q_rsqrt comes to the Jerk Store

Almost four years ago, I asked: how come q_rsqrt didn't force ufloat or udouble or whatever in her input. The Quake games never used this func for a negative input; this might raise a nasty native CPU error. Why not - I asked - force the positive input and crash gracefully?

Today I was watching some video on Youtube - I won't link it, it was AI - about the Year 2038 Bug. That's when the 31 bits, counting from the new year 1970, overflow. It's not 32 bits because it's a signed integer and they wanted to allow negative years, back to some time in 1901. I'm told December. Most people they cared about were born after then.

Another issue is that ye olde compilers from the earliest years of C, Ada, and Pascal were "type safe". If you had a big uint, they didn't like it when you made it an int. There was a chance you'd lop off the highest bit and make the whole thing meaningless. The compiler is your friend!

No really, he was written to be your friend. Programmers need to work with the compiler, not against him. Leave aside 2038. What could the Id Software doodz have done in the 1990s?

I'm thinking that before calling q_rsqrt, they could have sent their vectors into another function: which takes a float and squares it. "Pffft they probably did that already, x^2 or, better, x*x." Yeah, sure. And the base multiplication left the float as a float. We need a function that knows when x^[even uint] happens it sends back an unsigned value.

The problem is with the type of x. IEEE 754 didn't bother with "ufloat". There was no such thing in the 1990s. Why not? Because what "floats" is where the "point" is at, and sign is just one bit. They'd have to decide whether to add that bit to the top, or to the decimals. For the purpose of normalisation, which be taking the sum of three squares (so could be large), let's say we agreed to put it on the topside.

Now that we've decided to monkey with the structure of a hardwired type, which we can't do in software; we go to Intel HQ and we ring the doorbell with our proposal to alter their processor. It's 1994; maybe 1985 (Elite). Who's got space for that? And why does it matter so bad in, you know, a shmup game.

Blah blah blah, not worth the bother, never has been worth the bother. You know it, I (now) know it... everyone knows it (except apparently me). So why write alla'that. It's because here:

long i  = * ( long * ) &y;

This type could be unsigned. (It also happens that "long" then meant 32-bit.) I just ran this by Google AI and...

uint32_t i;
memcpy(&i, &y, sizeof(i));
i = 0x5f3759df - (i >> 1);
memcpy(&y, &i, sizeof(y));

Chew on that, Kasper Nielsen!

Early writings of Jacob in Edessa

Paul Ulishney a couple years ago got Correspondence of Jacob of Edessa and Eustathius of Dara into print. Jacob, per Ulishney, was then a forty-something monk esteemed as a theologian and an interpreter of Greek work.

Complicating matters, many of these names have other names. Jacob is (in English) sometimes called James. Edessa was usually Callirhoë in those days, which somewhat has a memory today as "Şanlı'Urfa". And Eustathius seems to have been in charge of saecular affairs in Dara to Ruha's east. Because, per Ulishney, Jacob addressed him as "the petty lord (kyriosuna)". But affectionately!

Also complicating is that little Jimmy whilst in Edessa veered off-and-on between being a monk and full bishop. We do know he wrote one of our letters at the age of 42 (bald, by then) but that one ain't dated and lacks any other real markers so, maddeningly, we still don't know when our man was born.

Wikipedia still thinks AD 672 was a possible year for Jacob's installation as bishop. Ulishney's rearrangement and interpretation agrees more with (early-)684 / 995. Such is the majority view since Omert J Shrier 1991 and is so assumed in Hoyland 1997-8. Ulishney doesn't defend Best O.J. against freakin' Wiki since, why should he condescend. So I'll do it.

