(FILECREATED "12-Jul-85 17:30:07" {ERIS}<LISPCORE>SOURCES>LLARITH.;29 49474
changes to: (VARS LLARITHCOMS)
previous date: "14-Apr-85 20:51:50" {ERIS}<LISPCORE>SOURCES>LLARITH.;28)
(* Copyright (c) 1982, 1983, 1984, 1985 by Xerox Corporation. All rights reserved. The following
program was created in 1982 but has not been published within the meaning of the copyright law, is
furnished under license, and may not be used, copied and/or disclosed except in accordance with the
terms of said license.)
(PRETTYCOMPRINT LLARITHCOMS)
(RPAQQ LLARITHCOMS [(LOCALVARS . T)
(COMS (* "OPCODES")
(FNS IDIFFERENCE IGREATERP IQUOTIENT)
(FNS \SLOWIPLUS2 \SLOWPLUS2 \SLOWIDIFFERENCE \SLOWDIFFERENCE \SLOWIGREATERP \SLOWLLSH1
\SLOWLLSH8 \SLOWLOGAND2 \SLOWLOGOR2 \SLOWLOGXOR2 \SLOWLRSH1 \SLOWLRSH8
\SLOWITIMES2 \SLOWTIMES2 \SLOWIQUOTIENT \SLOWQUOTIENT))
(COMS (* "IPLUS and IDIFFERENCE that smash result into their first arg")
(FNS \BOXIPLUS \BOXIDIFFERENCE))
(* "subfunctions")
(FNS \MAKENUMBER)
(FNS OVERFLOW)
(INITVARS (\OVERFLOW T))
(E (RESETSAVE (RADIX 10Q)))
(CONSTANTS (MAX.SMALLP 177777Q)
(MIN.SMALLP -200000Q)
(MAX.FIXP 17777777777Q)
(MIN.FIXP -20000000000Q)
(\SIGNBIT 100000Q))
(FNS \GETBASEFIXP \PUTBASEFIXP \PUTBASEFIXP.UFN)
(EXPORT (DECLARE: DONTCOPY (RECORDS FIXP)
(CONSTANTS (MAX.SMALL.INTEGER 177777Q)
(MAX.POS.HINUM 77777Q))
(MACROS .UNBOX. .NEGATE. .LLSH1. .LRSH1. .BOXIPLUS.)))
(FNS EQP FIX IQUOTIENT IREMAINDER LLSH LRSH LSH RSH)
(DECLARE: EVAL@COMPILE DONTCOPY (MACROS NBITS.OR.LESS .SUBSMALL. \IQUOTREM))
(* "Machine independent arithmetic functions")
(FNS MINUSP ILESSP IMINUS IPLUS ITIMES LOGAND LOGOR LOGXOR SUB1 ZEROP ADD1 GCD IEQP
INTEGERLENGTH)
(FNS ABS DIFFERENCE GREATERP PLUS QUOTIENT REMAINDER LESSP MINUS TIMES)
(FNS FMINUS FREMAINDER)
(FNS RANDSET RAND EXPT)
(DECLARE: DONTEVAL@LOAD DOCOPY (VARS (RANDSTATE)
(\TOL 9.999992E-6)))
(GLOBALVARS RANDSTATE \TOL)
[COMS (FNS PutUnboxed \PUTFIXP \PUTSWAPPEDFIXP \HINUM \LONUM)
(EXPORT (DECLARE: DONTCOPY (MACROS PutUnboxed]
(DECLARE: DONTEVAL@LOAD DOEVAL@COMPILE DONTCOPY COMPILERVARS
(ADDVARS (NLAMA)
(NLAML)
(LAMA MIN MAX IMIN IMAX FMIN FMAX ODDP EVENP TIMES PLUS LOGXOR LOGOR
LOGAND ITIMES IPLUS)))
(COMS (FNS POWEROFTWOP IMOD EVENP ODDP)
(DECLARE: DONTCOPY (MACROS .2↑NP.)))
(COMS (* * MIN and MAX)
(FNS FLESSP FMAX FMIN GEQ IGEQ ILEQ IMAX IMIN LEQ MAX MIN)
(DECLARE: EVAL@COMPILE (ADDVARS (GLOBALVARS MAX.INTEGER MIN.INTEGER MAX.FLOAT MIN.FLOAT]
)
(DECLARE: DOEVAL@COMPILE DONTCOPY
(LOCALVARS . T)
)
(* "OPCODES")
(DEFINEQ
(IDIFFERENCE
[LAMBDA (X Y) (* lmm "11-FEB-82 14:02")
((OPCODES IDIFFERENCE)
X Y])
(IGREATERP
[LAMBDA (X Y) (* lmm "11-FEB-82 14:02")
((OPCODES IGREATERP)
X Y])
(IQUOTIENT
[LAMBDA (X Y) (* lmm "11-FEB-82 14:02")
((OPCODES IQUOTIENT)
X Y])
)
(DEFINEQ
(\SLOWIPLUS2
[LAMBDA (X Y) (* lmm "12-Apr-85 08:51")
(\CALLME (QUOTE IPLUS))
(PROG (HX LX HY LY SIGNX)
(.UNBOX. X HX LX (GO RETBIG))
(.UNBOX. Y HY LY (GO RETBIG))
(SETQ SIGNX (IGREATERP HX MAX.POS.HINUM))
[SETQ HX (COND
[(IGREATERP HX (IDIFFERENCE MAX.SMALL.INTEGER HY))
(IDIFFERENCE HX (ADD1 (IDIFFERENCE MAX.SMALL.INTEGER HY]
(T (IPLUS HX HY] (* Add high parts)
[SETQ LX (COND
[(IGREATERP LX (IDIFFERENCE MAX.SMALL.INTEGER LY))
(* Carry into high part.)
[SETQ HX (COND
((EQ HX MAX.SMALL.INTEGER)
0)
(T (ADD1 HX]
(IDIFFERENCE LX (ADD1 (IDIFFERENCE MAX.SMALL.INTEGER LY]
(T (IPLUS LX LY]
(COND
((AND (EQ SIGNX (IGREATERP HY MAX.POS.HINUM))
(NEQ SIGNX (IGREATERP HX MAX.POS.HINUM)))
(* overflow occurs if X and Y are same sign, but result
is opposite sign)
(GO RETBIG)))
(RETURN (\MAKENUMBER HX LX))
RETBIG
(RETURN (\BIGNUM.PLUS X Y])
(\SLOWPLUS2
[LAMBDA (X Y) (* lmm "21-Aug-84 16:20")
(* UFN for PLUS Microcode generally handles the case of
two args both FIXPs)
(\CALLME (QUOTE PLUS))
(PROG NIL
LP (RETURN (COND
((OR (FLOATP X)
(FLOATP Y))
(FPLUS X Y))
((NOT (FIXP X))
(SETQ X (LISPERROR "NON-NUMERIC ARG" X T))
(GO LP))
((NOT (FIXP Y))
(SETQ Y (LISPERROR "NON-NUMERIC ARG" Y T))
(GO LP))
(T (IPLUS X Y])
(\SLOWIDIFFERENCE
[LAMBDA (X Y) (* lmm "12-Apr-85 07:37")
(\CALLME (QUOTE IDIFFERENCE))
(PROG (HX LX HY LY SIGNX)
(.UNBOX. X HX LX (GO RETBIG))
(.UNBOX. Y HY LY (GO RETBIG)) (* Allow this unboxing before the following test so
that error checking will be performed on Y)
[COND
((EQ Y 0)
(RETURN (\MAKENUMBER HX LX]
(.NEGATE. HY LY)
(SETQ SIGNX (IGREATERP HX MAX.POS.HINUM))
(COND
([COND
((AND (ZEROP LY)
(EQ HY \SIGNBIT)) (* Y = -Y = Min.integer. Overflow occurs if X is
positive)
(SETQ HX (LOGXOR HX HY))
(NOT SIGNX))
(T [SETQ HX (COND
[(IGREATERP HX (IDIFFERENCE MAX.SMALL.INTEGER HY))
(IDIFFERENCE HX (ADD1 (IDIFFERENCE MAX.SMALL.INTEGER HY]
(T (IPLUS HX HY] (* Add high parts)
[SETQ LX (COND
[(IGREATERP LX (IDIFFERENCE MAX.SMALL.INTEGER LY))
(* Carry into high part.)
