/usr/share/gap/pkg/float/lib/mpc.gi is in gap-float 0.7.4+ds-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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##
#W mpc.gi GAP library Laurent Bartholdi
##
#Y Copyright (C) 2008 Laurent Bartholdi
##
## This file deals with complex floats
##
################################################################
# viewers
################################################################
InstallMethod(ViewString, "float", [IsMPCFloat],
function(obj)
return VIEWSTRING_MPC(obj,FLOAT.VIEW_DIG);
end);
InstallMethod(String, "float, int", [IsMPCFloat, IsInt],
function(obj,len)
return STRING_MPC(obj,len);
end);
InstallMethod(String, "float", [IsMPCFloat],
obj->STRING_MPC(obj,0));
BindGlobal("MPCBITS@", function(obj)
local s;
s := ValueOption("bits");
if IsInt(s) then return s; fi;
if IsMPCFloat(obj) then return PrecisionFloat(obj); fi;
return MPC.constants.MANT_DIG;
end);
BindGlobal("MPCFLOAT_STRING", s->MPC_STRING(s,MPCBITS@(fail)));
################################################################
# constants
################################################################
EAGER_FLOAT_LITERAL_CONVERTERS.c := MPCFLOAT_STRING;
DeclareCategory("IsMPCPseudoField", IsFloatPseudoField);
BindGlobal("MPC_PSEUDOFIELD",
Objectify(NewType(CollectionsFamily(MPCFloatsFamily),
IsMPCPseudoField and IsAttributeStoringRep),rec()));
SetName(MPC_PSEUDOFIELD, FLOAT_COMPLEX_STRING);
SetLeftActingDomain(MPC_PSEUDOFIELD,Rationals);
SetCharacteristic(MPC_PSEUDOFIELD,0);
SetDimension(MPC_PSEUDOFIELD,infinity);
SetSize(MPC_PSEUDOFIELD,infinity);
SetIsWholeFamily(MPC_PSEUDOFIELD,true);
SetZero(MPC_PSEUDOFIELD,MPC_INT(0));
SetOne(MPC_PSEUDOFIELD,MPC_INT(1));
InstallMethod( \in, [IsMPCFloat,IsMPCPseudoField], ReturnTrue);
SetIsUFDFamily(MPCFloatsFamily,true);
SetZero(MPCFloatsFamily,MPC_INT(0));
SetOne(MPCFloatsFamily,MPC_INT(1));
InstallValue(MPC, rec(
creator := MPCFLOAT_STRING,
eager := 'c',
filter := IsMPCFloat,
field := MPC_PSEUDOFIELD,
reals := MPFR,
constants := rec(INFINITY := MPC_MAKEINFINITY(1),
VIEW_DIG := 6,
DECIMAL_DIG := 30,
MANT_DIG := 100,
NAN := MPC_MAKENAN(1),
recompute := function(r,prec)
r.PI := MPC_MPFR(MPFR_PI(prec));
r.1_PI := Inverse(r.PI);
r.2PI := MPC_INT(2)*r.PI;
r.2_PI := MPC_INT(2)*r.1_PI;
r.2_SQRTPI := MPC_INT(2)/Sqrt(r.PI);
r.PI_2 := r.PI/MPC_INT(2);
r.PI_4 := r.PI_2/MPC_INT(2);
r.SQRT2 := Sqrt(MPC_INTPREC(2,prec));
r.1_SQRT2 := Inverse(r.SQRT2);
r.E := Exp(MPC_INTPREC(1,prec));
r.LN2 := Log(MPC_INTPREC(2,prec));
r.LN10 := Log(MPC_INTPREC(10,prec));
r.LOG10E := Inverse(r.LN10);
r.LOG2E := Inverse(r.LN2);
r.I := MPC_2MPFR(MPFR_INT(0),MPFR_INTPREC(1,prec));
r.2IPI := r.I*r.2PI;
r.OMEGA := MPC_2MPFR(MPFR_INT(1),Sqrt(MPFR_INTPREC(3,prec)))/MPC_INT(2);
end)));
InstallMethod(ObjByExtRep, [IsMPCFloatFamily,IsCyclotomicCollection],
function(family,obj)
return OBJBYEXTREP_MPC(obj);
end);
################################################################
# unary operations
################################################################
CallFuncList(function(arg)
local i;
for i in arg do
InstallOtherMethod(VALUE_GLOBAL(i[1]), "MPC float", [IsMPCFloat], i[2]);
od;
end, [["AINV",AINV_MPC],
["AINV_MUT",AINV_MPC],
["INV",INV_MPC],
["INV_MUT",INV_MPC],
["AbsoluteValue",ABS_MPC],
["ZeroMutable",ZERO_MPC],
["ZeroImmutable",ZERO_MPC],
["ZeroSameMutability",ZERO_MPC],
["OneMutable",ONE_MPC],
["OneImmutable",ONE_MPC],
["OneSameMutability",ONE_MPC],
["ComplexI",CXI_MPC],
["Sqrt",SQRT_MPC],
["Cos",COS_MPC],
