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Groups > comp.lang.c++ > #121263
| From | Tim Rentsch <tr.17687@z991.linuxsc.com> |
|---|---|
| Newsgroups | comp.lang.c++ |
| Subject | Re: constexpr is really very smart! |
| Date | 2024-12-19 00:40 -0800 |
| Organization | A noiseless patient Spider |
| Message-ID | <86zfksf4lb.fsf@linuxsc.com> (permalink) |
| References | <vjndub$2glcu$1@paganini.bofh.team> <20241216112808.00003f74@yahoo.com> <86jzbyghdw.fsf@linuxsc.com> <20241218013342.0000518a@yahoo.com> <20241218135131.00000006@yahoo.com> |
Michael S <already5chosen@yahoo.com> writes:
> On Wed, 18 Dec 2024 01:33:42 +0200
> Michael S <already5chosen@yahoo.com> wrote:
>
>> I am pretty sure that better variant exists, but for tonight it's
>> enough.
>
> Morning fibs.
>
> Recursive:
>
> struct pair_t {
> long long a,b;
> };
>
> // return .a=fib(n), .b=fib(n+1)
> static struct pair_t fib2(long n)
> {
> if (n <= 0) {
> struct pair_t ret = { .a = 0, .b = n==0 ? 1 : 0 };
> return ret;
> }
> // for n > 0
> // fib(n*2) = (fib(n-1)+fib(n+1))*fib(n)
> // fib(n*2+1) = fib(n)*fib(n)+fib(n+1)*fib(n+1)
> long m = (n-1) >> 1;
> struct pair_t ret = fib2(m);
> long long a = ret.a, b = ret.b;
> long long c = a + b;
> if ((n & 1)==0) { // (m,m+1) => ((m+1)*2,(m+1)*2*2+1)
> ret.a = (a + c)*b;
> ret.b = b*b + c*c;
> } else { // (m,m+1) => (m*2+1,(m+1)*2)
> ret.a = a*a + b*b;
> ret.b = (a + c)*b;
> }
> return ret;
> }
>
> static long long fib(long n)
> {
> struct pair_t x = fib2(n-1);
> return x.b;
> }
I may have inadvertently misled you. Here is a simple linear
formulation that uses recursion:
typedef unsigned long long NN;
static NN fibonacci_3( NN, NN, unsigned );
NN
fibonacci( unsigned n ){
return fibonacci_3( 1, 0, n );
}
NN
fibonacci_3( NN a, NN b, unsigned n ){
return n == 0 ? b : fibonacci_3( b, a+b, n-1 );
}
Can you apply this idea to your logarithmic scheme?
> Iterative:
>
> static long long fib(long n)
> {
> if (n <= 0)
> return 0;
> // find MS bit
> unsigned long tmp = n;
> unsigned long bit = 1;
> while (tmp > 1) {
> bit += bit;
> tmp /= 2;
> }
> // for n > 0
> // fib(n*2) = (fib(n-1)+fib(n+1))*fib(n)
> // fib(n*2+1) = fib(n)*fib(n)+fib(n+1)*fib(n+1)
> long long a = 0, b = 1;
> while (bit > 1) {
> long long c = a + b; // fib(n+1)
> bit /= 2;
> if ((n & bit)==0) { // (n-1,n) => (n*2-1,n*2)
> c += a;
> a = a*a + b*b;
> b = c*b;
> } else { // (n-1,n) => (n*2,n*2+1)
> a = (a + c)*b;
> b = b*b + c*c;
> }
> }
> return b;
> }
>
>
> Both variants above are O(log(n)).
> In practice for n in range 0 to 92 my measurement gear does not detect
> differences in speed vs simple loop. If anything, simple loop is a
> little faster.
Yes, the log(n) can be beaten by simpler schemes for small n.
I wrote a (recursive) log(n) fibonacci in python. It was able
to compute fibonacci( 10000000 ) in just under 3 seconds.
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constexpr is really very smart! Student Project <student@invalid.invalid> - 2024-12-15 20:20 +0000
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-16 11:28 +0200
Re: constexpr is really very smart! David Brown <david.brown@hesbynett.no> - 2024-12-16 11:18 +0100
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-16 13:23 +0200
Re: constexpr is really very smart! David Brown <david.brown@hesbynett.no> - 2024-12-16 13:43 +0100
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-17 11:08 +0200
Re: constexpr is really very smart! David Brown <david.brown@hesbynett.no> - 2024-12-17 11:10 +0100
Re: constexpr is really very smart! Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-18 03:26 -0800
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-18 14:39 +0200
Re: constexpr is really very smart! Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-18 07:42 -0800
Re: constexpr is really very smart! Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-17 12:54 -0800
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-18 01:33 +0200
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-18 13:51 +0200
Re: constexpr is really very smart! Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-19 00:40 -0800
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-20 02:17 +0200
Re: constexpr is really very smart! Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-20 14:59 -0800
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-22 00:07 +0200
Re: constexpr is really very smart! Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-22 10:25 -0800
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-23 17:47 +0200
Re: constexpr is really very smart! Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-24 05:21 -0800
Bignum multiplication in Python vs GMP (was: constexpr is really very smart!) Michael S <already5chosen@yahoo.com> - 2024-12-25 11:05 +0200
Re: Bignum multiplication in Python vs GMP (was: constexpr is really very smart!) Michael S <already5chosen@yahoo.com> - 2024-12-25 13:33 +0200
Re: Bignum multiplication in Python vs GMP (was: constexpr is really very smart!) Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-26 18:54 -0800
Re: Bignum multiplication in Python vs GMP (was: constexpr is really very smart!) Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-26 18:42 -0800
Re: constexpr is really very smart! Student Project <student@invalid.invalid> - 2024-12-19 19:14 +0000
Re: constexpr is really very smart! Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-18 09:45 -0800
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-18 22:00 +0200
Re: constexpr is really very smart! Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-19 00:57 -0800
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-19 23:45 +0200
Re: constexpr is really very smart! Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-20 14:31 -0800
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-22 00:14 +0200
Re: constexpr is really very smart! James Kuyper <jameskuyper@alumni.caltech.edu> - 2024-12-21 17:55 -0500
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-22 02:22 +0200
Re: constexpr is really very smart! Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-22 10:33 -0800
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-23 00:05 +0200
Re: constexpr is really very smart! Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-12-22 17:17 -0800
Re: constexpr is really very smart! Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-12-17 12:20 -0800
Re: constexpr is really very smart! Student Project <student@invalid.invalid> - 2024-12-18 04:45 +0000
Re: constexpr is really very smart! Michael S <already5chosen@yahoo.com> - 2024-12-18 14:17 +0200
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