E
Eric Sosman
Several recent threads, and for that matter a great number of
threads in years past, have debated whether C should be extended to
permit operator overloading. Proponents argue that overloading
would improve readability by allowing a user-defined quaternion type
(for example) to be manipulated with familiar arithmetic operators
rather than with verbose sequences of function calls. Opponents say
that overloading would, on the contrary, disimprove readability by
making the ordinary + sign an uncertain symbol whose meaning can
only be discovered by extensive detective work. Successive debates
have trodden this same ground so often that it is now hard-packed,
with no green and growing thing left upon it.
But the discussions thus far have ignored another vital matter,
namely, the robustness of code that uses overloaded operators.
After all, the "over" in "overload" doesn't just mean "more," but
"too much more." An overloaded bridge may crumble and drown its
traffic in the river below. Overload an electrical circuit and
you'll get at best a blown breaker or perhaps a fire. We all know
what happens when one last straw overloads the camel's back.
Any proposal to add operator overloading to C must therefore
address the issue of catastrophic failure of operators under
overload conditions. It turns out that at least some of C's
operators are structurally delicate to the point of fragility, and
cannot sustain overload as they stand.
The division operator is perhaps the most glaring example. It
sits on a slant, its only support one lonesome pivot point on the
baseline. Add even a small load to a / and it will topple to a _,
completely changing its meaning -- in fact, transforming it from an
operator to an identifier! The additional load acts through a lever
arm that the unsupported division operator is powerless to resist.
Other operators may also be unable to sustain overload. It
takes only a modest amount of pressure to flatten the kinks out of
the bitwise complement operator ~ and make it indistinguishable from
the - unary negation operator. The exclusive or ^ resists pressure
somewhat better, but eventually it, too, collapses to -. So when a
compiler encounters what looks like a -, it might be an actual - or
an overloaded ~ or ^, and the compiler has no way to know what was
intended. The best it can do may be to flip a three-sided coin
(available at specialty stores) and choose randomly in hopes of
being right some of the time.
Some operators suffer deformation but usually retain enough of
their form to remain recognizable and useful. No amount of pressure
will squeeze the . operator any smaller than it already is. The +
operator might have an arm snapped off, but unless it loses both it
will still be distinguishable from |. | itself may bend to resemble
( or ), but if the load is well-centered this will seldom happen.
The * operator will get squashed to the semblance of a road-killed
hedgehog, but will still be recognizable because no other operator
flattens to that form.
How shall we address this precarious state of affairs? The
first impulse may be to build the operators more sturdily, with
heavier structural members. Instead of `x + y / z' we could write
||| ///
||| ///|
||| ///||
-----|||----- /// ||
x ------+------ y /// || z
-----|||----- /// ||
||| /// ||
||| /// ||
||| /// ||
using thicker lines (and giving the division operator a much-needed
stabilizing leg) to sustain higher loads than the wispy strokes of
today's feeble glyphs can handle. But this approach is unsatis-
factory because it does not scale to really large loads. For a
two-dimensional figure like a source glyph, the cross-section
(hence, the strength to sustain load) increases linearly with size,
but the character's area (hence, mass) increases as the square.
Thus, there's a built-in limit to how far this strategy can take us:
At some point we'll need to make the symbol larger to support
greater loads, but the increase in mass will add load faster than
the growth in cross-section adds strength. The bloated operator
will eventually collapse under its own weight. Growth is not the
answer.
How about leaving the operators at (or near) their current
sizes, but building them of sturdier stuff? Materials technology
can now produce substances far stronger than were available four
decades ago when C's operators were invented, things like rare-earth
composites and carbon nanotubes. The noted Iraqi materials
scientist Maq'it al-Egos graciously consented to study the problem.
He began by separating the question of stronger pixels from that
of stronger print, since screen displays and paper-borne glyphs face
radically different problems. On a screen, it turns out that the
structural strength of a pixel depends mostly on its color. (He
found it surprising that the display technology had relatively
little to do with the matter; the same colors were strong or weak
regardless of whether they were generated by liquid crystal, plasma,
or cathode rays on phosphor.) The strongest pixels are almost white
with a slight bluish tinge, easily produced on RGB displays by
driving the blue component to its maximum while letting red and
green hover a few percent below theirs.
