24 GFLOPS available in multiple, parallel pipelines in the GPU and people are still screwing around with ints (even very long ones) on a RISC processor for crying out loud. Get real, as in real numbers folks, or at least floating-point numbers, as the Pi SoC has both the GPU and a floating-point hardware unit. IEEE standard 754-2008 quadruple-precision floating-point provides 112 bits of mantissa (roughly 34 decimal digits) and you can get as many digits of accuracy as you want by just keeping track of the last couple of bits of the mantissa when doing extended-precision, cascaded calculations. I'll see your puny 64-bit, int-based calculation and raise you 48 bits at a whack
This once again points up how most people just don't get how they should be using the Pi - it's the GPU, stoopid! Poor Eben, James, and the rest of the crew have been slaving over hot pipelines to rev up that wonderful VideoCore IV warp drive and you guys are still fiddling with a friggin' carburetor - and a single-barreled one at that! Better check your points - and the rest of the Lucas-built electrical componentry while you're under the hood, boys!
It reminds me of the joke about who was more intelligent, a mathematician or an engineer. They were placed at one end in a room, with a ravishing naked, um, "technician" in a reclined position on a couch at the other end of the room, and a clock on the wall over the "tech". They were instructed that they could advance half the distance to the "tech" as each minute passed on the clock. When the first minute expired, the engineer advanced halfway across the room, but the mathematician remained in his original place against the wall. Another minute went by and the engineer advanced to three-quarters of the way across the room, but the mathematician remained fixed in place. The organizers stopped the contest to ask the mathematician if he understood the rules, to which he smugly replied, "Well, anyone with a wit's worth of intelligence knows that you could advance toward the 'tech' for an infinite amount of time and still never actually get there." The organizers said to the engineer, "Well, it seems the mathematician has bested you, old boy.", to which the engineer quickly shot back, "Oh, yeah? Well give me ten more minutes and I'll be close enough for engineering approximations!"
Think outside the box, folks - it's a wonderful new world out here
The best things in life aren't things ... but, a Pi comes pretty darned close!
"Education is not the filling of a pail, but the lighting of a fire." -- W.B. Yeats
In theory, theory & practice are the same - in practice, they aren't!!!