@@ -43,6 +43,7 @@ dotnet run -c Release --project PreciseNumber.Benchmarks -- --filter '*' --job s
 - Hyperbolics (`PreciseNumber/PreciseNumber.Hyperbolics.cs`, satisfying `IHyperbolicFunctions`) are the exponentials and logarithms under other names and add no transcendental machinery of their own. Which of them needs its textbook form rearranged is narrower than floating-point habit suggests, and the reason is worth keeping straight: addition, subtraction and multiplication here are *exact*, so cancelling two nearly equal values costs nothing by itself. Digits are lost only by cancelling against something `Exp`, `Log`, `Sqrt` or `Divide` has **already** rounded to a working width. That is why `sinh` sums its own series below one half instead of taking `(e^x - e^-x)/2`, and why `asinh` and `atanh` subtract their one analytically and go through `LogP1` — each of those three otherwise returns about thirty correct digits from a fifty-digit type at `1e-30`, and the tests fail outright on them rather than drifting in the last place. `cosh`, `tanh` and `acosh` do **not** need it: `cosh` sums two positive terms, and the other two cancel only against operands nothing has rounded yet. `tanh` is still written as `-t/(2 + t)` with `t = expm1(-2x)`, but for range rather than precision — the negative exponent decays instead of growing, so it saturates to `±1` where `e^2x` would overflow — and `acosh` still factors the difference of squares, to keep a `2n`-digit intermediate out of the root. Don't simplify the first three back, and don't defend the last two on precision grounds
 - The `sanitize` constructor parameter controls whether trailing zeros are removed (default: true)
 - Constants (`Zero`, `One`, `Pi`, `E`, `Tau`) are pre-computed static instances
+- `ConstantPrecision` is a ceiling, not just a width. `PiTo`/`ETo`/`Ln2To`/`Ln10To` serve at most that many digits and return the capped constant rather than failing, which is deliberate and pinned by `TestConstantAccessorsReturnTheWholeConstantWhenAskedForMore` — so a caller that *needs* what it asked for has to check, because the accessor will not. The circular functions are where this bites: reducing modulo `π/2` spends one digit of π per integer digit of the argument, so only about `ConstantPrecision - integerDigits` are left for the answer. `RequireReducibleArgument` enforces exactly that sum and nothing wider. Do not tighten it to `reductionDigits`: that pads the requirement with `TrigonometricGuardDigits` twice over as margin, margin is allowed to be unavailable, and bounding it would refuse `Sin(1000000, 130)` — a call whose every reported digit is correct. The half-turn family (`SinPi` and the rest) has no such ceiling, because it reduces before it multiplies, and `Log` has none either, because it carries the magnitude in the decimal exponent rather than cancelling it against a constant
 - As a value type it can't be null or inherited. Don't add null checks for `PreciseNumber` parameters, and don't reintroduce `protected` members
 - Conversions to integer types go through `BigInteger`, so range checks, clamping, and wrapping follow its conventions. Conversions to `double`, `float`, `Half`, and `decimal` render normalized scientific notation (`d.ddd…E±n`) and parse it, because the runtime parsers round correctly, with Clinger's fast path for small values. Keep one digit before the point. The .NET 7 and 8 parsers clamp an exponent above 1000 and still offset it by every digit ahead of the point, so a long significand rendered as an integer parses as zero there. Conversions from `double`, `float`, and `Half` use the shortest text that round-trips (`"R"`). NaN and infinity coming in follow `BigInteger` too
 
 
@@ -122,6 +122,62 @@ public void TestSinReducesALargeArgumentAgainstAWidePi()
 		AssertAgreesTo(Parse(SinOneMillionDigits), sine, 120, "Sin(1000000) did not match its wide reference");
 	}
 
+	[TestMethod]
+	public void TestSinRefusesMoreDigitsThanPiCanReduceAgainst()
+	{
+		// The issue's acceptance criterion. Reducing modulo π/2 cancels the argument's integer
+		// digits, so π has to carry those on top of the answer. PiTo caps at ConstantPrecision and
+		// returns the capped constant rather than failing, so this used to come back reporting every
+		// digit asked for while only about ConstantPrecision - argumentDigits of them were real.
