share/simplification/rducon.lisp

   1 ;;; -*- Mode: Lisp; Package: Macsyma -*-                                 ;;;
   2 ;;;    (c) Copyright 1984 the Regents of the University of California.   ;;;
   3 ;;;        All Rights Reserved.                                          ;;;
   4 ;;;        This work was produced under the sponsorship of the           ;;;
   5 ;;;        U.S. Department of Energy.  The Government retains            ;;;
   6 ;;;        certain rights therein.                                       ;;;
   7 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
   8
   9 (macsyma-module rducon)
  10
  11 (eval-when
  12     (:load-toplevel :execute)
  13   (or (get 'expens 'version)
  14       ($load "expense")))
  15
  16 (defmvar $const_eqns (list '(mlist simp))
  17          "List of equations of constant expressions found by REDUCE_CONSTS."
  18          modified-commands '$reduce_consts)
  19
  20 (defmvar $const_prefix '$xx
  21          "String used to prefix all symbols generated by REDUCE_CONSTS to
  22    represent constant expressions."
  23          modified-commands '$reduce_consts)
  24
  25 (defmvar $const_counter 1
  26          "Integer index used to uniquely identify all constant expressions
  27    found by calling REDUCE_CONSTS."
  28          fixnum
  29          modified-commands '$reduce_consts)
  30
  31 (defmacro minus-constantp (x)
  32   `(and (eq (caar ,x) 'mtimes)
  33         (= (length ,x) 3)
  34         (equal (cadr ,x) -1)))
  35
  36 (defun query-const-table (x)
  37    (do ((p (cdr $const_eqns) (cdr p)))
  38        ((null p))
  39      (and (alike1 (caddar p) x)
  40           (return (cadar p)))))
  41
  42 (defun new-name (default-name)
  43    (let ((name (or default-name
  44                    (prog1
  45                     (implode (nconc (exploden $const_prefix)
  46                                     (exploden $const_counter)))
  47                     (incf $const_counter)))))
  48      (MFUNCALL '$declare name '$constant)
  49      name))
  50
  51 (defun log-const (exp name)
  52    (let ((inconst (new-name name)))
  53      (setq $const_eqns `(,.$const_eqns ,`((mequal simp) ,inconst ,exp)))
  54      inconst))
  55
  56 (defun obtain-constant (key curr-const)
  57  (let ((inkey key))
  58    (or (query-const-table key)
  59        (do ((pursue (cdr $const_eqns) (cdr pursue))
  60             (pointer)
  61             (hold)
  62             (op)
  63             (expense ($expense key))
  64             (negative (mul -1 key))
  65             (sum? (mplusp key)))
  66            ((null pursue)
  67             (and pointer
  68                  (setq inkey
  69                        (cond ((eq op 'sum) (add (cadar pointer) hold))
  70                              ((eq op 'neg) (mul -1 (add (cadar pointer) hold)))
  71                              (t (mul (cadar pointer) hold))))
  72                  (do ((recheck (cdr $const_eqns) (cdr recheck))
  73                       (minkey (mul -1 inkey)))
  74                      ((null recheck))
  75                    (let ((exp (caddar recheck))
  76                          (lab (cadar recheck)))
  77                      (cond ((alike1 exp inkey) (return lab))
  78                            ((alike1 exp minkey)
  79                             (return (mul -1 lab))))))))
  80          (let ((rhs (caddar pursue)))
  81            (cond ((alike1 negative rhs) (return (mul -1 (cadar pursue))))
  82                  ((and sum?