[SETQ HX (COND
((EQ HX MAX.SMALL.INTEGER)
0)
(T (ADD1 HX]
(IDIFFERENCE LX (ADD1 (IDIFFERENCE MAX.SMALL.INTEGER LY]
(T (IPLUS LX LY] (* overflow occurs if X and Y are same sign, but result
is opposite sign)
(AND (EQ SIGNX (IGREATERP HY MAX.POS.HINUM))
(NEQ SIGNX (IGREATERP HX MAX.POS.HINUM]
(GO RETBIG)))
(RETURN (\MAKENUMBER HX LX))
RETBIG
(RETURN (\BIGNUM.DIFFERENCE X Y])
(\SLOWDIFFERENCE
[LAMBDA (X Y) (* lmm "21-Aug-84 16:21")
(* UFN for DIFFERENCE Microcode generally handles the
case of two args both FIXPs)
(\CALLME (QUOTE DIFFERENCE))
(PROG NIL
LP (RETURN (COND
((OR (FLOATP X)
(FLOATP Y))
(FDIFFERENCE X Y))
((NOT (FIXP X))
(SETQ X (LISPERROR "NON-NUMERIC ARG" X T))
(GO LP))
((NOT (FIXP Y))
(SETQ Y (LISPERROR "NON-NUMERIC ARG" Y T))
(GO LP))
(T (IDIFFERENCE X Y])
(\SLOWIGREATERP
[LAMBDA (X Y) (* lmm "12-Apr-85 07:35")
(\CALLME (QUOTE IGREATERP))
(PROG (HX LX HY LY)
(.UNBOX. X HX LX (GO RETBIG))
(.UNBOX. Y HY LY (GO RETBIG))
[RETURN (COND
((EQ HX HY)
(IGREATERP LX LY))
(T (IGREATERP (LOGXOR HX \SIGNBIT)
(LOGXOR HY \SIGNBIT]
RETBIG
(RETURN (EQ 1 (\BIGNUM.COMPARE X Y])
(\SLOWLLSH1
[LAMBDA (X) (* lmm "13-OCT-82 15:27")
(PROG (LO HI)
(.UNBOX. X HI LO)
(RETURN (\MAKENUMBER (IPLUS (LLSH (LOGAND HI 77777Q)
1)
(COND
((IGREATERP LO 77777Q)
1)
(T 0)))
(LLSH (LOGAND LO 77777Q)
1])
(\SLOWLLSH8
[LAMBDA (X) (* lmm "13-OCT-82 15:28")
(PROG (HI LO)
(.UNBOX. X HI LO)
(RETURN (\MAKENUMBER (IPLUS (LLSH (LOGAND HI 377Q)
10Q)
(LRSH LO 10Q))
(LLSH (LOGAND LO 377Q)
10Q])
(\SLOWLOGAND2
[LAMBDA (X Y) (* lmm "12-Apr-85 07:44")
(\CALLME (QUOTE LOGAND))
(PROG (XH XL YH YL)
(.UNBOX. X XH XL (GO RETBIG))
(.UNBOX. Y YH YL (GO RETBIG))
(RETURN (\MAKENUMBER (LOGAND XH YH)
(LOGAND XL YL)))
RETBIG
(RETURN (\BIGNUM.LOGAND X Y])
(\SLOWLOGOR2
[LAMBDA (X Y) (* lmm "12-Apr-85 07:48")
(\CALLME (QUOTE LOGOR))
(PROG (XH XL YH YL)
(.UNBOX. X XH XL (GO RETBIG))
(.UNBOX. Y YH YL (GO RETBIG))
(RETURN (\MAKENUMBER (LOGOR XH YH)
(LOGOR XL YL)))
RETBIG
(RETURN (\BIGNUM.LOGOR X Y])
(\SLOWLOGXOR2
[LAMBDA (X Y) (* lmm "12-Apr-85 07:51")
(\CALLME (QUOTE LOGXOR))
(PROG (XH XL YH YL)
(.UNBOX. X XH XL (GO RETBIG))
(.UNBOX. Y YH YL (GO RETBIG))
(RETURN (\MAKENUMBER (LOGXOR XH YH)
(LOGXOR XL YL)))
RETBIG
(RETURN (\BIGNUM.LOGXOR X Y])
(\SLOWLRSH1
(LAMBDA (X) (* JonL "27-Sep-84 22:59")
(PROG (HI LO)
(.UNBOX. X HI LO)
(RETURN (\MAKENUMBER (LRSH HI 1)
(IPLUS (LRSH LO 1)
(COND
((EQ 0 (LOGAND HI 1))
0)
(T 32768))))))))
(\SLOWLRSH8
[LAMBDA (X) (* lmm "13-OCT-82 15:29")
(PROG (HI LO)
(.UNBOX. X HI LO)
(RETURN (\MAKENUMBER (LRSH HI 10Q)
(IPLUS (LLSH (LOGAND HI 377Q)
10Q)
(LRSH LO 10Q])
(\SLOWITIMES2
[LAMBDA (X Y) (* lmm "12-Apr-85 08:52")
(\CALLME (QUOTE ITIMES))
(COND
((OR (EQ X 0)
(EQ Y 0))
0)
(T (PROG (HX HY LX LY SIGN (HR 0)
(LR 0)
CARRY)
(.UNBOX. X HX LX (GO RETBIG))
(.UNBOX. Y HY LY (GO RETBIG))
(COND
((IGREATERP HX MAX.POS.HINUM)
(if (EQUAL X MIN.FIXP)
then (GO RETBIG))
(.NEGATE. HX LX)
(SETQ SIGN T)))
[COND
((IGREATERP HY MAX.POS.HINUM)
(if (EQUAL Y MIN.FIXP)
then (GO RETBIG))
(.NEGATE. HY LY)
(SETQ SIGN (NOT SIGN]
(COND
((NEQ HY 0)
(COND
((NEQ HX 0)
(GO OVER)))
(swap LX LY)
(swap HX HY)))
MLP [COND
([ODDP (PROG1 LY (SETQ LY (LRSH LY 1]
(COND
((IGREATERP LR (IDIFFERENCE MAX.SMALL.INTEGER LX))
(* low parts overflow)
(* make the low word be the less significant bits and
return the carry.)
[SETQ LR (IDIFFERENCE LR (IDIFFERENCE MAX.SMALL.INTEGER (SUB1 LX]
(SETQ CARRY 1))
(T (* no carry just add the low halves.)
