On Tue, Apr 21, 2020 at 6:07 AM Schachner, Joseph <joseph.schach...@teledyne.com> wrote: > > 16 base 10 digits / log base10( 2) = 53.1508495182 bits. Obviously, > fractional bits don't exist, so 53 bits. If you note that the first non-zero > digit as 4, and the first digit after the 15 zeroes was 2, then you got an > extra bit. 54 bits. Where did the extra bit come from? It came from the > IEEE format's assumption that the top bit of the mantissa of a normalized > floating point value must be 1. Since we know what it must be, there is no > reason to use an actual bit for it. The 53 bits in the mantissa do not > include the assumed top bit. > > Isn't floating point fun? >
IEEE 64-bit packed floating point has 53 bits of mantissa, 11 scale bits (you've heard of "scale birds" in art? well, these are "scale bits"), and 1 sign bit. 53 + 11 + 1 == 64. Yep, floating point is fun. That assumed top 1 bit is always there, except when it isn't. Because denormal numbers are a thing. They don't have that implied 1 bit. Yep, floating point is fun. ChrisA -- https://mail.python.org/mailman/listinfo/python-list
