FP Accuracy proposal


  • Bruce Hoult
  • Allen Baum
  • Dan Petroski
  • Jacob Lifshay

TODO: complete writeup

Zfpacc: a proposal to allow implementations to dynamically set the bit-accuracy of floating-point results, trading speed (reduced latency) at runtime for accuracy (higher latency). IEEE754 format is preserved: instruction operand and result format requirements are unmodified by this proposal. Only ULP (Unit in Last Place) of the instruction result is permitted to meet alternative accuracy requirements, whilst still retaining the instruction's requested format.

This proposal is only suitable for adding pre-existing accuracy standards where it is clearly established, well in advance of applications being written that conform to that standard, that dealing with variations in accuracy across hardware implementations is the responsibility of the application writer. This is the case for both Vulkan and OpenCL.

This proposal is not suitable for inclusion of "de-facto" (proprietary) accuracy standards (historic IBM Mainframe vs Ahmdahl incompatibility) where there was no prior agreement or notification to applications writers that variations in accuracy across hardware implementations would occur. In the unlikely event that they are ever to be included (n the future, rather than as a Custom Extension, then, unlike Vulkan and OpenCL, they must only be added as "bit-for-bit compatible".

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.


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.


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

FCSR to be modified to include accuracy bits:

31....11 10..8 7..5 4....0
reserved facc frm fflags

The values for the field facc to include the following:

facc mode description
0b000 IEEE754 correctly rounded
0b010 ULP<1 Unit Last Place < 1
0b100 Vulkan Vulkan compliant
0b110 Appx Machine Learning

(TODO: review alternative idea: ULP0.5, ULP1, ULP2, ULP4, ULP16)


  • facc=0 to match current RISC-V behaviour, where these bits were formerly reserved and set to zero.
  • The format of the operands and result remain the same for all opcodes. The only change is in the accuracy of the result, not its format.
  • facc sets the minimum accuracy. It is acceptable to provide more accurate results than is requested by a given facc mode (although, clearly, the opportunity for reduced power and latency would be missed).


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?

extra mode suggestions:

it might be reasonable to add a mode saying you're prepared to accept
worse then 0.5 ULP accuracy, perhaps with a few options: 1, 2, 4,
16 or something like that.

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


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):


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


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


function accuracy in standards (opencl, vulkan)

resources for OpenCL and Vulkan

Vulkan requires full ieee754 precision for all F/D instructions except for fdiv and fsqrt.


Source is here: https://github.com/KhronosGroup/Vulkan-Docs/blob/master/appendices/spirvenv.txt#L1172

OpenCL slightly different, suggest adding as an extra entry.


Link, finds version 2.1 of opencl environment specification, table 8.4.1 however needs checking if it is the same as the above, which has "SPIRV" in it and is 2.2 not 2.1


2.1 superceded by 2.2 https://github.com/KhronosGroup/OpenCL-Docs/blob/master/env/numerical_compliance.asciidoc


Dan Petroski:

It’s a bit more complicated than that. Different FP
representations/algorithms have different quantization ranges, so you
can get more or less precise depending on how large the arguments are.

For instance, machine A can compute within ULP3 from 0 to 10000, but
ULP2 from 10000 upwards. Machine B can compute within ULP2 from 0 to
6000, then ULP3 for 6000+. How do you design a compliance suite which
guarantees behavior across all fpaccs?

and from Allen Baum:

In the example above, you'd need a ratified spec with the defined
ranges  (possbily per range and per op) - and then implementations
would need to at least meet that spec (but could be more accurate)

so - not impossible, but a lot more work to write different kinds
of tests than standard IEEE compatible test would have.

And, by the way, if you want it to be a ratified spec, it needs a
compliance suite, and whoever has defined the spec is responsible
for writing it.,