APyFloat

APyTypes provide a class for configurable floating-point numbers: APyFloat.

The numbers are created from the sign-bit, the exponent and the mantissa (without hidden one) and the corresponding wordlengths. However, there are also convenience methods to do this either from a float or from a bit-pattern.

from apytypes import APyFloat

a = APyFloat(True, 3, 5, 4, 5)
a

APyFloat(sign=1, exp=3, man=5, exp_bits=4, man_bits=5)

b = APyFloat.from_float(2.25, 3, 2)
b

APyFloat(sign=0, exp=4, man=0, exp_bits=3, man_bits=2)

c = APyFloat.from_bits(int("10110101"), 3, 4)
c

APyFloat(sign=1, exp=1, man=5, exp_bits=3, man_bits=4)

Standard arithmetic operations are supported. The resulting number of exponent and mantissa bits are the maximum of the involved terms.

a + b

APyFloat(sign=0, exp=7, man=30, exp_bits=4, man_bits=5)

a * c

APyFloat(sign=0, exp=1, man=17, exp_bits=4, man_bits=5)

Standard string formatting is supported

str(a)

'-0.0722656'

Comparisons with integers and floats are supported

(b >= 7, a < -1.2)

(False, False)

Arithmetic with Python integers and floats is supported, although not recommended, by automatically casting the number to the same format of the APyType-object

b + 1.125

APyFloat(sign=0, exp=4, man=2, exp_bits=3, man_bits=2)

Which is equivalent to

b + APyFloat.from_float(1.125, exp_bits=b.exp_bits, man_bits=b.man_bits, bias=b.bias)

APyFloat(sign=0, exp=4, man=2, exp_bits=3, man_bits=2)

However, while it is convenient to let APyTypes convert numbers automatically, it is not recommended as it can yield unexpected results. Consider the expression

2 + 2 + APyFloat.from_float(8, exp_bits=4, man_bits=1)

APyFloat(sign=0, exp=10, man=1, exp_bits=4, man_bits=1)

which would yield a different result from

APyFloat.from_float(8, exp_bits=4, man_bits=1) + 2 + 2

APyFloat(sign=0, exp=10, man=0, exp_bits=4, man_bits=1)

To change the word length of a APyFloat, the method cast() can be used

(a + b).cast(4, 3)

APyFloat(sign=0, exp=8, man=0, exp_bits=4, man_bits=3)