Rounding a floating point number

[jacob navia]

Hi

"How can I round a number to x decimal places" ?

This question keeps appearing. I would propose the following
solution

#include <float.h>
#include <math.h>

double roundto(double x, int digits)
{
int sgn=1;

if (x == 0)
return 0;
if (digits DBL_DIG)
digits = DBL_DIG;
else if (digits < 1)
digits = 1;

if(x < 0.0) {
sgn = -sgn;
x = -x;
}
double p = floorl(log10l(x ));
p--;
p = digits-p;
double pow10 = pow(10.0, p);
return sgn*floor(x*pow 10+0.5)/pow10;
}

long double roundtol(long double x, int digits)
{
int sgn=1;

if (x == 0)
return 0;
if (digits LDBL_DIG)
digits = LDBL_DIG;
else if (digits < 1)
digits = 1;

if(x < 0.0) {
sgn = -sgn;
x = -x;
}
long double p = floorl(log10l(x ));
p--;
p = digits-p;
long double pow10 = powl(10.0, p);
return sgn*floorl(x*po w10+0.5)/pow10;
}
#include <stdio.h>
int main(void)
{
double d = 1.7888889988996 678;
long double ld = 1.7888889988996 678998877L;

for (int i = 0; i<=DBL_DIG;i++ ) {
printf("i=%d: %.15g\n",i,roun dto(d,i));
}
printf("\n 1.7888889988996 678\n");
for (int i = 0; i<=LDBL_DIG;i++ ) {
printf("i=%d: %.18Lg\n",i,rou ndtol(ld,i));
}
printf("\n 1.7888889988996 678998877L\n");
return 0;
}

--------------------------------------------------------------------
I would propose it to add it to the FAQ.
--
jacob navia
jacob at jacob point remcomp point fr
logiciels/informatique
http://www.cs.virginia.edu/~lcc-win32

[user923005]

On Feb 25, 2:18*am, jacob navia <ja...@nospam.c omwrote:

Hi

"How can I round a number to x decimal places" ?

This question keeps appearing. I would propose the following
solution

#include <float.h>
#include <math.h>

double roundto(double x, int digits)
{
* * * * int sgn=1;

* * * * if (x == 0)
* * * * * * * * return 0;
* * * * if (digits DBL_DIG)
* * * * * * * * digits = DBL_DIG;
* * * * else if (digits < 1)
* * * * * * * * digits = 1;

* * * * if(x < 0.0) {
* * * * * * * * sgn = -sgn;
* * * * * * * * x = -x;
* * * * }
* * * * double p = floorl(log10l(x ));
* * * * p--;
* * * * p = digits-p;
* * * * double pow10 = pow(10.0, p);
* * * * return sgn*floor(x*pow 10+0.5)/pow10;

}

long double roundtol(long double x, int digits)
{
* * * * int sgn=1;

* * * * if (x == 0)
* * * * * * * * return 0;
* * * * if (digits LDBL_DIG)
* * * * * * * * digits = LDBL_DIG;
* * * * else if (digits < 1)
* * * * * * * * digits = 1;

* * * * if(x < 0.0) {
* * * * * * * * sgn = -sgn;
* * * * * * * * x = -x;
* * * * }
* * * * long double p = floorl(log10l(x ));
* * * * p--;
* * * * p = digits-p;
* * * * long double pow10 = powl(10.0, p);
* * * * return sgn*floorl(x*po w10+0.5)/pow10;}

#include <stdio.h>
int main(void)
{
* * * * double d = 1.7888889988996 678;
* * * * long double ld = 1.7888889988996 678998877L;

* * * * for (int i = 0; i<=DBL_DIG;i++ ) {
* * * * * * * * printf("i=%d: %.15g\n",i,roun dto(d,i));
* * * * }
* * * * printf("\n * * *1.788888998899 6678\n");
* * * * for (int i = 0; i<=LDBL_DIG;i++ ) {
* * * * * * * * printf("i=%d: %.18Lg\n",i,rou ndtol(ld,i));
* * * * }
* * * * printf("\n * * *1.788888998899 6678998877L\n") ;
* * * * return 0;

}

--------------------------------------------------------------------
I would propose it to add it to the FAQ.

