1925 lines
82 KiB
C#
1925 lines
82 KiB
C#
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using System;
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using System.Runtime.CompilerServices;
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using System.Runtime.InteropServices;
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namespace Unity.Burst
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{
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#if BURST_COMPILER_SHARED
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internal static partial class BurstStringInternal
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#else
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internal static partial class BurstString
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#endif
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{
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// This file provides an implementation for formatting floating point numbers that is compatible
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// with Burst
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// ------------------------------------------------------------------------------
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// Part of code translated to C# from http://www.ryanjuckett.com/programming/printing-floating-point-numbers
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// with the following license:
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/******************************************************************************
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Copyright (c) 2014 Ryan Juckett
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http://www.ryanjuckett.com/
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This software is provided 'as-is', without any express or implied
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warranty. In no event will the authors be held liable for any damages
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arising from the use of this software.
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Permission is granted to anyone to use this software for any purpose,
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including commercial applications, and to alter it and redistribute it
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freely, subject to the following restrictions:
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1. The origin of this software must not be misrepresented; you must not
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claim that you wrote the original software. If you use this software
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in a product, an acknowledgment in the product documentation would be
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appreciated but is not required.
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2. Altered source versions must be plainly marked as such, and must not be
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misrepresented as being the original software.
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3. This notice may not be removed or altered from any source
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distribution.
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******************************************************************************/
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//******************************************************************************
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// Get the log base 2 of a 32-bit unsigned integer.
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// http://graphics.stanford.edu/~seander/bithacks.html#IntegerLogLookup
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//******************************************************************************
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private static readonly byte[] logTable = new byte[256]
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{
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0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3,
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4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
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5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
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5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
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6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
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6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
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6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
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6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
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7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
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7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
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7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
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7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
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7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
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7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
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7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
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7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
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};
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private static uint LogBase2(uint val)
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{
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uint temp;
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temp = val >> 24;
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if (temp != 0)
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return (uint)(24 + logTable[(int)temp]);
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temp = val >> 16;
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if (temp != 0)
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return (uint)(16 + logTable[temp]);
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temp = val >> 8;
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if (temp != 0)
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return (uint)(8 + logTable[temp]);
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return logTable[val];
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}
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//******************************************************************************
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// This structure stores a high precision unsigned integer. It uses a buffer
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// of 32 bit integer blocks along with a length. The lowest bits of the integer
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// are stored at the start of the buffer and the length is set to the minimum
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// value that contains the integer. Thus, there are never any zero blocks at the
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// end of the buffer.
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//******************************************************************************
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public unsafe struct tBigInt
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{
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//******************************************************************************
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// Maximum number of 32 bit blocks needed in high precision arithmetic
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// to print out 64 bit IEEE floating point values.
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//******************************************************************************
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const int c_BigInt_MaxBlocks = 35;
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//// Copy integer
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//tBigInt & operator=(tBigInt &rhs)
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//{
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// uint length = rhs.m_length;
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// uint* pLhsCur = m_blocks;
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// for (uint* pRhsCur = rhs.m_blocks, *pRhsEnd = pRhsCur + length;
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// pRhsCur != pRhsEnd;
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// ++pLhsCur, ++pRhsCur)
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// {
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// *pLhsCur = *pRhsCur;
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// }
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// m_length = length;
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// return *this;
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//}
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// Data accessors
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public int GetLength() { return m_length; }
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public uint GetBlock(int idx) { return m_blocks[idx]; }
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// Zero helper functions
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public void SetZero() { m_length = 0; }
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public bool IsZero() { return m_length == 0; }
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// Basic type accessors
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public void SetU64(ulong val)
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{
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if (val > 0xFFFFFFFF)
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{
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m_blocks[0] = (uint)(val & 0xFFFFFFFF);
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m_blocks[1] = (uint)(val >> 32 & 0xFFFFFFFF);
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m_length = 2;
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}
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else if (val != 0)
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{
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m_blocks[0] = (uint)(val & 0xFFFFFFFF);
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m_length = 1;
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}
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else
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{
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m_length = 0;
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}
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}
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public void SetU32(uint val)
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{
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if (val != 0)
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{
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m_blocks[0] = val;
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m_length = (val != 0) ? 1 : 0;
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}
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else
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{
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m_length = 0;
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}
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}
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public uint GetU32() { return (m_length == 0) ? 0 : m_blocks[0]; }
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// Member data
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public int m_length;
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public fixed uint m_blocks[c_BigInt_MaxBlocks];
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}
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//******************************************************************************
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// Returns 0 if (lhs = rhs), negative if (lhs < rhs), positive if (lhs > rhs)
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//******************************************************************************
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private static unsafe int BigInt_Compare(in tBigInt lhs, in tBigInt rhs)
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{
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// A bigger length implies a bigger number.
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int lengthDiff = lhs.m_length - rhs.m_length;
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if (lengthDiff != 0)
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return lengthDiff;
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// Compare blocks one by one from high to low.
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for (int i = (int)lhs.m_length - 1; i >= 0; --i)
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{
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if (lhs.m_blocks[i] == rhs.m_blocks[i])
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continue;
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else if (lhs.m_blocks[i] > rhs.m_blocks[i])
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return 1;
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else
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return -1;
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}
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// no blocks differed
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return 0;
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}
