(FILECREATED "21-Aug-84 16:24:49" {ERIS}<LISPCORE>SOURCES>LLARITH.;10 136054Q
changes to: (VARS LLARITHCOMS)
(FNS \SLOWQUOTIENT \SLOWTIMES2 \SLOWDIFFERENCE \SLOWPLUS2 RANDSET)
previous date: " 8-Aug-84 11:51:11" {ERIS}<LISPCORE>SOURCES>LLARITH.;8)
(* Copyright (c) 1982, 1983, 1984 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 0))
(E (RESETSAVE (RADIX 8)))
(CONSTANTS (MAX.SMALLP 65535)
(MIN.SMALLP -65536)
(MAX.FIXP 2147483647)
(MIN.FIXP -2147483648)
(\SIGNBIT 32768))
(COMS (* "For Compatibility. Someday these two names should be flushed -- JonL 7/25/83")
(CONSTANTS (MAX.INTEGER 2147483647)
(MIN.INTEGER -2147483648)))
(EXPORT (DECLARE: DONTCOPY (RECORDS FIXP)
(CONSTANTS (MAX.SMALL.INTEGER 65535)
(MAX.POS.HINUM 32767))
(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 TRUNCATEMULTIPLY)
(EXPORT (DECLARE: DONTCOPY (MACROS PutUnboxed]
(DECLARE: DONTEVAL@LOAD DOEVAL@COMPILE DONTCOPY COMPILERVARS
(ADDVARS (NLAMA)
(NLAML)
(LAMA TIMES PLUS LOGXOR LOGOR LOGAND ITIMES IPLUS])
(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 " 2-Jul-84 17:10")
(\CALLME (QUOTE IPLUS))
(PROG (HX LX HY LY SIGNX)
(.UNBOX. X HX LX)
(.UNBOX. Y HY LY)
(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)
(SELECTQ \OVERFLOW
(T (LISPERROR "OVERFLOW" (\MAKENUMBER HX LX)))
[NIL (* return max/min)
(RETURN (COND
(SIGNX MIN.INTEGER)
(T MAX.INTEGER]
NIL)))
(RETURN (\MAKENUMBER HX LX])
(\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 " 2-Jul-84 17:10")
(\CALLME (QUOTE IDIFFERENCE))
(PROG (HX LX HY LY SIGNX)
(.UNBOX. X HX LX)
(.UNBOX. Y HY LY) (* 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]
(SELECTQ \OVERFLOW
(T (LISPERROR "OVERFLOW" (\MAKENUMBER HX LX)))
[NIL (* return max/min)
(RETURN (COND
(SIGNX MIN.INTEGER)
(T MAX.INTEGER]
NIL)))
(RETURN (\MAKENUMBER HX LX])
(\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 " 2-Jul-84 17:10")
(\CALLME (QUOTE IGREATERP))
(PROG (HX LX HY LY)
(.UNBOX. X HX LX)
(.UNBOX. Y HY LY)
(RETURN (COND
((EQ HX HY)
(IGREATERP LX LY))
(T (IGREATERP (LOGXOR HX \SIGNBIT)
(LOGXOR HY \SIGNBIT])
(\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 (A B) (* lmm " 2-Jul-84 17:11")
(\CALLME (QUOTE LOGAND))
(PROG (AH AL BH BL)
(.UNBOX. A AH AL)
(.UNBOX. B BH BL)
(RETURN (\MAKENUMBER (LOGAND AH BH)
(LOGAND AL BL])
(\SLOWLOGOR2
[LAMBDA (A B) (* lmm " 2-Jul-84 17:11")
(\CALLME (QUOTE LOGOR))
(PROG (AH AL BH BL)
(.UNBOX. A AH AL)
(.UNBOX. B BH BL)
(RETURN (\MAKENUMBER (LOGOR AH BH)
(LOGOR AL BL])
(\SLOWLOGXOR2
[LAMBDA (A B) (* lmm " 2-Jul-84 17:11")
(\CALLME (QUOTE LOGXOR))
(PROG (AH AL BH BL)
(.UNBOX. A AH AL)
(.UNBOX. B BH BL)
(RETURN (\MAKENUMBER (LOGXOR AH BH)
(LOGXOR AL BL])
(\SLOWLRSH1
[LAMBDA (X) (* lmm "13-OCT-82 15:29")
(PROG (HI LO)
(.UNBOX. X HI LO)
(RETURN (\MAKENUMBER (LRSH HI 1)
(IPLUS (LRSH LO 1)
(COND
((ZEROP (LOGAND HI 1))
0)
(T 100000Q])
(\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 "11-Jul-84 18:35")
(\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)
(.UNBOX. Y HY LY)
(COND
((IGREATERP HX MAX.POS.HINUM)
(.NEGATE. HX LX)
(SETQ SIGN T)))
[COND
((IGREATERP HY MAX.POS.HINUM)