(SETQ LR (IPLUS LR LX))
(SETQ CARRY 0)))
(* the low order part of the answer has been set and CARRY is the numeric value of the carry from the low part
either 0 or 1)
(COND
((IGREATERP (SETQ HR (IPLUS HR HX CARRY))
MAX.POS.HINUM)
(COND
((AND (EQ LY 0)
SIGN
(EQ HR (ADD1 MAX.POS.HINUM))
(EQ LR 0))
(RETURN MIN.FIXP)))
(GO OVER]
(COND
((ZEROP LY)
(GO RET)))
(COND
((IGEQ HX (LRSH (ADD1 MAX.POS.HINUM)
1))
(GO OVERTEST)))
(.LLSH1. HX LX)
(GO MLP)
OVERTEST
(COND
((AND (EQ HX (LRSH (ADD1 MAX.POS.HINUM)
1))
(ZEROP LX)
SIGN
(EQ LY 1)
(EQ HR 0)
(EQ LR 0)) (* odd special case)
(RETURN MIN.FIXP)))
OVER(GO RETBIG)
RET (COND
(SIGN (.NEGATE. HR LR)))
(RETURN (\MAKENUMBER HR LR))
RETBIG
(RETURN (\BIGNUM.TIMES X Y])
(\SLOWTIMES2
[LAMBDA (X Y) (* lmm "21-Aug-84 16:22")
(* UFN for TIMES Microcode generally handles the case of
two args both FIXPs)
(\CALLME (QUOTE TIMES))
(PROG NIL
LP (RETURN (COND
((OR (FLOATP X)
(FLOATP Y))
(FTIMES X Y))
((NOT (FIXP X))
(SETQ X (LISPERROR "NON-NUMERIC ARG" X T))
(GO LP))
((NOT (FIXP Y))
(SETQ Y (LISPERROR "NON-NUMERIC ARG" Y T))
(GO LP))
(T (ITIMES X Y])
(\SLOWIQUOTIENT
[LAMBDA (X Y) (* lmm " 2-Jul-84 17:12")
(\CALLME (QUOTE IQUOTIENT))
(\IQUOTREM X Y X)
X])
(\SLOWQUOTIENT
[LAMBDA (X Y) (* lmm "21-Aug-84 16:22")
(* UFN for QUOTIENT Microcode generally handles the case
of two args both FIXPs)
(\CALLME (QUOTE QUOTIENT))
(PROG NIL
LP (RETURN (COND
((OR (FLOATP X)
(FLOATP Y))
(FQUOTIENT X Y))
((NOT (FIXP X))
(SETQ X (LISPERROR "NON-NUMERIC ARG" X T))
(GO LP))
((NOT (FIXP Y))
(SETQ Y (LISPERROR "NON-NUMERIC ARG" Y T))
(GO LP))
(T (IQUOTIENT X Y])
)
(* "IPLUS and IDIFFERENCE that smash result into their first arg")
(DEFINEQ
(\BOXIPLUS
[LAMBDA (X Y) (* lmm " 8-Aug-84 11:49")
(* UFN for BOXIPLUS ipcode)
(.BOXIPLUS. X Y])
(\BOXIDIFFERENCE
[LAMBDA (X Y) (* lmm " 8-Aug-84 11:49")
(PROG ((HX (\GETBASE X 0))
(LX (\GETBASE X 1))
HY LY)
(.UNBOX. Y HY LY)
(.NEGATE. HY LY)
[SETQ HX (COND
[(IGREATERP HX (IDIFFERENCE MAX.SMALL.INTEGER HY))
(IDIFFERENCE HX (ADD1 (IDIFFERENCE MAX.SMALL.INTEGER HY]
(T (IPLUS HX HY] (* Add high parts)
[\PUTBASE X 1 (COND
[(IGREATERP LX (IDIFFERENCE MAX.SMALL.INTEGER LY))
(* Carry into high part.)
[SETQ HX (COND
((EQ HX MAX.SMALL.INTEGER)
0)
(T (ADD1 HX]
(IDIFFERENCE LX (ADD1 (IDIFFERENCE MAX.SMALL.INTEGER LY]
(T (IPLUS LX LY]
(\PUTBASE X 0 HX)
(RETURN X])
)
(* "subfunctions")
(DEFINEQ
(\MAKENUMBER
(LAMBDA (N0 N1) (* JonL " 1-Jan-84 00:11")
(* used as punt case for arith opcodes which create
large numbers)
(SETQ N1 (.COERCE.TO.SMALLPOSP. N1))
(SELECTC (SETQ N0 (.COERCE.TO.SMALLPOSP. N0))
(0 N1)
(65535 (* This is a word's worth of 1 bits)
(\VAG2 \SmallNegHi N1))
(create FIXP
HINUM ← N0
LONUM ← N1))))
)
(DEFINEQ
(OVERFLOW
[LAMBDA (FLG) (* lmm: 14-JAN-76 1 6)
(PROG1 \OVERFLOW (SETQ \OVERFLOW (SELECTQ FLG
(NIL NIL)
(T T)
0])
)
(RPAQ? \OVERFLOW T)
(DECLARE: EVAL@COMPILE
(RPAQQ MAX.SMALLP 177777Q)
(RPAQQ MIN.SMALLP -200000Q)
(RPAQQ MAX.FIXP 17777777777Q)
(RPAQQ MIN.FIXP -20000000000Q)
(RPAQQ \SIGNBIT 100000Q)
(CONSTANTS (MAX.SMALLP 177777Q)
(MIN.SMALLP -200000Q)
(MAX.FIXP 17777777777Q)
(MIN.FIXP -20000000000Q)
(\SIGNBIT 100000Q))
)
(DEFINEQ
(\GETBASEFIXP
[LAMBDA (BASE OFFST) (* lmm " 5-Jan-85 23:11")
([LAMBDA (\NewBaseAddr)
(\MAKENUMBER (\GETBASE \NewBaseAddr 0)
(\GETBASE \NewBaseAddr 1]
(\ADDBASE BASE OFFST])
(\PUTBASEFIXP
[LAMBDA (BASE OFFST VAL) (* lmm " 5-Jan-85 23:16")
(PROG (HI LO)
(.XUNBOX. VAL HI LO)
(\PUTBASE BASE OFFST HI)
(\PUTBASE BASE (ADD1 OFFST)
LO)
VAL (RETURN VAL])
(\PUTBASEFIXP.UFN
[LAMBDA (BASE VAL OFFST) (* lmm " 5-Jan-85 23:25")
(PROG (HI LO)
(.XUNBOX. VAL HI LO)
(\PUTBASE BASE OFFST HI)
(\PUTBASE BASE (ADD1 OFFST)
LO)
VAL (RETURN VAL])
)
(* FOLLOWING DEFINITIONS EXPORTED)
(DECLARE: DONTCOPY
[DECLARE: EVAL@COMPILE
(BLOCKRECORD FIXP ((HINUM WORD)
(LONUM WORD))
(CREATE (CREATECELL \FIXP))
(TYPE? (EQ (NTYPX DATUM)
\FIXP)))
]
(DECLARE: EVAL@COMPILE
(RPAQQ MAX.SMALL.INTEGER 177777Q)
(RPAQQ MAX.POS.HINUM 77777Q)
(CONSTANTS (MAX.SMALL.INTEGER 177777Q)
(MAX.POS.HINUM 77777Q))
)
(DECLARE: EVAL@COMPILE
[PUTPROPS .UNBOX. MACRO ((V HV LV BIGNUMFORM)
(PROG NIL UBLP (SELECTC (NTYPX V)
(\FIXP (SETQ HV (ffetch (FIXP HINUM)
of V))
(SETQ LV (ffetch (FIXP LONUM)
of V)))
[\SMALLP (COND ((ILEQ 0 V)
(SETQ HV 0)
(SETQ LV V))
(T (SETQ HV 177777Q)
(SETQ LV (\LOLOC V]
(\FLOATP (SETQ V (\FIXP.FROM.FLOATP V))
(GO UBLP))
(if (TYPENAMEP V (QUOTE BIGNUM))
then
(if (QUOTE BIGNUMFORM)
then BIGNUMFORM else (SETQ V (\LISPERROR V "ARG NOT FIXP"
T))
(GO UBLP))
else
(SETQ V (LISPERROR "NON-NUMERIC ARG" V T))
(GO UBLP]
[PUTPROPS .NEGATE. MACRO ((HY LY)
(COND [(EQ 0 LY)
(AND (NEQ HY 0)
(SETQ HY (ADD1 (IDIFFERENCE MAX.SMALL.INTEGER HY]
(T (SETQ HY (IDIFFERENCE MAX.SMALL.INTEGER HY))
(SETQ LY (ADD1 (IDIFFERENCE MAX.SMALL.INTEGER LY]
[PUTPROPS .LLSH1. MACRO ((HI LO)
(* shift the pair left one, assuming no overflow)
(SETQ HI (LLSH HI 1))
(SETQ LO (LLSH (COND ((IGREATERP LO MAX.POS.HINUM)
(add HI 1)
(LOGAND LO MAX.POS.HINUM))
(T LO))
1]
[PUTPROPS .LRSH1. MACRO ((HI LO)
(SETQ LO (LRSH LO 1))
[COND ((NEQ (LOGAND HI 1)
0)
(SETQ LO (IPLUS LO \SIGNBIT]
(SETQ HI (LRSH HI 1]
[PUTPROPS .BOXIPLUS. MACRO (OPENLAMBDA (X Y)
(PROG ((HX (\GETBASE X 0))
(LX (\GETBASE X 1))
HY LY)
(.UNBOX. Y HY LY)
[SETQ HX (COND [(IGREATERP HX (IDIFFERENCE
MAX.SMALL.INTEGER HY))
(IDIFFERENCE HX (ADD1 (IDIFFERENCE
MAX.SMALL.INTEGER HY]
(T (IPLUS HX HY]
(* Add high parts)
[\PUTBASE X 1 (COND [(IGREATERP LX (IDIFFERENCE
MAX.SMALL.INTEGER LY))
(* Carry into high part.)