The snippets solution, tweaked a little bit:

#include <math.h>
/* round number n to d decimal points */
long double roundl(const long double n, const unsigned d)
{
long double p = powl(10., d);
return floorl(n * p + .5) / p;
}

/* round number n to d decimal points */
double roundd(const double n, const unsigned d)
{
return (double) roundl((long double) n, d);
}

/* round number n to d decimal points */
double roundf(const float n, const unsigned d)
{
return (float) roundl((long double) n, d);
}
#ifdef UNIT_TEST
#include <stdio.h>
#include <stdlib.h>
#include <float.h>
int main(void)
{
long double pi = 3.1415926535897 932384626433832 795;
long double npi = -pi;
unsigned digits;
for (digits = 0; digits <= LDBL_DIG; digits++) {
printf("Roundin g by printf gives: %20.*f\n",
digits, pi);
printf("Roundin g approximation by function gives: %20.*f\n",
LDBL_DIG, roundl(pi, digits));
printf("Roundin g approximation by function gives: %20.*f\n",
DBL_DIG, roundd(pi, digits));
printf("Roundin g approximation by function gives: %20.*f\n\n",
FLT_DIG, roundf(pi, digits));
}
for (digits = 0; digits <= LDBL_DIG; digits++) {
printf("Roundin g by printf gives: %20.*f\n",
digits, npi);
printf("Roundin g approximation by function gives: %20.*f\n",
LDBL_DIG, roundl(npi, digits));
printf("Roundin g approximation by function gives: %20.*f\n",
DBL_DIG, roundd(npi, digits));
printf("Roundin g approximation by function gives: %20.*f\n\n",
FLT_DIG, roundf(npi, digits));
}
return 0;
}
#endif
/*
Rounding by printf gives: 3
Rounding approximation by function gives: 3.0000000000000 00
Rounding approximation by function gives: 3.0000000000000 00
Rounding approximation by function gives: 3.000000

Rounding by printf gives: 3.1
Rounding approximation by function gives: 3.1000000000000 00
Rounding approximation by function gives: 3.1000000000000 00
Rounding approximation by function gives: 3.100000

Rounding by printf gives: 3.14
Rounding approximation by function gives: 3.1400000000000 00
Rounding approximation by function gives: 3.1400000000000 00
Rounding approximation by function gives: 3.140000

Rounding by printf gives: 3.142
Rounding approximation by function gives: 3.1420000000000 00
Rounding approximation by function gives: 3.1420000000000 00
Rounding approximation by function gives: 3.142000

Rounding by printf gives: 3.1416
Rounding approximation by function gives: 3.1416000000000 00
Rounding approximation by function gives: 3.1416000000000 00
Rounding approximation by function gives: 3.141600

Rounding by printf gives: 3.14159
Rounding approximation by function gives: 3.1415900000000 00
Rounding approximation by function gives: 3.1415900000000 00
Rounding approximation by function gives: 3.141590

Rounding by printf gives: 3.141593
Rounding approximation by function gives: 3.1415930000000 00
Rounding approximation by function gives: 3.1415930000000 00
Rounding approximation by function gives: 3.141593

Rounding by printf gives: 3.1415927
Rounding approximation by function gives: 3.1415927000000 00
Rounding approximation by function gives: 3.1415927000000 00
Rounding approximation by function gives: 3.141593

Rounding by printf gives: 3.14159265
Rounding approximation by function gives: 3.1415926500000 00
Rounding approximation by function gives: 3.1415926500000 00
Rounding approximation by function gives: 3.141593

Rounding by printf gives: 3.141592654
Rounding approximation by function gives: 3.1415926540000 00
Rounding approximation by function gives: 3.1415926540000 00
Rounding approximation by function gives: 3.141593

