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using System;
namespace ChocolArm64.Instruction
{
static class ASoftFloat
{
static ASoftFloat()
{
InvSqrtEstimateTable = BuildInvSqrtEstimateTable();
RecipEstimateTable = BuildRecipEstimateTable();
}
private static readonly byte[] RecipEstimateTable;
private static readonly byte[] InvSqrtEstimateTable;
private static byte[] BuildInvSqrtEstimateTable()
{
byte[] Table = new byte[512];
for (ulong index = 128; index < 512; index++)
{
ulong a = index;
if (a < 256)
{
a = (a << 1) + 1;
}
else
{
a = (a | 1) << 1;
}
ulong b = 256;
while (a * (b + 1) * (b + 1) < (1ul << 28))
{
b++;
}
b = (b + 1) >> 1;
Table[index] = (byte)(b & 0xFF);
}
return Table;
}
private static byte[] BuildRecipEstimateTable()
{
byte[] Table = new byte[256];
for (ulong index = 0; index < 256; index++)
{
ulong a = index | 0x100;
a = (a << 1) + 1;
ulong b = 0x80000 / a;
b = (b + 1) >> 1;
Table[index] = (byte)(b & 0xFF);
}
return Table;
}
public static float InvSqrtEstimate(float x)
{
return (float)InvSqrtEstimate((double)x);
}
public static double InvSqrtEstimate(double x)
{
ulong x_bits = (ulong)BitConverter.DoubleToInt64Bits(x);
ulong x_sign = x_bits & 0x8000000000000000;
long x_exp = (long)((x_bits >> 52) & 0x7FF);
ulong scaled = x_bits & ((1ul << 52) - 1);
if (x_exp == 0x7FF && scaled != 0)
{
// NaN
return BitConverter.Int64BitsToDouble((long)(x_bits | 0x0008000000000000));
}
if (x_exp == 0)
{
if (scaled == 0)
{
// Zero -> Infinity
return BitConverter.Int64BitsToDouble((long)(x_sign | 0x7ff0000000000000));
}
// Denormal
while ((scaled & (1 << 51)) == 0)
{
scaled <<= 1;
x_exp--;
}
scaled <<= 1;
}
if (x_sign != 0)
{
// Negative -> NaN
return BitConverter.Int64BitsToDouble((long)0x7ff8000000000000);
}
if (x_exp == 0x7ff && scaled == 0)
{
// Infinity -> Zero
return BitConverter.Int64BitsToDouble((long)x_sign);
}
if (((ulong)x_exp & 1) == 1)
{
scaled >>= 45;
scaled &= 0xFF;
scaled |= 0x80;
}
else
{
scaled >>= 44;
scaled &= 0xFF;
scaled |= 0x100;
}
ulong result_exp = ((ulong)(3068 - x_exp) / 2) & 0x7FF;
ulong estimate = (ulong)InvSqrtEstimateTable[scaled];
ulong fraction = estimate << 44;
ulong result = x_sign | (result_exp << 52) | fraction;
return BitConverter.Int64BitsToDouble((long)result);
}
public static float RecipEstimate(float x)
{
return (float)RecipEstimate((double)x);
}
public static double RecipEstimate(double x)
{
ulong x_bits = (ulong)BitConverter.DoubleToInt64Bits(x);
ulong x_sign = x_bits & 0x8000000000000000;
ulong x_exp = (x_bits >> 52) & 0x7FF;
ulong scaled = x_bits & ((1ul << 52) - 1);
if (x_exp >= 2045)
{
if (x_exp == 0x7ff && scaled != 0)
{
// NaN
return BitConverter.Int64BitsToDouble((long)(x_bits | 0x0008000000000000));
}
// Infinity, or Out of range -> Zero
return BitConverter.Int64BitsToDouble((long)x_sign);
}
if (x_exp == 0)
{
if (scaled == 0)
{
// Zero -> Infinity
return BitConverter.Int64BitsToDouble((long)(x_sign | 0x7ff0000000000000));
}
// Denormal
if ((scaled & (1ul << 51)) == 0)
{
x_exp = ~0ul;
scaled <<= 2;
}
else
{
scaled <<= 1;
}
}
scaled >>= 44;
scaled &= 0xFF;
ulong result_exp = (2045 - x_exp) & 0x7FF;
ulong estimate = (ulong)RecipEstimateTable[scaled];
ulong fraction = estimate << 44;
if (result_exp == 0)
{
fraction >>= 1;
fraction |= 1ul << 51;
}
else if (result_exp == 0x7FF)
{
result_exp = 0;
fraction >>= 2;
fraction |= 1ul << 50;
}
ulong result = x_sign | (result_exp << 52) | fraction;
return BitConverter.Int64BitsToDouble((long)result);
}
public static float RecipStep(float op1, float op2)
{
return (float)RecipStep((double)op1, (double)op2);
}
public static double RecipStep(double op1, double op2)
{
op1 = -op1;
ulong op1_bits = (ulong)BitConverter.DoubleToInt64Bits(op1);
ulong op2_bits = (ulong)BitConverter.DoubleToInt64Bits(op2);
ulong op1_sign = op1_bits & 0x8000000000000000;
ulong op2_sign = op2_bits & 0x8000000000000000;
ulong op1_other = op1_bits & 0x7FFFFFFFFFFFFFFF;
ulong op2_other = op2_bits & 0x7FFFFFFFFFFFFFFF;
bool inf1 = op1_other == 0x7ff0000000000000;
bool inf2 = op2_other == 0x7ff0000000000000;
bool zero1 = op1_other == 0;
bool zero2 = op2_other == 0;
if ((inf1 && zero2) || (zero1 && inf2))
{
return 2.0;
}
else if (inf1 || inf2)
{
// Infinity
return BitConverter.Int64BitsToDouble((long)(0x7ff0000000000000 | (op1_sign ^ op2_sign)));
}
return 2.0 + op1 * op2;
}
public static float ConvertHalfToSingle(ushort x)
{
uint x_sign = (uint)(x >> 15) & 0x0001;
uint x_exp = (uint)(x >> 10) & 0x001F;
uint x_mantissa = (uint)x & 0x03FF;
if (x_exp == 0 && x_mantissa == 0)
{
// Zero
return BitConverter.Int32BitsToSingle((int)(x_sign << 31));
}
if (x_exp == 0x1F)
{
// NaN or Infinity
return BitConverter.Int32BitsToSingle((int)((x_sign << 31) | 0x7F800000 | (x_mantissa << 13)));
}
int exponent = (int)x_exp - 15;
if (x_exp == 0)
{
// Denormal
x_mantissa <<= 1;
while ((x_mantissa & 0x0400) == 0)
{
x_mantissa <<= 1;
exponent--;
}
x_mantissa &= 0x03FF;
}
uint new_exp = (uint)((exponent + 127) & 0xFF) << 23;
return BitConverter.Int32BitsToSingle((int)((x_sign << 31) | new_exp | (x_mantissa << 13)));
}
}
}
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