1 # Zftrans - transcendental operations
5 * <http://bugs.libre-riscv.org/show_bug.cgi?id=127>
6 * <https://www.khronos.org/registry/spir-v/specs/unified1/OpenCL.ExtendedInstructionSet.100.html>
7 * Discussion: <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002342.html>
8 * [[rv_major_opcode_1010011]] for opcode listing.
9 * [[zfpacc_proposal]] for accuracy settings proposal
13 * **Zftrans**: standard transcendentals (best suited to 3D)
14 * **ZftransExt**: extra functions (useful, not generally needed for 3D,
15 can be synthesised using Ztrans)
16 * **Ztrigpi**: trig. xxx-pi sinpi cospi tanpi
17 * **Ztrignpi**: trig non-xxx-pi sin cos tan
18 * **Zarctrigpi**: arc-trig. a-xxx-pi: atan2pi asinpi acospi
19 * **Zarctrignpi**: arc-trig. non-a-xxx-pi: atan2, asin, acos
20 * **Zfhyp**: hyperbolic/inverse-hyperbolic. sinh, cosh, tanh, asinh,
21 acosh, atanh (can be synthesised - see below)
22 * **ZftransAdv**: much more complex to implement in hardware
23 * **Zfrsqrt**: Reciprocal square-root.
25 Minimum recommended requirements for 3D: Zftrans, Ztrigpi, Zarctrigpi,
32 * Decision on accuracy, moved to [[zfpacc_proposal]]
33 <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002355.html>
34 * Errors **MUST** be repeatable.
35 * How about four Platform Specifications? 3DUNIX, UNIX, 3DEmbedded and Embedded?
36 <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002361.html>
37 Accuracy requirements for dual (triple) purpose implementations must
38 meet the higher standard.
39 * Reciprocal Square-root is in its own separate extension (Zfrsqrt) as
40 it is desirable on its own by other implementors. This to be evaluated.
42 # Proposed Opcodes vs Khronos OpenCL Opcodes <a name="khronos_equiv"></a>
44 This list shows the (direct) equivalence between proposed opcodes and
45 their Khronos OpenCL equivalents.
48 <https://www.khronos.org/registry/spir-v/specs/unified1/OpenCL.ExtendedInstructionSet.100.html>
50 Special FP16 opcodes are *not* being proposed, except by indirect / inherent
51 use of the "fmt" field that is already present in the RISC-V Specification.
53 "Native" opcodes are *not* being proposed: implementors will be expected
54 to use the (equivalent) proposed opcode covering the same function.
56 "Fast" opcodes are *not* being proposed, because the Khronos Specification
57 fast\_length, fast\_normalise and fast\_distance OpenCL opcodes require
58 vectors (or can be done as scalar operations using other RISC-V instructions).
60 The OpenCL FP32 opcodes are **direct** equivalents to the proposed opcodes.
61 Deviation from conformance with the Khronos Specification - including the
62 Khronos Specification accuracy requirements - is not an option.
65 Proposed opcode | OpenCL FP32 | OpenCL FP16 | OpenCL native | OpenCL fast |
66 FSIN | sin | half\_sin | native\_sin | NONE |
67 FCOS | cos | half\_cos | native\_cos | NONE |
68 FTAN | tan | half\_tan | native\_tan | NONE |
69 FASIN | asin | NONE | NONE | NONE |
70 FACOS | acos | NONE | NONE | NONE |
71 FSINPI | sinpi | NONE | NONE | NONE |
72 FCOSPI | cospi | NONE | NONE | NONE |
73 FTANPI | tanpi | NONE | NONE | NONE |
74 FASINPI | asinpi | NONE | NONE | NONE |
75 FACOSPI | acospi | NONE | NONE | NONE |
76 FATANPI | atanpi | NONE | NONE | NONE |
77 FSINH | sinh | NONE | NONE | NONE |
78 FCOSH | cosh | NONE | NONE | NONE |
79 FTANH | tanh | NONE | NONE | NONE |
80 FASINH | asinh | NONE | NONE | NONE |
81 FACOSH | acosh | NONE | NONE | NONE |
82 FATANH | atanh | NONE | NONE | NONE |
83 FRSQRT | rsqrt | half\_rsqrt | native\_rsqrt | NONE |
84 FCBRT | cbrt | NONE | NONE | NONE |
85 FEXP2 | exp2 | half\_exp2 | native\_exp2 | NONE |
86 FLOG2 | log2 | half\_log2 | native\_log2 | NONE |
87 FEXPM1 (1) | expm1 | NONE | NONE | NONE |
88 FLOG1P (1) | log1p | NONE | NONE | NONE |
89 FEXP (1) | exp | half\_exp | native\_exp | NONE |
90 FLOG (1) | log | half\_log | native\_log | NONE |
91 FEXP10 | exp10 | half\_exp10 | native\_exp10 | NONE |
92 FLOG10 | log10 | half\_log10 | native\_log10 | NONE |
93 FATAN2 | atan2 | NONE | NONE | NONE |
94 FATAN2PI | atan2pi | NONE | NONE | NONE |
95 FPOW | pow | NONE | NONE | NONE |
96 FROOT | rootn | NONE | NONE | NONE |
97 FHYPOT | hypot | NONE | NONE | NONE |
100 Note (1): See "synthesis", below. FEXPM1, FEXP and FLOG1P, FLOG, may
101 be synthesised in terms of the other. FEXPM1 and FLOG1P are more accurate.