(.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.INTEGER)))
(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.INTEGER)))
OVER[SELECTQ \OVERFLOW
(T (LISPERROR "OVERFLOW" (\MAKENUMBER HR LR)))
[NIL (RETURN (COND
((NULL SIGN)
MAX.INTEGER)
(T MIN.INTEGER]
(PROGN (* truncate -
this is awful code, but it works)
(RETURN (TRUNCATEMULTIPLY X Y]
RET (COND
(SIGN (.NEGATE. HR LR)))
(RETURN (\MAKENUMBER HR LR])
(\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 0)
(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))
)
(* "For Compatibility. Someday these two names should be flushed -- JonL 7/25/83")
(DECLARE: EVAL@COMPILE
(RPAQQ MAX.INTEGER 17777777777Q)
(RPAQQ MIN.INTEGER -20000000000Q)
(CONSTANTS (MAX.INTEGER 17777777777Q)
(MIN.INTEGER -20000000000Q))
)
(* 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)
(PROG NIL
UBLP(SELECTC (NTYPX V)
(\FIXP (SETQ HV (fetch (FIXP HINUM) of V))
(SETQ LV (fetch (FIXP LONUM) of V)))
[\SMALLP (COND
((SMALLPOSP V)
(SETQ HV 0)
(SETQ LV V))
(T (SETQ HV 177777Q)
(SETQ LV (LOLOC V]
(\FLOATP (SETQ V (\FIXP.FROM.FLOATP V))
(GO UBLP))
(PROGN (SETQ V (LISPERROR "NON-NUMERIC ARG" V))
(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 "13-OCT-82 15:30")
(COND
[(ILEQ N 0)
(COND
((EQ N 0)
X)
(T (RSH X (IMINUS N]
((IGREATERP N (CONSTANT (DIFFERENCE (TIMES 2 BITSPERWORD)
2))) (* Shifting more than the non-sign bits just returns the
sign bit)
(COND
((MINUSP X) (* X was negative)
(AND (EQ \OVERFLOW T)
(NEQ X -1)
(LISPERROR "OVERFLOW" (CONSTANT MIN.INTEGER)))
(CONSTANT MIN.INTEGER))
(T (AND (EQ \OVERFLOW T)
(NEQ X 0)
(LISPERROR "OVERFLOW" 0))
0)))
(T (PROG (XHI XLO (XSIGNBIT 0))
(.UNBOX. X XHI XLO)
(COND
((IGEQ XHI \SIGNBIT)
(SETQ XSIGNBIT \SIGNBIT)))
[COND
((IGEQ N (CONSTANT BITSPERWORD))
(AND (EQ \OVERFLOW T)
[COND
((EQ XSIGNBIT 0)
(OR (NEQ XHI 0)
(NEQ (LOGAND XLO \SIGNBIT)
0)))
(T (OR (NEQ XHI MAX.SMALL.INTEGER)
(EQ (LOGAND XLO \SIGNBIT)
0]
(LISPERROR "OVERFLOW" X))
(SETQ XHI XLO)
(SETQ XLO 0)
(SETQ N (IDIFFERENCE N (CONSTANT BITSPERWORD]
(* N must be less than BITSPERWORD, i.e. 16, now)
[COND
((IGREATERP N 7)
(PROGN (AND (EQ \OVERFLOW T)
(NEQ (LOGAND XHI 77400Q)
(COND
((NEQ XSIGNBIT 0)
77400Q)
(T 0)))
(LISPERROR "OVERFLOW" X))
(SETQ XHI (LOGOR (LLSH XHI 10Q)
(LRSH XLO 10Q)))
(SETQ XLO (LLSH (LOGAND XLO 377Q)
10Q))
(SETQ N (IDIFFERENCE N 10Q]
(FRPTQ N (AND (EQ \OVERFLOW T)
(COND
((ZEROP (LOGAND XHI 40000Q))
(NEQ XSIGNBIT 0))
(T (EQ XSIGNBIT 0)))
(LISPERROR "OVERFLOW" X))
[SETQ XHI (COND
((ZEROP (LOGAND XLO \SIGNBIT))
(LLSH XHI 1))
(T (* Flush the high-order bit, so subsequent LSH of XLO
won't overflow the SMALLP range)
(SETQ XLO (LOGXOR XLO \SIGNBIT))
(LOGOR (LLSH XHI 1)
1]
(SETQ XLO (LLSH XLO 1)))
(SETQ XHI (LOGOR XSIGNBIT (LOGAND XHI MAX.POS.HINUM)))
(RETURN (\MAKENUMBER XHI XLO])
(RSH
[LAMBDA (X N) (* lmm "13-OCT-82 15:30")
(COND
((IGREATERP 0 N)
(LSH X (IMINUS N)))
(T (PROG (XHI XLO)
(.UNBOX. X XHI XLO)
[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
((ZEROP (LOGAND XHI 1))
0)
(T 100000Q]
(SETQ XHI (IPLUS (LRSH XHI 1)
(LOGAND XHI 100000Q]
