Nibble to Hexadecimal in 3 Cycles for Java and C

Ignore this post, dear reader.
Everything in it is correct, as far as it goes.
However, it has become abundantly clear that modern CPUs
allow mundane solutions to outperform those presented here.
This post will be revised accordingly, but will likely seem rather pointless.

I’m unsatisfied with Java’s typical bits-to-hex methods (*.toHexString and printf). That’s why—not for the first time—I was examining an issue generally considered settled or unimportant. I hope other malcontents find value in this work.

I created this nibble-to-hex conversion early in January 2025 (and, perhaps, one or more times in preceding years, without thinking twice about it). There is no telling how many programmers invented this before me, so I claim only its independent invention. That said, if these algorithms are new to you, I’d appreciate credit (a line comment will suffice). Even in January of 2026 (the time of publication), Gemini Pro was unaware of precedents for these algorithms, and it confirmed they are optimal. (No alternate approach uses fewer cycles, and no variant can simultaneously convert a sequence of nibbles.)

Returning to the subject…

Store a nibble in an “int” named “nibble” (its high 28 bits must be clear) then use one of the following expressions to obtain the corresponding ASCII/ISO-8859-1/Unicode code-point.

Nibble to Uppercase Hex Notation (3 Cycles)

(char) ((nibble | 0x30) + (9 - nibble >>> 29))

Nibble to Lowercase Hex Notation (4 Cycles)

(char) ((nibble | 0x30) + (9 - nibble >> 31 & 39))

That’s all there is to it. Java methods with detailed documentation, and C ports, are below the fold.

Those cycle counts are correct for the x86 and ARM64 architectures. Both depend on immediate operands, but only x86 benefits from instruction-level parallelism. Unlike x86, the ARM64 SUB instruction does not support an immediate minuend, so loading operand 9 prevents replication of the x86 parallelism. Instead, ARM64 saves a cycle at the end by using a “shifted-add” instruction to perform the logical right shift and addition in one cycle. That, I gather, is a trick x86 cannot perform. So, both architectures show limitations here, but they cancel-out.

(I spent many years programming in assembly on a daily basis, but that time has passed. I still look at microarchitecture documentation, but that does not produce an understanding of instruction sets and architectures comparable to someone who actually writes assembly code for the architectures. So, now, I double-check my conclusions with Gemini Pro.)

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Java Method Implementations

private static char nibbleToHexDigitUc
(
    final int               nibble
){
//  Repetition of the following expression may appear tedious, and invites mistakes,
//  hence this method. The expression is short enough to ensure inlining.

/*  Clause 1, "nibble | 0x30" (equivalent to "nibble + '0'" in US-ASCII), produces
    "int" value "c1", ranging from 0x30 ('0') for "nibble" 0x0, to 0x3F ('?') for
    "nibble" 0xF.

    Clause 2, "9 - nibble", differentiates nibbles represented by US-ASCII
    characters '0'-'9' from those represented by 'A'-'F':
        (A) non-negative when "nibble" ≤ 9, or
        (B) negative when "nibble" ≥ 0xA.

    Clause 3, "c2 >>> 29", uses the high 3 bits of "c2" to produce "int" value "c3",
    the "c1" addend either converting US-ASCII characters ':'-'?' (produced from
    nibbles ≥ 0xA) to characters 'A'-'F', or leaving characters '0'-'9' unchanged:
        (A) 0 from "c2A", or
        (B) 7 from "c2B".
    Because "c3" is either 0, or a sequence of consecutive 1 bits, this clause is
    not adaptable to lowercase hex production, which would require a "c3B" value
    of 39 (0b100111).

    Clause 4, "c1 + c3" produces "int" value "c4": the US-ASCII code-point of the 
    hexadecimal digit representing "nibble".

    Note: The whole expression allows two instances of instruction-level parallelism:
          clauses 1 and 2. That will not provide a great performance gain, because
          every operator is single-cycle, and eliminating one cycle is good, but not
          great. Nonetheless, some parallelism is better than none, and executing
          50% of its operators in parallel is better than most expressions.
*/
    //noinspection MagicNumber
    return (char) ((nibble | 0x30) + (9 - nibble >>> 29));
}

private static char nibbleToHexDigitLc
(
    final int               nibble
){
//  Repetition of the following expression may appear tedious, and invites mistakes,
//  hence this method. The expression is short enough to ensure inlining.

