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#!/usr/bin/python3
"""
A simple script to generate the tables used in halffloat.c. The algorithms in
this script are based upon the paper `Fast Half Float Conversions`_, referenced
by the Wikipedia article on `half-precision floating point`_.
.. _half-precision floating point:
https://en.wikipedia.org/wiki/Half-precision_floating-point_format
.. _Fast Half Float Conversions:
ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf
"""
from itertools import zip_longest
def grouper(iterable, n, fillvalue=None):
args = [iter(iterable)] * n
return zip_longest(*args, fillvalue=fillvalue)
def sigtable():
print("static const uint32_t sigtable[] = {")
values = (
0 if i == 0 else convertsig(i) if 1 <= i < 1024 else 0x38000000 + ((i - 1024) << 13)
for i in range(2048)
)
values = (f"{i:#010x}" for i in values)
for row in grouper(values, 8):
print(" " + (", ".join(row)) + ",")
print("};")
def exptable():
values = (
0
if i == 0
else 0x47800000
if i == 31
else 0x80000000
if i == 32
else i << 23
if 1 <= i < 31
else 0x80000000 + ((i - 32) << 23)
if 33 <= i < 63
else 0xC7800000 # i == 63
for i in range(64)
)
print("static const uint32_t exptable[] = {")
values = (f"{i:#010x}" for i in values)
for row in grouper(values, 8):
print(" " + (", ".join(row)) + ",")
print("};")
def offsettable():
values = (0 if i in (0, 32) else 1024 for i in range(64))
print("static const uint16_t offsettable[] = {")
values = (f"{i:#06x}" for i in values)
for row in grouper(values, 8):
print(" " + (", ".join(row)) + ",")
print("};")
def convertsig(i):
if not i:
return 0
m = i << 13
e = 0
while not m & 0x00800000:
e -= 0x00800000
m <<= 1
m &= ~0x00800000
e += 0x38800000
return m | e
def basetable():
values = [0] * 512
for i in range(256):
e = i - 127
if e < -24: # underflow to 0
values[i | 0x000] = 0
values[i | 0x100] = 0x8000
elif e < -14: # smalls to denorms
values[i | 0x000] = 0x400 >> (-e - 14)
values[i | 0x100] = (0x400 >> (-e - 14)) | 0x8000
elif e < 15: # normal case
values[i | 0x000] = (e + 15) << 10
values[i | 0x100] = ((e + 15) << 10) | 0x8000
elif e < 128: # overflow to inf
values[i | 0x000] = 0x7C00
values[i | 0x100] = 0xFC00
else: # inf and nan
values[i | 0x000] = 0x7C00
values[i | 0x100] = 0xFC00
print("static const uint16_t basetable[] = {")
values = (f"{i:#06x}" for i in values)
for row in grouper(values, 8):
print(" " + (", ".join(row)) + ",")
print("};")
def shifttable():
values = [0] * 512
for i in range(256):
e = i - 127
if e < -24: # underflow to 0
values[i | 0x000] = 24
values[i | 0x100] = 24
elif e < -14: # smalls to denorms
values[i | 0x000] = -e - 1
values[i | 0x100] = -e - 1
elif e < 15: # normal case
values[i | 0x000] = 13
values[i | 0x100] = 13
elif e < 128: # overflow to inf
values[i | 0x000] = 24
values[i | 0x100] = 24
else: # inf and nan
values[i | 0x000] = 13
values[i | 0x100] = 13
print("static const uint16_t shifttable[] = {")
values = (f"{i:#06x}" for i in values)
for row in grouper(values, 8):
print(" " + (", ".join(row)) + ",")
print("};")
sigtable()
print()
exptable()
print()
offsettable()
print()
basetable()
print()
shifttable()
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