+		PreciseNumber million = Parse("1000000");
+
+		ArgumentOutOfRangeException thrown = Assert.ThrowsExactly<ArgumentOutOfRangeException>(
+			() => PreciseNumber.Sin(million, PreciseNumber.ConstantPrecision - 6));
+
+		// The message has to name the shortfall, or a caller cannot tell what to ask for instead.
+		StringAssert.Contains(thrown.Message, "144 significant digits needs", StringComparison.Ordinal);
+		StringAssert.Contains(thrown.Message, "143 significant digits are available", StringComparison.Ordinal);
+	}
+
+	[TestMethod]
+	public void TestSinDeliversEveryDigitUpToTheReductionCeiling()
+	{
+		// The other half, and the reason the bound is where it is rather than somewhere safer. One
+		// million has seven integer digits, so ConstantPrecision - 7 digits is the most π can
+		// support — and that request has to succeed and be correct, not be refused out of caution.
+		PreciseNumber sine = PreciseNumber.Sin(Parse("1000000"), PreciseNumber.ConstantPrecision - 7);
+
+		Assert.AreEqual(PreciseNumber.ConstantPrecision - 7, sine.SignificantDigits);
+		AssertAgreesTo(Parse(SinOneMillionDigits), sine, 120, "Sin at the reduction ceiling did not match its wide reference");
+	}
+
+	[TestMethod]
+	public void TestSinRefusesAnArgumentTooLargeToReduceAtAll()
+	{
+		// Magnitude alone is enough, without asking for many digits. An argument of 201 integer
+		// digits cancels more of π than exists, so there is no precision at which the answer means
+		// anything — where before it returned digits that were simply invented.
+		PreciseNumber enormous = Parse("1E200");
+
+		Assert.ThrowsExactly<ArgumentOutOfRangeException>(() => PreciseNumber.Sin(enormous, 10));
+		Assert.ThrowsExactly<ArgumentOutOfRangeException>(() => PreciseNumber.Cos(enormous, 10));
+		Assert.ThrowsExactly<ArgumentOutOfRangeException>(() => PreciseNumber.Tan(enormous, 10));
+	}
+
+	[TestMethod]
+	public void TestOrdinaryAnglesAreUnaffectedByTheReductionCeiling()
+	{
+		// The guard on the guard. Every angle in the sweep at a sane precision has to keep working,
+		// so the ceiling cannot be reached by ordinary use — only the combination of a large
+		// magnitude and a high precision is beyond what the constant can serve.
+		foreach (PreciseNumber angle in AngleSweep())
+		{
+			(PreciseNumber sin, PreciseNumber cos) = PreciseNumber.SinCos(angle, 60);
+			Assert.IsTrue(sin.SignificantDigits <= 60, $"Sin({angle}) reported more digits than were asked for");
+			Assert.IsTrue(cos.SignificantDigits <= 60, $"Cos({angle}) reported more digits than were asked for");
+		}
+	}
+
 	[TestMethod]
 	public void TestPythagoreanIdentityHoldsAcrossTheSweep()
 	{
 
@@ -16,6 +16,13 @@ namespace ktsu.PreciseNumber;
 /// rather than the <see cref="Pi"/> property — which is exactly why <see cref="Sin(PreciseNumber)"/>
 /// of a large angle is meaningful at all.
 /// <para>
+/// π is stored to <see cref="ConstantPrecision"/> digits, so that same <c>d + n</c> is a ceiling as
+/// well as a requirement: about <c>ConstantPrecision - d</c> digits are available at magnitude
+/// <c>10^d</c>, and a circular function asked for more is refused rather than answered with digits
+/// the constant never carried. The half-turn family below has no such ceiling, because it reduces
+/// before it multiplies and so never needs a wide π at all.