There is an edge effect to worry about. Strong blue-white
pixels adjacent to weaker-colored pixels are themselves weakened
slightly, and they in turn weaken their stronger neighbors. If
unchecked, weak pixels surrounding an operator painted in strong
pixels will "corrode" the formerly-strong pixels and bring on the
very collapse we're trying to prevent. But the counter-measure is
simple: Paint the strong-pixel operator on a background of the same
strong color, and there will be no such corrosive effect. The
entire screen will be strong, able to sustain extreme loads easily.
We can consider this problem solved.
The print question still resists solution. al-Egos has been
able to develop sufficiently strong inks and toners, but has reached
the point at which the paper itself fails and tears; the operators,
even though intact, lose much of their readability when the paper
they're printed on turns to powder. Experiments with rhodium foil
as a paper substitute seem promising, but are at present in the
early stages. The foil is rather expensive in laboratory quantities
(around US$3 per square centimeter), but in commercial production we
can expect the price to drop by half, perhaps even by two-thirds.
Besides, printed books are going the way of the dinosaurs, so their
durability is not all that great a concern.
The essay to this point would have been posted a couple weeks
ago, but I mentioned the matter to my friend Druncan O'Blivion in a
bar late at night on Saint Patrick's Day, and he came up with a
radically different approach that needed additional study. I
confess that my recollection of what he said that night is none too
clear, but I still have the cocktail napkin on which he drew his
diagrams and made his calculations. (I would post an image of the
napkin, but Druncan also drew on it an astonishingly lifelike sketch
of the barmaid, with details I presume are hypotheses rather than
experimentally verified facts, and this is a family newsgroup.)
Druncan works for NASAL ("It *is* rocket science!" he likes to
say), and his solution arises from astrophysics. He pointed out
that the force of gravity varies as the inverse square of the
distance between the attracting masses. A small mass at a great
distance from a large attractor feels very little attractive force,
and that small force can be resisted by even a feeble structure.
Thus, we can overload our familiar operators, just as we know them
today, provided we place them high enough that their loads are light
and sustainable. The familiar quadratic formula can be written as
= - + ( * - * * ) / *
x ( b sqrt b b 4 a c ) (2 a)
improving structural integrity with only a small loss in clarity.
In actual code one would use more vertical distance than in this
condensed example, enough to put the operators into low Earth orbit
where they would be in free fall and essentially gravityless.
Druncan pointed out that we must not go too high (although we
were both rather high at the time), lest we place the operators in
the Van Allen belts belts where radiation could damage them. For
example, the commonest isotope of the right-shift operator, >>36,
transmutes to the array-index operator []40 upon absorption of an
alpha particle. This isotope of [] is unstable and quickly decays
to >> again, but to >>37 instead of >>36. Both >>36 and >>37 are
stable isotopes and both are right-shift operators, but >>37 affects
the sign bit differently. It may be that the existence of two
stable >> isotopes is the cause of much of the confusion about the
behavior of the shift operators.
(As a side-note, researchers at SCORN have been collecting code
samples from Usenet and bombarding them with energetic electron
beams. Preliminary reports indicate little change in code entropy,
as most code samples are maximally chaotic to begin with. After
irradiation, some code stops working altogether; the researchers
indicate that this is usually an improvement. Further experiments
are planned with heavy-particle beams, now that the Large Hardon
Collider is, er, up.)
In summary, this note describes some of the structural
challenges that must be considered when overloading C's operators.
For screen display, painting the operators blue-white on a blue-
white background seems an entirely satisfactory solution. For
display on monochrome screens or to color-blind viewers, O'Blivion's
technique can be used by any organization able to muster sufficient
near-Earth throw weight. The matter of overloaded operators in
print needs better solutions, but the authors of "C Unchained" will
surely think of something in time for the next edition.