  83                        (mplusp rhs)
  84                        (let ((trial (sub key rhs))
  85                              (trial-2 (sub negative rhs)))
  86                          (let ((estim (1+ ($expense trial)))
  87                                (estim-2 (1+ ($expense trial-2))))
  88                            (cond ((< estim estim-2)
  89                                   (and (< estim expense)
  90                                        (setq pointer pursue
  91                                              op 'sum
  92                                              expense estim
  93                                              hold trial)))
  94                                  (t
  95                                   (and (< estim-2 expense)
  96                                        (setq pointer pursue
  97                                              op 'neg
  98                                              expense estim-2
  99                                              hold trial-2))))))))
 100                  (t
 101                   (let* ((trial (div key rhs))
 102                          (estim (1+ ($expense trial))))
 103                     (and (< estim expense)
 104                          (setq pointer pursue
 105                                op 'prod
 106                                expense estim
 107                                hold trial)))))))
 108        (log-const inkey curr-const))))
 109
 110 (defun find-constant (x)
 111    (cond ((and (symbolp x) ($constantp x)) x)
 112          ((mtimesp x)
 113           (do ((fcon x (cdr fcon)))
 114               ((null (cdr fcon)))
 115             (let ((qcon (cadr fcon)))
 116               (and (symbolp qcon) ($constantp qcon) (return qcon)))))
 117          (t nil)))
 118
 119 (defun reduce-constants (x &optional newconst)
 120    (cond ((or ($mapatom x)
 121               (and (eq (caar x) 'mtimes)
 122                    (equal (cadr x) -1)
 123                    ($mapatom (caddr x))
 124                    (null (cdddr x))))
 125           x)
 126          ((query-const-table x))
 127          ((and (eq (caar x) 'mexpt)
 128                ($constantp x)
 129                (let ((xexpon (caddr x)) (xbase (cadr x)))
 130                  (do ((p (cdr $const_eqns) (cdr p))
 131                       (nstate (integerp xexpon))
 132                       (follow $const_eqns p))
 133                      ((null p))
 134                    (let ((obj (caddar p)))
 135                      (and (mexptp obj)
 136                           (alike1 xbase (cadr obj))
 137                           (let ((inquir-expon (caddr obj)))
 138                             (let ((both-fix (and nstate (integerp inquir-expon))))
 139                               (let ((dif (cond (both-fix (- xexpon inquir-expon))
 140                                                (t (sub xexpon inquir-expon))))
 141                                     (gcd (cond (both-fix (gcd xexpon inquir-expon))
 142                                                (t ($gcd xexpon inquir-expon)))))
 143                                 (or (and (integerp dif)
 144                                          (cond ((equal 1 dif)
 145                                                 (let ((new-exp (mul (cadar p) xbase)))
 146                                                   (return (or (query-const-table new-exp)
 147                                                               (log-const new-exp newconst)))))
 148                                                ((equal -1 dif)
 149                                                 (let ((inc (new-name newconst)))
 150                                                   (rplaca (cddar p) (mul inc xbase))
 151                                                   (rplacd follow (append `(((mequal simp) ,inc ,x)) p))
 152                                                   (return inc)))))
 153                                     (or (and (integerp gcd) (equal gcd 1))
 154                                         (let ((pw1 (cond (both-fix (quotient xexpon gcd))
 155                                                          (t (div xexpon gcd))))
 156                                               (pw2 (cond (both-fix (quotient inquir-expon gcd))
 157                                                          (t (div inquir-expon gcd)))))
 158                                           (cond ((and (integerp pw2) (equal pw2 1))
 159                                                  (let ((new-exp (power (cadar p) pw1)))
 160                                                    (return (or (query-const-table new-exp)
 161                                                                (log-const new-exp newconst)))))
 162                                                 ((and (integerp pw1) (equal pw1 1))
 163                                                  (let ((inc (new-name newconst)))
 164                                                    (rplaca (cddar p) (power inc pw2))
 165                                                    (rplacd follow (append `(((mequal simp) ,inc ,x)) p))
 166                                                    (return inc)))
 167                                                 (t (let ((inc (new-name nil)))
 168                                                      (rplaca (cddar p) (power inc pw2))
 169                                                      (rplacd follow (append `(((mequal simp) ,inc ,(power xbase gcd))) p))
 170                                                      (return (log-const (power inc pw1) newconst)))))))))))))))))
 171          (($constantp x) (obtain-constant x newconst))
 172          (t
 173           (let ((opr (caar x)))
 174             (cond ((member opr '(mtimes mplus) :test #'eq)
 175                    (let* ((product (eq opr 'mtimes))
 176                           (negative (and product (equal (cadr x) -1))))
 177                      (or (and negative (null (cdddr x))
 178                               (let ((new? (query-const-table (caddr x))))
 179                                 (and new? (mul -1 new?))))
