+**OBSOLETE**, superceded by [[openpower/transcendentals]]
+
# Zftrans - transcendental operations
-With thanks to:
+Summary:
+
+*This proposal extends RISC-V scalar floating point operations to add IEEE754 transcendental functions (pow, log etc) and trigonometric functions (sin, cos etc). These functions are also 98% shared with the Khronos Group OpenCL Extended Instruction Set.*
+
+Authors/Contributors:
+* Luke Kenneth Casson Leighton
* Jacob Lifshay
* Dan Petroski
* Mitch Alsup
* **ZftransAdv**: much more complex to implement in hardware
* **Zfrsqrt**: Reciprocal square-root.
-Minimum recommended requirements for 3D: Zftrans, Ztrigpi, Ztrignpi, Zarctrigpi,
-Zarctrignpi
+Minimum recommended requirements for 3D: Zftrans, Ztrignpi,
+Zarctrignpi, with Ztrigpi and Zarctrigpi as augmentations.
-Minimum recommended requirements for Mobile-Embedded 3D: Ztrigpi, Zftrans, Ztrignpi
+Minimum recommended requirements for Mobile-Embedded 3D: Ztrignpi, Zftrans, with Ztrigpi as an augmentation.
# TODO:
This proposal is designed to meet a wide range of extremely diverse needs,
allowing implementors from all of them to benefit from the tools and hardware
-cost reductions associated with common standards adoption.
+cost reductions associated with common standards adoption in RISC-V (primarily IEEE754 and Vulkan).
**There are *four* different, disparate platform's needs (two new)**:
may not be sold and also make a claim of being, for example, "Vulkan
compatible".
-This in turn reinforces and makes a hard requirement a need for public
+For 3D, this in turn reinforces and makes a hard requirement a need for public
compliance with such standards, over-and-above what would otherwise be
set by a RISC-V Standards Development Process, including both the
software compliance and the knock-on implications that has for hardware.
+For libraries such as libm and numpy, accuracy is paramount, for software interoperability across multiple platforms. Some algorithms critically rely on correct IEEE754, for example.
+The conflicting accuracy requirements can be met through the zfpacc extension.
+
**Collaboration**:
The case for collaboration on any Extension is already well-known.
with huge (non-uniform) market diversity even with similarly large
numbers of potential opcodes. BitManip is the perfect counter-example.
-# Proposed Opcodes vs Khronos OpenCL Opcodes <a name="khronos_equiv"></a>
+# Proposed Opcodes vs Khronos OpenCL vs IEEE754-2019<a name="khronos_equiv"></a>
+
+This list shows the (direct) equivalence between proposed opcodes,
+their Khronos OpenCL equivalents, and their IEEE754-2019 equivalents.
+98% of the opcodes in this proposal that are in the IEEE754-2019 standard
+are present in the Khronos Extended Instruction Set.
-This list shows the (direct) equivalence between proposed opcodes and
-their Khronos OpenCL equivalents.
For RISCV opcode encodings see
[[rv_major_opcode_1010011]]
See
<https://www.khronos.org/registry/spir-v/specs/unified1/OpenCL.ExtendedInstructionSet.100.html>
+and <https://ieeexplore.ieee.org/document/8766229>
* Special FP16 opcodes are *not* being proposed, except by indirect / inherent
use of the "fmt" field that is already present in the RISC-V Specification.
results in non-compliance, and the vendor may not use the Trademarked words
"Vulkan" etc. in conjunction with their product.
+IEEE754-2019 Table 9.1 lists "additional mathematical operations".
+Interestingly the only functions missing when compared to OpenCL are
+compound, exp2m1, exp10m1, log2p1, log10p1, pown (integer power) and powr.
