ztrans_proposal.mdwn

   1 # Zftrans - transcendental operations
   2
   3 See:
   4
   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
  10
  11 Extension subsets:
  12
  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.
  24
  25 Minimum recommended requirements for 3D: Zftrans, Ztrigpi, Zarctrigpi,
  26 Zarctrignpi
  27
  28 [[!toc levels=2]]
  29
  30 # TODO:
  31
  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.
  41
  42 # Proposed Opcodes vs Khronos OpenCL Opcodes <a name="khronos_equiv"></a>
  43
  44 This list shows the (direct) equivalence between proposed opcodes and
  45 their Khronos OpenCL equivalents.
  46
  47 See
  48 <https://www.khronos.org/registry/spir-v/specs/unified1/OpenCL.ExtendedInstructionSet.100.html>
  49
  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.
  52
  53 "Native" opcodes are *not* being proposed: implementors will be expected
  54 to use the (equivalent) proposed opcode covering the same function.
  55
  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).
  59
  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.
  63
  64 [[!table data="""
  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 NONE (3)        | atan        | NONE        | NONE          | NONE        |
  72 FSINPI          | sinpi       | NONE        | NONE          | NONE        |
  73 FCOSPI          | cospi       | NONE        | NONE          | NONE        |
  74 FTANPI          | tanpi       | NONE        | NONE          | NONE        |
  75 FASINPI         | asinpi      | NONE        | NONE          | NONE        |
  76 FACOSPI         | acospi      | NONE        | NONE          | NONE        |
  77 NONE (2)        | atanpi      | NONE        | NONE          | NONE        |
  78 FSINH           | sinh        | NONE        | NONE          | NONE        |
  79 FCOSH           | cosh        | NONE        | NONE          | NONE        |
  80 FTANH           | tanh        | NONE        | NONE          | NONE        |
  81 FASINH          | asinh       | NONE        | NONE          | NONE        |
  82 FACOSH          | acosh       | NONE        | NONE          | NONE        |
  83 FATANH          | atanh       | NONE        | NONE          | NONE        |
  84 FRSQRT          | rsqrt       | half\_rsqrt | native\_rsqrt | NONE        |
  85 FCBRT           | cbrt        | NONE        | NONE          | NONE        |
  86 FEXP2           | exp2        | half\_exp2  | native\_exp2  | NONE        |
  87 FLOG2           | log2        | half\_log2  | native\_log2  | NONE        |
  88 FEXPM1          | expm1       | NONE        | NONE          | NONE        |
  89 FLOG1P          | log1p       | NONE        | NONE          | NONE        |
  90 FEXP            | exp         | half\_exp   | native\_exp   | NONE        |
  91 FLOG            | log         | half\_log   | native\_log   | NONE        |
  92 FEXP10          | exp10       | half\_exp10 | native\_exp10 | NONE        |
  93 FLOG10          | log10       | half\_log10 | native\_log10 | NONE        |
  94 FATAN2          | atan2       | NONE        | NONE          | NONE        |
  95 FATAN2PI        | atan2pi     | NONE        | NONE          | NONE        |
  96 FPOW            | pow         | NONE        | NONE          | NONE        |
  97 FROOT           | rootn       | NONE        | NONE          | NONE        |
  98 FHYPOT          | hypot       | NONE        | NONE          | NONE        |
  99 """]]
