :shared :default below,
; in order to make the table a bit more efficient in the uniprocessing case --
; though probably efficiency isn't particularly important for this hash table.

    (mf-mht)))

(defg *memoize-info-ht*

; This hash table associates memoized function symbols with various
; information.  It has two mappings in one (see setf forms in memoize-fn), that
; is, two kinds of keys: symbols and numbers.
;
;   1. It maps each currently memoized function symbol, fn, to a DEFREC record
;      of type MEMO-INFO-HT-ENTRY.  One field of that record is :NUM.
;
;   2. It maps each such :NUM value back to the corresponding symbol, fn.

  (initial-memoize-info-ht))

(declaim (hash-table *memoize-info-ht*))

(defparameter *memo-max-sizes*

; This hash table binds function names to memo-max-sizes-entry structures.

; Jared originally added this table because he wanted to know how big
; memoization tables were getting (so that he could set up appropriate initial
; sizes), but when tables are cleared they are thrown away, so for tables that
; are frequently cleared it wasn't possible to see how large the table had
; become.

; After seeing the information, it seemed a good idea to use it to infer what a
; good table size might be when the memo table is re-created.

  (mf-mht :shared :default))

(defun initial-memoize-call-array (n)

; Warning: It is assumed in sync-memoize-call-array that this array has a
; length of 1 when n is 1.

  (make-array n :element-type 'mfixnum :initial-element 0))

(defg *memoize-call-array*
  (initial-memoize-call-array 1))

; Essay on the *Memoize-Call-Array*

; *Memoize-call-array*, `ma' for short, is a 1D array that is used to store
; information about how many times one memoized function calls another and how
; much time is spent in such calls.  It also holds performance data on the
; callers themselves (independent of which subroutines they're calling).

; This array is conceptually two-dimensional.  To read from or write to this
; array, see ma-index and the ma-index-xxx macros.  Each "dimension" of ma is
; twice the maximum number of memoized functions; so the length is 4 times the
; square of the maximum number of memoized functions.  This is a very
; inefficient scheme; roughly half of the allocated space is unused!  See
; below.

; The length of this array is both a fixnum and an mfixnum; see
; memoize-call-array-grow.

; Ma is initialized in memoize-init.  Think of ma as a two dimensional array
; with dimensions (twice the max number of memoized functions) x (twice the max
; number of memoized functions).

; COLUMNS.  Each 'column' corresponds to info about a memoized function, but
; the first five columns are 'special'.  We count rows and columns starting at
; 0.  Column 0 is used as scratch space by compute-calls-and-times for sums
; across all functions.  Columns 1, 2, and 3 are not currently used at all.
; Column 4 is for the anonymous 'outside caller'.  Column 5 is for the first
; memoized function, column 6 is for the second, and so on.

; ROWS.  In columns 5 and greater, row 0 is used to count 'bytes', row 1 counts
; 'hits', row 2 counts mht calls, and row 4 counts pons calls that don't simply
; return a number (i.e., an address in the static-hons case).  (3 was formerly
; used to count hons calls, but that is no longer the case.)  The elements of
; an ma column starting at row 10 (twice the number assigned to the first
; memoized function) are for counting and timing info.  Suppose column 7
; corresponds to the memoized function FOO and column 12 corresponds to the
; memoized function BAR.  Whenever FOO calls BAR, element 2*12 of column 7 will
; be incremented by 1, and the total elapsed ticks for the call will be added
; to element 2*12+1 of column 7.  See the picture below.

; Though ma may 'grow', it may not grow while any memoized function is running,
; and here is why: every memoized function has a cached opinion about the size
; of ma.  (Here is a technical explanation, which one may wish to ignore.  For
; example, memoize-fn binds the variable fn-col-base to (ma-index fnn), which
; is computed based on the size of ma at the time the function is memoized.
; Fn-col-base is passed to memoize-fn-outer-body, where it is used to generated
; code for the memoized function.)

; Here is an ASCII picture of the *memoize-call-array* with a key to explain
; what is stored where.

;      <--------------max---------------><--------------max------------>
;       0  1  2  3  4  5         i                                      ^
;                                                                       |
; 0    [ ][x][x][x][ ][ ]  ...  [b]  ...  [x][x][x][x] ... [x][x][x][x] |
; 1    [ ][x][x][x][ ][ ]  ...  [h]  ...  [x][x][x][x] ... [x][x][x][x] |
; 2    [ ][x][x][x][ ][ ]  ...  [m]  ...  [x][x][x][x] ... [x][x][x][x] |
; 3    [ ][x][x][x][ ][ ]  ...  [x]  ...  [x][x][x][x] ... [x][x][x][x] |
; 4    [ ][x][x][x][ ][ ]  ...  [p]  ...
; 5    [ ][x][x][x][ ][ ]  ...  [ ]  ...  ...                      ... max
;      ...                 ...       ...
; 2j   [s][x][x][x][ ][ ]  ...  [c]  ...  [x][x][x][x] ... [x][x][x][x] |
; 2j+1 [s][x][x][x][ ][ ]  ...  [t]  ...  [x][x][x][x] ... [x][x][x][x] |
;      ...                 ...       ...                                |
;      [ ][x][x][x][ ][ ]  ...       ...  [x][x][x][x] ... [x][x][x][x] |
;      [ ][x][x][x][ ][ ]  ...       ...  [x][x][x][x] ... [x][x][x][x] v
;      ...                 ...       ...  [x][x][x][x] ... [x][x][x][x] ^
;      ...                 ...       ...  [x][x][x][x] ... [x][x][x][x] |
;      ...                 ...       ...  ...                     ...  max
;      ...                 ...       ...  [x][x][x][x] ... [x][x][x][x] |
;      [ ][x][x][x][ ][ ]  ...       ...  [x][x][x][x] ... [x][x][x][x] |
;      [ ][x][x][x][ ][ ]  ...       ...  [x][x][x][x] ... [x][x][x][x] v

; Dimensions:  (2 * max number of memoized fns)^2

; Contents:
; s -- scratch space for compute-calls-and-times as it sums across all functions
;      (for calls in even-numbered rows and ticks in odd-numbered rows)
; b -- number of bytes used in calls of fni
; h -- number of hits on calls of fni
; m -- number of mht calls on fni
; x -- unused
; p -- number of pons calls for fni
; c -- number of times fni called fnj
; t -- number of ticks spent when fni called fnj

; Each memoized function symbol is assigned a number.  The first ``real''
; function number is 5.  Because rows 0-4 of every function's column are
; devoted to performance data about that function, and due to a poorly realized
; desire to make a function's number serve both as its column number and its
; row number, we end up wasting columns 0-4 in every row because we use rows
; 0-4 in every column (!).  We don't entirely waste them: column 0 is used for
; scratch space and column 4 is used for the generic outside caller, but we
; have not found a use for columns 1, 2, or 3, or for column 0 of the odd rows.

; The uniformity of treating a function's number both as its column and row
; number is ``poorly realized'' because two rows are allocated to every
; function, e.g., data for function j resides in row 2j and row 2j+1, so the
; actual row number is not the function's number after all!

; Clearly this whole scheme -- evolved over several steps from Boyer and Hunt's
; original prototype -- is very wasteful but we are reluctant to change it
; simply because it works and we have not apparently suffered for lack of space
; for ma.

; The functions ma-index-calls and ma-index-ticks return index in the actual 1D
; array containing the call count and tick count, respectively, of the
; corresponding call from function i to function j.

; The following function, which is not part of our code, illustrates how to map
; from a pair of symbols, parent and child (caller and callee), to the index of
; the *memoize-call-array* containing the number of times parent called child.
; It calls symbol-to-fixnum, which maps a memoized function symbol to its
; natural number counterpart.

; (defun call-count (parent child)
; ; Return the number of times parent has called child, as per
; ; *memoize-call-array*.
;   (let* ((parent-index (symbol-to-fixnum parent))
;          (child-index (symbol-to-fixnum child))
;          (calls-index (ma-index-calls child-index parent-index))
;          (calls (aref *memoize-call-array* calls-index)))
;     (values calls
;             :parent-index parent-index
;             :child-index child-index
;             :calls-index calls-index)))

; For example,

; (defun f1 (x) (declare (xargs :guard t)) (cons x x))
; (defun f2 (x) (declare (xargs :guard t)) (cons (f1 x) (f1 x)))
; (memoize 'f1)
; (memoize 'f2)
; (f2 7)
; (f2 8)
; (f2 9)
; :q
; ; These return T:
; (equal (call-count 'f2 'f1) 6)
; (equal (call-count 'f1 'f2) 0)
; ; This gives more complete information, namely call-count,
; ; parent index, child index, index of call count:
; (call-count 'f2 'f1)

; The assignment of numbers to function symbols is handled by
; *memoize-info-ht*.  Use (maphash (function (lambda (fn val) (print (list fn
; val)))) *memoize-info-ht*) to inspect.

; As of this writing (Version_7.0), the number 4 is assigned to the
; non-function "outside-caller" (denoting the caller of outermost call of a
; memoized function) and 5-7 are assigned to the first three built-in functions
; listed below; they are always memoized by explicit calls to memoize in
; boot-strap-pass-2-b.lisp.  Of course, this set and the particular numbers may
; change in future releases, but we include this information here to indicate
; aspects of the basic scheme.  BAD-LISP-OBJECTP may not always be memoized,
; i.e., it is not in ACL2(hp).  See *thread-unsafe-builtin-memoizations* for a
; list of functions that are not memoized in ACL2(hp).

; fn                               number assigned
; "outside-caller"                     4
; FCHECKSUM-OBJ                        5
; PKG-NAMES-MEMOIZE                    6
; WORSE-THAN-BUILTIN                   7
; BAD-LISP-OBJECTP                     8

; By the way, the assignment of a unique number to each memoized function is
; done initially by symbol-to-fixnum-create.

(declaim (type (simple-array mfixnum (*))
               *memoize-call-array*))

(defg *callers-array*

; At the end of a call of compute-calls-and-times, which is called by
; memoize-summary, (aref *callers-array* n) will contain the numbers of the
; functions that have called the function numbered n.

  (make-array 0))

(declaim (type (simple-array t (*)) *callers-array*))

(defconstant *ma-bytes-index*       0)
(defconstant *ma-hits-index*        1)
(defconstant *ma-mht-index*         2)
; Originally there was an *ma-hons-index* of 3, but we no longer count honses.
(defconstant *ma-pons-index*        4)

; We associate memoized function symbols with fixnums, and vice versa.  See
; symbol-to-fixnum-create.

(declaim (type (and mfixnum

; Normally we are happy to declare variables in this file to be of mfixnum type
; only, but here we also declare these of type fixnum so that indices i below
; such variables may safely appear in forms (loop for i fixnum ...).

                    fixnum)
               *max-symbol-to-fixnum*
               *initial-2max-memoize-fns*
;              *initial-max-symbol-to-fixnum* ; defconstant, below
               *2max-memoize-fns*))

(defconstant *initial-max-symbol-to-fixnum* 4)

(defg *max-symbol-to-fixnum* *initial-max-symbol-to-fixnum*)

(defv *initial-2max-memoize-fns* 1000)

(defg *2max-memoize-fns* ; length of *memoize-call-array*
  *initial-2max-memoize-fns*)

(defg *memoize-init-done* nil)

(defg *hons-gentemp-counter* 0)

(defg *memoize-use-attachment-warning-p* t)

(defv *number-of-arguments-and-values-ht*

; Mf-note-arity is an interface for updating this variable.

; This hash table maps a symbol fn to a cons pair (a . d), where a is the
; number of inputs and d is the number of outputs of fn.  NIL for a or d
; indicates 'don't know'.

  (mf-mht :shared :default))

(declaim (hash-table *number-of-arguments-and-values-ht*))

; Globals not included in this section:
; - *caller*
; - *10-days*
; - *float-internal-time-units-per-second*

; SECTION: Our-syntax

(defmacro our-syntax (&rest args)

; This macro extends Common Lisp's with-standard-io-syntax by binding *package*
; and *readtable*.  It may not be necessary to bind *readtable* here, but it
; has been done historically and it seems harmless.  We bind *package* because
; the Common Lisp utility with-standard-io-syntax binds *package* to the
; CL-USER package.

; The settings in our-syntax are oriented towards reliable, standard, vanilla,
; mechanical reading and printing, and less towards human readability.

; Please, before changing the following, consider existing uses of this macro
; insofar as the changes might impact reliable, standard, vanilla, mechanical
; printing.

; Consider using our-syntax-nice.

  `(with-standard-io-syntax
    (let ((*package* (find-package-fast
                      (f-get-global 'current-package *the-live-state*)))
          (*readtable* *acl2-readtable*))
      ,@args)))

(defmacro our-syntax-nice (&rest args)

; Our-syntax-nice may offer slightly more pleasant human readability than
; our-syntax.  Although we stopped using it ourselves in Sept. 2014, we leave
; it for now since it is used in some books.

  `(our-syntax
    (setq *print-case*                 :downcase)
    (setq *print-pretty*               t)
    (setq *print-readably*             nil)
    (setq *print-right-margin*         ,*mf-print-right-margin*)
    (setq *print-miser-width*          100)
    ,@args))

; SECTION: Number of Arguments

(defun mf-note-arity (fn nargs nvals)

; This raw Lisp function declares that fn has the indicated number of inputs
; and outputs.

; Note: Consider locking uses of this function, since it updates a global
; hash-table.

  (mf-sethash fn (cons nargs nvals) *number-of-arguments-and-values-ht*))

(defun memoize-look-up-def-raw (sym quiet-p)

; This function attempts to return the definition of sym as an s-expression
; (not a symbol-function), as (name formals . rest).  When that attempt fails,
; then an error occurs if quiet-p is nil but nil is returned otherwise.

; For CCL, we could evaluate the following two forms so that
; function-lambda-expression will return the form used in the defun of
; a function symbol.

;    (setq ccl::*save-definitions* t)
;    (setq ccl::*fasl-save-definitions* t)

; However, while memoization is implemented with some features specific to CCL
; (e.g., RDTSC, though this is now used in SBCL as well), in general we prefer
; that the functionality be independent of the host Lisp, so that books are
; less likely to fail certification when changing host Lisps (or versions of a
; given host Lisp).  Moreover, an ACL2 regression based on CCL took close to 2%
; longer when including those forms in acl2.lisp:

; With the above forms:
; 33606.972u 498.459s 1:16:57.09 738.6%   0+0k 0+2676744io 0pf+0w

; Without the above forms:
; 32964.076u 475.053s 1:15:31.71 737.8%   0+0k 135096+2542696io 78pf+0w

; (- 1 (/ (+ 32964.076 475.053) (+ 33606.972 498.459)))
; = 0.019536536570964436

; (- 1 (/ (+ 3600 (* 60 15) 31.71) (+ 3600 (* 60 16) 57.09)))
; = 0.01849216714424018

; The property acl2-saved-def, which appears below, is installed when save-def
; is used; see for example bad-lisp-objectp.

  (let ((temp (get sym 'acl2-saved-def)))
    (cond (temp (cdr temp))
          (t (let* ((fn (symbol-function sym))
                    (lam (and fn
                              #+gcl ; accommodate early GCL 2.6.13
                              (and (fboundp 'function-lambda-expression)
                                   (funcall 'function-lambda-expression fn))
                              #-gcl
                              (function-lambda-expression fn))))
               (cond (lam (assert (or (eq (car lam) 'lambda)
                                      #+sbcl
                                      (eq (car lam) 'SB-INT::NAMED-LAMBDA)))
                          lam)
                     (quiet-p nil)
                     (t (error "Lisp cannot find a definition for ~
                                ~s.~%Consider using ~s or supplying to ~
                                ~%memoize(-fn) an explicit :CL-DEFUN ~
                                argument.~a"
                               sym
                               'save-def
                               #-ccl
                               ""
                               #+ccl
                               (format
                                nil
                                "~%Alternatively, you might solve this ~%~
                                 problem, for CCL only, by setting Lisp ~%~
                                 globals CCL::*SAVE-DEFINITIONS* and ~%~
                                 CCL::*FASL-SAVE-DEFINITIONS* to T before~%~
                                 defining ~a (though this might slow down~%~
                                 performance)."
                                sym)))))))))

(defun-one-output mf-len-inputs (fn)

; This function returns the length of the inputs of fn, or nil for "don't
; know".

  (assert (symbolp fn))
  (assert (fboundp fn))
  (assert (not (macro-function fn)))
  (assert (not (special-operator-p fn)))

  (or (let ((pair (mf-gethash fn *number-of-arguments-and-values-ht*)))
        (and (consp pair)
             (integerp (car pair))
             (car pair)))
      (let ((formals
             (getpropc fn 'formals t (w *the-live-state*))))
        (and (not (eq t formals))
             (length formals)))
      (let ((def (memoize-look-up-def-raw fn t)))
        (and def (length (cadr def))))))

(defun-one-output mf-len-outputs (fn)

; This function returns the length of the outputs of fn, or nil for "don't
; know".

  (assert (symbolp fn))
  (assert (fboundp fn))
  (assert (not (macro-function fn)))
  (assert (not (special-operator-p fn)))

  (or (let ((pair (mf-gethash fn *number-of-arguments-and-values-ht*)))
        (and (consp pair)
             (integerp (cdr pair))
             (cdr pair)))
      (let* ((state *the-live-state*)
             (w (w state)))
        (and (not (eq t (getpropc fn 'formals t w)))
             (len (stobjs-out fn w))))
      (and (get fn 'acl2-saved-def)

; Save-def guarantees that there is a single output of the defined function.

           1)))

; SECTION: Timing Utilities

; WARNING: Whenever using *float-ticks/second*, consider whether it should be
; properly initialized if that has not already been done.  Here is the story:

; In order to set *float-ticks/second* to a reasonably accurate value, there is
; a one-time delay due to a call of sleep in float-ticks/second-init, which
; might be noticeable when starting up ACL2.  We avoid this delay until we need
; the accuracy.  For example, fix-ticks is used in the wrappers of memoized
; functions, making it performance-critical, but it only uses
; float-ticks/second to compute a heuristic sanity check; so we avoid that
; delay in fix-ticks.  On the other hand, for many purposes we want
; *float-ticks/second* to be accurate, such as in calls of total-time (for
; printing memoize-summary information).  For those, we tolerate the delay.

; The community book books/centaur/memoize/timer.lsp provides some potentially
; useful ideas, but as of this writing (late August 2014) we stick pretty close
; to what has previously been done here.

(defconstant *10-days-in-seconds* (* 10 24 60 60))

(defun 10-days ()
  (let ((n (* *10-days-in-seconds*
              (ceiling *float-ticks/second*))))
    n))

(defg *10-days*

; We get a reasonable approximation based on *float-ticks/second*, which is
; improved after calling float-ticks/second-init.

  (10-days))

(declaim (type mfixnum *10-days*))

(defg *float-internal-time-units-per-second*
  (float internal-time-units-per-second))

(declaim (float *float-internal-time-units-per-second*))

(defmacro internal-real-ticks ()

; We use logand below instead of mod because it is faster (see below).  This
; use of logand relies on the fact that the binary representation of
; most-positive-mfixnum is a sequence of ones.

; The following tests use values of i that are fixnums, because that is what we
; expect to encounter in most cases and they avoid the overhead of building
; bignums.  But there is no reason to expect the overwhelming advantage of
; avoiding mod to disappear if bignums are involved.  Indeed, if "to
; most-positive-mfixnum" is replaced by "(+ most-positive-mfixnum n)" below,
; convincing results are still obtained.

;   (defun my-test-0 (n)
;     (loop for i from (- most-positive-mfixnum n) to most-positive-mfixnum
;           when (eql (the integer i)
;                     -1)
;           do (error "Found 0!")))
;
;   (defun my-test-1 (n)
;     (loop for i from (- most-positive-mfixnum n) to most-positive-mfixnum
;           when (eql (the integer (logand i most-positive-mfixnum))
;                     -1)
;           do (error "Found 0!")))
;
;   (defun my-test-2 (n)
;     (loop for i from (- most-positive-mfixnum n) to most-positive-mfixnum
;           when (eql (the integer (mod i most-positive-mfixnum))
;                     -1)
;           do (error "Found 0!")))
;
;   (time$ (my-test-0 10000000))
;   (time$ (my-test-1 10000000))
;   (time$ (my-test-2 10000000)) ; much slower than the others

; Note that (ccl::rdtsc) returns a fixnum; see
; http://trac.clozure.com/ccl/wiki/ReleaseNotes.

  #+(and RDTSC (not 32-bit-target)) ; faster for 64
  '(the-mfixnum (rdtsc))
  #+(and RDTSC 32-bit-target)          ; slower for 32
  '(the-mfixnum (logand (rdtsc64) ; don't truncate at 32-bit CCL fixnum
                        most-positive-mfixnum))
  #-RDTSC
  '(the-mfixnum (logand (the-mfixnum (get-internal-real-time))
                        most-positive-mfixnum)))

(defun-one-output float-ticks/second-init ()

; [Jared] multithreading note: I think it's fine not to protect this with a
; lock; if two threads happen to recompute it, that seems harmless enough.

