221270db90
* More accurate impl of FMINNM/FMAXNM, add vector variants * Optimize for the 0 case when op1 != op2 * Address PR feedback
537 lines
16 KiB
C#
537 lines
16 KiB
C#
using System;
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namespace ChocolArm64.Instruction
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{
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static class ASoftFloat
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{
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static ASoftFloat()
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{
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InvSqrtEstimateTable = BuildInvSqrtEstimateTable();
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RecipEstimateTable = BuildRecipEstimateTable();
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}
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private static readonly byte[] RecipEstimateTable;
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private static readonly byte[] InvSqrtEstimateTable;
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private static byte[] BuildInvSqrtEstimateTable()
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{
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byte[] Table = new byte[512];
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for (ulong index = 128; index < 512; index++)
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{
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ulong a = index;
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if (a < 256)
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{
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a = (a << 1) + 1;
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}
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else
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{
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a = (a | 1) << 1;
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}
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ulong b = 256;
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while (a * (b + 1) * (b + 1) < (1ul << 28))
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{
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b++;
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}
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b = (b + 1) >> 1;
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Table[index] = (byte)(b & 0xFF);
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}
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return Table;
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}
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private static byte[] BuildRecipEstimateTable()
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{
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byte[] Table = new byte[256];
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for (ulong index = 0; index < 256; index++)
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{
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ulong a = index | 0x100;
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a = (a << 1) + 1;
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ulong b = 0x80000 / a;
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b = (b + 1) >> 1;
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Table[index] = (byte)(b & 0xFF);
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}
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return Table;
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}
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public static float InvSqrtEstimate(float x)
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{
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return (float)InvSqrtEstimate((double)x);
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}
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public static double InvSqrtEstimate(double x)
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{
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ulong x_bits = (ulong)BitConverter.DoubleToInt64Bits(x);
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ulong x_sign = x_bits & 0x8000000000000000;
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long x_exp = (long)((x_bits >> 52) & 0x7FF);
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ulong scaled = x_bits & ((1ul << 52) - 1);
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if (x_exp == 0x7FF && scaled != 0)
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{
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// NaN
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return BitConverter.Int64BitsToDouble((long)(x_bits | 0x0008000000000000));
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}
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if (x_exp == 0)
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{
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if (scaled == 0)
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{
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// Zero -> Infinity
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return BitConverter.Int64BitsToDouble((long)(x_sign | 0x7FF0000000000000));
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}
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// Denormal
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while ((scaled & (1 << 51)) == 0)
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{
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scaled <<= 1;
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x_exp--;
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}
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scaled <<= 1;
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}
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if (x_sign != 0)
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{
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// Negative -> NaN
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return BitConverter.Int64BitsToDouble((long)0x7FF8000000000000);
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}
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if (x_exp == 0x7ff && scaled == 0)
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{
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// Infinity -> Zero
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return BitConverter.Int64BitsToDouble((long)x_sign);
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}
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if (((ulong)x_exp & 1) == 1)
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{
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scaled >>= 45;
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scaled &= 0xFF;
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scaled |= 0x80;
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}
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else
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{
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scaled >>= 44;
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scaled &= 0xFF;
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scaled |= 0x100;
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}
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ulong result_exp = ((ulong)(3068 - x_exp) / 2) & 0x7FF;
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ulong estimate = (ulong)InvSqrtEstimateTable[scaled];
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ulong fraction = estimate << 44;
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ulong result = x_sign | (result_exp << 52) | fraction;
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return BitConverter.Int64BitsToDouble((long)result);
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}
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public static float RecipEstimate(float x)
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{
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return (float)RecipEstimate((double)x);
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}
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public static double RecipEstimate(double x)
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{
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ulong x_bits = (ulong)BitConverter.DoubleToInt64Bits(x);
