98 lines
3.7 KiB
Python
98 lines
3.7 KiB
Python
"""
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The 8-bit float formats used here are from a proposal supported by Graphcore, AMD and Qualcomm.
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See https://arxiv.org/abs/2206.02915
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"""
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import struct
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import zlib
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import array
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import bitarray
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from bitstring.luts import binary8_luts_compressed
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import math
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class Binary8Format:
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"""8-bit floating point formats based on draft IEEE binary8"""
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def __init__(self, exp_bits: int, bias: int):
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self.exp_bits = exp_bits
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self.bias = bias
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self.pos_clamp_value = 0b01111111
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self.neg_clamp_value = 0b11111111
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def __str__(self):
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return f"Binary8Format(exp_bits={self.exp_bits}, bias={self.bias})"
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def decompress_luts(self):
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binary8_to_float_compressed, float16_to_binary8_compressed = binary8_luts_compressed[(self.exp_bits, self.bias)]
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self.lut_float16_to_binary8 = zlib.decompress(float16_to_binary8_compressed)
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dec = zlib.decompress(binary8_to_float_compressed)
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self.lut_binary8_to_float = struct.unpack(f'<{len(dec) // 4}f', dec)
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def create_luts(self):
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self.lut_binary8_to_float = self.createLUT_for_binary8_to_float()
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self.lut_float16_to_binary8 = self.createLUT_for_float16_to_binary8()
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def float_to_int8(self, f: float) -> int:
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"""Given a Python float convert to the best float8 (expressed as an integer in 0-255 range)."""
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# First convert the float to a float16, then a 16 bit uint
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try:
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b = struct.pack('>e', f)
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except (OverflowError, struct.error):
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# Return the largest representable positive or negative value
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return self.pos_clamp_value if f > 0 else self.neg_clamp_value
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f16_int = int.from_bytes(b, byteorder='big')
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# Then use this as an index to our large LUT
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return self.lut_float16_to_binary8[f16_int]
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def createLUT_for_float16_to_binary8(self) -> bytes:
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# Used to create the LUT that was compressed and stored for the fp8 code
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import gfloat
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fi = gfloat.formats.format_info_p3109(8 - self.exp_bits)
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fp16_to_fp8 = bytearray(1 << 16)
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for i in range(1 << 16):
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b = struct.pack('>H', i)
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f, = struct.unpack('>e', b)
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fp = gfloat.round_float(fi, f)
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if math.isnan(fp):
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fp8_i = 0b10000000
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else:
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fp8_i = self.lut_binary8_to_float.index(fp)
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fp16_to_fp8[i] = fp8_i
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return bytes(fp16_to_fp8)
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def createLUT_for_binary8_to_float(self):
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"""Create a LUT to convert an int in range 0-255 representing a float8 into a Python float"""
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i2f = []
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for i in range(256):
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b = bitarray.util.int2ba(i, length=8, endian='big', signed=False)
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sign = b[0]
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exponent = bitarray.util.ba2int(b[1:1 + self.exp_bits])
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significand = b[1 + self.exp_bits:]
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if exponent == 0:
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significand = bitarray.bitarray('0') + significand
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exponent = -self.bias + 1
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else:
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significand = bitarray.bitarray('1') + significand
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exponent -= self.bias
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f = float(bitarray.util.ba2int(significand)) / (2.0 ** (7 - self.exp_bits))
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f *= 2 ** exponent
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i2f.append(f if not sign else -f)
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# One special case for minus zero
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i2f[0b10000000] = float('nan')
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# and for plus and minus infinity
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i2f[0b01111111] = float('inf')
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i2f[0b11111111] = float('-inf')
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return array.array('f', i2f)
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# We create the 1.5.2 and 1.4.3 formats.
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p4binary_fmt = Binary8Format(exp_bits=4, bias=8)
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p3binary_fmt = Binary8Format(exp_bits=5, bias=16)
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def decompress_luts():
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p4binary_fmt.decompress_luts()
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p3binary_fmt.decompress_luts()
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