public static EFloat operator *(EFloat a, EFloat b)
{
var v = a.v * b.v;
var prod = new[]
{
a.LowerBound *b.LowerBound,
a.UpperBound *b.LowerBound,
a.LowerBound *b.UpperBound,
a.UpperBound *b.UpperBound,
};
var low = Utils.NextFloatDown(
Math.Min(
Math.Min(prod[0], prod[1]),
Math.Min(prod[2], prod[3])));
var high = Utils.NextFloatUp(
Math.Max(
Math.Max(prod[0], prod[1]),
Math.Max(prod[2], prod[3])));
#if DEBUG
var vp = a.vp * b.vp;
EFloat.Validate(v, vp, low, high);
return(new EFloat(v, vp, low, high));
#else
return(new EFloat(v, low, high));
#endif
}
public static EFloat operator -(EFloat a, EFloat b)
{
var v = a.v - b.v;
var low = Utils.NextFloatDown(a.LowerBound - b.UpperBound);
var high = Utils.NextFloatUp(a.UpperBound - b.LowerBound);
#if DEBUG
var vp = a.vp - b.vp;
EFloat.Validate(v, vp, low, high);
return(new EFloat(v, vp, low, high));
#else
return(new EFloat(v, low, high));
#endif
}
// Negative values of `f` are not supported
public static EFloat Sqrt(EFloat f)
{
var v = (float)Math.Sqrt(f.v);
var low = Utils.NextFloatDown((float)Math.Sqrt(f.low));
var high = Utils.NextFloatUp((float)Math.Sqrt(f.high));
#if DEBUG
var vp = Math.Sqrt(f.vp);
EFloat.Validate(v, vp, low, high);
return(new EFloat(v, vp, low, high));
#else
return(new EFloat(v, low, high));
#endif
}
public static EFloat operator -(EFloat a)
{
var v = -a.v;
var low = -a.high;
var high = -a.low;
#if DEBUG
var vp = -a.vp;
EFloat.Validate(v, vp, low, high);
return(new EFloat(v, vp, low, high));
#else
return(new EFloat(v, low, high));
#endif
}
public static EFloat operator /(EFloat a, EFloat b)
{
var v = a.v / b.v;
float low, high;
if (b.low < 0 && b.high > 0)
{
// Guard against divide by zero;
// return interval of everything
low = float.NegativeInfinity;
high = float.PositiveInfinity;
}
else
{
var div = new[]
{
a.LowerBound / b.LowerBound,
a.UpperBound / b.LowerBound,
a.LowerBound / b.UpperBound,
a.UpperBound / b.UpperBound,
};
low = Utils.NextFloatDown(
Math.Min(
Math.Min(div[0], div[1]),
Math.Min(div[2], div[3])));
high = Utils.NextFloatUp(
Math.Max(
Math.Max(div[0], div[1]),
Math.Max(div[2], div[3])));
}
#if DEBUG
var vp = a.vp / b.vp;
EFloat.Validate(v, vp, low, high);
return(new EFloat(v, vp, low, high));
#else
return(new EFloat(v, low, high));
#endif
}