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ulong x_sign = x_bits & 0x8000000000000000;
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ulong x_exp = (x_bits >> 52) & 0x7FF;
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ulong scaled = x_bits & ((1ul << 52) - 1);
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if (x_exp >= 2045)
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{
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if (x_exp == 0x7ff && scaled != 0)
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{
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// NaN
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return BitConverter.Int64BitsToDouble((long)(x_bits | 0x0008000000000000));
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}
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// Infinity, or Out of range -> Zero
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return BitConverter.Int64BitsToDouble((long)x_sign);
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}
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if (x_exp == 0)
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{
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if (scaled == 0)
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{
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// Zero -> Infinity
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return BitConverter.Int64BitsToDouble((long)(x_sign | 0x7FF0000000000000));
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}
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// Denormal
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if ((scaled & (1ul << 51)) == 0)
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{
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x_exp = ~0ul;
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scaled <<= 2;
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}
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else
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{
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scaled <<= 1;
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}
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}
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scaled >>= 44;
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scaled &= 0xFF;
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ulong result_exp = (2045 - x_exp) & 0x7FF;
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ulong estimate = (ulong)RecipEstimateTable[scaled];
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ulong fraction = estimate << 44;
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if (result_exp == 0)
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{
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fraction >>= 1;
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fraction |= 1ul << 51;
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}
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else if (result_exp == 0x7FF)
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{
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result_exp = 0;
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fraction >>= 2;
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fraction |= 1ul << 50;
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}
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ulong result = x_sign | (result_exp << 52) | fraction;
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return BitConverter.Int64BitsToDouble((long)result);
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}
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public static float RecipStep(float op1, float op2)
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{
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return (float)RecipStep((double)op1, (double)op2);
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}
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public static double RecipStep(double op1, double op2)
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{
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op1 = -op1;
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ulong op1_bits = (ulong)BitConverter.DoubleToInt64Bits(op1);
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ulong op2_bits = (ulong)BitConverter.DoubleToInt64Bits(op2);
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ulong op1_sign = op1_bits & 0x8000000000000000;
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ulong op2_sign = op2_bits & 0x8000000000000000;
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ulong op1_other = op1_bits & 0x7FFFFFFFFFFFFFFF;
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ulong op2_other = op2_bits & 0x7FFFFFFFFFFFFFFF;
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bool inf1 = op1_other == 0x7FF0000000000000;
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bool inf2 = op2_other == 0x7FF0000000000000;
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bool zero1 = op1_other == 0;
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bool zero2 = op2_other == 0;
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if ((inf1 && zero2) || (zero1 && inf2))
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{
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return 2.0;
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}
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else if (inf1 || inf2)
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{
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// Infinity
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return BitConverter.Int64BitsToDouble((long)(0x7FF0000000000000 | (op1_sign ^ op2_sign)));
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}
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return 2.0 + op1 * op2;
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}
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public static float ConvertHalfToSingle(ushort x)
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{
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uint x_sign = (uint)(x >> 15) & 0x0001;
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uint x_exp = (uint)(x >> 10) & 0x001F;
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uint x_mantissa = (uint)x & 0x03FF;
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if (x_exp == 0 && x_mantissa == 0)
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{
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// Zero
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return BitConverter.Int32BitsToSingle((int)(x_sign << 31));
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}
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if (x_exp == 0x1F)
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{
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// NaN or Infinity
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return BitConverter.Int32BitsToSingle((int)((x_sign << 31) | 0x7F800000 | (x_mantissa << 13)));
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}
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int exponent = (int)x_exp - 15;
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if (x_exp == 0)
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{
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// Denormal
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x_mantissa <<= 1;
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while ((x_mantissa & 0x0400) == 0)
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{
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x_mantissa <<= 1;
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exponent--;
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}
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x_mantissa &= 0x03FF;
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}
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uint new_exp = (uint)((exponent + 127) & 0xFF) << 23;
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return BitConverter.Int32BitsToSingle((int)((x_sign << 31) | new_exp | (x_mantissa << 13)));
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}
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public static float MaxNum(float op1, float op2)
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{