/*  Clause 1, "nibble | 0x30" (equivalent to "nibble + '0'" in US-ASCII), produces
    "int" value "c1", ranging from 0x30 ('0') for "nibble" 0x0, to 0x3F ('?') for
    "nibble" 0xF.

    Clause 2, "9 - nibble", differentiates nibbles represented by US-ASCII
    characters '0'-'9' from those represented by 'A'-'F':
        (A) non-negative when "nibble" ≤ 9, or
        (B) negative when "nibble" ≥ 0xA.

    Clause 3, "c2 >> 31", produces "int" value "c3":
        (A)  0 from "c2A", or
        (B) -1 from "c2B".
    Thus, "c3" is an all-or-nothing mask determining whether clause 4 produces an
    addend altering "c1", or 0 which leaves "c1" unchanged.

    Clause 4, "c3 & 39", produces "int" value "c4", the "c1" addend converting
    US-ASCII characters ':'-'?' (produced from nibbles ≥ 0xA) to characters 'a'-'f',
    while leaving characters '0'-'9' unchanged:
        (A)  0 when "nibble" ≤ 9, or
        (B) 39 when "nibble" ≥ 0xA.
    Value "c4B" makes this clause responsible for the letter case of hexadecimal digits
    > 9. As is, hexadecimal digits > 9 are lowercase. Uppercase digits would result
    from replacing 39 with 7 ... *except* there is no point to doing so, because a
    simpler, faster expression produces uppercase hex.

    Clause 5, "c1 + c4" produces "int" value "c5": the US-ASCII code-point of the
    hexadecimal digit representing "nibble".

    Note: The whole expression allows two instances of instruction-level parallelism:
          clauses 1 and 2. That will not provide a significant performance gain
          (every operator is single-cycle, so only one cycle is saved), but 40%
          parallelism is better than none.
*/
    //noinspection MagicNumber
    return (char) ((nibble | 0x30) + (9 - nibble >> 31 & 39));
}

Those are the implementations for Java, my language of choice since the late 1990s. If porting, keep in mind: (1) both expressions implicitly operate on 32-bit, big-endian, two’s-complement integers throughout, (2) operator “>>>” is an unsigned right shift (JLS terminology), otherwise known as a “logical right shift” (typical assembly language terminology), and (3) operator “>>” is a signed (“arithemtic”) right shift.

C Ports (C99 and C23)

C, and, I think, most C-inspired languages, lack an equivalent operator. (Originally, C didn’t specify the sign-extension behavior of its right shift operator, >>, so one might encounter either behavior depending on the CPU and the compiler, although arithmetic [sign-extending] right shifts seem to have been the most common.) Although I spent 15 years programming in C (now designated “K&R C” or “C78”), I never encountered any of C’s standardized versions, and my only C documentation remains the 1978 edition of K&R. However, I gather C99 standardized logical right shift for unsigned integers, so the ports below are deterministic, unless one builds for a CPU that doesn’t use two’s-complement arithmetic on signed integers (apologies to Unisys developers).

Nibble to Uppercase Hex Notation, C99, 3 Cycles

Where “nibble” is of type “int32_t”, its high 28 bits are clear, and two’s-complement arithmetic remains the norm:

(nibble | 0x30) + ((uint32_t) (9 - nibble) >> 29)

Nibble to Lowercase Hex Notation, C99, 5 Cycles

Where “nibble” is of type “int32_t”, its high 28 bits are clear, and two’s-complement arithmetic remains the norm:

(nibble | 0x30) + ((-(int32_t) ((uint32_t) 9 - nibble >> 31)) & 39)

Nibble to Lowercase Hex Notation, C23, 4 Cycles

Where “nibble” is of type “int32_t”, and its high 28 bits are clear:

(nibble | 0x30) + (9 - nibble >> 31 & 39)

The Neighborhood Squirrels

After shelling its pecan, a contented fox squirrel prepares to eat.

Two years ago to this day, I made my first friend among my neighborhood’s fox squirrels. Most of the others became friends soon after. In this case “friend” means they’ve decided to trust me enough to take nuts from between my fingers, or, in some cases, from a short distance (personalities vary).

For the preceding twenty five years or so, the local squirrels had been substantially made-from, and fueled-by, the contents of my bird feeder. That was fine with me; I wouldn’t want squirrels dumb enough to overlook such an obvious food source (all the neighbors would laugh at the guy with the stupid squirrels). However, I felt very misunderstood when the squirrels (and all the other local critters) fled for their lives every time I showed my face, even to refill the bird feeder and bath.