In the earlier 680s - AG 990s to nonbarbarians - a small schism broke out cutting the "east" from the Antioch-Edessa mainline. These will be the now-historic sees of Tikrit, Singara, and mount Alpap. The patriarch Severus wanted to be a Syrian pope like his contemporary in Egypt acted as pope, appointing bishops or at least demanding a veto. (Investiture was always a problem for churches.) Severus enlisted Jacob as secretary. Ulishney reasonably assumes they'd not force this upon a bishop, but the bishops may well call in the smartest monk in the area. And Jacob, much as it pains us dyotheletes, was a genius. His contemporary Athanasius of Balad agreed; as Athanasius II he'll get Jacob that episcopacy as one of his first acts in office. I don't hear that anyone in Edessa complained... at the time. (Read on.)

All this stuff is in the British Library, still in manuscript: "Add. 12,172". Still unedited. On the other hand, now that Ulishney has organised it better, maybe we'll get to read it soon. Put Alison Salvesen on it. Is there some Copt who can send a grant?

Eustathius will enjoy a career after these letters, as well. He was the Nicodemus of the north Christian Arabs, founding a martyrion for Muʿâdh of the Taghlib. Michael the Syrian will post that to AG 1020 which we call 708-9 (against some "Muhammad" but assuredly under al-Walîd's command), I assume based on that church's records and plaques.

In these letters Jacob also dealt with the Romans and the Nestorians, as well a Syrian Miaphysite might. Jacob as an intellectual was no enemy to Greeks as such; but he might have grown disenchanted with the imperial Romans, Latin-speaking or otherwise. Constantine IV was asserting his primacy in Constantinople (681/993-on), and preparing to throw off the Monotheletism which his father had tolerated. As for the Nestorians: Jacob and Athanasius would have to worry their rivals might be eager to embrace their wayward brethren. There's also the issue that Jacob knew the earth was round unlike some idiots over there.

Jacob will outlast his pope, but not long outlast him. Athanasius was known in his (meagre) correspondence to be a stickler for, basically, Christian halakha. For instance he forbade to consume halal (Holger Zellentin has a good book on this). The next patriarch Julian - contemporary with Justinian II - proved more lax in such ordinances. By then and for this, the Edessenes preferred Julian over their own neoRabboula. Jacob resigned in a huff and retvrned to monk-ing. And to writing manifesti.

Per Salvesen's translation, Jacob's frustrations spilled into the scholion on the edition of 1 Kings / 3 Reigns 14 he was compiling there. Also extant is a "Testamentum Domini" from this circle which may well be by Jacob himself. Dunno about that Pseudo-Methodius tho', that Sinjari seems more oecumenical.

Hot shot, part deuce

So I kinda/sorta trusted VAERS when deciding on the booster in fall 2021. I rolled those dice having taken Pfizer's original schedule that spring and then catching some yuck in June. Stayed un-boosted.

That RS means it is a reporting system for the V.A. Events. That database accumulated a lot of such reportage. Less from Pfizer than from Moderna I think, but the second jab I took had some statistical problems. And people were freaking out over - all of them, as the same "Clot Shot". Which might skew the results, like all those geezers and morons freaked out over sudden acceleration in the late-1980s Audi.

There could have been some signal-to-noise correction in how various agencies read the VAEs from the RS. The British Medical Journal est. 1840 must report on what happened.

This journal is not some Slay News fly-by-night; they are generally pro-vax, like for shingles.

The journal notes that by mid-2021 the FDA knew there was a noise problem in VAERS. It further uncovers a letter which, in September 2022, then-CDC-director Rochelle Walensky sent: Walensky was worried that it was all getting stupid over at the FDA. The FDA meanwhile was muzzling the people raising the concerns the prior year.

By noise, BMJ means the FDA simply ignored myocarditis, pericarditis, or tinnitus as not-counting as a real vaccine adverse event. The "-card-" root means cardio - the heart.

The FDA honcho during this time was Peter Marks. He'd been a big force in "Operation Warp Speed" in May 2020. Robert Kennedy demanded Marks' resignation 28 March 2025. You can now find Marks at Eli Lilly in DC.

Starshot v Starfire: the race to Sedna

Given the ongoing investments into sunsail and Direct Fusion, outer system missions are coming into view. In one case, the outer system is coming to us: Sedna. We have until 2075 when this visitor from the Oort gets into perihelion (76 AU). Last year, Elena Ancona, Roman Ya. Kezerashvili, Savino Longo compared the two methods.

