feat(padic): add p-adic numbers

configure.ac

@@ -393,7 +393,7 @@ AS_IF([test -f "$srcdir/extern/zstd/zlibWrapper/zstd_zlibwrapper.h"], [],
 # Check for flint
 AC_ARG_WITH([flint],
 	[AS_HELP_STRING([--with-flint@<:@=DIR@:>@],
-		[use flint for polynomial arithmetic (installed in prefix DIR) @<:@default=check@:>@])],
+		[use flint for polynomial arithmetic and p-adics (installed in prefix DIR) @<:@default=check@:>@])],
 	[AS_IF([test "x$withval" != xyes && test "x$withval" != xno && test "x$withval" != xcheck],
 		[with_flint=yes
 		CPPFLAGS="$CPPFLAGS -I$withval/include"
@@ -423,7 +423,7 @@ AS_IF([test "x$with_flint" != xno],
 				[MATH_LIBS="$ac_cv_search_pow"])])])
 	AS_IF([$flag], [AC_CHECK_LIB([flint], [fmpz_mpoly_init], [LIBS="-lflint $MATH_LIBS $LIBS"], [flag=false], [$MATH_LIBS])])
 	AS_IF([$flag],
-		[AC_DEFINE(WITHFLINT, [], [Define to use flint for polynomial arithmetic.])
+		[AC_DEFINE(WITHFLINT, [], [Define to use flint for polynomial arithmetic and p-adics.])
 		with_flint=yes],
 		[AS_IF([test "x$with_flint" = xyes],
 			[AC_MSG_FAILURE([test for flint failed. Give --without-flint if you want to compile without flint])])

sources/Makefile.am

@@ -89,7 +89,8 @@ if WITHFLINT
 SRCBASE += \
 	flintinterface.cc \
 	flintinterface.h \
-	flintwrap.cc
+	flintwrap.cc \
+	padic.c
 endif
 
 if WITHFLOAT

sources/argument.c

@@ -171,6 +171,9 @@ int execarg(PHEAD WORD *term, WORD level)
 					if ( m[1] == 2 ) {
 #ifdef WITHFLOAT
 						if ( *t != FLOATFUN || TestFloat(t) == 0 )
+#endif
+#ifdef WITHFLINT
+						if ( *t != PADICFUN || TestPadic(t) == 0 )
 #endif
 						{
 							m += 2;
@@ -181,6 +184,11 @@ int execarg(PHEAD WORD *term, WORD level)
 						else {
 							m += 2;
 						}
+#endif
+#ifdef WITHFLINT
+						else {
+							m += 2;
+						}
 #endif
 					}
 					else {