  (unless *float-ticks/second-initialized*
    #+RDTSC (let ((i1 (rdtsc64))
                  (i2 (progn (sleep .1) (rdtsc64))))
              (cond
               ((> i2 i1)
                (setq *float-ticks/second*
                      (* 10 (float (- i2 i1)))))
               (t ; retain initial value of *float-ticks/second*
                (format t
                        "~%***WARNING***: Float-ticks/second-init ~
                         failed;~%using arbitrary default value.~%Memoize ~
                         timings may be unreliable.~%")
                (force-output *standard-output*))))
    #-RDTSC (setq *float-ticks/second*
                  *float-internal-time-units-per-second*)

    ;; We found that occasionally *float-ticks/second* is insane, probably
    ;; due to RDTSC flakiness when switching processors, etc.  So, if it is
    ;; really clearly insane, try to fudge it back to something reasonably
    ;; sensible.  See community book centaur/memoize/timer.lsp for relevant
    ;; comments.
    #+RDTSC
    (when (> *float-ticks/second*
             (* 20
                1000 ;; khz
                1000 ;; mhz
                1000 ;; ghz
                ))
      (format t "*** Tick-based timing seems to be broken.~%")
      (format t "*** Our estimated *float-ticks/second* is ~s; seems too ~
                 large.~%"
              *float-ticks/second*)
      (format t "*** Is your processor really running at ~s GHz?~%"
              (/ *float-ticks/second* (* 1000 1000 1000)))
      (format t "*** Fudging speed to 2 GHz.  Profiling may be inaccurate.~%")
      (setq *float-ticks/second* (* 2.0 1000 1000 1000)))

    (setq *10-days* (10-days))
    (setq *float-ticks/second-initialized* t)
    (check-type *float-ticks/second*
                (and float (satisfies plusp)))))

; SECTION: Safe-incf

(defun safe-incf-aux-error (x inc where)
  (declare (type mfixnum x inc))
  (cond
   (where
    (error "~%; SAFE-INCF-AUX: ** Error: ~a."
           (list :x x :inc inc :where where)))
   (t (setf (the mfixnum x)
            most-positive-mfixnum)))
  nil)

(defmacro safe-incf-aux (x inc &optional where)

; This is essentially safe-incf, but where inc is known to have a positive
; integer value.

  (cond
   ((not (or (symbolp inc)
             (and (< inc most-positive-mfixnum)
                  (> inc 0))))
    (safe-incf-aux-error x inc where))
   ((and (true-listp x) ; e.g., x is (aref ar (.. expr ..))
         (equal (len x) 3)
         (member (car x) '(aref svref))
         (symbolp (nth 1 x))
         (consp (nth 2 x)))
    (let ((idx (make-symbol "IDX")))
      `(let ((,idx (the-mfixnum ,(nth 2 x))))
         (declare (type mfixnum ,idx))
         (safe-incf (,(nth 0 x)
                     ,(nth 1 x)
                     ,idx)
                    ,inc
                    ',where))))
   (t (let ((v (make-symbol "V")))
        `(let ((,v (the-mfixnum ,x)))
           (declare (type mfixnum ,v))
           (cond ((<= ,v (the-mfixnum
                              (- most-positive-mfixnum
                                 (the-mfixnum ,inc))))
                  (setf (the mfixnum ,x)
                        (the-mfixnum (+ ,v (the-mfixnum ,inc))))
                  nil)
                 (t (safe-incf-aux-error ',x ',inc ',where))))))))

(defmacro safe-incf (x inc &optional where)

; Summary: we increment nonnegative mfixnum x by nonnegative mfixnum inc,
; returning nil.  But if the result is too large to be of type mfixnum, then we
; cause an error if where is non-nil, else we set x to most-positive-mfixnum.

; SAFE-INCF is a raw Lisp macro that behaves the same as INCF when both X and
; INC are nonnegative MFIXNUMs and their sum is a nonnegative MFIXNUM.  In a
; call of (SAFE-INCF x inc), X must be a place that holds an MFIXNUM.  INC must
; evaluate to an MFIXNUM.  Both X and INC must evaluate without side effects,
; so that it is impossible to tell which was executed first or whether only one
; or both were executed.  If INC is not positive, no update takes place at all.
; Otherwise, if the sum of the values of X and INC is not an MFIXNUM, which is
; tested without causing an error, a run-time error will be caused.  Else, if
; the sum is an MFIXNUM then, as with INCF, the place X will be set to hold the
; sum of the old value of that place and the value of INC.  The value returned
; by SAFE-INCF is NIL.  Caution: INC may be evaluated first, which is why side
; effects are prohibited.

; An optional third parameter is merely to help with error location
; identification.

; In (SAFE-INCF (AREF A (FOO)) INC), (FOO) is only evaluated once.
; Same for SVREF.

; The argument, where, is only used in reporting errors.  When where is
; non-nil, an error occurs if (+ x inc) is too large to be an mfixnum;
; otherwise, x is set to most-positive-mfixnum.  Note that nil is always
; returned; the only purpose is to increment x, not return a value.

  (cond ((integerp inc)
         (if (<= inc 0)
             nil
           `(safe-incf-aux ,x ,inc ,where)))
        ((symbolp inc)
         `(if (>= 0 (the-mfixnum ,inc))
              nil
            (safe-incf-aux ,x ,inc ,where)))
        (t (let ((incv (make-symbol "INCV")))
             `(let ((,incv (the-mfixnum ,inc)))
                (declare (type mfixnum ,incv))
                (if (>= 0 ,incv)
                    nil
                  (safe-incf-aux ,x ,incv ,where)))))))

; SECTION: Ponsing: Creating keys ("ponses") for memoization tables

; Pons differs from hons in that it does not honsify its arguments and in that
; it takes a hash table as a third argument.  We use pons in memoization.

; We use pons instead of hons in memoization because we could not afford to
; honsify (using fast-alist-fork!, say) certain alists in certain biology
; tests.  About the same time, we (gratuitously) decided to stop hons'ifying
; the output of memoized functions.

; Most of the comments and code in this section were initially derived from
; books/centaur/memoize/pons.lsp, authored by Jared Davis and, as stated there,
; "a descendant of the memoization scheme developed by Bob Boyer and Warren
; A. Hunt, Jr. which was incorporated into the HONS version of ACL2, sometimes
; called ACL2(h)."

; Pons is the critical function for generating memoization keys.  To a rough
; approximation, here is how we memoize (F arg1 arg2 ... argN):
;
;     PONS := (PIST* arg1 ... argN)
;     LOOK := MemoTableForF[PONS]
;     if (LOOK exists)
;        return LOOK
;     else
;        RESULT := (F arg1 arg2 ... argN)
;        MemoTableForF[PONS] = RESULT
;        return RESULT
;
; In other words, we use (PIST* arg1 ... argN) to create the hash key for the
; arguments arg1 ... argN.  And PIST* is defined in terms of PONS.
;
;    (PIST*)          = NIL
;    (PIST* X1)       = X1
;    (PIST* X1 X2)    = (PONS X1 X2)
;    (PIST* X1 X2 X3) = (PONS X1 (PONS X2 X3))
;      ...                ...
;
; As its name suggests, PONS is similar to a HONS.  The main difference is that
; whereas (HONS X Y) requires us to recursively generate a "canonical" version
; of X and Y, (PONS X Y) does not descend into its arguments.
;
; It is worth noting that in the 0 and 1-ary cases of PIST*, no PONSing is
; necessary!  Because of this it can be considerably cheaper to memoize unary
; and zero-ary functions than higher-arity functions.  Note also that as the
; arity of the function increases, the amount of ponsing (and hence its cost)
; increases.
;
; The soundness requirement on PIST* is that two argument lists should produce
; EQL keys only if they are pairwise EQUAL.  This follows from a stronger
; property of PONS:
;
;     (EQL (PONS A B) (PONS C D))  --->  (EQL A C) && (EQL B D).
;
; Why is this property sufficient?  The 0-2 argument cases are trivial.  Here
; is a sketch of the 3-ary case, which generalizes easily to the N-ary case:
;
;    Our goal is to ensure:
;
;       If   (EQL (PIST* A1 B1 C1) (PIST* A2 B2 C2))
;       Then (EQUAL A1 A2) && (EQUAL B1 B2) && (EQUAL C2 C2)
;
;    Assume the hypothesis:
;
;       (EQL (PONS A1 (PONS B1 C1)) (PONS A2 (PONS B2 C2)))
;
;    Then from our PONS property it follows immediately that
;
;      1. (EQL A1 A2), and hence (EQUAL A1 A2) since EQL implies EQUAL.
;      2. (EQL (PONS B1 C1) (PONS B2 C2)).
;
;    From 2, again from our PONS property it follows that
;
;      1. (EQL B1 B2), and hence (EQUAL B1 B2) since EQL implies EQUAL.
;      2. (EQL C1 C2), and hence (EQUAL C1 C2) since EQL implies EQUAL.
;
;    Which is what we wanted to show.
;
; For our memoization scheme to be effective, it is desirable for PIST* to
; produce EQL keys when given pairwise-EQL argument lists.  This follows easily
; if our PONS property holds in both directions, that is:
;
;     (EQL (PONS A B) (PONS C D))  <--->  (EQL A C) && (EQL B D).
;
; Okay, so how does PONS actually work?  First we will introduce a "slow"
; ponsing scheme, and then explain an optimization that avoids slow ponsing in
; many cases.
;
;
; Slow Ponsing.
;
; The above discussion hides the fact that PONS and PIST* take an additional
; argument, called the Pons Table.  This table is essentially a scheme for
; remembering which keys we have produced for argument lists that have been
; encountered thus far.  Note that the act of PONSing implicitly modifies the
; Pons Table.
;
; The Pons Table is similar to the CDR-HT-EQL in the Classic Honsing scheme;
; see the Essay on Classic Honsing.  That is, it is an EQL hash table that
; binds each
;
;    Y ->  { key : key is the key for (PONS X Y) }
;
; As in classic honsing, these sets are represented as Flex Alists.  The basic
; implementation of (PONS X Y), then, is as follows:
;
;     Y_KEYS := PonsTable[Y]
;     XY_KEY := FlexAssoc(X, Y_KEYS)
;     If (XY_KEY was found)
;        return XY_KEY
;     Else
;        NewKey = (CONS X Y)
;        Y_KEYS := FlexAcons(NewKey, Y_KEYS)
;        PonsTable[Y] := Y_KEYS
;        return NewKey
;
; In other words, we build a new (X . Y) cons and use it as the key, unless we
; had previously seen these same arguments and such a key is already available.
;
;
; Avoiding Slow Ponsing.
;
; When static honsing is enabled, we activate an improvement to slow ponsing.
;
; In particular, if X and Y can be assigned addresses (see the discussion of
; Static Hons Addressing from hons-raw.lisp) without the use of an OTHER-HT or
; STR-HT, then we can just combine their addresses with hl-addr-combine (which
; is one-to-one) and use the resulting integer as our key.  In many cases this
; allows us to avoid the hash table lookups required in Slow Ponsing.
;
; The basic ideas here are:
;
;   - Some ACL2 objects (any static conses, symbol, or small fixnum) have
;     addresses, but other objects (larger numbers, characters, strings, and
;     ordinary conses) do not.
;
;   - If (PONS X Y) is given X and Y that both have addresses, we basically
;     just hash their addresses with hl-addr-combine.  The resulting integer is
;     used as the key.
;
;   - Otherwise, we fall back to Slow Ponsing.  Since slow ponsing always
;     creates a cons instead of an integer, there's no possibility of confusion
;     between the keys from the two schemes.

; Note that unlike much of the memoization code, pons address calculation can
; traffic in fixnums rather than mfixnums.

#+static-hons
(defun pons-addr-of-argument (x)

; Warning: *default-hs* needs to have been initialized before calling this
; function.  As of this writing, pons-addr-of-argument is called only by
; pons-addr-hash, which is called only by pons, which calls
; (hl-maybe-initialize-default-hs) before calling pons-addr-hash.

; Warning: Keep this in sync with hl-addr-of and hl-addr-of-unusual-atom.

; See hl-addr-of.  This is similar, except without the STR-HT or OTHER-HT we
; can simply fail to assign addresses to strings, large numbers, rationals, and
; so forth.

  (cond ((eq x nil) 256)
        ((eq x t)   257)
        ((symbolp x)
         (hl-symbol-addr x))
        ((and (typep x 'fixnum)
              (<= hl-minimum-static-int (the fixnum x))
              (<= (the fixnum x) hl-maximum-static-int))
         (the fixnum
              (+ hl-static-int-shift (the fixnum x))))
        ((characterp x)
         (char-code x))
        ((and (consp x)
              (hl-hspace-truly-static-honsp x *default-hs*))

; Note that a honsp is not garbage collected unless it is first freed from its
; addr-table.  So the following value will correspond to x until a hons-wash or
; hons-clear is done, which is long enough since those operations clear all
; pons tables (in the #+static-hons case, which is the case we are in here).

; [Jared] Is this OK for multithreaded memoize?  I think so.  The scenario here
; is:
;
;  - The memo tables are shared across all threads
;  - Each thread has its own hons space and their own notion of which
;    conses are hl-hspace-truly-static-honsp
;  - It is NOT OK (as in, it would be a soundness bug) for us to keep memo
;    table entries after hons spaces get washed or cleared, because the index
;    we're computing could then be reassigned to some other cons, as described
;    in the comment below about "mistake" and "contradiction".
;
; The current strategy is to have the hons wash/clear functions clear all the
; memo tables to ensure this doesn't happen.  I think that's sufficient even in
; a multithreaded context: even though some honses in space A may not be honses
; in space B, they still have uniquely assigned indices (their hl-staticp
; indices), and that's all we're relying on here.  In other words, I think we
; may get memoize misses because of differences in whether things are honsed,
; but we aren't going to get any false hits.

         (+ hl-dynamic-base-addr (hl-staticp x)))
        (t

; It is perhaps a bit tempting to add a case for (hl-staticp x), and then
; proceed as in the consp case of hl-addr-of.  But if x is later garbage
; collected, then afterwards, each entry in the pons table created using this
; address is likely to be stale.  In fact, such treatment of static conses
; allowed the following book to be certified in ACL2(h) Versions 6.5 and 5.0
; (and quite possibly all versions inbetween and maybe some earlier).

;  (in-package "ACL2")
;
;  (defn foo (x y) (+ (len x) (nfix y)))
;
;  (memoize 'foo :recursive nil)
;
;  (value-triple (progn$ (foo (hons-copy '(a)) 0)
;                        (foo (hons-copy '(b)) 0)
;                        (foo (hons-copy '(c)) 0)
;                        (foo (hons-copy '(d)) 0)
;                        (hons-wash)
;                        nil))
;
;  (defthm mistake
;    (equal (foo (hons-copy '(a b)) 0)
;           1)
;    :hints (("Goal" :in-theory (e/d (foo (hons-copy))
;                                    (hons-copy))))
;    :rule-classes nil)
;
;  (defthm contradiction
;    nil
;    :hints (("Goal" :use mistake))
;    :rule-classes nil)

         nil)))

; [Jared] multithreading notes.  Pons tables are hash tables that will be
; shared.  There are no locks in the pons code, because we assume that the lock
; will be grabbed before we start ponsing.

#+static-hons
(defabbrev pons-addr-hash (x y)

; Warning: *default-hs* needs to have been initialized before calling this
; function, because it calls pons-addr-of-argument.  As of this writing,
; pons-addr-of-argument is called only by pons-addr-hash, which is called only
; by pons, which calls (hl-maybe-initialize-default-hs) before calling
; pons-addr-hash.

; We try to compute the addresses of X and Y and hash them together.  If either
; doesn't have an address, we just return NIL.

  (let ((xaddr (pons-addr-of-argument x)))
    (if (not xaddr)
        nil
      (let ((yaddr (pons-addr-of-argument y)))
        (if (not yaddr)
            nil
          (hl-addr-combine* xaddr yaddr))))))

(defmacro incf-pons-calls ()
  '(safe-incf *pons-call-counter* 1))

(defmacro incf-pons-misses ()
  '(safe-incf *pons-misses-counter* 1))

(defun pons (x y ht)

; We avoid any lock in this function, since it is called under the lock
; installed by with-global-memoize-lock-static in the memoized definition; see
; memoize-fn-def.

  (declare (hash-table ht))

; With static honsing pons calls pons-addr-hash, which calls
; pons-addr-of-argument, which can access *default-hs*.  So here, we make sure
; that *default-hs* is initialized with static honsing.  This is inexpensive
; compared to pons, for two reasons:

; - When *default-hs* has already been initialized, the call just below is
;   essentially just a read of a special variable.

; - Pons is only called on behalf of memoized functions with at least two
;   arguments.

  #+static-hons
  (hl-maybe-initialize-default-hs)

  #+static-hons
  (let ((addr (pons-addr-hash x y)))
    (when addr (return-from pons addr)))

  (incf-pons-calls)

  (let* ((flex-alist (mf-gethash y ht))
         (entry      (hl-flex-assoc x flex-alist)))
    (cond
     (entry)
     (t
      (incf-pons-misses)
      (let* ((was-alistp (listp flex-alist))
             (new-cons

; It might be tempting to think about creating a static cons here.
; But in order to benefit from that, we would need to find a good way
; to use its index, perhaps in place of new-cons as a key of the pons
; table.  But in that case we would still need to hang on to that
; (static) cons so that it isn't garbage collected; so there is no
; obvious benefit to creating a static cons here, after all.

              (cons x y))
             (new-flex-alist (mf-flex-acons new-cons flex-alist)))

; Ctrl+C safety is subtle.  If was-alistp, then the above was applicative.  We
; now install the flex alist, which occurs as a single update to the hash
; table.

        (when was-alistp
          (mf-sethash y new-flex-alist ht))

; Otherwise, the flex-acons was non-applicative and the table was already
; extended, so there's nothing more we need to do.

        new-cons)))))

(defmacro pist* (table &rest x)
  (cond ((atom x) x)
        ((atom (cdr x)) (car x))
        (t (list 'pons
                 (car x)
                 (cons 'pist* (cons table (cdr x)))
                 table))))

; SECTION: Identifying functions that are unsafe to memoize

(defun initialize-never-memoize-ht ()

; Our goal is to avoid memoizing functions that support the implementation of
; memoization.  So we disallow functions defined in file hons-raw.lisp or in
; file memoize-raw.lisp, as well as built-ins Common Lisp functions.  This
; might not be a complete list, and it might even be too comprehensive; but it
; seems like a reasonable start.

  (let ((ht (mf-mht :test 'eq :shared :default)))
    (note-fns-in-file "hons-raw.lisp" ht) ; its fns may be used in this file
    (note-fns-in-file "memoize-raw.lisp" ht)
    (flet ((update-nmht (fn)
                        (when (and (fboundp fn)
                                   (not (macro-function fn)))

; We only memoize functions, so we can restrict according to the test above.

                          (never-memoize-fn fn))))
      (mf-maphash (lambda (key val)
                    (declare (ignore val))
                    (update-nmht key))
                  ht)
      (loop for fn in *common-lisp-symbols-from-main-lisp-package*
            do
            (update-nmht fn))))
  nil)

(defun never-memoize-fn (fn)

; Warning: Keep the return values in sync for the logic and raw Lisp.

; Note: Consider locking uses of this function, since it updates a global
; hash-table.

  (mf-sethash fn t *never-memoize-ht*)
  nil)

(defun never-memoize-p (fn)
  (mf-gethash fn *never-memoize-ht*))

; SECTION: Preliminary memoization support

(defrec memoize-info-ht-entry

; The *memoize-info-ht* associates memoized function symbols with these
; records.

; The fields are vaguely ordered by most frequently referenced first, but it's
; not clear that this is important for efficiency, except perhaps for
; ext-anc-attachments (see update-memo-entry-for-attachments).

  (ext-anc-attachments ; see the Essay on Memoization with Attachments

; Start-ticks is a symbol whose value is the start time (in float ticks) of the
; current, outermost call of fn, or -1 if no call of fn is in progress.

   start-ticks   ; see above
   num           ; an integer, unique to fn
   tablename     ; a symbol whose value is the memoize table for fn
   ponstablename ; a symbol whose value is the pons table for fn
   condition     ; :condition passed to memoize-fn (but nil for *nil*)
   inline        ; T or NIL :inline arg, as passed to memoize-fn
   memoized-fn   ; the new value of (symbol-function fn)
   old-fn        ; the old value of (symbol-function fn), or nil
   fn            ; a symbol, the name of the function being memoized
   sts           ; the stobj memo-table lists for fn

; Cl-defun is the function body actually used, in the inline=t case, as
; supplied (or as computed, if not supplied).

   cl-defun             ; see above
   formals              ; as supplied (or as computed, if not supplied)
   commutative          ; asserts this is a binary commutative function
   specials             ; hack for raw Lisp functions that read specials
   stobjs-in            ; as supplied (or as computed, if not supplied)
   stobjs-out           ; as supplied (or as computed, if not supplied)
   record-bytes         ; value as bound at the time MEMOIZE-FN is called
   record-calls         ;        ''
   record-hits          ;        ''
   record-mht-calls     ;        ''
   record-pons-calls    ;        ''
   record-time          ;        ''
   forget               ; Boolean, clears memo when outermost call exits
   memo-table-init-size ; integer, reasonable default of *mht-default-size*
   aokp                 ; use of attachments is allowed

; [Jared] multithreading notes: we could probably add a lock here that was only
; on a per-function basis.  That could help avoid needing the global lock, much
; of the time.