[SETQ HX (COND ((EQ HX
MAX.SMALL.INTEGER)
0)
(T (ADD1 HX]
(IDIFFERENCE LX
(ADD1 (IDIFFERENCE
MAX.SMALL.INTEGER LY]
(T (IPLUS LX LY]
(\PUTBASE X 0 HX)
(RETURN X]
)
)
(* END EXPORTED DEFINITIONS)
(DEFINEQ
(EQP
[LAMBDA (X Y) (* lmm "21-JAN-82 08:20")
(COND
((EQ X Y))
[(AND (NUMBERP X)
(NUMBERP Y))
(COND
((OR (FLOATP X)
(FLOATP Y))
(FEQP X Y))
(T (IEQP X Y]
((EQ (NTYPX X)
(NTYPX Y))
(SELECTC (NTYPX X)
(\STACKP (EQ (fetch (STACKP EDFXP) of X)
(fetch (STACKP EDFXP) of Y)))
(\ARRAYP (AND (EQ (fetch (ARRAYP TYP) of X)
\ST.CODE)
(EQDEFP X Y)))
NIL))
(T NIL])
(FIX
[LAMBDA (N) (* lmm "18-APR-80 18:08")
(* FIX compiles open)
(IPLUS N 0])
(IQUOTIENT
[LAMBDA (X Y) (* lmm "11-FEB-82 14:02")
((OPCODES IQUOTIENT)
X Y])
(IREMAINDER
[LAMBDA (X Y) (* edited: "29-APR-82 05:01")
(\IQUOTREM X Y NIL Y)
Y])
(LLSH
[LAMBDA (X N) (* lmm "13-OCT-82 15:30")
(COND
((IGREATERP 0 N)
(LRSH X (IMINUS N)))
(T (PROG (XHI XLO)
(.UNBOX. X XHI XLO)
(COND
((IGREATERP N 37Q)
(RETURN 0)))
[COND
((IGREATERP N 17Q)
(SETQ XHI XLO)
(SETQ XLO 0)
(SETQ N (IDIFFERENCE N 20Q]
[COND
((IGREATERP N 7)
(SETQ XHI (IPLUS (LLSH (LOGAND XHI 377Q)
10Q)
(LRSH XLO 10Q)))
(SETQ XLO (LLSH (LOGAND XLO 377Q)
10Q))
(SETQ N (IDIFFERENCE N 10Q]
(FRPTQ N (SETQ XHI (LOGAND XHI MAX.POS.HINUM))
(.LLSH1. XHI XLO))
(RETURN (\MAKENUMBER XHI XLO])
(LRSH
[LAMBDA (X N) (* lmm "13-OCT-82 15:30")
(* assumes case where n is constant and 10Q or 1 handled
in microcode or by \SLOWLRSHn)
(COND
((IGREATERP 0 N)
(LLSH X (IMINUS N)))
(T (PROG (XHI XLO)
(.UNBOX. X XHI XLO)
(COND
((IGREATERP N 37Q)
(RETURN 0)))
[COND
((IGREATERP N 17Q)
(SETQ XLO XHI)
(SETQ XHI 0)
(SETQ N (IDIFFERENCE N 20Q]
[COND
((IGREATERP N 7)
(SETQ XLO (IPLUS (LRSH XLO 10Q)
(LLSH (LOGAND XHI 377Q)
10Q)))
(SETQ XHI (LRSH XHI 10Q))
(SETQ N (IDIFFERENCE N 10Q]
(FRPTQ N (.LRSH1. XHI XLO))
(RETURN (\MAKENUMBER XHI XLO])
(LSH
[LAMBDA (X N) (* lmm "12-Apr-85 07:55")
(COND
[(ILEQ N 0)
(COND
((EQ N 0)
X)
(T (RSH X (IMINUS N]
((EQ X 0)
0)
((IGREATERP N (CONSTANT (INTEGERLENGTH MAX.FIXP)))
(\BIGNUM.LSH X N))
(T (FRPTQ N (SETQ X (IPLUS X X)))
X])
(RSH
[LAMBDA (X N) (* lmm "12-Apr-85 07:55")
(COND
((IGREATERP 0 N)
(LSH X (IMINUS N)))
((EQ X 0)
0)
(T (PROG (XHI XLO)
(.UNBOX. X XHI XLO (GO RETBIG))
[COND
((IGREATERP N 37Q)
(RETURN (COND
((IGREATERP XHI 77777Q) (* X WAS NEGATIVE)
-1)
(T 0]
[COND
((IGREATERP N 17Q)
(SETQ XLO XHI)
(SETQ XHI (COND
((IGREATERP XHI 77777Q)
177777Q)
(T 0)))
(SETQ N (IDIFFERENCE N 20Q]
[COND
((IGREATERP N 7)
(SETQ XLO (IPLUS (LRSH XLO 10Q)
(LLSH (LOGAND XHI 377Q)
10Q)))
[SETQ XHI (IPLUS (LRSH XHI 10Q)
(COND
((IGREATERP XHI 77777Q)
177400Q)
(T 0]
(SETQ N (IDIFFERENCE N 10Q]
[FRPTQ N [SETQ XLO (IPLUS (LRSH XLO 1)
(COND
((EQ 0 (LOGAND XHI 1))
0)
(T 100000Q]
(SETQ XHI (IPLUS (LRSH XHI 1)
(LOGAND XHI 100000Q]
(RETURN (\MAKENUMBER XHI XLO))
RETBIG
(RETURN (\BIGNUM.LSH X (IMINUS N])
)
(DECLARE: EVAL@COMPILE DONTCOPY
(DECLARE: EVAL@COMPILE
[PUTPROPS NBITS.OR.LESS MACRO ((X N)
(ILESSP X (CONSTANT (LLSH 1 N]
[PUTPROPS .SUBSMALL. MACRO ((X Y)
(* Subtract Y from X, returning the borrow out of the next word)
(COND ((ILEQ Y X)
(SETQ X (IDIFFERENCE X Y))
0)
(T [SETQ X (ADD1 (IDIFFERENCE MAX.SMALL.INTEGER (IDIFFERENCE Y X]
1]
[PUTPROPS \IQUOTREM MACRO ((X Y QUO REM)
(PROG (HX LX HY LY SIGNQUOTIENT SIGNREMAINDER (CNT 0)
(HZ 0)
(LZ 0))
(.UNBOX. X HX LX (GO RETBIG))
(.UNBOX. Y HY LY (GO RETBIG))
[COND ((IGREATERP HX MAX.POS.HINUM)
(.NEGATE. HX LX)
(SETQ SIGNQUOTIENT (SETQ SIGNREMAINDER T]
(* Remainder has sign of dividend)
[COND ((IGREATERP HY MAX.POS.HINUM)
(.NEGATE. HY LY)
(SETQ SIGNQUOTIENT (NOT SIGNQUOTIENT]
(COND ((NEQ HX 0)
(GO BIGDIVIDEND))
((NEQ HY 0)
(* Y is big, X is small, so result is 0)
(GO DONE))
((EQ 0 LX)
(GO RET0))
((EQ 0 LY)
(GO DIVZERO))
((EQ LY 1)
(SETQ LZ LX)
(SETQ LX 0)
(GO DONE)))
(* here we are dividing small X by small Y, and we know Y gt 1)
LP1
(* shift Y left until it is as big as X, and count how many times)
(COND ((AND (ILESSP LY LX)
(ILEQ LY MAX.POS.HINUM))
(SETQ LY (LLSH LY 1))
(SETQ CNT (ADD1 CNT))
(GO LP1)))
LP2
(* now start dividing Y into X by subtracting and shifting, ending up with Y shifted
back where it started)
[COND ((ILEQ LY LX)
(SETQ LX (IDIFFERENCE LX LY))
(* Y divides X once, so add bit into quotient)
(SETQ LZ (ADD1 LZ]
(SETQ LY (LRSH LY 1))
(SETQ CNT (SUB1 CNT))
(COND ((IGEQ CNT 0)
(SETQ LZ (LLSH LZ 1))
(GO LP2)))
(GO DONE)
BIGDIVIDEND
(* X is big, so result may be big. Algorithm is same as above, but everything is
