Sin/Cos/SinCos/Tan at default precision throw ArgumentOutOfRangeException on the library's own constants (e.g. Sin(PreciseNumber.Pi)) #124

What's wrong

The overloads that take no precision (Sin(x), Cos(x), SinCos(x), Tan(x), in PreciseNumber/PreciseNumber.Trigonometry.cs:101-102, 129-130, 157-158, 220-221) use DefaultTrigonometricPrecision(x) (line 736), which returns max(x.SignificantDigits, 50).

The built-in constants carry ConstantPrecision (150) digits and have one integer digit. For them the default asks for 150 digits, and reducing a one-integer-digit argument to 150 digits needs π to 151 digits. RequireReducibleArgument then throws. In other words, the overload that picks its own precision picks one it will refuse.

This contradicts two pieces of documentation:

• The XML docs for these overloads promise the result is "produced to the significant digits of x" and list no ArgumentOutOfRangeException.
• The remark on DefaultTrigonometricPrecision says it exists so that a constant carrying ConstantPrecision digits is handled.

Reproduction

Sin(PreciseNumber.Pi) → ArgumentOutOfRangeException: Reducing an argument of 1 integer digits to 150 significant digits needs π to 151 digits, but it is stored to 150. At most 149 …
Cos(Pi), Cos(Tau), Sin(E), SinCos(Pi) → same exception
Sin(Ln2) → works (0 integer digits)
Exp(Pi), Log(Pi), Pow(Pi, E), Sinh(Pi), Atan(Pi), Atan2(Pi, E), Asin(Pi/4) → all work at 150 digits

The same exception is thrown for any computed value that has at least 150 significant digits and at least one integer digit, for example a quotient or root of two constants.

Why it matters

Math.Sin(Math.PI)-style code is the most basic use of the API, and every other transcendental function handles these inputs. Callers can't predict which values will throw without knowing the internal ceiling on π digits.

Suggested fix

• In the default-precision overloads only, clamp the precision to what can be delivered: Math.Min(DefaultTrigonometricPrecision(x), ConstantPrecision - IntegerDigitCount(x)), with a floor of 1.
• Keep throwing only when even the clamped value is impossible, such as 1e200, which the existing refusal test already pins.
• The explicit (x, significantDigits) overloads keep their current strict behaviour, as intended by Trig/exp/log functions silently return under-precision (or wrong) digits once required working precision exceeds the 150-digit π/e/ln constants #96/Refuse a sine whose reduction needs more of π than exists [patch] #97.
• Add tests that Sin(Pi), Cos(Tau), SinCos(Pi) and Tan(Pi / 4) return values and do not throw.

Related: Tan's guard digits make the ceiling even lower for Tan, which I'm filing separately.