Other methods had earlier been mooted such as VASIMR (perhaps-foremost), but these run in the timeframes of decades. Democracies don't build cathedrals.

Other important constraints include that the mission requires a power source that isn't solar, that far away. It also needs communication with Earth. These techs were last refined in New Horizons - a flyby.

This DFD, which is assumed Princeton's Starfire, would be running 1.6 MW under its own power. This is to extend the lifetime of the superconductor over ten years; the ceiling would be thirteen.

With as much time as they have, either could (and should) borrow Jupiter for gravity-assist, probably Venus too. Dunno about outer planets. The DFD would further be able to flip-n'-burn and inject into the planetoid's orbit. That would however add some years onto the trip.

One-way sunsail would get out there in seven years; the Starfire in ten. There is no reason that exploration-agencies cannot do both, given that a sunsail might be cheaper. Especially given that other missions will be bidding against Princeton for its 300g of He-3.

On-board variable propulsion

Ion drives like VASIMR, and adjustable NERVA like the shockwave rotor, can squeeze more efficiency from their drives by feeding in energy and/or adjusting the exhaust throat. It occurs to me that this means recalculating the rocket equation in real time. As in: on the rocket, not outsourced to orbital data. That drinks more energy for compute, which then must be controlled somehow; probably by radiating out.

These are exponent and logarithm equations. If we were using a TSR-80 extended BASIC processor, welcome to Taylor series.

Needless to say, that is some bull-tish. Don't we have some tricks to turn a float into a 32?bit long(ish)int? Just shift the integer over bro. *(long*), subtract some magic number, then <<= bro. Like when the exponent was -1/2.

That'd be great if the ratios were all integers. They... probably aren't. Because they aren't, this method requires to poll the ratio until it reaches an integer and then run the calc.

We'd hope to force integers on all four values of the Tsiolkovsky to some cromulent unit-length, like millimeters and grams. We'll see. Instead of exp(dv/ve) it's exp(dv) × root-ve(e). One multiplication operation. Gotta be better than Taylor(8). Ln(m0/mf) meanwhile is [lb(m0) - lb(mf)] × ln(2). Now we have to ponder overflow: 32-bit integers go only to 2³¹. So, no; these are going to be km/s maybe even Mm/s which we have to rescale after the calc.

Depending on the unit-lengths I might even consider storing the exponent-powers and the e-roots in tables. Data got corrupted on Voyager but I suspect our triage is better today; so's our shielding. On arrival at the destination our need to punch the engine shouldn't be as dire, so the memory used in the tables can be wiped, for reüse in the actual mission.

This was imprecise for q_rsqrt and will be imprecise now. Those 1990s gamers applied Newton's method upon that approx "y", thus: y * ( 1.5F - ( x * 0.5F * y * y ) ). Lotsa multiplications, here. And that's second-order because this was just a square. And, to remind: we're talking about high exponents and high roots. May as well devolve to Taylor.

Kasper Nielsen's cheat-sheet of "float tricks" may offer an out. We have NVIDIA's "piecewise linear approximation" which shouldn't overflow. Ian Stephenson does one better for Pow2 which "approximates the error with a quadratic".

There are other unsafe-code solutions in the roster, some just straight assembler with no overflow checks. Good news: I doubt we need 'em for the floating fractions. The mass ratio as wet/dry[-er] even at some Apolloesque 96 isn't going to have ln(x) all that high (4.6ish here), and this is going down as we drive. The velocity ratio working with inner-system delta-V and as-good exhaust as they'll allow us (like, 14 km/s) should also be low, enough for exp[x] anyway.

MEMORY COPY 9/19: If you know we're on positives.

Types... deletes... and stuff

Sydney Sweeney should not be supporting gambling in sports. This support is a failure of character on her part.

I recall when Instapundit lambasted Busey for appearing in the Turkish film Valley of the Wolves. I recall he called Busey a "whore". Euphoria, I propose, was just as disgusting a project. So it is not like Sweeney hasn't already telegraphed that she, like Busey, was willing to appear in whatever paid.