(This essay may be redistributed in electronic form without
restriction. Each recipient is permitted to print one copy for his
or her own personal use. All photocopies require individual
licenses, from originator's own lawyers.)
threads in years past, have debated whether C should be extended to
permit operator overloading. Proponents argue that overloading
would improve readability by allowing a user-defined quaternion type
(for example) to be manipulated with familiar arithmetic operators
rather than with verbose sequences of function calls. Opponents say
that overloading would, on the contrary, disimprove readability by
making the ordinary + sign an uncertain symbol whose meaning can
only be discovered by extensive detective work. Successive debates
have trodden this same ground so often that it is now hard-packed,
with no green and growing thing left upon it.
But the discussions thus far have ignored another vital matter,
namely, the robustness of code that uses overloaded operators.
After all, the "over" in "overload" doesn't just mean "more," but
"too much more." An overloaded bridge may crumble and drown its
traffic in the river below. Overload an electrical circuit and
you'll get at best a blown breaker or perhaps a fire. We all know
what happens when one last straw overloads the camel's back.
Any proposal to add operator overloading to C must therefore
address the issue of catastrophic failure of operators under
overload conditions. It turns out that at least some of C's
operators are structurally delicate to the point of fragility, and
cannot sustain overload as they stand.
The division operator is perhaps the most glaring example. It
sits on a slant, its only support one lonesome pivot point on the
baseline. Add even a small load to a / and it will topple to a _,
completely changing its meaning -- in fact, transforming it from an
operator to an identifier! The additional load acts through a lever
arm that the unsupported division operator is powerless to resist.
Other operators may also be unable to sustain overload. It
takes only a modest amount of pressure to flatten the kinks out of
the bitwise complement operator ~ and make it indistinguishable from
the - unary negation operator. The exclusive or ^ resists pressure
somewhat better, but eventually it, too, collapses to -. So when a
compiler encounters what looks like a -, it might be an actual - or
an overloaded ~ or ^, and the compiler has no way to know what was
intended. The best it can do may be to flip a three-sided coin
(available at specialty stores) and choose randomly in hopes of
being right some of the time.
Some operators suffer deformation but usually retain enough of
their form to remain recognizable and useful. No amount of pressure
will squeeze the . operator any smaller than it already is. The +
operator might have an arm snapped off, but unless it loses both it
will still be distinguishable from |. | itself may bend to resemble
( or ), but if the load is well-centered this will seldom happen.
The * operator will get squashed to the semblance of a road-killed
hedgehog, but will still be recognizable because no other operator
flattens to that form.
How shall we address this precarious state of affairs? The
first impulse may be to build the operators more sturdily, with
heavier structural members. Instead of `x + y / z' we could write
||| ///
||| ///|
||| ///||
-----|||----- /// ||
x ------+------ y /// || z
-----|||----- /// ||
||| /// ||
||| /// ||
||| /// ||
using thicker lines (and giving the division operator a much-needed
stabilizing leg) to sustain higher loads than the wispy strokes of
today's feeble glyphs can handle. But this approach is unsatis-
factory because it does not scale to really large loads. For a
two-dimensional figure like a source glyph, the cross-section
(hence, the strength to sustain load) increases linearly with size,
but the character's area (hence, mass) increases as the square.
Thus, there's a built-in limit to how far this strategy can take us:
At some point we'll need to make the symbol larger to support
greater loads, but the increase in mass will add load faster than
the growth in cross-section adds strength. The bloated operator
will eventually collapse under its own weight. Growth is not the
answer.
How about leaving the operators at (or near) their current
sizes, but building them of sturdier stuff? Materials technology
can now produce substances far stronger than were available four
decades ago when C's operators were invented, things like rare-earth
composites and carbon nanotubes. The noted Iraqi materials
scientist Maq'it al-Egos graciously consented to study the problem.
He began by separating the question of stronger pixels from that
of stronger print, since screen displays and paper-borne glyphs face
radically different problems. On a screen, it turns out that the
structural strength of a pixel depends mostly on its color. (He
found it surprising that the display technology had relatively
little to do with the matter; the same colors were strong or weak
regardless of whether they were generated by liquid crystal, plasma,
or cathode rays on phosphor.) The strongest pixels are almost white
with a slight bluish tinge, easily produced on RGB displays by
driving the blue component to its maximum while letting red and
green hover a few percent below theirs.
