Fibonacci function doesn't calculate properly - c++

I've defined this macro
#define FIB(n) (( 4 << n*(3+n))/((4 << (2*n)) - (2 << n) - 1))%(2 << n)
and when I try to get an answer, doesn't work properly, by example if I call FIB(7),it gives me 0, that clearly is wrong. I tested this function in python and it works perfectly. So, anyone can explain me why doesn't it work in C and C++?

4 << n*(3+n) becomes 4 << 7*(3+7) when replace n with 7.
It means 4 << 70. If the size of int is 32 bits or 64 bits, shifting 70 bits is too much and this invokes undefined behavior in C.
Python supports multiple-precision arithmetic, so it may work well.

Related

How '<<' operator does work with #define in C++

I have two operation, and I am assuming both are doing ShiftLeft bitwise operation.
#define TACH_MAX_OWN_ORDERS 1<<6
int myVal = 1<<6
cout<<"Value after operation|"<<myVal <<"|"<<TACH_MAX_OWN_ORDERS<<endl;
output of TACH_MAX_OWN_ORDERS value always surprise me.
Value after operation|64|16
Do anyone have any clue, how it comes???
Thanks
Macros replace text as is, so it will result in
cout<<"Value after operation|"<<myVal <<"|"<<1<<6<<endl;
the << won't result in (int)1<<6 but rather ([...] << 1) << 6 where [...] will have std::cout at the deepest level. This means your macro will always result in 16 when used in std::cout, because 1 and 6 are shifted into the out stream ("1" + "6") instead of the actual numerical value 64.
You should put parantheses around the statement to avoid this:
#define TACH_MAX_OWN_ORDERS (1<<6)
or even better, since you should avoid macros, if available try to use compile time constants:
constexpr int TACH_MAX_OWN_ORDERS = 1 << 6;

Left shifting with a unit64_t - Gives warning

I am trying to do the following. However I am not sure where I might be going wrong
uint64_t x = (1 << 46);
std::cout << x;
I get the
-warning: left shift count >= width of type [-Wshift-count-overflow]
I get the output 0. I was expecting something a decimal output of a binary like this
1 0000........00 (46 0s)
My question is why am I getting this warning ? isnt uint64_t 64 bit ? also why am I getting the output 0 ?
The problem is that you are not shifting a 64-bit constant: 1 is a constant of type int, which is less than 64 bits on your platform (probably 32 bits; it is implementation-defined).
You can fix this by using UINT64_C macro around the constant:
uint64_t x = (UINT64_C(1) << 46);
1 is a 32-bit constant. The compiler (correctly) computes the constant expression as 0 --- the 1 shifted beyound the size of an int32. If the arguments to << were variables, an x86 cpu would return (1 << 14), i.e. 1 << (46 % 32).
Try "1ULL << 46".

Somewhat unexpected behaviour from left shift <<

This is a 32-bit MFC application currently running on Windows 10. Compiled with Visual C++ 2013.
std::cout << "sizeof(long long) = " << sizeof(long long) << std::endl;
int rot{ 32 };
long long bits{ (1 << rot) };
std::cout << "bits with variable = " << bits << std::endl;
long long bits2 = (1 << 32);
std::cout << "bits2 with constant = " << bits2 << std::endl;
system("pause");
The size of long long is 8 bytes, sufficient to manage my 32 bits, I was thinking. Here is the output of the debug build:
sizeof(long long) = 8
bits with variable = 1
bits2 with constant = 0
Press any key to continue . . .
And here is the output of the release build:
sizeof(long long) = 8
bits with variable = 0
bits2 with constant = 0
Press any key to continue . . .
So, apparently my single bit is leftshifted into oblivion even with a 64 bit data type. But I'm really puzzled to why the debug build produces different outputs if I shift with a variable as a parameter compared to a constant?
You need a long long type for 64 bits.
The expression 1 << 32 will be evaluated with int types for the operands, irrespective of the type of the variable to which this result is assigned.
You will have more luck with 1LL << 32, and 1LL << rot. That causes the expression to be evaluated using long long types.
Currently the behaviour of your program is undefined as you are overshifting a type when you write 1 << 32. Note also that 1 << 32 is a compile time evaluable constant expression whereas 1 << rot isn't. That probably accounts for the observed difference between using a variable and a constant.
The expression 1 << rot, when rot is an int, will give you an int result. It doesn't matter if you then place it into a long long since the damage has already been done(a).
Use 1LL << rot instead.
(a) And, by damage, I mean undefined behaviour, as per C11 6.5.7 Bitwise shift operators:
The integer promotions are performed on each of the operands. The type of the result is that of the promoted left operand. If the value of the right operand is negative or is greater than or equal to the width of the promoted left operand, the behavior is undefined.
As to "why the debug build produces different outputs if I shift with a variable as a parameter compared to a constant", that's one of the vagaries of undefined behaviour - literally anything that's possible is allowed to happen. It's perfectly within its rights to play derisive_laughter.ogg and format your hard disk :-)

what's the purpose of this code? is it counting number of digits?

if ((16 << (int)(4*((num.length()-2)-i))) == 0)
What does it mean? Is it a bit manipulation? It could be written much more simpler if it's only counting the digits, this is why I thought it might be something different than what I know.
<< is the left shift operator. Shifting left by nis the same as multiplying by 2 n times. If you shift far enough, all set bits will "fall over the edge" and the result will be 0.
16 << n will become 0 if n > sizeof(int)* BITS_PER_CHAR - 4.
So the expression can be written as:
if ((sizeof(int) * BITS_PER_CHAR - 4) < (int)(4*((num.length()-2)-i))
BITS_PER_CHAR is 8 on any POSIX-compliant system. sizeof(int)*BITS_PER_CHAR is usually 32, but can be other values.

