import struct
import numpy
# display functions
[docs]class UndefinedCastError(FloatingPointError):
"""
Unable to case a number.
"""
pass
[docs]def display_int(ival, sign=1, exponent=8, mantissa=23):
"""
Displays an integer as bits.
:param ival: value to display (float32)
:param sign: number of bits for the sign
:param exponent: number of bits for the exponent
:param mantissa: number of bits for the mantissa
:return: string
"""
t = sign + exponent + mantissa
s = bin(ival)[2:]
s = "0" * (t - len(s)) + s
s1 = s[:sign]
s2 = s[sign : sign + exponent]
s3 = s[sign + exponent :]
return ".".join([s1, s2, s3])
[docs]def display_float32(value, sign=1, exponent=8, mantissa=23):
"""
Displays a float32 into b.
:param value: value to display (float32)
:param sign: number of bits for the sign
:param exponent: number of bits for the exponent
:param mantissa: number of bits for the mantissa
:return: string
"""
return display_int(
int.from_bytes(struct.pack("<f", numpy.float32(value)), "little"),
sign=sign,
exponent=exponent,
mantissa=mantissa,
)
[docs]def display_float16(value, sign=1, exponent=5, mantissa=10):
"""
Displays a float32 into b.
:param value: value to display (float16)
:param sign: number of bits for the sign
:param exponent: number of bits for the exponent
:param mantissa: number of bits for the mantissa
:return: string
"""
return display_int(
numpy.float16(value).view("H"), sign=sign, exponent=exponent, mantissa=mantissa
)
[docs]def display_fexmx(value, sign, exponent, mantissa):
"""
Displays any float encoded with 1 bit for the sign,
*exponent* bit for the exponent and *mantissa* bit for the
mantissa.
:param value: value to display (int)
:param sign: number of bits for the sign
:param exponent: number of bits for the exponent
:param mantissa: number of bits for the mantissa
:return: string
"""
return display_int(value, sign=sign, exponent=exponent, mantissa=mantissa)
[docs]def display_fe4m3(value, sign=1, exponent=4, mantissa=3):
"""
Displays a float 8 E4M3 into b.
:param value: value to display (int)
:param sign: number of bits for the sign
:param exponent: number of bits for the exponent
:param mantissa: number of bits for the mantissa
:return: string
"""
return display_fexmx(value, sign=1, exponent=4, mantissa=3)
[docs]def display_fe5m2(value, sign=1, exponent=4, mantissa=3):
"""
Displays a float 8 E5M2 into binary format.
:param value: value to display (int)
:param sign: number of bits for the sign
:param exponent: number of bits for the exponent
:param mantissa: number of bits for the mantissa
:return: string
"""
return display_fexmx(value, sign=1, exponent=5, mantissa=2)
# cast from float 8 to float 32
[docs]def fe4m3_to_float32_float(ival: int, fn: bool = True, uz: bool = False) -> float:
"""
Casts a float 8 encoded as an integer into a float.
:param ival: byte
:param fn: no infinite values
:param uz: no negative zero
:return: float (float 32)
"""
if not fn:
raise NotImplementedError("fn=False is not implemented.")
if ival < 0 or ival > 255:
raise ValueError(f"{ival} is not a float8.")
if ival == 0:
return numpy.float32(0)
if uz:
if ival == 0x80:
return numpy.float32(numpy.nan)
sign = ival & 0x80
ival &= 0x7F
expo = ival >> 3
mant = ival & 0x07
powe = expo & 0x0F
if expo == 0:
powe -= 7
fraction = 0
else:
powe -= 8
fraction = 1
fval = float(mant / 8 + fraction) * 2.0**powe
if sign:
fval = -fval
return numpy.float32(fval)
else:
if ival == 255:
return numpy.float32(-numpy.nan)
if ival == 127:
return numpy.float32(numpy.nan)
sign = ival & 0x80
if ival == 0 and sign > 0:
return -numpy.float32(0)
ival &= 0x7F
expo = ival >> 3
mant = ival & 0x07
powe = expo & 0x0F
if expo == 0:
powe -= 6
fraction = 0
else:
powe -= 7
fraction = 1
fval = float(mant / 8 + fraction) * 2.0**powe
if sign:
fval = -fval
return numpy.float32(fval)
[docs]def fe5m2_to_float32_float(ival: int, fn: bool = False, uz: bool = False) -> float:
"""
Casts a float 8 encoded as an integer into a float.