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//******************************************************************************
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// result = lhs + rhs
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//******************************************************************************
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private static unsafe void BigInt_Add(out tBigInt pResult, in tBigInt lhs, in tBigInt rhs)
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{
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if (lhs.m_length < rhs.m_length)
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{
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BigInt_Add_internal(out pResult, rhs, lhs);
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}
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else
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{
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BigInt_Add_internal(out pResult, lhs, rhs);
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}
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}
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private static unsafe void BigInt_Add_internal(out tBigInt pResult, in tBigInt pLarge, in tBigInt pSmall)
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{
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int largeLen = pLarge.m_length;
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int smallLen = pSmall.m_length;
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// The output will be at least as long as the largest input
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pResult.m_length = largeLen;
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// Add each block and add carry the overflow to the next block
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ulong carry = 0;
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fixed (uint * pLargeCur1 = pLarge.m_blocks)
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fixed (uint * pSmallCur1 = pSmall.m_blocks)
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fixed (uint * pResultCur1 = pResult.m_blocks)
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{
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uint* pLargeCur = pLargeCur1;
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uint* pSmallCur = pSmallCur1;
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uint* pResultCur = pResultCur1;
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uint* pLargeEnd = pLargeCur + largeLen;
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uint* pSmallEnd = pSmallCur + smallLen;
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while (pSmallCur != pSmallEnd)
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{
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ulong sum = carry + (ulong) (*pLargeCur) + (ulong) (*pSmallCur);
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carry = sum >> 32;
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(*pResultCur) = (uint)(sum & 0xFFFFFFFF);
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++pLargeCur;
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++pSmallCur;
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++pResultCur;
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}
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// Add the carry to any blocks that only exist in the large operand
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while (pLargeCur != pLargeEnd)
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{
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ulong sum = carry + (ulong) (*pLargeCur);
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carry = sum >> 32;
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(*pResultCur) = (uint)(sum & 0xFFFFFFFF);
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++pLargeCur;
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++pResultCur;
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}
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// If there's still a carry, append a new block
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if (carry != 0)
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{
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//RJ_ASSERT(carry == 1);
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//RJ_ASSERT((uint)(pResultCur - pResult.m_blocks) == largeLen && (largeLen < c_BigInt_MaxBlocks));
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*pResultCur = 1;
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pResult.m_length = largeLen + 1;
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}
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else
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{
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pResult.m_length = largeLen;
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}
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}
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}
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//******************************************************************************
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// result = lhs * rhs
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//******************************************************************************
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private static unsafe void BigInt_Multiply(out tBigInt pResult, in tBigInt lhs, in tBigInt rhs)
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{
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if (lhs.m_length < rhs.m_length)
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{
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BigInt_Multiply_internal(out pResult, rhs, lhs);
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}
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else
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{
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BigInt_Multiply_internal(out pResult, lhs, rhs);
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}
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}
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private static unsafe void BigInt_Multiply_internal(out tBigInt pResult, in tBigInt pLarge, in tBigInt pSmall)
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{
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// set the maximum possible result length
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int maxResultLen = pLarge.m_length + pSmall.m_length;
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// RJ_ASSERT( maxResultLen <= c_BigInt_MaxBlocks );
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// clear the result data
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// uint * pCur = pResult.m_blocks, *pEnd = pCur + maxResultLen; pCur != pEnd; ++pCur
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for (int i = 0; i < maxResultLen; i++)
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pResult.m_blocks[i] = 0;
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// perform standard long multiplication
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fixed (uint *pLargeBeg1 = pLarge.m_blocks)
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{
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uint* pLargeBeg = pLargeBeg1;
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uint* pLargeEnd = pLargeBeg + pLarge.m_length;
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// for each small block
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fixed (uint* pResultStart1 = pResult.m_blocks)
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fixed (uint* pSmallCur1 = pSmall.m_blocks)
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{
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uint* pSmallCur = pSmallCur1;
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uint* pSmallEnd = pSmallCur + pSmall.m_length;
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uint* pResultStart = pResultStart1;
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for (; pSmallCur != pSmallEnd; ++pSmallCur, ++pResultStart)
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{
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// if non-zero, multiply against all the large blocks and add into the result
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uint multiplier = *pSmallCur;
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if (multiplier != 0)
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{
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uint* pLargeCur = pLargeBeg;
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uint* pResultCur = pResultStart;
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ulong carry = 0;
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do
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{
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ulong product = (*pResultCur) + (*pLargeCur) * (ulong) multiplier + carry;
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carry = product >> 32;
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*pResultCur = (uint)(product & 0xFFFFFFFF);
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++pLargeCur;
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++pResultCur;
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} while (pLargeCur != pLargeEnd);
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//RJ_ASSERT(pResultCur < pResult.m_blocks + maxResultLen);
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*pResultCur = (uint) (carry & 0xFFFFFFFF);
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}
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}
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// check if the terminating block has no set bits
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if (maxResultLen > 0 && pResult.m_blocks[maxResultLen - 1] == 0)
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pResult.m_length = maxResultLen - 1;
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else
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pResult.m_length = maxResultLen;
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}
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}
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}
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//******************************************************************************
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// result = lhs * rhs
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//******************************************************************************
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private static unsafe void BigInt_Multiply(out tBigInt pResult, in tBigInt lhs, uint rhs)
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{
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// perform long multiplication
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uint carry = 0;
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fixed (uint* pResultCur1 = pResult.m_blocks)
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fixed (uint* pLhsCur1 = lhs.m_blocks)
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{
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uint* pResultCur = pResultCur1;
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uint* pLhsCur = pLhsCur1;
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uint* pLhsEnd = pLhsCur + lhs.m_length;
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for (; pLhsCur != pLhsEnd; ++pLhsCur, ++pResultCur)
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{
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ulong product = (ulong) (*pLhsCur) * rhs + carry;
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*pResultCur = (uint) (product & 0xFFFFFFFF);
|
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carry = (uint)(product >> 32);
|
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}
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// if there is a remaining carry, grow the array
|
||
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if (carry != 0)
|
||
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{
|
||
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// grow the array
|
||
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//RJ_ASSERT(lhs.m_length + 1 <= c_BigInt_MaxBlocks);
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||
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*pResultCur = (uint) carry;
|
||
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pResult.m_length = lhs.m_length + 1;
|
||
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}
|
||
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else
|
||
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{
|
||
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pResult.m_length = lhs.m_length;
|
||
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}
|
||
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}
|
||
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}
|
||
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||
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//******************************************************************************
|
||
|
|
// result = in * 2
|
||
|
|
//******************************************************************************
|
||
|
|
private static unsafe void BigInt_Multiply2(out tBigInt pResult, in tBigInt input)
|
||
|
|
{
|
||
|
|
// shift all the blocks by one
|
||
|
|
uint carry = 0;
|
||
|
|
|
||
|
|
fixed (uint* pResultCur1 = pResult.m_blocks)
|
||
|
|
fixed (uint* pLhsCur1 = input.m_blocks)
|
||
|
|
{
|
||
|
|
uint* pResultCur = pResultCur1;
|
||
|
|
uint* pLhsCur = pLhsCur1;
|
||
|
|
uint* pLhsEnd = pLhsCur + input.m_length;
|
||
|
|
for (; pLhsCur != pLhsEnd; ++pLhsCur, ++pResultCur)
|
||
|
|
{
|
||
|
|
uint cur = *pLhsCur;
|
||
|
|
*pResultCur = (cur << 1) | carry;
|
||
|
|
carry = cur >> 31;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (carry != 0)
|
||
|
|
{
|
||
|
|
// grow the array
|
||
|
|
// RJ_ASSERT(input.m_length + 1 <= c_BigInt_MaxBlocks);