I spent most of my career on a college campus, peanuts in pocket, ready to feed any squirrel I met. They never complained. (Well, each season’s pups needed some convincing, but that was perfectly understandable.) One would climb the brick wall of a building each day to sit in a second story window and have lunch with a friend and me. From one pair of trees, shortly after sunset, I could call down a large multi-generation family. The old matriarch was always the final one to descend, and did so with an air of grudginly doing me the favor of taking my peanuts, but down she always came.

Even so, my neighborhood squirrels fled on sight, every single day, decade after decade.

After retiring, it occurred to me I might correct that problem. Many months of experimental squirrel bribery were required, but, eventually, sufficiently appealing bribes were found, one squirrel made the connection between bribes and briber, and soon a bit of coaxing had her visiting my back door, rather than risking losing those treats to other squirrels. Happily, she still visits, and I always find her an extra large nut.

Now, I often wake to find a squirrel watching for my stirrings through the bedroom window. The breakfast rush can be intense, so it’s worth some waiting to be ahead of it.

Unexpectedly, having acquired a good reference from the squirrels, the birds reconsidered me, and are now relatively untroubled by my presence. The local flock of blue jays have found me a welcome source of peanuts, a few wrens come seeking nuts (provided I remove the shells for them), and a dove sometimes walks just ahead of me as I go to fill the bird feeder - my self-appointed escort for that all-important task.

Authoritarian Followers

Dr. Bob Altemeyer, a retired professor of psychology at the University of Manitoba, devoted forty years to studying authoritarianism, and literally wrote the book on it in 2006 (highly recommended, and conveniently free). Much shorter, and directly addressing recent years, his 2016 post Donald Trump and Authoritarian Followers deserves a fresh look¹. (Those who’ve read it can skip this post; Bob’s the expert, I’m just saying his work is important, go and see and judge for yourselves.) The portion of that 2016 post I most want to point-out is the enumeration, in Trump’s context, of authoritarian followers’ pschological traits. Those traits strike this writer as essential pieces missing from the mental puzzles many people are struggling to assemble as they try to understand Trump’s coup attempt of January 6th, his insurrectionists, the enablers of both within the Republican party and right-wing echo chambers, where those people came from, and where they’ll go.

Bob Altemeyer:

We know a lot about authoritarian followers, but unfortunately most of what we know indicates it will be almost impossible to change their minds, especially in a few months. Here are some things established by experiments. See if you recognize any of these behaviors in Trump supporters. Compared with most people:

They are highly ethnocentric, highly inclined to see the world as their in-group versus everyone else. Because they are so committed to their in-group, they are very zealous in its cause. They will trust their leaders no matter what they say, and distrust whomever the leader says to distrust.

They are highly fearful of a dangerous world. Their parents taught them, more than parents usually do, that the world is dangerous. They may also be genetically predisposed to experience stronger fear than people skilled at “keeping their heads while others are losing theirs.”

They are highly self-righteous. They believe they are the “good people” and this unlocks a lot of hostile impulses against those they consider bad.

They are aggressive. Given the chance to attack someone with the approval of an authority, they will lower the boom.

They are highly prejudiced against racial and ethnic minorities, non-heterosexuals, and women in general.

They will support their authorities, and even help them, persecute almost any identifiable group in the country.

Their beliefs are a mass of contradictions. They have highly compartmentalized minds, in which opposite beliefs live independent lives in separate boxes. As a result, their thinking is full of double-standards.

They reason poorly. If they like the conclusion of an argument, they don’t pay much attention to whether the evidence is valid or the argument is consistent. They especially have trouble realizing a conclusion is invalid.

They are highly dogmatic. Because they have mainly gotten their beliefs from the authorities in their lives, rather than think things out for themselves, they have no real defense when facts or events indicate they are wrong. So they just dig in their heels and refuse to change.

They are very dependent on social reinforcement of their beliefs. They think they are right because almost everyone they know and listen to tells them they are. That happens because they screen out sources that will suggest that they are wrong.

Because they severely limit their exposure to different people and ideas, they vastly overestimate the extent to which other people agree with them. And thinking they are “the moral majority” supports their attacks on the “evil minorities” they see in the country.

They believe strongly in group cohesiveness, and being loyal. They are highly energized when surrounded by a crowd of fellow-believers because it makes them feel powerful and supports their belief that “all the good people” agree with them.

