GAP (FLOAT) - Chapter 2: Float package

The extended floating-point capabilities of GAP are installed by loading the package via LoadPackage("float"); and selecting new floating-point handlers via SetFloats(MPFR), SetFloats(MPFI), SetFloats(MPC) orSetFloats(CXSC), depending on whether high-precision real, interval or complex arithmetic are desired, or whether a fast package containing all four real/complex element/interval arithmetic is desired:

gap> LoadPackage("float");
Loading FLOAT 0.7.0 ...
true
gap> SetFloats(MPFR); # floating-point
gap> x := 4*Atan(1.0);
.314159e1
gap> Sin(x);
.169569e-30
gap> SetFloats(MPFR,1000); # 1000 bits
gap> x := 4*Atan(1.0);
.314159e1
gap> Sin(x);
.125154e-300
gap> String(x,300);
".3141592653589793238462643383279502884197169399375105820974944592307816406286\
208998628034825342117067982148086513282306647093844609550582231725359408128481\
117450284102701938521105559644622948954930381964428810975665933446128475648233\
78678316527120190914564856692346034861045432664821339360726024914127e1"
gap>
gap> SetFloats(MPFI); # intervals
gap> x := 4*Atan(1.0);
.314159e1(99)
gap> AbsoluteDiameter(x); Sup(x); Inf(x);
.100441e-29
.314159e1
.314159e1
gap> Sin(x);
-.140815e-29(97)
gap> 0.0 in last;
true
gap> 1.0; # exact representation
.1e1(∞)
gap> IncreaseInterval(last,0.001); # now only 8 significant bits
.1e1(8)
gap> IncreaseInterval(last,-0.002); # now becomes empty
∅
gap> r2 := Sqrt(2.0);
.141421e1(99)
gap> MinimalPolynomial(Rationals,r2);
-2*x_1^2+1
gap> Cyc(r2);
E(8)-E(8)^3
gap>
gap> SetFloats(MPC); # complex numbers
gap> z := 5.0-1.0i;
.5e1-.1e1i
gap> (1+1.0i)*last^4*(239+1.0i);
.228488e6
gap> Exp(6.2835i);
.1e1+.314693e-3i

2 Float package

2.1 A sample run