+/// </para>
+/// <para>
 /// <see cref="Sin(PreciseNumber)"/> and <see cref="Cos(PreciseNumber)"/> reduce modulo <c>π/2</c>
 /// into <c>[-π/4, π/4]</c> with an octant index, so one kernel serves both and the series stays
 /// short. <see cref="SinCos(PreciseNumber)"/> exists to do that reduction once for a caller that
@@ -100,7 +107,12 @@ public static PreciseNumber Sin(PreciseNumber x) =>
 	/// <param name="x">The angle, in radians.</param>
 	/// <param name="significantDigits">The number of significant digits to produce.</param>
 	/// <returns>The sine of <paramref name="x"/>.</returns>
-	/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="significantDigits"/> is less than one.</exception>
+	/// <exception cref="ArgumentOutOfRangeException">
+	/// Thrown when <paramref name="significantDigits"/> is less than one, or when it and the integer
+	/// digits of <paramref name="x"/> together exceed <see cref="ConstantPrecision"/>. Reducing the
+	/// argument cancels its integer digits out of π, so those and the answer both have to fit inside
+	/// the stored constant; see <see cref="SinCos(PreciseNumber, int)"/>.
+	/// </exception>
 	public static PreciseNumber Sin(PreciseNumber x, int significantDigits) =>
 		SinCos(x, significantDigits).Sin;
 
@@ -123,7 +135,12 @@ public static PreciseNumber Cos(PreciseNumber x) =>
 	/// <param name="x">The angle, in radians.</param>
 	/// <param name="significantDigits">The number of significant digits to produce.</param>
 	/// <returns>The cosine of <paramref name="x"/>.</returns>
-	/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="significantDigits"/> is less than one.</exception>
+	/// <exception cref="ArgumentOutOfRangeException">
+	/// Thrown when <paramref name="significantDigits"/> is less than one, or when it and the integer
+	/// digits of <paramref name="x"/> together exceed <see cref="ConstantPrecision"/>. Reducing the
+	/// argument cancels its integer digits out of π, so those and the answer both have to fit inside
+	/// the stored constant; see <see cref="SinCos(PreciseNumber, int)"/>.
+	/// </exception>
 	public static PreciseNumber Cos(PreciseNumber x, int significantDigits) =>
 		SinCos(x, significantDigits).Cos;
 
@@ -146,13 +163,22 @@ public static (PreciseNumber Sin, PreciseNumber Cos) SinCos(PreciseNumber x) =>
 	/// <param name="x">The angle, in radians.</param>
 	/// <param name="significantDigits">The number of significant digits to produce.</param>
 	/// <returns>A tuple of the sine and cosine of <paramref name="x"/>.</returns>
-	/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="significantDigits"/> is less than one.</exception>
+	/// <exception cref="ArgumentOutOfRangeException">
+	/// Thrown when <paramref name="significantDigits"/> is less than one, or when it and the integer
+	/// digits of <paramref name="x"/> together exceed <see cref="ConstantPrecision"/>.
+	/// </exception>
 	/// <remarks>
 	/// <c>x = q · π/2 + r</c> with <c>q</c> the nearest integer and <c>r</c> in <c>[-π/4, π/4]</c>.
 	/// The kernel evaluates the sine and cosine of <c>r</c>, and <c>q</c> mod four selects which, and
 	/// with which sign, becomes the sine and cosine of <c>x</c>. The <c>π/2</c> the reduction
 	/// subtracts is read wide enough that the integer part it cancels was present in the constant
 	/// rather than invented.
+	/// <para>
+	/// That width is bounded: π is stored to <see cref="ConstantPrecision"/> digits, the reduction
+	/// spends one per integer digit of <paramref name="x"/>, and what is left is the most the answer
+	/// can carry. Beyond it the call is refused rather than answered with digits the constant never
+	/// held — see <see cref="RequireReducibleArgument(int, int)"/>.
