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Groups > comp.lang.c++ > #121248
| From | Michael S <already5chosen@yahoo.com> |
|---|---|
| Newsgroups | comp.lang.c++ |
| Subject | Re: constexpr is really very smart! |
| Date | 2024-12-18 13:51 +0200 |
| Organization | A noiseless patient Spider |
| Message-ID | <20241218135131.00000006@yahoo.com> (permalink) |
| References | <vjndub$2glcu$1@paganini.bofh.team> <20241216112808.00003f74@yahoo.com> <86jzbyghdw.fsf@linuxsc.com> <20241218013342.0000518a@yahoo.com> |
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;
}
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.
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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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