--* From BMT%WATSON.vnet.ibm.com@yktvmh.watson.ibm.com Thu Dec 30 11:32:50 1993 --* Received: from yktvmh.watson.ibm.com by leonardo.watson.ibm.com (AIX 3.2/UCB 5.64/4.03) --* id AA25800; Thu, 30 Dec 1993 11:32:50 -0500 --* Received: from watson.vnet.ibm.com by yktvmh.watson.ibm.com (IBM VM SMTP V2R3) --* with BSMTP id 5592; Thu, 30 Dec 93 11:38:57 EST --* Received: from YKTVMH by watson.vnet.ibm.com with "VAGENT.V1.0" --* id --* for asbugs@watson; Thu, 30 Dec 93 11:38:56 -0500 --* Received: from YKTVMH by watson.vnet.ibm.com with "VAGENT.V1.0" --* id 8453; Thu, 30 Dec 1993 11:38:55 EST --* Received: from cyst.watson.ibm.com by yktvmh.watson.ibm.com (IBM VM SMTP V2R3) --* with TCP; Thu, 30 Dec 93 11:38:54 EST --* Received: from spadserv.watson.ibm.com by cyst.watson.ibm.com (AIX 3.2/UCB 5.64/900528) --* id AA40472; Thu, 30 Dec 1993 11:38:44 -0500 --* Received: by spadserv.watson.ibm.com (AIX 3.2/UCB 5.64/900524) --* id AA30914; Thu, 30 Dec 1993 11:40:54 -0500 --* Date: Thu, 30 Dec 1993 11:40:54 -0500 --* From: bmt@spadserv.watson.ibm.com --* X-External-Networks: yes --* Message-Id: <9312301640.AA30914@spadserv.watson.ibm.com> --* To: asbugs@watson.ibm.com --* Subject: [4] compiler dies with program fault [bug2.as][33.4 (current)] --@ Fixed by: SSD Mon Apr 18 15:06:10 1994 --@ Tested by: none --@ Summary: Call tfExpr instead of tfGetExpr. -- PI: the crash is in tinfer phase -- PI2 (3/28/94): now is no more crashing, but giving some error msgs. -- Or is a substituion bug or not a bug #include "aslib.as" MODRING ==> ModularRing EMR ==> EuclideanModularRing MODFIELD ==> ModularField one?(xxx) ==> xxx = 1 CommutativeRing:Category == Ring with *: (Integer,%) -> % coerce: Integer -> % +++ ModularRing(R: CommutativeRing,Mod: AbelianMonoid,reduction: (R,Mod) -> R, merge: (Mod,Mod) -> Partial(Mod),exactQuo: (R,R,Mod) -> Partial(R)): with CommutativeRing; modulus: % -> Mod; coerce: % -> R; reduce: (R,Mod) -> %; exQuo: (%,%) -> Partial(%); recip: % -> Partial(%); inv: % -> %; == add Rep ==> Record(val: R,modulo: Mod); import from Mod; import from R; import from Rep; import from Partial Mod import from Partial % import from Partial R default x,y: %; modulus (x:%):Mod == (rep(x)).modulo; coerce (x:%):R == (rep(x)).val; coerce (i:Integer):% == per([i::R,0]$Rep); (i:Integer) * (x:%):% == i::% * x; -- coerce (x:%):OutputForm == (rep(x)).val::OutputForm; apply(p:OutPort,x:%):OutPort == p(rep(x).val) reduce(a:R,m:Mod):% == per([reduction(a,m),m]$Rep); 0:% == per([0$R,0$Mod]$Rep); 1:% == per([1$R,0$Mod]$Rep); zero? (x:%):Boolean == zero?( (rep(x)).val); -- one? (x:%):Boolean == one?( (rep(x)).val); newmodulo(m1:Mod,m2:Mod):Mod == r := merge(m1,m2); r case "failed" => error "incompatible moduli"; r::Mod; (x:%) = (y:%):Boolean == { (rep(x)).val = (rep(y)).val => true; (rep(x)).modulo = (rep(y)).modulo => false; (rep(x - y)).val = 0; } (x:%) + (y:%):% == { reduce((rep(x)).val +$R (rep(y)).val, newmodulo((rep(x)).modulo,(rep(y)).modulo)) } (x:%) - (y:%):% == { reduce((rep(x)).val -$R (rep(y)).val, newmodulo((rep(x)).modulo,(rep(y)).modulo)) } - (x:%):% == reduce(-$R (rep(x)).val,(rep(x)).modulo); (x:%) * (y:%):% == { reduce((rep(x)).val *$R (rep(y)).val, newmodulo((rep(x)).modulo,(rep(y)).modulo)) } exQuo(x:%,y:%):Partial(%) == { xm := (rep(x)).modulo; if not (xm =$Mod (rep(y)).modulo) then xm := newmodulo(xm,(rep(y)).modulo); r := exactQuo((rep(x)).val,(rep(y)).val,xm); r case "failed" => failed; per([r::R,xm]$Rep)::Partial % } recip (x:%):Partial(%) == { r := exactQuo(1$R,(rep(x)).val,(rep(x)).modulo); r case "failed" => failed; per([r::R,(rep(x)).modulo]$Rep)::Partial % } inv (x:%):% == { (u := recip x) case "failed" => error("not invertible"); u::% }; UnivariatePolynomialCategory(S:CommutativeRing):Category == with CommutativeRing degree: % -> Integer leadingCoefficient: % -> S reductum: % -> % monicDivide: (%, %) -> Record(quotient: %, remainder: %) coerce: S -> % EuclideanDomain:Category == with CommutativeRing QuotientRemainder GcdDomain EuclideanModularRing(S:CommutativeRing,R:UnivariatePolynomialCategory S, Mod:AbelianMonoid,reduction:(R,Mod) -> R, merge:(Mod,Mod) -> Partial Mod, exactQuo : (R,R,Mod) -> Partial(R)): EuclideanDomain with modulus : % -> Mod coerce : % -> R reduce : (R,Mod) -> % exQuo : (%,%) -> Partial(%) recip : % -> Partial(%) inv : % -> % -- if S has IntegerNumberSystem then -- frobenius: % -> % == ModularRing(R,Mod,reduction,merge,exactQuo) add --representation Rep ==> Record(val:R,modulo:Mod) import from Rep import from Mod import from S import from Partial(Mod) --declarations default x,y,z: % divide(x:%,y:%):Record(quotient:%, remainder:%) == t:=merge(rep(x).modulo,rep(y).modulo) t case "failed" => error "incompatible moduli" xm:=t::Mod yv:=rep(y).val local invlcy:R if one? leadingCoefficient yv then invlcy:=1 else invlcy:=rep(inv reduce((leadingCoefficient yv)::R,xm)).val yv:=reduction(invlcy*yv,xm) r:=monicDivide(rep(x).val,yv) [reduce(invlcy*r.quotient,xm),reduce(r.remainder,xm)] (x:%) rem (y:%):% == t:=merge(x.modulo,y.modulo) t case "failed" => error "incompatible moduli" xm:=t::Mod yv:=rep(y).val local invlcy:R if not one? leadingCoefficient yv then invlcy:=rep(inv reduce((leadingCoefficient yv)::R,xm)).val yv:=reduction(invlcy*yv,xm) r:=monicDivide(rep(x).val,yv) reduce(r.remainder,xm) euclideanSize(x:%):Integer == degree( rep(x).val) unitCanonical(x:%):% == zero? x => x degree(rep(x).val) = 0 => 1 one? leadingCoefficient(rep(x).val) => x invlcx:%:=inv reduce((leadingCoefficient(rep(x).val))::R,rep(x).modulo) invlcx * x unitNormal(x:%):Record(unit:%, corr:%, assoc:%) == zero?(x) or one?(leadingCoefficient(rep(x).val)) => [1, x, 1] lcx := reduce((leadingCoefficient(rep(x).val))::R,rep(x).modulo) invlcx:=inv lcx degree(rep(x).val) = 0 => [lcx, 1, invlcx] [lcx, invlcx * x, invlcx] -- if S has IntegerNumberSystem then -- frobenius x == -- zero?(m:=x.modulo) => x -- e := convert(m)@Integer::PositiveInteger -- xp := monomial(1,e) --)abb domain MODFIELD ModularField ModularField(R:CommutativeRing,Mod:AbelianMonoid, reduction:(R,Mod) -> R, merge:(Mod,Mod) -> Partial(Mod), exactQuo : (R,R,Mod) -> Partial(R)): Field with modulus : % -> Mod coerce : % -> R reduce : (R,Mod) -> % exQuo : (%,%) -> Partial(%) == ModularRing(R,Mod,reduction,merge,exactQuo) add