:param ival: byte
:param fn: no infinite values
:param uz: no negative zero
:return: float (float 32)
"""
if ival < 0 or ival > 255:
raise ValueError(f"{ival} is not a float8.")
if fn and uz:
if ival == 0x80:
return numpy.float32(numpy.nan)
exponent_bias = 16
elif not fn and not uz:
if ival in (255, 254, 253):
return numpy.float32(-numpy.nan)
if ival in (127, 126, 125):
return numpy.float32(numpy.nan)
if ival == 252:
return -numpy.float32(numpy.inf)
if ival == 124:
return numpy.float32(numpy.inf)
if (ival & 0x7F) == 0:
return numpy.float32(0)
exponent_bias = 15
else:
raise NotImplementedError("fn and uz must be both True or False.")
sign = ival & 0x80
ival &= 0x7F
expo = ival >> 2
mant = ival & 0x03
powe = expo & 0x1F
if expo == 0:
powe -= exponent_bias - 1
fraction = 0
else:
powe -= exponent_bias
fraction = 1
fval = float(mant / 4 + fraction) * 2.0**powe
if sign:
fval = -fval
return numpy.float32(fval)
[docs]def fe4m3_to_float32(ival: int, fn: bool = True, uz: bool = False) -> float:
"""
Casts a float E4M3 encoded as an integer into a float.
:param ival: byte
:param fn: no inifinite values
:param uz: no negative zero
:return: float (float 32)
"""
if not fn:
raise NotImplementedError("fn=False is not implemented.")
if ival < 0 or ival > 255:
raise ValueError(f"{ival} is not a float8.")
if uz:
exponent_bias = 8
if ival == 0x80:
return numpy.nan
else:
exponent_bias = 7
if ival == 255:
return numpy.float32(-numpy.nan)
if ival == 127:
return numpy.float32(numpy.nan)
expo = (ival & 0x78) >> 3
mant = ival & 0x07
sign = ival & 0x80
res = sign << 24
if expo == 0:
if mant > 0:
expo = 0x7F - exponent_bias
if mant & 0x4 == 0:
mant &= 0x3
mant <<= 1
expo -= 1
if mant & 0x4 == 0:
mant &= 0x3
mant <<= 1
expo -= 1
res |= (mant & 0x3) << 21
res |= expo << 23
else:
res |= mant << 20
expo += 0x7F - exponent_bias
res |= expo << 23
f = numpy.uint32(res).view(numpy.float32) # pylint: disable=E1121
return f
[docs]def fe5m2_to_float32(ival: int, fn: bool = False, uz: bool = False) -> float:
"""
Casts a float E5M2 encoded as an integer into a float.
:param ival: byte
:param fn: no inifinite values
:param uz: no negative values
:return: float (float 32)
"""
if ival < 0 or ival > 255:
raise ValueError(f"{ival} is not a float8.")
if fn and uz:
if ival == 0x80:
return numpy.float32(numpy.nan)
exponent_bias = 16
elif not fn and not uz:
if ival in {253, 254, 255}:
return numpy.float32(-numpy.nan)
if ival in {125, 126, 127}:
return numpy.float32(numpy.nan)
if ival == 252:
return numpy.float32(-numpy.inf)
if ival == 124:
return numpy.float32(numpy.inf)
exponent_bias = 15
else:
raise NotImplementedError("fn and uz must be both False or True.")
