FP Accuracy proposal

TODO: complete writeup

Zfpacc: a proposal to allow implementations to dynamically set the bit-accuracy of results, trading speed (reduced latency) for accuracy (higher latency).

Extension of FCSR

Zfpacc would use some of the the reserved bits of FCSR. It would be treated very similarly to how dynamic frm is treated.

frm is treated as follows:

  • Floating-point operations use either a static rounding mode encoded in the instruction, or a dynamic rounding mode held in frm.
  • Rounding modes are encoded as shown in Table 11.1 of the RISC-V ISA Spec
  • A value of 111 in the instruction’s rm field selects the dynamic rounding mode held in frm. If frm is set to an invalid value (101–111), any subsequent attempt to execute a floating-point operation with a dynamic rounding mode will raise an illegal instruction exception.

If we wish to support up to 4 accuracy modes, that would require 2 'fam' bits. The Default would be IEEE754-compliant, encoded as 00. This means that all current hardware would be compliant with the default mode.

Unsupported modes cause a trap to allow emulation where traps are supported. Emulation of unsupported modes would be required for UNIX platforms. As with frm, an implementation may choose to support any permutation of dynamic fam-instruction pairs. It will illegal-instruction trap upon executing an unsupported fam-instruction pair. The implementation can then emulate the accuracy mode required.

If the bits are in FCSR, then the switch itself would be exposed to user mode. User-mode would not be able to detect emulation vs hardware supported instructions, however (by design). That would require some platform-specific code.

Emulation of unsupported modes would be required for unix platforms.

TODO:

A mechanism for user mode code to detect which modes are emulated (csr? syscall?) (if the supervisor decides to make the emulation visible) that would allow user code to switch to faster software implementations if it chooses to.

TODO:

Choose which accuracy modes are required

Which accuracy modes should be included is a question outside of
my expertise and would require a literature review of instruction
frequency in key workloads, PPA analysis of simple and advanced
implementations, etc.

TODO: reduced accuracy

I don't see why Unix should be required to emulate some arbitrary
reduced accuracy ML mode.  My guess would be that Unix Platform Spec
requires support for IEEE, whereas arbitrary ML platform requires
support for Mode XYZ.  Of course, implementations of either platform
would be free to support any/all modes that they find valuable.
Compiling for a specific platform means that support for required
accuracy modes is guaranteed (and therefore does not need discovery
sequences), while allowing portable code to execute discovery
sequences to detect support for alternative accuracy modes.

Dynamic accuracy CSR

maybe a solution would be to add an extra field to the fp control csr to allow selecting one of several accurate or fast modes:

  • machine-learning-mode: fast as possible (maybe need additional requirements such as monotonicity for atanh?)
  • GPU-mode: accurate to within a few ULP (see Vulkan, OpenGL, and OpenCL specs for accuracy guidelines)
  • almost-accurate-mode: accurate to <1 ULP (would 0.51 or some other value be better?)
  • fully-accurate-mode: correctly rounded in all cases
  • maybe more modes?

Question: should better accuracy than is requested be permitted? Example: Ahmdahl-370 issues.

Comments:

Yes, embedded systems typically can do with 12, 16 or 32 bit
accuracy. Rarely does it require 64 bits. But the idea of making
a low power 32 bit FPU/DSP that can accommodate 64 bits is already
being done in other designs such as PIC etc I believe. For embedded
graphics 16 bit is more than adequate. In fact, Cornell had a very
innovative 18-bit floating point format described here (useful for
FPGA designs with 18-bit DSPs):

<https://people.ece.cornell.edu/land/courses/ece5760/FloatingPoint/index.html>

A very interesting GPU using the 18-bit FPU is also described here:

<https://people.ece.cornell.edu/land/courses/ece5760/FinalProjects/f2008/ap328_sjp45/website/hardwaredesign.html>

There are also 8 and 9-bit floating point formats that could be useful

<https://en.wikipedia.org/wiki/Minifloat>