   )
  t)

(defmacro ma-index (col &optional (row 0) (2mmf '*2max-memoize-fns*))

; This function creates an index into the one-dimensional array,
; *memoize-call-array*.  That array is conceptually a two-dimensional array,
; and the arguments are a corresponding column and row of that 2D array.  If
; row is not supplied, then the index returned points to the start of the
; column (i.e., for a row of 0).

  (let ((col-base `(* ,2mmf
                      (the-mfixnum ,col))))
    (if (eql row 0)
        `(the-mfixnum ,col-base)
      `(ma-index-from-col-base ,col-base ,row))))

(defmacro ma-index-from-col-base (col-base row)

; This function creates an index into the one-dimensional array,
; *memoize-call-array*.  That array is conceptually a two-dimensional array,
; and the arguments are a corresponding column and row of that 2D array.
; Col-base is an index into *memoize-call-array* representing the start of a
; column, and row represents a row of the 2D array.

  `(the-mfixnum (+ (the-mfixnum ,col-base)
                   (the-mfixnum ,row))))

(defmacro ma-index-calls (child &optional
                                (parent 0)
                                (2mmf '*2max-memoize-fns*))

; When parent calls child, we will make an entry in *memoize-call-array* for
; the "column" of parent at a "row" corresponding to child, where "column" and
; "row" are in quotes because while we think of *memoize-call-array* as a
; two-dimensional array, it actually has only one dimension.  This macro
; computes the index into *memoize-call-array* for that entry.  A special case
; is "column" 0 of *memoize-call-array*, which is used as scratch space by
; COMPUTE-CALLS-AND-TIMES for sums across all functions.  In that case there is
; no "parent" -- we are just accumulating all calls regardless of any notion of
; "parent".

  (let ((2child `(the-mfixnum (* 2 (the-mfixnum ,child)))))
    (if (eql parent 0)
        2child ; simplification of `(ma-index 0 ,2child ,2mmf)
      `(ma-index ,parent ,2child ,2mmf))))

(defmacro ma-index-ticks (child &optional
                               (parent 0)
                               (2mmf '*2max-memoize-fns*))

; This macro is similar to ma-index-calls, but it counts ticks instead of
; calls.  See comments in ma-index-calls.

  (let ((2child+1 `(the-mfixnum
                        (1+ (the-mfixnum (* 2 (the-mfixnum ,child)))))))
    (if (eql parent 0)
        2child+1 ; simplification of `(ma-index 0 ,2child+1 ,2mmf)
      `(ma-index ,parent ,2child+1 ,2mmf))))

(defun outside-caller-col-base ()

; See *caller*.  Notice that although we pass *initial-max-symbol-to-fixnum*
; explicitly below, the value also depends on the global *2max-memoize-fns*.

  (ma-index *initial-max-symbol-to-fixnum*))

(defvar *caller*

; This variable represents the index into *memoize-call-array* that starts the
; layout of the "column" for the innermost memoized function call being
; evaluated (or, in the case of its initial value, the column for
; "outside-caller" = (mf-gethash *initial-max-symbol-to-fixnum*
; *memoize-info-ht*).  The idea is to accumulate calls and ticks into that
; "column".

; When memoized functions are executing in parallel, the value of *caller* and
; of statistics derived therefrom may be meaningless and random.

; At one time we introduced this variable using defg instead of defvar.  To see
; why we now use defvar, see the comment about unwind-protect in
; memoize-fn-outer-body.

  (let ((val (outside-caller-col-base)))
    (check-type val mfixnum)
    val))

(declaim (type mfixnum *caller*))

(defrec memo-max-sizes-entry

; This represents a single entry in the *memo-table-max-sizes* table.

  (num-clears   ; how many times has this table been cleared (nat)
   max-pt-size  ; maximum size of the pons table before any clear (nat)
   max-mt-size  ; maximum size of the memo table before any clear (nat)
   avg-pt-size  ; average size of the pons table before any clear (float)
   avg-mt-size  ; average size of the memo table before any clear (float)
   )
  t)

(defparameter *memoize-verbose* nil)

(defun memoize-table-desired-size (fn min-size)

; Fn is the name of a function.  Min-size is the minimum size of the table we
; we will create --- perhaps a size that the user says to use.  We want to
; create and return a new hash table for this function's memoization table.
; One possible implementation of this function would just be:
;
;    (mf-mht :size min-size)
;
; But we hope to do better.  Our idea is to look at how large the table has
; been in the past, and use that size to make a good prediction of how large
; the table will be this time.
;
; The idea here is to build a table that's just slightly bigger than the
; average size we've seen so far.  We arbitrarily say that "slightly bigger"
; means 1.2x the previous average.
;
; By itself this would be scary.  Big hash tables can use a lot of memory.  In
; early versions of this code we thought that 1 MB of space provided about
; 44,000 entries.  But here we see in CCL that 1 MB of space can buy you about
; 53,000 entries:

;      ? [RAW LISP] (time (make-hash-table :size 53102))
;      (MAKE-HASH-TABLE :SIZE 53102)
;      took 606 microseconds (0.000606 seconds) to run.
;      During that period, and with 4 available CPU cores,
;           453 microseconds (0.000453 seconds) were spent in user mode
;           126 microseconds (0.000126 seconds) were spent in system mode
;       999,984 bytes of memory allocated.
;      #<HASH-TABLE :TEST EQL size 0/53102 #x30200276BDDD>
;      ? [RAW LISP]

; We want to avoid creating a hundred-megabyte memo table for a function just
; because it was used heavily for a short while and then cleared once before.
; On the other hand, if a memo table truly does get large on a regular basis,
; then we do want to guess a big size for it.
;
; So in this code, we enforce an artificial maximum on our guess, but allow
; this maximum to grow with the number of times we've cleared the table.
; Basically we're comfortable allowing the maximum guess to grow at a rate of 1
; MB per clear.  If a table has been cleared 100 times, we have a pretty good
; sense of its average usage and we can be comfortable allocating up to 100 MB
; for it.  If it's been cleared more than 1000 times, the cap is a gigabyte.
; But of course, to actually reach such a large guess, you'd have to be
; repeatedly filling up the table to contain millions of entries and then
; clearing it.

; Note: The 44,000 in the code below stems from our earlier estimate that it's
; equivalent to 1 MB.  We have no data to suggest this slightly smaller growth
; rate (.83 MB instead of 1 MB) hurts us and so we have left it.

  (let* ((max-sizes ; previously recorded sizes of this table, if any exist
          (mf-gethash fn *memo-max-sizes*)))
    (if (not max-sizes)

; We never cleared this memoize table before, so we don't have anything to add.
; Fall through to the default.

        min-size
      (let* ((nclears       (access memo-max-sizes-entry max-sizes :num-clears))
             (avg-mt-size   (access memo-max-sizes-entry max-sizes :avg-mt-size))
             (our-guess     (ceiling (* 1.20 avg-mt-size)))
             (capped-guess  (min our-guess (* nclears 44000)))
             (final-guess   (max *mht-default-size* min-size capped-guess)))
        (when (and (< (integer-length (- nclears 1))
                      (integer-length nclears))
                   *memoize-verbose*)
          (format t "; ~s memo table: ~s clears, avg size ~s, guess ~s, final ~
                     ~s~%"
                  fn nclears avg-mt-size our-guess final-guess))
        final-guess))))

(defun pons-table-desired-size (fn min-size)

; This is similar to memoize-table-desired-size, but for the pons table.

  (let* ((max-sizes (mf-gethash fn *memo-max-sizes*)))
    (if (not max-sizes)

; We've never cleared this pons table before, so we don't have anything to go
; on besides what the user says.  Now, this is subtle.  Originally we just
; returned min-size here, i.e., "do what the user says."  But while this makes
; sense for the memo table, it doesn't necessarily make much sense for the pons
; table.  In particular, we can sometimes avoid ponsing by using our
; static-cons-index-hashing scheme.

; In some sense it would probably be good to give the user explicit control
; over the pons table size.  But for now, the main use of our memoize table
; size controls is to set things up for big BDD/AIG/SEXPR operations where
; we've got honsed data.  So, we just use *mht-default-size* here, which seems
; as reasonable a choice as any, so that the memo-table-init-size argument of
; memoize-fn only affects the memoize table and not the initial pons table.

        *mht-default-size*
      (let* ((nclears       (access memo-max-sizes-entry max-sizes :num-clears))
             (avg-pt-size   (access memo-max-sizes-entry max-sizes :avg-pt-size))
             (our-guess     (ceiling (* 1.20 avg-pt-size)))
             (capped-guess  (min our-guess (* nclears 44000)))
             (final-guess   (max *mht-default-size*
                                 min-size
                                 capped-guess)))
        (when (and (< (integer-length (- nclears 1))
                      (integer-length nclears))
                   *memoize-verbose*)
          (format t "; ~s pons table: ~s clears, avg size ~s, guess ~s, final ~
                     ~s~%"
                  fn nclears avg-pt-size our-guess final-guess))
        final-guess))))

(defun make-initial-memoize-hash-table (fn init-size)

; This table is essentially blown away and reconstituted by rememoize-all,
; hence by (mf-multiprocessing t).  So we avoid using :shared :default below,
; in order to make the table a bit more efficient in the uniprocessing case.

  (with-global-memoize-lock
    (mf-mht :size (memoize-table-desired-size fn init-size))))

(defun make-initial-memoize-pons-table (fn init-size)

; This table is essentially blown away and reconstituted by rememoize-all,
; hence by (mf-multiprocessing t).  So we avoid using :shared :default below,
; in order to make the table a bit more efficient in the uniprocessing case.

  (with-global-memoize-lock
    (mf-mht :size (pons-table-desired-size fn init-size))))

(defun update-memo-max-sizes (fn pt-size mt-size)

; Fn is a memoized function with a non-nil pons-table or memo-table, which is
; about to receive a new pons-table and memo-table of size pt-size and mt-size
; respectively (perhaps nil initially, in which case the size is 1).  We update
; the *memo-max-sizes* entry associated with f.  The :max-pt-size and
; :max-mt-size are not used any more; they were used by Jared to track how big
; the tables were growing.

; We won't count clears that occur when the tables are completely unpopulated,
; because we want to know how many entries get used when we do use the table,
; not when we don't.

  (when (or (< 0 mt-size) (< 0 pt-size))
    (with-global-memoize-lock
     (let ((old (mf-gethash fn *memo-max-sizes*)))
       (if (not old)
           (mf-sethash fn
                       (make memo-max-sizes-entry
                             :num-clears 1
                             :max-pt-size pt-size
                             :max-mt-size mt-size
                             :avg-pt-size (coerce pt-size 'float)
                             :avg-mt-size (coerce mt-size 'float))
                       *memo-max-sizes*)
         (let* ((old.num-clears  (access memo-max-sizes-entry old :num-clears))
                (old.max-pt-size (access memo-max-sizes-entry old :max-pt-size))
                (old.max-mt-size (access memo-max-sizes-entry old :max-mt-size))
                (old.avg-pt-size (access memo-max-sizes-entry old :avg-pt-size))
                (old.avg-mt-size (access memo-max-sizes-entry old :avg-mt-size))
                (new.num-clears  (+ 1 old.num-clears)))
           (mf-sethash fn
                       (make memo-max-sizes-entry
                             :num-clears  new.num-clears
                             :max-pt-size (max pt-size old.max-pt-size)
                             :max-mt-size (max mt-size old.max-mt-size)
                             :avg-pt-size (/ (+ pt-size (* old.avg-pt-size
                                                           old.num-clears))
                                             new.num-clears)
                             :avg-mt-size (/ (+ mt-size (* old.avg-mt-size
                                                           old.num-clears))
                                             new.num-clears))
                       *memo-max-sizes*))))))
  nil)

(defun print-memo-max-sizes ()

; Note (Matt K., 9/2014): This is just a printing function, probably rarely
; used, so I haven't really reviewed this code, though I did test it
; successfully.

  (with-global-memoize-lock
   (when (equal (mf-hash-table-count *memo-max-sizes*) 0)
     (return-from print-memo-max-sizes nil))
   (format t "Memo table statistics gathered at each from when they were ~
             cleared:~%~%")
   (let ((indent 8) ; initial value of 8 is the length of "Function"
         indent-str)
     (mf-maphash (lambda (fn entry)
                   (declare (ignore entry))
                   (setq indent (max indent (length (symbol-name fn)))))
                 *memo-max-sizes*)
     (setq indent-str (format nil "~a" (+ 2 indent)))
     (format t (concatenate 'string "~" indent-str ":@a") "Function")
     (format t " ~10:@a | ~15:@a ~15:@a | ~15:@a ~15:@a~%"
             "Clears" "PT Max" "PT Avg" "MT Max" "MT Avg")
     (mf-maphash
      (lambda (fn entry)
        (let* ((num-clears  (access memo-max-sizes-entry entry :num-clears))
               (max-pt-size (access memo-max-sizes-entry entry :max-pt-size))
               (max-mt-size (access memo-max-sizes-entry entry :max-mt-size))
               (avg-pt-size (access memo-max-sizes-entry entry :avg-pt-size))
               (avg-mt-size (access memo-max-sizes-entry entry :avg-mt-size)))
          (format t
                  (concatenate 'string "~" indent-str
                               ":@a ~10:D | ~15:D ~15:D | ~15:D ~15:D~%")
                  fn num-clears
                  max-pt-size (floor avg-pt-size)
                  max-mt-size (floor avg-mt-size))))
      *memo-max-sizes*)
     (format t "~%")))
  nil)

; Essay on Memoization Involving Stobjs

; We allow memoization of functions that take user-defined stobjs (not state)
; as arguments but do not return stobjs.  The key is the use of memoize-flush
; to "forget" all that was remembered for certain functions that use certain
; stobjs.  We must keep memoize-flush very fast in execution so as not to slow
; down stobj update or resize operations in general.  Indeed, memoize-flush may
; (according to tests run) incur essentially no cost (after Version_4.3) as
; long as no functions with stobj arguments are actually memoized.

; The following example shows why we disallow memoization of functions that
; return stobjs.  First, redefine memoize-table-chk by eliminating the branch
; that causes an error in the presence of stobj names in stobjs-out.  Then
; start up ACL2 and submit the forms below.  The problem is that we do not
; inhibit storing a result in the case that the stobj has changed from the time
; the function was called to the time the result is to be stored.

; (defstobj st fld)
; (defun foo (st)
;   (declare (xargs :stobjs st))
;   (let ((st (update-fld (cons (fld st) (fld st)) st)))
;     (mv (fld st) st)))
; (foo st) ; updates (fld st), returns (mv (nil) st)
; (memoize 'foo)
; (foo st) ; updates (fld st), returns (mv ((nil) nil) st)
; (foo st) ; no longer updates (fld st)
; (foo st) ; no longer updates (fld st)
; (fld st) ; still ((nil) nil), whereas if we hadn't
;          ; memoized foo (fld st) would be:
;          ; ((((NIL) NIL) (NIL) NIL) ((NIL) NIL) (NIL) NIL)

(defun memoize-flush1 (lst)

; Lst is the list of names of memoize tables, typically the tables associated
; with all the memoized stobj-using (but not stobj-returning) functions on a
; given stobj st.

; Experiments showed that when lst is nil, it is faster to call this function
; than to inline its code into the body of memoize-flush.

; We "forget" all memoized values by clearing all necessary memoize tables; see
; the comment about memoize-flush in memoize-fn.  We leave the pons table alone
; in order to keep this flushing operation as fast as possible.  Note that the
; pons table merely stores keys to be looked up in the memo table, so there is
; no soundness issue, and in fact those pons table entries might remain useful;
; the cost is the space taken up by the pons tables.

  (with-global-memoize-lock
   (loop for sym in lst do
         (when (boundp (the symbol sym)) ; not sure if this test is needed
           (let ((old (symbol-value (the symbol sym))))
             (unless (or (null old)
                         (eql 0 (mf-hash-table-count old)))
               (setf (symbol-value (the symbol sym)) nil)))))))

(defmacro memoize-flush (st)

; St is a stobj name and (st-lst st), below, returns returns a symbol whose
; value is a list in which are saved the names of the memoize tables that will
; be set to nil whenever the stobj st is changed.

; See memoize-flush1 for a relevant discussion.

  (and st
       (let ((s (st-lst st)))
         `(when ,s ; optimization
            (memoize-flush1 ,s)))))

(defun sync-memoize-call-array ()

; Warning: Be careful if you call this function from other than memoize-init or
; memoize-call-array-grow.  In particular, it is probably a mistake to call
; this function while memoized functions are running, since *caller* is
; supposed to depend on the innermost memoized function call being evaluated,
; but sync-memoize-call-array sets *caller* to denote the "outside" caller.

; We assume that *2max-memoize-fns* is the intended length of
; *memoize-call-array* and *max-symbol-to-fixnum* is the maximum fixnum
; associated with a memoized function symbol (so far).

; It should be rare that this function is called after its call by
; memoize-init, i.e., by a call from memoize-call-array-grow.  That is:
; memoize-call-array-grow should be rare.  This code historically often cleared
; *memoize-call-array* and *callers-array* in most cases when called by
; memoize-call-array-grow.  For simplicity, we make that be the case always,
; and clearly.

  (with-global-memoize-lock
   (let ((n1 (ma-index *2max-memoize-fns*))
         (n2 (1+ *max-symbol-to-fixnum*)))
     (declare (type (and fixnum mfixnum) n1 n2))
     (setq *memoize-call-array* (initial-memoize-call-array 1))
     (setq *callers-array* (make-array 0))
     (gc$)
     (setq *memoize-call-array* (initial-memoize-call-array n1))
     (setq *callers-array* (make-array n2 :initial-element nil))
     (setq *caller* (outside-caller-col-base)))))

(defun memoize-call-array-grow (&optional
                                (2nmax
                                 (* 2 (ceiling
                                       (* 3/2 (/ *2max-memoize-fns* 2))))))

; In our own code we call this function with no arguments.  However, as of this
; writing, community book file centaur/memoize/old/profile-raw.lsp calls it
; with an argument.  The argument will become the new dimension of the
; (virtual) 2D square array, *memoize-call-array*.

; This function has the potential to corrupt the state, but we cause errors in
; cases where that potential seems real.  In order to avoid having this
; function invoked automatically, consider using the following hack.

; :q
; (setq *memoize-init-done* nil)
; (setq *initial-2max-memoize-fns* 10000)
; (memoize-init)
; (lp)
; (clear-memoize-tables)
; (clear-memoize-statistics)

  (with-global-memoize-lock
   (unless (integerp 2nmax)
     (error "(memoize-call-array-grow ~s).  Arg must be an integer."
            2nmax))
   (unless (evenp 2nmax)
     (error "(memoize-call-array-grow ~s).  Arg must be even." 2nmax))
   (unless (> 2nmax 100)
     (error "(memoize-call-array-grow ~s).  Arg must be > 100." 2nmax))
   (when (<= 2nmax *2max-memoize-fns*)
     (cw "; memoize-call-array-grow: *memoize-call-array* already big enough.~%")
     (return-from memoize-call-array-grow))
   (unless (<= (* 2nmax 2nmax) most-positive-mfixnum)
     (error "memoize-call-array-grow:  most-positive-mfixnum exceeded.  Too ~
             many memoized functions."))
   (unless (<= (* 2nmax 2nmax) most-positive-fixnum)
     (error "memoize-call-array-grow:  most-positive-fixnum exceeded.  Too ~
             many memoized functions."))
   (unless (< (* 2nmax 2nmax) array-total-size-limit)
     (error "memoize-call-array-grow: ARRAY-TOTAL-SIZE-LIMIT exceeded.  Too ~
             many memoized functions."))
   (unless (< (* 2nmax 2nmax) array-dimension-limit)
     (error "memoize-call-array-grow: ARRAY-DIMENSION-LIMIT exceeded.  Too ~
             many memoized functions."))
   (unless (eql *caller* (outside-caller-col-base))

; Ouch.  We are about to blow away and reconstitute the memoization structures,
; including memoized definitions, yet we are inside a memoized definition!
; This seems like a potentially terrible situation; presumably the original
; definition continues executing in this case even though the function has been
; redefined, and probably the only thing wrong is the statistics gathering.
; But are we sure?  Fortunately, we are only here when we need more than the
; initial limit of about 500 memoized functions, and it seems unlikely that
; this will happen when inside a memoized function.  (It might happen when
; calling profile-all or profile-acl2 in raw Lisp, as defined in community book
; books/centaur/memoize/old/profile.lisp.  But it seems unlikely that these
; would be called inside some other memoized function!)