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uint op1_bits = (uint)BitConverter.SingleToInt32Bits(op1);
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uint op2_bits = (uint)BitConverter.SingleToInt32Bits(op2);
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if (IsQNaN(op1_bits) && !IsQNaN(op2_bits))
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{
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op1 = float.NegativeInfinity;
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}
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else if (!IsQNaN(op1_bits) && IsQNaN(op2_bits))
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{
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op2 = float.NegativeInfinity;
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}
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return Max(op1, op2);
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}
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public static double MaxNum(double op1, double op2)
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{
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ulong op1_bits = (ulong)BitConverter.DoubleToInt64Bits(op1);
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ulong op2_bits = (ulong)BitConverter.DoubleToInt64Bits(op2);
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if (IsQNaN(op1_bits) && !IsQNaN(op2_bits))
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{
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op1 = double.NegativeInfinity;
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}
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else if (!IsQNaN(op1_bits) && IsQNaN(op2_bits))
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{
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op2 = double.NegativeInfinity;
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}
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return Max(op1, op2);
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}
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public static float Max(float op1, float op2)
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{
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// Fast path
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if (op1 > op2)
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{
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return op1;
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}
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if (op1 < op2 || (op1 == op2 && op2 != 0))
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{
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return op2;
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}
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uint op1_bits = (uint)BitConverter.SingleToInt32Bits(op1);
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uint op2_bits = (uint)BitConverter.SingleToInt32Bits(op2);
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// Handle NaN cases
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if (ProcessNaNs(op1_bits, op2_bits, out uint op_bits))
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{
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return BitConverter.Int32BitsToSingle((int)op_bits);
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}
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// Return the most positive zero
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if ((op1_bits & op2_bits) == 0x80000000u)
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{
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return BitConverter.Int32BitsToSingle(int.MinValue);
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}
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return 0;
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}
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public static double Max(double op1, double op2)
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{
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// Fast path
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if (op1 > op2)
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{
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return op1;
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}
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if (op1 < op2 || (op1 == op2 && op2 != 0))
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{
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return op2;
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}
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ulong op1_bits = (ulong)BitConverter.DoubleToInt64Bits(op1);
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ulong op2_bits = (ulong)BitConverter.DoubleToInt64Bits(op2);
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// Handle NaN cases
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if (ProcessNaNs(op1_bits, op2_bits, out ulong op_bits))
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{
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return BitConverter.Int64BitsToDouble((long)op_bits);
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}
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// Return the most positive zero
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if ((op1_bits & op2_bits) == 0x8000000000000000ul)
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{
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return BitConverter.Int64BitsToDouble(long.MinValue);
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}
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return 0;
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}
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public static float MinNum(float op1, float op2)
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{
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uint op1_bits = (uint)BitConverter.SingleToInt32Bits(op1);
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uint op2_bits = (uint)BitConverter.SingleToInt32Bits(op2);
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if (IsQNaN(op1_bits) && !IsQNaN(op2_bits))
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{
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op1 = float.PositiveInfinity;
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}
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else if (!IsQNaN(op1_bits) && IsQNaN(op2_bits))
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{
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op2 = float.PositiveInfinity;
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}
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return Max(op1, op2);
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}
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public static double MinNum(double op1, double op2)
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{
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ulong op1_bits = (ulong)BitConverter.DoubleToInt64Bits(op1);
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ulong op2_bits = (ulong)BitConverter.DoubleToInt64Bits(op2);
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if (IsQNaN(op1_bits) && !IsQNaN(op2_bits))
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{
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op1 = double.PositiveInfinity;
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}
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else if (!IsQNaN(op1_bits) && IsQNaN(op2_bits))
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{
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op2 = double.PositiveInfinity;
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}
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return Min(op1, op2);
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}
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public static float Min(float op1, float op2)
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{
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// Fast path
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if (op1 < op2)
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{
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return op1;
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}
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if (op1 > op2 || (op1 == op2 && op2 != 0))