If you think I am being cheap: some of the shots which Insta is levelling at her detractors are cheap. (And if we must Go There, the lady northwest would probably look about as good as 30-year-old Sweeney sans makeup and airbrush. I've personally dated northeast.)

I might further ask, from the support of Instapundit and others, to what degree they have been bought off too.

So you want 70 tonnes in Venus-Earth Hohmann

The Superheavy has pushed a 75 tonne load into LEO; maybe some krauts have pushed 70 t. This load is headed for Venus. v_inf, for that, is 2.5 km/s. Leviathan expect to pay Elon Musk MONEY to send it all in a 160 tonne Starship; and MO' MONEY, for the fuel top-up in LEO. Presently the paper hasn't stated how much fuel they need but Google has told me, 400 t (megagrams). In this poast, I compete for that blank cheque. We are all about branching paths here.

An interplanetary Hohmann operates by regular launch windows, Earth/Venus on that pentagram synod of 583.92 days. In this case we're not sending any time-sensitive cargo (like monkeys): Leviathan is supposed to work for a year, so what's a coupla'more months. This means I don't have to blast immediately after getting to LEO and topping up. I can afford to wait; to adjust my cargo's trajectory from LEO to something better nudged into.

We start by renting the Tamil Tether. This yanks my cargo into HEO, here standing for high eccentric orbit. Apogee 200-300 megameters well over GEO. Weee!

That is delta-v 2.83 km/s; if I'm shifting only 75t, momentum 2.1e8 kgm/s. This can be spread over a minute or two so most tether materials would work. The 2.3 terajoules of total energy will, however, lower the tether's altitude. Raja's tax must be paid.

From this apogee, I'm in range of a possible second tether which promises up to 100 t - although here the tether material must be ... stiff. In this case I must spend the remnant 25 t budget on a dedicated Venus-entry vessel because I'll not fit a full Starship on that poor thing. Copilot didn't even suggest the idea.

Instead Copilot adds solar-electric tugs operating for several weeks in that 200-300 Mm domain. I could even have a near-empty spare 160 t Starship hanging around up there (which is why we discussed only the 75 t above). We don't need to park them on the spaceline although that will be nice too.

Above all (heh) the tugs can push my 235 tonnes into a Molniya trajectory, that almost hits Earth. It is at perigee, the velocity is highest, yay Kepler, at 10.8-11 km/s. At the right moment, we do the Crazy Hermann off to Hohmann. This delta-V is 248 m/s. For this push, propellant mass runs just 16.1 metric tons. With 16.5 MN thrust allowed by six Raptors, it is burned in 3.65 s.

Leviathan conceded a multiple-launch mission, the moment they mooted refueling. My mission architecture reduces the launches to two. One sends the load, which competitors can bid for; tethers hurl this into HEO. The other sends a whole Starship (under)laden, which... tethers hurl into HEO. The 16.1 t (plus) of fuel is probably in the latter, for simplicity. The load and the 'ship, they dock (because Leviathan assumes docking is possible) in HEO. At some point, I send my mission via Oberth with much less fuel than that for which SpaceX will charge them. I do assume infrastructure, but that infrastructure is available for future missions. Like for that Sunbird > Saturn mission.

I might add that Elon could use something like this architecture to get his 'ships back. Could be he's loaded enough propellant for a cycler-trajectory, to drop off the cargo and keep goin', so Earth gets it back... whenever. 3-0-2-9 promises 4.8 sidereal years; Hop David's scheme awaits the whole eight year metonic. Maybe Elon doesn't want to let his 'ship rot in the Solar well for years so sends over propellant, to load onto the 'ship, which waits in high Venus ellipse-orbit for the next direct Hohmann.

Either way there's likely to be additional burn, for 3-0-2-9 probably on its next return at Venus, to adjust the angle as to intersect Earth. I say likely because over eight years, cap'n Hop David might be able to trim thar sails.