102 It is likely therefore that FLOG and FEXP will be removed.
104 # List of 2-arg opcodes
107 opcode | Description | pseudo-code | Extension |
108 FATAN2 | atan2 arc tangent | rd = atan2(rs2, rs1) | Zarctrignpi |
109 FATAN2PI | atan arc tangent / pi | rd = atan2(rs2, rs1) / pi | Zarctrigpi |
110 FPOW | x power of y | rd = pow(rs1, rs2) | ZftransAdv |
111 FROOT | x power 1/y | rd = pow(rs1, 1/rs2) | ZftransAdv |
112 FHYPOT | hypotenuse | rd = sqrt(rs1^2 + rs2^2) | Zftrans |
115 # List of 1-arg transcendental opcodes
118 opcode | Description | pseudo-code | Extension |
119 FRSQRT | Reciprocal Square-root | rd = sqrt(rs1) | Zfrsqrt |
120 FCBRT | Cube Root | rd = pow(rs1, 3) | Zftrans |
121 FEXP2 | power-of-2 | rd = pow(2, rs1) | Zftrans |
122 FLOG2 | log2 | rd = log2(rs1) | Zftrans |
123 FEXPM1 | exponent minus 1 | rd = pow(e, rs1) - 1.0 | Zftrans |
124 FLOG1P | log plus 1 | rd = log(e, 1 + rs1) | Zftrans |
125 FEXP | exponent | rd = pow(e, rs1) | ZftransExt |
126 FLOG | natural log (base e) | rd = log(e, rs1) | ZftransExt |
127 FEXP10 | power-of-10 | rd = pow(10, rs1) | ZftransExt |
128 FLOG10 | log base 10 | rd = log10(rs1) | ZftransExt |
131 # List of 1-arg trigonometric opcodes
134 opcode | Description | pseudo-code | Extension |
135 FSIN | sin (radians) | rd = sin(rs1) | Ztrignpi |
136 FCOS | cos (radians) | rd = cos(rs1) | Ztrignpi |
137 FTAN | tan (radians) | rd = tan(rs1) | Ztrignpi |
138 FASIN | arcsin (radians) | rd = asin(rs1) | Zarctrignpi |
139 FACOS | arccos (radians) | rd = acos(rs1) | Zarctrignpi |
140 FSINPI | sin times pi | rd = sin(pi * rs1) | Ztrigpi |
141 FCOSPI | cos times pi | rd = cos(pi * rs1) | Ztrigpi |
142 FTANPI | tan times pi | rd = tan(pi * rs1) | Ztrigpi |
143 FASINPI | arcsin times pi | rd = asin(pi * rs1) | Zarctrigpi |
144 FACOSPI | arccos times pi | rd = acos(pi * rs1) | Zarctrigpi |
145 FATANPI | arctan times pi | rd = atan(pi * rs1) | Zarctrigpi |
146 FSINH | hyperbolic sin (radians) | rd = sinh(rs1) | Zfhyp |
147 FCOSH | hyperbolic cos (radians) | rd = cosh(rs1) | Zfhyp |
148 FTANH | hyperbolic tan (radians) | rd = tanh(rs1) | Zfhyp |
149 FASINH | inverse hyperbolic sin | rd = asinh(rs1) | Zfhyp |
150 FACOSH | inverse hyperbolic cos | rd = acosh(rs1) | Zfhyp |
151 FATANH | inverse hyperbolic tan | rd = atanh(rs1) | Zfhyp |
154 # Synthesis, Pseudo-code ops and macro-ops
156 The pseudo-ops are best left up to the compiler rather than being actual
157 pseudo-ops, by allocating one scalar FP register for use as a constant
158 (loop invariant) set to "1.0" at the beginning of a function or other
161 * FRCP rd, rs1 - pseudo-code alias for rd = 1.0 / rs1
162 * FATAN - pseudo-code alias for rd = atan2(rs1, 1.0) - FATAN2
163 * FATANPI - pseudo alias for rd = atan2pi(rs1, 1.0) - FATAN2PI
164 * FSINCOS - fused macro-op between FSIN and FCOS (issued in that order).
165 * FSINCOSPI - fused macro-op between FSINPI and FCOSPI (issued in that order).
167 FATANPI example pseudo-code:
169 lui t0, 0x3F800 // upper bits of f32 1.0
171 fatan2pi.s rd, rs1, ft0
173 Hypotenuse example (obviates need for Zfhyp except for high-performance):
175 ASINH( x ) = ln( x + SQRT(x**2+1)
179 LOG(x) = LOGP1(x) + 1.0
180 EXP(x) = EXPM1(x-1.0)
182 # To evaluate: should LOG be replaced with LOG1P (and EXP with EXPM1)?
184 RISC principle says "exclude LOG because it's covered by LOGP1 plus an ADD".
185 Research needed to ensure that implementors are not compromised by such
187 <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002358.html>