expo = (ival & 0x7C) >> 2
mant = ival & 0x03
sign = ival & 0x80
res = sign << 24
if expo == 0:
if mant > 0:
expo = 0x7F - exponent_bias
if mant & 0x2 == 0:
mant &= 0x1
mant <<= 1
expo -= 1
res |= (mant & 0x1) << 22
res |= expo << 23
else:
res |= mant << 21
expo += 0x7F - exponent_bias
res |= expo << 23
f = numpy.uint32(res).view(numpy.float32) # pylint: disable=E1121
return f
# cast from float32 to float 8
class CastFloat8Sets:
values_e4m3fn = list(
sorted(
(fe4m3_to_float32_float(i), i) for i in range(0, 256) if i not in (255, 127)
)
)
values_e4m3fnuz = list(
sorted(
(fe4m3_to_float32_float(i, uz=True), i) for i in range(0, 256) if i != 0x80
)
)
values_e5m2 = list(
sorted(
(fe5m2_to_float32_float(i), i)
for i in range(0, 256)
if i not in {253, 254, 255, 125, 126, 127}
)
)
values_e5m2fnuz = list(
sorted(
(fe5m2_to_float32_float(i, fn=True, uz=True), i)
for i in range(0, 256)
if i != 0x80
)
)
[docs]class CastFloat8(CastFloat8Sets):
"""
Helpers to cast float8 into float32 or the other way around.
"""
values_e4m3fn_max_value = max(
v
for v in CastFloat8Sets.values_e4m3fn
if not numpy.isinf(v[0]) and not numpy.isnan(v[0])
)
values_e4m3fnuz_max_value = max(
v
for v in CastFloat8Sets.values_e4m3fnuz
if not numpy.isinf(v[0]) and not numpy.isnan(v[0])
)
values_e5m2_max_value = max(
v
for v in CastFloat8Sets.values_e5m2
if not numpy.isinf(v[0]) and not numpy.isnan(v[0])
)
values_e5m2fnuz_max_value = max(
v
for v in CastFloat8Sets.values_e5m2fnuz
if not numpy.isinf(v[0]) and not numpy.isnan(v[0])
)
[docs] @staticmethod
def find_closest_value(value, sorted_values):
"""
Search a value into a sorted array of values.
:param value: float32 value to search
:param sorted_values: list of tuple `[(float 32, byte)]`
:return: byte
The function searches into the first column the closest value and
return the value on the second columns.
"""
a = 0
b = len(sorted_values)
while a < b:
m = (a + b) // 2
th = sorted_values[m][0]
if value == th:
return sorted_values[m][1]
if value < th:
b = m
elif a == m:
break
else:
a = m
# finds the closest one
if b < len(sorted_values):
d1 = value - sorted_values[a][0]
d2 = sorted_values[b][0] - value
if d1 < d2:
return sorted_values[a][1]
if d1 == d2:
# Applies rule tie to even
ca, cb = sorted_values[a][1], sorted_values[b][1]
return cb if ca & 1 == 1 else ca
return sorted_values[b][1]
return sorted_values[a][1]
[docs]def search_float32_into_fe4m3(
value: float, fn: bool = True, uz: bool = False, saturate: bool = True
) -> int:
"""
Casts a float 32 into a float E4M3.
:param value: float
:param fn: no infinite values
:param uz: no negative zero
:param saturate: to convert out of range and infinities to max value if True
:return: byte
"""
if not fn:
raise NotImplementedError("fn=False is not implemented.")
b = int.from_bytes(struct.pack("<f", numpy.float32(value)), "little")
ret = (b & 0x80000000) >> 24 # sign
if uz:
if numpy.isnan(value):
return 0x80
if numpy.isinf(value) and not saturate:
return 0x80
set_values = CastFloat8.values_e4m3fnuz
max_value = CastFloat8.values_e4m3fnuz_max_value
if value > max_value[0]:
return max_value[1] if saturate else 0x80
if value < -max_value[0]:
return (max_value[1] | ret) if saturate else 0x80
else:
if numpy.isnan(value) or numpy.isinf(value):
return 0x7F | ret
set_values = CastFloat8.values_e4m3fn
max_value = CastFloat8.values_e4m3fn_max_value
if value > max_value[0]:
return max_value[1] if saturate else 0x7F | ret
if value < -max_value[0]:
return (max_value[1] | ret) if saturate else 0x7F | ret
f = numpy.float32(value)
i = CastFloat8.find_closest_value(f, set_values)
return (i & 0x7F) | ret
[docs]def search_float32_into_fe5m2(
value: float, fn: bool = False, uz: bool = False, saturate: bool = True
) -> int:
"""
Casts a float 32 into a float E5M2.
