HP Prime Miscalculating

[cyrille de brébisson]

Hello,

>Why does prime only have 48 bits of mantissa for doubles?

Le me expand on what Bernard is saying.
The CAS does use a 8 bytes data structure to save a mathematical object.
The first 5 bits (Least significant bits) of this structure is the object type (real, integer, vector...), the rest of free for use for each possible individual type.

In the case of a structure being a real, then the rest of the 64 bits is the double. BUT since 5 bits are already used for the type, this double is truncated by 5 bits (which have been stolen to indicate the type). Hence the 48 bits of mantissa (the other bits being the sign and exponent).

One could wonder: Why make real less precise? But remember that in CAS worlds, precision is achieved through "perfect" integers, not through floating points numbers, so the reasoning is quire sound. If you want precision: use integers as floating points will ALWAYS be inaccurate, regardless of the mantissa size. hence it it not a problem to remove 5 bits of precision.

Cyrille