doubled in length)
(COND ((EQ 0 HY)
(COND ((EQ 0 (SETQ HY LY))
(GO DIVZERO))
((AND SIGNREMAINDER (NULL SIGNQUOTIENT)
(EQ 1 LY)
(EQ HX \SIGNBIT)
(EQ 0 LX))
(* Means that X is MIN.FIXP and Y is -1)
(GO RETBIG)))
(SETQ LY 0)
(SETQ CNT 20Q))
((AND SIGNREMAINDER (NULL SIGNQUOTIENT)
(EQ 0 LX)
(EQ HX \SIGNBIT)
(EQ 0 HY)
(EQ 1 LY))
(* Means that X is MIN.FIXP and Y is -1)
(GO RETBIG)))
BIGLP
(COND ((AND (OR (AND (EQ HY HX)
(ILESSP LY LX))
(ILESSP HY HX))
(ILESSP HY MAX.POS.HINUM))
(.LLSH1. HY LY)
(SETQ CNT (ADD1 CNT))
(GO BIGLP)))
BIGLP2
(COND ((OR (ILESSP HY HX)
(AND (EQ HY HX)
(ILEQ LY LX)))
(* Y divides X, so subtract Y from X and put a bit in quotient)
(SETQ HX (IDIFFERENCE (IDIFFERENCE HX HY)
(.SUBSMALL. LX LY)))
(SETQ LZ (ADD1 LZ))
(* note that this never overflows, because of the preceding left shift)))
(.LRSH1. HY LY)
(SETQ CNT (SUB1 CNT))
(COND ((IGEQ CNT 0)
(.LLSH1. HZ LZ)
(GO BIGLP2)))
DONE
[COND ((QUOTE REM)
(* remainder is left in X)
(COND (SIGNREMAINDER (.NEGATE. HX LX)))
(SETQ REM (\MAKENUMBER HX LX]
[COND ((QUOTE QUO)
(COND (SIGNQUOTIENT (.NEGATE. HZ LZ)))
(SETQ QUO (\MAKENUMBER HZ LZ]
(RETURN)
DIVZERO
(SELECTQ \OVERFLOW (T (ERROR "DIVIDE BY ZERO" Y))
(GO RET0))
RET0
(COND ((QUOTE REM)
(SETQ REM 0)))
(COND ((QUOTE QUO)
(SETQ QUO 0)))
(RETURN)
RETBIG
(if (QUOTE QUO)
then
(SETQ QUO (\BIGNUM.QUOTIENT X Y)))
(if (QUOTE REM)
then
(SETQ REM (\BIGNUM.REMAINDER X Y)))
(RETURN]
)
)
(* "Machine independent arithmetic functions")
(DEFINEQ
(MINUSP
[LAMBDA (X) (* lmm "17-DEC-80 20:56")
(COND
((FLOATP X)
(FGREATERP 0.0 X))
(T (IGREATERP 0 X])
(ILESSP
[LAMBDA (X Y)
(IGREATERP Y X])
(IMINUS
[LAMBDA (X)
(IDIFFERENCE 0 X])
(IPLUS
[LAMBDA N (* lmm " 2-MAR-82 10:05")
(* called only by interpreted code -
this defn relies on fact that compiler turns IPLUS calls
into sequences of opcodes)
(SELECTQ N
(2 (IPLUS (ARG N 1)
(ARG N 2)))
(1 (IPLUS (ARG N 1)))
(0 (IPLUS))
(PROG ((R (IPLUS (ARG N 1)
(ARG N 2)
(ARG N 3)))
(J 4))
LP (COND
((ILEQ J N)
(SETQ R (IPLUS R (ARG N J)))
(SETQ J (ADD1 J))
(GO LP)))
(RETURN R])
(ITIMES
[LAMBDA N (* lmm " 2-MAR-82 10:05")
(* called only by interpreted code -
this defn relies on fact that compiler turns ITIMES
calls into sequences of opcodes)
(SELECTQ N
(2 (ITIMES (ARG N 1)
(ARG N 2)))
(1 (ITIMES (ARG N 1)))
(0 (ITIMES))
(PROG ((R (ITIMES (ARG N 1)
(ARG N 2)
(ARG N 3)))
(J 4))
LP (COND
((ILEQ J N)
(SETQ R (ITIMES R (ARG N J)))
(SETQ J (ADD1 J))
(GO LP)))
(RETURN R])
(LOGAND
[LAMBDA N (* lmm " 2-MAR-82 10:05")
(* called only by interpreted code -
this defn relies on fact that compiler turns LOGAND
calls into sequences of opcodes)
(SELECTQ N
(2 (LOGAND (ARG N 1)
(ARG N 2)))
(1 (LOGAND (ARG N 1)))
(0 (LOGAND))
(PROG ((R (LOGAND (ARG N 1)
(ARG N 2)
(ARG N 3)))
(J 4))
LP (COND
((ILEQ J N)
(SETQ R (LOGAND R (ARG N J)))
(SETQ J (ADD1 J))
(GO LP)))
(RETURN R])
(LOGOR
[LAMBDA N (* lmm " 2-MAR-82 10:05")
(* called only by interpreted code -
this defn relies on fact that compiler turns LOGOR calls
into sequences of opcodes)
(SELECTQ N
(2 (LOGOR (ARG N 1)
(ARG N 2)))
(1 (LOGOR (ARG N 1)))
(0 (LOGOR))
(PROG ((R (LOGOR (ARG N 1)
(ARG N 2)
(ARG N 3)))
(J 4))
LP (COND
((ILEQ J N)
(SETQ R (LOGOR R (ARG N J)))
(SETQ J (ADD1 J))
(GO LP)))
(RETURN R])
(LOGXOR
[LAMBDA N (* lmm " 2-MAR-82 10:05")
(* called only by interpreted code -
this defn relies on fact that compiler turns LOGXOR
calls into sequences of opcodes)
(SELECTQ N
(2 (LOGXOR (ARG N 1)
(ARG N 2)))
(1 (LOGXOR (ARG N 1)))
(0 (LOGXOR))
(PROG ((R (LOGXOR (ARG N 1)
(ARG N 2)
(ARG N 3)))
(J 4))
LP (COND
((ILEQ J N)
(SETQ R (LOGXOR R (ARG N J)))
(SETQ J (ADD1 J))
(GO LP)))
(RETURN R])
(SUB1
[LAMBDA (X) (* lmm " 5-MAR-80 23:07")
(IDIFFERENCE X 1])
(ZEROP
(LAMBDA (X) (* JonL "27-Sep-84 22:54")
(\MACRO.MX (ZEROP X))))
(ADD1
[LAMBDA (X)
(IPLUS X 1])
(GCD
[LAMBDA (N1 N2) (* jds "10-Jan-85 15:42")
(* Greatest common divisor, using Euler's Method)
(COND
((EQ 0 N2)
N1)
((MINUSP N2) (* GCD is always positive)
(GCD (MINUS N2)
N1))
(T (GCD N2 (IREMAINDER N1 N2])
(IEQP
(LAMBDA (X Y) (* JonL " 1-May-84 22:23")
(EQ 0 (IDIFFERENCE X Y))))
(INTEGERLENGTH
[LAMBDA (X) (* lmm "12-Apr-85 16:21")
(SELECTC (NTYPX X)
[\SMALLP [COND
((ILESSP X 0)
(SETQ X (IDIFFERENCE 0 X]
(COND
((NBITS.OR.LESS X 20Q)
(COND
((NBITS.OR.LESS X 10Q)
(COND
((NBITS.OR.LESS X 4)
(COND
((NBITS.OR.LESS X 2)
(COND
((NBITS.OR.LESS X 1)
(COND
((EQ X 0)
0)
(T 1)))