:param value: float
:param fn: no infinite values
:param uz: no negative zero
:param saturate: to convert out of range and infinities to max value if True
:return: byte
"""
b = int.from_bytes(struct.pack("<f", numpy.float32(value)), "little")
ret = (b & 0x80000000) >> 24 # sign
if fn and uz:
if numpy.isnan(value):
return 0x80
if numpy.isinf(value) and not saturate:
return 0x80
set_values = CastFloat8.values_e5m2fnuz
max_value = CastFloat8.values_e5m2fnuz_max_value
if value > max_value[0]:
return max_value[1] if saturate else 0x80
if value < -max_value[0]:
return (max_value[1] | ret) if saturate else 0x80
elif not fn and not uz:
if numpy.isnan(value):
return 0x7F | ret
set_values = CastFloat8.values_e5m2
max_value = CastFloat8.values_e5m2_max_value
if value > max_value[0]:
return max_value[1] if saturate else (0x7C | ret)
if value < -max_value[0]:
return (max_value[1] | ret) if saturate else (0x7C | ret)
else:
raise NotImplementedError("fn and uz must both True or False.")
f = numpy.float32(value)
i = CastFloat8.find_closest_value(f, set_values)
return (i & 0x7F) | ret
[docs]def float32_to_fe4m3(x, fn: bool = True, uz: bool = False, saturate: bool = True):
"""
Converts a float32 into a float E4M3.
:param x: numpy.float32
:param fn: no infinite values
:param uz: no negative zero
:param saturate: to convert out of range and infinities to max value if True
:return: byte
"""
if not fn:
raise NotImplementedError("fn=False is not implemented.")
if not isinstance(x, numpy.float32):
x = numpy.float32(x)
b = int.from_bytes(struct.pack("<f", x), "little")
ret = (b & 0x80000000) >> 24 # sign
if uz:
if (b & 0x7FFFFFFF) == 0x7F800000:
# infinity
if saturate:
return ret | 127
return 0x80
if (b & 0x7F800000) == 0x7F800000:
return 0x80
e = (b & 0x7F800000) >> 23 # exponent
m = b & 0x007FFFFF # mantissa
if e != 0:
if e < 116:
pass
elif e < 120:
# denormalized number
ex = e - 119
if ex >= -2:
ret |= 1 << (2 + ex)
ret |= m >> (21 - ex)
elif m > 0:
ret |= 1
mask = 1 << (20 - ex)
if m & mask and (
ret & 1
or m & (mask - 1) > 0
or (m & mask and m & (mask << 1) and m & (mask - 1) == 0)
):
# rounding
ret += 1
elif e < 135:
# normalized number
ex = e - 119 # 127 - 8
if ex == 0:
ret |= 0x4
ret |= m >> 21
else:
ret |= ex << 3
ret |= m >> 20
if m & 0x80000 and ((m & 0x100000) or (m & 0x7FFFF)):
if (ret & 0x7F) < 0x7F:
# rounding
ret += 1
elif not saturate:
return 0x80
elif saturate:
ret |= 0x7F # 01111110
else:
ret = 0x80
elif m == 0:
# -0
ret = 0
return int(ret)
else:
if (b & 0x7FFFFFFF) == 0x7F800000:
# infinity
if saturate:
return ret | 126
return 0x7F | ret
if (b & 0x7F800000) == 0x7F800000:
# non
return 0x7F | ret
e = (b & 0x7F800000) >> 23 # exponent
m = b & 0x007FFFFF # mantissa
if e != 0:
if e < 117:
pass
elif e < 121:
# denormalized number
ex = e - 120
if ex >= -2:
ret |= 1 << (2 + ex)
ret |= m >> (21 - ex)
elif m > 0:
ret |= 1
mask = 1 << (20 - ex)
if m & mask and (
ret & 1
or m & (mask - 1) > 0
or (m & mask and m & (mask << 1) and m & (mask - 1) == 0)
):
# rounding
ret += 1
elif e < 136:
# normalized number
ex = e - 120
if ex == 0:
ret |= 0x4
ret |= m >> 21
else:
ret |= ex << 3
ret |= m >> 20
if (ret & 0x7F) == 0x7F:
ret &= 0xFE
if (m & 0x80000) and ((m & 0x100000) or (m & 0x7FFFF)):
if (ret & 0x7F) < 0x7E:
# rounding
ret += 1
elif not saturate:
ret |= 0x7F
elif saturate:
ret |= 126 # 01111110
else:
ret |= 0x7F
return int(ret)
[docs]def float32_to_fe5m2(x, fn: bool = False, uz: bool = False, saturate: bool = True):
"""
Converts a float32 into a float E5M2.