Rounding by printf gives: 3.1415926536
Rounding approximation by function gives: 3.1415926536000 00
Rounding approximation by function gives: 3.1415926536000 00
Rounding approximation by function gives: 3.141593

Rounding by printf gives: 3.14159265359
Rounding approximation by function gives: 3.1415926535900 00
Rounding approximation by function gives: 3.1415926535900 00
Rounding approximation by function gives: 3.141593

Rounding by printf gives: 3.141592653590
Rounding approximation by function gives: 3.1415926535900 00
Rounding approximation by function gives: 3.1415926535900 00
Rounding approximation by function gives: 3.141593

Rounding by printf gives: 3.1415926535898
Rounding approximation by function gives: 3.1415926535898 00
Rounding approximation by function gives: 3.1415926535898 00
Rounding approximation by function gives: 3.141593

Rounding by printf gives: 3.1415926535897 9
Rounding approximation by function gives: 3.1415926535897 90
Rounding approximation by function gives: 3.1415926535897 90
Rounding approximation by function gives: 3.141593

Rounding by printf gives: 3.1415926535897 93
Rounding approximation by function gives: 3.1415926535897 93
Rounding approximation by function gives: 3.1415926535897 93
Rounding approximation by function gives: 3.141593

Rounding by printf gives: -3
Rounding approximation by function gives: -3.0000000000000 00
Rounding approximation by function gives: -3.0000000000000 00
Rounding approximation by function gives: -3.000000

Rounding by printf gives: -3.1
Rounding approximation by function gives: -3.1000000000000 00
Rounding approximation by function gives: -3.1000000000000 00
Rounding approximation by function gives: -3.100000

Rounding by printf gives: -3.14
Rounding approximation by function gives: -3.1400000000000 00
Rounding approximation by function gives: -3.1400000000000 00
Rounding approximation by function gives: -3.140000

Rounding by printf gives: -3.142
Rounding approximation by function gives: -3.1420000000000 00
Rounding approximation by function gives: -3.1420000000000 00
Rounding approximation by function gives: -3.142000

Rounding by printf gives: -3.1416
Rounding approximation by function gives: -3.1416000000000 00
Rounding approximation by function gives: -3.1416000000000 00
Rounding approximation by function gives: -3.141600

Rounding by printf gives: -3.14159
Rounding approximation by function gives: -3.1415900000000 00
Rounding approximation by function gives: -3.1415900000000 00
Rounding approximation by function gives: -3.141590

Rounding by printf gives: -3.141593
Rounding approximation by function gives: -3.1415930000000 00
Rounding approximation by function gives: -3.1415930000000 00
Rounding approximation by function gives: -3.141593

Rounding by printf gives: -3.1415927
Rounding approximation by function gives: -3.1415927000000 00
Rounding approximation by function gives: -3.1415927000000 00
Rounding approximation by function gives: -3.141593

Rounding by printf gives: -3.14159265
Rounding approximation by function gives: -3.1415926500000 00
Rounding approximation by function gives: -3.1415926500000 00
Rounding approximation by function gives: -3.141593

Rounding by printf gives: -3.141592654
Rounding approximation by function gives: -3.1415926540000 00
Rounding approximation by function gives: -3.1415926540000 00
Rounding approximation by function gives: -3.141593

Rounding by printf gives: -3.1415926536
Rounding approximation by function gives: -3.1415926536000 00
Rounding approximation by function gives: -3.1415926536000 00
Rounding approximation by function gives: -3.141593

Rounding by printf gives: -3.14159265359
Rounding approximation by function gives: -3.1415926535900 00
Rounding approximation by function gives: -3.1415926535900 00
Rounding approximation by function gives: -3.141593

Rounding by printf gives: -3.141592653590
Rounding approximation by function gives: -3.1415926535900 00
Rounding approximation by function gives: -3.1415926535900 00
Rounding approximation by function gives: -3.141593