(T 2)))
((NBITS.OR.LESS X 3)
3)
(T 4)))
((NBITS.OR.LESS X 6)
(COND
((NBITS.OR.LESS X 5)
5)
(T 6)))
((NBITS.OR.LESS X 7)
7)
(T 10Q)))
((NBITS.OR.LESS X 14Q)
(COND
((NBITS.OR.LESS X 12Q)
(COND
((NBITS.OR.LESS X 11Q)
11Q)
(T 12Q)))
((NBITS.OR.LESS X 13Q)
13Q)
(T 14Q)))
((NBITS.OR.LESS X 16Q)
(COND
((NBITS.OR.LESS X 15Q)
15Q)
(T 16Q)))
((NBITS.OR.LESS X 17Q)
17Q)
(T 20Q)))
(T (SHOULDNT]
[\FIXP (PROG ((HX (fetch (FIXP HINUM) of X)))
(if (IGREATERP HX MAX.POS.HINUM)
then (* So X is negative)
([LAMBDA (LX)
(if (AND (EQ HX \SIGNBIT)
(EQ LX 0))
then (* So X is EQP to the minimum FIXP integer)
(RETURN (CONSTANT BITS.PER.FIXP))
else (.NEGATE. HX LX]
(fetch (FIXP LONUM) of X)))
(RETURN (if (EQ HX 0)
then
(* This bizarre case shouldn't really happen, but I wouldn't like to rule it out -- a non-normalized FIXP that realy
should be a SMALLP)
(INTEGERLENGTH (fetch (FIXP LONUM) of X))
else (IPLUS (INTEGERLENGTH HX)
BITSPERWORD]
(if (TYPENAMEP X (QUOTE BIGNUM))
then (\BIGNUM.INTEGERLENGTH X)
else (INTEGERLENGTH (SETQ X (LISPERROR "NON-NUMERIC ARG" X T])
)
(DEFINEQ
(ABS
(LAMBDA (X) (* JonL "17-Mar-84 22:24")
(COND
((FIXP X)
(COND
((ILESSP X 0)
(IDIFFERENCE 0 X))
(T X)))
((FLOATP X)
(COND
((FLESSP X 0.0)
(FDIFFERENCE 0.0 X))
(T X)))
(T (* Note that there is no "contagion" for this function,
as there is for PLUS and TIMES)
(LISPERROR "NON-NUMERIC ARG" X)))))
(DIFFERENCE
[LAMBDA (X Y) (* lmm "11-FEB-82 14:02")
((OPCODES DIFFERENCE)
X Y])
(GREATERP
[LAMBDA (X Y) (* lmm: 17-DEC-75 23Q 65Q)
(COND
((AND (FIXP X)
(FIXP Y))
(IGREATERP X Y))
(T (FGREATERP X Y])
(PLUS
(LAMBDA N (* JonL "17-Mar-84 22:17")
(* Microcode generally handles the case of two args both
FIXPs)
(PROG (R (J 0))
LP (COND
((NEQ J N)
(SETQ J (ADD1 J))
(SETQ R (COND
((AND (FIXP (ARG N J))
(NOT (FLOATP R)))
(IPLUS (OR R 0)
(ARG N J)))
(T (FPLUS (OR R 0.0)
(ARG N J)))))
(GO LP)))
(RETURN R))))
(QUOTIENT
[LAMBDA (X Y) (* lmm: 17-DEC-75 25Q 36Q)
(COND
((AND (FIXP X)
(FIXP Y))
(IQUOTIENT X Y))
(T (FQUOTIENT X Y])
(REMAINDER
[LAMBDA (X Y) (* lmm: 17-DEC-75 25Q 36Q)
(COND
((AND (FIXP X)
(FIXP Y))
(IREMAINDER X Y))
(T (FREMAINDER X Y])
(LESSP
[LAMBDA (X Y) (* lmm: 17-DEC-75 23Q 73Q)
(COND
((AND (FIXP Y)
(FIXP X))
(IGREATERP Y X))
(T (FGREATERP Y X])
(MINUS
(LAMBDA (X) (* JonL "17-Mar-84 22:21")
(COND
((FIXP X)
(IDIFFERENCE 0 X))
(T (FDIFFERENCE 0.0 X)))))
(TIMES
(LAMBDA N (* JonL "17-Mar-84 22:22")
(PROG (R (J 0))
LP (COND
((NEQ J N)
(SETQ J (ADD1 J))
(SETQ R (COND
((AND (FIXP (ARG N J))
(NOT (FLOATP R)))
(ITIMES (OR R 1)
(ARG N J)))
(T (FTIMES (OR R 1.0)
(ARG N J)))))
(GO LP)))
(RETURN R))))
)
(DEFINEQ
(FMINUS
[LAMBDA (X) (* lmm " 5-MAR-80 23:12")
(FDIFFERENCE 0.0 X])
(FREMAINDER
[LAMBDA (X Y) (* rrb "24-APR-80 10:37")
(FDIFFERENCE X (FTIMES (FLOAT (FIX (FQUOTIENT X Y)))
Y])
)
(DEFINEQ
(RANDSET
[LAMBDA (X) (* lmm "21-Aug-84 14:42")
(PROG (RS RS1 RS2)
(COND
((NULL X)
(GO OUT))
((EQ X T) (* initialize with clock)
(SETQ RS1 (CLOCK))
(SETQ RS2 (IDATE)))
((AND (FIXP (CDR (LISTP X)))
(FIXP (CAR X))) (* user supplies initialization, old-style)
(SETQ RS1 (CAR X))
(SETQ RS2 (CDR X)))
((AND (EQ (LENGTH X)
67Q)
(EVERY X (FUNCTION FIXP)))
[SETQ RS (MAPCAR X (FUNCTION (LAMBDA (N)
(IPLUS N]
(GO XX))
(T (ERROR (QUOTE "ARG NOT PREVIOUS VALUE OF RANDSET")
X)))
[PROG ((\OVERFLOW 0))
(DECLARE (SPECVARS \OVERFLOW))
(SETQ RS
(MAPCAR (QUOTE (150177Q 134506Q 2372Q 154626Q 170230Q 66113Q 25744Q 40670Q 105776Q
171521Q 26405Q 111676Q 103564Q 151Q 162576Q 66157Q 23404Q
10171Q 157167Q 73124Q 57746Q 2565Q 152474Q 151770Q 124444Q
7426Q 114136Q 26172Q 146043Q 2037Q 1673Q 37700Q 46706Q
162146Q 6277Q 176221Q 3250Q 41735Q 156764Q 41547Q 144665Q
135532Q 63240Q 10560Q 5504Q 145075Q 114776Q 176503Q 160605Q
104147Q 12303Q 27516Q 35414Q 23625Q 25100Q))
(FUNCTION (LAMBDA (Z)
(SETQ RS1 (LOGAND RS1 177777Q))
(LOGXOR Z (SETQ RS2 (PROG1 (LOGAND (IPLUS (ITIMES RS1 46635Q)
RS1)
177777Q)
(SETQ RS1 RS2]
XX (FRPLACD (LAST RS)
RS)
(SETQ RANDSTATE (CONS RS (FNTH RS 37Q)))
OUT (RETURN (for X in (CAR RANDSTATE) as I from 1 to 67Q collect X])
(RAND
[LAMBDA (LOWER UPPER) (* edited: "29-Mar-84 15:49")
(* This function implements the XRAND subroutine described in Stanford memo STAN-CS-77-601, Analysis of Additive
Random Number Generators, by John F. Reiser, on p 28.0 Rather than storing the X values in an array and computing
indexes I and J, however, I have elected to retain state in a circular list of 63Q elements.
