catan errors

catan errors

[Rich Felker]

[-- Attachment #1: Type: text/plain, Size: 994 bytes --]

The OpenBSD catan implementation we're using has a number of
nonsensical "overflow" (goto ovrf) conditions that aren't errors,
reported by mepholic on irc. I think the attached patch fixes them
without introducing new problems, but I'm not sure if any other
problems remain.

Note that, of the three cases removed:

1. Is not an exceptional case at all, and made no sense to begin with.

2. Is only exceptional if x and a are both zero; atan(2x,0) is
   perfectly well-defined.

3. Is only possible if y==1.0 and x==0.0, which is the only real
   exceptional case for atan: z==I.

I opted to replace the non-obvious (3) with an explicit check for z==I
but this isn't necessary.

As written the patch does not address raising exception flags; that
should be fixed before it's committed but right now I'm just
submitting this for comments.

Prior to the patch, at least the following (utterly dumb -- the first
is a very real input!) cases are broken:

- catan(1.0)
- catan(2*I)
- catan(I)

Rich

[-- Attachment #2: catan.diff --]
[-- Type: text/plain, Size: 687 bytes --]

diff --git a/src/complex/catan.c b/src/complex/catan.c
index 39ce6cf..9c2fccf 100644
--- a/src/complex/catan.c
+++ b/src/complex/catan.c
@@ -91,21 +91,17 @@ double complex catan(double complex z)
 	x = creal(z);
 	y = cimag(z);
 
-	if (x == 0.0 && y > 1.0)
+	if (x == 0.0 && y == 1.0)
 		goto ovrf;
 
 	x2 = x * x;
 	a = 1.0 - x2 - (y * y);
-	if (a == 0.0)
-		goto ovrf;
 
 	t = 0.5 * atan2(2.0 * x, a);
 	w = _redupi(t);
 
 	t = y - 1.0;
 	a = x2 + (t * t);
-	if (a == 0.0)
-		goto ovrf;
 
 	t = y + 1.0;
 	a = (x2 + t * t)/a;
@@ -113,7 +109,6 @@ double complex catan(double complex z)
 	return w;
 
 ovrf:
-	// FIXME
-	w = MAXNUM + MAXNUM * I;
+	w = CMPLX(0, INFINITY);
 	return w;
 }

Re: catan errors

[dgutson .]

[-- Attachment #1: Type: text/plain, Size: 1714 bytes --]

On Tue, Apr 10, 2018 at 4:50 PM, Rich Felker <dalias@libc.org> wrote:

> The OpenBSD catan implementation we're using has a number of
> nonsensical "overflow" (goto ovrf) conditions that aren't errors,
> reported by mepholic on irc. I think the attached patch fixes them
> without introducing new problems, but I'm not sure if any other
> problems remain.
>
> Note that, of the three cases removed:
>
> 1. Is not an exceptional case at all, and made no sense to begin with.
>
> 2. Is only exceptional if x and a are both zero; atan(2x,0) is
>    perfectly well-defined.
>
> 3. Is only possible if y==1.0 and x==0.0, which is the only real
>    exceptional case for atan: z==I.
>


Besides the trigonometric case, are you considering de-normalized numbers,
such as 4.94066e-324 as divisor?
For example:
    double x = 1.0;
    double y = 5E-324;
x / y is inf, and y != 0.0.
Shouldn't 'a' be checked against that number or its absolute value >=
minimum?


>
> I opted to replace the non-obvious (3) with an explicit check for z==I
> but this isn't necessary.
>
> As written the patch does not address raising exception flags; that
> should be fixed before it's committed but right now I'm just
> submitting this for comments.
>
> Prior to the patch, at least the following (utterly dumb -- the first
> is a very real input!) cases are broken:
>
> - catan(1.0)
> - catan(2*I)
> - catan(I)
>
> Rich
>



-- 
Who’s got the sweetest disposition?
One guess, that’s who?
Who’d never, ever start an argument?
Who never shows a bit of temperament?
Who's never wrong but always right?
Who'd never dream of starting a fight?
Who get stuck with all the bad luck?