|
||
|
|
*pResultCur = carry;
|
||
|
|
pResult.m_length = input.m_length + 1;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
pResult.m_length = input.m_length;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// result = result * 2
|
||
|
|
//******************************************************************************
|
||
|
|
private static unsafe void BigInt_Multiply2(ref tBigInt pResult)
|
||
|
|
{
|
||
|
|
// shift all the blocks by one
|
||
|
|
uint carry = 0;
|
||
|
|
|
||
|
|
fixed (uint* pCur1 = pResult.m_blocks)
|
||
|
|
{
|
||
|
|
uint* pCur = pCur1;
|
||
|
|
uint* pEnd = pCur + pResult.m_length;
|
||
|
|
for (; pCur != pEnd; ++pCur)
|
||
|
|
{
|
||
|
|
uint cur = *pCur;
|
||
|
|
*pCur = (cur << 1) | carry;
|
||
|
|
carry = cur >> 31;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (carry != 0)
|
||
|
|
{
|
||
|
|
// grow the array
|
||
|
|
// RJ_ASSERT(pResult.m_length + 1 <= c_BigInt_MaxBlocks);
|
||
|
|
*pCur = carry;
|
||
|
|
++pResult.m_length;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// result = result * 10
|
||
|
|
//******************************************************************************
|
||
|
|
private static unsafe void BigInt_Multiply10(ref tBigInt pResult)
|
||
|
|
{
|
||
|
|
// multiply all the blocks
|
||
|
|
ulong carry = 0;
|
||
|
|
|
||
|
|
fixed (uint* pCur1 = pResult.m_blocks)
|
||
|
|
{
|
||
|
|
uint* pCur = pCur1;
|
||
|
|
uint* pEnd = pCur + pResult.m_length;
|
||
|
|
for (; pCur != pEnd; ++pCur)
|
||
|
|
{
|
||
|
|
ulong product = (ulong) (*pCur) * 10 + carry;
|
||
|
|
(*pCur) = (uint) (product & 0xFFFFFFFF);
|
||
|
|
carry = product >> 32;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (carry != 0)
|
||
|
|
{
|
||
|
|
// grow the array
|
||
|
|
//RJ_ASSERT(pResult.m_length + 1 <= c_BigInt_MaxBlocks);
|
||
|
|
*pCur = (uint) carry;
|
||
|
|
++pResult.m_length;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
//******************************************************************************
|
||
|
|
private static readonly uint[] g_PowerOf10_U32 = new uint[]
|
||
|
|
{
|
||
|
|
1, // 10 ^ 0
|
||
|
|
10, // 10 ^ 1
|
||
|
|
100, // 10 ^ 2
|
||
|
|
1000, // 10 ^ 3
|
||
|
|
10000, // 10 ^ 4
|
||
|
|
100000, // 10 ^ 5
|
||
|
|
1000000, // 10 ^ 6
|
||
|
|
10000000, // 10 ^ 7
|
||
|
|
};
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// Note: This has a lot of wasted space in the big integer structures of the
|
||
|
|
// early table entries. It wouldn't be terribly hard to make the multiply
|
||
|
|
// function work on integer pointers with an array length instead of
|
||
|
|
// the tBigInt struct which would allow us to store a minimal amount of
|
||
|
|
// data here.
|
||
|
|
//******************************************************************************
|
||
|
|
private static unsafe tBigInt g_PowerOf10_Big(int i)
|
||
|
|
{
|
||
|
|
tBigInt result;
|
||
|
|
// 10 ^ 8
|
||
|
|
if (i == 0)
|
||
|
|
{
|
||
|
|
// { 1, { 100000000 } },
|
||
|
|
result.m_length = 1;
|
||
|
|
result.m_blocks[0] = 100000000;
|
||
|
|
}
|
||
|
|
else if (i == 1)
|
||
|
|
{
|
||
|
|
// 10 ^ 16
|
||
|
|
// { 2, { 0x6fc10000, 0x002386f2 } },
|
||
|
|
result.m_length = 2;
|
||
|
|
result.m_blocks[0] = 0x6fc10000;
|
||
|
|
result.m_blocks[1] = 0x002386f2;
|
||
|
|
}
|
||
|
|
else if (i == 2)
|
||
|
|
{
|
||
|
|
// 10 ^ 32
|
||
|
|
// { 4, { 0x00000000, 0x85acef81, 0x2d6d415b, 0x000004ee, } },
|
||
|
|
result.m_length = 4;
|
||
|
|
result.m_blocks[0] = 0x00000000;
|
||
|
|
result.m_blocks[1] = 0x85acef81;
|
||
|
|
result.m_blocks[2] = 0x2d6d415b;
|
||
|
|
result.m_blocks[3] = 0x000004ee;
|
||
|
|
}
|
||
|
|
else if (i == 3)
|
||
|
|
{
|
||
|
|
// 10 ^ 64
|
||
|
|
// { 7, { 0x00000000, 0x00000000, 0xbf6a1f01, 0x6e38ed64, 0xdaa797ed, 0xe93ff9f4, 0x00184f03, } },
|
||
|
|
result.m_length = 7;
|
||
|
|
result.m_blocks[0] = 0x00000000;
|
||
|
|
result.m_blocks[1] = 0x00000000;
|
||
|
|
result.m_blocks[2] = 0xbf6a1f01;
|
||
|
|
result.m_blocks[3] = 0x6e38ed64;
|
||
|
|
result.m_blocks[4] = 0xdaa797ed;
|
||
|
|
result.m_blocks[5] = 0xe93ff9f4;
|
||
|
|
result.m_blocks[6] = 0x00184f03;
|
||
|
|
}
|
||
|
|
else if (i == 4)
|
||
|
|
{
|
||
|
|
// 10 ^ 128
|
||
|
|
//{
|
||
|
|
// 14, {
|
||
|
|
// 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x2e953e01, 0x03df9909, 0x0f1538fd,
|
||
|
|
// 0x2374e42f, 0xd3cff5ec, 0xc404dc08, 0xbccdb0da, 0xa6337f19, 0xe91f2603, 0x0000024e, }
|
||
|
|
//},
|
||
|
|
result.m_length = 14;
|
||
|
|
result.m_blocks[0] = 0x00000000;
|
||
|
|
result.m_blocks[1] = 0x00000000;
|
||
|
|
result.m_blocks[2] = 0x00000000;
|
||
|
|
result.m_blocks[3] = 0x00000000;
|
||
|
|
result.m_blocks[4] = 0x2e953e01;
|
||
|
|
result.m_blocks[5] = 0x03df9909;
|
||
|
|
result.m_blocks[6] = 0x0f1538fd;
|
||
|
|
result.m_blocks[7] = 0x2374e42f;
|
||
|
|
result.m_blocks[8] = 0xd3cff5ec;
|
||
|
|
result.m_blocks[9] = 0xc404dc08;
|
||
|
|
result.m_blocks[10] = 0xbccdb0da;
|
||
|
|
result.m_blocks[11] = 0xa6337f19;
|
||
|
|
result.m_blocks[12] = 0xe91f2603;
|
||
|
|
result.m_blocks[13] = 0x0000024e;
|
||
|
|
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// 10 ^ 256
|
||
|
|
//{
|
||
|
|
// 27, {
|
||
|
|
// 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
|
||
|
|
// 0x00000000, 0x982e7c01, 0xbed3875b, 0xd8d99f72, 0x12152f87, 0x6bde50c6, 0xcf4a6e70,
|
||
|
|
// 0xd595d80f, 0x26b2716e, 0xadc666b0, 0x1d153624, 0x3c42d35a, 0x63ff540e, 0xcc5573c0,
|
||
|
|
// 0x65f9ef17, 0x55bc28f2, 0x80dcc7f7, 0xf46eeddc, 0x5fdcefce, 0x000553f7,
|
||
|
|
// }
|
||
|
|
//}
|
||
|
|
result.m_length = 27;
|
||
|
|
result.m_blocks[0] = 0x00000000;
|
||
|
|
result.m_blocks[1] = 0x00000000;
|
||
|
|
result.m_blocks[2] = 0x00000000;
|
||
|
|
result.m_blocks[3] = 0x00000000;
|
||
|
|
result.m_blocks[4] = 0x00000000;
|
||
|
|
result.m_blocks[5] = 0x00000000;
|
||
|
|
result.m_blocks[6] = 0x00000000;
|
||
|
|
result.m_blocks[7] = 0x00000000;
|
||
|
|
result.m_blocks[8] = 0x982e7c01;
|
||
|
|
result.m_blocks[9] = 0xbed3875b;
|
||
|
|
result.m_blocks[10] = 0xd8d99f72;
|
||
|
|
result.m_blocks[11] = 0x12152f87;
|
||
|
|
result.m_blocks[12] = 0x6bde50c6;
|
||
|
|
result.m_blocks[13] = 0xcf4a6e70;
|
||
|
|
result.m_blocks[14] = 0xd595d80f;
|
||
|
|
result.m_blocks[15] = 0x26b2716e;
|
||
|
|
result.m_blocks[16] = 0xadc666b0;
|
||
|
|
result.m_blocks[17] = 0x1d153624;
|
||
|
|
result.m_blocks[18] = 0x3c42d35a;
|
||
|
|
result.m_blocks[19] = 0x63ff540e;
|
||
|
|
result.m_blocks[20] = 0xcc5573c0;
|
||
|
|
result.m_blocks[21] = 0x65f9ef17;
|
||
|
|
result.m_blocks[22] = 0x55bc28f2;
|
||
|
|
result.m_blocks[23] = 0x80dcc7f7;
|
||
|
|
result.m_blocks[24] = 0xf46eeddc;
|
||
|
|
result.m_blocks[25] = 0x5fdcefce;
|
||
|
|
result.m_blocks[26] = 0x000553f7;
|
||
|
|
}
|
||
|
|
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// result = 10^exponent
|
||
|
|
//******************************************************************************
|
||
|
|
private static void BigInt_Pow10(out tBigInt pResult, uint exponent)
|
||
|
|
{
|
||
|
|
// make sure the exponent is within the bounds of the lookup table data
|
||
|
|
// RJ_ASSERT(exponent < 512);
|
||
|
|
|
||
|
|
// create two temporary values to reduce large integer copy operations
|
||
|
|
tBigInt temp1 = default;
|
||
|
|
tBigInt temp2 = default;
|
||
|
|
ref tBigInt pCurTemp = ref temp1;
|
||
|
|
ref tBigInt pNextTemp = ref temp2;
|
||
|
|
|
||
|
|
// initialize the result by looking up a 32-bit power of 10 corresponding to the first 3 bits
|
||
|
|
uint smallExponent = exponent & 0x7;
|
||
|
|
pCurTemp.SetU32(g_PowerOf10_U32[smallExponent]);
|
||
|
|
|
||
|
|
// remove the low bits that we used for the 32-bit lookup table
|
||
|
|
exponent >>= 3;
|
||
|
|
int tableIdx = 0;
|
||
|
|
// while there are remaining bits in the exponent to be processed
|
||
|
|
while (exponent != 0)
|
||
|
|
{
|
||
|
|
// if the current bit is set, multiply it with the corresponding power of 10
|
||
|
|
if ((exponent & 1) != 0)
|
||
|
|
{
|
||
|
|
// multiply into the next temporary
|
||
|
|
BigInt_Multiply(out pNextTemp, pCurTemp, g_PowerOf10_Big(tableIdx));
|
||
|
|
|
||
|
|
// swap to the next temporary
|
||
|
|
ref tBigInt pSwap = ref pCurTemp;
|
||
|
|
pCurTemp = pNextTemp;
|
||
|
|
pNextTemp = pSwap;
|
||
|
|
}
|
||
|
|
|
||
|
|
// advance to the next bit
|
||
|
|
++tableIdx;
|
||
|
|
exponent >>= 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
// output the result
|
||
|
|
pResult = pCurTemp;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// result = in * 10^exponent
|
||
|
|
//******************************************************************************
|
||
|
|
private static unsafe void BigInt_MultiplyPow10(out tBigInt pResult, in tBigInt input, uint exponent)
|
||
|
|
{
|
||
|
|
// make sure the exponent is within the bounds of the lookup table data
|
||
|
|
// RJ_ASSERT(exponent < 512);
|
||
|
|
|
||
|
|
// create two temporary values to reduce large integer copy operations
|
||
|
|
tBigInt temp1 = default;
|
||
|
|
tBigInt temp2 = default;
|
||
|
|
ref tBigInt pCurTemp = ref temp1;
|
||
|
|
ref tBigInt pNextTemp = ref temp2;
|
||
|
|
|
||
|
|
// initialize the result by looking up a 32-bit power of 10 corresponding to the first 3 bits
|
||
|
|
uint smallExponent = exponent & 0x7;
|
||
|
|
if (smallExponent != 0)
|
||
|
|
{
|
||
|
|
BigInt_Multiply(out pCurTemp, input, g_PowerOf10_U32[smallExponent]);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
pCurTemp = input;
|
||
|
|
}
|
||
|
|
|
||
|
|
// remove the low bits that we used for the 32-bit lookup table
|
||
|
|
exponent >>= 3;
|
||
|
|
int tableIdx = 0;
|
||
|
|
|
||
|
|
// while there are remaining bits in the exponent to be processed
|
||
|
|
while (exponent != 0)
|
||
|
|
{
|
||
|
|
// if the current bit is set, multiply it with the corresponding power of 10
|
||
|
|
if((exponent & 1) != 0)
|
||
|
|
{
|
||
|
|
// multiply into the next temporary
|
||
|
|
BigInt_Multiply( out pNextTemp, pCurTemp, g_PowerOf10_Big(tableIdx) );
|
||
|
|
|
||
|
|
// swap to the next temporary
|
||
|
|
ref tBigInt pSwap = ref pCurTemp;
|
||
|
|
pCurTemp = pNextTemp;
|
||
|
|
pNextTemp = pSwap;
|
||
|
|
}
|
||
|
|
|
||
|
|
// advance to the next bit
|
||
|
|
++tableIdx;
|
||
|
|
exponent >>= 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
// output the result
|
||
|
|
pResult = pCurTemp;
|
||
|
|
}
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// result = 2^exponent
|
||
|
|
//******************************************************************************
|
||
|
|
private static unsafe void BigInt_Pow2(out tBigInt pResult, uint exponent)
|
||
|
|
{
|
||
|
|
int blockIdx = (int)exponent / 32;
|
||
|
|
//RJ_ASSERT(blockIdx < c_BigInt_MaxBlocks);
|
||
|
|
|
||
|
|
for (uint i = 0; i <= blockIdx; ++i)
|
||
|
|
pResult.m_blocks[i] = 0;
|
||
|
|
|
||
|
|
pResult.m_length = blockIdx + 1;
|
||
|
|
|
||
|
|
int bitIdx = ((int)exponent % 32);
|
||
|
|
pResult.m_blocks[blockIdx] |= (uint)(1 << bitIdx);
|
||
|
|
}
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// This function will divide two large numbers under the assumption that the
|
||
|
|
// result is within the range [0,10) and the input numbers have been shifted
|
||
|
|
// to satisfy:
|
||
|
|
// - The highest block of the divisor is greater than or equal to 8 such that
|
||
|
|
// there is enough precision to make an accurate first guess at the quotient.
|
||
|
|
// - The highest block of the divisor is less than the maximum value on an
|
||
|
|
// unsigned 32-bit integer such that we can safely increment without overflow.
|
||
|
|
// - The dividend does not contain more blocks than the divisor such that we
|
||
|
|
// can estimate the quotient by dividing the equivalently placed high blocks.
|
||
|
|
//
|
||
|
|
// quotient = floor(dividend / divisor)
|
||
|
|
// remainder = dividend - quotient*divisor
|
||
|
|
//
|
||
|
|
// pDividend is updated to be the remainder and the quotient is returned.
|
||
|
|
//******************************************************************************
|
||
|
|
private static unsafe uint BigInt_DivideWithRemainder_MaxQuotient9(ref tBigInt pDividend, in tBigInt divisor)
|
||
|
|
{
|
||
|
|
// Check that the divisor has been correctly shifted into range and that it is not
|
||
|
|
// smaller than the dividend in length.
|
||
|
|
//RJ_ASSERT( !divisor.IsZero() &&
|
||
|
|
// divisor.m_blocks[divisor.m_length-1] >= 8 &&
|
||
|
|
// divisor.m_blocks[divisor.m_length-1] < 0xFFFFFFFF &&
|
||
|
|
// pDividend->m_length <= divisor.m_length );
|
||
|
|
|
||
|
|
// If the dividend is smaller than the divisor, the quotient is zero and the divisor is already
|
||
|
|
// the remainder.
|
||
|
|
int length = divisor.m_length;
|
||
|
|
if (pDividend.m_length < divisor.m_length)
|
||
|
|
return 0;
|
||
|
|
|
||
|
|
fixed (uint* pDivisorCur1 = divisor.m_blocks)
|
||
|
|
fixed (uint* pDividendCur1 = pDividend.m_blocks)
|
||
|
|
{
|
||
|
|
uint* pDivisorCur = pDivisorCur1;
|
||
|
|
uint* pDividendCur = pDividendCur1;
|
||
|
|
|
||
|
|
uint* pFinalDivisorBlock = pDivisorCur + length - 1;
|
||
|
|
uint* pFinalDividendBlock = pDividendCur + length - 1;
|
||
|
|
|
||
|
|
// Compute an estimated quotient based on the high block value. This will either match the actual quotient or
|
||
|
|
// undershoot by one.
|
||
|
|
uint quotient = *pFinalDividendBlock / (*pFinalDivisorBlock + 1);
|
||
|
|
//RJ_ASSERT(quotient <= 9);
|
||
|
|
|
||
|
|
// Divide out the estimated quotient
|
||
|
|
if (quotient != 0)
|
||
|
|
{
|
||
|
|
// dividend = dividend - divisor*quotient
|
||
|
|
ulong borrow = 0;
|
||
|
|
ulong carry = 0;
|
||
|
|
do
|
||
|
|
{
|
||
|
|
ulong product = (ulong) *pDivisorCur * (ulong) quotient + carry;
|
||
|
|
carry = product >> 32;
|
||
|
|
|
||
|
|
ulong difference = (ulong) *pDividendCur - (product & 0xFFFFFFFF) - borrow;
|
||
|
|
borrow = (difference >> 32) & 1;
|
||
|
|
|
||
|
|
*pDividendCur = (uint) (difference & 0xFFFFFFFF);
|
||
|
|
|
||
|
|
++pDivisorCur;
|
||
|
|
++pDividendCur;
|
||
|
|
} while (pDivisorCur <= pFinalDivisorBlock);
|
||
|
|
|
||
|
|
// remove all leading zero blocks from dividend
|
||
|
|
while (length > 0 && pDividend.m_blocks[length - 1] == 0)
|
||
|
|
--length;
|
||
|
|
|
||
|
|
pDividend.m_length = length;
|
||
|
|
}
|
||
|
|
|
||
|
|
// If the dividend is still larger than the divisor, we overshot our estimate quotient. To correct,
|
||
|
|
// we increment the quotient and subtract one more divisor from the dividend.