RANDSTATE is (CONS X (NTH X 37Q)); each time RAND is called, both CAR and CDR of RANDSTATE are CDR'ed to
effectively increment the index. In addition, the numbers are stored as 20Q bit binary fractions
(i.e. the decimal point is on the left of the 16-bit quantity))
(PROG (I J)
(OR (LISTP RANDSTATE)
(PROGN (RANDSET T)
RANDSTATE))
(SETQ I (CDAR RANDSTATE))
(SETQ J (CDDR RANDSTATE))
(RPLNODE RANDSTATE I J)
(RPLACA I (LOGAND (IDIFFERENCE (CAR I)
(CAR J))
MAX.SMALLP)))
(COND
[(NOT UPPER)
(COND
((NULL LOWER) (* both UPPER and LOWER nil. Return number
(0 .. MAX.SMALLP) -
not documented)
(CAAR RANDSTATE))
((FIXP LOWER) (* (RAND n) = (RAND 0 n-1))
(IREMAINDER (CAAR RANDSTATE)
LOWER))
(T (* (RAND N) N floating. Return
(RAND 0 N))
(FTIMES LOWER (FQUOTIENT (CAAR RANDSTATE)
(CONSTANT (FLOAT (ADD1 MAX.SMALLP]
[(AND (FIXP LOWER)
(FIXP UPPER))
(OR (IGREATERP UPPER LOWER)
(swap UPPER LOWER))
(SETQ UPPER (IDIFFERENCE UPPER LOWER))
(COND
((IGREATERP UPPER MAX.SMALLP)
(IPLUS (IMOD (\MAKENUMBER (CAAR RANDSTATE)
(CADAR RANDSTATE))
(ADD1 UPPER))
LOWER))
(T (IPLUS (IREMAINDER (CAAR RANDSTATE)
(ADD1 UPPER))
LOWER]
(T (FPLUS [FTIMES (FDIFFERENCE UPPER LOWER)
(FQUOTIENT (CAAR RANDSTATE)
(CONSTANT (FLOAT (ADD1 MAX.SMALLP]
LOWER])
(EXPT
[LAMBDA (A N) (* JonL " 2-Jul-84 16:08")
(if (FIXP N)
then (if (FIXP A)
then (if (NOT (IGREATERP N 0))
then (if (EQ 0 N)
then 1
else (FEXPT A N))
elseif (EQ 0 A)
then 0
else (* Integer EXPonentiation -- works by clever
bit-dissection method)
(PROG ((V 1))
LP (if (ODDP N)
then (SETQ V (TIMES A V)))
(if (EQ 0 (SETQ N (RSH N 1)))
then (RETURN V))
(SETQ A (TIMES A A))
(GO LP)))
elseif (FEQP 0.0 (SETQ A (FLOAT A)))
then (if (EQ 0 N)
then 1.0
else 0.0)
else (* Real EXPonentiation -- works by clever
bit-dissection method)
(PROG ((V 1.0))
(if (ILESSP N 0)
then (SETQ A (FQUOTIENT 1.0 A))
(SETQ N (IMINUS N)))
LP (if (ODDP N)
then (SETQ V (TIMES A V)))
(if (EQ 0 (SETQ N (LRSH N 1)))
then (RETURN V))
(SETQ A (TIMES A A))
(GO LP)))
else (FEXPT A N])
)
(DECLARE: DONTEVAL@LOAD DOCOPY
(RPAQQ RANDSTATE NIL)
(RPAQQ \TOL 9.999992E-6)
)
(DECLARE: DOEVAL@COMPILE DONTCOPY
(GLOBALVARS RANDSTATE \TOL)
)
(DEFINEQ
(PutUnboxed
(LAMBDA (PTR NUM) (* JonL "25-JUL-83 02:29")
(\PUTFIXP PTR NUM)))
(\PUTFIXP
[LAMBDA (PTR NUM) (* lmm "11-DEC-80 15:10")
(PROG (HI LO)
(.UNBOX. NUM HI LO)
(replace (FIXP HINUM) of PTR with HI)
(replace (FIXP LONUM) of PTR with LO)
(RETURN NUM])
(\PUTSWAPPEDFIXP
[LAMBDA (PTR NUM) (* edited: " 7-JUN-83 10:34")
(* store in MESA order rather than LISP order)
(PROG (HI LO)
(.UNBOX. NUM HI LO)
(replace (FIXP LONUM) of PTR with HI)
(replace (FIXP HINUM) of PTR with LO)
(RETURN NUM])
(\HINUM
[LAMBDA (NUM) (* lmm "12-APR-81 22:01")
(PROG (HI LO)
(.UNBOX. NUM HI LO)
(RETURN HI])
(\LONUM
[LAMBDA (NUM) (* lmm "12-APR-81 22:02")
(PROG (HI LO)
(.UNBOX. NUM HI LO)
(RETURN LO])
)
(* FOLLOWING DEFINITIONS EXPORTED)
(DECLARE: DONTCOPY
(DECLARE: EVAL@COMPILE
(PUTPROPS PutUnboxed DMACRO (= . \PUTFIXP))
)
)
(* END EXPORTED DEFINITIONS)
(DECLARE: DONTEVAL@LOAD DOEVAL@COMPILE DONTCOPY COMPILERVARS
(ADDTOVAR NLAMA )
(ADDTOVAR NLAML )
(ADDTOVAR LAMA MIN MAX IMIN IMAX FMIN FMAX ODDP EVENP TIMES PLUS LOGXOR LOGOR LOGAND ITIMES IPLUS)
)
(DEFINEQ
(POWEROFTWOP
[LAMBDA (X)
(DECLARE (LOCALVARS . T)) (* lmm "12-Apr-85 09:57")
(* Non-NIL iff arg is some power of 2)
(if (AND (EQ (SYSTEMTYPE)
(QUOTE D))
(NOT (SMALLP X)))
then [AND (FIXP X)
(IGREATERP X 0)
(if (EQ [LOGAND X (CONSTANT (SUB1 (EXPT 2 20Q]
0)
then (POWEROFTWOP (RSH X 20Q))
else (AND (EQ (RSH X 20Q)
0)
(.2↑NP. (LOGAND X (SUB1 (EXPT 2 20Q]
else (if (IGREATERP X 0)
then (.2↑NP. X])
(IMOD
[LAMBDA (X N) (* lmm "20-OCT-82 15:07")
(COND
((IGEQ (SETQ X (IREMAINDER X N))
0)
X)
(T (IPLUS N X])
(EVENP
[LAMBDA X (* bvm: "14-Feb-85 23:52")
(EQ (IMOD (ARG X 1)
(if (EQ X 2)
then (ARG X 2)
else 2))
0])
(ODDP
[LAMBDA X (* bvm: "14-Feb-85 23:52")
(NEQ (IMOD (ARG X 1)
(if (EQ X 2)
then (ARG X 2)
else 2))
0])
)
(DECLARE: DONTCOPY
(DECLARE: EVAL@COMPILE
(PUTPROPS .2↑NP. MACRO (OPENLAMBDA (X)
(EQ (LOGAND X (SUB1 X))
0)))
)
)
(* * MIN and MAX)