[-- Attachment #2: Type: text/html, Size: 2528 bytes --]

Re: catan errors

[Rich Felker]

On Tue, Apr 10, 2018 at 05:23:12PM -0300, dgutson . wrote:
> On Tue, Apr 10, 2018 at 4:50 PM, Rich Felker <dalias@libc.org> wrote:
> 
> > The OpenBSD catan implementation we're using has a number of
> > nonsensical "overflow" (goto ovrf) conditions that aren't errors,
> > reported by mepholic on irc. I think the attached patch fixes them
> > without introducing new problems, but I'm not sure if any other
> > problems remain.
> >
> > Note that, of the three cases removed:
> >
> > 1. Is not an exceptional case at all, and made no sense to begin with.
> >
> > 2. Is only exceptional if x and a are both zero; atan(2x,0) is
> >    perfectly well-defined.
> >
> > 3. Is only possible if y==1.0 and x==0.0, which is the only real
> >    exceptional case for atan: z==I.
> >
> 
> 
> Besides the trigonometric case, are you considering de-normalized numbers,
> such as 4.94066e-324 as divisor?
> For example:
>     double x = 1.0;
>     double y = 5E-324;
> x / y is inf, and y != 0.0.
> Shouldn't 'a' be checked against that number or its absolute value >=
> minimum?

Can you clarify where you think something goes wrong?

Rich

Re: catan errors

[dgutson .]

[-- Attachment #1: Type: text/plain, Size: 1902 bytes --]

On Tue, Apr 10, 2018 at 5:32 PM, Rich Felker <dalias@libc.org> wrote:

> On Tue, Apr 10, 2018 at 05:23:12PM -0300, dgutson . wrote:
> > On Tue, Apr 10, 2018 at 4:50 PM, Rich Felker <dalias@libc.org> wrote:
> >
> > > The OpenBSD catan implementation we're using has a number of
> > > nonsensical "overflow" (goto ovrf) conditions that aren't errors,
> > > reported by mepholic on irc. I think the attached patch fixes them
> > > without introducing new problems, but I'm not sure if any other
> > > problems remain.
> > >
> > > Note that, of the three cases removed:
> > >
> > > 1. Is not an exceptional case at all, and made no sense to begin with.
> > >
> > > 2. Is only exceptional if x and a are both zero; atan(2x,0) is
> > >    perfectly well-defined.
> > >
> > > 3. Is only possible if y==1.0 and x==0.0, which is the only real
> > >    exceptional case for atan: z==I.
> > >
> >
> >
> > Besides the trigonometric case, are you considering de-normalized
> numbers,
> > such as 4.94066e-324 as divisor?
> > For example:
> >     double x = 1.0;
> >     double y = 5E-324;
> > x / y is inf, and y != 0.0.
> > Shouldn't 'a' be checked against that number or its absolute value >=
> > minimum?
>
> Can you clarify where you think something goes wrong?
>

-	if (a == 0.0)
-		goto ovrf;

 	t = y + 1.0;
 	a = (x2 + t * t)/a;


The check you removed does not look correct for me because what I mentioned.
However, shouldn't you check, before the division, that a is not the
nearest to zero (+ or -) denormalized representable double,
in order to avoid ending in inf?



>
> Rich
>



-- 
Who’s got the sweetest disposition?
One guess, that’s who?
Who’d never, ever start an argument?
Who never shows a bit of temperament?
Who's never wrong but always right?
Who'd never dream of starting a fight?
Who get stuck with all the bad luck?

[-- Attachment #2: Type: text/html, Size: 3354 bytes --]

Re: catan errors

[Rich Felker]

On Tue, Apr 10, 2018 at 05:41:46PM -0300, dgutson . wrote:
> On Tue, Apr 10, 2018 at 5:32 PM, Rich Felker <dalias@libc.org> wrote:
> 
> > On Tue, Apr 10, 2018 at 05:23:12PM -0300, dgutson . wrote:
> > > On Tue, Apr 10, 2018 at 4:50 PM, Rich Felker <dalias@libc.org> wrote:
> > >
> > > > The OpenBSD catan implementation we're using has a number of
> > > > nonsensical "overflow" (goto ovrf) conditions that aren't errors,
> > > > reported by mepholic on irc. I think the attached patch fixes them
> > > > without introducing new problems, but I'm not sure if any other
> > > > problems remain.
> > > >
> > > > Note that, of the three cases removed:
> > > >
> > > > 1. Is not an exceptional case at all, and made no sense to begin with..
> > > >
> > > > 2. Is only exceptional if x and a are both zero; atan(2x,0) is
> > > >    perfectly well-defined.
> > > >
> > > > 3. Is only possible if y==1.0 and x==0.0, which is the only real
> > > >    exceptional case for atan: z==I.
> > > >
> > >
> > >
> > > Besides the trigonometric case, are you considering de-normalized
> > numbers,
> > > such as 4.94066e-324 as divisor?
> > > For example:
> > >     double x = 1.0;
> > >     double y = 5E-324;
> > > x / y is inf, and y != 0.0.
> > > Shouldn't 'a' be checked against that number or its absolute value >=
> > > minimum?
> >
> > Can you clarify where you think something goes wrong?
> >
> 
> -	if (a == 0.0)
> -		goto ovrf;
> 
>  	t = y + 1.0;
>  	a = (x2 + t * t)/a;
> 
> 
> The check you removed does not look correct for me because what I mentioned..
> However, shouldn't you check, before the division, that a is not the
> nearest to zero (+ or -) denormalized representable double,
> in order to avoid ending in inf?