They are easily duped by manipulators who pretend to espouse their causes when all the con-artists really want is personal gain.

They are largely blind to themselves. They have little self-understanding and insight into why they think and do what they do. They are heavily into denial.

I hasten to add that studies find examples of all these things in lots of others, not just authoritarian followers. But not as consistently, and not nearly as much.

Thank you, Bob.

Returning to two issues from the opening paragraph — where Trump's base came from, and where they’ll go post-Trump: Trump’s base isn’t his at all; authoritarian followers have always been a part of our society. Trump merely borrowed the current batch, and put them to work. Even if Trump were to magically vanish tomorrow, they’re not going anywhere, and won’t be changing their minds about much of anything. They’ll be waiting for the next leader who tells them they’re right and good, their desires will be fulfilled, and those they hate will be punished. No matter how many partisan divides are healed, people with their psychological traits will continue to appear in the population, find each other, form self-reinforcing groups, seek leaders to follow, and, tragically, break their children as badly as they themselves were broken.

That’s all bad, but it’s also nothing new.

The good news? A healthy society is likely to reduce the toxicity of authoritarian followers from one generation to the next¹, while a dysfunctional society will increase it. So, this writer’s master plan for America remains unchanged (and short on details): A United States government devoted to maximizing the quality of life of every American, at no harm to the rest of the world. Also, short-term, let’s finally take terrorism by white people seriously, and find some more checks and balances to protect the nation from authoritarians in its government, so we all arrive at the long-term in one piece.

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1. See also Bob Altemeyer’s 2018 post Why Do Trump’s Supporters Stand by Him, No Matter What?. It ends on a hopeful note, but should be read in context.

Spectacular SpaceX Video of Falcon 9 Recovery Experiment

Rocket explosions are always spectacular and, provided no one is harmed, something to see if you appreciate the flash, bang, crash of it all. Therefore, I duly provide a link to a Spaceflight Now article that includes the video released by SpaceX of their attempt to propulsively land the first stage of the Falcon 9 rocket that successfully sent supplies to the International Space Station last week. This landing was performed on an autonomous barge in the Atlantic ocean, about 200 miles downrange from the Cape Canaveral launch site.

In fairness, you should also see a video of one of the many successful full-scale test flights that led up to this recovery experiment.

I imagine the crash video will get a lot of play, because—hey—crash! explosion! flying debris!, but probably without the proper context which is roughly this: nobody else has ever attempted to do what SpaceX attempted here: recovery of a rocket after it has flown its mission into space … and not only that, but recovery entirely intact, such that, after appropriate checkouts and repairs, it can fly again.

(As a nation, America had a great opportunity to build an even more economical and re-usable vehicle—that’s “reusable" as in airliner, not “partially salvageable” as in Space Shuttle—with the proposed Delta Clipper project, whose sub-scale prototype, referred to by the shorthand "DC-X”, is mentioned at the bottom of the Spaceflight Now article, but NASA management bungled that possibility utterly when they selected Lockheed to develop an un-prototyped and completely different design as the “follow-on” X-33 project.)

SpaceX and this rocket, the Falcon 9, have already changed the worldwide launch market by delivering large payloads to space (and optionally bringing materials back in their Dragon capsule, as they do with each of their supply flights to the International Space Station) at an excellent price (and so far their reliability has been 100%).

If SpaceX can succeed in making recoverable the Falcon 9 first stage, and later the second stage (as is their stated goal), they’ll revolutionize the launch market with their ability to profitably launch large payloads into space at an unbeatable fraction of the price charged by their competitors. That’ll be a great thing for everyone except their competitors (in the short run), and their competitors are already receiving a long-overdue and badly-needed kick in the ass, as SpaceX runs rings around them in terms of technology, the rate at which they can bring it to market, their willingness to fund more-or-less everything out of their own pocket (including very-high-risk experiments like stage recoverability), and so on. I’m reminded of the stagnant “smart” phone market prior to the (seemingly) sudden appearance of the iPhone, which changed everything. It’s good when the complacent market leaders have the rug pulled out from under them by a brilliant upstart.

While I’m sure SpaceX wants to recover the hardware from every flight, and in time they can probably manage that (or come very close), in the meantime I can’t help but be reminded of the quality control criteria for one of America’s secret weapons in WW II: the proximity fuse. It was decided that anti-aircraft shells equipped with those fuses were so effective against enemy aircraft, that it was OK if the fuses failed 50% of the time - the half that worked more than made-up for the half that didn’t. I think the same is true here: even if only 50% of the recoveries are successful, it would make a huge difference to the price point at which SpaceX could offer launches.