sources/compcomm.c

@@ -58,6 +58,9 @@ static KEYWORD formatoptions[] = {
 	,{"mathematica",	(TFUN)0,	MATHEMATICAMODE,	0}
 	,{"normal",			(TFUN)0,	NORMALFORMAT,		1}
 	,{"nospaces",		(TFUN)0,	NOSPACEFORMAT,		3}
+#ifdef WITHFLINT
+	,{"padicprint",		(TFUN)0,	0,					6}
+#endif
 	,{"pfortran",		(TFUN)0,	PFORTRANMODE,		0}
 	,{"quadfortran",	(TFUN)0,	QUADRUPLEFORTRANMODE,	0}
 	,{"quadruplefortran",	(TFUN)0,	QUADRUPLEFORTRANMODE,	0}
@@ -410,6 +413,39 @@ WrongOption:		MesPrint("&Illegal option in Format FloatPrecision: %s",s);
 					error = 1;
 				}
 			}
+#endif
+#ifdef WITHFLINT
+			else if ( key->flags == 6 ) {
+/*
+				Syntax: Format PadicPrint [on];
+				        Format PadicPrint off;
+*/
+				while ( FG.cTable[*s] == 0 ) s++;
+				while ( *s == ' ' || *s == '\t' || *s == ',' ) s++;
+				if ( *s == 0 ) {
+					AO.PadicPrint = 1;
+				}
+				else if ( tolower(*s) == 'o' && tolower(s[1]) == 'n' ) {
+					ss = s;
+					s += 2;
+					while ( *s == ' ' || *s == '\t' || *s == ',' ) s++;
+					if ( *s ) { s = ss; goto WrongPadicOption; }
+					AO.PadicPrint = 1;
+				}
+				else if ( tolower(*s) == 'o' && tolower(s[1]) == 'f'
+				&& tolower(s[2]) == 'f' ) {
+					ss = s;
+					s += 3;
+					while ( *s == ' ' || *s == '\t' || *s == ',' ) s++;
+					if ( *s ) { s = ss; goto WrongPadicOption; }
+					AO.PadicPrint = 0;
+				}
+				else {
+WrongPadicOption:
+					MesPrint("&Illegal option in Format PadicPrint: %s",s);
+					error = 1;
+				}
+			}
 #endif
 		}
 		else if ( ( *s == 'c' || *s == 'C' ) && ( FG.cTable[s[1]] == 1 ) ) {
@@ -2069,6 +2105,19 @@ doset:					if ( Sets[number].type != CFUNCTION ) goto nofun;
 								error = 1;
 							}
 						}
+#endif
+#ifdef WITHFLINT
+						{
+							WORD *r1, *r2;
+							r1 = SetElements + Sets[number].first;
+							r2 = SetElements + Sets[number].last;
+							while ( r1 < r2 ) {
+								if ( *r1++ == PADICFUN ) {
+									MesPrint("&Illegal use of argument environment and padic_.");
+									error = 1;
+								}
+							}
+						}
 #endif
 						*w++ = CSET; *w++ = number;
 					}
@@ -2078,6 +2127,12 @@ doset:					if ( Sets[number].type != CFUNCTION ) goto nofun;
 							MesPrint("&Illegal use of argument environment and float_.");
 							error = 1;
 						}
+#endif
+#ifdef WITHFLINT
+						if ( (number + FUNCTION) == PADICFUN ) {
+							MesPrint("&Illegal use of argument environment and padic_.");
+							error = 1;
+						}
 #endif
 						*w++ = CFUNCTION; *w++ = number + FUNCTION;
 					}
@@ -3604,6 +3659,12 @@ int CoModulus(UBYTE *inp)
 		MesPrint("&Simultaneous use of floating point and modulus arithmetic makes no sense.");
 		Retval = 1;
 	}
+#endif
+#ifdef WITHFLINT
+	if ( AC.activePadic ) {
+		MesPrint("&Simultaneous use of p-adic and modulus arithmetic makes no sense.");
+		Retval = 1;
+	}
 #endif
 	AC.modmode = 0;
 	if ( *inp == '-' ) {
@@ -5403,6 +5464,12 @@ int CoPolyFun(UBYTE *s)
 		MesPrint("&Simultaneous use of PolyFun and float_ is not allowed.");
 		error = 1;
 	}
+#endif
+#ifdef WITHFLINT
+	if ( AC.activePadic ) {
+		MesPrint("&Simultaneous use of PolyFun and padic_ is not allowed.");
+		error = 1;
+	}
 #endif
 	return(error);
 }
@@ -5435,6 +5502,12 @@ int CoPolyRatFun(UBYTE *s)
 		MesPrint("&Simultaneous use of PolyFun and float_ is not allowed.");
 		error = 1;
 	}
+#endif
+#ifdef WITHFLINT
+	if ( AC.activePadic ) {
+		MesPrint("&Simultaneous use of PolyFun and padic_ is not allowed.");
+		error = 1;
+	}
 #endif
 	if ( ( ( type = GetName(AC.varnames,s,&numfun,WITHAUTO) ) != CFUNCTION )
 	|| ( functions[numfun].spec != 0 ) || ( functions[numfun].commute != 0 ) ) {