Rounding by printf gives: -3.1415926535898
Rounding approximation by function gives: -3.1415926535898 00
Rounding approximation by function gives: -3.1415926535898 00
Rounding approximation by function gives: -3.141593

Rounding by printf gives: -3.1415926535897 9
Rounding approximation by function gives: -3.1415926535897 90
Rounding approximation by function gives: -3.1415926535897 90
Rounding approximation by function gives: -3.141593

Rounding by printf gives: -3.1415926535897 93
Rounding approximation by function gives: -3.1415926535897 93
Rounding approximation by function gives: -3.1415926535897 93
Rounding approximation by function gives: -3.141593
*/

[CBFalconer]

jacob navia wrote:

>
"How can I round a number to x decimal places" ?

This question keeps appearing. I would propose the following

.... snip 75 or so lines ...

Why all this gyration? I found the following in the c standard:

7.12.9.6 The round functions
Synopsis
[#1]
#include <math.h>
double round(double x);
float roundf(float x);
long double roundl(long double x);

Description

[#2] The round functions round their argument to the nearest
integer value in floating-point format, rounding halfway
cases away from zero, regardless of the current rounding
direction.

Returns

[#3] The round functions return the rounded integer value.

--
[mail]: Chuck F (cbfalconer at maineline dot net)
[page]: <http://cbfalconer.home .att.net>
Try the download section.

--
Posted via a free Usenet account from http://www.teranews.com

[Ben Pfaff]

CBFalconer <cb********@yah oo.comwrites:

jacob navia wrote:

>>
"How can I round a number to x decimal places" ?

This question keeps appearing. I would propose the following

... snip 75 or so lines ...

Why all this gyration? I found the following in the c standard:

7.12.9.6 The round functions

Those functions are new in C99.
--
char a[]="\n .CJacehknorstu" ;int putchar(int);in t main(void){unsi gned long b[]
={0x67dffdff,0x 9aa9aa6a,0xa77f fda9,0x7da6aa6a ,0xa67f6aaa,0xa a9aa9f6,0x11f6} ,*p
=b,i=24;for(;p+ =!*p;*p/=4)switch(0[p]&3)case 0:{return 0;for(p--;i--;i--)case+
2:{i++;if(i)bre ak;else default:continu e;if(0)case 1:putchar(a[i&15]);break;}}}

[user923005]

On Feb 25, 4:29*pm, Ben Pfaff <[e-mail] rd.eduwrote:

CBFalconer <cbfalco...@yah oo.comwrites:

jacob navia wrote:

"How can I round a number to x decimal places" ?

This question keeps appearing. I would propose the following

... snip 75 or so lines ...

Why all this gyration? *I found the following in the c standard:

* 7.12.9.6 *The round functions

Those functions are new in C99.

And they don't round to x decimal places, unless x happens to be
zero. (Admittedly, you could manually scale it.)

[Keith Thompson]

Ben Pfaff <bl*@cs.stanfor d.eduwrites:

CBFalconer <cb********@yah oo.comwrites:

>jacob navia wrote:

>>"How can I round a number to x decimal places" ?

This question keeps appearing. I would propose the following

... snip 75 or so lines ...

Why all this gyration? I found the following in the c standard:

7.12.9.6 The round functions

Those functions are new in C99.

So are floorl and log10l, which jacob's code uses; it also mixes
declarations and statements within a block. An implementation that
can handle jacob's code should provide the round functions.

--
Keith Thompson (The_Other_Keit h) <ks***@mib.or g>
Nokia
"We must do something. This is something. Therefore, we must do this."
-- Antony Jay and Jonathan Lynn, "Yes Minister"

[user923005]

On Feb 25, 10:15*pm, Keith Thompson <[e-mail] rote:

Ben Pfaff <[e-mail] rd.eduwrites:

CBFalconer <cbfalco...@yah oo.comwrites:

jacob navia wrote:
"How can I round a number to x decimal places" ?