(RETURN (\MAKENUMBER XHI XLO])
)
(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)
(.UNBOX. Y HY LY)
[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)
(SELECTQ \OVERFLOW
(T (ERROR "DIVISION OVERFLOW" Y))
(GO RET0]
(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)
(SELECTQ \OVERFLOW
(T (ERROR "DIVISION OVERFLOW" Y))
(GO RET0]
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
(REM (* remainder is left in X)
(COND
(SIGNREMAINDER (.NEGATE. HX LX)))
(SETQ REM (\MAKENUMBER HX LX]
[COND
(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
(REM (SETQ REM 0)))
(COND
(QUO (SETQ QUO 0)))
(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)
(EQ X 0])
(ADD1
[LAMBDA (X)
(IPLUS X 1])
(GCD
[LAMBDA (N1 N2) (* edited: "22-APR-82 05:26")
(COND
((ZEROP N2)
N1)
((MINUSP N2)
(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) (* JonL "18-OCT-82 21:51")
(SELECTQ (SYSTEMTYPE)
(D (* Foo, INTEGERLENGTH currently "boxes" on negative
arguments)
(SELECTC (NTYPX X)
(\SMALLP (COND
((ILESSP X 0)
(SETQ X (MINUS 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)))))
(PROGN
(* Someday we'd like (COND ((OPEN-BIGNUMP X) (SETQ X (BNDS X)) (LET* ((N (SUB1 (BNDS-LENGTH X)))
(HIGH-DIGIT (BNDS-REF X N))) (IPLUS (INTEGERLENGTH HIGH-DIGIT) (ITIMES (CONSTANT BIGNUMDIGIT.LENGTH) N))))))
(INTEGERLENGTH (FIX X)))))
(PROG ((LEN (CONSTANT (LRSH (SUB1 BITS.PER.FIXP)
1)))
(BIT (CONSTANT (LLSH 1 (LRSH (SUB1 BITS.PER.FIXP)
1))))
(SHIFTER (CONSTANT (LLSH 1 (SUB1 (LRSH (SUB1 BITS.PER.FIXP)
1)))))
(ONEUP 0)) (* 'len' IS LENGTH OF FIRST TRIAL 'bit')
(* 'shifter' IS amount by which to shift the 'bit' ON
this round)
(IF (NOT (FIXP X))
THEN (SETQ X (FIX X)))
SCANBITS
(if (IGEQ X BIT)
then (if (ILESSP X (SETQ ONEUP (LSH BIT 1)))
then (* Here, we've boiled it down to between two powers of
2)
(RETURN LEN)
elseif (EQ ONEUP (CONSTANT (SUB1 BITS.PER.FIXP)))
then (* May be it was actually the higher bit)
(RETURN (CONSTANT (SUB1 BITS.PER.FIXP))))
(SETQ BIT (LLSH BIT SHIFTER))
(SETQ LEN (IPLUS LEN SHIFTER))
elseif (IGEQ X (LRSH BIT 1))
then (RETURN (SUB1 LEN))
else (SETQ BIT (LRSH BIT SHIFTER))
(SETQ LEN (IDIFFERENCE LEN SHIFTER)))
(OR (EQ SHIFTER 1)
(SETQ SHIFTER (LRSH SHIFTER 1)))
(GO SCANBITS)))))
)
(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: 17-DEC-75 23Q 65Q)
(COND
((AND (FIXP X)
(FIXP Y))
(IDIFFERENCE X Y))
(T (FDIFFERENCE 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 (LRSH 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
(ADDTOVAR 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])
(TRUNCATEMULTIPLY
[LAMBDA (X Y) (* lmm "13-OCT-80 12:19")
(* this is a dreadful kludge. -
do unsigned multiply mod 32)
(COND
((ZEROP Y)
0)
[(EQ (LOGAND Y 1)
1)
(IPLUS X (TRUNCATEMULTIPLY (LLSH X 1)
(LRSH Y 1]
(T (TRUNCATEMULTIPLY (LLSH X 1)
(LRSH Y 1])
)
(* 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 TIMES PLUS LOGXOR LOGOR LOGAND ITIMES IPLUS)
)
(PUTPROPS LLARITH COPYRIGHT ("Xerox Corporation" T 3676Q 3677Q 3700Q))
(DECLARE: DONTCOPY
(FILEMAP (NIL (4760Q 5657Q (IDIFFERENCE 4772Q . 5213Q) (IGREATERP 5215Q . 5436Q) (IQUOTIENT 5440Q .