; So we cause a somewhat scary continuable error here, and leave it up to the
; user whether to continue at his or her own risk.  If this problem really
; occurs in practice, someone can point it out, and some attention can perhaps
; be given to the problem of whether there is any reasonable way to guarantee
; that all is well in this circumstance.

     (cerror "Continue at your own risk."
             "MEMOIZE-CALL-ARRAY-GROW was called while a memoized function~%~
              was executing, so all bets are off.  Continue only at your own~%~
              risk.  That risk may be low, but at the least, memoization~%~
              reports (in particular, from memsum) will probably be~%~
              inaccurate."))
   (setq *2max-memoize-fns* 2nmax)
   (let ((state *the-live-state*))
     (observation 'memoize-call-array-grow
                  "Now reinitializing memoization structures.  This will ~
                   erase saved values and statistics."))
   (sync-memoize-call-array)
   (rememoize-all))
  nil)

(defun-one-output symbol-to-fixnum-create (s)

; We return the number n associated with function symbol s, in the sense that
; (mf-gethash n *memoize-info-ht*) = s.  If no such number n yet exists, the
; next available number is returned -- but this function does not actually add
; the association; that is done by its caller, memoize-fn.

  (check-type s symbol)
  (with-global-memoize-lock
   (let ((g (mf-gethash s *memoize-info-ht*)))
     (if g
         (access memoize-info-ht-entry g :num)
       (let (new)
         (loop for i fixnum
               from (1+ *initial-max-symbol-to-fixnum*)
               below (the fixnum (floor *2max-memoize-fns* 2))
               do (unless (mf-gethash i *memoize-info-ht*)
                    (setq new i)
                    (return)))
         (cond (new (setq *max-symbol-to-fixnum*
                          (max *max-symbol-to-fixnum* new))
                    new)
               (t (memoize-call-array-grow)

; Everything has been blown away!  So try again.

                  (symbol-to-fixnum-create s))))))))

(defun-one-output symbol-to-fixnum (s)
; This is like symbol-to-fixnum-create, but assumes that s is already memoized.
  (check-type s symbol)
  (let ((g (mf-gethash s *memoize-info-ht*)))
    (if g
        (access memoize-info-ht-entry g :num)
      (error "(symbol-to-fixnum ~s).  Illegal symbol." s))))

(defun-one-output fixnum-to-symbol (n)
  (check-type n fixnum)
  (or (mf-gethash n *memoize-info-ht*)
      (error "(fixnum-to-symbol ~s). Illegal number." n)))

(defun-one-output hons-gentemp (root)
  (check-type root string)
  (loop
   (safe-incf *hons-gentemp-counter* 1 hons-gentemp)
   (let ((name (our-syntax
                (format nil "HONS-G-~s,~s" root *hons-gentemp-counter*))))
     (multiple-value-bind (sym status)
         (intern name (find-package "ACL2_INVISIBLE"))
       (if (null status) (return sym))))))

(defun-one-output st-lst (st)

; ST-LST returns a symbol whose value is a list in which are saved the
; names of the memoize tables that will be set to nil whenever the
; stobj st is changed.

  (check-type st symbol)
  (intern (our-syntax (format nil "HONS-S-~s,~s"
                              (package-name (symbol-package st))
                              (symbol-name st)))
          (find-package "ACL2_INVISIBLE")))

(defun-one-output mf-dcls (l)

; Drop any (IGNORE ...) from within a list of declarations, ((DECLARE ...)
; (DECLARE ...) ...) and return the resulting list of DECLAREs.

  (loop for dec in l nconc
        (let ((temp
               (if (consp dec)
                   (loop for d in (cdr dec) nconc
                         (if (and (consp d) (eq (car d) 'ignore))
                             nil ; ignorable is added in memoize-fn-def
                           (cons d nil))))))
          (if temp (cons (cons 'declare temp) nil)))))

(defun memoize-use-attachment-warning (fn at-fn)
  (when *memoize-use-attachment-warning-p*
    (let ((state *the-live-state*))
      (warning$ 'top-level "Attachment"
                "Although the function ~x0 is memoized, a result is not being ~
                 stored because ~@1.  Warnings such as this one, about not ~
                 storing results, will remain off for all functions for the ~
                 remainder of the session unless the variable ~x2 is set to a ~
                 non-nil value in raw Lisp."
                fn
                (mv-let (lookup-p at-fn)
                        (if (consp at-fn)

; Then at-fn is of the form (:lookup . f), where f was memoized with :aokp t
; and a saved value for f was used, as explained in the lookup-p case below.

                            (assert$ (eq (car at-fn) :lookup)
                                     (mv t (cdr at-fn)))
                          (mv nil at-fn))
                        (cond (lookup-p
                               (msg "a stored result was used from a call of ~
                                     memoized function ~x0, which may have ~
                                     been computed using attachments"
                                    at-fn))
                              (t
                               (msg "an attachment to function ~x0 was used ~
                                     during evaluation of one of its calls"
                                    at-fn))))
                '*memoize-use-attachment-warning-p*))
    (setq *memoize-use-attachment-warning-p* nil)))

(defun-one-output memoize-fn-suffix (str sym)
  (check-type str string)
  (check-type sym symbol)
  (let ((spkn (package-name (symbol-package sym)))
        (sn (symbol-name sym)))

; Sometimes we use our-syntax for calls like this, and sometimes we don't.
; It's not clear that it much matters, so we have tended to preserve what was
; true historically.

    (format nil "~s,~s,~s" str spkn sn)))

(defmacro mf-index (x &optional known-not-rational)
  (assert (symbolp x)) ; else we should use defabbrev here
  `(cond ,@(unless known-not-rational
             `(((typep ,x 'fixnum) ,x)))
         #+static-hons
         (t

; Since this function is only heuristic, it is sound to use the weak staticp
; check below, instead of using consp and hl-hspace-truly-static-honsp checks
; as we do in pons-addr-of-argument.  We are hopeful that this decision won't
; result in expensive needless misses when checking memoization tables, but
; perhaps more thought about that would be useful here.

          (hl-staticp ,x))))

(defun-one-output mis-ordered-commutative-args (x y)

; This "function" need not return the same value for every call on the same
; input argument list.  We use this function in the creation of a suitable
; memoization table key, specifically to decide whether to reorder x and y
; before calling pist* (see memoize-fn).  Such reordering is justified for an
; ACL2 function of two arguments that has been proven commutative, because such
; reordering causes no difference in the result that can be detected by the
; ACL2 logic.

; The basic idea is to create an "index" for each argument.  For static conses
; we use hl-staticp as the index; but some Lisps have no static conses.  Of
; course, it is always legal to return nil.  Perhaps in the future we will use
; machine addresses or some other technique for sorting the arguments.

; We order objects that are rational or have an index before objects that are
; neither.

  (cond
   ((eql x y) nil)
   (t (let ((idx (mf-index x)))
        (declare (type (or null fixnum) idx))
        (cond
         (idx
          (let ((idy (mf-index y)))
            (declare (type (or null fixnum) idy))
            (cond
             (idy (< (the fixnum idy)
                     (the fixnum idx)))
             ((rationalp y)
              (< y (the fixnum idx))))))
         ((rationalp x)
          (let ((idy (mf-index y)))
            (declare (type (or null fixnum) idy))
            (cond
             (idy (< (the fixnum idy)
                     x))
             ((rationalp y)
              (< y x)))))
         ((or (rationalp y)
              (mf-index y t))))))))

(defun memoize-look-up-def (fn cl-defun inline wrld
                               &key quiet-p)

; This function returns a definition (fn formals ...), that is, without the
; initial DEFUN.  It returns cl-defun unchanged (other than stripping off the
; car if it is DEFUN), unless cl-defun is :DEFAULT -- which won't happen when
; memoize is called in the ACL2 loop (search in the definition of add-trip for
; the form (assert$ cl-defun (memoize-fn (nth 1 tuple) ...)).  In that :DEFAULT
; case, a reasonable attempt is made to find a definition.

; In memoize-fn, we rely on the fact that when memoize-look-up-def is called
; with a non-nil value of inline and it returns without error, then it returns
; a non-nil definition (which is a true list).

  (cond ((eq cl-defun :default)
         (cond
          ((null inline) nil)
          ((not (fboundp fn))
           (error "MEMOIZE-LOOK-UP-DEF: ** ~a is undefined." fn))
          ((let ((def (cltl-def-from-name fn wrld)))
             (cond (def (assert (eq (car def) 'defun))
                        (cdr def)))))
          (t (memoize-look-up-def-raw fn quiet-p))))
        ((eq (car cl-defun) 'defun)
         (cdr cl-defun))
        (t
         cl-defun)))

(defg *memoize-timing-bugs* 0)

(defmacro fix-ticks (ticks ctx)

; Warning: If you make this a function and add a declaim form first such as
;   (declaim (ftype (function (mfixnum t) (values mfixnum))
;                   fix-ticks))
; then in GCL, make sure that after the build, the symbol-plist shows the
; correct declaim information.  We have seen a version of GCL 2.6.12pre for
; which this was not the case, which apparently was the cause of an unexpected
; error.

  `(let ((ticks ,ticks)
         (ctx ,ctx))
     (declare (type mfixnum ticks))
     (the-mfixnum
      (cond
       ((and (<= 0 (the-mfixnum ticks))
             (< (the-mfixnum ticks)
                (the-mfixnum *10-days*)))
        (the-mfixnum ticks))
       (t
        (incf *memoize-timing-bugs*)
        (when (<= *memoize-timing-bugs* 10)
          (format t "Ignoring time increment of ~a sec for ~a~%"
                  (/ ticks *float-ticks/second*) ctx)
          (when (eql *memoize-timing-bugs* 10)
            (format
             t
             "Timing is very dubious.  Suppressing further messages.~%")))
        0)))))

; SECTION: The main code for creating memoized function definitions:
; memoize-fn, unmemoize-fn, etc.

(defun-one-output memoizedp-raw (fn)
  (and (symbolp fn)
       (values (mf-gethash fn *memoize-info-ht*))))

(defmacro mf-make-symbol (&rest r) ; for forming symbols in package ACL2
  `(our-syntax (intern (format nil ,@r) *acl2-package*)))

(defun memoize-fn-init (fn inline wrld &aux (state *the-live-state*))

; Do initial stuff for memoize-fn, including error checking.  Quite possibly
; only a few of the checks below (if any) are necessary if memoize-fn is called
; by way of an invocation of memoize in the ACL2 loop.

  (with-global-memoize-lock

   (unless (symbolp fn)
     (error "Memoize-fn: ~s is not a symbol." fn))

   (maybe-untrace! fn) ; See the comment about Memoization in trace$-def.

   (unless *memoize-init-done*
     (error "Memoize-fn:  *MEMOIZE-INIT-DONE* is still nil."))

   (unless (fboundp fn)
     (error "Memoize-fn: ~s is not fboundp." fn))

   (when (or (macro-function fn)
             (special-operator-p fn)
             (and (fboundp 'compiler-macro-function) ; for GCL as of 5/2013
                  (compiler-macro-function fn)))
     (error "Memoize-fn: ~s is a macro or a special operator or has a ~
             compiler macro."
            fn))

   (when (never-memoize-p fn)
     (error "Memoize-fn: ~s must never be memoized" fn))

   (when (and inline
              (or (member-eq fn
                             (f-get-global 'logic-fns-with-raw-code state))
                  (member-eq fn
                             (f-get-global 'program-fns-with-raw-code state))))
     (error "Memoize-fn: ~s must never be memoized with :inline t,~%~
             because it belongs to the list stored in state global~%~
             variable ~s and thus runs code different~%~
             than that stored in the ACL2 logical world, as is typically~%~
             used when inserting inlined code for memoization."
            fn
            (if (member-eq fn
                           (f-get-global 'logic-fns-with-raw-code state))
                'logic-fns-with-raw-code
              'program-fns-with-raw-code)))

   (when (memoizedp-raw fn)
     (observation 'memoize
                  "~s0 is currently memoized. We will first unmemoize it, ~
                   then memoize it again."
                  fn)
     (unmemoize-fn fn))

   (when (member fn (eval '(trace)))
     (observation 'memoize
                  "Untracing ~s before memoizing it."
                  fn)
     (eval `(untrace ,fn)))

; TRACE, UNTRACE, OLD-TRACE, and OLD-UNTRACE are macros that get
; redefined sometimes.  So we use EVAL in calling them.

   #+ccl
   (when (ccl::%advised-p fn)
     (error "~%; Memoize-fn: Please unadvise ~s before calling memoize-fn on ~
             it." fn))

   (when (and (fboundp 'old-trace)
              (member fn (eval '(old-trace))))
     (observation 'memoize
                  "Old-untracing ~s before memoizing it."
                  fn)
     (eval `(old-untrace ,fn)))

   (when (getpropc fn 'constrainedp nil wrld)
     (error "Memoize-fn: ~s is constrained; you may instead wish to memoize a ~
             caller or to memoize its attachment (see :DOC defattach)."
            fn))

   #+ccl
   (when (multiple-value-bind (req opt restp keys)
                              (ccl::function-args (symbol-function fn))
                              (or restp
                                  keys
                                  (not (integerp req))
                                  (not (eql opt 0))))

; This sanity check will never cause an error when memoization is invoked using
; memoize inside the ACL2 loop.

; CCL documentation returned by
; (documentation 'ccl::function-args 'function)
; justifies the four bound variables above.  The additional 5 values returned
; by ccl::function-args are discarded, as per the CL HyperSpec documentation of
; multiple-value-bind.

     (error "Memoize-fn: ~a has non-simple arguments." fn))))

(defun memoize-fn-init-2 (fn formals condition stobjs-in stobjs-out)

; Do more initial stuff for memoize-fn after formals is computed.

  (unless (and (symbol-listp formals)
               (no-duplicatesp formals)
               (loop for x in formals never (constantp x)))

; This sanity check is unnecessary when memoization is invoked using memoize
; inside the ACL2 loop.

    (error "Memoize-fn: FORMALS, ~a, must be a true list of distinct, ~
            nonconstant symbols."
           formals))

  (when (intersection lambda-list-keywords formals)

; This sanity check is unnecessary when memoization is invoked using memoize
; inside the ACL2 loop.

    (error "Memoize-fn: FORMALS, ~a, may not intersect LAMBDA-LIST-KEYWORDS."
           formals))

  (when (and condition (or (member 'state stobjs-in)
                           (member 'state stobjs-out)))

; This sanity check is unnecessary when memoization is invoked using memoize
; inside the ACL2 loop, because in memoize-table-chk, we disallow state as a
; formal and we disallow every stobj as an output.

; Although we don't support memoization of functions involving state, we do
; allow user-defined stobjs as inputs, by laying down code in stobj-let-fn-raw
; and defstobj-field-fns-raw-defs to flush memo tables as necessary.  But there
; is no such accommodation for the ACL2 state.

    (error "Memoize-fn:  ~s uses STATE." fn)))

(defun memoize-fn-inner-body (fn condition body fn-col-base
                                 tablename localtablename
                                 ponstablename localponstablename
                                 memo-table-init-size
                                 formals specials stobjs-out number-of-args
                                 commutative aokp prog1-fn)

; This is the main part of the body of the function defined by memoize-fn.

; Comments saying "performance counting*" are intended to mark code that might
; best be ignored on a first reading.  A long comment in *memoize-call-array*
; outlines how performance counting is implemented.

  ;; [Jared] multithreading note: all of this is going to be protected with the
  ;; global lock, so we shouldn't need any locking inside here.  See
  ;; memoize-fn-def.

  (let ((mf-record-mht ; performance counting
         (and *record-mht-calls*
              `((safe-incf
                 (aref ,*mf-ma*
                       ,(ma-index-from-col-base fn-col-base *ma-mht-index*))
                 1))))
        (mf-record-hit ; performance counting
         (and *record-hits*
              condition ; never record hits when profiling
              `((safe-incf
                 (aref ,*mf-ma*
                       ,(ma-index-from-col-base fn-col-base *ma-hits-index*))
                 1)))))
    `(cond
      ,@(and (not (member-equal condition '('t t))) ; minor optimization
             `(((not ,condition)

; See the comment in the definition of *condition-nil-as-hit*.

                ,@(and *condition-nil-as-hit*
                       mf-record-hit)
                ,body)))
      ,@(and
         condition ; else dead code
         `((t
            (let (,*mf-ans* ,*mf-args* ,*mf-ans-p*)
              (declare (ignorable ,*mf-ans* ,*mf-args* ,*mf-ans-p*))
              (when (null ,tablename) ; e.g., after (clear-memoize-tables)
                ,@mf-record-mht
                (setq ,tablename (make-initial-memoize-hash-table
                                  ',fn ,memo-table-init-size)))
              (setq ,localtablename ,tablename)
              ,@(and (> number-of-args 1)
                     `((when (null ,ponstablename)
                         (setq ,ponstablename
                               (make-initial-memoize-pons-table
                                ',fn ,memo-table-init-size)))
                       (setq ,localponstablename ,ponstablename)))

; Generate the pons key.  If there is just one arg, pist* just returns the arg
; and doesn't do any ponsing.

              (setq ,*mf-args*
                    ,(cond
                      (commutative
                       `(cond ((mis-ordered-commutative-args
                                ,(car formals)
                                ,(cadr formals))
                               (pist* ,localponstablename
                                      ,(cadr formals)
                                      ,(car formals)
                                      ,@specials))
                              (t
                               (pist* ,localponstablename
                                      ,(car formals)
                                      ,(cadr formals)
                                      ,@specials))))
                      (t `(pist* ,localponstablename
                                 ,@formals
                                 ,@specials))))

; Attempt to find the saved result.

              (multiple-value-setq
               (,*mf-ans* ,*mf-ans-p*)
               ,(let ((gethash-form `(mf-gethash ,*mf-args* ,localtablename)))
                  (cond (aokp `(cond
                                (*aokp* ,gethash-form)
                                (t (values nil nil))))
                        (t gethash-form))))
              (cond
               (,*mf-ans-p*

; Memoized lookup succeeded.  Update performance counts and return result.

                ,@(and aokp

; We note that a saved value for fn was used, which may have depended on an
; attachment since aokp is true.  See memoize-use-attachment-warning for how
; this special lookup-marker (:lookup . fn) is used.

                       `((update-attached-fn-called ',(cons :lookup fn))))
                ,@mf-record-hit
                ,@(cond ((null (cdr stobjs-out))
                         `(,*mf-ans*))
                        (t

; The result stored in the memo table is of the form (list* x1 x2 ... xk),
; where k is the length of stobjs-out.  This result was stored when the
; returned value was (mv x1 x2 ... xk).  We build an expression (mv e1 e2
; ... ek), where each ei except the last is the result of popping the variable
; stored in *mf-ans*, i.e., #:ANS, leaving ek as that variable itself.

                         (let ((len-1 (1- (length stobjs-out))))
                           `(,(cons
                               'mv
                               (nconc (loop for i fixnum below len-1
                                            collect `(pop ,*mf-ans*))
                                      (list *mf-ans*))))))))
               (t

; Memoized lookup failed.  Now call the function and perhaps store what is
; returned by the call.

                ,(let* ((vars

; Vars is the list of variables (O0 O1 ... 0N) for the outputs, where N is the
; length of stobjs-out.  (We play it safe and use (O0) if somehow stobjs-out is
; nil.)

                         (loop for i fixnum below
                               (if (cdr stobjs-out)
                                   (length stobjs-out)
                                 1)
                               collect (mf-make-symbol "O~a" i))))
                   (cond
                    (aokp
                     `(mv?-let
                       ,vars
                       ,body
                       (progn (mf-sethash ,*mf-args*
                                          (list* ,@vars)
                                          ,localtablename)
                              (mv? ,@vars))))
                    (t ; (not aokp); so avoid using attachments
                     `(let (,*attached-fn-temp*)
                        (mv?-let
                         ,vars
                         (let ((*aokp* (and *aokp* t)))
                           (,prog1-fn
                            ,body
                            (when (not (member *aokp* '(t nil) :test #'eq))
                              (setq ,*attached-fn-temp* *aokp*))))
                         (progn
                           (cond
                            (,*attached-fn-temp*
                             (memoize-use-attachment-warning
                              ',fn
                              ,*attached-fn-temp*))
                            (t ; Save the results in the memo table.
                             (mf-sethash ,*mf-args*
                                         (list* ,@vars)
                                         ,localtablename)))

; Special variable *aokp* was protected by a LET above when executing body,
; which could have set it to a function symbol whose attachment was used.  That
; value was however saved in *attached-fn-temp*, which we now use to update
; *aokp* since *sokp* was restored, after the execution of body, to its
; previous value (by popping out of its binding scope).

                           (when ,*attached-fn-temp* ; optimization
                             (assert *aokp*)
                             (update-attached-fn-called ,*attached-fn-temp*))
                           (mv? ,@vars))))))))))))))))

(defun memoize-fn-outer-body (inner-body fn fn-col-base start-ticks forget
                                         prog1-fn)

; The code returned below will be put in the context of outer-body in the code
; returned by memoize-fn-def.  It is a wrapper for inner-body, and it is used
; when the special variable symbol stored in start-ticks has a symbol-value of
; -1, indicating that we are looking at an outermost call of fn.  This
; mechanism avoids double-counting for recursive calls of fn.