|
||
|
|
if (BigInt_Compare(pDividend, divisor) >= 0)
|
||
|
|
{
|
||
|
|
++quotient;
|
||
|
|
|
||
|
|
// dividend = dividend - divisor
|
||
|
|
pDivisorCur = pDivisorCur1;
|
||
|
|
pDividendCur = pDividendCur1;
|
||
|
|
|
||
|
|
ulong borrow = 0;
|
||
|
|
do
|
||
|
|
{
|
||
|
|
ulong difference = (ulong) *pDividendCur - (ulong) *pDivisorCur - borrow;
|
||
|
|
borrow = (difference >> 32) & 1;
|
||
|
|
|
||
|
|
*pDividendCur = (uint)(difference & 0xFFFFFFFF);
|
||
|
|
|
||
|
|
++pDivisorCur;
|
||
|
|
++pDividendCur;
|
||
|
|
} while (pDivisorCur <= pFinalDivisorBlock);
|
||
|
|
|
||
|
|
// remove all leading zero blocks from dividend
|
||
|
|
while (length > 0 && pDividend.m_blocks[length - 1] == 0)
|
||
|
|
--length;
|
||
|
|
|
||
|
|
pDividend.m_length = length;
|
||
|
|
}
|
||
|
|
|
||
|
|
return quotient;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// result = result << shift
|
||
|
|
//******************************************************************************
|
||
|
|
private static unsafe void BigInt_ShiftLeft(ref tBigInt pResult, uint shift)
|
||
|
|
{
|
||
|
|
// RJ_ASSERT( shift != 0 );
|
||
|
|
|
||
|
|
int shiftBlocks = (int)shift / 32;
|
||
|
|
int shiftBits = (int)shift % 32;
|
||
|
|
|
||
|
|
int inLength = pResult.m_length;
|
||
|
|
// RJ_ASSERT( inLength + shiftBlocks <= c_BigInt_MaxBlocks );
|
||
|
|
|
||
|
|
// check if the shift is block aligned
|
||
|
|
if (shiftBits == 0)
|
||
|
|
{
|
||
|
|
// process blocks high to low so that we can safely process in place
|
||
|
|
fixed (uint* pInBlocks1 = pResult.m_blocks)
|
||
|
|
{
|
||
|
|
uint* pInBlocks = pInBlocks1;
|
||
|
|
uint* pInCur = pInBlocks + inLength - 1;
|
||
|
|
uint* pOutCur = pInCur + shiftBlocks;
|
||
|
|
|
||
|
|
// copy blocks from high to low
|
||
|
|
for (; pInCur >= pInBlocks; --pInCur, --pOutCur)
|
||
|
|
{
|
||
|
|
*pOutCur = *pInCur;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// zero the remaining low blocks
|
||
|
|
for ( uint i = 0; i < shiftBlocks; ++i)
|
||
|
|
pResult.m_blocks[i] = 0;
|
||
|
|
|
||
|
|
pResult.m_length += shiftBlocks;
|
||
|
|
}
|
||
|
|
// else we need to shift partial blocks
|
||
|
|
else
|
||
|
|
{
|
||
|
|
int inBlockIdx = inLength - 1;
|
||
|
|
int outBlockIdx = inLength + shiftBlocks;
|
||
|
|
|
||
|
|
// set the length to hold the shifted blocks
|
||
|
|
//RJ_ASSERT( outBlockIdx < c_BigInt_MaxBlocks );
|
||
|
|
pResult.m_length = outBlockIdx + 1;
|
||
|
|
|
||
|
|
// output the initial blocks
|
||
|
|
int lowBitsShift = (32 - shiftBits);
|
||
|
|
uint highBits = 0;
|
||
|
|
uint block = pResult.m_blocks[inBlockIdx];
|
||
|
|
uint lowBits = block >> lowBitsShift;
|
||
|
|
while ( inBlockIdx > 0 )
|
||
|
|
{
|
||
|
|
pResult.m_blocks[outBlockIdx] = highBits | lowBits;
|
||
|
|
highBits = block << shiftBits;
|
||
|
|
|
||
|
|
--inBlockIdx;
|
||
|
|
--outBlockIdx;
|
||
|
|
|
||
|
|
block = pResult.m_blocks[inBlockIdx];
|
||
|
|
lowBits = block >> lowBitsShift;
|
||
|
|
}
|
||
|
|
|
||
|
|
// output the final blocks
|
||
|
|
// RJ_ASSERT( outBlockIdx == shiftBlocks + 1 );
|
||
|
|
pResult.m_blocks[outBlockIdx] = highBits | lowBits;
|
||
|
|
pResult.m_blocks[outBlockIdx-1] = block << shiftBits;
|
||
|
|
|
||
|
|
// zero the remaining low blocks
|
||
|
|
for ( uint i = 0; i < shiftBlocks; ++i)
|
||
|
|
pResult.m_blocks[i] = 0;
|
||
|
|
|
||
|
|
// check if the terminating block has no set bits
|
||
|
|
if (pResult.m_blocks[pResult.m_length - 1] == 0)
|
||
|
|
--pResult.m_length;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// Different modes for terminating digit output
|
||
|
|
//******************************************************************************
|
||
|
|
public enum CutoffMode
|
||
|
|
{
|
||
|
|
Unique, // as many digits as necessary to print a uniquely identifiable number
|
||
|
|
TotalLength, // up to cutoffNumber significant digits
|
||
|
|
FractionLength, // up to cutoffNumber significant digits past the decimal point
|
||
|
|
};
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// This is an implementation the Dragon4 algorithm to convert a binary number
|
||
|
|
// in floating point format to a decimal number in string format. The function
|
||
|
|
// returns the number of digits written to the output buffer and the output is
|
||
|
|
// not NUL terminated.
|
||
|
|
//
|
||
|
|
// The floating point input value is (mantissa * 2^exponent).
|
||
|
|
//
|
||
|
|
// See the following papers for more information on the algorithm:
|
||
|
|
// "How to Print Floating-Point Numbers Accurately"
|
||
|
|
// Steele and White
|
||
|
|
// http://kurtstephens.com/files/p372-steele.pdf
|
||
|
|
// "Printing Floating-Point Numbers Quickly and Accurately"
|
||
|
|
// Burger and Dybvig
|
||
|
|
// http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.72.4656&rep=rep1&type=pdf
|
||
|
|
//******************************************************************************
|
||
|
|
private static unsafe uint Dragon4
|
||
|
|
(
|
||
|
|
ulong mantissa, // value significand
|
||
|
|
int exponent, // value exponent in base 2
|
||
|
|
uint mantissaHighBitIdx, // index of the highest set mantissa bit
|
||
|
|
bool hasUnequalMargins, // is the high margin twice as large as the low margin
|
||
|
|
CutoffMode cutoffMode, // how to determine output length
|
||
|
|
uint cutoffNumber, // parameter to the selected cutoffMode
|
||
|
|
byte* pOutBuffer, // buffer to output into
|
||
|
|
uint bufferSize, // maximum characters that can be printed to pOutBuffer
|
||
|
|
out int pOutExponent // the base 10 exponent of the first digit
|
||
|
|
)
|
||
|
|
{
|
||
|
|
byte* pCurDigit = pOutBuffer;
|
||
|
|
|
||
|
|
// RJ_ASSERT( bufferSize > 0 );
|
||
|
|
|
||
|
|
// if the mantissa is zero, the value is zero regardless of the exponent
|
||
|
|
if (mantissa == 0)
|
||
|
|
{
|
||
|
|
*pCurDigit = (byte)'0';
|
||
|
|
pOutExponent = 0;
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
// compute the initial state in integral form such that
|
||
|
|
// value = scaledValue / scale
|
||
|
|
// marginLow = scaledMarginLow / scale
|
||
|
|
tBigInt scale = default; // positive scale applied to value and margin such that they can be
|
||
|
|
// represented as whole numbers
|
||
|
|
tBigInt scaledValue = default; // scale * mantissa
|
||
|
|
tBigInt scaledMarginLow = default; // scale * 0.5 * (distance between this floating-point number and its
|
||
|
|
// immediate lower value)
|
||
|
|
|
||
|
|
// For normalized IEEE floating point values, each time the exponent is incremented the margin also
|
||
|
|
// doubles. That creates a subset of transition numbers where the high margin is twice the size of
|
||
|
|
// the low margin.
|
||
|
|
tBigInt * pScaledMarginHigh;
|
||
|
|
tBigInt optionalMarginHigh = default;
|
||
|
|
|
||
|
|
if ( hasUnequalMargins )
|
||
|
|
{
|
||
|
|
// if we have no fractional component
|
||
|
|
if (exponent > 0)
|
||
|
|
{
|
||
|
|
// 1) Expand the input value by multiplying out the mantissa and exponent. This represents
|
||
|
|
// the input value in its whole number representation.
|
||
|
|
// 2) Apply an additional scale of 2 such that later comparisons against the margin values
|
||
|
|
// are simplified.
|
||
|
|
// 3) Set the margin value to the lowest mantissa bit's scale.
|
||
|
|
|
||
|
|
// scaledValue = 2 * 2 * mantissa*2^exponent
|
||
|
|
scaledValue.SetU64( 4 * mantissa );
|
||
|
|
BigInt_ShiftLeft(ref scaledValue, (uint)exponent);
|
||
|
|
|
||
|
|
// scale = 2 * 2 * 1
|
||
|
|
scale.SetU32( 4 );
|
||
|
|
|
||
|
|
// scaledMarginLow = 2 * 2^(exponent-1)
|
||
|
|
BigInt_Pow2( out scaledMarginLow, (uint)exponent );
|
||
|
|
|
||
|
|
// scaledMarginHigh = 2 * 2 * 2^(exponent-1)
|
||
|
|
BigInt_Pow2( out optionalMarginHigh, (uint)(exponent + 1));
|
||
|
|
}
|
||
|
|
// else we have a fractional exponent
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// In order to track the mantissa data as an integer, we store it as is with a large scale
|
||
|
|
|
||
|
|
// scaledValue = 2 * 2 * mantissa
|
||
|
|
scaledValue.SetU64( 4 * mantissa );
|
||
|
|
|
||
|
|
// scale = 2 * 2 * 2^(-exponent)
|
||
|
|
BigInt_Pow2(out scale, (uint)(-exponent + 2));
|
||
|
|
|
||
|
|
// scaledMarginLow = 2 * 2^(-1)
|
||
|
|
scaledMarginLow.SetU32( 1 );
|
||
|
|
|
||
|
|
// scaledMarginHigh = 2 * 2 * 2^(-1)
|
||
|
|
optionalMarginHigh.SetU32( 2 );
|
||
|
|
}
|
||
|
|
|
||
|
|
// the high and low margins are different
|
||
|
|
pScaledMarginHigh = &optionalMarginHigh;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// if we have no fractional component
|
||
|
|
if (exponent > 0)
|
||
|
|
{
|
||
|
|
// 1) Expand the input value by multiplying out the mantissa and exponent. This represents
|
||
|
|
// the input value in its whole number representation.
|
||
|
|
// 2) Apply an additional scale of 2 such that later comparisons against the margin values
|
||
|
|
// are simplified.
|
||
|
|
// 3) Set the margin value to the lowest mantissa bit's scale.