There is an edge effect to worry about. Strong blue-white
pixels adjacent to weaker-colored pixels are themselves weakened
slightly, and they in turn weaken their stronger neighbors. If
unchecked, weak pixels surrounding an operator painted in strong
pixels will "corrode" the formerly-strong pixels and bring on the
very collapse we're trying to prevent. But the counter-measure is
simple: Paint the strong-pixel operator on a background of the same
strong color, and there will be no such corrosive effect. The
entire screen will be strong, able to sustain extreme loads easily.
We can consider this problem solved.
The print question still resists solution. al-Egos has been
able to develop sufficiently strong inks and toners, but has reached
the point at which the paper itself fails and tears; the operators,
even though intact, lose much of their readability when the paper
they're printed on turns to powder. Experiments with rhodium foil
as a paper substitute seem promising, but are at present in the
early stages. The foil is rather expensive in laboratory quantities
(around US$3 per square centimeter), but in commercial production we
can expect the price to drop by half, perhaps even by two-thirds.
Besides, printed books are going the way of the dinosaurs, so their
durability is not all that great a concern.
The essay to this point would have been posted a couple weeks
ago, but I mentioned the matter to my friend Druncan O'Blivion in a
bar late at night on Saint Patrick's Day, and he came up with a
radically different approach that needed additional study. I
confess that my recollection of what he said that night is none too
clear, but I still have the cocktail napkin on which he drew his
diagrams and made his calculations. (I would post an image of the
napkin, but Druncan also drew on it an astonishingly lifelike sketch
of the barmaid, with details I presume are hypotheses rather than
experimentally verified facts, and this is a family newsgroup.)
Druncan works for NASAL ("It *is* rocket science!" he likes to
say), and his solution arises from astrophysics. He pointed out
that the force of gravity varies as the inverse square of the
distance between the attracting masses. A small mass at a great
distance from a large attractor feels very little attractive force,
and that small force can be resisted by even a feeble structure.
Thus, we can overload our familiar operators, just as we know them
today, provided we place them high enough that their loads are light
and sustainable. The familiar quadratic formula can be written as
= - + ( * - * * ) / *
x ( b sqrt b b 4 a c ) (2 a)
improving structural integrity with only a small loss in clarity.
In actual code one would use more vertical distance than in this
condensed example, enough to put the operators into low Earth orbit
where they would be in free fall and essentially gravityless.
Druncan pointed out that we must not go too high (although we
were both rather high at the time), lest we place the operators in
the Van Allen belts belts where radiation could damage them. For
example, the commonest isotope of the right-shift operator, >>36,
transmutes to the array-index operator []40 upon absorption of an
alpha particle. This isotope of [] is unstable and quickly decays
to >> again, but to >>37 instead of >>36. Both >>36 and >>37 are
stable isotopes and both are right-shift operators, but >>37 affects
the sign bit differently. It may be that the existence of two
stable >> isotopes is the cause of much of the confusion about the
behavior of the shift operators.
(As a side-note, researchers at SCORN have been collecting code
samples from Usenet and bombarding them with energetic electron
beams. Preliminary reports indicate little change in code entropy,
as most code samples are maximally chaotic to begin with. After
irradiation, some code stops working altogether; the researchers
indicate that this is usually an improvement. Further experiments
are planned with heavy-particle beams, now that the Large Hardon
Collider is, er, up.)
In summary, this note describes some of the structural
challenges that must be considered when overloading C's operators.
For screen display, painting the operators blue-white on a blue-
white background seems an entirely satisfactory solution. For
display on monochrome screens or to color-blind viewers, O'Blivion's
technique can be used by any organization able to muster sufficient
near-Earth throw weight. The matter of overloaded operators in
print needs better solutions, but the authors of "C Unchained" will
surely think of something in time for the next edition.
(This essay may be redistributed in electronic form without
restriction. Each recipient is permitted to print one copy for his
or her own personal use. All photocopies require individual
licenses, from originator's own lawyers.)