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
  43 # List of 2-arg opcodes
  44
  45 [[!table  data="""
  46 opcode    | Description           | pseudo-code                | Extension |
  47 FATAN2    | atan2 arc tangent     | rd = atan2(rs2, rs1)       | Zarctrignpi |
  48 FATAN2PI  | atan arc tangent / pi | rd = atan2(rs2, rs1) / pi  | Zarctrigpi |
  49 FPOW      | x power of y          | rd = pow(rs1, rs2)         | ZftransAdv |
  50 FROOT     | x power 1/y           | rd = pow(rs1, 1/rs2)       | ZftransAdv |
  51 FHYPOT    | hypotenuse            | rd = sqrt(rs1^2 + rs2^2)       | Zftrans    |
  52 """]]
  53
  54 # List of 1-arg transcendental opcodes
  55
  56 [[!table  data="""
  57 opcode   | Description              | pseudo-code             | Extension |
  58 FRSQRT   | Reciprocal Square-root   | rd = sqrt(rs1)          | Zfrsqrt    |
  59 FCBRT    | Cube Root                | rd = pow(rs1, 3)        | Zftrans    |
  60 FEXP2    | power-of-2               | rd = pow(2, rs1)        | Zftrans    |
  61 FLOG2    | log2                     | rd = log2(rs1)          | Zftrans    |
  62 FEXPM1   | exponent minus 1         | rd = pow(e, rs1) - 1.0  | Zftrans    |
  63 FLOG1P   | log plus 1               | rd = log(e, 1 + rs1)    | Zftrans    |
  64 FEXP     | exponent                 | rd = pow(e, rs1)        | ZftransExt |
  65 FLOG     | natural log (base e)     | rd = log(e, rs1)        | ZftransExt |
  66 FEXP10   | power-of-10              | rd = pow(10, rs1)       | ZftransExt |
  67 FLOG10   | log base 10              | rd = log10(rs1)         | ZftransExt |
  68 """]]
  69
  70 # List of 1-arg trigonometric opcodes
  71
  72 [[!table  data="""
  73 opcode   | Description              | pseudo-code             | Extension |
  74 FSIN     | sin (radians)            | rd = sin(rs1)           | Ztrignpi    |
  75 FCOS     | cos (radians)            | rd = cos(rs1)           | Ztrignpi    |
  76 FTAN     | tan (radians)            | rd = tan(rs1)           | Ztrignpi    |
  77 FASIN    | arcsin (radians)         | rd = asin(rs1)          | Zarctrignpi |
  78 FACOS    | arccos (radians)         | rd = acos(rs1)          | Zarctrignpi |
  79 FSINPI   | sin times pi             | rd = sin(pi * rs1)      | Ztrigpi |
  80 FCOSPI   | cos times pi             | rd = cos(pi * rs1)      | Ztrigpi |
  81 FTANPI   | tan times pi             | rd = tan(pi * rs1)      | Ztrigpi |
  82 FASINPI  | arcsin times pi          | rd = asin(pi * rs1)     | Zarctrigpi |
  83 FACOSPI  | arccos times pi          | rd = acos(pi * rs1)     | Zarctrigpi |
  84 FATANPI  | arctan times pi          | rd = atan(pi * rs1)     | Zarctrigpi |
  85 FSINH    | hyperbolic sin (radians) | rd = sinh(rs1)          | Zfhyp |
  86 FCOSH    | hyperbolic cos (radians) | rd = cosh(rs1)          | Zfhyp |
  87 FTANH    | hyperbolic tan (radians) | rd = tanh(rs1)          | Zfhyp |
  88 FASINH   | inverse hyperbolic sin   | rd = asinh(rs1)         | Zfhyp |
  89 FACOSH   | inverse hyperbolic cos   | rd = acosh(rs1)         | Zfhyp |
  90 FATANH   | inverse hyperbolic tan   | rd = atanh(rs1)         | Zfhyp |
  91 """]]
  92
  93 # List of Our Proposed Functions vs Khronos OpenCL Functions
  94
  95 [[!table data="""
  96 Our proposed opcode | OpenCL FP32 | OpenCL FP16 | OpenCL native | OpenCL fast |
  97 FSIN                              | sin                   | half_sin           | native_sin         | NONE |
  98 FCOS                            | cos                  | half_cos          | native_cos        | NONE |
  99 FTAN                             | tan                  | half_tan           | native_tan        | NONE |
 100 FASIN                            | asin                 | NONE             | NONE               | NONE |
 101 FACOS                          | acos                | NONE              | NONE               | NONE |
 102 FSINPI                           | sinpi                | NONE              | NONE               | NONE |
 103 FCOSPI                         | cospi               | NONE              | NONE               | NONE |