|
||
|
|
|
||
|
|
// scaledValue = 2 * mantissa*2^exponent
|
||
|
|
scaledValue.SetU64( 2 * mantissa );
|
||
|
|
BigInt_ShiftLeft(ref scaledValue, (uint)exponent);
|
||
|
|
|
||
|
|
// scale = 2 * 1
|
||
|
|
scale.SetU32( 2 );
|
||
|
|
|
||
|
|
// scaledMarginLow = 2 * 2^(exponent-1)
|
||
|
|
BigInt_Pow2(out scaledMarginLow, (uint)exponent );
|
||
|
|
}
|
||
|
|
// else we have a fractional exponent
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// In order to track the mantissa data as an integer, we store it as is with a large scale
|
||
|
|
|
||
|
|
// scaledValue = 2 * mantissa
|
||
|
|
scaledValue.SetU64( 2 * mantissa );
|
||
|
|
|
||
|
|
// scale = 2 * 2^(-exponent)
|
||
|
|
BigInt_Pow2(out scale, (uint)(-exponent + 1));
|
||
|
|
|
||
|
|
// scaledMarginLow = 2 * 2^(-1)
|
||
|
|
scaledMarginLow.SetU32( 1 );
|
||
|
|
}
|
||
|
|
|
||
|
|
// the high and low margins are equal
|
||
|
|
pScaledMarginHigh = &scaledMarginLow;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Compute an estimate for digitExponent that will be correct or undershoot by one.
|
||
|
|
// This optimization is based on the paper "Printing Floating-Point Numbers Quickly and Accurately"
|
||
|
|
// by Burger and Dybvig http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.72.4656&rep=rep1&type=pdf
|
||
|
|
// We perform an additional subtraction of 0.69 to increase the frequency of a failed estimate
|
||
|
|
// because that lets us take a faster branch in the code. 0.69 is chosen because 0.69 + log10(2) is
|
||
|
|
// less than one by a reasonable epsilon that will account for any floating point error.
|
||
|
|
//
|
||
|
|
// We want to set digitExponent to floor(log10(v)) + 1
|
||
|
|
// v = mantissa*2^exponent
|
||
|
|
// log2(v) = log2(mantissa) + exponent;
|
||
|
|
// log10(v) = log2(v) * log10(2)
|
||
|
|
// floor(log2(v)) = mantissaHighBitIdx + exponent;
|
||
|
|
// log10(v) - log10(2) < (mantissaHighBitIdx + exponent) * log10(2) <= log10(v)
|
||
|
|
// log10(v) < (mantissaHighBitIdx + exponent) * log10(2) + log10(2) <= log10(v) + log10(2)
|
||
|
|
// floor( log10(v) ) < ceil( (mantissaHighBitIdx + exponent) * log10(2) ) <= floor( log10(v) ) + 1
|
||
|
|
const double log10_2 = 0.30102999566398119521373889472449;
|
||
|
|
var digitExponentDoubleValue = (double) ((int) mantissaHighBitIdx + exponent) * log10_2 - 0.69;
|
||
|
|
digitExponentDoubleValue = Math.Ceiling(digitExponentDoubleValue);
|
||
|
|
int digitExponent = (int)digitExponentDoubleValue;
|
||
|
|
|
||
|
|
// if the digit exponent is smaller than the smallest desired digit for fractional cutoff,
|
||
|
|
// pull the digit back into legal range at which point we will round to the appropriate value.
|
||
|
|
// Note that while our value for digitExponent is still an estimate, this is safe because it
|
||
|
|
// only increases the number. This will either correct digitExponent to an accurate value or it
|
||
|
|
// will clamp it above the accurate value.
|
||
|
|
if (cutoffMode == CutoffMode.FractionLength && digitExponent <= -(int)cutoffNumber)
|
||
|
|
{
|
||
|
|
digitExponent = -(int)cutoffNumber + 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Divide value by 10^digitExponent.
|
||
|
|
if (digitExponent > 0)
|
||
|
|
{
|
||
|
|
// The exponent is positive creating a division so we multiply up the scale.
|
||
|
|
tBigInt temp;
|
||
|
|
BigInt_MultiplyPow10( out temp, scale, (uint)digitExponent );
|
||
|
|
scale = temp;
|
||
|
|
}
|
||
|
|
else if (digitExponent < 0)
|
||
|
|
{
|
||
|
|
// The exponent is negative creating a multiplication so we multiply up the scaledValue,
|
||
|
|
// scaledMarginLow and scaledMarginHigh.
|
||
|
|
tBigInt pow10;
|
||
|
|
BigInt_Pow10(out pow10, (uint)(-digitExponent));
|
||
|
|
|
||
|
|
tBigInt temp;
|
||
|
|
BigInt_Multiply( out temp, scaledValue, pow10);
|
||
|
|
scaledValue = temp;
|
||
|
|
|
||
|
|
BigInt_Multiply( out temp, scaledMarginLow, pow10);
|
||
|
|
scaledMarginLow = temp;
|
||
|
|
|
||
|
|
if (pScaledMarginHigh != &scaledMarginLow)
|
||
|
|
BigInt_Multiply2( out *pScaledMarginHigh, scaledMarginLow );
|
||
|
|
}
|
||
|
|
|
||
|
|
// If (value >= 1), our estimate for digitExponent was too low
|
||
|
|
if( BigInt_Compare(scaledValue,scale) >= 0 )
|
||
|
|
{
|
||
|
|
// The exponent estimate was incorrect.
|
||
|
|
// Increment the exponent and don't perform the premultiply needed
|
||
|
|
// for the first loop iteration.
|
||
|
|
digitExponent = digitExponent + 1;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// The exponent estimate was correct.
|
||
|
|
// Multiply larger by the output base to prepare for the first loop iteration.
|
||
|
|
BigInt_Multiply10( ref scaledValue );
|
||
|
|
BigInt_Multiply10( ref scaledMarginLow );
|
||
|
|
if (pScaledMarginHigh != &scaledMarginLow)
|
||
|
|
BigInt_Multiply2( out *pScaledMarginHigh, scaledMarginLow );
|
||
|
|
}
|
||
|
|
|
||
|
|
// Compute the cutoff exponent (the exponent of the final digit to print).
|
||
|
|
// Default to the maximum size of the output buffer.
|
||
|
|
int cutoffExponent = digitExponent - (int)bufferSize;
|
||
|
|
switch (cutoffMode)
|
||
|
|
{
|
||
|
|
// print digits until we pass the accuracy margin limits or buffer size
|
||
|
|
case CutoffMode.Unique:
|
||
|
|
break;
|
||
|
|
|
||
|
|
// print cutoffNumber of digits or until we reach the buffer size
|
||
|
|
case CutoffMode.TotalLength:
|
||
|
|
{
|
||
|
|
int desiredCutoffExponent = digitExponent - (int) cutoffNumber;
|
||
|
|
if (desiredCutoffExponent > cutoffExponent)
|
||
|
|
cutoffExponent = desiredCutoffExponent;
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
|
||
|
|
// print cutoffNumber digits past the decimal point or until we reach the buffer size
|
||
|
|
case CutoffMode.FractionLength:
|
||
|
|
{
|
||
|
|
int desiredCutoffExponent = -(int) cutoffNumber;
|
||
|
|
if (desiredCutoffExponent > cutoffExponent)
|
||
|
|
cutoffExponent = desiredCutoffExponent;
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Output the exponent of the first digit we will print
|
||
|
|
pOutExponent = digitExponent-1;
|
||
|
|
|
||
|
|
// In preparation for calling BigInt_DivideWithRemainder_MaxQuotient9(),
|
||
|
|
// we need to scale up our values such that the highest block of the denominator
|
||
|
|
// is greater than or equal to 8. We also need to guarantee that the numerator
|
||
|
|
// can never have a length greater than the denominator after each loop iteration.
|
||
|
|
// This requires the highest block of the denominator to be less than or equal to
|
||
|
|
// 429496729 which is the highest number that can be multiplied by 10 without
|
||
|
|
// overflowing to a new block.
|
||
|
|
// RJ_ASSERT( scale.GetLength() > 0 );
|
||
|
|
uint hiBlock = scale.GetBlock( scale.GetLength() - 1 );
|
||
|
|
if (hiBlock < 8 || hiBlock > 429496729)
|
||
|
|
{
|
||
|
|
// Perform a bit shift on all values to get the highest block of the denominator into
|
||
|
|
// the range [8,429496729]. We are more likely to make accurate quotient estimations
|
||
|
|
// in BigInt_DivideWithRemainder_MaxQuotient9() with higher denominator values so
|
||
|
|
// we shift the denominator to place the highest bit at index 27 of the highest block.
|
||
|
|
// This is safe because (2^28 - 1) = 268435455 which is less than 429496729. This means
|
||
|
|
// that all values with a highest bit at index 27 are within range.
|
||
|
|
uint hiBlockLog2 = LogBase2(hiBlock);
|
||
|
|
// RJ_ASSERT(hiBlockLog2 < 3 || hiBlockLog2 > 27);
|
||
|
|
uint shift = (32 + 27 - hiBlockLog2) % 32;
|
||
|
|
|
||
|
|
BigInt_ShiftLeft( ref scale, shift );
|
||
|
|
BigInt_ShiftLeft( ref scaledValue, shift);
|
||
|
|
BigInt_ShiftLeft( ref scaledMarginLow, shift);
|
||
|
|
if (pScaledMarginHigh != &scaledMarginLow)
|
||
|
|
BigInt_Multiply2( out *pScaledMarginHigh, scaledMarginLow );
|
||
|
|
}
|
||
|
|
|
||
|
|
// These values are used to inspect why the print loop terminated so we can properly
|
||
|
|
// round the final digit.
|
||
|
|
bool low; // did the value get within marginLow distance from zero
|
||
|
|
bool high; // did the value get within marginHigh distance from one
|
||
|
|
uint outputDigit; // current digit being output
|
||
|
|
|
||
|
|
if (cutoffMode == CutoffMode.Unique)
|
||
|
|
{
|
||
|
|
// For the unique cutoff mode, we will try to print until we have reached a level of
|
||
|
|
// precision that uniquely distinguishes this value from its neighbors. If we run
|
||
|
|
// out of space in the output buffer, we terminate early.
|
||
|
|
for (;;)
|
||
|
|
{
|
||
|
|
digitExponent = digitExponent-1;
|
||
|
|
|
||
|
|
// divide out the scale to extract the digit
|
||
|
|
outputDigit = BigInt_DivideWithRemainder_MaxQuotient9(ref scaledValue, scale);
|
||
|
|
//RJ_ASSERT( outputDigit < 10 );
|
||
|
|
|
||
|
|
// update the high end of the value
|
||
|
|
tBigInt scaledValueHigh;
|
||
|
|
BigInt_Add( out scaledValueHigh, scaledValue, *pScaledMarginHigh );
|
||
|
|
|
||
|
|
// stop looping if we are far enough away from our neighboring values
|
||
|
|
// or if we have reached the cutoff digit
|
||
|
|
low = BigInt_Compare(scaledValue, scaledMarginLow) < 0;
|
||
|
|
high = BigInt_Compare(scaledValueHigh, scale) > 0;
|
||
|
|
if (low | high | (digitExponent == cutoffExponent))
|
||
|
|
break;
|
||
|
|
|
||
|
|
// store the output digit
|
||
|
|
*pCurDigit = (byte)('0' + outputDigit);
|
||
|
|
++pCurDigit;
|
||
|
|
|
||
|
|
// multiply larger by the output base
|
||
|
|
BigInt_Multiply10( ref scaledValue );
|
||
|
|
BigInt_Multiply10( ref scaledMarginLow );
|
||
|
|
if (pScaledMarginHigh != &scaledMarginLow)
|
||
|
|
BigInt_Multiply2( out *pScaledMarginHigh, scaledMarginLow );
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// For length based cutoff modes, we will try to print until we
|
||
|
|
// have exhausted all precision (i.e. all remaining digits are zeros) or
|
||
|
|
// until we reach the desired cutoff digit.
