PTO-ARCH-PROFILE-E8M0-CONVERSION

1// PTO-UNIT: {"id":"PTO-ARCH-PROFILE-E8M0-CONVERSION","surface":"arch","classification":["profile","e8m0-conversion"],"depends_on":["PTO-ARCH-PROFILE-REFERENCE-QUANTIZATION","PTO-ARCH-DATA-TYPES-NUMERIC-FORMATS"]}2
3// NDF-BEGIN: PTO-TCVT-E8M0-PROFILE-0014// ndf: kind=executable level=L3 layer=architecture status=accepted5// TCVT to E8M0 MUST accept only FP16, BF16, and FP32 sources. Positive6// finite values MUST round their base-two exponent under the selected RMode.7// Zero, negative values, and NaNs MUST produce 0xFF with NV. Positive8// infinity and finite range overflow or underflow MUST produce 0xFF when Sat9// is zero and the corresponding finite endpoint when Sat is one, with exact10// OF or UF plus NX status. Canonicalize MUST retain its representation role.11// NDF-END: PTO-TCVT-E8M0-PROFILE-00112
13// DOC-BEGIN: operation14pure func HardwareTCVTE8M0SourceTypeSupported(15    source_type: TileDataType) => boolean16begin17    return source_type == TileDataType_FP16 ||18           source_type == TileDataType_BF16 ||19           source_type == TileDataType_FP32;20end;21
22pure func HardwareTCVTTypePairSupported(23    source_type: TileDataType,24    destination_type: TileDataType) => boolean25begin26    if destination_type == TileDataType_E8M0 then27        return HardwareTCVTE8M0SourceTypeSupported(source_type);28    end;29    return TRUE;30end;31
32pure func ReferenceE8M0HighestSetBit(33    significand: Word) => integer {0..63}34begin35    assert !IsZero(significand);36    var highest: integer {0..63} = 0;37    for position = 0 to 63 do38        if significand[position] == '1' then39            highest = position as integer {0..63};40        end;41    end;42    return highest;43end;44
45pure func ReferenceE8M0RoundExponent(46    significand: Word,47    exponent: integer {-1074..1023},48    mode: NumericRoundingMode) => (integer {-149..128}, boolean)49begin50    let highest = ReferenceE8M0HighestSetBit(significand);51    let floor_candidate = exponent + highest;52    assert -149 <= floor_candidate && floor_candidate <= 127;53    let floor_exponent = floor_candidate as integer {-149..127};54    let exact_power = significand ==55        LSL(Zeros{PTO_XLEN} + 1, highest);56    if exact_power then57        return (floor_exponent, TRUE);58    end;59
60    let ceiling_exponent = (floor_exponent + 1) as integer {-148..128};61    if mode == NumericRound_RTM then62        return (floor_exponent, FALSE);63    elsif mode == NumericRound_RTP then64        return (ceiling_exponent, FALSE);65    elsif mode == NumericRound_RTZ then66        if floor_exponent < 0 then67            return (ceiling_exponent, FALSE);68        else return (floor_exponent, FALSE);69        end;70    elsif mode == NumericRound_RTO then71        if floor_exponent MOD 2 != 0 then72            return (floor_exponent, FALSE);73        else return (ceiling_exponent, FALSE);74        end;75    end;76
77    let square = MultiplyWord(significand, significand);78    let boundary_shift = 2 * highest + 1;79    assert boundary_shift <= 127;80    let boundary = LSL(81        Zeros{PTO_XLEN} + 1,82        boundary_shift as integer {0..127});83    if UInt(square) < UInt(boundary) then84        return (floor_exponent, FALSE);85    elsif UInt(square) > UInt(boundary) then86        return (ceiling_exponent, FALSE);87    elsif mode == NumericRound_RNE then88        if floor_exponent MOD 2 == 0 then89            return (floor_exponent, FALSE);90        else return (ceiling_exponent, FALSE);91        end;92    elsif mode == NumericRound_RNA then93        if floor_exponent < 0 then94            return (floor_exponent, FALSE);95        else return (ceiling_exponent, FALSE);96        end;97    else98        assert mode == NumericRound_RHB;99        return (ceiling_exponent, FALSE);100    end;101end;102
103func ReferenceFloatToE8M0(104    value: Word,105    source_type: TileDataType,106    control: NumericExecutionControl) => (Word, bits(5))107begin108    assert HardwareTCVTE8M0SourceTypeSupported(source_type);109    let value_class = TileNumericValueClass(source_type, value);110    if value_class == NumericValue_InvalidEncoding ||111       NumericValueClassIsNaN(value_class) ||112       NumericValueClassIsZero(value_class) ||113       value_class == NumericValue_NegativeInfinity ||114       value_class == NumericValue_NegativeNormal ||115       value_class == NumericValue_NegativeSubnormal then116        return (Zeros{PTO_XLEN} + 0xff, Zeros{5} + 0x01);117    elsif value_class == NumericValue_PositiveInfinity then118        return (119            if control.saturating then Zeros{PTO_XLEN} + 0xfe120            else Zeros{PTO_XLEN} + 0xff,121            Zeros{5} + 0x14);122    end;123
124    let (available, negative, significand, exponent) =125        TileNumericFiniteDecomposition(source_type, value);126    assert available && !negative && !IsZero(significand);127    let highest = ReferenceE8M0HighestSetBit(significand);128    let floor_candidate = exponent + highest;129    assert -149 <= floor_candidate && floor_candidate <= 127;130    let floor_exponent = floor_candidate as integer {-149..127};131    let exact_power = significand ==132        LSL(Zeros{PTO_XLEN} + 1, highest);133    if floor_exponent < -127 then134        return (135            if control.saturating then Zeros{PTO_XLEN}136            else Zeros{PTO_XLEN} + 0xff,137            Zeros{5} + 0x18);138    elsif floor_exponent == 127 && !exact_power then139        return (140            if control.saturating then Zeros{PTO_XLEN} + 0xfe141            else Zeros{PTO_XLEN} + 0xff,142            Zeros{5} + 0x14);143    end;144
145    let (rounded_exponent, exact) = ReferenceE8M0RoundExponent(146        significand, exponent, control.rounding_mode);147    assert -127 <= rounded_exponent && rounded_exponent <= 127;148    let code = (rounded_exponent + 127) as integer {0..254};149    return (150        Zeros{PTO_XLEN} + code,151        if exact then Zeros{5} else Zeros{5} + 0x10);152end;153
154implementation func TileProfileConvert(155    value: Word,156    source_type: TileDataType,157    destination_type: TileDataType,158    control: NumericExecutionControl) => (Word, bits(5))159begin160    if destination_type == TileDataType_E8M0 then161        return ReferenceFloatToE8M0(value, source_type, control);162    elsif !TileDataTypeIsFloating(destination_type) then163        return (164            NormalizeTileInteger(value, destination_type),165            Zeros{5});166    end;167    return (value, Zeros{5});168end;169// DOC-END: operation170