I could imagine a reason #5: you are porting programs from a language that supports 80bits.
On Nov 10, 2012, at 4:41 PM, Neil Toronto wrote: > On 11/09/2012 06:56 AM, Dmitry Pavlov wrote: >> 2. Maybe we are cutting blocks with a razor here? >> If there is any simpler way to have native 80-bit >> floating point in Racket (say Racket->ASM compilation, >> Racket->C, LLVM, anything), please do tell me. > > Here's another razor/brick-related question: What does 80 bits get you? > > I'm not staunchly defending 64-bit floats, and I'm not trying to turn down > your kind offer to improve to Racket. I just wonder whether there's an easier > way to get what you need. > > Some problems bigger floats would help with are: > > 1. Computing large values whose fractional parts are significant. Large > physics simulations, for example: you don't want orbits to go erroneously > wobbly far from the origin, where floats are much sparser. > > 2. You need exponents greater than 308 and/or less than -308. > > 3. You need to compute sort-of-stable solutions or long-running simulations > accurately. > > 4. You have some difficult computations that suffer from overflow, underflow, > or severe cancellation. > > If your problem is #4, I may have a good enough 64-bit solution. > > An example of #4 is (x/k)^k * exp(k-x), which shows up embarrassingly often > in gamma-related functions, and is impossible to compute accurately for large > x and k without using more bits. (To avoid under-/overflow, you must accept > cancellation errors.) If just this one function were computed accurately, all > of these gamma-related functions could be computed accurately. As it is, > nobody has ever implemented an accurate 64-bit incomplete gamma integral. > > There's a body of work on floating-point "expansions," which represent > numbers as the sum of multiple non-overlapping floats. Two 64-bit floats, for > example, is equivalent to one 117-bit float (1 sign, 11 exponent, 105 > significand). I've just implemented 117-bit arithmetic, log1p, expm1, and > exp. I'm going to use these judiciously, because they're a bit expensive; I > think a two-float multiply is 17 flops. > > I was planning to keep this part of the math library private on the first > release, but I could put it in something like math/unstable for now if it > could help with your problem. > > But if what you need 80 bits for is pervasive, or if you're simply committed > to it, I'll just look forward to having them. :) I'll be happy to consult as > well. > > Neil ⊥ > > ____________________ > Racket Users list: > http://lists.racket-lang.org/users
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