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| From | BGB <cr88192@hotmail.com> |
| Newsgroups | comp.lang.java.programmer |
| Subject | Re: higher precision doubles |
| Date | Tue, 09 Aug 2011 02:44:11 -0700 |
| Organization | albasani.net |
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On 8/8/2011 4:08 PM, Jan Burse wrote:
> BGB schrieb:
>> division is mostly calculating the reciprocal of the second value, and
>> multiplying the first by this (can be done using Newton's Method).
>
> I don't know exactly what you understand by
> this algorithm. But if I understand this as
> calculating the reciprocal first adn then
> multiplying, you will have as a result:
>
> o(x*o(1/y))
>
> Instead of
>
> o(x/y).
>
> you will usually get less accurate results
> since by the reciprocal-math option method
> two approximations will be involved.
>
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>
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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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