Here a=x²+(y-1)², so unless both x==0 and y==1, the smallest a can be
is DBL_EPSILON². When a is small, the numerator in the last line is
also small (x²+(1+y)² < 2) so dividing by a does not overflow.

Rich

Re: catan errors

[dgutson .]

[-- Attachment #1: Type: text/plain, Size: 2877 bytes --]

On Tue, Apr 10, 2018 at 5:50 PM, Rich Felker <dalias@libc.org> wrote:

> On Tue, Apr 10, 2018 at 05:41:46PM -0300, dgutson . wrote:
> > On Tue, Apr 10, 2018 at 5:32 PM, Rich Felker <dalias@libc.org> wrote:
> >
> > > On Tue, Apr 10, 2018 at 05:23:12PM -0300, dgutson . wrote:
> > > > On Tue, Apr 10, 2018 at 4:50 PM, Rich Felker <dalias@libc.org>
> wrote:
> > > >
> > > > > The OpenBSD catan implementation we're using has a number of
> > > > > nonsensical "overflow" (goto ovrf) conditions that aren't errors,
> > > > > reported by mepholic on irc. I think the attached patch fixes them
> > > > > without introducing new problems, but I'm not sure if any other
> > > > > problems remain.
> > > > >
> > > > > Note that, of the three cases removed:
> > > > >
> > > > > 1. Is not an exceptional case at all, and made no sense to begin
> with..
> > > > >
> > > > > 2. Is only exceptional if x and a are both zero; atan(2x,0) is
> > > > >    perfectly well-defined.
> > > > >
> > > > > 3. Is only possible if y==1.0 and x==0.0, which is the only real
> > > > >    exceptional case for atan: z==I.
> > > > >
> > > >
> > > >
> > > > Besides the trigonometric case, are you considering de-normalized
> > > numbers,
> > > > such as 4.94066e-324 as divisor?
> > > > For example:
> > > >     double x = 1.0;
> > > >     double y = 5E-324;
> > > > x / y is inf, and y != 0.0.
> > > > Shouldn't 'a' be checked against that number or its absolute value >=
> > > > minimum?
> > >
> > > Can you clarify where you think something goes wrong?
> > >
> >
> > -     if (a == 0.0)
> > -             goto ovrf;
> >
> >       t = y + 1.0;
> >       a = (x2 + t * t)/a;
> >
> >
> > The check you removed does not look correct for me because what I
> mentioned..
> > However, shouldn't you check, before the division, that a is not the
> > nearest to zero (+ or -) denormalized representable double,
> > in order to avoid ending in inf?
>
> Here a=x²+(y-1)², so unless both x==0 and y==1, the smallest a can be
>

I was worried by the case when x is 0 and y is the next (or previous)
representable value nearest to 1.0; the y == 1.0 check will fail, but the
division may get big; so I did a small program and verified that the result
of the division is about 3.24519e+32 when going towards negative and
8.11296e+31 when going towards positive, so everything is OK (I didn't dig
in the atan2 arguments though).


> is DBL_EPSILON². When a is small, the numerator in the last line is
> also small (x²+(1+y)² < 2) so dividing by a does not overflow.
>
> Rich
>



-- 
Who’s got the sweetest disposition?
One guess, that’s who?
Who’d never, ever start an argument?
Who never shows a bit of temperament?
Who's never wrong but always right?
Who'd never dream of starting a fight?
Who get stuck with all the bad luck?

