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"""
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()
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