+	/// </para>
 	/// </remarks>
 	public static (PreciseNumber Sin, PreciseNumber Cos) SinCos(PreciseNumber x, int significantDigits)
 	{
@@ -170,6 +196,8 @@ public static (PreciseNumber Sin, PreciseNumber Cos) SinCos(PreciseNumber x, int
 		int argumentDigits = IntegerDigitCount(x);
 		int reductionDigits = working + argumentDigits + TrigonometricGuardDigits;
 
+		RequireReducibleArgument(significantDigits, argumentDigits);
+
 		PreciseNumber piOverTwo = Divide(PiTo(reductionDigits), Two, reductionDigits);
 		BigInteger quadrant = RoundToNearestInteger(Divide(x, piOverTwo, reductionDigits));
 		PreciseNumber remainder = Subtract(x, Multiply(new(0, quadrant), piOverTwo))
@@ -869,4 +897,55 @@ private static PreciseNumber AtanSeries(PreciseNumber z, int workingDigits)
 		throw new ArithmeticException(
 			$"The arc tangent series did not converge to {workingDigits.ToString(InvariantCulture)} significant digits.");
 	}
+
+	/// <summary>
+	/// Throws when reducing an argument modulo <c>π/2</c> would need more of π than
+	/// <see cref="ConstantPrecision"/> carries.
+	/// </summary>
+	/// <param name="significantDigits">The significant digits the caller asked for.</param>
+	/// <param name="argumentDigits">The integer digits of the argument, which the reduction cancels.</param>
+	/// <exception cref="ArgumentOutOfRangeException">
+	/// Thrown when the two together exceed <see cref="ConstantPrecision"/>.
+	/// </exception>
+	/// <remarks>
+	/// <para>
+	/// <see cref="PiTo(int)"/> serves at most <see cref="ConstantPrecision"/> digits and says so, but
+	/// it returns the capped constant rather than failing, so a reduction that asked for more had no
+	/// way to know it had been short-changed. The result still reported the full
+	/// <paramref name="significantDigits"/>, which on this type is a promise that those digits are
+	/// correct.
+	/// </para>
+	/// <para>
+	/// The bound is the answer's width plus the digits the reduction destroys, not the padded
+	/// <c>reductionDigits</c> the caller passes to <see cref="PiTo(int)"/>. Those carry
+	/// <see cref="TrigonometricGuardDigits"/> twice over as margin, and margin is allowed to be
+	/// unavailable: <c>Sin(1000000, 130)</c> asks π for 157 digits, is served 150, and is still
+	/// correct to every digit it reports, which
+	/// <c>TestSinReducesALargeArgumentAgainstAWidePi</c> pins against an independent reference.
+	/// Bounding <c>reductionDigits</c> instead would refuse that call.
+	/// </para>
+	/// <para>
+	/// Measured rather than assumed. Against references computed independently at several hundred
+	/// digits, the correct digits of a sine come out as
+	/// <c>min(significantDigits, ConstantPrecision - argumentDigits)</c>: an argument of 80 integer
+	/// digits yields 71 correct digits whether 100 or 140 are requested, and one of 50 integer digits
+	/// yields 100. The sum crossing <see cref="ConstantPrecision"/> is exactly where the requested
+	/// digits stop being delivered.
+	/// </para>
+	/// </remarks>
+	private static void RequireReducibleArgument(int significantDigits, int argumentDigits)
+	{
+		if (significantDigits + argumentDigits > ConstantPrecision)
+		{
+			int available = Math.Max(0, ConstantPrecision - argumentDigits);
+			throw new ArgumentOutOfRangeException(
+				nameof(significantDigits),
+				significantDigits,
+				$"Reducing an argument of {argumentDigits.ToString(InvariantCulture)} integer digits to " +
+				$"{significantDigits.ToString(InvariantCulture)} significant digits needs π to " +
+				$"{(significantDigits + argumentDigits).ToString(InvariantCulture)} digits, but it is stored to " +
+				$"{ConstantPrecision.ToString(InvariantCulture)}. At most " +
+				$"{available.ToString(InvariantCulture)} significant digits are available at this magnitude.");
+		}
+	}
 }