| Current Path : /usr/share/gap/lib/ |
Linux ift1.ift-informatik.de 5.4.0-216-generic #236-Ubuntu SMP Fri Apr 11 19:53:21 UTC 2025 x86_64 |
| Current File : //usr/share/gap/lib/ieee754.g |
#############################################################################
##
#W ieee754.g GAP library Steve Linton
## Stefan Kohl
## Laurent Bartholdi
##
##
#Y Copyright (C) 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## This file deals with macfloats
##
#############################################################################
##
#M Constructors . . . . . . . . . . . . . . . . . . . . . . . . for integers
##
INSTALLFLOATCREATOR("for IsIEEE754FloatRep and integer",
[ IsIEEE754FloatRep, IsInt ],
function ( filter, n )
local x, b, pow, sgn;
if n < 0 then n := -n; sgn := -1; else sgn := 1; fi;
x := MACFLOAT_INT(0);
b := MACFLOAT_INT(65536); pow := MACFLOAT_INT(1);
while n > 0 do
x := x + pow * MACFLOAT_INT(n mod 65536);
n := QUO_INT(n,65536);
pow := pow * b;
od;
return MACFLOAT_INT(sgn) * x;
end);
#############################################################################
##
#M Constructor. . . . . . . . . . . . . . . . . . . . . . . . . for strings
##
INSTALLFLOATCREATOR("for IsIEEE754FloatRep and string",
[ IsIEEE754FloatRep, IsString ],
function ( filter, s )
return MACFLOAT_STRING(s);
end);
#############################################################################
##
#M String( x ) . . . . . . . . . . . . . . . . . . . . . . . . for macfloats
##
BindGlobal("MACFLOAT_STRING_DOTTIFY", function(s)
local p;
if '.' in s or Intersection(s,"0123456789")=[] then return s; fi;
for p in [1..Length(s)] do
if not s[p] in "+-0123456789" then p := p-1; break; fi;
od;
Add(s,'.',p+1);
return s;
end);
InstallMethod( String, "for macfloats", [ IsIEEE754FloatRep ],
f->MACFLOAT_STRING_DOTTIFY(STRING_DIGITS_MACFLOAT(FLOAT.DECIMAL_DIG,f)));
InstallMethod( ViewString, "for macfloats", [ IsIEEE754FloatRep ],
f->MACFLOAT_STRING_DOTTIFY(STRING_DIGITS_MACFLOAT(FLOAT.VIEW_DIG,f)));
#############################################################################
##
#M Int( x ) . . . . . . . . . . . . . . . . . . . . . . . . . . . for macfloats
##
InstallMethod( Int, "for macfloats", true, [ IsIEEE754FloatRep ], 0, INTFLOOR_MACFLOAT );
#############################################################################
##
#M Sqrt, etc. for macfloats
##
InstallMethod( Sin, "for macfloats", [ IsIEEE754FloatRep ], SIN_MACFLOAT );
InstallMethod( Cos, "for macfloats", [ IsIEEE754FloatRep ], COS_MACFLOAT );
InstallMethod( Tan, "for macfloats", [ IsIEEE754FloatRep ], TAN_MACFLOAT );
InstallMethod( Acos, "for macfloats", [ IsIEEE754FloatRep ], ACOS_MACFLOAT );
InstallMethod( Asin, "for macfloats", [ IsIEEE754FloatRep ], ASIN_MACFLOAT );
InstallMethod( Atan, "for macfloats", [ IsIEEE754FloatRep ], ATAN_MACFLOAT );
InstallMethod( Atan2, "for macfloats", [ IsIEEE754FloatRep, IsIEEE754FloatRep ], ATAN2_MACFLOAT );
InstallMethod( Log, "for macfloats", [ IsIEEE754FloatRep ], LOG_MACFLOAT );
InstallMethod( Exp, "for macfloats", [ IsIEEE754FloatRep ], EXP_MACFLOAT );
if IsBound(LOG2_MACFLOAT) then
InstallMethod( Log2, "for macfloats", [ IsIEEE754FloatRep ], LOG2_MACFLOAT );
fi;
if IsBound(LOG10_MACFLOAT) then
InstallMethod( Log10, "for macfloats", [ IsIEEE754FloatRep ], LOG10_MACFLOAT );
fi;
if IsBound(LOG1P_MACFLOAT) then
InstallMethod( Log1p, "for macfloats", [ IsIEEE754FloatRep ], LOG1P_MACFLOAT );
fi;
if IsBound(EXP2_MACFLOAT) then
InstallMethod( Exp2, "for macfloats", [ IsIEEE754FloatRep ], EXP2_MACFLOAT );
fi;
if IsBound(EXPM1_MACFLOAT) then