; Comments about "performance counting" mark code that might best be ignored on
; a first reading.  A long comment in *memoize-call-array* outlines how
; performance counting is implemented.

; This code is what sets the special variable, *caller*, to the appropriate
; index for fn into *memoize-call-array* (namey fn-col-base, which points to
; the column for fn).  So, any immediately subsidiary calls of memoized
; functions will be "charged" to fn, and *caller* will only be re-assigned by
; subsidiary top-level calls of other memoized functions.

  ;; [Jared] multithreading note: all of this is going to be protected with the
  ;; global lock, so we shouldn't need any locking inside here.  See
  ;; memoize-fn-def.

  `(let (#+(or ccl sbcl)
         ,@(and *record-bytes* ; performance counting
                `((,*mf-start-bytes* (heap-bytes-allocated))))
         ,@(and *record-pons-calls* ; performance counting
                `((,*mf-start-pons* *pons-call-counter*)))
         (,start-ticks ,(if *record-time*
                            '(internal-real-ticks)
                          '0)))
     (declare
      (ignorable #+(or ccl sbcl)
                 ,@(and *record-bytes* `(,*mf-start-bytes*))
                 ,@(and *record-pons-calls* `(,*mf-start-pons*)))
      (type mfixnum
            ,start-ticks
            ,@(and *record-pons-calls* `(,*mf-start-pons*))
            #+(or ccl sbcl)
            ,@(and *record-bytes* `(,*mf-start-bytes*))))
     (,(cond ((or *record-pons-calls*
                  #+(or ccl sbcl) *record-bytes*
                  *record-time*
                  forget)

; The test above is the condition under which there are statistics-gathering
; forms following the inner-body call below.  In this case, there is at least
; one statistics-gathering form following the inner-body form, below.  There is
; then the danger that when computations are aborted, some of the statistics
; might be skewed, and some tables might not be flushed when forget is true.
; However, we usually don't want to pay the price of using unwind-protect to
; avoid such problems, because very simple experiments have shown that prog1
; and multiple-value-prog1 are much cheaper than unwind-protect.  However, we
; make it possible for users to ensure execution of statistics-gathering forms,
; at some cost to performance, by setting state global
; 'protect-memoize-statistics before memoizing their functions.

              (if (f-get-global 'protect-memoize-statistics *the-live-state*)
                  'unwind-protect-disable-interrupts-during-cleanup
                prog1-fn))
             (t

; There are no statistics-gathering forms to protect, so we simply lay down a
; progn (which presumably will be compiled away).

              'progn))
      ,(cond ((or *record-bytes*
                  *record-calls*
                  *record-hits*
                  *record-mht-calls*
                  *record-pons-calls*
                  *record-time*)

; Then we are gathering performance counting statistics for this function, so
; we need to make a note of the caller.  Otherwise, this function is invisible
; from the standpoint of performance counting, and we should let the caller
; stay as it was.

              `(let ((*caller* ,fn-col-base)) ; performance counting
                 ,inner-body))
             (t inner-body))
      ,@(and *record-pons-calls* ; performance counting
             `((safe-incf
                (aref ,*mf-ma*
                      ,(ma-index-from-col-base fn-col-base *ma-pons-index*))
                (the-mfixnum (- *pons-call-counter* ,*mf-start-pons*)))))
      #+(or ccl sbcl)
      ,@(and *record-bytes* ; performance counting
             `((safe-incf
                (aref ,*mf-ma*
                      ,(ma-index-from-col-base fn-col-base *ma-bytes-index*))
                (the-mfixnum (- (heap-bytes-allocated) ,*mf-start-bytes*)))))
      ,@(and *record-time* ; performance counting
             `((safe-incf
                (the mfixnum
                     (aref ,*mf-ma* (the-mfixnum (1+ ,*mf-count-loc*))))
                (the-mfixnum
                 (fix-ticks (the-mfixnum (- (internal-real-ticks)
                                            ,start-ticks))
                            ',fn)))))
      ,@(and forget

; Clear the hash table or set it to NIL, using the usual heuristics.
; Historically we always set them to NIL, but it seems better to use clrhash
; when it's cheap, to avoid excessive memory allocation.

             `((clear-memoize-table ',fn))))))

(defun memoize-fn-def (inner-body outer-body
                                  fn formals specials dcls fnn start-ticks
                                  localtablename localponstablename)

; Comments about "performance counting" mark code that might best be ignored on
; a first reading.  A long comment in *memoize-call-array* outlines how
; performance counting is implemented.

; See example below.

  `(defun ,fn ,formals ,@dcls
     (declare (ignorable ,@formals ,@specials))
     (with-global-memoize-lock-static

      ;; Special case.  This is the lock that will be grabbed when executing
      ;; the memoized function.  For maximum performance in the single threaded
      ;; case, we use the less-safe, static version of lock grabbing.

      (let* ((,*mf-count-loc* ; performance counting
              ,(if (or *record-calls* *record-time*)

; The following expression is similar to `(ma-index-calls ,fnn *caller*),
; except that *caller* is already a column (that is, already multiplied by the
; square dimension of *memoize-call-array*).

                   `(the-mfixnum (+ *caller* ,(* 2 fnn)))
                 0))
             (,*mf-ma* *memoize-call-array*)
             ,localtablename ,localponstablename)
        (declare (type mfixnum ,*mf-count-loc*)
                 (ignorable ,*mf-count-loc* ,*mf-ma*
                            ,localponstablename
                            ,localtablename)
                 (type (simple-array mfixnum (*))
                       ,*mf-ma*))
        ,@(and *record-calls* ; performance counting
               `((safe-incf (aref ,*mf-ma* ,*mf-count-loc*) 1)))

; At one time we introduced an flet to share code for the original body, which
; can occur twice or three times below.  But we changed this on 10/18/2014
; because we think that the code expansion might be worth it, in case flet
; reduces performance.  Probably this is not a sufficiently important issue to
; pursue further.

        (if (eql -1 ,start-ticks)
            ,outer-body
          ,inner-body)))))

; Here is an example of the memoization of a simple function, fib, defined as:

; ACL2 !>(defun fib (n)
;          (declare (xargs :guard (natp n)))
;          (if (zp n)  0 (if (eql n 1) 1 (+ (fib (- n 1)) (fib (- n 2))))))

; In the following, let the two long names in the ACL2_INVISIBLE package
; below be denoted by the short names shown:

; long name                                                          short name
; ACL2_INVISIBLE::|HONS-G-"\\"START-TICKS-\\",\\"ACL2\\",\\"FIB\\"",13|  sticks
; ACL2_INVISIBLE::|HONS-G-"\\"MEMOIZE-HT-FOR-\\",\\"ACL2\\",\\"FIB\\"",14|  mht

; Here is the raw Lisp defun of fib produced by (memoize 'fib).  It was
; obtained as follows.

;  :q
;  (old-trace memoize-fn-def)
;  (lp)
;  (memoize 'fib)
;  ; Then copy result of memoize-fn-def into a file foo, make the two
;  ; replacements above (globally), and save foo after:
;  ; (setq xxx (defun ...) )
;  :q
;  (load foo)
;  xxx
;  (pprint *)
;  ; Now replace STICKS and MHT by sticks and mht, resp., in the output.

; (DEFUN FIB (N)
;   (DECLARE (XARGS :GUARD (NATP N)))
;   (DECLARE (IGNORABLE N))
;   (WITH-GLOBAL-MEMOIZE-LOCK-STATIC
;     (LET* ((#:MF-COUNT-LOC (THE-MFIXNUM (+ *CALLER* 18)))
;            (#:MA *MEMOIZE-CALL-ARRAY*)
;            #:TABLENAME
;            #:PONSTABLENAME)
;       (DECLARE (TYPE MFIXNUM #:MF-COUNT-LOC)
;        (IGNORABLE #:MF-COUNT-LOC #:MA #:PONSTABLENAME #:TABLENAME)
;        (TYPE (SIMPLE-ARRAY MFIXNUM (*)) #:MA))
;       (SAFE-INCF (AREF #:MA #:MF-COUNT-LOC) 1)
;       (IF (EQL -1 sticks)
;           (LET ((#:START-BYTES (HEAP-BYTES-ALLOCATED))
;                 (#:START-PONS *PONS-CALL-COUNTER*)
;                 (sticks (INTERNAL-REAL-TICKS)))
;             (DECLARE (IGNORABLE #:START-BYTES #:START-PONS)
;              (TYPE MFIXNUM sticks #:START-PONS #:START-BYTES))
;             (PROG1 (LET ((*CALLER* 9000))
;                      (COND (T
;                             (LET (#:ANS #:ARGS #:ANS-P)
;                               (DECLARE
;                                (IGNORABLE #:ANS #:ARGS #:ANS-P))
;                               (WHEN
;                                (NULL mht)
;                                (SAFE-INCF (AREF #:MA 9002) 1)
;                                (SETQ
;                                 mht
;                                 (MAKE-INITIAL-MEMOIZE-HASH-TABLE
;                                  'FIB
;                                  60)))
;                               (SETQ #:TABLENAME mht)
;                               (SETQ #:ARGS (PIST* #:PONSTABLENAME N))
;                               (MULTIPLE-VALUE-SETQ
;                                (#:ANS #:ANS-P)
;                                (MF-GETHASH #:ARGS #:TABLENAME))
;                               (COND
;                                (#:ANS-P
;                                 (SAFE-INCF (AREF #:MA 9001) 1)
;                                 #:ANS)
;                                (T
;                                 (LET
;                                  (#:ATTACHED-FN-TEMP)
;                                  (MV?-LET
;                                   (O0)
;                                   (LET
;                                    ((*AOKP* (AND *AOKP* T)))
;                                    (PROG1
;                                     (IF
;                                      (ZP N)
;                                      0
;                                      (IF
;                                       (EQL N 1)
;                                       1
;                                       (+
;                                        (FIB (- N 1))
;                                        (FIB (- N 2)))))
;                                     (WHEN
;                                      (NOT
;                                       (MEMBER
;                                        *AOKP*
;                                        '(T NIL)
;                                        :TEST
;                                        #'EQ))
;                                      (SETQ
;                                       #:ATTACHED-FN-TEMP
;                                       *AOKP*))))
;                                   (PROGN
;                                    (COND
;                                     (#:ATTACHED-FN-TEMP
;                                      (MEMOIZE-USE-ATTACHMENT-WARNING
;                                       'FIB
;                                       #:ATTACHED-FN-TEMP))
;                                     (T
;                                      (MF-SETHASH
;                                       #:ARGS
;                                       (LIST* O0)
;                                       #:TABLENAME)))
;                                    (WHEN
;                                     #:ATTACHED-FN-TEMP
;                                     (ASSERT *AOKP*)
;                                     (UPDATE-ATTACHED-FN-CALLED
;                                      #:ATTACHED-FN-TEMP))
;                                    (MV? O0))))))))))
;                    (SAFE-INCF (AREF #:MA 9004)
;                               (THE-MFIXNUM
;                                (- *PONS-CALL-COUNTER* #:START-PONS)))
;                    (SAFE-INCF (AREF #:MA 9000)
;                               (THE-MFIXNUM
;                                (-
;                                 (HEAP-BYTES-ALLOCATED)
;                                 #:START-BYTES)))
;                    (SAFE-INCF (THE
;                                MFIXNUM
;                                (AREF
;                                 #:MA
;                                 (THE-MFIXNUM (1+ #:MF-COUNT-LOC))))
;                               (THE-MFIXNUM
;                                (FIX-TICKS
;                                 (THE-MFIXNUM
;                                  (- (INTERNAL-REAL-TICKS) sticks))
;                                 'FIB)))))
;           (COND (T
;                  (LET (#:ANS #:ARGS #:ANS-P)
;                    (DECLARE (IGNORABLE #:ANS #:ARGS #:ANS-P))
;                    (WHEN (NULL mht)
;                      (SAFE-INCF (AREF #:MA 9002) 1)
;                      (SETQ mht
;                            (MAKE-INITIAL-MEMOIZE-HASH-TABLE
;                              'FIB
;                              60)))
;                    (SETQ #:TABLENAME mht)
;                    (SETQ #:ARGS (PIST* #:PONSTABLENAME N))
;                    (MULTIPLE-VALUE-SETQ (#:ANS #:ANS-P)
;                      (MF-GETHASH #:ARGS #:TABLENAME))
;                    (COND (#:ANS-P
;                           (SAFE-INCF (AREF #:MA 9001) 1)
;                           #:ANS)
;                          (T
;                           (LET (#:ATTACHED-FN-TEMP)
;                             (MV?-LET (O0)
;                                      (LET
;                                       ((*AOKP* (AND *AOKP* T)))
;                                       (PROG1
;                                        (IF
;                                         (ZP N)
;                                         0
;                                         (IF
;                                          (EQL N 1)
;                                          1
;                                          (+
;                                           (FIB (- N 1))
;                                           (FIB (- N 2)))))
;                                        (WHEN
;                                         (NOT
;                                          (MEMBER
;                                           *AOKP*
;                                           '(T NIL)
;                                           :TEST
;                                           #'EQ))
;                                         (SETQ
;                                          #:ATTACHED-FN-TEMP
;                                          *AOKP*))))
;                                      (PROGN
;                                       (COND
;                                        (#:ATTACHED-FN-TEMP
;                                         (MEMOIZE-USE-ATTACHMENT-WARNING
;                                          'FIB
;                                          #:ATTACHED-FN-TEMP))
;                                        (T
;                                         (MF-SETHASH
;                                          #:ARGS
;                                          (LIST* O0)
;                                          #:TABLENAME)))
;                                       (WHEN
;                                        #:ATTACHED-FN-TEMP
;                                        (ASSERT *AOKP*)
;                                        (UPDATE-ATTACHED-FN-CALLED
;                                         #:ATTACHED-FN-TEMP))
;                                       (MV? O0)))))))))))))

(defun-one-output memoize-eval-compile (def old-fn)
  #+(or ccl sbcl) ; all functions are compiled
  (declare (ignore old-fn))
  (unless (and (consp def)
               (eq 'defun (car def))
               (consp (cdr def))
               (symbolp (cadr def)))
    (error "MEMOIZE-EVAL-COMPILE:  Bad input:~%~s." def))
  #+(or ccl sbcl)
  (compile (eval def)) ; probably the compile is unnecessary but harmless
  #-(or ccl sbcl)
  (if (and old-fn (compiled-function-p old-fn))
      (compile (eval def))
    (eval def))
  nil)

(defun memoize-fn-formals (fn wrld inline
                              &key
                              (cl-defun :default cl-defun-p))

; This function is used not only below, but also in community book
; books/centaur/memoize/old/profile.lisp (actually profile-raw.lsp).

  (let ((formals (getpropc fn 'formals t wrld)))
    (if (eq formals t)
        (let ((cl-defun (if cl-defun-p
                            cl-defun
                          (memoize-look-up-def fn cl-defun inline wrld
                                               :quiet-p t))))
          (if (consp cl-defun)
              (cadr cl-defun)
            (let ((n (mf-len-inputs fn)))
              (if n
                  (loop for i fixnum below n
                        collect (mf-make-symbol "X~a" i))
                t ; error
                ))))
      formals)))

(defun memoize-fn (fn &key
                      (condition t)
                      (inline t)
                      (cl-defun :default)
                      (formals :default)
                      (stobjs-in :default)
                      (specials nil)
                      (commutative nil)
                      (stobjs-out :default)
                      (forget nil)
                      (memo-table-init-size *mht-default-size*)
                      (aokp nil)
                      &aux
                      (wrld (w *the-live-state*))
                      (memoize-fn-signature-error
                       "Memoize-fn: could not determine a signature for ~a.~%~
  To assert the signature of ~:*~a, use (mf-note-arity '~:*~a nargs nvals),~%~
  for example, (mf-note-arity '~:*~a 3 1).)  If there are stobjs arguments~%~
  then do not use that mechanism; instead, pass suitable arguments to~%~
  memoize-fn."))

; Warning: Keep the argument list for this function in sync with memoize-info,
; as explained  there.

; We do not claim that memoize-fn is bulletproof when called directly in raw
; Lisp, rather than via a call to memoize in the ACL2 loop.  However, we make
; some effort for it to behave reasonably.

; If the :CONDITION parameter is NIL we record performance data but not the
; values computed; this is used in our profiling tool.  Indeed, simple
; profiling is just memoizing with :condition nil and :inline nil.

; If the :INLINE parameter is T, then the body of FN is placed inline in the
; memoized definition; otherwise, a funcall of the original function is placed
; there.

; Comments about "performance counting" mark code that might best be ignored on
; a first reading.  A long comment in the Essay on the *Memoize-Call-Array*
; outlines how performance counting is implemented.

; Old documentation, which may be updated soon and/or merged into the :doc:

  "The documentation for MEMOIZE-FN is very incomplete.  One may invoke
  (MEMOIZE-FN fn) on the name of a Common Lisp function FN from outside the
  ACL2 loop to get results of possible interest in terms of memoization
  activity and profiling information.  MEMOIZE-FN already has a dozen
  parameters.

  MEMOIZE-FN replaces the SYMBOL-FUNCTION for the symbol FN with 'enhanced'
  raw Common Lisp code that, supposedly, does not affect the value returned by
  FN but may make some notes and may even obtain some return values by
  remembering them from a previous call.

  If the CONDITION parameter is not NIL or 'NIL, then whenever FN is called,
  and there is not as yet any value remembered for a call of FN on the given
  arguments, then if the evaluation of the CONDITION parameter (where the
  formals of FN are bound to its actuals) is not NIL or 'NIL, the values that
  are computed for FN on the given arguments will be saved under the given
  arguments.

  If the INLINE parameter is T, then when MEMOIZE-FN creates a new body for FN,
  we place the old body of FN within the new body, i.e., 'in line'.  However,
  if the INLINE parameter is NIL, then we place code that calls the existing
  SYMBOL-FUNCTION for FN within the new body.  One might well argue that our
  parity for the INLINE parameter to MEMOIZE-fn is backwards, but we don't
  think so.

  One may lie to MEMOIZE-FN to force the memoization of a function that has
  ACL2's state as an explicit parameter by using fraudulent FORMALS, STOBJS-IN,
  and STOBJS-OUT parameters to MEMOIZE-FN.

  If the COMMUTATIVE parameter is not NIL, then the two arguments may be
  swapped before further processing.  We hope/presume that ACL2 will have been
  used first to prove that commutativity.

  If the CL-DEFUN parameter is not NIL, we pretend that the current body of FN
  is that parameter, and similarly for FORMALS, STOBJS-IN, and STOBJS-OUT.

  If FN is a raw Common Lisp function and not an ACL2-approved function, it may
  make reference to a variable, say S, that has a SPECIAL binding, in which
  case one needs to consider what in the world the meaning is for memoizing
  such a function at all.  If S is a member of the SPECIALS parameter, then it
  is assumed that FN does not alter but only refers to S.  MEMOIZE-FN acts as
  though FN had S as an extra argument for purposes of memoization.

  If the FORGET parameter is not NIL, the pons and memo tables of FN are
  discarded at the end of every outermost call of FN."

  #-hons
  (return-from memoize-fn
               (progn (when (not (zerop *ld-level*))
                        (warning$ 'memoize nil
                                  "No change for function ~x0: Memoization ~
                                   requests are ignored in this ACL2 ~
                                   executable because it is not hons-enabled."
                                  fn))
                      fn))
  (when (equal condition *nil*)
    (setq condition nil))
  (with-global-memoize-lock

    ;; [Jared] note that this lock protects the operation of the memoize
    ;; command, itself.  The definition of the newly memoized function has
    ;; its own, separate lock.  See memoize-fn-def.

; Perhaps this lock is not necessary; after all, it seems unlikely that
; different threads would be memoizing at the same time.  On the other hand, we
; really don't want to worry about the possibility that some structures are
; installed and others are not if another thread tries to call a function that
; is in the process of being memoized; so we use a lock here.

   (with-warnings-suppressed ; e.g., might avoid redefinition warnings
    (memoize-fn-init fn inline wrld)
    (let* ((cl-defun (memoize-look-up-def fn cl-defun inline wrld))
           (formals
            (cond
             ((eq formals :default)
              (let ((formals (memoize-fn-formals fn wrld inline
                                                 :cl-defun cl-defun)))
                (if (eq formals t)
                    (error memoize-fn-signature-error fn)
                  formals)))
             (t formals)))
           (stobjs-in
            (if (eq stobjs-in :default)
                (let ((s (getpropc fn 'stobjs-in t wrld)))
                  (if (eq s t)
                      (make-list (len formals)) ; assume no stobjs
                    s))
              stobjs-in))
           (stobjs-out
            (if (eq stobjs-out :default)
                (let ((s

; Note that the never-memoize-p check made in memoize-fn-init guarantees that
; here, we are not taking the stobjs-out of functions in *stobjs-out-invalid*.

