There aren't a lot of advantages to putting quadruple precision into the hardware. Typically with numeric code you don't run out of exponent space you run into precision limits. To increase precision you can use software techniques like double-double representation. This doubles precision and keeps the exponent range the same at the cost of increased numbers of instructions.
The real action is in FMA (fused multiply-add) instructions. These instructions do two operations then a correct rounding of the result (e.g. round(a*b+c)). FMA in hardware is great. It lets you write functions with provably tight errors or even provably correct rounding of the result. More and more platforms are providing FMA [1].
Do you know of any specific applications? "many" seems like an extraordinary claim. I'm under the impression that quad precision is fringe. Double precision support on GPUs is fairly recent.
Sure. Just for a start, some of David Bailey's papers (http://www.davidhbailey.com/dhbpapers/), e.g. "High-Precision Arithmetic: Progress and Challenges" and "High-Precision Floating-Point Arithmetic in Scientific Computation" show some concrete examples. You will find many others by searching for papers containing the words "quad double arithmetic", "high precision arithmetic", "multiple precision arithmetic" or similar terms. Most applications are probably in physics, and of course in pure mathematics.
Comments
Is there any x86 instruction set that supports quadruple precision floating point numbers? If not, why not? Is it not useful enough?
There aren't a lot of advantages to putting quadruple precision into the hardware. Typically with numeric code you don't run out of exponent space you run into precision limits. To increase precision you can use software techniques like double-double representation. This doubles precision and keeps the exponent range the same at the cost of increased numbers of instructions.
The real action is in FMA (fused multiply-add) instructions. These instructions do two operations then a correct rounding of the result (e.g. round(a*b+c)). FMA in hardware is great. It lets you write functions with provably tight errors or even provably correct rounding of the result. More and more platforms are providing FMA [1].
[1]: http://en.wikipedia.org/wiki/Multiply%E2%80%93accumulate_ope...
Where exactly is it useful? Double is already an overkill in all multimedia operations, and finance folks use fixed-point anyway.
Quadruple (or higher) precision is needed in many scientific applications.
Do you know of any specific applications? "many" seems like an extraordinary claim. I'm under the impression that quad precision is fringe. Double precision support on GPUs is fairly recent.
Sure. Just for a start, some of David Bailey's papers (http://www.davidhbailey.com/dhbpapers/), e.g. "High-Precision Arithmetic: Progress and Challenges" and "High-Precision Floating-Point Arithmetic in Scientific Computation" show some concrete examples. You will find many others by searching for papers containing the words "quad double arithmetic", "high precision arithmetic", "multiple precision arithmetic" or similar terms. Most applications are probably in physics, and of course in pure mathematics.