InstallMethod( Expm1, "for macfloats", [ IsIEEE754FloatRep ], EXPM1_MACFLOAT );
fi;
if IsBound(EXP10_MACFLOAT) then
InstallMethod( Exp10, "for macfloats", [ IsIEEE754FloatRep ], EXP10_MACFLOAT );
fi;
InstallMethod( Sqrt, "for macfloats", [ IsIEEE754FloatRep ], SQRT_MACFLOAT );
InstallMethod( Round, "for macfloats", [ IsIEEE754FloatRep ], RINT_MACFLOAT );
InstallMethod( Floor, "for macfloats", [ IsIEEE754FloatRep ], FLOOR_MACFLOAT );
InstallMethod( Ceil, "for macfloats", [ IsIEEE754FloatRep ], CEIL_MACFLOAT );
InstallMethod( AbsoluteValue, "for macfloats", [ IsIEEE754FloatRep ], ABS_MACFLOAT );
InstallMethod( SignFloat, "for macfloats", [ IsIEEE754FloatRep ], SIGN_MACFLOAT );
InstallMethod( SignBit, "for macfloats", [ IsIEEE754FloatRep ], SIGNBIT_MACFLOAT );
InstallMethod( Hypothenuse, "for macfloats", [ IsIEEE754FloatRep, IsIEEE754FloatRep ], HYPOT_MACFLOAT );
InstallMethod( LdExp, "for macfloat,int", [ IsIEEE754FloatRep, IsInt ], LDEXP_MACFLOAT );
InstallMethod( FrExp, "for macfloat", [ IsIEEE754FloatRep ], FREXP_MACFLOAT );
InstallMethod( EqFloat, "for macfloats", [ IsIEEE754FloatRep, IsIEEE754FloatRep ], EQ_MACFLOAT );
InstallMethod( Zero, "for macfloats", [ IsIEEE754FloatRep ], x->MACFLOAT_INT(0));
InstallMethod( One, "for macfloats", [ IsIEEE754FloatRep ], x->MACFLOAT_INT(1));
InstallMethod( RealPart, "for macfloats", [ IsIEEE754FloatRep ], x->x);
InstallMethod( ImaginaryPart, "for macfloats", [ IsIEEE754FloatRep ], Zero);
InstallMethod( ComplexConjugate, "for macfloats", [ IsIEEE754FloatRep ], x->x);
#############################################################################
# default constructor record
DeclareCategory("IsIEEE754PseudoField", IsFloatPseudoField);
BindGlobal("IEEE754_PSEUDOFIELD",
Objectify(NewType(CollectionsFamily(IEEE754FloatsFamily),
IsIEEE754PseudoField and IsAttributeStoringRep),rec()));
SetName(IEEE754_PSEUDOFIELD, "IEEE754_PSEUDOFIELD");
SetLeftActingDomain(IEEE754_PSEUDOFIELD,Rationals);
SetCharacteristic(IEEE754_PSEUDOFIELD,0);
SetDimension(IEEE754_PSEUDOFIELD,infinity);
SetSize(IEEE754_PSEUDOFIELD,infinity);
SetIsWholeFamily(IEEE754_PSEUDOFIELD,true);
SetZero(IEEE754_PSEUDOFIELD,MACFLOAT_INT(0));
SetOne(IEEE754_PSEUDOFIELD,MACFLOAT_INT(1));
InstallMethod( \in, [IsIEEE754FloatRep,IsIEEE754PseudoField], ReturnTrue);
BindGlobal("IEEE754FLOAT", rec(
constants := rec(
DIG := 15,
VIEW_DIG := 6,
MANT_DIG := 53,
MAX_10_EXP := 308,
MAX_EXP := 1024,
MIN_10_EXP := -307,
MIN_EXP := -1021,
DECIMAL_DIG := 17,
INFINITY := MACFLOAT_STRING("inf"),
NINFINITY := MACFLOAT_STRING("-inf"),
NAN := MACFLOAT_STRING("nan")),
filter := IsIEEE754FloatRep,
field := IEEE754_PSEUDOFIELD,
creator := MACFLOAT_STRING,
eager := 'l'));
SetIsUFDFamily(IEEE754FloatsFamily,true);
SetZero(IEEE754FloatsFamily, NewFloat(IsIEEE754FloatRep,0));
SetOne(IEEE754FloatsFamily, NewFloat(IsIEEE754FloatRep,0));
InstallMethod( PrecisionFloat, "for macfloats", [ IsIEEE754FloatRep ], x->IEEE754FLOAT.constants.MANT_DIG );
IEEE754FLOAT.constants.EPSILON := LDEXP_MACFLOAT(MACFLOAT_INT(1),1-IEEE754FLOAT.constants.MANT_DIG);
IEEE754FLOAT.constants.MAX := LDEXP_MACFLOAT(NewFloat(IsIEEE754FloatRep,2^IEEE754FLOAT.constants.MANT_DIG-1),IEEE754FLOAT.constants.MAX_EXP-IEEE754FLOAT.constants.MANT_DIG);
IEEE754FLOAT.constants.MIN := LDEXP_MACFLOAT(MACFLOAT_INT(1),IEEE754FLOAT.constants.MIN_EXP-1);
if IsHPCGAP then
MakeReadOnlyObj( IEEE754FLOAT );
fi;
# finally install the default floateans
INSTALLFLOATCONSTRUCTORS(IEEE754FLOAT);
SetFloats(IEEE754FLOAT);
#############################################################################
##
#E