|
||
|
|
low = false;
|
||
|
|
high = false;
|
||
|
|
|
||
|
|
for (;;)
|
||
|
|
{
|
||
|
|
digitExponent = digitExponent-1;
|
||
|
|
|
||
|
|
// divide out the scale to extract the digit
|
||
|
|
outputDigit = BigInt_DivideWithRemainder_MaxQuotient9(ref scaledValue, scale);
|
||
|
|
//RJ_ASSERT( outputDigit < 10 );
|
||
|
|
|
||
|
|
if ( scaledValue.IsZero() | (digitExponent == cutoffExponent) )
|
||
|
|
break;
|
||
|
|
|
||
|
|
// store the output digit
|
||
|
|
*pCurDigit = (byte)('0' + outputDigit);
|
||
|
|
++pCurDigit;
|
||
|
|
|
||
|
|
// multiply larger by the output base
|
||
|
|
BigInt_Multiply10(ref scaledValue);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// round off the final digit
|
||
|
|
// default to rounding down if value got too close to 0
|
||
|
|
bool roundDown = low;
|
||
|
|
|
||
|
|
// if it is legal to round up and down
|
||
|
|
if (low == high)
|
||
|
|
{
|
||
|
|
// round to the closest digit by comparing value with 0.5. To do this we need to convert
|
||
|
|
// the inequality to large integer values.
|
||
|
|
// compare( value, 0.5 )
|
||
|
|
// compare( scale * value, scale * 0.5 )
|
||
|
|
// compare( 2 * scale * value, scale )
|
||
|
|
BigInt_Multiply2(ref scaledValue);
|
||
|
|
int compare = BigInt_Compare(scaledValue, scale);
|
||
|
|
roundDown = compare < 0;
|
||
|
|
|
||
|
|
// if we are directly in the middle, round towards the even digit (i.e. IEEE rouding rules)
|
||
|
|
if (compare == 0)
|
||
|
|
roundDown = (outputDigit & 1) == 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// print the rounded digit
|
||
|
|
if (roundDown)
|
||
|
|
{
|
||
|
|
*pCurDigit = (byte)('0' + outputDigit);
|
||
|
|
++pCurDigit;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// handle rounding up
|
||
|
|
if (outputDigit == 9)
|
||
|
|
{
|
||
|
|
// find the first non-nine prior digit
|
||
|
|
for (;;)
|
||
|
|
{
|
||
|
|
// if we are at the first digit
|
||
|
|
if (pCurDigit == pOutBuffer)
|
||
|
|
{
|
||
|
|
// output 1 at the next highest exponent
|
||
|
|
*pCurDigit = (byte)'1';
|
||
|
|
++pCurDigit;
|
||
|
|
pOutExponent += 1;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
|
||
|
|
--pCurDigit;
|
||
|
|
if (*pCurDigit != (byte)'9')
|
||
|
|
{
|
||
|
|
// increment the digit
|
||
|
|
*pCurDigit += 1;
|
||
|
|
++pCurDigit;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// values in the range [0,8] can perform a simple round up
|
||
|
|
*pCurDigit = (byte)((byte)'0' + outputDigit + 1);
|
||
|
|
++pCurDigit;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// return the number of digits output
|
||
|
|
uint outputLen = (uint)(pCurDigit - pOutBuffer);
|
||
|
|
// RJ_ASSERT(outputLen <= bufferSize);
|
||
|
|
return outputLen;
|
||
|
|
}
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
//******************************************************************************
|
||
|
|
public enum PrintFloatFormat
|
||
|
|
{
|
||
|
|
Positional, // [-]ddddd.dddd
|
||
|
|
Scientific, // [-]d.dddde[sign]ddd
|
||
|
|
}
|
||
|
|
|
||
|
|
//******************************************************************************\
|
||
|
|
// Helper union to decompose a 32-bit IEEE float.
|
||
|
|
// sign: 1 bit
|
||
|
|
// exponent: 8 bits
|
||
|
|
// mantissa: 23 bits
|
||
|
|
//******************************************************************************
|
||
|
|
[StructLayout(LayoutKind.Explicit)]
|
||
|
|
public struct tFloatUnion32
|
||
|
|
{
|
||
|
|
public bool IsNegative() { return (m_integer >> 31) != 0; }
|
||
|
|
public uint GetExponent() { return (m_integer >> 23) & 0xFF; }
|
||
|
|
public uint GetMantissa() { return m_integer & 0x7FFFFF; }
|
||
|
|
|
||
|
|
[FieldOffset(0)]
|
||
|
|
public float m_floatingPoint;
|
||
|
|
|
||
|
|
[FieldOffset(0)]
|
||
|
|
public uint m_integer;
|
||
|
|
};
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// Helper union to decompose a 64-bit IEEE float.
|
||
|
|
// sign: 1 bit
|
||
|
|
// exponent: 11 bits
|
||
|
|
// mantissa: 52 bits
|
||
|
|
//******************************************************************************
|
||
|
|
[StructLayout(LayoutKind.Explicit)]
|
||
|
|
public struct tFloatUnion64
|
||
|
|
{
|
||
|
|
public bool IsNegative() { return (m_integer >> 63) != 0; }
|
||
|
|
public uint GetExponent() { return (uint)((m_integer >> 52) & 0x7FF); }
|
||
|
|
public ulong GetMantissa() { return m_integer & 0xFFFFFFFFFFFFFUL; }
|
||
|
|
|
||
|
|
[FieldOffset(0)]
|
||
|
|
public double m_floatingPoint;
|
||
|
|
|
||
|
|
[FieldOffset(0)]
|
||
|
|
public ulong m_integer;
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// Outputs the positive number with positional notation: ddddd.dddd
|
||
|
|
// The output is always NUL terminated and the output length (not including the
|
||
|
|
// NUL) is returned.
|
||
|
|
//******************************************************************************
|
||
|
|
private static unsafe int FormatPositional
|
||
|
|
(
|
||
|
|
byte* pOutBuffer, // buffer to output into
|
||
|
|
uint bufferSize, // maximum characters that can be printed to pOutBuffer
|
||
|
|
ulong mantissa, // value significand
|
||
|
|
int exponent, // value exponent in base 2
|
||
|
|
uint mantissaHighBitIdx, // index of the highest set mantissa bit
|
||
|
|
bool hasUnequalMargins, // is the high margin twice as large as the low margin
|
||
|
|
int precision // Negative prints as many digits as are needed for a unique
|
||
|
|
// number. Positive specifies the maximum number of
|
||
|
|
// significant digits to print past the decimal point.
|
||
|
|
)
|
||
|
|
{
|
||
|
|
//RJ_ASSERT(bufferSize > 0);
|
||
|
|
|
||
|
|
int printExponent;
|
||
|
|
uint numPrintDigits;
|
||
|
|
|
||
|
|
uint maxPrintLen = bufferSize - 1;
|
||
|
|
|
||
|
|
if (precision < 0)
|
||
|
|
{
|
||
|
|
numPrintDigits = Dragon4(mantissa,
|
||
|
|
exponent,
|
||
|
|
mantissaHighBitIdx,
|
||
|
|
hasUnequalMargins,
|
||
|
|
CutoffMode.Unique,
|
||
|
|
0,
|
||
|
|
pOutBuffer,
|
||
|
|
maxPrintLen,
|
||
|
|
out printExponent);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
numPrintDigits = Dragon4(mantissa,
|
||
|
|
exponent,
|
||
|
|
mantissaHighBitIdx,
|
||
|
|
hasUnequalMargins,
|
||
|
|
CutoffMode.FractionLength,
|
||
|
|
(uint)precision,
|
||
|
|
pOutBuffer,
|
||
|
|
maxPrintLen,
|
||
|
|
out printExponent);
|
||
|
|
}
|
||
|
|
|
||
|
|
//RJ_ASSERT(numPrintDigits > 0);
|
||
|
|
//RJ_ASSERT(numPrintDigits <= bufferSize);
|
||
|
|
|
||
|
|
// track the number of digits past the decimal point that have been printed
|
||
|
|
uint numFractionDigits = 0;
|
||
|
|
|
||
|
|
// if output has a whole number
|
||
|
|
if (printExponent >= 0)
|
||
|
|
{
|
||
|
|
// leave the whole number at the start of the buffer
|
||
|
|
uint numWholeDigits = (uint)(printExponent + 1);
|
||
|
|
if (numPrintDigits < numWholeDigits)
|
||
|
|
{
|
||
|
|
// don't overflow the buffer
|
||
|
|
if (numWholeDigits > maxPrintLen)
|
||
|
|
numWholeDigits = maxPrintLen;
|
||
|
|
|
||
|
|
// add trailing zeros up to the decimal point
|
||
|
|
for (; numPrintDigits < numWholeDigits; ++numPrintDigits)
|
||
|
|
pOutBuffer[numPrintDigits] = (byte)'0';
|
||
|
|
}
|
||
|
|
// insert the decimal point prior to the fraction
|
||
|
|
else if (numPrintDigits > (uint)numWholeDigits)
|
||
|
|
{
|
||
|
|
numFractionDigits = numPrintDigits - numWholeDigits;
|
||
|
|
uint maxFractionDigits = maxPrintLen - numWholeDigits - 1;
|
||
|
|
if (numFractionDigits > maxFractionDigits)
|
||
|
|
numFractionDigits = maxFractionDigits;
|
||
|
|
Unsafe.CopyBlock(pOutBuffer + numWholeDigits + 1, pOutBuffer + numWholeDigits, numFractionDigits);
|
||
|
|
pOutBuffer[numWholeDigits] = (byte)'.';
|
||
|
|
numPrintDigits = numWholeDigits + 1 + numFractionDigits;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// shift out the fraction to make room for the leading zeros
|
||
|
|
if (maxPrintLen > 2)
|
||
|
|
{
|
||
|
|
uint numFractionZeros = (uint)( - printExponent - 1);
|
||
|
|
uint maxFractionZeros = maxPrintLen - 2;
|
||
|
|
if (numFractionZeros > maxFractionZeros)
|
||
|
|
numFractionZeros = maxFractionZeros;
|
||
|
|
|
||
|
|
uint digitsStartIdx = 2 + numFractionZeros;
|
||
|
|
|
||
|
|
// shift the significant digits right such that there is room for leading zeros
|
||
|
|
numFractionDigits = numPrintDigits;
|
||
|
|
uint maxFractionDigits = maxPrintLen - digitsStartIdx;
|
||
|
|
if (numFractionDigits > maxFractionDigits)
|
||
|
|
numFractionDigits = maxFractionDigits;
|
||
|
|
Unsafe.CopyBlock(pOutBuffer + digitsStartIdx, pOutBuffer, numFractionDigits);
|
||
|
|
|
||
|
|
// insert the leading zeros
|
||
|
|
for (uint i = 2; i < digitsStartIdx; ++i)
|
||
|
|
pOutBuffer[i] = (byte)'0';
|
||
|
|
|
||
|
|
// update the counts
|
||
|
|
numFractionDigits += numFractionZeros;
|
||
|
|
numPrintDigits = numFractionDigits;
|
||
|
|
}
|
||
|
|
|
||
|
|
// add the decimal point
|
||
|
|
if (maxPrintLen > 1)
|
||
|
|
{
|
||
|
|
pOutBuffer[1] = (byte)'.';
|
||
|
|
numPrintDigits += 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
// add the initial zero
|
||
|
|
if (maxPrintLen > 0)
|
||
|
|
{
|
||
|
|
pOutBuffer[0] = (byte)'0';
|
||
|
|
numPrintDigits += 1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// add trailing zeros up to precision length
|
||
|
|
if (precision > (int)numFractionDigits && numPrintDigits < maxPrintLen)
|
||
|
|
{
|
||
|
|
// add a decimal point if this is the first fractional digit we are printing
|
||
|
|
if (numFractionDigits == 0)
|
||
|
|
{
|
||
|
|
pOutBuffer[numPrintDigits++] = (byte)'.';
|
||
|
|
}
|
||
|
|
|
||
|
|
// compute the number of trailing zeros needed
|
||
|
|
uint totalDigits = (uint)(numPrintDigits + (precision - (int)numFractionDigits));
|
||
|
|
if (totalDigits > maxPrintLen)
|
||
|
|
totalDigits = maxPrintLen;
|
||
|
|
|
||
|
|
for (; numPrintDigits < totalDigits; ++numPrintDigits)
|
||
|
|
pOutBuffer[numPrintDigits] = (byte)'0';
|
||
|
|
}
|
||
|
|
|
||
|
|
// terminate the buffer
|
||
|
|
//RJ_ASSERT(numPrintDigits <= maxPrintLen);
|
||
|
|
//pOutBuffer[numPrintDigits] = '\0';
|
||
|
|
|
||
|
|
return (int)numPrintDigits;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// Outputs the positive number with scientific notation: d.dddde[sign]ddd
|
||
|
|
// The output is always NUL terminated and the output length (not including the
|
||
|
|
// NUL) is returned.