:param x: numpy.float32
:param fn: no infinite values
:param uz: no negative zero
:param saturate: to convert out of range and infinities to max value if True
:return: byte
"""
b = int.from_bytes(struct.pack("<f", numpy.float32(x)), "little")
ret = (b & 0x80000000) >> 24 # sign
if fn and uz:
if (b & 0x7FFFFFFF) == 0x7F800000:
# inf
if saturate:
return ret | 0x7F
return 0x80
if (b & 0x7F800000) == 0x7F800000:
# nan
return 0x80
e = (b & 0x7F800000) >> 23 # exponent
m = b & 0x007FFFFF # mantissa
if e != 0:
if e < 109:
pass
elif e < 112:
# denormalized number
ex = e - 111
if ex >= -1:
ret |= 1 << (1 + ex)
ret |= m >> (22 - ex)
elif m > 0:
ret |= 1
mask = 1 << (21 - ex)
if m & mask and (
ret & 1
or m & (mask - 1) > 0
or (m & mask and m & (mask << 1) and m & (mask - 1) == 0)
):
# rounding
ret += 1
elif e < 143:
# normalized number
ex = e - 111
ret |= ex << 2
ret |= m >> 21
if m & 0x100000 and ((m & 0xFFFFF) or (m & 0x200000)):
if (ret & 0x7F) < 0x7F:
# rounding
ret += 1
elif not saturate:
ret = 0x80
elif e == 255 and m == 0: # inf
ret = 0x80
elif saturate:
ret |= 0x7F # last possible number
else:
ret = 0x80
elif m == 0:
# -0
ret = 0
return int(ret)
elif not fn and not uz:
if (b & 0x7FFFFFFF) == 0x7F800000:
# inf
if saturate:
return 0x7B | ret
return 0x7C | ret
if (b & 0x7F800000) == 0x7F800000:
# nan
return 0x7F | ret
e = (b & 0x7F800000) >> 23 # exponent
m = b & 0x007FFFFF # mantissa
if e != 0:
if e < 110:
pass
elif e < 113:
# denormalized number
ex = e - 112
if ex >= -1:
ret |= 1 << (1 + ex)
ret |= m >> (22 - ex)
elif m > 0:
ret |= 1
mask = 1 << (21 - ex)
if m & mask and (
ret & 1
or m & (mask - 1) > 0
or (m & mask and m & (mask << 1) and m & (mask - 1) == 0)
):
# rounding
ret += 1
elif e < 143:
# normalized number
ex = e - 112
ret |= ex << 2
ret |= m >> 21
if m & 0x100000 and ((m & 0xFFFFF) or (m & 0x200000)):
if (ret & 0x7F) < 0x7B:
# rounding
ret += 1
elif saturate:
ret |= 0x7B
else:
ret |= 0x7C
elif saturate:
ret |= 0x7B
else:
ret |= 0x7C
return int(ret)
else:
raise NotImplementedError("fn and uz must be both False or True.")