 100
 101 Note (2) FATANPI is a synthesised alias, below.
 102
 103 Note (3) FATAN2 is a sythesised alias, below.
 104
 105 # List of 2-arg opcodes
 106
 107 [[!table  data="""
 108 opcode    | Description            | pseudo-code                | Extension   |
 109 FATAN2    | atan2 arc tangent      | rd = atan2(rs2, rs1)       | Zarctrignpi |
 110 FATAN2PI  | atan2 arc tangent / pi | rd = atan2(rs2, rs1) / pi  | Zarctrigpi  |
 111 FPOW      | x power of y           | rd = pow(rs1, rs2)         | ZftransAdv  |
 112 FROOT     | x power 1/y            | rd = pow(rs1, 1/rs2)       | ZftransAdv  |
 113 FHYPOT    | hypotenuse             | rd = sqrt(rs1^2 + rs2^2)   | Zftrans     |
 114 """]]
 115
 116 # List of 1-arg transcendental opcodes
 117
 118 [[!table  data="""
 119 opcode   | Description              | pseudo-code             | Extension  |
 120 FRSQRT   | Reciprocal Square-root   | rd = sqrt(rs1)          | Zfrsqrt    |
 121 FCBRT    | Cube Root                | rd = pow(rs1, 3)        | Zftrans    |
 122 FEXP2    | power-of-2               | rd = pow(2, rs1)        | Zftrans    |
 123 FLOG2    | log2                     | rd = log2(rs1)          | Zftrans    |
 124 FEXPM1   | exponential minus 1      | rd = pow(e, rs1) - 1.0  | Zftrans    |
 125 FLOG1P   | log plus 1               | rd = log(e, 1 + rs1)    | Zftrans    |
 126 FEXP     | exponential              | rd = pow(e, rs1)        | ZftransExt |
 127 FLOG     | natural log (base e)     | rd = log(e, rs1)        | ZftransExt |
 128 FEXP10   | power-of-10              | rd = pow(10, rs1)       | ZftransExt |
 129 FLOG10   | log base 10              | rd = log10(rs1)         | ZftransExt |
 130 """]]
 131
 132 # List of 1-arg trigonometric opcodes
 133
 134 [[!table  data="""
 135 opcode   | Description              | pseudo-code             | Extension |
 136 FSIN     | sin (radians)            | rd = sin(rs1)           | Ztrignpi    |
 137 FCOS     | cos (radians)            | rd = cos(rs1)           | Ztrignpi    |
 138 FTAN     | tan (radians)            | rd = tan(rs1)           | Ztrignpi    |
 139 FASIN    | arcsin (radians)         | rd = asin(rs1)          | Zarctrignpi |
 140 FACOS    | arccos (radians)         | rd = acos(rs1)          | Zarctrignpi |
 141 FSINPI   | sin times pi             | rd = sin(pi * rs1)      | Ztrigpi |
 142 FCOSPI   | cos times pi             | rd = cos(pi * rs1)      | Ztrigpi |
 143 FTANPI   | tan times pi             | rd = tan(pi * rs1)      | Ztrigpi |
 144 FASINPI  | arcsin / pi              | rd = asin(rs1) / pi     | Zarctrigpi |
 145 FACOSPI  | arccos / pi              | rd = acos(rs1) / pi     | Zarctrigpi |
 146 FATANPI  | arctan / pi              | rd = atan(rs1) / pi     | Zarctrigpi |
 147 FSINH    | hyperbolic sin (radians) | rd = sinh(rs1)          | Zfhyp |
 148 FCOSH    | hyperbolic cos (radians) | rd = cosh(rs1)          | Zfhyp |
 149 FTANH    | hyperbolic tan (radians) | rd = tanh(rs1)          | Zfhyp |
 150 FASINH   | inverse hyperbolic sin   | rd = asinh(rs1)         | Zfhyp |
 151 FACOSH   | inverse hyperbolic cos   | rd = acosh(rs1)         | Zfhyp |
 152 FATANH   | inverse hyperbolic tan   | rd = atanh(rs1)         | Zfhyp |
 153 """]]
 154
 155 # Synthesis, Pseudo-code ops and macro-ops
 156
 157 The pseudo-ops are best left up to the compiler rather than being actual
 158 pseudo-ops, by allocating one scalar FP register for use as a constant
 159 (loop invariant) set to "1.0" at the beginning of a function or other
 160 suitable code block.
 161
 162 * FRCP rd, rs1 - pseudo-code alias for rd = 1.0 / rs1
 163 * FATAN - pseudo-code alias for rd = atan2(rs1, 1.0) - FATAN2
 164 * FATANPI - pseudo alias for rd = atan2pi(rs1, 1.0) - FATAN2PI
 165 * FSINCOS - fused macro-op between FSIN and FCOS (issued in that order).
 166 * FSINCOSPI - fused macro-op between FSINPI and FCOSPI (issued in that order).
 167
 168 FATANPI example pseudo-code:
 169
 170     lui t0, 0x3F800 // upper bits of f32 1.0
 171     fmv.x.s ft0, t0
 172     fatan2pi.s rd, rs1, ft0
 173
 174 Hyperbolic function example (obviates need for Zfhyp except for high-performance or correctly-rounding):
 175
 176     ASINH( x ) = ln( x + SQRT(x**2+1))
 177
 178 LOG / LOGP1 example:
 179
 180     LOG(x) = LOGP1(x - 1.0)
 181     EXP(x) = EXPM1(x) + 1.0
 182
 183 # To evaluate: should LOG be replaced with LOG1P (and EXP with EXPM1)?
 184
 185 RISC principle says "exclude LOG because it's covered by LOGP1 plus an ADD".
 186 Research needed to ensure that implementors are not compromised by such
 187 a decision
 188 <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002358.html>
 189
 190 correctly-rounded LOG will return different results than LOGP1 and ADD.
 191 Likewise for EXP and EXPM1
 192