                       (getpropc fn 'stobjs-out t wrld)))
                  (if (eq s t)
                      (let ((n (mf-len-outputs fn)))
                        (cond (n (make-list n))
                              ((null condition)

; This case is impossible when memoization is invoked using memoize inside the
; ACL2 loop, so we do not need to expect perfection here.  Fortunately,
; stobjs-out is probably irrelevant when condition is nil; so we assume that a
; single non-stobj value is returned.

                               (list nil))
                              (t (error memoize-fn-signature-error fn))))
                    s))
              stobjs-out)))
      (memoize-fn-init-2 fn formals condition stobjs-in stobjs-out)
      (mf-sethash fn
                  (cons (length stobjs-in) (length stobjs-out))
                  *number-of-arguments-and-values-ht*)
      (let* ((fnn ; performance counting
              (symbol-to-fixnum-create fn))
             (fn-col-base ; performance counting
              (ma-index fnn))
             (old-fn (symbol-function fn))
             (body
              (progn
                (assert old-fn)
                (cond
                 (inline

; When memoize-look-up-def is called with a non-nil value of inline and it
; returns without error, then it returns a non-nil definition (which is a true
; list).

                   (assert (consp cl-defun))
                   (car (last cl-defun)))
                 (t `(funcall
                      #-gcl ,old-fn
                      #+gcl ',old-fn ; old-fn could be (lisp:lambda-block ...)
                      ,@formals)))))
             (dcls (mf-dcls (cddr (butlast cl-defun))))
             (start-ticks

; Submit a defg form and return the generated name:

              (let ((v (hons-gentemp
                        (memoize-fn-suffix "START-TICKS-" fn))))
                (eval `(prog1 (defparameter ,v -1)
                         (declaim (type mfixnum ,v))))))
             (tablename

; Submit a defg form and return the generated name:

              (eval `(defg
                       ,(hons-gentemp (memoize-fn-suffix "MEMOIZE-HT-FOR-" fn))
                       nil)))
             (ponstablename

; Submit a defg form and returns the generated name:

              (eval `(defg
                       ,(hons-gentemp (memoize-fn-suffix "PONS-HT-FOR-" fn))
                       nil)))
             (localtablename (make-symbol "TABLENAME"))
             (localponstablename (make-symbol "PONSTABLENAME"))
             (sts

; Here we support memoize-flush, which keeps memoize tables coherent in the
; presence of user-defined stobjs.  For each (user-level) stobj input name, st,
; we collect up the variable (st-lst st), whose value is the list of names of
; memoize tables that need to be cleared whenever that stobj changes.  Below,
; we will push the present function's table name onto each of these lists.

; Ultimately, stobj updates are made by stobj primitives.  After the stobj
; primitive for stobj st makes an update, the memo table for a function f
; taking st as its nth argument (say) is no longer valid for saved calls of f
; for which the nth argument is st.  Because of congruent stobjs and abstract
; stobjs, that nth argument need not be st, and we believe that in principle,
; we could restrict flushing of memo table entries of f to those whose nth
; argument is eq to the stobj being updated (whether st, congruent to st, or an
; abstract stobj whose concrete stobj is congruent to st).  But for now we take
; the coarser approach, which has the advantage that we simply throw away the
; memo-table for f when flushing, leaving it to be garbage collected; see
; memoize-flush1.

              (and condition ; else no memo table usage, so skip flushing
                   (remove-duplicates-eq
                    (loop for st in (union stobjs-in stobjs-out)
                          when st
                          collect
                          (assert$
                           (not (eq st 'state)) ; see memoize-table-chk
                           (st-lst (congruent-stobj-rep

; In the case that st is an abstract stobj, we replace it with the
; corresponding concrete stobj before getting a canonical (congruent)
; representative; see the rather long comment just above that mentions
; "abstract" stobjs.

                                    (or (concrete-stobj st wrld)
                                        st)
                                    wrld)))))))
             (number-of-args

; This is the number of arguments.  Specials only matter for raw Lisp
; functions; see the notes above in memoize-fn.  Basically if the function
; reads from specials we want to count them as arguments.

              (+ (len formals) (len specials)))
             (prog1-fn (if (cdr stobjs-out)
                           'multiple-value-prog1
                         'prog1))
             (inner-body
              (memoize-fn-inner-body
               fn condition body fn-col-base
               tablename localtablename ponstablename localponstablename
               memo-table-init-size
               formals specials stobjs-out number-of-args
               commutative aokp prog1-fn))
             (outer-body
              (memoize-fn-outer-body
               inner-body fn fn-col-base start-ticks forget prog1-fn))
             (def
              (memoize-fn-def
               inner-body outer-body
               fn formals specials dcls fnn start-ticks
               localtablename localponstablename))
             (success nil))
        (unwind-protect
            (progn
              (let ((ma *memoize-call-array*))
                (declare (type (simple-array mfixnum (*)) ma))
                (loop for i of-type mfixnum ; performance counting
                      from fn-col-base      ; loop through this column
                      below
                      (ma-index-from-col-base fn-col-base *2max-memoize-fns*)
                      unless (eql (aref ma i) 0)
                      do (setf (aref ma i) 0)))
              (memoize-eval-compile def old-fn)
              (mf-sethash fn
                          (make memoize-info-ht-entry
                                :ext-anc-attachments
                                (and aokp (ext-ancestors-attachments fn wrld))
                                :start-ticks start-ticks
                                :num fnn
                                :tablename tablename
                                :ponstablename ponstablename
                                :condition condition
                                :inline inline
                                :memoized-fn (symbol-function fn)
                                :old-fn old-fn
                                :fn fn
                                :sts sts
                                :cl-defun cl-defun
                                :formals formals
                                :commutative commutative
                                :specials specials
                                :stobjs-in stobjs-in
                                :stobjs-out stobjs-out
                                :record-bytes      *record-bytes*
                                :record-calls      *record-calls*
                                :record-hits       *record-hits*
                                :record-mht-calls  *record-mht-calls*
                                :record-pons-calls *record-pons-calls*
                                :record-time       *record-time*
                                :forget            forget
                                :memo-table-init-size memo-table-init-size
                                :aokp aokp)
                    *memoize-info-ht*)
              (mf-sethash fnn fn *memoize-info-ht*)
              (and condition (loop for s in sts do
                                   (push tablename
                                         (symbol-value (the symbol s)))))
              (setq success t))
          (unless success
            (without-interrupts ; perhaps already the case in some Lisps
             (setf (symbol-function fn) old-fn)
             (remhash fn *memoize-info-ht*)
             (remhash fnn *memoize-info-ht*)
             (and condition
                  (loop for s in sts
                        when (eq tablename
                                 (car (symbol-value (the symbol s))))
                        do (pop (symbol-value (the symbol s)))))
             (setq fn nil) ; in case we decide not to cause an error
             (error "Memoize-fn:  Failed to memoize ~s." fn))))))))
  fn)

(defun-one-output unmemoize-fn (fn)

; Warning: Do not be tempted to remove the definition of the condition
; function.  If fn was memoized using the memoize macro in the ACL2 loop, then
; a non-trivial condition is a first-class ACL2 function.

  #-hons
  (return-from unmemoize-fn
               (progn (when (not (zerop *ld-level*))
                        (warning$ 'unmemoize nil
                                  "No change for function ~x0: Unmemoization ~
                                   requests are ignored in this ACL2 ~
                                   executable because it is not hons-enabled."
                                  fn))
                      fn))
  (with-global-memoize-lock
   (maybe-untrace! fn) ; See the comment about Memoization in trace$-def.
   (let ((rec (memoizedp-raw fn)))
     (unless rec ; expect rec=nil in the loop, else unmemoize is redundant
       (error "Unmemoize-fn: ~s is not memoized." fn))
     (let* ((num (the-mfixnum (access memoize-info-ht-entry rec
                                      :num)))
            (tablename (access memoize-info-ht-entry rec
                               :tablename))
            (ponstablename (access memoize-info-ht-entry rec
                                   :ponstablename))
            (sts (access memoize-info-ht-entry rec
                         :sts))
            (col-base (ma-index num))
            (saved-table (symbol-value (the symbol tablename)))
            (saved-ponstable (symbol-value (the symbol ponstablename)))
            (saved-fn-entry (mf-gethash fn *memoize-info-ht*))
            (saved-num-entry (mf-gethash num *memoize-info-ht*))
            (ma *memoize-call-array*)
            (success nil))
       (declare (type mfixnum num col-base)
                (type (simple-array mfixnum (*)) ma))
       (unwind-protect
           (progn
             (format nil "unmemoizing ~s" fn)
             (let (#+ccl (ccl:*warn-if-redefine-kernel* nil))
               (let ((old-fn (access memoize-info-ht-entry rec :old-fn)))
                 (assert old-fn)
                 (setf (symbol-function (the symbol fn))
                       old-fn)))
             (loop for i of-type mfixnum
                   from col-base ; loop through col-base column
                   below (ma-index-from-col-base col-base *2max-memoize-fns*)
                   unless (eql (aref ma i) 0)
                   do (setf (aref ma i) 0))
             (remhash fn *memoize-info-ht*)
             (remhash num *memoize-info-ht*)
             (setf (symbol-value (the symbol tablename)) nil)
             (setf (symbol-value (the symbol ponstablename)) nil)
             (loop for s in sts do
                   (when (boundp s)
                     (setf (symbol-value (the symbol s))
                           (remove tablename (symbol-value (the symbol s))))))
             (setq success t))
         (unless success
           (without-interrupts ; perhaps already the case in some Lisps

; We don't restore *memoize-call-array*; those statistics are simply lost.

            (setf (symbol-value (the symbol tablename)) saved-table)
            (setf (symbol-value (the symbol ponstablename)) saved-ponstable)
            (mf-sethash fn saved-fn-entry *memoize-info-ht*)
            (mf-sethash num saved-num-entry *memoize-info-ht*)
            (loop for s in sts do
                  (when (boundp s)
                    (push tablename (symbol-value (the symbol s)))))))))))
  fn)

(defun-one-output maybe-unmemoize (fn)

; We rely on the normal undoing mechanism (for :ubt etc.) to take care of
; unmemoization.  However, as a courtesy to users who memoize using raw Lisp,
; we provide this interface for unmemoizing functions that might not be known
; to ACL2 (via the memoize-table) as being memoized.

  (with-global-memoize-lock

; We use a lock here to prevent the possibility that another thread unmemoizes
; after our memoizedp-raw test but before our unmemoize-fn call.  We don't
; expect many calls of maybe-unmemoize, so this lock should be cheap.

   (when (and (memoizedp-raw fn)
              (not (cdr (assoc-eq fn (table-alist 'memoize-table
                                                  (w *the-live-state*))))))
     (unmemoize-fn fn))))

(defun-one-output memoized-functions ()

; We return the names of all memoized functions as a list.

  (with-global-memoize-lock
   (let (ans)
     (mf-maphash (lambda (fn info)
                   (declare (ignore info))
                   (when (symbolp fn)
                     (push fn ans)))
                 *memoize-info-ht*)
     ans)))

(defun-one-output length-memoized-functions ()

; We return the number of currently memoized (or profiled) functions.  We
; subtract one for the outside-caller entry and divide by 2 since there are two
; entries for each memoized function: one for the function symbol and one that
; associates :num of that symbol's entry back to the symbol.

  (with-global-memoize-lock
   (values (floor (1- (mf-hash-table-count *memoize-info-ht*))
                  2))))

(defun-one-output unmemoize-all ()

; Unmemoize all currently memoized functions,including all profiled functions.

; Warning: This function does not deal with memoize-table.  ACL2 users should
; evaluate (clear-memo-table) instead of calling unmemoize-all directly.

; A warning to would-be code improvers.  It would be a bad idea to redefine
; unmemoize-all to maphash over *memoize-info-ht*, because of the ANSI rules
; restricting which hash table entries may be modified during a maphash.

  (loop for x in (memoized-functions) do (unmemoize-fn x)))

(defun-one-output memoize-info (k)

; Warning: Keep this in sync with memoize-fn and rememoize-all.

; We return the settings of the various arguments to memoize-fn and the
; settings of the special variables that influence memoize-fn during the
; memoization of the given function symbol.  The rather arcane structure
; returned is used in rememoize-all.

  (with-global-memoize-lock
   (let ((v (mf-gethash k *memoize-info-ht*)))
     (and v
          (list

; Warning: Keep the following list in sync with the argument list for
; memoize-fn.  Also note that the :fn must be first; see rememoize-all.

           (list (access memoize-info-ht-entry v :fn)
                 :condition
                 (access memoize-info-ht-entry v :condition)
                 :inline
                 (access memoize-info-ht-entry v :inline)
                 :cl-defun
                 (access memoize-info-ht-entry v :cl-defun)
                 :formals
                 (access memoize-info-ht-entry v :formals)
                 :stobjs-in
                 (access memoize-info-ht-entry v :stobjs-in)
                 :specials
                 (access memoize-info-ht-entry v :specials)
                 :commutative
                 (access memoize-info-ht-entry v :commutative)
                 :stobjs-out
                 (access memoize-info-ht-entry v :stobjs-out)
                 :forget
                 (access memoize-info-ht-entry v :forget)
                 :memo-table-init-size
                 (access memoize-info-ht-entry v :memo-table-init-size)
                 :aokp
                 (access memoize-info-ht-entry v :aokp))

; Warning: Keep the following list in sync with the set of *record-xxx*
; globals, and with rememoize-all.

           (list (access memoize-info-ht-entry v :record-bytes)
                 (access memoize-info-ht-entry v :record-calls)
                 (access memoize-info-ht-entry v :record-hits)
                 (access memoize-info-ht-entry v :record-mht-calls)
                 (access memoize-info-ht-entry v :record-pons-calls)
                 (access memoize-info-ht-entry v :record-time)))))))

(defun-one-output rememoize-all (&optional light)

; Warning: Keep this function in sync with memoize-info.

; If light is true, then we are simply replacing *memoize-info-ht* with a copy.
; In that case, we provide some unwind-protection.  Otherwise, we must be very
; careful; currently we invoke (rememoize-all) -- that is, without the optional
; argument -- only in memoize-call-array-grow.  If that is interrupted then the
; state may be corrupted, but with luck, that will be rare.  See
; memoize-call-array-grow.

  (with-global-memoize-lock
   (cond
    (light
     (let ((new-memoize-info-ht (initial-memoize-info-ht)))
       (unwind-protect
           (progn
             (mf-maphash (lambda (k v)
                           (setf (gethash k new-memoize-info-ht) v))
                         *memoize-info-ht*)
             (setq *memoize-info-ht* new-memoize-info-ht))
         (when (not (eq *memoize-info-ht* new-memoize-info-ht))
           (cond ((eq light :done)
                  (error "Fatal error in rememoize-all!~%Consider evaluating ~
                         ~s before continuing.~%"
                         '(unmemoize-all)))
                 (t
                  (format t "Error in rememoize-all; about to try again.~%")
                  (rememoize-all :done)))))))
    (t
     (let (lst)
       (mf-maphash (lambda (k v)
                     (declare (ignore v))
                     (when (symbolp k)
                       (push (memoize-info k) lst)))
                   *memoize-info-ht*)

; Note: memoize-info arranges that (caar x) is the memoized function symbol.

       (loop for x in lst do (unmemoize-fn (caar x)))
       (setq *memoize-info-ht* (initial-memoize-info-ht))
       (gc$)
       (setq *max-symbol-to-fixnum* *initial-max-symbol-to-fixnum*)
       (loop for x in lst do

; Warning: Keep the first argument below in sync with memoize-info.

             (progv '(*record-bytes*
                      *record-calls*
                      *record-hits*
                      *record-mht-calls*
                      *record-pons-calls*
                      *record-time*)
                    (cadr x)
                    (apply 'memoize-fn (car x)))))))))

(defun profile-fn (fn &rest r &key (condition nil) (inline nil)
                      &allow-other-keys)

; Note that :condition and :inline are laid down twice in the call of
; memoize-fn below: once explicitly and once in r.  There is no error in such
; repetition, as Section 3.4.1.4 ("Specifiers for keyword parameters") of the
; Common Lisp Hyperspec says: "If more than one such argument pair matches, the
; leftmost argument pair is used."  By including the :condition and :inline
; arguments explicitly below, which are specified in the argument list as nil,
; we guarantee that the resulting function is profiled and executes its
; original body.

  (apply #'memoize-fn fn
         :condition condition
         :inline inline
         r))

(defun-one-output profiled-functions ()

; For purposes of this function, the profiled functions are defined as those
; produced by memoize-fn with null :condition and :inline fields.  We could
; probably allow :inline to be non-nil, but it will always be nil for functions
; profiled using profile-fn in raw Lisp or profile in the loop, so we enforce a
; nil value for :inline, not just :condition.

  (with-global-memoize-lock
   (let (lst)
     (mf-maphash
      (lambda (k v)
        (when (and (symbolp k)
                   (null (access memoize-info-ht-entry v :condition))
                   (null (access memoize-info-ht-entry v :inline)))
          (push k lst)))
      *memoize-info-ht*)
     lst)))

(defun-one-output unmemoize-profiled ()

; This raw Lisp function unmemoizes (and hence unprofiles) all functions
; currently memoized with :condition nil and :inline nil.

  (loop for x in (profiled-functions) do
        (unmemoize-fn (car x))))

; SECTION: Statistics gathering and printing routines

(defun-one-output coerce-index (x)

; X is either a memoized function symbol or the associated number
; (symbol-to-fixnum, also column number in *memoize-call-array* and index in
; *callers-array*) of such.

; Note: We might be tempted to lock uses of this function, since it calls
; symbol-to-fixnum, which uses a global hash-table.  But currently that is not
; necessary: all callers of coerce-index are functions defined in this Section,
; and their intended use is in sorting of memsum results; see
; *memoize-summary-order-list*.

  (cond ((typep x 'fixnum) ; equivalently, x is a number
         (assert (and (>= (the fixnum x) 0)
                      (< (the fixnum x)
                         (the fixnum (ash (length *memoize-call-array*)
                                          -1)))))
         x)
        (t ; could (assert (symbolp x)) but probably not worth the cycles
         (symbol-to-fixnum x))))

(defun-one-output mf-num-to-string (n) ; for forming numbers

; Consider invoking this function in the context of our-syntax.

  (check-type n number)
  (if (= n 0) (setq n 0))
  (cond ((typep n '(integer -99 999))
         (format nil "~8d" n))
        ((or (< -1000 n -1/100)
             (< 1/100 n 1000))
         (format nil "~8,2f" n))
        (t (format nil "~8,2e" n))))

(defun mf-shorten (x n)

; Consider invoking this function in the context of our-syntax.

; Unless x is a string of length at most n, return a string that represents x,
; truncated to the first n characters, and associate x with that string in
; *mf-shorten-ht* (if there is not already such association).

  (cond ((and (stringp x) (<= (length x) n))
         x)
        (t
         (let ((x (if (stringp x)
                      (hons-copy x)
                    x)))
           ;; [Jared] I think there's no need to protect this hash table
           ;; because of the way it's used.
           (cond ((mf-gethash x *mf-shorten-ht*))
                 (t (let ((*print-pretty* nil)
                          (*print-length* 10)
                          (*print-level* 5)
                          (*print-lines* 2))
                      (let ((str
                             (with-output-to-string
                               (s)
                               (cond ((stringp x) (princ x s))
                                     (t (prin1 x s))))))
                        (mf-sethash x
                                    (cond ((<= (length str) n) str)
                                          (t (concatenate
                                              'string
                                              (subseq str 0 (max 0 n))
                                              "///")))
                                    *mf-shorten-ht*)))))))))

(defun-one-output mf-print-alist (alist separation)

; Consider invoking this function in the context of our-syntax.

  (check-type separation (integer 0))
  (setq alist
        (loop for x in alist collect
              (progn
                (check-type x
                            (cons (or string symbol)
                                  (cons (or string (integer 0))
                                        null)))
                (list (mf-shorten (car x) *mf-print-alist-width*)
                      (if (integerp (cadr x))
                          (mf-num-to-string (cadr x))
                        (cadr x))))))
  (let* ((max1 (loop for x in alist maximize (length (car x))))
         (max2 (loop for x in alist maximize (length (cadr x))))
         (width (max (or *print-right-margin*
                         *mf-print-right-margin*)
                     (+ separation max1 max2))))
    (loop for x in alist do
          (fresh-line)
          (princ (car x))
          (loop for i
                below (- width (+ (length (car x))
                                  (length (cadr x))))
                do (write-char #\Space))
          (princ (cadr x))))
  nil)

(defmacro safe-incf-pons (x inc)

; This function was originally called very-unsafe-incf, and as its name
; implied, it was defined to increment x by inc without checking that the
; result is of mfixnum type.  We are guessing that the cost of being safe is
; small, so we are renaming this function as safe-incf-pons, since it has only
; been used for reporting statistics related to pons.  It would certainly be
; fine to eliminate this extra layer altogether once we are confident that it
; causes only negligible slowdown in statistics reporting.

  `(safe-incf ,x ,inc))

(defun-one-output pons-summary ()

; Note: This function should probably either be made available in the loop or
; else eliminated.

