64-bit system or 62-bit system?

[charvista]

Hello friends,
I have tested some extremes, and found out that the Windows 7's 64-bit system is in fact a true 62-bit system....
The following program shows why.

Code: Select all

For i=1 To 64
    Debug "2 ^ "+Str(i)+"  =  "+Str(Pow(2,i))
Next

Apparently, it cannot make calculation safely higher than 2^62 as 63 and 64 are returning negative values when it had still to be positive. I am not sure why. I know that there is an extra bit for the sign.
Even the PureBasic manual states clearly that 64-bit-Integers and Quads have a range from -9223372036854775808 to +9223372036854775807.

[netmaestro]

Pow() returns a double, with smaller limits.

[Arctic Fox]

Code: Select all

a.q = 1

For i = 1 To 64
  a * 2
  Debug "2^" + Str(i) + ": " + Str(a)
Next i

Quad has a range from (-2^63) to (2^63 - 1). Note the -1.
For each multiplication by 2, the bits of the number are shifted one place to the left.

Thus 2^63 returns a negative number (and 2^64 returns zero).


Edit
@Charvista
In addition to netmaestro's reply, if you use StrD in your example, it returns positive numbers for 2^63 and 2^64, but it loses some significant digits in the end of the numbers (one of the 'side effects' of floating point numbers).

Code: Select all

For i=1 To 64
  Debug "2 ^ "+Str(i)+"  =  "+StrD(Pow(2,i))
Next

[wilbert]

if you use StrD in your example, it returns positive numbers for 2^63 and 2^64, but it loses some significant digits in the end of the numbers (one of the 'side effects' of floating point numbers).

It's true doubles have a limited accuracy. In this example however the results should be accurate.
A double consists of a sign bit, 11 bits for the exponent and 52 bits for the fraction.
In case of powers of 2, the fraction part isn't used, only the exponent. So even 2^1000 should be accurate.

[charvista]

I would like to thank you all for the explanations. I thought it was a kind of bug but now I understand. I have seen that accuracy is guaranteed up to 15 significant digits... So I'll keep that. It is very rare that we need such huge numbers, anyway... But when we need them, then better have them accurate...
Cheers