static bool IsSignOfSinePositive(EDecimal x, ConstantCache consts, EContext context)
{
//truncating to [-2*PI;2*PI]
TruncateToPeriodicInterval(ref x, consts, context);
//now x in [-2*PI;2*PI]
if (x.GreaterThanOrEquals(-consts.TwoPi) && x.LessThanOrEquals(-consts.Pi))
{
return(true);
}
if (x.GreaterThanOrEquals(-consts.Pi) && (x.IsNegative || x.IsZero))
{
return(false);
}
if (!x.IsNegative && x.LessThanOrEquals(consts.Pi))
{
return(true);
}
if (x.GreaterThanOrEquals(consts.Pi) && x.LessThanOrEquals(consts.TwoPi))
{
return(false);
}
throw new Core.Exceptions.AngouriBugException("Should not be reached");
}
public static ConstantCache Lookup(EContext context)
{
if (!constants.TryGetValue(context, out var cache))
{
lock (constants)
if (!constants.TryGetValue(context, out cache))
{
cache = new ConstantCache(context);
constants.Add(context, cache);
}
}
return(cache);
}
/// <summary>Analogy of <see cref="Math.Cos(double)"/></summary>
public static EDecimal Cos(this EDecimal x, EContext context)
{
if (!x.IsFinite)
{
return(EDecimal.NaN);
}
// TODO: this check should be here to improve the performance a little bit, but tests won't work with that
// if (Utils.IsGoodAsDouble(x)) return EDecimal.FromDouble(Math.Cos(x.ToDouble()));
// Of course this will fail! Math.Cos works with double - only ~15 digits of accuracy.
// We have precision of 100 by default - which is over 95 digits of accuracy,
// albeit the last few digits are off. You have rejected the use of double early on
// - as well as the entirety of System.Math. -- Happypig375
var consts = ConstantCache.Lookup(context);
//truncating to [-2*PI;2*PI]
TruncateToPeriodicInterval(ref x, consts, context);
// now x in (-2pi,2pi)
if (x.GreaterThanOrEquals(consts.Pi) && x.LessThanOrEquals(consts.TwoPi))
{
return(-Cos(x.Subtract(consts.Pi, context), context));
}
if (x.GreaterThanOrEquals(-consts.TwoPi) && x.LessThanOrEquals(-consts.Pi))
{
return(-Cos(x.Add(consts.Pi, context), context));
}
x = x.Multiply(x, context);
//y=1-x/2!+x^2/4!-x^3/6!...
var xx = -x.Multiply(consts.Half, context);
var y = xx.Increment();
var cachedY = y.Decrement();//init cache with different value
for (var i = 1; !cachedY.Equals(y); i++)
{
cachedY = y;
EDecimal factor = i * ((i << 1) + 3) + 1; //2i^2+2i+i+1=2i^2+3i+1
factor = -consts.Half.Divide(factor, context);
xx = xx.Multiply(x.Multiply(factor, context), context);
y = y.Add(xx, context);
}
return(y);
}
/// <summary>Analogy of <see cref="Math.Tan(double)"/></summary>
public static EDecimal Tan(this EDecimal x, EContext context)
{
if (!x.IsFinite)
{
return(EDecimal.NaN);
}
var consts = ConstantCache.Lookup(context);
var cos = Cos(x, context);
if (cos.IsZero)
{
return(EDecimal.NaN);
}
//calculate sin using cos
var sin = CalculateSinFromCos(x, cos, consts, context);
return(sin.Divide(cos, context));
}
/// <summary>Helper function for calculating sin(x) from cos(x)</summary>
static EDecimal CalculateSinFromCos(EDecimal x, EDecimal cos, ConstantCache consts, EContext context)
{