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floatconversion.py
82 lines | 2.2 KiB | text/x-python | PythonLexer
def ieee(f, word=32):
"""Generate the binary string representing a floating-point value in IEEE754 code."""
f = float(f)
if word not in (16, 32, 64, 128):
raise ValueError("IEEE754 is defined for 16, 32, 64 and 128 bit words.")
exp_bin = range({16:5, 32:8, 64:11, 128:15}[word])
frac_bin = range(word - len(exp_bin) - 1)
# Sign.
sign_bin = [int(f < 0)]
f = abs(f)
# Find exponent (adding the bias).
bias = 2**(len(exp_bin)-1) -1
exponent = bias
while f >= 2:
exponent += 1
f /= 2
while f < 1 and exponent > 0:
exponent -= 1
f *= 2
if not 0 <= exponent < 2*(bias+1):
raise ValueError("Exponent overflow: Absolute exponent must be smaller than %d." % (bias + 1))
# Encode exponent in binary.
for i in exp_bin[::-1]:
exp_bin[i] = int(exponent % 2)
exponent /= 2
# Remove the leading 1 bit.
f -= 1
for i in frac_bin:
f *= 2
frac_bin[i] = int(f >= 1)
f -= frac_bin[i]
# Join the binary string components together.
return "".join(map(str, sign_bin + exp_bin + frac_bin))
def ieee_decode(binary):
"""Decode a binary string representing a floating-point value in IEEE754 code."""
# Determine the word size of the binary.
word = len(binary)
if word not in (16, 32, 64, 128):
raise ValueError("IEEE754 is defined for 16, 32, 64 and 128 bit words.")
# Determine the length of the exponent.
e = {16:5, 32:8, 64:11, 128:15}[word]
# Turn the binary string into a bit-list.
binary = [int(c) for c in binary]
# Split the components.
sign = -2 * binary[0] + 1
exp_bin = binary[1:1+e]
frac_bin = binary[1+e:]
# Decode the exponent.
bias = 2**(e-1) - 1
exponent = -bias
c = 1
for i in exp_bin[::-1]:
exponent += i * c
c *= 2
# Decode the fraction.
f = float(2**exponent)
power = f
for i in frac_bin:
power *= 0.5
f += i * power
return sign * f
if __name__ == "__main__":
val = ieee(24.)
val
print val[:16]
print val[0], val[1], val[2]
val_in_int = int(val[:16], 2)
print val_in_int
print hex( val_in_int )