I’ve gone on too long, I think, but enjoy the kaboom. And here’s wishing the SpaceX folks complete success with their next attempt in two or three weeks.

Squirrels Removed, Owls Return

Screech owl cam’ viewers will be pleased to know that, although there's nothing to view yet, with the removal of the squirrels, the owls are checking out the nest box with increasing frequency. (Yeah, I'll probably graph it, but not at the moment.)

I have to hope that they won't actually begin nesting until March, as has been the case most years, because I still have to integrate a high-definition color/monochrome camera into the box, and into my homegrown owl cam’ software. The quickest way to integrate it into the box may be to build a new box using a much simpler design that I've been thinking about for a few years. The new design would solve a number of shortcomings in the current design that've become apparent over the last thirteen years, and would also add enough new interior space to accommodate the high-def camera, which, regrettably, is much larger than any other camera I've used in the nest box.

All I need in order to pull this off is sensible owls that will wait until March to nest, some monetary blood letting (as opposed to outright hemorrhaging) to complete the new audio/video setup, no nasty surprises from the new camera, a little luck with the software work, and a massive, sustained surge of energy that'll make it possible to accomplish all of that in whatever time I have. It's that last bit about the energy that worries me the most.

Interested parties may, as they see fit, wish me luck, knock on wood, and so forth.

Removing Squirrels from the Owl Box

One unpleasant chore done: I've removed three very nice fox squirrels from the owl box. It always makes me feel like a bully and a scoundrel, but if the owls are going to nest in the box, the squirrels have to go. It's likely they'll be back in about a week, but the process of making the owl box feel like a dangerous place to be a squirrel is underway. In the meantime, when the owls poke their heads in the box, they'll see that it's available and should return to nest in it again this year.

Longtime readers may recall that I thought I'd solved the squirrel-in-the-owl-box problem a few years back when I placed a dedicated squirrel box in the same tree as the owl nest box. The idea being that a squirrel, or family of squirrels, would occupy the squirrel box, and their natural territoriality would cause them to repel any other fox squirrels that wanted to move into their home tree.

That worked for two years. I think the problem this year is that the squirrel family unit living in the squirrel box has been successful enough over these years that it has exceeded the (comfortable) capacity of the squirrel box, causing various family members to seek lodging in the next best place in the tree: the owl box.

That said, the number of squirrels in the owl box on any given night this winter has varied from zero to three. So, they must have at least one other nest site, presumably the squirrel box. I hope the three I had to pick on tonight will simply move back into that box, and write-off the owl box as a promising, but ultimately failed, experiment. Regrettably, I have no cameras in the squirrel box, so I can only speculate about the goings on in there.

Meanwhile, I encountered one of my owls one night ago, so they're around, just as one would expect. I'm also trying to have some significant upgrades in place for this season. As usual, I've left it a bit late (I was hesitant to spend the money), but I haven't yet fully proved that the new gear will behave as desired, so worst case, it'll be a moot point. Best case, I'll soon be in a flat-out race against time to integrate the new stuff. Wish me luck, and remember that the owl cam' has had to relocate to www.ChrisOwlCam.net.

The Silent (Unthinking, Well-Educated) Majority

“Both the allegiance and socialization processes cause the educated to believe that what America does is right. Public opinion polls show the nonthinking results. In late spring 1966, just before the United States began bombing Hanoi and Haiphong in North Vietnam, Americans split 50-50 as to whether we should bomb these targets. After the bombing began, 85 percent favored the bombing while only 15 percent opposed. The sudden shift was the result, not the cause, of the government’s decision to bomb. The same allegiance and socialization processes operated again when policy changed in the opposite direction. In 1968, war sentiment was waning; but 51 percent of Americans opposed a bombing halt, partly because the United States was still bombing North Vietnam. A month later, after President Johnson announced a bombing halt, 71 percent favored the halt. Thus, 23 percent of our citizens changed their minds within a month, mirroring the shift in government policy. This swaying of thought by policy affects attitudes on issues ranging from our space program to environmental policy and shows the so-called “silent majority” to be an unthinking majority as well. Educated people are overrepresented among these straws in the wind.” [Emphasis added. —CWJ]

Excerpt from: James W. Loewen. “Lies My Teacher Told Me,” 2nd. edition. Perseus, 2010-09-16. iBooks.