|
||
|
|
//******************************************************************************
|
||
|
|
private static unsafe int FormatScientific
|
||
|
|
(
|
||
|
|
byte* pOutBuffer, // buffer to output into
|
||
|
|
uint bufferSize, // maximum characters that can be printed to pOutBuffer
|
||
|
|
ulong mantissa, // value significand
|
||
|
|
int exponent, // value exponent in base 2
|
||
|
|
uint mantissaHighBitIdx, // index of the highest set mantissa bit
|
||
|
|
bool hasUnequalMargins, // is the high margin twice as large as the low margin
|
||
|
|
int precision // Negative prints as many digits as are needed for a unique
|
||
|
|
// number. Positive specifies the maximum number of
|
||
|
|
// significant digits to print past the decimal point.
|
||
|
|
)
|
||
|
|
{
|
||
|
|
//RJ_ASSERT(bufferSize > 0);
|
||
|
|
|
||
|
|
int printExponent;
|
||
|
|
uint numPrintDigits;
|
||
|
|
|
||
|
|
if (precision < 0)
|
||
|
|
{
|
||
|
|
numPrintDigits = Dragon4(mantissa,
|
||
|
|
exponent,
|
||
|
|
mantissaHighBitIdx,
|
||
|
|
hasUnequalMargins,
|
||
|
|
CutoffMode.Unique,
|
||
|
|
0,
|
||
|
|
pOutBuffer,
|
||
|
|
bufferSize,
|
||
|
|
out printExponent);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
numPrintDigits = Dragon4(mantissa,
|
||
|
|
exponent,
|
||
|
|
mantissaHighBitIdx,
|
||
|
|
hasUnequalMargins,
|
||
|
|
CutoffMode.TotalLength,
|
||
|
|
(uint)(precision + 1),
|
||
|
|
pOutBuffer,
|
||
|
|
bufferSize,
|
||
|
|
out printExponent);
|
||
|
|
}
|
||
|
|
|
||
|
|
//RJ_ASSERT(numPrintDigits > 0);
|
||
|
|
//RJ_ASSERT(numPrintDigits <= bufferSize);
|
||
|
|
|
||
|
|
byte* pCurOut = pOutBuffer;
|
||
|
|
|
||
|
|
// keep the whole number as the first digit
|
||
|
|
if (bufferSize > 1)
|
||
|
|
{
|
||
|
|
pCurOut += 1;
|
||
|
|
bufferSize -= 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
// insert the decimal point prior to the fractional number
|
||
|
|
uint numFractionDigits = numPrintDigits - 1;
|
||
|
|
if (numFractionDigits > 0 && bufferSize > 1)
|
||
|
|
{
|
||
|
|
uint maxFractionDigits = bufferSize - 2;
|
||
|
|
if (numFractionDigits > maxFractionDigits)
|
||
|
|
numFractionDigits = maxFractionDigits;
|
||
|
|
Unsafe.CopyBlock(pCurOut + 1, pCurOut, numFractionDigits);
|
||
|
|
pCurOut[0] = (byte)'.';
|
||
|
|
pCurOut += (1 + numFractionDigits);
|
||
|
|
bufferSize -= (1 + numFractionDigits);
|
||
|
|
}
|
||
|
|
|
||
|
|
// add trailing zeros up to precision length
|
||
|
|
if (precision > (int)numFractionDigits && bufferSize > 1)
|
||
|
|
{
|
||
|
|
// add a decimal point if this is the first fractional digit we are printing
|
||
|
|
if (numFractionDigits == 0)
|
||
|
|
{
|
||
|
|
*pCurOut = (byte)'.';
|
||
|
|
++pCurOut;
|
||
|
|
--bufferSize;
|
||
|
|
}
|
||
|
|
|
||
|
|
// compute the number of trailing zeros needed
|
||
|
|
uint numZeros = (uint)(precision - numFractionDigits);
|
||
|
|
if (numZeros > bufferSize - 1)
|
||
|
|
numZeros = bufferSize - 1;
|
||
|
|
|
||
|
|
for (byte* pEnd = pCurOut + numZeros; pCurOut < pEnd; ++pCurOut)
|
||
|
|
*pCurOut = (byte)'0';
|
||
|
|
}
|
||
|
|
|
||
|
|
// print the exponent into a local buffer and copy into output buffer
|
||
|
|
if (bufferSize > 1)
|
||
|
|
{
|
||
|
|
var exponentBuffer = stackalloc byte[5];
|
||
|
|
exponentBuffer[0] = (byte)'e';
|
||
|
|
if (printExponent >= 0)
|
||
|
|
{
|
||
|
|
exponentBuffer[1] = (byte)'+';
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
exponentBuffer[1] = (byte)'-';
|
||
|
|
printExponent = -printExponent;
|
||
|
|
}
|
||
|
|
|
||
|
|
//RJ_ASSERT(printExponent < 1000);
|
||
|
|
uint hundredsPlace = (uint)(printExponent / 100);
|
||
|
|
uint tensPlace = (uint)((printExponent - hundredsPlace * 100) / 10);
|
||
|
|
uint onesPlace = (uint)((printExponent - hundredsPlace * 100 - tensPlace * 10));
|
||
|
|
|
||
|
|
exponentBuffer[2] = (byte)('0' + hundredsPlace);
|
||
|
|
exponentBuffer[3] = (byte)('0' + tensPlace);
|
||
|
|
exponentBuffer[4] = (byte)('0' + onesPlace);
|
||
|
|
|
||
|
|
// copy the exponent buffer into the output
|
||
|
|
uint maxExponentSize = bufferSize - 1;
|
||
|
|
uint exponentSize = (5 < maxExponentSize) ? 5 : maxExponentSize;
|
||
|
|
Unsafe.CopyBlock(pCurOut, exponentBuffer, exponentSize);
|
||
|
|
pCurOut += exponentSize;
|
||
|
|
bufferSize -= exponentSize;
|
||
|
|
}
|
||
|
|
|
||
|
|
//RJ_ASSERT(bufferSize > 0);
|
||
|
|
//pCurOut[0] = '\0';
|
||
|
|
|
||
|
|
return (int)(pCurOut - pOutBuffer);
|
||
|
|
}
|
||
|
|
|
||
|
|
//******************************************************************************
|
||
|
|
// Print special case values for infinities and NaNs.
|
||
|
|
// The output string is always NUL terminated and the string length (not
|
||
|
|
// including the NUL) is returned.
|
||
|
|
//******************************************************************************
|
||
|
|
private static readonly byte[] InfinityString = new byte[]
|
||
|
|
{
|
||
|
|
(byte) 'I',
|
||
|
|
(byte) 'n',
|
||
|
|
(byte) 'f',
|
||
|
|
(byte) 'i',
|
||
|
|
(byte) 'n',
|
||
|
|
(byte) 'i',
|
||
|
|
(byte) 't',
|
||
|
|
(byte) 'y',
|
||
|
|
};
|
||
|
|
|
||
|
|
private static readonly byte[] NanString = new byte[]
|
||
|
|
{
|
||
|
|
(byte) 'N',
|
||
|
|
(byte) 'a',
|
||
|
|
(byte) 'N',
|
||
|
|
};
|
||
|
|
|
||
|
|
private static unsafe void FormatInfinityNaN(byte* dest, ref int destIndex, int destLength, ulong mantissa, bool isNegative, FormatOptions formatOptions)
|
||
|
|
{
|
||
|
|
//RJ_ASSERT(bufferSize > 0);
|
||
|
|
int length = mantissa == 0 ? 8 + (isNegative ? 1 : 0) : 3;
|
||
|
|
int align = formatOptions.AlignAndSize;
|
||
|
|
|
||
|
|
// left align
|
||
|
|
if (AlignLeft(dest, ref destIndex, destLength, align, length)) return;
|
||
|
|
|
||
|
|
// Check for infinity
|
||
|
|
if (mantissa == 0)
|
||
|
|
{
|
||
|
|
if (isNegative)
|
||
|
|
{
|
||
|
|
if (destIndex >= destLength) return;
|
||
|
|
dest[destIndex++] = (byte)'-';
|
||
|
|
}
|
||
|
|
|
||
|
|
for (int i = 0; i < 8; i++)
|
||
|
|
{
|
||
|
|
if (destIndex >= destLength) return;
|
||
|
|
dest[destIndex++] = InfinityString[i];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
for (int i = 0; i < 3; i++)
|
||
|
|
{
|
||
|
|
if (destIndex >= destLength) return;
|
||
|
|
dest[destIndex++] = NanString[i];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// right align
|
||
|
|
AlignRight(dest, ref destIndex, destLength, align, length);
|
||
|
|
}
|
||
|
|
|
||
|
|
// ------------------------------------------------------------------------------
|
||
|
|
// Part of the following code is taking some constants and code from
|
||
|
|
// https://github.com/dotnet/runtime/blob/75036ffec9473dd1d948c052c041fdedd7784ac9/src/libraries/System.Private.CoreLib/src/System/Number.Formatting.cs
|
||
|
|
// Licensed to the .NET Foundation under one or more agreements.