+
[[!table data="""
-Proposed opcode | OpenCL FP32 | OpenCL FP16 | OpenCL native | OpenCL fast |
-FSIN | sin | half\_sin | native\_sin | NONE |
-FCOS | cos | half\_cos | native\_cos | NONE |
-FTAN | tan | half\_tan | native\_tan | NONE |
-NONE (1) | sincos | NONE | NONE | NONE |
-FASIN | asin | NONE | NONE | NONE |
-FACOS | acos | NONE | NONE | NONE |
-FATAN | atan | NONE | NONE | NONE |
-FSINPI | sinpi | NONE | NONE | NONE |
-FCOSPI | cospi | NONE | NONE | NONE |
-FTANPI | tanpi | NONE | NONE | NONE |
-FASINPI | asinpi | NONE | NONE | NONE |
-FACOSPI | acospi | NONE | NONE | NONE |
-FATANPI | atanpi | NONE | NONE | NONE |
-FSINH | sinh | NONE | NONE | NONE |
-FCOSH | cosh | NONE | NONE | NONE |
-FTANH | tanh | NONE | NONE | NONE |
-FASINH | asinh | NONE | NONE | NONE |
-FACOSH | acosh | NONE | NONE | NONE |
-FATANH | atanh | NONE | NONE | NONE |
-FRSQRT | rsqrt | half\_rsqrt | native\_rsqrt | NONE |
-FCBRT | cbrt | NONE | NONE | NONE |
-FEXP2 | exp2 | half\_exp2 | native\_exp2 | NONE |
-FLOG2 | log2 | half\_log2 | native\_log2 | NONE |
-FEXPM1 | expm1 | NONE | NONE | NONE |
-FLOG1P | log1p | NONE | NONE | NONE |
-FEXP | exp | half\_exp | native\_exp | NONE |
-FLOG | log | half\_log | native\_log | NONE |
-FEXP10 | exp10 | half\_exp10 | native\_exp10 | NONE |
-FLOG10 | log10 | half\_log10 | native\_log10 | NONE |
-FATAN2 | atan2 | NONE | NONE | NONE |
-FATAN2PI | atan2pi | NONE | NONE | NONE |
-FPOW | pow | NONE | NONE | NONE |
-FROOT | rootn | NONE | NONE | NONE |
-FHYPOT | hypot | NONE | NONE | NONE |
-FRECIP | NONE | half\_recip | native\_recip | NONE |
+opcode | OpenCL FP32 | OpenCL FP16 | OpenCL native | OpenCL fast | IEEE754 |
+FSIN | sin | half\_sin | native\_sin | NONE | sin |
+FCOS | cos | half\_cos | native\_cos | NONE | cos |
+FTAN | tan | half\_tan | native\_tan | NONE | tan |
+NONE (1) | sincos | NONE | NONE | NONE | NONE |
+FASIN | asin | NONE | NONE | NONE | asin |
+FACOS | acos | NONE | NONE | NONE | acos |
+FATAN | atan | NONE | NONE | NONE | atan |
+FSINPI | sinpi | NONE | NONE | NONE | sinPi |
+FCOSPI | cospi | NONE | NONE | NONE | cosPi |
+FTANPI | tanpi | NONE | NONE | NONE | tanPi |
+FASINPI | asinpi | NONE | NONE | NONE | asinPi |
+FACOSPI | acospi | NONE | NONE | NONE | acosPi |
+FATANPI | atanpi | NONE | NONE | NONE | atanPi |
+FSINH | sinh | NONE | NONE | NONE | sinh |
+FCOSH | cosh | NONE | NONE | NONE | cosh |
+FTANH | tanh | NONE | NONE | NONE | tanh |
+FASINH | asinh | NONE | NONE | NONE | asinh |
+FACOSH | acosh | NONE | NONE | NONE | acosh |
+FATANH | atanh | NONE | NONE | NONE | atanh |
+FATAN2 | atan2 | NONE | NONE | NONE | atan2 |
+FATAN2PI | atan2pi | NONE | NONE | NONE | atan2pi |
+FRSQRT | rsqrt | half\_rsqrt | native\_rsqrt | NONE | rSqrt |
+FCBRT | cbrt | NONE | NONE | NONE | NONE (2) |
+FEXP2 | exp2 | half\_exp2 | native\_exp2 | NONE | exp2 |
+FLOG2 | log2 | half\_log2 | native\_log2 | NONE | log2 |
+FEXPM1 | expm1 | NONE | NONE | NONE | expm1 |
+FLOG1P | log1p | NONE | NONE | NONE | logp1 |
+FEXP | exp | half\_exp | native\_exp | NONE | exp |
+FLOG | log | half\_log | native\_log | NONE | log |
+FEXP10 | exp10 | half\_exp10 | native\_exp10 | NONE | exp10 |
+FLOG10 | log10 | half\_log10 | native\_log10 | NONE | log10 |
+FPOW | pow | NONE | NONE | NONE | pow |
+FPOWN | pown | NONE | NONE | NONE | pown |
+FPOWR | powr | half\_powr | native\_powr | NONE | powr |
+FROOTN | rootn | NONE | NONE | NONE | rootn |
+FHYPOT | hypot | NONE | NONE | NONE | hypot |
+FRECIP | NONE | half\_recip | native\_recip | NONE | NONE (3) |
+NONE | NONE | NONE | NONE | NONE | compound |
+NONE | NONE | NONE | NONE | NONE | exp2m1 |
+NONE | NONE | NONE | NONE | NONE | exp10m1 |
+NONE | NONE | NONE | NONE | NONE | log2p1 |
+NONE | NONE | NONE | NONE | NONE | log10p1 |
"""]]
Note (1) FSINCOS is macro-op fused (see below).