Weird behavior of right shift operator (1 >> 32)

I recently faced a strange behavior using the right-shift operator.
The following program:
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <stdint.h>
int foo(int a, int b)
{
return a >> b;
}
int bar(uint64_t a, int b)
{
return a >> b;
}
int main(int argc, char** argv)
{
std::cout << "foo(1, 32): " << foo(1, 32) << std::endl;
std::cout << "bar(1, 32): " << bar(1, 32) << std::endl;
std::cout << "1 >> 32: " << (1 >> 32) << std::endl; //warning here
std::cout << "(int)1 >> (int)32: " << ((int)1 >> (int)32) << std::endl; //warning here
return EXIT_SUCCESS;
}
Outputs:
foo(1, 32): 1 // Should be 0 (but I guess I'm missing something)
bar(1, 32): 0
1 >> 32: 0
(int)1 >> (int)32: 0
What happens with the foo() function ? I understand that the only difference between what it does and the last 2 lines, is that the last two lines are evaluated at compile time. And why does it "work" if I use a 64 bits integer ?
Any lights regarding this will be greatly appreciated !
Surely related, here is what g++ gives:
> g++ -o test test.cpp
test.cpp: In function 'int main(int, char**)':
test.cpp:20:36: warning: right shift count >= width of type
test.cpp:21:56: warning: right shift count >= width of type
It's likely the CPU is actually computing
a >> (b % 32)
in foo; meanwhile, the 1 >> 32 is a constant expression, so the compiler will fold the constant at compile-time, which somehow gives 0.
Since the standard (C++98 §5.8/1) states that
The behavior is undefined if the right operand is negative, or greater than or equal to the length in bits of the promoted left operand.
there is no contradiction having foo(1,32) and 1>>32 giving different results.
On the other hand, in bar you provided a 64-bit unsigned value, as 64 > 32 it is guaranteed the result must be 1 / 232 = 0. Nevertheless, if you write
bar(1, 64);
you may still get 1.
Edit: The logical right shift (SHR) behaves like a >> (b % 32/64) on x86/x86-64 (Intel #253667, Page 4-404):
The destination operand can be a register or a memory location. The count operand can be an immediate value or the CL register. The count is masked to 5 bits (or 6 bits if in 64-bit mode and REX.W is used). The count range is limited to 0 to 31 (or 63 if 64-bit mode and REX.W is used). A special opcode encoding is provided for a count of 1.
However, on ARM (armv6&7, at least), the logical right-shift (LSR) is implemented as (ARMISA Page A2-6)
(bits(N), bit) LSR_C(bits(N) x, integer shift)
assert shift > 0;
extended_x = ZeroExtend(x, shift+N);
result = extended_x<shift+N-1:shift>;
carry_out = extended_x<shift-1>;
return (result, carry_out);
where (ARMISA Page AppxB-13)
ZeroExtend(x,i) = Replicate('0', i-Len(x)) : x
This guarantees a right shift of ≥32 will produce zero. For example, when this code is run on the iPhone, foo(1,32) will give 0.
These shows shifting a 32-bit integer by ≥32 is non-portable.
OK. So it's in 5.8.1:
The operands shall be of integral or enumeration type and integral promotions are performed. The type of the result is
that of the promoted left operand. The behavior is undefined if the right operand is negative, or greater than or equal to
the length in bits of the promoted left operand.
So you have an Undefined Behaviour(tm).
What happens in foo is that the shift width is greater than or equal to the size of the data being shifted. In the C99 standard that results in undefined behaviour. It's probably the same in whatever C++ standard MS VC++ is built to.
The reason for this is to allow compiler designers to take advantage of any CPU hardware support for shifts. For example, the i386 architecture has an instruction to shift a 32 bit word by a number of bits, but the number of bits is defined in a field in the instruction that is 5 bits wide. Most likely, your compiler is generating the instruction by taking your bit shift amount and masking it with 0x1F to get the bit shift in the instruction. This means that shifting by 32 is the same as shifting by 0.
I compiled it on 32 bit windows using VC9 compiler. It gave me the following warning. Since sizeof(int) is 4 bytes on my system compiler is indicating that right shifting by 32 bits results in undefined behavior. Since it is undefined, you can not predict the result. Just for checking I right shifted with 31 bits and all the warnings disappeared and the result was also as expected (i.e. 0).
I suppose the reason is that int type holds 32-bits (for most systems), but one bit is used for sign as it is signed type. So only 31 bits are used for actual value.
The warning says it all!
But in fairness I got bitten by the same error once.
int a = 1;
cout << ( a >> 32);
is completely undefined. In fact the compiler generally gives a different results than the runtime in my experience. What I mean by this is if the compiler can see to evaluate the shift expression at run time it may give you a different result to the expression evaluated at runtime.
foo(1,32) performs a rotate-shit, so bits that should disappear on the right reappear on the left. If you do it 32 times, the single bit set to 1 is back to its original position.
bar(1,32) is the same, but the bit is in the 64-32+1=33th bit, which is above the representable numbers for a 32-bit int. Only the 32 lowest bit are taken, and they are all 0's.
1 >> 32 is performed by the compiler. No idea why gcc uses a non-rotating shift here and not in the generated code.
Same thing for ((int)1 >> (int)32)