|
||
|
|
// The .NET Foundation licenses this file to you under the MIT license.
|
||
|
|
// See the https://github.com/dotnet/runtime/blob/master/LICENSE.TXT file for more information.
|
||
|
|
// ------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
// SinglePrecision and DoublePrecision represent the maximum number of digits required
|
||
|
|
// to guarantee that any given Single or Double can roundtrip. Some numbers may require
|
||
|
|
// less, but none will require more.
|
||
|
|
private const int SinglePrecision = 9;
|
||
|
|
private const int DoublePrecision = 17;
|
||
|
|
|
||
|
|
internal const int SingleNumberBufferLength = SinglePrecision + 1; // + zero
|
||
|
|
internal const int DoubleNumberBufferLength = DoublePrecision + 1; // + zero
|
||
|
|
|
||
|
|
// SinglePrecisionCustomFormat and DoublePrecisionCustomFormat are used to ensure that
|
||
|
|
// custom format strings return the same string as in previous releases when the format
|
||
|
|
// would return x digits or less (where x is the value of the corresponding constant).
|
||
|
|
// In order to support more digits, we would need to update ParseFormatSpecifier to pre-parse
|
||
|
|
// the format and determine exactly how many digits are being requested and whether they
|
||
|
|
// represent "significant digits" or "digits after the decimal point".
|
||
|
|
private const int SinglePrecisionCustomFormat = 7;
|
||
|
|
private const int DoublePrecisionCustomFormat = 15;
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Format a float 32-bit to a general format to the specified destination buffer.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="dest">Destination buffer.</param>
|
||
|
|
/// <param name="destIndex">Current index in destination buffer.</param>
|
||
|
|
/// <param name="destLength">Maximum length of destination buffer.</param>
|
||
|
|
/// <param name="value">The float 32 value to format.</param>
|
||
|
|
/// <param name="formatOptions">Formatting options.</param>
|
||
|
|
[MethodImpl(MethodImplOptions.NoInlining)]
|
||
|
|
private static unsafe void ConvertFloatToString(byte* dest, ref int destIndex, int destLength, float value, FormatOptions formatOptions)
|
||
|
|
{
|
||
|
|
// deconstruct the floating point value
|
||
|
|
tFloatUnion32 floatUnion = default;
|
||
|
|
floatUnion.m_floatingPoint = value;
|
||
|
|
uint floatExponent = floatUnion.GetExponent();
|
||
|
|
uint floatMantissa = floatUnion.GetMantissa();
|
||
|
|
|
||
|
|
// if this is a special value
|
||
|
|
if (floatExponent == 0xFF)
|
||
|
|
{
|
||
|
|
FormatInfinityNaN(dest, ref destIndex, destLength, floatMantissa, floatUnion.IsNegative(), formatOptions);
|
||
|
|
}
|
||
|
|
// else this is a number
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// factor the value into its parts
|
||
|
|
uint mantissa;
|
||
|
|
int exponent;
|
||
|
|
uint mantissaHighBitIdx;
|
||
|
|
bool hasUnequalMargins;
|
||
|
|
if (floatExponent != 0)
|
||
|
|
{
|
||
|
|
// normalized
|
||
|
|
// The floating point equation is:
|
||
|
|
// value = (1 + mantissa/2^23) * 2 ^ (exponent-127)
|
||
|
|
// We convert the integer equation by factoring a 2^23 out of the exponent
|
||
|
|
// value = (1 + mantissa/2^23) * 2^23 * 2 ^ (exponent-127-23)
|
||
|
|
// value = (2^23 + mantissa) * 2 ^ (exponent-127-23)
|
||
|
|
// Because of the implied 1 in front of the mantissa we have 24 bits of precision.
|
||
|
|
// m = (2^23 + mantissa)
|
||
|
|
// e = (exponent-127-23)
|
||
|
|
mantissa = (uint)((1UL << 23) | floatMantissa);
|
||
|
|
exponent = (int)(floatExponent - 127 - 23);
|
||
|
|
mantissaHighBitIdx = 23;
|
||
|
|
hasUnequalMargins = (floatExponent != 1) && (floatMantissa == 0);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// denormalized
|
||
|
|
// The floating point equation is:
|
||
|
|
// value = (mantissa/2^23) * 2 ^ (1-127)
|
||
|
|
// We convert the integer equation by factoring a 2^23 out of the exponent
|
||
|
|
// value = (mantissa/2^23) * 2^23 * 2 ^ (1-127-23)
|
||
|
|
// value = mantissa * 2 ^ (1-127-23)
|
||
|
|
// We have up to 23 bits of precision.
|
||
|
|
// m = (mantissa)
|
||
|
|
// e = (1-127-23)
|
||
|
|
mantissa = floatMantissa;
|
||
|
|
exponent = 1 - 127 - 23;
|
||
|
|
mantissaHighBitIdx = LogBase2(mantissa);
|
||
|
|
hasUnequalMargins = false;
|
||
|
|
}
|
||
|
|
|
||
|
|
var precision = formatOptions.Specifier == 0 ? -1 : formatOptions.Specifier;
|
||
|
|
var bufferSize = Math.Max(SingleNumberBufferLength, precision + 1);
|
||
|
|
|
||
|
|
var pOutBuffer = stackalloc byte[bufferSize];
|
||
|
|
if (precision < 0)
|
||
|
|
{
|
||
|
|
precision = SinglePrecisionCustomFormat;
|
||
|
|
}
|
||
|
|
|
||
|
|
int printExponent;
|
||
|
|
uint numPrintDigits = Dragon4(mantissa,
|
||
|
|
exponent,
|
||
|
|
mantissaHighBitIdx,
|
||
|
|
hasUnequalMargins,
|
||
|
|
CutoffMode.TotalLength,
|
||
|
|
(uint)precision,
|
||
|
|
pOutBuffer,
|
||
|
|
(uint)(bufferSize - 1),
|
||
|
|
out printExponent);
|
||
|
|
|
||
|
|
pOutBuffer[numPrintDigits] = 0;
|
||
|
|
|
||
|
|
// Negative 0 are displayed as 0
|
||
|
|
bool isNegative = floatUnion.IsNegative();
|
||
|
|
if (floatUnion.m_integer == ((uint)1 << 31))
|
||
|
|
{
|
||
|
|
isNegative = false;
|
||
|
|
}
|
||
|
|
|
||
|
|
var number = new NumberBuffer(NumberBufferKind.Float, pOutBuffer, (int)numPrintDigits, printExponent + 1, isNegative);
|
||
|
|
FormatNumber(dest, ref destIndex, destLength, ref number, precision, formatOptions);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Format a float 64-bit to a general format to the specified destination buffer.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="dest">Destination buffer.</param>
|
||
|
|
/// <param name="destIndex">Current index in destination buffer.</param>
|
||
|
|
/// <param name="destLength">Maximum length of destination buffer.</param>
|
||
|
|
/// <param name="value">The float 64 value to format.</param>
|
||
|
|
/// <param name="formatOptions">Formatting options.</param>
|
||
|
|
[MethodImpl(MethodImplOptions.NoInlining)]
|
||
|
|
private static unsafe void ConvertDoubleToString(byte* dest, ref int destIndex, int destLength, double value, FormatOptions formatOptions)
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{
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// deconstruct the floating point value
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tFloatUnion64 floatUnion = default;
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floatUnion.m_floatingPoint = value;
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uint floatExponent = floatUnion.GetExponent();
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ulong floatMantissa = floatUnion.GetMantissa();
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// if this is a special value
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if (floatExponent == 0x7FF)
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{
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FormatInfinityNaN(dest, ref destIndex, destLength, floatMantissa, floatUnion.IsNegative(), formatOptions);
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}
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// else this is a number
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else
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{
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// factor the value into its parts
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ulong mantissa;
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int exponent;
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uint mantissaHighBitIdx;
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bool hasUnequalMargins;
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if (floatExponent != 0)
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{
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// normal
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// The floating point equation is:
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// value = (1 + mantissa/2^52) * 2 ^ (exponent-1023)
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// We convert the integer equation by factoring a 2^52 out of the exponent
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// value = (1 + mantissa/2^52) * 2^52 * 2 ^ (exponent-1023-52)
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// value = (2^52 + mantissa) * 2 ^ (exponent-1023-52)
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// Because of the implied 1 in front of the mantissa we have 53 bits of precision.
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// m = (2^52 + mantissa)
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// e = (exponent-1023+1-53)
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mantissa = (1UL << 52) | floatMantissa;
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exponent = (int)(floatExponent - 1023 - 52);
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mantissaHighBitIdx = 52;
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hasUnequalMargins = (floatExponent != 1) && (floatMantissa == 0);
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}
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else
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{
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// subnormal
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// The floating point equation is:
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// value = (mantissa/2^52) * 2 ^ (1-1023)
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// We convert the integer equation by factoring a 2^52 out of the exponent
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// value = (mantissa/2^52) * 2^52 * 2 ^ (1-1023-52)
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// value = mantissa * 2 ^ (1-1023-52)
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// We have up to 52 bits of precision.
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// m = (mantissa)
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// e = (1-1023-52)
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mantissa = floatMantissa;
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exponent = 1 - 1023 - 52;
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mantissaHighBitIdx = LogBase2((uint)mantissa);
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hasUnequalMargins = false;
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}
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var precision = formatOptions.Specifier == 0 ? -1 : formatOptions.Specifier;
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var bufferSize = Math.Max(DoubleNumberBufferLength, precision + 1);
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var pOutBuffer = stackalloc byte[bufferSize];
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if (precision < 0)
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{
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precision = DoublePrecisionCustomFormat;
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}
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int printExponent;
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uint numPrintDigits = Dragon4(mantissa,
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exponent,
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mantissaHighBitIdx,
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hasUnequalMargins,
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CutoffMode.TotalLength,
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(uint)precision,
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pOutBuffer,
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(uint)(bufferSize - 1),
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out printExponent);
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pOutBuffer[numPrintDigits] = 0;
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// Negative 0 are displayed as 0
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bool isNegative = floatUnion.IsNegative();
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if (floatUnion.m_integer == ((ulong)1 << 63))
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{
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isNegative = false;
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}
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var number = new NumberBuffer(NumberBufferKind.Float, pOutBuffer, (int)numPrintDigits, printExponent + 1, isNegative);
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FormatNumber(dest, ref destIndex, destLength, ref number, precision, formatOptions);
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}
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}
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}
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}
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