 104 FTANPI                          | tanpi               | NONE              | NONE               | NONE |
 105 FASINPI                         | asinpi              | NONE              | NONE              | NONE |
 106 FACOSPI                       | acospi             | NONE              | NONE               | NONE |
 107 FATANPI                        | atanpi              | NONE             | NONE               | NONE |
 108 FSINH                            | sinh                 | NONE             | NONE               | NONE |
 109 FCOSH                          | cosh                | NONE             | NONE               | NONE |
 110 FTANH                           | tanh                | NONE             | NONE               | NONE |
 111 FASINH                          | asinh               | NONE             | NONE               | NONE |
 112 FACOSH                         | acosh             | NONE              | NONE              | NONE |
 113 FATANH                          | atanh              | NONE             | NONE               | NONE |
 114 FRSQRT                         | rsqrt                | half_rsqrt       | native_rsqrt      | NONE |
 115 FCBRT                            | cbrt                 | NONE            | NONE                | NONE |
 116 FEXP2                            | exp2                | half_exp2       | native_exp2      | NONE |
 117 FLOG2                            | log2                 | half_log2       | native_log2       | NONE |
 118 FEXPM1                         | expm1               | NONE            | NONE                | NONE |
 119 FLOG1P                          | log1p               | NONE             | NONE                | NONE |
 120 FEXP                              | exp                   | half_exp         | native_exp         | NONE |
 121 FLOG                              | log                   | half_log          | native_log          | NONE |
 122 FEXP10                          | exp10               | half_exp10      | native_exp10     | NONE |
 123 FLOG10                          | log10               | half_log10       | native_log10      | NONE |
 124 FATAN2                          | atan2               | NONE             | NONE                 | NONE |
 125 FATAN2PI                       | atan2pi            | NONE             | NONE                 | NONE |
 126 FPOW                             | pow                  | NONE             | NONE                | NONE |
 127 FROOT                            | rootn               | NONE             | NONE                 | NONE |
 128 FHYPOT                          | hypot              | NONE              | NONE                | NONE |
 129 """]]
 130
 131 # Synthesis, Pseudo-code ops and macro-ops
 132
 133 The pseudo-ops are best left up to the compiler rather than being actual
 134 pseudo-ops, by allocating one scalar FP register for use as a constant
 135 (loop invariant) set to "1.0" at the beginning of a function or other
 136 suitable code block.
 137
 138 * FRCP rd, rs1 - pseudo-code alias for rd = 1.0 / rs1
 139 * FATAN - pseudo-code alias for rd = atan2(rs1, 1.0) - FATAN2
 140 * FATANPI - pseudo alias for rd = atan2pi(rs1, 1.0) - FATAN2PI
 141 * FSINCOS - fused macro-op between FSIN and FCOS (issued in that order).
 142 * FSINCOSPI - fused macro-op between FSINPI and FCOSPI (issued in that order).
 143
 144 FATANPI example pseudo-code:
 145
 146     lui t0, 0x3F800 // upper bits of f32 1.0
 147     fmv.x.s ft0, t0
 148     fatan2pi.s rd, rs1, ft0
 149
 150 Hypotenuse example (obviates need for Zfhyp except for high-performance):
 151
 152     ASINH( x ) = ln( x + SQRT(x**2+1)
 153
 154 LOG / LOGP1 example:
 155
 156     LOG(x) = LOGP1(x) + 1.0
 157     EXP(x) = EXPM1(x-1.0)
 158
 159 # To evaluate: should LOG be replaced with LOG1P (and EXP with EXPM1)?
 160
 161 RISC principle says "exclude LOG because it's covered by LOGP1 plus an ADD".
 162 Research needed to ensure that implementors are not compromised by such
 163 a decision
 164 <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002358.html>
 165