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{
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return op2;
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}
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uint op1_bits = (uint)BitConverter.SingleToInt32Bits(op1);
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uint op2_bits = (uint)BitConverter.SingleToInt32Bits(op2);
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// Handle NaN cases
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if (ProcessNaNs(op1_bits, op2_bits, out uint op_bits))
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{
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return BitConverter.Int32BitsToSingle((int)op_bits);
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}
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// Return the most negative zero
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if ((op1_bits | op2_bits) == 0x80000000u)
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{
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return BitConverter.Int32BitsToSingle(int.MinValue);
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}
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return 0;
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}
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public static double Min(double op1, double op2)
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{
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// Fast path
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if (op1 < op2)
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{
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return op1;
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}
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if (op1 > op2 || (op1 == op2 && op2 != 0))
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{
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return op2;
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}
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ulong op1_bits = (ulong)BitConverter.DoubleToInt64Bits(op1);
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ulong op2_bits = (ulong)BitConverter.DoubleToInt64Bits(op2);
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// Handle NaN cases
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if (ProcessNaNs(op1_bits, op2_bits, out ulong op_bits))
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{
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return BitConverter.Int64BitsToDouble((long)op_bits);
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}
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// Return the most negative zero
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if ((op1_bits | op2_bits) == 0x8000000000000000ul)
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{
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return BitConverter.Int64BitsToDouble(long.MinValue);
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}
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return 0;
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}
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private static bool ProcessNaNs(uint op1_bits, uint op2_bits, out uint op_bits)
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{
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if (IsSNaN(op1_bits))
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{
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op_bits = op1_bits | (1u << 22); // op1 is SNaN, return QNaN op1
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}
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else if (IsSNaN(op2_bits))
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{
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op_bits = op2_bits | (1u << 22); // op2 is SNaN, return QNaN op2
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}
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else if (IsQNaN(op1_bits))
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{
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op_bits = op1_bits; // op1 is QNaN, return QNaN op1
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}
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else if (IsQNaN(op2_bits))
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{
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op_bits = op2_bits; // op2 is QNaN, return QNaN op2
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}
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else
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{
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op_bits = 0;
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return false;
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}
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return true;
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}
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private static bool ProcessNaNs(ulong op1_bits, ulong op2_bits, out ulong op_bits)
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{
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if (IsSNaN(op1_bits))
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{
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op_bits = op1_bits | (1ul << 51); // op1 is SNaN, return QNaN op1
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}
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else if (IsSNaN(op2_bits))
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{
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op_bits = op2_bits | (1ul << 51); // op2 is SNaN, return QNaN op2
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}
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else if (IsQNaN(op1_bits))
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{
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op_bits = op1_bits; // op1 is QNaN, return QNaN op1
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}
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else if (IsQNaN(op2_bits))
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{
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op_bits = op2_bits; // op2 is QNaN, return QNaN op2
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}
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else
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{
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op_bits = 0;
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return false;
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}
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return true;
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}
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private static bool IsQNaN(uint op_bits)
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{
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return (op_bits & 0x007FFFFF) != 0 &&
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(op_bits & 0x7FC00000) == 0x7FC00000;
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}
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private static bool IsQNaN(ulong op_bits)
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{
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return (op_bits & 0x000FFFFFFFFFFFFF) != 0 &&
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(op_bits & 0x7FF8000000000000) == 0x7FF8000000000000;
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}
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private static bool IsSNaN(uint op_bits)
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{
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return (op_bits & 0x007FFFFF) != 0 &&
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(op_bits & 0x7FC00000) == 0x7F800000;
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}
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private static bool IsSNaN(ulong op_bits)
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{
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return (op_bits & 0x000FFFFFFFFFFFFF) != 0 &&
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(op_bits & 0x7FF8000000000000) == 0x7FF0000000000000;
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}
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}
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} |