 180                          (do ((next (cdr x) (cdr next))
 181                               (itot 0)
 182                               (new)
 183                               (non-constants))
 184                              ((null next)
 185                               (cond ((and product (= (length new) 2) (equal (car new) -1))
 186                                      (muln (nconc new non-constants) nil))
 187                                     ((> (length new) 1)
 188                                      (let ((nc (obtain-constant (cond (product (muln new nil))
 189                                                                       (t (addn new nil)))
 190                                                                 newconst)))
 191                                        (cond ((not product) (addn `(,.non-constants ,nc) nil))
 192                                              ((atom nc) (muln `(,.non-constants ,nc) nil))
 193                                              (t (muln (nconc (cdr nc) non-constants) nil)))))
 194                                     ((or new non-constants)
 195                                      (let ((tot (nconc new non-constants)))
 196                                        (cond (product (muln tot nil))
 197                                              (t (addn tot nil)))))
 198                                     (t x)))
 199                            (declare (fixnum itot))
 200                            (let* ((exam (car next))
 201                                   (result (reduce-constants exam)))
 202                              (cond ((eq exam result)
 203                                     (cond (($constantp exam)
 204                                            (incf itot)
 205                                            (if (and (null new)
 206                                                     (cond (negative (> itot 2))
 207                                                           (t (> itot 1))))
 208                                                (do ((seplist (cdr x) (cdr seplist)))
 209                                                    ((eq seplist next))
 210                                                  (let ((element (car seplist)))
 211                                                    (cond (($constantp element)
 212                                                           (setq new `(,.new ,element)))
 213                                                          (t (setq non-constants `(,.non-constants ,element)))))))
 214                                            (and new (setq new `(,.new ,exam))))
 215                                           ((or new non-constants) (setq non-constants `(,.non-constants ,exam)))))
 216                                    (t
 217                                     (or new non-constants
 218                                         (do ((seplist (cdr x) (cdr seplist)))
 219                                             ((eq seplist next))
 220                                           (let ((element (car seplist)))
 221                                             (cond (($constantp element)
 222                                                    (setq new `(,.new ,element)))
 223                                                   (t (setq non-constants `(,.non-constants ,element)))))))
 224                                     (cond ((or (atom result) (minus-constantp result))
 225                                            (setq new
 226                                                  (cond ((or (atom result) (not product)) `(,.new ,result))
 227                                                        (t
 228                                                         (let ((number? (car new)))
 229                                                           (cond (($numberp number?)
 230                                                                  (let ((new-prod (mul number? result)))
 231                                                                    (cond ((mtimesp new-prod)
 232                                                                           (nconc (cdr new-prod) (ncons new-prod)))
 233                                                                          (t (nconc (cdr new) (ncons new-prod))))))
 234                                                                 (t (nconc (cdr result) new))))))))
 235                                           (t (setq non-constants `(,.non-constants ,result)))))))))))
 236                   (t
 237                    (do ((next (cdr x) (cdr next))
 238                         (new))
 239                        ((null next)
 240                         (cond ((null new) x)
 241                               ((not (eq opr 'mquotient))
 242                                (nconc (ncons (car x)) new))
 243                               (t
 244                                (let ((cnum (find-constant (car new)))
 245                                      (cden (find-constant (cadr new))))
 246                                  (cond ((and cnum cden)
 247                                         (let* ((ratio (obtain-constant (div cnum cden) newconst))
 248                                                (numerator (cond ((mtimesp (car new))
 249                                                                  (mul ratio (remove cnum (car new) :test #'eq)))
 250                                                                 (t ratio))))
 251                                           (cond ((mtimesp (cadr new))
 252                                                  (div numerator (muln (remove cden (cdadr new) :test #'eq) nil)))
 253                                                 (t numerator))))
 254                                        (t x))))))
 255                      (let* ((exam (car next))
 256                             (result (reduce-constants exam)))
 257                        (cond ((eq exam result)
 258                               (and new (setq new `(,.new ,exam))))
 259                              (t
 260                               (or new
 261                                   (do ((copy (cdr x) (cdr copy)))
 262                                       ((eq copy next))
 263                                     (setq new `(,.new ,(car copy)))))
 264                               (setq new `(,.new ,result))))))))))))
 265
 266 (defun $reduce_consts (x &optional newconstant)
 267    (cond ((atom x) x)
 268          (t (reduce-constants x newconstant))))