["Sin",SIN_MPC],
["Tan",TAN_MPC],
["Asin",ASIN_MPC],
["Acos",ACOS_MPC],
["Atan",ATAN_MPC],
["Cosh",COSH_MPC],
["Sinh",SINH_MPC],
["Tanh",TANH_MPC],
["Asinh",ASINH_MPC],
["Acosh",ACOSH_MPC],
["Atanh",ATANH_MPC],
["Log",LOG_MPC],
["Exp",EXP_MPC],
["Square",SQR_MPC],
["SphereProject",PROJ_MPC],
["FrExp",FREXP_MPC],
["Norm",NORM_MPC],
["Argument",ZERO_MPC],
["IsXInfinity",ISINF_MPC],
["IsPInfinity",ISINF_MPC],
["IsNInfinity",ISINF_MPC],
["IsFinite",ISNUMBER_MPC],
["IsNaN",ISNAN_MPC],
["ExtRepOfObj",EXTREPOFOBJ_MPC],
["RealPart",REAL_MPC],
["ImaginaryPart",IMAG_MPC],
["ComplexConjugate",CONJ_MPC],
["PrecisionFloat",PREC_MPC]]);
################################################################
# binary operations
################################################################
CallFuncList(function(arg)
local i;
for i in arg do
InstallMethod(VALUE_GLOBAL(i), "MPC float, MPC float", [IsMPCFloat, IsMPCFloat],
VALUE_GLOBAL(Concatenation(i,"_MPC")));
InstallMethod(VALUE_GLOBAL(i), "MPC float, MPFR float", [IsMPCFloat, IsMPFRFloat],
VALUE_GLOBAL(Concatenation(i,"_MPC_MPFR")));
InstallMethod(VALUE_GLOBAL(i), "MPFR float, MPC float", [IsMPFRFloat, IsMPCFloat],
VALUE_GLOBAL(Concatenation(i,"_MPFR_MPC")));
od;
end, ["SUM","DIFF","QUO","PROD","LQUO","POW","EQ","LT"]);
InstallMethod(LdExp, "MPC float, int", [IsMPCFloat, IsInt], LDEXP_MPC);
InstallMethod(RootsFloatOp, "MPC float list, MPC float",
[IsList,IsMPCFloat],
function(coeff,tag)
if ForAll(coeff,x->IsMPCFloat(x)) then
return ROOTPOLY_MPC(coeff,MPCBITS@(fail));
fi;
TryNextMethod();
end);
################################################################
# constructor
################################################################
INSTALLFLOATCREATOR("for list", [IsMPCFloat,IsList],
function(filter,list)
return OBJBYEXTREP_MPC(list);
end);
INSTALLFLOATCREATOR("for integers", [IsMPCFloat,IsInt],
function(filter,int)
return MPC_INTPREC(int,MPCBITS@(filter));
end);
INSTALLFLOATCREATOR("for rationals", [IsMPCFloat,IsRat], -1,
function(filter,rat)
local n, d, prec;
n := NumeratorRat(rat);
d := DenominatorRat(rat);
prec := MPCBITS@(filter);
return MPC_INTPREC(n,prec)/MPC_INTPREC(d,prec);
end);
INSTALLFLOATCREATOR("for strings", [IsMPCFloat,IsString],
function(filter,s)
return MPC_STRING(s,MPCBITS@(filter));
end);
INSTALLFLOATCREATOR("for MPC float", [IsMPCFloat,IsMPCFloat],
function(filter,obj)
return MPC_MPCPREC(obj,MPCBITS@(filter));
end);
INSTALLFLOATCREATOR("for MPFR float", [IsMPCFloat,IsMPFRFloat],
function(filter,obj)
return MPC_MPFR(obj);
end);
DECLAREFLOATCREATOR(IsMPCFloat,IsMPFRFloat,IsMPFRFloat);
INSTALLFLOATCREATOR("for 2 MPFR floats", [IsMPCFloat,IsMPFRFloat,IsMPFRFloat],
function(filter,re,im)
return MPC_2MPFR(re,im);
end);
DECLAREFLOATCREATOR(IsMPCFloat,IsInt,IsInt);
INSTALLFLOATCREATOR("for 2 ints", [IsMPCFloat,IsInt,IsInt],
function(filter,re,im)
return MPC_2MPFR(MPFR_INT(re),MPFR_INT(im));
end);
INSTALLFLOATCREATOR("for macfloat", [IsMPCFloat,IsIEEE754FloatRep],
function(filter,obj)
return MPC_MPFR(MPFR_MACFLOAT(obj));
end);
INSTALLFLOATCREATOR("for cyc", [IsMPCFloat,IsCyc], -2,
function(filter,obj)
local l, z;
l := ExtRepOfObj(obj);
z := MPC_2MPFR(0.0_r,2.0_r*MPFR_PI(MPCBITS@(filter)))/Length(l);
return l*List([0..Length(l)-1],i->Exp(z*i));
end);
INSTALLFLOATCONSTRUCTORS(MPC);
MPC.constants.recompute(MPC.constants,MPC.constants.MANT_DIG);
#############################################################################
##
#E
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