Possible error in INTEGER64 calculations

[bplus]

Need error flag for this:

Code: QB64: [Select]

1. Print ipower&&(7, 32)
2.  
3. Function ipower&& (x As _Integer64, e As _Unsigned Integer)
4.     'take x to an integer power
5.     Dim As _Integer64 z, y
6.     Dim As _Unsigned Integer n
7.     y = x
8.     n = e
9.     z = 1&&
10.     While n > 0
11.         outer = outer + 1
12.         While (n Mod 2) = 0 ' why have this?
13.             inner = inner + 1
14.             n = n \ 2
15.             y = y * y
16.         Wend
17.         n = n - 1
18.         z = y * z
19.     Wend
20.     ipower = z
21.     Print outer, inner
22. End Function

[jack]

        While (n Mod 2) = 0 ' why have this?

while n is even
    divide n by 2 and square the result
wend

[bplus]

Thanks @jack

Steve got here first to explain, clever idea!

We need error checking for when numbers get too big.

[jack]

bplus, can you think of an easy and efficient way to detect or prevent overflow?
there might be some ideas from this post https://stackoverflow.com/questions/3944505/detecting-signed-overflow-in-c-c

[SMcNeill]

bplus, can you think of an easy and efficient way to detect or prevent overflow?
there might be some ideas from this post https://stackoverflow.com/questions/3944505/detecting-signed-overflow-in-c-c

Precalculate values with _FLOATs.  If the result is greater than what an INT64 can hold, flag an error and reject them.

[jack]

never mind, it didn't work

[bplus]

Precalculate values with _FLOATs.  If the result is greater than what an INT64 can hold, flag an error and reject them.

I had similar thought getting out of bed this morning. The b ^ e = Exp(e * Log(b)) may fail in precision before the limit of _Integer64 though. Will be interesting challenge to test.

(Jack just posted as I was editing this. So I have yet to study your reply jack.)

wait... what am I thinking?  the precision for the calc using * will be fine as long as we don't go over.

[jack]

bplus, when I tested with x=2 it seemed to work but it doesn't work for other numbers

[jack]

bplus, this should work, it's up to the user to decide what to do when overflow occured
reference https://gcc.gnu.org/onlinedocs/gcc/Integer-Overflow-Builtins.html

Code: QB64: [Select]

1. Declare Library
2.     Function mul_overflow& Alias "__builtin_smulll_overflow" (ByVal a As _Integer64, Byval b As _Integer64, res As _Integer64)
3. End Declare
4.  
5. 'Print ipower(2&&, 3)
6. 'Print ipower(2&&, 4)
7. 'Print ipower(2&&, 5)
8. Print ipower(3&&, 40)
9.  
10. Function ipower&& (x As _Integer64, e As _Unsigned Integer)
11.     'take x to an integer power
12.     Dim As _Integer64 z, y
13.     Dim As _Unsigned Integer n
14.     Dim As Long f
15.     y = x
16.     n = e
17.     z = 1&&
18.     While n > 0
19.         While (n And 1) = 0
20.             n = n \ 2
21.             f = mul_overflow(y, y, y) 'y = y * y
22.             If f Then Print "an overflow occured"
23.         Wend
24.         n = n - 1
25.         f = mul_overflow(y, z, z) ' z = y * z
26.         If f Then Print "an overflow occured"
27.     Wend
28.     ipower = z
29. End Function
30.  

[jack]

a little better

Code: QB64: [Select]

1. ' reference https://gcc.gnu.org/onlinedocs/gcc/Integer-Overflow-Builtins.html
2. Declare Library
3.     Function mul_overflow& Alias "__builtin_smulll_overflow" (ByVal a As _Integer64, Byval b As _Integer64, res As _Integer64)
4. End Declare
5.  
6. Print ipower(3&&, 39)
7. Print ipower(3&&, 40)
8.  
9. Function ipower&& (x As _Integer64, e As _Unsigned Integer)
10.     'take x to an integer power
11.     Dim As _Integer64 z, y
12.     Dim As _Unsigned Integer n
13.  
14.     y = x
15.     n = e
16.     z = 1&&
17.     While n > 0
18.         While (n And 1) = 0
19.             n = n \ 2
20.             If mul_overflow(y, y, y) Then Print "an overflow occured"
21.         Wend
22.         n = n - 1
23.         If mul_overflow(y, z, z) Then Print "an overflow occured"
24.     Wend
25.     ipower = z
26. End Function
27.  

[jack]

hello everyone, why didn't you think of the obvious simple solution?
a positive integer that overflows will be negative
never mind, that doesn't always work

[bplus]

hello everyone, why didn't you think of the obvious simple solution?
a positive integer that overflows will be negative

But only for a little while then it builds up to positive number again, just wrong and way too small!

This https://www.qb64.org/forum/index.php?topic=4210.msg135991#msg135991
shows positive result only it's wrong.

Is it possible numbers could slip through negative detection while calculating result?

@jack your built-in detector of overflow (in C++ ?) may be the better.

[Pete]

String math
How'd you get so funky
String Math
Can you use a hot key
String Math
Made by an Egyptian
String Math
Even does division
Born in Windows 7
Works in Win-11
String Math

[Richard]

@david_uwi


https://www.qb64.org/forum/index.php?topic=2276.msg137521#msg137521  Reply #183


You may be interested in reading the above reply as it addresses the problem you are having. 

Note that there is a difference between "Overflow/Overrange" and "Numbers not representable".