sources/compiler.c

@@ -162,6 +162,9 @@ static KEYWORD com2commands[] = {
 	,{"factorize",      (TFUN)CoFactorize,        TOOUTPUT,     PARTEST}
 	,{"fill",           (TFUN)CoFill,             DECLARATION,  PARTEST}
 	,{"fillexpression", (TFUN)CoFillExpression,   DECLARATION,  PARTEST}
+#ifdef WITHFLINT
+	,{"frompadic",      (TFUN)CoFromPadic,        STATEMENT,    PARTEST}
+#endif
 	,{"frompolynomial", (TFUN)CoFromPolynomial,   STATEMENT,    PARTEST}
 	,{"funpowers",      (TFUN)CoFunPowers,        DECLARATION,  PARTEST}
 	,{"hide",           (TFUN)CoHide,             SPECIFICATION,PARTEST}
@@ -197,6 +200,9 @@ static KEYWORD com2commands[] = {
 	,{"on",             (TFUN)CoOn,               DECLARATION,  PARTEST}
 	,{"once",           (TFUN)CoOnce,             STATEMENT,    PARTEST}
 	,{"only",           (TFUN)CoOnly,             STATEMENT,    PARTEST}
+#ifdef WITHFLINT
+	,{"padictorat",     (TFUN)CoPadicToRat,       STATEMENT,    PARTEST}
+#endif
 	,{"particle",       (TFUN)CoParticle,         DECLARATION,  PARTEST}
 	,{"polyfun",        (TFUN)CoPolyFun,          DECLARATION,  PARTEST}
 	,{"polyratfun",     (TFUN)CoPolyRatFun,       DECLARATION,  PARTEST}
@@ -236,6 +242,9 @@ static KEYWORD com2commands[] = {
 	,{"threadbucketsize",(TFUN)CoThreadBucket,    DECLARATION,  PARTEST}
 #ifdef WITHFLOAT
 	,{"tofloat",        (TFUN)CoToFloat,          STATEMENT,    PARTEST}
+#endif
+#ifdef WITHFLINT
+	,{"topadic",        (TFUN)CoToPadic,          STATEMENT,    PARTEST}
 #endif
 	,{"topolynomial",   (TFUN)CoToPolynomial,     STATEMENT,    PARTEST}
 #ifdef WITHFLOAT

sources/declare.h

@@ -366,7 +366,6 @@ TP=T+1;while(TP<TT){if(*TP==AR.PolyFun){TP[2]|=(DIRTYFLAG|MUSTCLEANPRF);}TP+=TP[
 
 #endif
 
-
 /*
 	MesPrint("P-level popped to %d with %d",AP.PreAssignLevel,(WORD)(AC.iPointer - AC.iBuffer));
 
@@ -1637,6 +1636,8 @@ extern void  poly_free_poly_vars(PHEAD const char *);
 #ifdef WITHFLINT
 extern void  flint_final_cleanup_thread(void);
 extern void  flint_final_cleanup_master(void);
+extern WORD  flint_fmpz_get_form(void *, WORD *);
+extern void  flint_fmpz_set_form(void *, UWORD *, WORD);
 extern WORD* flint_div(PHEAD WORD *, WORD *, const WORD);
 extern int   flint_factorize_argument(PHEAD WORD *, WORD *);
 extern WORD* flint_factorize_dollar(PHEAD WORD *);
@@ -1773,6 +1774,33 @@ int CoStrictRounding(UBYTE *);
 int StrictRounding(PHEAD WORD *, WORD, WORD, WORD);
 #endif
 
+#ifdef WITHFLINT
+int TestPadic(WORD *);
+int TestPadicLimbTerm(const WORD *);
+int ExpandPadicArgument(WORD *, const WORD *);
+int ConvertPadicLimbs32(int32_t *, LONG, const int32_t *, int, int);
+
+int DoStartPadic(UBYTE *);
+int DoEndPadic(UBYTE *);
+int StartPadicSystem(UBYTE *, LONG);
+void ClearPadicSystem(void);
+int CoToPadic(UBYTE *);
+int CoPadicToRat(UBYTE *);
+int CoFromPadic(UBYTE *);
+int ToPadic(PHEAD WORD *,WORD);
+int PadicToRat(PHEAD WORD *,WORD);
+int FromPadic(PHEAD WORD *,WORD,WORD);
+int PrintPadic(WORD *fun);
+int AddWithPadic(PHEAD WORD **,WORD **);
+int MergeWithPadic(PHEAD WORD **,WORD **);
+int MulPadics(PHEAD WORD *, WORD *, WORD *);
+int DivPadics(PHEAD WORD *, WORD *, WORD *);
+int InvPadic(PHEAD WORD *, WORD *);
+int MulRatToPadic(PHEAD WORD *, WORD *, UWORD *, WORD);
+int NormalizePadicUnit(PHEAD WORD *, WORD *);
+void CheckPadicPrime(WORD *);
+#endif
+
 /*
   	#] Declarations : 
 */

