I have implemented a vector-based c# approximation of Log. It includes unsafe code. It's been working fine in a number of environments, but on a recent deployment has fallen over. The implementation uses SIMD through the System.Numerics.Vectors library.
Unfortunately I cannot test on the system where the software isn't working. However, I would like to know which assumptions I made about the library are invalid:
- Does Vector<float>.Count always return a power of 2 ?
- Does Vector<UInt64>.Count == Vector.Count * 2 ?
- Can I take a pointer of a vector using Unsafe.AsPointer, then perform standard operations as though it were N packed numbers in memory ?
- Are there any processors that dotNet 4 runs on that have different endian-ness or don't store floats in IEEE754 format?
The code is as follows:
const float invLn2 = 1.44269504089f; // 1 / ln(2)
const float pow2_126 = 8.5070592e+37f; //2^126
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector<float> QuickLog2(Vector<float> vecOrig)
{
//32 bit Float specification:
//Leftmost bit is sign bit.
//Next 8 bits are exponent
//Next 23 bits are mantissa
unsafe
{
var ints = Vector.AsVectorUInt32(vecOrig);
var exponents = Vector.BitwiseAnd(ints, new Vector<uint>(0x7F800000));
BitshiftVector23(Unsafe.AsPointer(ref exponents));
var unsignedExponents = exponents - new Vector<uint>(127);
var signedExponents = Vector.AsVectorInt32(unsignedExponents);
var localMantissBitmask = Vector.AsVectorSingle(new Vector<UInt32>(0x807FFFFF));
var maskedMantissas = Vector.BitwiseAnd(vecOrig, localMantissBitmask);
var mantissas = maskedMantissas * new Vector<float>(pow2_126);
var mantissasLogged = LogPolynomialFunction2(mantissas) * new Vector<float>(invLn2);
Vector<float> floatExponents;
#if false
floatExponents = Vector.ConvertToSingle(signedExponents);
#else
ConvertIntToFloatInPace(Unsafe.AsPointer(ref signedExponents));
floatExponents = Vector.AsVectorSingle(signedExponents);
#endif
return mantissasLogged + floatExponents;
}
}
const float log10_2 = 0.30102999566398119521373889472449f;
/// <summary>
/// A vectorized implementation of Log10(N). Uses bitshift, bitmasks, and unsafe code.
/// Does not have the same safety as Math.Log10: Behaviour for infities, zero, negative numbers are undefined.
/// </summary>
/// <param name="vec">The vector to take the log of</param>
/// <returns>The log, to the base 10, of the vector</returns>
/// <remarks>
/// Accurate to about 10^-7, which is the limit of a 32 bit float anyway.
/// In my (BS) tests, takes about twice as long to run on as Math.Log10(...), but operates on 8 numbers,
/// so 4x faster.
/// Reverts to Math.Log10(...) if vectors are not hardware accelerated.
/// Given the extra memory copies required, that will be much slower than using scalar code.
/// It'll be nice once intrinsics make it into dotNet and we can replace this with a single instruction...
/// </remarks>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector<float> QuickLog10(Vector<float> vec)
{
if (Vector.IsHardwareAccelerated)
return QuickLog2(vec) * new Vector<float>(log10_2);
else
{
float[] tmp = new float[Vector<float>.Count];
vec.CopyTo(tmp);
for (int i = 0; i < Vector<float>.Count; i++)
tmp[i] = (float)Math.Log10(tmp[i]);
return new Vector<float>(tmp);
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static unsafe void BitshiftVector23(void* vector)
{
UInt64* asUlong = (UInt64*)vector;
if (Vector<UInt64>.Count == 4)
{
*asUlong = *asUlong >> 23;
asUlong++;
*asUlong = *asUlong >> 23;
asUlong++;
*asUlong = *asUlong >> 23;
asUlong++;
*asUlong = *asUlong >> 23;
}
else if (Vector<UInt64>.Count == 8)
{
*asUlong = *asUlong >> 23;
asUlong++;
*asUlong = *asUlong >> 23;
asUlong++;
*asUlong = *asUlong >> 23;
asUlong++;
*asUlong = *asUlong >> 23;
asUlong++;
*asUlong = *asUlong >> 23;
asUlong++;
*asUlong = *asUlong >> 23;
asUlong++;
*asUlong = *asUlong >> 23;
asUlong++;
*asUlong = *asUlong >> 23;
}
else
for (int i = 0; i < Vector<UInt64>.Count; i++)
asUlong[i] = asUlong[i] >> 23;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static unsafe void ConvertIntToFloatInPace(void* vector)
{
int* asInt = (int*)vector;
if (Vector<int>.Count == 8)
{
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
}
else if (Vector<UInt64>.Count == 16)
{
for (int i = 0; i < 2; i++)
{
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
*(float*)asInt = *asInt;
asInt++;
}
}
else
for (int i = 0; i < Vector<UInt64>.Count; i++)
{
*(float*)asInt = *asInt;
asInt++;
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static Vector<float> LogPolynomialFunction2(Vector<float> mantissas)
{
var zm1 = mantissas;
var zp1 = mantissas + new Vector<float>(2f);
var zm1Divzp1 = Vector.Divide(zm1, zp1);
var squared = zm1Divzp1 * zm1Divzp1;
var cur = zm1Divzp1;
//Manual loop unwinding:
#if false
var mantissasLogged = Vector<float>.Zero;
for (float i = 0; i < 4; i++)
{
var fac = 2f / (2f * i + 1f);
mantissasLogged += cur * new Vector<float>(fac);
cur *= squared;
}
#else
//i = 0;
const float fac0 = 2f / (2 * 0 + 1);
var mantissasLogged = cur * new Vector<float>(fac0);
cur *= squared;
//i = 1;
const float fac1 = 2f / (2 * 1 + 1);
mantissasLogged += cur * new Vector<float>(fac1);
cur *= squared;
//i = 2;
const float fac2 = 2f / (2 * 2 + 1);
mantissasLogged += cur * new Vector<float>(fac2);
cur *= squared;
//i = 3;
const float fac3 = 2f / (2 * 3 + 1);
mantissasLogged += cur * new Vector<float>(fac3);
cur *= squared;
//i = 4;
const float fac4 = 2f / (2 * 4 + 1);
mantissasLogged += cur * new Vector<float>(fac4);
#endif
return mantissasLogged;
}
EDIT: I put some simple tests into the program on startup. Vector.IsHardwareAccelerated == true; Vector.Count == 4; This vectorised Log gives the correct answer for the first two inputs, but incorrect for the second two. Perhaps the assumption that Unsafe.AsPointer(Vector) gives me a pointer to the vector elements as four consecutive floats is incorrect.
Log outputs:
DEBUG Vector.IsHardwareAccelerated: True
DEBUG Vector<float>.Count: 4
DEBUG Vector<Uint64>.Count: 2
DEBUG MathUtils test input data: 5.967E+009,1.072E+006,9.521E+017,4.726E+000
DEBUG MathUtils required output: 9.776,6.030,17.979,0.674
DEBUG MathUtils actual output: 9.776,6.030,0.218,0.072
(Yet to have a chance to check the bit patterns...)