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