(DEFINEQ
(FLESSP
[LAMBDA (X Y)
(FGREATERP Y X])
(FMAX
[LAMBDA K (* bvm: "14-Feb-85 23:48")
(COND
((EQ K 0)
MIN.FLOAT)
(T (PROG ((J 1)
(X (FLOAT (ARG K 1)))
Y)
(OR (NUMBERP X)
(ERRORX (LIST 12Q X)))
LP (COND
((EQ J K)
(RETURN X)))
(ADD1VAR J)
(COND
((FGREATERP (SETQ Y (FLOAT (ARG K J)))
X)
(SETQ X Y)))
(GO LP])
(FMIN
[LAMBDA K (* bvm: "14-Feb-85 23:49")
(COND
((EQ K 0)
MAX.FLOAT)
(T (PROG ((J 1)
(X (FLOAT (ARG K 1)))
Y)
(OR (NUMBERP X)
(ERRORX (LIST 12Q X)))
LP (COND
((EQ J K)
(RETURN X)))
(ADD1VAR J)
(COND
([FGREATERP X (SETQ Y (FLOAT (ARG K J]
(SETQ X Y)))
(GO LP])
(GEQ
[LAMBDA (X Y)
(NOT (LESSP X Y])
(IGEQ
[LAMBDA (X Y)
(NOT (ILESSP X Y])
(ILEQ
[LAMBDA (X Y)
(NOT (IGREATERP X Y])
(IMAX
[LAMBDA K (* bvm: "14-Feb-85 23:49")
(COND
((EQ K 0)
MIN.INTEGER)
(T (PROG ((J 1)
(X (ARG K 1)))
LP (COND
((EQ J K)
(RETURN X)))
(ADD1VAR J)
[COND
((ILESSP X (ARG K J))
(SETQ X (ARG K J]
(GO LP])
(IMIN
[LAMBDA K (* bvm: "14-Feb-85 23:49")
(COND
((EQ K 0)
MAX.INTEGER)
(T (PROG ((J 1)
(X (ARG K 1)))
LP (COND
((EQ J K)
(RETURN X)))
(ADD1VAR J)
[COND
((IGREATERP X (ARG K J))
(SETQ X (ARG K J]
(GO LP])
(LEQ
[LAMBDA (X Y)
(NOT (GREATERP X Y])
(MAX
[LAMBDA K (* lmm "12-Apr-85 08:42")
(COND
((EQ K 0)
MIN.INTEGER)
(T (PROG ((J 1)
(X (ARG K 1))
Y)
(OR (NUMBERP X)
(ERRORX (LIST 12Q X)))
LP (COND
((EQ J K)
(RETURN X)))
(ADD1VAR J)
(COND
((GREATERP (SETQ Y (ARG K J))
X)
(SETQ X Y)))
(GO LP])
(MIN
[LAMBDA K (* lmm "12-Apr-85 08:42")
(COND
((EQ K 0)
MAX.INTEGER)
(T (PROG ((J 1)
(X (ARG K 1))
Y)
(OR (NUMBERP X)
(ERRORX (LIST 12Q X)))
LP (COND
((EQ J K)
(RETURN X)))
(ADD1VAR J)
(COND
((GREATERP X (SETQ Y (ARG K J)))
(SETQ X Y)))
(GO LP])
)
(DECLARE: EVAL@COMPILE
(ADDTOVAR GLOBALVARS MAX.INTEGER MIN.INTEGER MAX.FLOAT MIN.FLOAT)
)
(PUTPROPS LLARITH COPYRIGHT ("Xerox Corporation" T 1982 1983 1984 1985))
(DECLARE: DONTCOPY
(FILEMAP (NIL (2684 3131 (IDIFFERENCE 2694 . 2839) (IGREATERP 2841 . 2986) (IQUOTIENT 2988 . 3129)) (
3132 14683 (\SLOWIPLUS2 3142 . 4522) (\SLOWPLUS2 4524 . 5119) (\SLOWIDIFFERENCE 5121 . 6954) (
\SLOWDIFFERENCE 6956 . 7580) (\SLOWIGREATERP 7582 . 8085) (\SLOWLLSH1 8087 . 8457) (\SLOWLLSH8 8459 .
8787) (\SLOWLOGAND2 8789 . 9196) (\SLOWLOGOR2 9198 . 9600) (\SLOWLOGXOR2 9602 . 10013) (\SLOWLRSH1
10015 . 10351) (\SLOWLRSH8 10353 . 10653) (\SLOWITIMES2 10655 . 13291) (\SLOWTIMES2 13293 . 13892) (
\SLOWIQUOTIENT 13894 . 14066) (\SLOWQUOTIENT 14068 . 14681)) (14759 15895 (\BOXIPLUS 14769 . 14989) (
\BOXIDIFFERENCE 14991 . 15893)) (15923 16484 (\MAKENUMBER 15933 . 16482)) (16485 16675 (OVERFLOW 16495
. 16673)) (17033 17875 (\GETBASEFIXP 17043 . 17297) (\PUTBASEFIXP 17299 . 17583) (\PUTBASEFIXP.UFN
17585 . 17873)) (20482 24768 (EQP 20492 . 21020) (FIX 21022 . 21177) (IQUOTIENT 21179 . 21320) (
IREMAINDER 21322 . 21466) (LLSH 21468 . 22224) (LRSH 22226 . 23076) (LSH 23078 . 23456) (RSH 23458 .
24766)) (28359 35085 (MINUSP 28369 . 28523) (ILESSP 28525 . 28577) (IMINUS 28579 . 28631) (IPLUS 28633
. 29315) (ITIMES 29317 . 30003) (LOGAND 30005 . 30691) (LOGOR 30693 . 31375) (LOGXOR 31377 . 32063) (
SUB1 32065 . 32166) (ZEROP 32168 . 32308) (ADD1 32310 . 32354) (GCD 32356 . 32787) (IEQP 32789 . 32925
) (INTEGERLENGTH 32927 . 35083)) (35086 37534 (ABS 35096 . 35578) (DIFFERENCE 35580 . 35723) (GREATERP
35725 . 35898) (PLUS 35900 . 36427) (QUOTIENT 36429 . 36602) (REMAINDER 36604 . 36784) (LESSP 36786
. 36956) (MINUS 36958 . 37143) (TIMES 37145 . 37532)) (37535 37805 (FMINUS 37545 . 37646) (FREMAINDER
37648 . 37803)) (37806 43108 (RANDSET 37816 . 39502) (RAND 39504 . 41661) (EXPT 41663 . 43106)) (
43265 44430 (PutUnboxed 43275 . 43411) (\PUTFIXP 43413 . 43709) (\PUTSWAPPEDFIXP 43711 . 44130) (
\HINUM 44132 . 44279) (\LONUM 44281 . 44428)) (44806 46164 (POWEROFTWOP 44816 . 45522) (IMOD 45524 .
45728) (EVENP 45730 . 45943) (ODDP 45945 . 46162)) (46323 49282 (FLESSP 46333 . 46385) (FMAX 46387 .
46876) (FMIN 46878 . 47356) (GEQ 47358 . 47412) (IGEQ 47414 . 47470) (ILEQ 47472 . 47531) (IMAX 47533
. 47913) (IMIN 47915 . 48298) (LEQ 48300 . 48357) (MAX 48359 . 48822) (MIN 48824 . 49280)))))
STOP