; This function is not called anywhere else in the ACL2 sources, nor is it
; available from the loop.  Perhaps though it could be useful in tuning the
; implementation.

  (our-syntax
   (let ((sssub 0)     ; sum of sizes of subtables
         (nponses 0)   ; number of ponses
         (nsubs 0)     ; number of subsidiary hash tables (in flex alists)
         (nponstab 0)) ; number of pons tables
     (declare (type mfixnum sssub nponses nsubs))
     (format t "Pons-summary:~%")
     (with-global-memoize-lock
      (mf-maphash
       (lambda (k v)
         (when (symbolp k)
           (let ((tab (symbol-value (access memoize-info-ht-entry v
                                            :ponstablename))))
             (when tab
               (safe-incf-pons nponstab 1)
               (mf-maphash
                (lambda (k v)
                  (declare (ignore k))
                  (cond
                   ((not (listp v)) ; the flex-alist v is a hash table
                    (safe-incf-pons sssub (mf-hash-table-size v))
                    (safe-incf-pons nponses (mf-hash-table-count v))
                    (safe-incf-pons nsubs 1))
                   (t (safe-incf-pons nponses (length v)))))
                tab)))))
       *memoize-info-ht*))
     (mf-print-alist
      `((" Pons hits/calls"
         ,(let* ((c *pons-call-counter*)
                 (m *pons-misses-counter*)
                 (h (- c m)))
            (format nil "~,1e / ~,1e = ~,2f" h c (if (eql c 0) 0 (/ h c)))))
        (" Number of pons tables" ,(mf-num-to-string nponstab))
        (" Number of pons sub tables" ,(mf-num-to-string nsubs))
        (" Sum of pons sub table sizes" ,(mf-num-to-string sssub))
        (" Number of ponses" ,(mf-num-to-string nponses)))
      5)
     (format t ")")
     (force-output *standard-output*)
     nil)))

(defun memoized-values (&optional (fn (memoized-functions)))

; Note: This function should probably either be made available in the loop or
; else eliminated.

; We print all the currently memoized values for the given function symbol or
; list of function symbols, which by default is the list of all memoized
; function symbols.

  (with-global-memoize-lock
   (cond ((listp fn) (mapc #'memoized-values fn))
         ((not (memoizedp-raw fn))
          (format t "~%; Memoized-values:  ~s is not memoized." fn))
         (t (let ((tb (symbol-value
                       (access memoize-info-ht-entry
                               (mf-gethash fn *memoize-info-ht*)
                               :tablename))))
              (cond ((and tb (not (eql 0 (mf-hash-table-count tb))))
                     (format t "~%; Memoized values for ~s." fn)
                     (mf-maphash (lambda (key v)
                                   (format t "~%~s~%=>~%~s" key v))
                                 tb)))))))
  (force-output *standard-output*)
  nil)

(defun print-call-stack ()

; Note: This function should probably either be made available in the loop or
; else eliminated.

; (Print-call-stack) prints the stack of memoized function calls currently
; running and the time they have been running.

  (float-ticks/second-init)
  (our-syntax
   (let (lst
         (ticks (internal-real-ticks))
         (*print-case* :downcase))
     (with-global-memoize-lock
      (mf-maphash
       (lambda (k v)
         (when (symbolp k)
           (let ((x (symbol-value (the symbol
                                       (access memoize-info-ht-entry
                                               v :start-ticks)))))
             (declare (type mfixnum x))
             (when (> x 0) ; in particular, on the stack (x not -1)
               (push (cons k x) lst)))))
       *memoize-info-ht*))
     (setq lst (sort lst #'< :key #'cdr))
     (setq lst (loop for pair in lst collect
                     (list (car pair)
                           (mf-num-to-string (/ (the-mfixnum
                                                     (- ticks (cdr pair)))
                                                *float-ticks/second*)))))
     (when lst
       (terpri *standard-output*)
       (mf-print-alist
        (cons '("Stack of monitored function calls."
                "Time since outermost call.")
              lst)
        5))))
  (force-output *standard-output*)
  nil)

(defun-one-output pons-calls (x)

; This function symbol can be included in *memoize-summary-order-list*.

; For a memoized function x, (pons-calls x) is the number of times that x has
; called pons.

  (setq x (coerce-index x))
  (aref *memoize-call-array*
        (ma-index x *ma-pons-index*)))

#+(or ccl sbcl)
(defun-one-output bytes-allocated (x)

; This function symbol can be included in *memoize-summary-order-list*.

; For a memoized function x, (bytes-allocated x) is the number of
; heap bytes x has caused to be allocated on the heap.

  (setq x (coerce-index x))
  (aref *memoize-call-array*
        (ma-index x *ma-bytes-index*)))

(defun-one-output number-of-hits (x)

; This function symbol can be included in *memoize-summary-order-list*.

; For a memoized function x, (number-of-hits x) is the number of
; times that a call of x returned a remembered answer.

  (setq x (coerce-index x))
  (aref *memoize-call-array*
        (ma-index x *ma-hits-index*)))

(defun-one-output number-of-memoized-entries (x)

; This function symbol can be included in *memoize-summary-order-list*.

; For a memoized function x, (number-of-memoized-entries x) is the number of
; entries currently stored for x."

  (setq x (coerce-index x))
  (with-global-memoize-lock
   (let ((h (mf-gethash x *memoize-info-ht*)))
     (unless h (error "~a is not memoized." x))
     (let* ((sym (access memoize-info-ht-entry
                         h
                         :tablename))
            (val (symbol-value sym)))
       (if (hash-table-p val) ; note: val is nil after clear-memoize-table
           (mf-hash-table-count val)
         0)))))

(defun-one-output number-of-mht-calls (x)

; This function symbol can be included in *memoize-summary-order-list*.

; For a memoized function x, (number-of-mht-calls x) is the number
; of times that the memoize hash-table for x was created.

  (setq x (coerce-index x))
  (aref *memoize-call-array*
        (ma-index x *ma-mht-index*)))

(defun-one-output total-time (x)

; This function symbol can be included in *memoize-summary-order-list*.

; For a memoized function x, (total-time x) is the total time spent inside
; (all outermost) calls of x.

; One must first call compute-calls-and-times to get sensible results.

  (setq x (coerce-index x))
  (float-ticks/second-init)
  (/ (aref *memoize-call-array* (ma-index-ticks x))
     *float-ticks/second*))

(defun-one-output number-of-calls (x)

; This function symbol can be included in *memoize-summary-order-list*.

; For a memoized function x, (number-of-calls x) is the total number of calls
; of x.

; One must first call compute-calls-and-times to get sensible results.

  (setq x (coerce-index x))
  (aref *memoize-call-array*
        (ma-index-calls x)))

(defun-one-output time-for-non-hits/call (x)

; This function symbol can be included in *memoize-summary-order-list*.

; One must first call compute-calls-and-times to get sensible results.

  (setq x (coerce-index x))
  (let ((n (- (number-of-calls x) (number-of-hits x))))
    (if (zerop n) 0 (/ (total-time x) n))))

(defun-one-output time/call (x)

; This function symbol can be included in *memoize-summary-order-list*.

; One must first call compute-calls-and-times to get sensible results.

  (setq x (coerce-index x))
  (let ((n (number-of-calls x)))
    (if (zerop n) 0 (/ (total-time x) n))))

(defun-one-output hits/calls (x)

; This function symbol can be included in *memoize-summary-order-list*.

; One must first call compute-calls-and-times to get sensible results.

  (setq x (coerce-index x))
  (let ((n (number-of-calls x)))
    (if (zerop n)
        0
      (/ (number-of-hits x)

; Why (float n) instead of n?  We see no clear reason, but we leave this
; historical call of float in place.

         (float n)))))

#+(or ccl sbcl)
(defun-one-output bytes-allocated/call (x)

; This function symbol can be included in *memoize-summary-order-list*.

; One must first call compute-calls-and-times to get sensible results.

  (setq x (coerce-index x))
  (let ((n (number-of-calls x)))
    (if (zerop n) 0 (/ (bytes-allocated x) n))))

(defun char-list-fraction (l)
  (if (atom l)
      0
    (+ (char-code (car l))
       (/ (char-list-fraction (cdr l))
          256))))

(defun symbol-name-order (s)

; Symbol-name-order maps symbols to rationals preserving lexicographic order.

; This function symbol can be included in *memoize-summary-order-list*.

  (unless (symbolp s) (setq s (fixnum-to-symbol s)))
  (- (char-list-fraction (coerce (symbol-name s) 'list))))

(defun-one-output execution-order (s)

; This function symbol can be included in *memoize-summary-order-list*.

  (unless (symbolp s) (setq s (fixnum-to-symbol s)))
  (the-mfixnum (symbol-value
               (the symbol
                 (access memoize-info-ht-entry
                         (mf-gethash s *memoize-info-ht*)
                         :start-ticks)))))

(defun compute-calls-and-times ()
  (with-global-memoize-lock ; perhaps not necessary for this, but harmless
   (let ((ma *memoize-call-array*)
         (2m *2max-memoize-fns*)
         (ca *callers-array*)
         (n ; fixnum, because *max-symbol-to-fixnum* <= 1/2 *2max-memoize-fns*
          (the fixnum (1+ *max-symbol-to-fixnum*))))
     (declare (type (simple-array mfixnum (*)) ma)
              (type (simple-array t (*)) ca)
              (type fixnum 2m n))
     (cond ((eql (length ca) n)
            (loop for i fixnum below n
                  do (setf (aref ca i) nil)))
           (t (setq *callers-array* (make-array n :initial-element nil))
              (setq ca *callers-array*)))
     (loop for i fixnum below (ma-index-calls n 0 2m)

; fixnum, because (ma-index-calls n 0 2m) = 2n <= *2max-memoize-fns*

; Initialize column 0 of *memoize-call-array* to set to 0, for each i < n, both
; (ma-index-calls i 0 2m) and (ma-index-ticks i 0 2m).

           do (setf (aref ma i) 0))
     (loop for i fixnum ; column, for caller
           from *initial-max-symbol-to-fixnum*
           to *max-symbol-to-fixnum* ; indeed a fixnum; see comments above
           do
           (let ((col-base (ma-index i 0 2m)))
             (declare (type mfixnum col-base))
             (loop for j fixnum ; row
                   from *initial-max-symbol-to-fixnum*
                   to *max-symbol-to-fixnum* ; indeed a fixnum; see above
                   do
                   (let* ((calls-row (ma-index-calls j))
                          (index (ma-index-from-col-base col-base calls-row))
                          (calls (the-mfixnum (aref ma index))))
                     (declare (type mfixnum calls-row index calls))
                     (when (> calls 0)
                       (let* ((ticks-index

; The index for ticks is (ma-index-from-col-base col-base (ma-index-ticks j)).
; But that is just (1+ index), so we use the latter, more efficient form.

                               (the-mfixnum (1+ index)))
                              (ticks (aref ma ticks-index))
                              (ticks-row ; (ma-index-ticks j)
                               (the-mfixnum (1+ calls-row))))
                         (declare (type mfixnum ticks-index ticks ticks-row))
                         (safe-incf (aref ma calls-row)
                                    calls
                                    compute-calls-and-times)
                         (safe-incf (aref ma ticks-row)
                                    ticks
                                    compute-calls-and-times)
                         (push i ; Add i to the callers of j.
                               (aref ca j)))))))))))

(defun-one-output print-not-called ()

; Note: This function should probably either be made available in the loop or
; else eliminated.

; (Print-not-called) prints, one to a line, in alphabetic order, the currently
; memoized functions that have never been called.  This utility may be useful
; when looking for test coverage.

  (with-global-memoize-lock
   (compute-calls-and-times)
   (let ((ans nil))
     (mf-maphash (lambda (k v)
                   (declare (ignore v))
                   (when (and (symbolp k)
                              (eql 0 (number-of-calls k)))
                     (push k ans)))
                 *memoize-info-ht*)
     (loop for x in (sort ans 'alphorder)
           do (print x)))))

(defun-one-output memoize-summary-sort ()
  (labels
   ((lex-> (l1 l2)
           (cond ((or (atom l1)
                      (atom l2))
                  nil)
                 ((> (car l1) (car l2)) t)
                 ((< (car l1) (car l2)) nil)
                 (t (lex-> (cdr l1) (cdr l2))))))
   (let (pairs)
     (with-global-memoize-lock
      (mf-maphash
       (lambda (fn v)
         (when (symbolp fn)
           (let ((num (access memoize-info-ht-entry v :num)))
             (declare (type mfixnum num))
             (when (< 0 (number-of-calls num))
               (push (cons fn (loop for order
                                    in *memoize-summary-order-list*
                                    collect (funcall order fn)))
                     pairs)))))
       *memoize-info-ht*)
      (sort pairs
            (if *memoize-summary-order-reversed*
                (lambda (x y) (lex-> y x))
              #'lex->)
            :key #'cdr)))))

(defun-one-output outside-caller-p (x)
  (with-global-memoize-lock
   (or (<= x *initial-max-symbol-to-fixnum*)
       (null (mf-gethash x *memoize-info-ht*)))))

(defun-one-output memoize-condition (fn)
  (with-global-memoize-lock
   (let ((x (mf-gethash fn *memoize-info-ht*)))
     (and x
          (access memoize-info-ht-entry x :condition)))))

(defun-one-output memoize-summary-after-compute-calls-and-times ()

; One must first call compute-calls-and-times to get sensible results.

  (with-global-memoize-lock ; perhaps not necessary for this, but harmless
   (float-ticks/second-init)
   (our-syntax
    (let* ((fn-pairs (memoize-summary-sort))
           (ma *memoize-call-array*)
           (len-orig-fn-pairs (len fn-pairs))
           (len-fn-pairs 0)      ; set below
           #+(or ccl sbcl)
           (global-bytes-allocated 0) ; set below
           (global-pons-calls 0)      ; set below
           )
      (declare (type (simple-array mfixnum (*)) ma)
               (type fixnum len-orig-fn-pairs len-fn-pairs))
      (when (and *memoize-summary-limit*
                 (> len-orig-fn-pairs *memoize-summary-limit*))
        (setq fn-pairs (take *memoize-summary-limit* fn-pairs)))
      (setq len-fn-pairs (len fn-pairs))
      (when (> len-fn-pairs 0)
        (format t
                "~%Sorted by *memoize-summary-order-list* = ~s."
                *memoize-summary-order-list*)
        (when (< len-fn-pairs len-orig-fn-pairs)
          (format t
                  "~%Reporting on ~:d of ~:d functions because ~
                   *memoize-summary-limit* = ~a."
                  len-fn-pairs
                  len-orig-fn-pairs
                  *memoize-summary-limit*)))
      #+(or ccl sbcl)
      (setq global-bytes-allocated
            (loop for pair in fn-pairs sum
                  (bytes-allocated (car pair))))
      (setq global-pons-calls
            (loop for pair in fn-pairs sum (pons-calls (car pair))))
      (when (null fn-pairs)
        (format t "~%(memoize-summary) has nothing to report.~%"))
      (loop for pair in fn-pairs do
            (let* ((fn (car pair))
                   (entry (mf-gethash fn *memoize-info-ht*))
                   (tablename
                    (symbol-value
                     (access memoize-info-ht-entry entry :tablename)))
                   (ponstablename
                    (symbol-value
                     (access memoize-info-ht-entry entry :ponstablename)))
                   (start-ticks
                    (the-mfixnum
                     (symbol-value
                      (the symbol
                           (access memoize-info-ht-entry entry
                                   :start-ticks)))))
                   (num (the-mfixnum (access memoize-info-ht-entry entry
                                             :num)))
                   (nhits (the-mfixnum (number-of-hits num)))
                   (nmht (the-mfixnum (number-of-mht-calls num)))
                   (ncalls (the-mfixnum (number-of-calls num)))
                   (pons-calls (the-mfixnum (pons-calls num)))
                   (no-hits (or (not *report-hits*)
                                (null (memoize-condition fn))))
                   #+(or ccl sbcl)
                   (bytes-allocated (bytes-allocated num))
                   (tt (max .000001

; Why insist that tt be at least .000001?  That has been the case historically,
; and it might be reasonable since a smaller time might be unlikely and anyhow,
; .000001 is not unreasonable if only as "noise".  So we leave this code alone.

                            (total-time num)))
                   (t/c (time/call num))
                   (in-progress-str
                    (if (eql start-ticks -1) "" " (running)"))
                   (selftime tt))
              (declare (type integer start-ticks)
                       (type mfixnum num nhits nmht ncalls
                             pons-calls
                             #+(or ccl sbcl) bytes-allocated))
              (format t "~%(~s~%" fn)
              (mf-print-alist
               `(,@(when (or *report-calls* *report-hits*)
                     `((,(format nil " ~a~a"
                                 (if no-hits "Calls" "Hits/calls")
                                 in-progress-str)
                        ,(cond
                          (no-hits (format nil "~a" (mf-num-to-string ncalls)))
                          ((zerop ncalls)
                           (format nil "~8,2e/~8,2e = ????%"
                                   nhits
                                   0))
                          (t (format nil "~8,2e/~8,2e = ~4,1f%"
                                     nhits
                                     ncalls
                                     (* 100 (/ nhits (float ncalls)))))))))
                 ,@(when (and *report-mht-calls*

; The following inequality was here historically, perhaps because nmht is
; always at least 1 (not sure about that); anyhow, it seems OK to leave it.

                              (>= nmht 2))
                     `((" Number of calls to mht" ,(mf-num-to-string nmht))))
                 ,@(when *report-time*
                     `((" Time of all outermost calls"
                        ,(format nil "~a"
                                 (mf-num-to-string tt)))
                       (" Time per call" ,(mf-num-to-string t/c))))

; The commented-out code (when ...), below, has been here historically (through
; August 2014), but it's not clear why.  Note that the "Heisenberg" note is
; only made for profiled functions; what's so special about the profiling case?
; Let's just leave it to the user to decide what to make of a very small time
; per call.  To see such a case, you can try this:

; (defn foo (x) x)
; (profile 'foo)
; (foo 1)
; (foo 2)
; (memsum)