[-- Attachment #2: Type: text/html, Size: 4214 bytes --]

Re: catan errors

[Rich Felker]

On Tue, Apr 10, 2018 at 06:27:24PM -0300, dgutson . wrote:
> On Tue, Apr 10, 2018 at 5:50 PM, Rich Felker <dalias@libc.org> wrote:
> 
> > On Tue, Apr 10, 2018 at 05:41:46PM -0300, dgutson . wrote:
> > > On Tue, Apr 10, 2018 at 5:32 PM, Rich Felker <dalias@libc.org> wrote:
> > >
> > > > On Tue, Apr 10, 2018 at 05:23:12PM -0300, dgutson . wrote:
> > > > > On Tue, Apr 10, 2018 at 4:50 PM, Rich Felker <dalias@libc.org>
> > wrote:
> > > > >
> > > > > > The OpenBSD catan implementation we're using has a number of
> > > > > > nonsensical "overflow" (goto ovrf) conditions that aren't errors,
> > > > > > reported by mepholic on irc. I think the attached patch fixes them
> > > > > > without introducing new problems, but I'm not sure if any other
> > > > > > problems remain.
> > > > > >
> > > > > > Note that, of the three cases removed:
> > > > > >
> > > > > > 1. Is not an exceptional case at all, and made no sense to begin
> > with..
> > > > > >
> > > > > > 2. Is only exceptional if x and a are both zero; atan(2x,0) is
> > > > > >    perfectly well-defined.
> > > > > >
> > > > > > 3. Is only possible if y==1.0 and x==0.0, which is the only real
> > > > > >    exceptional case for atan: z==I.
> > > > > >
> > > > >
> > > > >
> > > > > Besides the trigonometric case, are you considering de-normalized
> > > > numbers,
> > > > > such as 4.94066e-324 as divisor?
> > > > > For example:
> > > > >     double x = 1.0;
> > > > >     double y = 5E-324;
> > > > > x / y is inf, and y != 0.0.
> > > > > Shouldn't 'a' be checked against that number or its absolute value >=
> > > > > minimum?
> > > >
> > > > Can you clarify where you think something goes wrong?
> > > >
> > >
> > > -     if (a == 0.0)
> > > -             goto ovrf;
> > >
> > >       t = y + 1.0;
> > >       a = (x2 + t * t)/a;
> > >
> > >
> > > The check you removed does not look correct for me because what I
> > mentioned..
> > > However, shouldn't you check, before the division, that a is not the
> > > nearest to zero (+ or -) denormalized representable double,
> > > in order to avoid ending in inf?
> >
> > Here a=x²+(y-1)², so unless both x==0 and y==1, the smallest a can be
> >
> 
> I was worried by the case when x is 0 and y is the next (or previous)
> representable value nearest to 1.0; the y == 1.0 check will fail, but the
> division may get big; so I did a small program and verified that the result
> of the division is about 3.24519e+32 when going towards negative and
> 8.11296e+31 when going towards positive, so everything is OK (I didn't dig
> in the atan2 arguments though).

That's basically what I said here, without working out any actual
numbers:

> > is DBL_EPSILON². When a is small, the numerator in the last line is
> > also small (x²+(1+y)² < 2) so dividing by a does not overflow.

The result of a subtraction cannot be smaller than the order of
DBL_EPSILON times the larger-magnitude operand. In particular numbers
like (y-1) are never small in any absolute sense.

Rich

Re: catan errors

[Szabolcs Nagy]

* Rich Felker <dalias@libc.org> [2018-04-10 15:50:07 -0400]:
> 
> 3. Is only possible if y==1.0 and x==0.0, which is the only real
>    exceptional case for atan: z==I.
> 
> I opted to replace the non-obvious (3) with an explicit check for z==I
> but this isn't necessary.
> 
...
>  	t = y - 1.0;
>  	a = x2 + (t * t);
> -	if (a == 0.0)
> -		goto ovrf;

why does a==0 imply x==0?

if |x| < sqrt(2)*0x1p-538, x2 underflows to 0 in nearest rounding mode.

to handle this correctly extra work would need to be done, so i think
either way is fine (leaving the goto there or not are both wrong, but
we dont guarantee correct complex functions yet)

Re: catan errors

[Rich Felker]

[-- Attachment #1: Type: text/plain, Size: 1035 bytes --]

On Wed, Apr 11, 2018 at 01:08:50AM +0200, Szabolcs Nagy wrote:
> * Rich Felker <dalias@libc.org> [2018-04-10 15:50:07 -0400]:
> > 
> > 3. Is only possible if y==1.0 and x==0.0, which is the only real
> >    exceptional case for atan: z==I.
> > 
> > I opted to replace the non-obvious (3) with an explicit check for z==I
> > but this isn't necessary.
> > 
> ....
> >  	t = y - 1.0;
> >  	a = x2 + (t * t);
> > -	if (a == 0.0)
> > -		goto ovrf;
> 
> why does a==0 imply x==0?

