Sqrt precision ?!

[Marcin]

Hello!

How I can make SQRT(2) with 20 digits precision (after float point)?

[Michael Mair]

Marcin wrote:

Hello!

How I can make SQRT(2) with 20 digits precision (after float point)?

You probably mean sqrt(2.0) or sqrtl(2.0L); if DBL_DIG or LDBL_DIG is
smaller than 21 (1.[20Digits] makes 21 digits), you can either look
for a large floating point implementation, write one yourself or
store the value in a string.
#include <math.h>
#include <float.h>
#include <stdio.h>

int main (void)
{
long double r;

r = sqrtl(2.0L);
printf("Precision: %d digits; %.*Lg\n",LDBL_DIG,LDBL_DIG,r);

return 0;
}

I am not sure whether C89 standard libraries provide sqrtl()
(in this case, you would have to go for double r, sqrt(2.0), %.*g and
DBL_DIG).

Cheers
Michael
--
E-Mail: Mine is a gmx dot de address.

[Gregory Toomey]

Marcin wrote:

Hello!

How I can make SQRT(2) with 20 digits precision (after float point)?

Newtons algorithm with double precision floating point, if the inbuilt one
is insufficient.

gtoomey

[Michael Mair]

Gregory Toomey wrote:

Marcin wrote:

Hello!

How I can make SQRT(2) with 20 digits precision (after float point)?

Newtons algorithm with double precision floating point, if the inbuilt one
is insufficient.

The problem is that the OP wants 21 (decimal) digits precision which
implies that we need 70 binary digits precision.
This in turn means that you average system's double will not suffice.
If you are lucky, long double will do. Otherwise, you will have to
use either non-standard stuff or make your own floating point data type.
Cheers
Michael
--
E-Mail: Mine is a gmx dot de address.

[pete]

Marcin wrote:

Hello!

How I can make SQRT(2) with 20 digits precision (after float point)?

/* sq_rtl will get you all of the pecision of type long double. */

#include <errno.h>
#include <math.h>

long double sq_rtl(long double x);

long double sq_rtl(long double x)
{
long n;
long double a, b;

if (x > 0) {
for (n = 0; x > 2; x /= 4) {
++n;
}
while (0.5 > x) {
--n;
x *= 4;
}
a = x;
b = (1 + x) / 2;
do {
x = b;
b = (a / x + x) / 2;
} while (x > b);
while (n > 0) {
x *= 2;
--n;
}
while (0 > n) {
x /= 2;
++n;
}
} else {
if (0 > x) {
errno = EDOM;
x = -HUGE_VAL;
}
}
return x;
}

/* This wasn't a question about how to use printf, was it? */

--
pete

[jacob navia]

Marcin wrote:

Hello!

How I can make SQRT(2) with 20 digits precision (after float point)?

Lcc-win32 offers a higher precision floating point
(100 digits precision)

Using that you can write:

#include <stdio.h>
#include <qfloat.h>
int main(void)
{
qfloat q = 2;
qfloat r = sqrt(q);
printf("%80.70qf\n",r);
}

Result:

1.414213562373095048801688724209698078569671875376 9480731766797379907325

http://www.cs.virginia.edu/~lcc-win32

[Chris Croughton]

On 27 Jan 2005 01:55:11 -0800, Marcin
<mj***@pf.pl> wrote:

How I can make SQRT(2) with 20 digits precision (after float point)?

If your platform doesn't allow 21 digits of precision (x86 long double
is only 19 digits) then you will have to do it either with implementing
your own "big number" routines or use a large precision library like
gmp.

<OT>
When I was at school we had mechanical adding machines which were
cranked with a handle, with 10 digits plus overflow on each. We once
calculated sqrt(2) to 100 places, using 10 machines and doing the
'carry' manually from one to the next, it took us around 10 weeks of
lunch breaks. We called that 'fun'...

But it did teach me the techniques for doing large precision arithmetic
using smaller registers, which has been valuable since. Do they still
even teach "long division" in schools?
</OT>

Chris C

[gooch]

But it did teach me the techniques for doing large precision arithmetic using smaller registers, which has been valuable since. Do they still even teach "long division" in schools?

Surre they show the kids how to push the correct button on the
calculator.

[CBFalconer]

jacob navia wrote:

Marcin wrote:

How I can make SQRT(2) with 20 digits precision (after float point)?

Lcc-win32 offers a higher precision floating point
(100 digits precision)

Using that you can write:

#include <stdio.h>
#include <qfloat.h>
int main(void)
{
qfloat q = 2;
qfloat r = sqrt(q);
printf("%80.70qf\n",r);
}

Result:

1.414213562373095048801688724209698078569671875376 9480731766797379907325

.....1.4142135623730950488016887242096980785696718 75376948073176679737990732478462107038850387534327 6415727

Result from bc. Seems to agree.

--
"If you want to post a followup via groups.google.com, don't use
the broken "Reply" link at the bottom of the article. Click on
"show options" at the top of the article, then click on the
"Reply" at the bottom of the article headers." - Keith Thompson

[CBFalconer]

Chris Croughton wrote:

.... snip ...
But it did teach me the techniques for doing large precision
arithmetic using smaller registers, which has been valuable since.
Do they still even teach "long division" in schools?

I wonder if they teach addition. I can wow most of the present
generation by simply adding a column of numbers. Meanwhile they
are making entry errors on a 4 function calculator.

--
"If you want to post a followup via groups.google.com, don't use
the broken "Reply" link at the bottom of the article. Click on
"show options" at the top of the article, then click on the
"Reply" at the bottom of the article headers." - Keith Thompson

[Martin Ambuhl]

Marcin wrote:

Hello!

How I can make SQRT(2) with 20 digits precision (after float point)?

By using an implementation for which DBL_DIG >= 21 or by using one of
the freely availble extended precision libraries. Learn to use a search
engine.

[jacob navia]

CBFalconer wrote:

jacob navia wrote:

Marcin wrote:

How I can make SQRT(2) with 20 digits precision (after float point)?

Lcc-win32 offers a higher precision floating point
(100 digits precision)

Using that you can write:

#include <stdio.h>
#include <qfloat.h>
int main(void)
{
qfloat q = 2;
qfloat r = sqrt(q);
printf("%80.70qf\n",r);
}

Result:

1.414213562373095048801688724209698078569671875376 9480731766797379907325

....1.41421356237309504880168872420969807856967187 53769480731766797379907324784621070388503875343276 415727

Result from bc. Seems to agree.

And is correctly rounded, as bc confirms.

I had some problems with rounding that I corrected some weeks ago.

This is one of the "standard extensions" that the
standard proposes.