sources/execute.c

@@ -1244,6 +1244,9 @@ int PutBracket(PHEAD WORD *termin)
 	if ( AR.PolyFun && AT.PolyAct ) tStop = termin + AT.PolyAct;
 #ifdef WITHFLOAT
 	else if ( AT.FloatPos ) tStop = termin + AT.FloatPos;
+#endif
+#ifdef WITHFLINT
+	else if ( AT.PadicPos ) tStop = termin + AT.PadicPos;
 #endif
 	else tStop = tStopa - i;
 	t++;

sources/flintwrap.cc

@@ -52,6 +52,22 @@ void flint_final_cleanup_master(void) {
 }
 /*
 	#] flint_final_cleanup_master :
+	#[ flint_fmpz_get_form :
+*/
+WORD flint_fmpz_get_form(void *z, WORD *a)
+{
+	return flint::fmpz_get_form((fmpz *)z, a);
+}
+/*
+	#] flint_fmpz_get_form :
+	#[ flint_fmpz_set_form :
+*/
+void flint_fmpz_set_form(void *z, UWORD *a, WORD na)
+{
+	flint::fmpz_set_form((fmpz *)z, a, na);
+}
+/*
+	#] flint_fmpz_set_form :
 	#[ flint_div :
 */
 WORD* flint_div(PHEAD WORD *a, WORD *b, const WORD must_fit_term) {

sources/ftypes.h

@@ -345,6 +345,10 @@ typedef int (*TFUN1)(UBYTE *,int);
 #define MINVECTOR 10
 #define SETEXP 11
 #define DOLLAREXPR2 12
+#ifdef WITHFLINT
+#define PADICLIMBS 13
+#define PADICLIMBHEAD 3 /* type, positive object length, signed limb count */
+#endif
 #define HAAKJE0 9
 #define FUNCTION 20
 
@@ -469,7 +473,8 @@ typedef int (*TFUN1)(UBYTE *,int);
 #define EXPFUNCTION 124
 #define HPLFUNCTION 125
 #define MPLFUNCTION 126
-#define MAXBUILTINFUNCTION 126
+#define PADICFUN 127
+#define MAXBUILTINFUNCTION 127
 
 #define FIRSTUSERFUNCTION 150
 
@@ -597,6 +602,11 @@ typedef int (*TFUN1)(UBYTE *,int);
 #define TYPESTRICTROUNDING 91
 #define TYPECHOP 92
 #endif
+#ifdef WITHFLINT
+#define TYPETOPADIC 93
+#define TYPEPADICTORAT 94
+#define TYPEFROMPADIC 95
+#endif
 
 /*
 	The codes for the 'operations' that are part of TYPEOPERATION.
@@ -1140,4 +1150,3 @@ typedef int (*TFUN1)(UBYTE *,int);
 #define CYCLR           8388608
 #define FLOOP           16777216
 #define NOTFLOOP        33554432
-

sources/function.c

@@ -845,6 +845,10 @@ int MatchFunction(PHEAD WORD *pattern, WORD *interm, WORD *wilds)
 	// functions and tensors are handled specially. 
 	if ( *interm == FLOATFUN ) return(0);
 #endif
+#ifdef WITHFLINT
+	// Pattern matching against padic_ functions is currently disabled.
+	if ( *interm == PADICFUN ) return(0);
+#endif
 /*
 	Test first for a straight match
 */

sources/inivar.h

@@ -254,6 +254,7 @@ static struct fixedfun {
 	,{"eexp_"       ,0 ,0             ,0               ,0} /* EXPFUNCTION */
 	,{"hpl_"        ,0 ,0             ,0               ,0} /* HPLFUNCTION */
 	,{"mpl_"        ,0 ,0             ,0               ,0} /* MPLFUNCTION */
+	,{"padic_"      ,0 ,0             ,0               ,0} /* PADICFUN */
 };
 
 FIXEDSET fixedsets[] = {