5655Q)) (5660Q 33376Q (\SLOWIPLUS2 5672Q . 10550Q) (\SLOWPLUS2 10552Q . 11675Q) (\SLOWIDIFFERENCE
11677Q . 15427Q) (\SLOWDIFFERENCE 15431Q . 16611Q) (\SLOWIGREATERP 16613Q . 17407Q) (\SLOWLLSH1 17411Q
. 20173Q) (\SLOWLLSH8 20175Q . 20705Q) (\SLOWLOGAND2 20707Q . 21364Q) (\SLOWLOGOR2 21366Q . 22037Q) (
\SLOWLOGXOR2 22041Q . 22516Q) (\SLOWLRSH1 22520Q . 23220Q) (\SLOWLRSH8 23222Q . 23676Q) (\SLOWITIMES2
23700Q . 30616Q) (\SLOWTIMES2 30620Q . 31747Q) (\SLOWIQUOTIENT 31751Q . 32225Q) (\SLOWQUOTIENT 32227Q
. 33374Q)) (33512Q 35672Q (\BOXIPLUS 33524Q . 34060Q) (\BOXIDIFFERENCE 34062Q . 35670Q)) (35726Q
37007Q (\MAKENUMBER 35740Q . 37005Q)) (37010Q 37306Q (OVERFLOW 37022Q . 37304Q)) (45464Q 61401Q (EQP
45476Q . 46516Q) (FIX 46520Q . 46753Q) (IQUOTIENT 46755Q . 47172Q) (IREMAINDER 47174Q . 47414Q) (LLSH
47416Q . 51002Q) (LRSH 51004Q . 52526Q) (LSH 52530Q . 57232Q) (RSH 57234Q . 61377Q)) (72335Q 112250Q (
MINUSP 72347Q . 72601Q) (ILESSP 72603Q . 72667Q) (IMINUS 72671Q . 72755Q) (IPLUS 72757Q . 74231Q) (
ITIMES 74233Q . 75511Q) (LOGAND 75513Q . 76771Q) (LOGOR 76773Q . 100245Q) (LOGXOR 100247Q . 101525Q) (
SUB1 101527Q . 101674Q) (ZEROP 101676Q . 101744Q) (ADD1 101746Q . 102022Q) (GCD 102024Q . 102410Q) (
IEQP 102412Q . 102622Q) (INTEGERLENGTH 102624Q . 112246Q)) (112251Q 117135Q (ABS 112263Q . 113225Q) (
DIFFERENCE 113227Q . 113512Q) (GREATERP 113514Q . 113771Q) (PLUS 113773Q . 115012Q) (QUOTIENT 115014Q
. 115271Q) (REMAINDER 115273Q . 115557Q) (LESSP 115561Q . 116033Q) (MINUS 116035Q . 116326Q) (TIMES
116330Q . 117133Q)) (117136Q 117554Q (FMINUS 117150Q . 117315Q) (FREMAINDER 117317Q . 117552Q)) (
117555Q 131655Q (RANDSET 117567Q . 123015Q) (RAND 123017Q . 127174Q) (EXPT 127176Q . 131653Q)) (
132123Q 135172Q (PutUnboxed 132135Q . 132345Q) (\PUTFIXP 132347Q . 133017Q) (\PUTSWAPPEDFIXP 133021Q
. 133664Q) (\HINUM 133666Q . 134111Q) (\LONUM 134113Q . 134336Q) (TRUNCATEMULTIPLY 134340Q . 135170Q)
))))
STOP