+Note (2) synthesised in IEEE754-2019 as "pown(x, 3)"
+
+Note (3) synthesised in IEEE754-2019 using "1.0 / x"
+
## List of 2-arg opcodes
[[!table data="""
FATAN2 | atan2 arc tangent | rd = atan2(rs2, rs1) | Zarctrignpi |
FATAN2PI | atan2 arc tangent / pi | rd = atan2(rs2, rs1) / pi | Zarctrigpi |
FPOW | x power of y | rd = pow(rs1, rs2) | ZftransAdv |
-FROOT | x power 1/y | rd = pow(rs1, 1/rs2) | ZftransAdv |
+FPOWN | x power of n (n int) | rd = pow(rs1, rs2) | ZftransAdv |
+FPOWR | x power of y (x +ve) | rd = exp(rs1 log(rs2)) | ZftransAdv |
+FROOTN | x power 1/n (n integer)| rd = pow(rs1, 1/rs2) | ZftransAdv |
FHYPOT | hypotenuse | rd = sqrt(rs1^2 + rs2^2) | ZftransAdv |
"""]]
FATAN | arctan (radians) | rd = atan(rs1) | Zarctrignpi |
FSINPI | sin times pi | rd = sin(pi * rs1) | Ztrigpi |
FCOSPI | cos times pi | rd = cos(pi * rs1) | Ztrigpi |
-
FTANPI | tan times pi | rd = tan(pi * rs1) | Ztrigpi |
FASINPI | arcsin / pi | rd = asin(rs1) / pi | Zarctrigpi |
FACOSPI | arccos / pi | rd = acos(rs1) / pi | Zarctrigpi |
F3 - fsqrt (square root)
F4 - fexp2 (2^x)
F5 - flog2
- F6 - fsin
- F7 - fcos
+ F6 - fsin1pi
+ F7 - fcos1pi
F9 - fatan_pt1
These in FP32 and FP16 only: no FP32 hardware, at all.
AMD's R600 GPU (R600\_Instruction\_Set\_Architecture.pdf) and the
RDNA ISA (RDNA\_Shader\_ISA\_5August2019.pdf, Table 22, Section 6.3) have:
- COS (appx)
+ COS2PI (appx)
EXP2
LOG (IEEE754)
RECIP
RSQRT
SQRT
- SIN (appx)
+ SIN2PI (appx)
AMD RDNA has F16 and F32 variants of all the above, and also has F64
variants of SQRT, RSQRT and RECIP. It is interesting that even the
### Zfhyp
-These are the hyperbolic/inverse-hyperbolic finctions: SINH, COSH, TANH,
-ASINH, ACOSH, ATANH. Their use in 3D is limited.
+SINH, COSH, TANH, ASINH, ACOSH, ATANH
+
+These are the hyperbolic/inverse-hyperbolic functions. Their use in 3D is limited.
They can all be synthesised using LOG, SQRT and so on, so depend
on Zftrans. However, once again, at the limits of the range, IEEE754
HPC and high-end GPUs are likely markets for these.
-## ZftransAdv
+### ZftransAdv
-CBRT, POW, ROOT (inverse of POW): these are simply much more complex
-to implement in hardware, and typically will only be put into HPC
-applications.
+CBRT, POW, POWN, POWR, ROOTN
-ROOT is included as well as POW because at the extreme ranges one is
-more accurate than the other.
+These are simply much more complex to implement in hardware, and typically
+will only be put into HPC applications.
* **Zfrsqrt**: Reciprocal square-root.
### Ztrigpi vs Ztrignpi
-* **Ztrigpi**: SINPI COSPI TANPI * **Ztrignpi**: SIN COS TAN
+* **Ztrigpi**: SINPI COSPI TANPI
+* **Ztrignpi**: SIN COS TAN
Ztrignpi are the basic trigonometric functions through which all others
could be synthesised, and they are typically the base trigonometrics
provided by GPUs for 3D, warranting their own subset.
-However as can be correspondingly seen from other sections, there is an
-accuracy penalty for doing so which will not be acceptable for IEEE754
-compliance.
-
In the case of the Ztrigpi subset, these are commonly used in for loops
with a power of two number of subdivisions, and the cost of multiplying
by PI inside each loop (or cumulative addition, resulting in cumulative
In for example CORDIC the multiplication by PI may be moved outside of
the hardware algorithm as a loop invariant, with no power or area penalty.
-Thus again, the same general argument applies to give Ztrignpi and
-Ztrigpi as subsets.
+Again, therefore, if SINPI (etc.) were excluded, programmers would be penalised by being forced to divide by PI in some circumstances. Likewise if SIN were excluded, programmers would be penaslised by being forced to *multiply* by PI in some circumstances.
+
+Thus again, a slightly different application of the same general argument applies to give Ztrignpi and
+Ztrigpi as subsets. 3D GPUs will almost certainly provide both.
### Zarctrigpi and Zarctrignpi
-* **Zarctrigpi**: ATAN2PI ASINPI ACOSPI * **Zarctrignpi**: ATAN2 ACOS ADIN
+* **Zarctrigpi**: ATAN2PI ASINPI ACOSPI
+* **Zarctrignpi**: ATAN2 ACOS ASIN
These are extra trigonometric functions that are useful in some
applications, but even for 3D GPUs, particularly embedded and mobile class
projects / libreriscv.git / blobdiff