OK, at least by my reasoning it's only algebraically true not
necessarily as doubles.

> if |x| < sqrt(2)*0x1p-538, x2 underflows to 0 in nearest rounding mode.
> 
> to handle this correctly extra work would need to be done, so i think
> either way is fine (leaving the goto there or not are both wrong, but
> we dont guarantee correct complex functions yet)

I'm fine with just moving the check back here. But the special case
(maybe not near-special cases with internal over/underflow though)
works fine just replacing the *I with CMPLX. See attached.

Rich

[-- Attachment #2: catan2.diff --]
[-- Type: text/plain, Size: 636 bytes --]

diff --git a/src/complex/catan.c b/src/complex/catan.c
index 39ce6cf..7dc2afe 100644
--- a/src/complex/catan.c
+++ b/src/complex/catan.c
@@ -91,29 +91,17 @@ double complex catan(double complex z)
 	x = creal(z);
 	y = cimag(z);
 
-	if (x == 0.0 && y > 1.0)
-		goto ovrf;
-
 	x2 = x * x;
 	a = 1.0 - x2 - (y * y);
-	if (a == 0.0)
-		goto ovrf;
 
 	t = 0.5 * atan2(2.0 * x, a);
 	w = _redupi(t);
 
 	t = y - 1.0;
 	a = x2 + (t * t);
-	if (a == 0.0)
-		goto ovrf;
 
 	t = y + 1.0;
 	a = (x2 + t * t)/a;
-	w = w + (0.25 * log(a)) * I;
-	return w;
-
-ovrf:
-	// FIXME
-	w = MAXNUM + MAXNUM * I;
+	w = CMPLX(w, 0.25 * log(a));
 	return w;
 }

Re: catan errors

[Szabolcs Nagy]

* Rich Felker <dalias@libc.org> [2018-04-10 19:23:28 -0400]:
> On Wed, Apr 11, 2018 at 01:08:50AM +0200, Szabolcs Nagy wrote:
> > * Rich Felker <dalias@libc.org> [2018-04-10 15:50:07 -0400]:
> > >  	t = y - 1.0;
> > >  	a = x2 + (t * t);
> > > -	if (a == 0.0)
> > > -		goto ovrf;
> > 
> > why does a==0 imply x==0?
> 
> OK, at least by my reasoning it's only algebraically true not
> necessarily as doubles.
> 
> > if |x| < sqrt(2)*0x1p-538, x2 underflows to 0 in nearest rounding mode.
> > 
> > to handle this correctly extra work would need to be done, so i think
> > either way is fine (leaving the goto there or not are both wrong, but
> > we dont guarantee correct complex functions yet)
> 
> I'm fine with just moving the check back here. But the special case
> (maybe not near-special cases with internal over/underflow though)
> works fine just replacing the *I with CMPLX. See attached.
> 

i think this makes sense for now.

> Rich

> diff --git a/src/complex/catan.c b/src/complex/catan.c
> index 39ce6cf..7dc2afe 100644
> --- a/src/complex/catan.c
> +++ b/src/complex/catan.c
> @@ -91,29 +91,17 @@ double complex catan(double complex z)
>  	x = creal(z);
>  	y = cimag(z);
>  
> -	if (x == 0.0 && y > 1.0)
> -		goto ovrf;
> -
>  	x2 = x * x;
>  	a = 1.0 - x2 - (y * y);
> -	if (a == 0.0)
> -		goto ovrf;
>  
>  	t = 0.5 * atan2(2.0 * x, a);
>  	w = _redupi(t);
>  
>  	t = y - 1.0;
>  	a = x2 + (t * t);
> -	if (a == 0.0)
> -		goto ovrf;
>  
>  	t = y + 1.0;
>  	a = (x2 + t * t)/a;
> -	w = w + (0.25 * log(a)) * I;
> -	return w;
> -
> -ovrf:
> -	// FIXME
> -	w = MAXNUM + MAXNUM * I;
> +	w = CMPLX(w, 0.25 * log(a));
>  	return w;
>  }