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import array
import math
import struct
import bitarray
from bitstring.luts import mxfp_luts_compressed
import zlib
from typing import Optional
def round_to_nearest_ties_to_even(lut_int_to_float, lower: int, f: float) -> Optional[int]:
upper = lower + 1
# Special case for LUTs without a negative zero.
lower_float = 0.0 if lower == 128 else lut_int_to_float[lower]
upper_float = lut_int_to_float[upper]
if upper_float < lower_float:
lower, upper = upper, lower
lower_float, upper_float = upper_float, lower_float
if f == lower_float:
return lower
if f == upper_float:
return upper
if lower_float < f < upper_float:
d1 = f - lower_float
d2 = upper_float - f
if d1 < d2:
return lower
if d2 < d1:
return upper
return lower if lower % 2 == 0 else upper
return None
class MXFPFormat:
"""Defining an MXFP micro-scaling floating point format"""
def __init__(self, exp_bits: int, mantissa_bits: int, bias: int, mxfp_overflow: str):
self.exp_bits = exp_bits
self.mantissa_bits = mantissa_bits
self.bias = bias
self.mxfp_overflow = mxfp_overflow
self.pos_clamp_value = (1 << (self.exp_bits + self.mantissa_bits)) - 1
self.neg_clamp_value = (1 << (1 + self.exp_bits + self.mantissa_bits)) - 1
# Special cases for e4m3 and e5m2
if self.exp_bits == 4 and self.mantissa_bits == 3:
if self.mxfp_overflow == 'saturate':
self.pos_clamp_value = 0b01111110 # 448
self.neg_clamp_value = 0b11111110 # -448
else:
self.pos_clamp_value = self.neg_clamp_value = 0b11111111 # NaN
if self.exp_bits == 5 and self.mantissa_bits == 2:
if self.mxfp_overflow == 'saturate':
self.pos_clamp_value = 0b01111011 # 57344
self.neg_clamp_value = 0b11111011 # -57344
else:
self.pos_clamp_value = 0b01111100 # +inf
self.neg_clamp_value = 0b11111100 # -inf
# If we calculate these LUTs now it creates a bootstrap problem in generate_luts.py.
self.lut_float16_to_mxfp = None
self.lut_int_to_float = None
def __str__(self):
return f"MXFPFormat(exp_bits={self.exp_bits}, mantissa_bits={self.mantissa_bits}, bias={self.bias}, mxfp_overflow='{self.mxfp_overflow}')"
def decompress_luts(self):
int_to_float_compressed, float16_to_mxfp_compressed = mxfp_luts_compressed[(self.exp_bits, self.mantissa_bits, self.bias, self.mxfp_overflow)]
self.lut_float16_to_mxfp = zlib.decompress(float16_to_mxfp_compressed)
dec = zlib.decompress(int_to_float_compressed)
self.lut_int_to_float = struct.unpack(f'<{len(dec) // 4}f', dec)
def create_luts(self):
self.lut_int_to_float = self.createLUT_for_int_to_float()
self.lut_float16_to_mxfp = self.createLUT_for_float16_to_mxfp()
def float_to_int(self, f: float) -> int:
"""Given a Python float convert to the best mxfp float (expressed as an int) that represents it."""
# 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_mxfp[f16_int]
def slow_float_to_int(self, f: float) -> int:
# Slow, but easier to follow than the faster version.
# The output int has the binary sequence needed for the float.
length = 1 + self.exp_bits + self.mantissa_bits
values = 1 << length
# First get the NaN case out of the way
if math.isnan(f):
if length == 8:
return 0xff # Works for both e5m2 and e4m3
# For smaller lengths, NaN isn't supported so we instead return an invalid value to detect later
return 0xff
# This is so we can distinguish between 0.0 and -0.0
is_positive = math.copysign(1.0, f) == 1.0
if is_positive:
# Positive, so top bit is not set
for i in range(values // 2 - 1):
upper = self.lut_int_to_float[i + 1]
if upper == float('inf'):
break
x = round_to_nearest_ties_to_even(self.lut_int_to_float, i, f)
if x is not None:
return x
return self.pos_clamp_value
else:
# Negative, so top bit is set
for i in range(values // 2, values - 1):
lower = self.lut_int_to_float[i + 1]
if lower == float('-inf'):
break
x = round_to_nearest_ties_to_even(self.lut_int_to_float, i, f)
if x is not None:
return x
# Clip to negative max
return self.neg_clamp_value
def createLUT_for_int_to_float(self) -> array.array:
"""Create a LUT to convert an int in representing a MXFP float into a Python float"""
i2f = []
length = 1 + self.exp_bits + self.mantissa_bits
for i in range(1 << length):
b = bitarray.util.int2ba(i, length=length, 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 ** self.mantissa_bits)
f *= 2 ** exponent
if length == 8:
# Some special cases
if self.exp_bits == 5:
if i in [0b01111100, 0b11111100]:
f = float('inf')
if i in [0b01111101, 0b11111101, 0b01111110, 0b11111110, 0b01111111, 0b11111111]:
f = float('nan')
if self.exp_bits == 4:
if i in [0b01111111, 0b11111111]:
f = float('nan')
i2f.append(f if not sign else -f)
return array.array('f', i2f)
def createLUT_for_float16_to_mxfp(self) -> bytes:
"""Create a LUT to convert a float16 into a MXFP format"""
# Used to create the LUT that was compressed and stored for the fp8 code
length = 1 + self.exp_bits + self.mantissa_bits
if length == 8:
import gfloat
from gfloat.formats import format_info_ocp_e5m2, format_info_ocp_e4m3
fi = format_info_ocp_e5m2 if self.exp_bits == 5 else format_info_ocp_e4m3
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, sat=self.mxfp_overflow == 'saturate')
if math.isnan(fp):
fp8_i = 0b11111111
else:
# Special case for negative zero
if fp == 0.0 and math.copysign(1.0, fp) == -1.0:
fp8_i = 0b10000000
else:
fp8_i = self.lut_int_to_float.index(fp)
fp16_to_fp8[i] = fp8_i
return bytes(fp16_to_fp8)
else:
assert length in [4, 6]
fp16_to_fp8 = bytearray(1 << 16)
for i in range(1 << 16):
b = struct.pack('>H', i)
f, = struct.unpack('>e', b)
fp8_i = self.slow_float_to_int(f)
fp16_to_fp8[i] = fp8_i
return bytes(fp16_to_fp8)
e2m1mxfp_fmt = MXFPFormat(exp_bits=2, mantissa_bits=1, bias=1, mxfp_overflow='saturate')
e2m3mxfp_fmt = MXFPFormat(exp_bits=2, mantissa_bits=3, bias=1, mxfp_overflow='saturate')
e3m2mxfp_fmt = MXFPFormat(exp_bits=3, mantissa_bits=2, bias=3, mxfp_overflow='saturate')
e4m3mxfp_saturate_fmt = MXFPFormat(exp_bits=4, mantissa_bits=3, bias=7, mxfp_overflow='saturate')
e5m2mxfp_saturate_fmt = MXFPFormat(exp_bits=5, mantissa_bits=2, bias=15, mxfp_overflow='saturate')
e4m3mxfp_overflow_fmt = MXFPFormat(exp_bits=4, mantissa_bits=3, bias=7, mxfp_overflow='overflow')
e5m2mxfp_overflow_fmt = MXFPFormat(exp_bits=5, mantissa_bits=2, bias=15, mxfp_overflow='overflow')
def decompress_luts():
e2m1mxfp_fmt.decompress_luts()
e2m3mxfp_fmt.decompress_luts()
e3m2mxfp_fmt.decompress_luts()
e4m3mxfp_saturate_fmt.decompress_luts()
e5m2mxfp_saturate_fmt.decompress_luts()
e4m3mxfp_overflow_fmt.decompress_luts()
e5m2mxfp_overflow_fmt.decompress_luts()
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