>This question keeps appearing. I would propose the following

... snip 75 or so lines ...

Why all this gyration? *I found the following in the c standard:

* 7.12.9.6 *The round functions

Those functions are new in C99.

So are floorl and log10l, which jacob's code uses; it also mixes
declarations and statements within a block. *An implementation that
can handle jacob's code should provide the round functions.

You will still have to multiply and divide by powers of 10 and use
floor() to achieve the same thing because the C99 round() functions
round to nearest integer. They do not round to nearest k decimal
places.

[CBFalconer]

user923005 wrote:

>

.... snip float rounding discussion ...

>
You will still have to multiply and divide by powers of 10 and use
floor() to achieve the same thing because the C99 round() functions
round to nearest integer. They do not round to nearest k decimal
places.

Are you claiming that such multiplication and division by 10 is too
complex for the average reader of c.l.c? :-)

--
[mail]: Chuck F (cbfalconer at maineline dot net)
[page]: <http://cbfalconer.home .att.net>
Try the download section.

--
Posted via a free Usenet account from http://www.teranews.com

[user923005]

On Feb 26, 2:24*pm, CBFalconer <cbfalco...@yah oo.comwrote:

user923005 wrote:

... snip float rounding discussion ...

You will still have to multiply and divide by powers of 10 and use
floor() to achieve the same thing because the C99 round() functions
round to nearest integer. *They do not round to nearest k decimal
places.

Are you claiming that such multiplication and division by 10 is too
complex for the average reader of c.l.c? *:-)

No, but I am claiming that using the C99 functions to round to N
digits will take twice as much work as a function that does it
directly, since the multiplication and division by a power of ten and
the floor function are all that is necessary in either case. And so
while you can round to N digits using the C99 rounding functions, it
really does not make a lot of sense to do it that way.

[CBFalconer]

user923005 wrote:

CBFalconer <cbfalco...@yah oo.comwrote:

>user923005 wrote:

... snip float rounding discussion ...

>>You will still have to multiply and divide by powers of 10 and
use floor() to achieve the same thing because the C99 round()
functions round to nearest integer. They do not round to
nearest k decimal places.

Are you claiming that such multiplication and division by 10 is
too complex for the average reader of c.l.c? :-)

No, but I am claiming that using the C99 functions to round to N
digits will take twice as much work as a function that does it
directly, since the multiplication and division by a power of
ten and the floor function are all that is necessary in either
case. And so while you can round to N digits using the C99
rounding functions, it really does not make a lot of sense to do
it that way.

Let me also point out that such rounding is rarely needed. Most of
the time maintaining the original alleged precision and rounding
only the output, via printf, is needed.

--
[mail]: Chuck F (cbfalconer at maineline dot net)
[page]: <http://cbfalconer.home .att.net>
Try the download section.

--
Posted via a free Usenet account from http://www.teranews.com

[user923005]

On Feb 27, 8:10*am, CBFalconer <cbfalco...@yah oo.comwrote:

user923005 wrote:

CBFalconer <cbfalco...@yah oo.comwrote:

user923005 wrote:

... snip float rounding discussion ...

>You will still have to multiply and divide by powers of 10 and
use floor() to achieve the same thing because the C99 round()
functions round to nearest integer. *They do not round to
nearest k decimal places.

Are you claiming that such multiplication and division by 10 is
too complex for the average reader of c.l.c? *:-)

No, but I am claiming that using the C99 functions to round to N
digits will take twice as much work as a function that does it
directly, since the multiplication and division by a power of
ten and the floor function are all that is necessary in either
case. *And so while you can round to N digits using the C99
rounding functions, it really does not make a lot of sense to do
it that way.

Let me also point out that such rounding is rarely needed. *Most of
the time maintaining the original alleged precision and rounding
only the output, via printf, is needed.

I would go one step further:
It's better than rounding the original data.
But sometimes people want to do it anyway.