Optimize BigInteger.ToString for large decimal string

[kzrnm]

This PR is a counterpart to #55121. divide-and-conquer algorithm

Number.FormatBigInteger() can run in $D(n)log(N)$ time using the Divide and Conquer algorithm, where $D(n)$ represents the computational complexity of BigInteger division.

The computational complexity of division will be improved by #96895. Once 96895 is merged, I will add a benchmark and set the PR to "ready for review."

[dotnet-policy-service]

Tagging subscribers to this area: @dotnet/area-system-numerics
See info in area-owners.md if you want to be subscribed.

[huoyaoyuan]

If the length doesn't need to be exact, you can use integer estimation instead, similar to what I did in NumberToBigInteger.

[kzrnm]

Which part are you referring to? NumberToBigInteger also used $\log_{2^{32}}(10^9)$.

runtime/src/libraries/System.Runtime.Numerics/src/System/Number.BigInteger.cs

Lines 562 to 573 in 264e39c

	// shrink buffer to the currently used portion.
	// First, calculate the rough size of the buffer from the ratio that the number
	// of digits follows. Then, shrink the size until there is no more space left.
	// The Ratio is calculated as: log_{2^32}(10^9)
	constdoubledigitRatio=0.934292276687070661;
	currentBufferSize=Math.Min((int)(bufferSize*digitRatio)+1,bufferSize);
	Debug.Assert(buffer.Length==currentBufferSize||buffer[currentBufferSize]==0);
	while(0<currentBufferSize&&buffer[currentBufferSize-1]==0)
	{
	currentBufferSize--;
	}
	currentBuffer=buffer.Slice(0,currentBufferSize);

I rewrote it to use $\log_{2^{32}}(10)$ in pull request #97589, but it is essentially the same.

runtime/src/libraries/System.Runtime.Numerics/src/System/Number.BigInteger.cs

Lines 372 to 379 in 0d426df

	constdoubledigitRatio=0.10381025297;// log_{2^32}(10)
	intresultLength=checked((int)(digitRatio*number.Scale)+1+2);
	uint[]?resultBufferFromPool=null;
	Span<uint>resultBuffer=(
	resultLength<=BigIntegerCalculator.StackAllocThreshold
	?stackallocuint[BigIntegerCalculator.StackAllocThreshold]
	:resultBufferFromPool=ArrayPool<uint>.Shared.Rent(resultLength)).Slice(0,resultLength);
	resultBuffer.Clear();

[huoyaoyuan]

Is it required to calculate exact buffer length? Can it be relaxed, and let the algorithm to strip unnecessary zeros?

[kzrnm]

Is there a concise way to calculate the inexact buffer length? It would be most concise to find out from the predefined buffer length.

[dotnet-policy-service]

Draft Pull Request was automatically closed for 30 days of inactivity. Please let us know if you'd like to reopen it.