;              ,@(when (and (null (access memoize-info-ht-entry entry
;                                         :condition))
;                           (null (access memoize-info-ht-entry entry
;                                         :inline))
;                           (< t/c 1e-6))
;                  `((,(format nil " Doubtful timing info for ~a." fn)
;                     "Heisenberg effect.")))
                 #+(or ccl sbcl)
                 ,@(when (and (> bytes-allocated 0) *report-bytes*)
                     (assert (> global-bytes-allocated 0))
                     `((" Heap bytes allocated"
                        ,(format nil "~a; ~4,1f%"
                                 (mf-num-to-string bytes-allocated)
                                 (* 100 (/ bytes-allocated
                                           global-bytes-allocated))))
                       (" Heap bytes allocated per call"
                        ,(mf-num-to-string (/ bytes-allocated ncalls)))))
                 ,@(when (and (> pons-calls 0)
                              *report-pons-calls*)
                     (assert (> global-pons-calls 0))
                     `((" Pons calls"
                        ,(format nil "~a; ~4,1f%"
                                 (mf-num-to-string pons-calls)
                                 (* 100 (/ pons-calls global-pons-calls))))))
                 ,@(when (and *report-hits* *report-time* (not (eql 0 nhits)))
                     `((" Time per missed call"
                        ,(mf-num-to-string (time-for-non-hits/call num)))))
                 ,@(when *report-calls-to*
                     (let ((lst nil)
                           (outside-fn-time 0)
                           (outside-fn-count 0))
                       (declare (type mfixnum outside-fn-count))
                       (loop
                        for callern in ; collect fns called by fn
                        (loop for i below (length *callers-array*)
                              when (member num (aref *callers-array* i))
                              collect i)
                        do
                        (let* ((call-loc (ma-index-calls callern num))
                               (calls (aref ma call-loc))
                               (ticks-loc ; (ma-index-ticks callern num)
                                (the-mfixnum (1+ call-loc)))
                               (ticks (aref ma ticks-loc))
                               (local-tt (/ ticks *float-ticks/second*)))
                          (declare
                           (type mfixnum call-loc calls ticks-loc ticks))
                          (decf selftime local-tt)
                          (cond
                           ((or (outside-caller-p callern)
                                (< (* 100 local-tt) tt))
                            (incf outside-fn-time local-tt)
                            (safe-incf
                             outside-fn-count
                             calls
                             memoize-summary-after-compute-calls-and-times))
                           (t (push
                               `((,(format nil
                                           " To ~s"
                                           (fixnum-to-symbol callern))
                                  ,(format nil
                                           "~8,2e calls took~8,2e; ~a%"
                                           calls
                                           local-tt
                                           (cond
                                            ((> (* 10000 local-tt) tt)
                                             (assert (< 0 tt))
                                             (format
                                              nil
                                              "~4,1f"
                                              (* 100 (/ local-tt tt))))
                                            (t "<0.01"))))
                                 . ,(if *sort-to-from-by-calls*
                                        calls
                                      local-tt))
                               lst)))))
                       (when (> outside-fn-time 0)
                         (assert (< 0 tt))
                         (push
                          `((,(format nil " To other functions")
                             ,(format
                               nil
                               "~8,2e calls took~8,2e; ~a%"
                               outside-fn-count
                               outside-fn-time
                               (if (> (* 10000 outside-fn-time) tt)
                                   (format nil
                                           "~4,1f"
                                           (* 100 (/ outside-fn-time tt)))
                                 "<0.01")))
                            . ,(if *sort-to-from-by-calls*
                                   outside-fn-count
                                 outside-fn-time))
                          lst))
                       (when (and (> selftime 0)
                                  (not (= selftime tt)))
                         (assert (< 0 tt))
                         (push `((" To self/unprofiled functions"
                                  ,(format
                                    nil
                                    "~8,2e; ~a%"
                                    selftime
                                    (if (> (* 10000 selftime) tt)
                                        (format nil
                                                "~4,1f"
                                                (* 100 (/ selftime tt)))
                                      "<0.01")))
                                 . ,(if *sort-to-from-by-calls*
                                        0 ; unknown number of calls; just use 0
                                      selftime))
                               lst))
                       (setq lst (sort lst #'> :key #'cdr))
                       (strip-cars lst)))
                 ,@(when *report-calls-from*
                     (let ((lst nil)
                           (outside-caller-time 0)
                           (outside-caller-count 0))
                       (loop
                        for callern in (aref *callers-array* num)
                        do
                        (let* ((call-loc (ma-index-calls num callern))
                               (calls (aref ma call-loc))
                               (ticks-loc ; (ma-index-ticks num callern)
                                (the-mfixnum (1+ call-loc)))
                               (ticks (aref ma ticks-loc))
                               (local-tt (/ ticks *float-ticks/second*)))
                          (declare
                           (type mfixnum call-loc calls ticks-loc ticks))
                          (cond
                           ((or (outside-caller-p callern)
                                (< (* 100 local-tt) tt))
                            (incf outside-caller-time local-tt)
                            (incf outside-caller-count calls))
                           (t (push
                               `((,(format
                                    nil
                                    " From ~s"
                                    (fixnum-to-symbol callern))
                                  ,(format
                                    nil
                                    "~8,2e calls took~8,2e; ~a%"
                                    calls
                                    local-tt
                                    (if (and (<= .001 local-tt)
                                             (<= local-tt tt))
                                        (format nil
                                                "~4,1f"
                                                (* 100 (/ local-tt tt)))
                                      "?")))
                                 . ,(if *sort-to-from-by-calls*
                                        calls
                                      local-tt))
                               lst)))))
                       (when (> outside-caller-time 0)
                         (push
                          `((,(format nil " From other functions")
                             ,(format
                               nil
                               "~8,2e calls took~8,2e; ~a%"
                               outside-caller-count
                               outside-caller-time
                               (if (and (<= .001 outside-caller-time)
                                        (<= outside-caller-time tt))
                                   (format
                                    nil
                                    "~4,1f"
                                    (* 100 (/ outside-caller-time tt)))
                                 "?")))
                            . ,(if *sort-to-from-by-calls*
                                   outside-caller-count
                                 outside-caller-time))
                          lst))
                       (setq lst (sort lst #'> :key #'cdr))
                       (strip-cars lst)))
                 ,@(when (or *report-on-memo-tables* *report-on-pons-tables*)
                     (let ((sum-pons-sub-sizes 0)
                           (nponses 0)
                           (nponssubs 0))
                       (declare (type mfixnum
                                      sum-pons-sub-sizes nponses nponssubs))
                       (and
                        ponstablename
                        *report-on-pons-tables*
                        (mf-maphash
                         (lambda (key value)
                           (declare (ignore key))
                           (cond
                            ((not (listp value))
                             (safe-incf-pons sum-pons-sub-sizes
                                             (mf-hash-table-size value))
                             (safe-incf-pons nponses
                                             (mf-hash-table-count value))
                             (safe-incf-pons nponssubs 1))
                            (t (safe-incf-pons nponses (length value)))))
                         ponstablename))
                       `(,@(and
                            tablename
                            *report-on-memo-tables*
                            (let ((count (mf-hash-table-count tablename))
                                  (size (mf-hash-table-size tablename)))
                              `((,(format nil " Memoize table count/size")
                                 ,(format
                                   nil
                                   "~8,2e/~8,2e = ~4,1f%"
                                   count size (* 100 (/ count size)))))))
                         ,@(and
                            ponstablename
                            *report-on-pons-tables*
                            (let ((count (mf-hash-table-count ponstablename))
                                  (size (mf-hash-table-size ponstablename)))
                              `((" (Pons table count/size"
                                 ,(format
                                   nil
                                   "~:d/~:d = ~4,1f%)"
                                   count
                                   size
                                   (* 100 (/ count size))))
                                (" (Number of pons sub tables"
                                 ,(format
                                   nil
                                   "~a)"
                                   (mf-num-to-string nponssubs)))
                                (" (Sum of pons sub table sizes"
                                 ,(format
                                   nil
                                   "~a)"
                                   (mf-num-to-string sum-pons-sub-sizes)))
                                (" (Number of ponses"
                                 ,(format
                                   nil
                                   "~a)"
                                   (mf-num-to-string nponses))))))))))
               5))
            (format t ")"))))
   (terpri *standard-output*)
   (force-output *standard-output*))
  nil)

(defun-one-output memoize-summary ()

; Warning: Keep the return values in sync for the logic and raw Lisp.

; (Memoize-summary) reports data stored during the execution of the functions
; in (memoized-functions).

; Typically each call of a memoized function, fn, is counted.  The elapsed time
; until an outermost function call of fn ends, the number of heap bytes
; allocated in that period (CCL and SBCL only), and other 'charges' are
; 'billed' to fn.  That is, quantities such as elapsed time and heap bytes
; allocated are not charged to subsidiary recursive calls of fn while an
; outermost call of fn is running.  Recursive calls of fn, and memoized 'hits',
; are counted, unless fn was memoized with nil as the value of the :inline
; parameter of memoize.

; The settings of the following determine, at the time a function is
; given to memoize, the information that is collected for calls of
; the function:

;        Variable              type

;        *record-bytes*       boolean    (available in CCL and SBCL only)
;        *record-calls*       boolean
;        *record-hits*        boolean
;        *record-mht-calls*   boolean
;        *record-pons-calls*  boolean
;        *record-time*        boolean

; The settings of the following determine, at the time that
; memoize-summary is called, what information is printed:

;        *report-bytes*       boolean   (available in CCL and SBCL only)
;        *report-calls*       boolean
;        *report-calls-from*  boolean
;        *report-calls-to*    boolean
;        *report-hits*        boolean
;        *report-mht-calls*   boolean
;        *report-pons-calls*  boolean
;        *report-time*        boolean

;        *report-on-memo-tables*   boolean
;        *report-on-pons-tables*   boolean
;        *memoize-summary-limit*            (or integerp null)
;        *memoize-summary-order-list*       (symbol symbol ... symbol)
;        *memoize-summary-order-reversed*   boolean

; Functions are sorted lexicographically according to the ordering
; induced by the function names in *memoize-summary-order-list*, each
; member of which must be a unary function that returns a rational.

; (Clear-memoize-tables) forgets the remembered values of all memoized function
; calls.  It does not alter a function's status as being a memoized function,
; nor does it alter the monitoring data accumulated.

; (Unmemoize-all) undoes the memoization status of all memoized
; functions.

; (Clear-memoize-call-array) zeroes out the monitoring information for
; all functions.  It does not alter any function's status as a
; memoized function nor does it change the values remembered for any
; memoized function.

; Here is an example of hacking with *memoize-summary-order-list* that
; instructs memoize-summary to print information about, say,
; 1st-mod-err first:

;   (push (lambda (fn)
;           (if (eq fn '1st-mod-err) 1 0))
;         *memoize-summary-order-list*)."

; Note that like the "Time of all outermost calls", the "Pons calls" reported
; are cumulative.  For example, we get 8 pons calls for G (not 4) in the
; following example, using CCL: 4 for G, and 4 for the subsidiary calls of F.

;   (defn f (x y) (cons x y))
;   (defn g (x y) (f x y))
;   (memoize 'f)
;   (memoize 'g)
;   (g '(3 . 4) '(5 . 6))
;   (g '(3 . 5) '(5 . 6))
;   (g '(3 . 6) '(5 . 6))
;   (g '(3 . 7) '(5 . 6))
;   (memsum)

  (compute-calls-and-times)
  (memoize-summary-after-compute-calls-and-times)
  nil)

; SECTION: Clearing and initialization

(defun clear-one-memo-and-pons-hash (l strategy)

; Strategy is :CLEAR, :NULL, or :AUTO.
;   :CLEAR means always use clrhash.
;   :NULL means always set it to NIL.
;   :AUTO means try to be smart.

;  For the :AUTO mode, we need to decide between (1) clrhash and (2) setting to
;  NIL.  (1) has the advantage of not allocating new memory/making new garbage.
;  However, it has the disadvantage of preventing us from shrinking the table
;  to a more reasonable size, if the current table is exceptionally large.

;  See the discussion in memoize-table-desired-size for a heuristic that we
;  use to estimate how large a table "should" be (based on its historic sizes
;  as it has been cleared/freed in the past).  Here we use this heuristic so
;  that:

;     - If we have used less than the "expected" slots, clrhash is probably
;       relatively cheap and we think it'd be better to just reuse the table.
;       (Note: we actually compare our current count to the
;       memoize-table-desired-size for the new table, which grows to 1.2x the
;       average size.)

;     - Otherwise, the table we have right now is (perhaps much) larger than we
;       think it ought to be; clrhash would be expensive and it may be better
;       to just start afresh to get back to a reasonable size.

  (with-global-memoize-lock
   (let* ((fn (access memoize-info-ht-entry l :fn))
          (mt (symbol-value (access memoize-info-ht-entry l :tablename)))
          (pt (symbol-value (access memoize-info-ht-entry l :ponstablename)))
          (mt-count (and mt (mf-hash-table-count mt)))
          (pt-count (and pt (mf-hash-table-count pt))))
     (when mt
       (let* ((mt-target-size (memoize-table-desired-size fn 0)))
         (if (or (eq strategy :clear)
                 (and (eq strategy :auto)
                      (< mt-count mt-target-size)))
             (unless (eql 0 mt-count) (clrhash mt))
           (setf (symbol-value (access memoize-info-ht-entry l :tablename))
                 nil))))
     (when pt
       (let* ((pt-target-size (pons-table-desired-size fn 0)))
         (if (or (eq strategy :clear)
                 (and (eq strategy :auto)
                      (< pt-count pt-target-size)))
             (unless (eql 0 pt-count) (clrhash pt))
           (setf (symbol-value (access memoize-info-ht-entry l :ponstablename))
                 nil))))
     (when (or mt-count pt-count)
       (update-memo-max-sizes fn (or pt-count 1) (or mt-count 1)))))
  nil)

(defun-one-output clear-memoize-table (k)

; Warning: Keep the return values in sync for the logic and raw Lisp.

  (with-global-memoize-lock
   (when (symbolp k)
     (let ((l (mf-gethash k *memoize-info-ht*)))
       (when l (clear-one-memo-and-pons-hash l :auto)))))
  k)

(defun-one-output clear-memoize-tables ()

; Warning: Keep the return values in sync for the logic and raw Lisp.

  (with-global-memoize-lock
   (let (success)
     (unwind-protect
         (progn
           (mf-maphash (lambda (k l)
                         (when (symbolp k)
                           (clear-one-memo-and-pons-hash l :null)))
                       *memoize-info-ht*)
           (setq success t))
       (or success (error "clear-memoize-tables failed."))))
   (setq *pons-call-counter* 0)
   (setq *pons-misses-counter* 0))
  nil)

(defun clear-memoize-call-array ()

; (Clear-memoize-call-array) zeros out all records of function calls for
; purposes of reporting, for example by memoize-summary.

  (with-global-memoize-lock
   (let ((ma *memoize-call-array*))
     (declare (type (simple-array mfixnum (*)) ma))
     (let ((len (length ma)))
       (cond ((typep len 'fixnum)
              (loop for i fixnum below len
                    do (setf (aref ma i) 0)))
             (t ; maybe impossible?
              (loop for i of-type integer below len
                    do (setf (aref ma i) 0))))))))

(defun clear-memoize-statistics ()

; Warning: Keep the return values in sync for the logic and raw Lisp.

  (with-global-memoize-lock
   (setq *pons-call-counter* 0)
   (setq *pons-misses-counter* 0)
   (clear-memoize-call-array))
  nil)

(defun-one-output memoize-init ()

; This function initializes most globals that are managed automatically by the
; memoization implementation, i.e., that are not user-settable.

  (with-global-memoize-lock
   (when *memoize-init-done*
     (return-from memoize-init nil))
   (unless (eql *caller* (the-mfixnum (outside-caller-col-base)))
     (error "memoize-init:  A memoized function is running."))
   (let (success)
     (unwind-protect
         (progn
           (setq *pons-call-counter* 0)
           (setq *pons-misses-counter* 0)
           (setq *memoize-info-ht* (initial-memoize-info-ht))
           (mf-sethash *initial-max-symbol-to-fixnum*
                       "outside-caller"
                       *memoize-info-ht*)
           (setq *max-symbol-to-fixnum* *initial-max-symbol-to-fixnum*)
           (setq *2max-memoize-fns* *initial-2max-memoize-fns*)
           (sync-memoize-call-array)
           (setq *memo-max-sizes* (mf-mht :shared :default))
           (setq success t))
       (if success
           (setq *memoize-init-done* t)
         (error "memoize-init failed.")))))
  nil)

(defmacro with-lower-overhead (&rest r)

; Warning: Keep this in sync with lower-overhead and with-higher-overhead.

  `(let ((*record-bytes* nil)
         (*record-calls*

; It has been a mystery why we have needed to set *record-calls* to t in
; LispWorks.  We found that otherwise, for example, evaluation hangs for
; (bad-lisp-objectp (make-list 100000)) when bad-lisp-objectp is in the initial
; memoized state produced by calling acl2h-init (see acl2h-init-memoizations)
; It might well be worth looking into this again.

          #-lispworks nil #+lispworks t)
         (*record-hits* nil)
         (*record-mht-calls* nil)
         (*record-pons-calls* nil)
         (*record-time* nil))
     ,@r))

(defmacro with-higher-overhead (&rest r)

; Warning: Keep this in sync with lower-overhead and with-lower-overhead.

  `(let ((*record-bytes* t)
         (*record-calls* t)
         (*record-hits* t)
         (*record-mht-calls* t)
         (*record-pons-calls* t)
         (*record-time* t))
     ,@r))

(defmacro with-overhead (val form)
  (let ((v (gensym)))
    `(let ((,v ,val))
       (cond ((eq ,v :default) ,form)
             ((null ,v) (with-lower-overhead ,form))
             (t (with-higher-overhead ,form))))))

(defun acl2h-init-memoizations ()

; The memoizations performed here, for certain built-in functions, may be
; important for performance in applications that traffic in large objects or
; terms.  Some of these memoizations are undone by acl2h-init-unmemoizations,
; which is called by ACL2(hp) when waterfall-parallelism is turned on, in order
; to avoid errors during the waterfall due the fact that memoization is not
; thread-safe.

  (loop for entry in
        *thread-unsafe-builtin-memoizations*
        when (not (memoizedp-raw (car entry)))

; If you change the following code, consider similarly changing
; set-bad-lisp-consp-memoize.

        do (with-lower-overhead
            (apply 'memoize-fn entry))))

(defun set-bad-lisp-consp-memoize (arg)

; Warning: Keep the return values in sync for the logic and raw Lisp.

  (cond (arg (when (not (memoizedp-raw 'bad-lisp-consp))

; If you change the following code, consider similarly changing
; acl2h-init-memoizations.

               (with-lower-overhead
                (apply 'memoize-fn *bad-lisp-consp-memoization*))))
        (t (when (memoizedp-raw 'bad-lisp-consp)
             (unmemoize-fn 'bad-lisp-consp)))))

(defun-one-output acl2h-init ()

; ACL2-DEFAULT-RESTART is called whenever a saved image for any version of ACL2
; is started up.  For ACL2(h), ACL2-DEFAULT-RESTART calls ACL2H-INIT only the
; first time we save an image, not after save-exec, so that *print-array* and
; the gc-strategy persist after save-exec.

; (memoize-init) ; skipped, since this call is in exit-boot-strap-mode

  #+static-hons
  (setq *print-array*

; With *print-array* turned on, we end up sometimes seeing the SBITS array in
; backtraces, etc, which can effectively kill your session (can't interrupt,
; etc.).  This is only a problem with static-honsing since classic honsing
; doesn't have sbits anyway.

        nil)

; We have decided not to print garbage collector messages, since these can be
; distracting to ordinary users.  Those who want such messages can put
; (gc-verbose t), or even (gc-verbose t t), in their ~/acl2-customization.lsp
; files.  We queried the acl2-help mailing list on [16 Jan 2015 17:34:36] and
; gave people the opportunity to object (albeit not particularly inviting such
; objections), but nobody did.  We keep the following historical comment (and
; code), which provides insight for why this decision required thought.  Note
; that gc messages are turned off, where we know how to do so, in source file
; acl2.lisp.

;   It is can be helpful for the user to know what the garbage collector is
;   doing when using HONS and MEMOIZE.  We leave full-gc messages on but turn
;   EGC messages off.  We're disabling EGC anyway, but when we've experimented
;   with leaving it on, the EGC messages are way too verbose.

;   #+(or ccl cmu gcl) ; Lisps where gc-verbose is supported
;   (gc-verbose t nil)

  #+ccl
  (set-gc-strategy (if cl-user::*acl2-egc-on* :egc :delay))

  nil)

; SECTION: Miscellaneous (e.g.  shorter, older names)

; Note: memsum is defined in memoize.lisp.

(defun memstat (&rest r)
  (apply #'memoized-values r))

(defun clear-memo-tables ()
  (clear-memoize-tables))

(defun lower-overhead ()

; Warning: Keep this in sync with with-lower-overhead and
; with-higher-overhead.

; An old comment here claims that lower-overhead does not help much (in
; speeding things up, presumably).  It might be interesting to test that.

  (setq *record-bytes* nil)
  (setq *record-calls*

; See the comment about LispWorks in with-lower-overhead; we make the analogous
; adjustment for LispWorks here, in case it's necessary.

        #-lispworks nil #+lispworks t)
  (setq *record-hits* nil)
  (setq *record-mht-calls* nil)
  (setq *record-pons-calls* nil)
  (setq *record-time* nil))

(defun update-memo-entry-for-attachments (fns entry wrld)

; See the Essay on Memoization with Attachments.

; This function is called by update-memo-entries-for-attachments.  We return
; (mv changed-p new-entry), where if changed-p is not t or nil then it is a
; function symbol whose attachment has changed, which requires clearing of the
; corresponding memo table.

  (let* ((ext-anc-attachments
          (access memoize-info-ht-entry entry :ext-anc-attachments))
         (valid-p
          (if (eq fns :clear)
              :clear
            (or (null ext-anc-attachments)
                (ext-anc-attachments-valid-p fns ext-anc-attachments wrld
                                             t)))))
    (cond ((eq valid-p t) (mv nil entry))
          (t
           (mv (if (eq valid-p nil) t valid-p)
               (change memoize-info-ht-entry entry
                       :ext-anc-attachments
                       (ext-ancestors-attachments
                        (access memoize-info-ht-entry entry :fn)
                        wrld)))))))

(defun update-memo-entries-for-attachments (fns wrld state)

; See the Essay on Memoization with Attachments.  Here is a brief, high-level
; summary of what is going on.

; This function is called by update-wrld-structures, which is called when the
; world is updated.  When a defattach event is added or removed from the world,
; variable *defattach-fns* collects the name of the function with an attachment
; (either being added or removed).  Ultimately, *defattach-fns* is passed as
; the fns parameter to the present function, and functions' entries in
; *memoize-info-ht* are correspondingly updated as necessary, in particular
; clearing tables whose values may have depended on attachments that are no
; longer present.

  (let ((ctx 'top-level)
        (fns (if (eq fns :clear)
                 :clear
               (strict-merge-sort-symbol-<
                (loop for fn in fns
                      collect (canonical-sibling fn wrld))))))
    (when (eq fns :clear)
      (observation ctx
                   "Memoization tables for functions memoized with :AOKP T ~
                    are being cleared."))
    (when fns ; optimization
      (with-global-memoize-lock
       (mf-maphash
        (lambda (k entry)
          (when (symbolp k)
            (mv-let (changedp new-entry)
                    (update-memo-entry-for-attachments fns entry wrld)
                    (when changedp
                      (when (not (or (eq changedp t)
                                     (eq fns :clear)))
                        (observation ctx
                                     "Memoization table for function ~x0 is ~
                                      being cleared because attachment to ~
                                      function ~x1 has changed."
                                     k changedp)
                        (clear-one-memo-and-pons-hash entry :auto))
                      (mf-sethash k new-entry *memoize-info-ht*)))))
        *memoize-info-ht*)))))