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Groups > comp.lang.java.programmer > #6923
| From | BGB <cr88192@hotmail.com> |
|---|---|
| Newsgroups | comp.lang.java.programmer |
| Subject | Re: higher precision doubles |
| Date | 2011-08-09 13:15 -0700 |
| Organization | albasani.net |
| Message-ID | <j1s4pj$c8c$1@news.albasani.net> (permalink) |
| References | (14 earlier) <j1o1sk$427$1@news.albasani.net> <j1pif0$lr4$1@news.albasani.net> <j1pq9c$6d0$1@news.albasani.net> <j1qvqa$mti$1@news.albasani.net> <j1r3h1$v0p$1@news.albasani.net> |
On 8/9/2011 3:52 AM, Jan Burse wrote:
> BGB schrieb:
>> yes, but try to find a good way to directly calculate x/y...
>> it is a much easier problem to calculate x*(1.0/y)...
>>
>>
>> Newton's Method is a reasonably good way to calculate 1.0/y, and in my
>> case (with 128-bit floats), usually manages to converge in approx 12
>> iterations.
>>
>>
>> here is some code from my own implementation (in C):
>>
>> fv128_t fv128_rcp(fv128_t a)
>> {
>> fv128_t f, g, xo, xn;
>> int i;
>>
>> if(fv128_eq1p(a))
>> return(a);
>>
>> i=fv128_getExponent(a);
>> xo=fv128_pow2x(fv128_const_one, -i);
>>
>> for(i=0; i<100; i++)
>> {
>> f=fv128_mul(a, xo);
>> g=fv128_sub(fv128_const_two, f);
>> xn=fv128_mul(xo, g);
>> if(fv128_eqp(xo, xn))
>> return(xn);
>> xo=xn;
>> }
>> return(xn);
>> }
>>
>> fv128_t fv128_div(fv128_t a, fv128_t b)
>> {
>> return(fv128_mul(a, fv128_rcp(b)));
>> }
>>
>>
>>
>> <snip>
>
> Yeah good old Newton.
>
> f(x) = a - 1/x.
> zero at: 1/a.
>
> f'(x) = 1 / x^2.
> x_n+1 = x_n - f(x_n)/f'(x_n)
> = x_n - (a - 1/x_n) / (1/x_n^2)
> = x_n - a * x_n^2 + x_n
> = x_n * (2 - a * x_n)
>
> But diverge or stays constant in certain intervals.
>
> Here for a=1.5:
>
> x_1=-2/3: Asymptotically reaches -inf
> x_1=-1/3: Asymptotically reaches -inf
> x_1=0: Stays constant at 0
> x_1=1/3: Converges to 2/3
> x_1=2/3: Converges to 2/3
> x_1=1: Converges to 2/3
> x_1=1 1/3: Stays constant at 0 after x_2
> x_1=1 2/3: Asymptotically reaches -inf
>
> And does eventually not converge very good:
>
> x_1=0.0001: Slowly recovers
> x_1=1 1/3 + 0.0001: Slowly recovers
>
> Hope your initial pick is good.
>
dunno...
quick test, and the posted code gives me 0.66666666...
tried with 1.0/(-1.5), and got +Inf, so this may be a bug (I think the
code is not well suited to negatives, so I may need to add a sign hack
or similar).
so, yeah, some of this is not ideally well tested...
the initial pick for 1.5 should be 0.5 or similar.
initial pick is:
2^(-(exp-bias))
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higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-06 00:20 +0200
Re: higher precision doubles Patricia Shanahan <pats@acm.org> - 2011-08-06 03:35 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-06 13:03 +0200
Re: higher precision doubles BGB <cr88192@hotmail.com> - 2011-08-06 12:20 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-06 23:30 +0200
Re: higher precision doubles BGB <cr88192@hotmail.com> - 2011-08-06 16:12 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-07 01:35 +0200
Re: higher precision doubles BGB <cr88192@hotmail.com> - 2011-08-06 19:26 -0700
Re: higher precision doubles supercalifragilisticexpialadiamaticonormalizeringelimatisticantations <supercalifragilisticexpialadiamaticonormalizeringelimatisticantations@averylongandannoyingdomainname.com> - 2011-08-09 00:42 -0400
Re: higher precision doubles Patricia Shanahan <pats@acm.org> - 2011-08-09 04:07 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-09 14:00 +0200
Re: higher precision doubles Patricia Shanahan <pats@acm.org> - 2011-08-09 09:07 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-10 08:50 +0200
Re: higher precision doubles supercalifragilisticexpialadiamaticonormalizeringelimatisticantations <supercalifragilisticexpialadiamaticonormalizeringelimatisticantations@averylongandannoyingdomainname.com> - 2011-08-10 20:16 -0400
Re: higher precision doubles Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-08-09 10:11 -0500
Re: higher precision doubles Arne Vajhøj <arne@vajhoej.dk> - 2011-08-09 22:40 -0400
Re: higher precision doubles Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-08-09 22:06 -0500
Re: higher precision doubles BGB <cr88192@hotmail.com> - 2011-08-10 08:53 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-06 21:24 +0200
Re: higher precision doubles markspace <-@.> - 2011-08-06 13:29 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-06 23:20 +0200
Re: higher precision doubles markspace <-@.> - 2011-08-06 15:43 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-07 01:06 +0200
Re: higher precision doubles Patricia Shanahan <pats@acm.org> - 2011-08-06 16:21 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-07 01:34 +0200
Re: higher precision doubles Patricia Shanahan <pats@acm.org> - 2011-08-06 21:32 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-07 17:24 +0200
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-07 17:39 +0200
Re: higher precision doubles Patricia Shanahan <pats@acm.org> - 2011-08-07 09:26 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-07 21:23 +0200
Re: higher precision doubles Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-08-07 20:48 -0400
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-08 09:05 +0200
Re: higher precision doubles Patricia Shanahan <pats@acm.org> - 2011-08-08 05:37 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-08 19:08 +0200
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-08 19:16 +0200
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-08 19:29 +0200
Re: higher precision doubles Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-08-08 21:34 -0500
Re: higher precision doubles BGB <cr88192@hotmail.com> - 2011-08-08 13:49 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-09 01:08 +0200
Re: higher precision doubles BGB <cr88192@hotmail.com> - 2011-08-09 02:44 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-09 12:52 +0200
Re: higher precision doubles BGB <cr88192@hotmail.com> - 2011-08-09 13:15 -0700
Re: higher precision doubles BGB <cr88192@hotmail.com> - 2011-08-07 13:51 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-07 01:59 +0200
Re: higher precision doubles Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-08-08 21:03 -0500
Re: higher precision doubles Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-08-06 17:33 -0400
Re: higher precision doubles Patricia Shanahan <pats@acm.org> - 2011-08-06 14:51 -0700
Re: higher precision doubles Jan Burse <janburse@fastmail.fm> - 2011-08-07 00:57 +0200
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