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
  10 Extension subsets:
  11
  12 * **Zftrans**: standard transcendentals (best suited to 3D)
  13 * **ZftransExt**: extra functions (useful, not generally needed for 3D, can be synthesised using Ztrans)
  14 * **Ztrigpi**: trig. xxx-pi sinpi cospi tanpi
  15 * **Ztrignpi**: trig non-xxx-pi sin cos tan
  16 * **Zarctrigpi**: arc-trig. a-xxx-pi: atan2pi asinpi acospi
  17 * **Zarctrignpi**: arc-trig. non-a-xxx-pi: atan2, asin, acos
  18 * **Zfhyp**: hyperbolic/inverse-hyperbolic.  sinh, cosh, tanh, asinh, acosh, atanh
  19 * **ZftransAdv**: much more complex to implement in hardware
  20
  21 Minimum recommended requirements for 3D: Zftrans, Ztrigpi, Zarctrigpi,
  22 Zarctrignpi
  23
  24 [[!toc levels=2]]
  25
  26 # TODO:
  27
  28 * Decision on accuracy <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002355.html>
  29
  30 # List of 2-arg opcodes
  31
  32 [[!table  data="""
  33 opcode    | Description           | pseudo-code                | Extension |
  34 FATAN2    | atan2 arc tangent     | rd = atan2(rs2, rs1)       | Zarctrignpi |
  35 FATAN2PI  | atan arc tangent / pi | rd = atan2(rs2, rs1) / pi  | Zarctrigpi |
  36 FPOW      | x power of y          | rd = pow(rs1, rs2)         | ZftransAdv |
  37 FROOT     | x power 1/y           | rd = pow(rs1, 1/rs2)       | ZftransAdv |
  38 FHYPOT    | hypotenuse            | rd = sqrt(rs1^2 + rs2^2)       | Zftrans    |
  39 """]]
  40
  41 # List of 1-arg transcendental opcodes
  42
  43 [[!table  data="""
  44 opcode   | Description              | pseudo-code             | Extension |
  45 FCBRT    | Cube Root                | rd = pow(rs1, 3)        | Zftrans    |
  46 FEXP2    | power-of-2               | rd = pow(2, rs1)        | Zftrans    |
  47 FLOG2    | log2                     | rd = log2(rs1)          | Zftrans    |
  48 FEXPM1   | exponent minus 1         | rd = pow(e, rs1) - 1.0  | Zftrans    |
  49 FLOG1P   | log plus 1               | rd = log(e, 1 + rs1)    | Zftrans    |
  50 FEXP     | exponent                 | rd = pow(e, rs1)        | ZftransExt |
  51 FLOG     | natural log (base e)     | rd = log(e, rs1)        | ZftransExt |
  52 FEXP10   | power-of-10              | rd = pow(10, rs1)       | ZftransExt |
  53 FLOG10   | log base 10              | rd = log10(rs1)         | ZftransExt |
  54 """]]
  55
  56 # List of 1-arg trigonometric opcodes
  57
  58 [[!table  data="""
  59 opcode   | Description              | pseudo-code             | Extension |
  60 FSIN     | sin (radians)            | rd = sin(rs1)           | Ztrignpi    |
  61 FCOS     | cos (radians)            | rd = cos(rs1)           | Ztrignpi    |
  62 FTAN     | tan (radians)            | rd = tan(rs1)           | Ztrignpi    |
  63 FASIN    | arcsin (radians)         | rd = asin(rs1)          | Zarctrignpi |
  64 FACOS    | arccos (radians)         | rd = acos(rs1)          | Zarctrignpi |
  65 FSINPI   | sin times pi             | rd = sin(pi * rs1)      | Ztrigpi |
  66 FCOSPI   | cos times pi             | rd = cos(pi * rs1)      | Ztrigpi |
  67 FTANPI   | tan times pi             | rd = tan(pi * rs1)      | Ztrigpi |
  68 FASINPI  | arcsin times pi          | rd = asin(pi * rs1)     | Zarctrigpi |
  69 FACOSPI  | arccos times pi          | rd = acos(pi * rs1)     | Zarctrigpi |
  70 FATANPI  | arctan times pi          | rd = atan(pi * rs1)     | Zarctrigpi |
  71 FSINH    | hyperbolic sin (radians) | rd = sinh(rs1)          | Zfhyp |
  72 FCOSH    | hyperbolic cos (radians) | rd = cosh(rs1)          | Zfhyp |
  73 FTANH    | hyperbolic tan (radians) | rd = tanh(rs1)          | Zfhyp |
  74 FASINH   | inverse hyperbolic sin   | rd = asinh(rs1)         | Zfhyp |
  75 FACOSH   | inverse hyperbolic cos   | rd = acosh(rs1)         | Zfhyp |
  76 FATANH   | inverse hyperbolic tan   | rd = atanh(rs1)         | Zfhyp |
  77 """]]
  78
  79 # Pseudo-code ops and macro-ops
  80
  81 The pseudo-ops are best left up to the compiler rather than being actual
  82 pseudo-ops, by allocating one scalar FP register for use as a constant
  83 (loop invariant) set to "1.0" at the beginning of a function or other
  84 suitable code block.
  85
  86 * FRCP rd, rs1 - pseudo-code alias for rd = 1.0 / rs1
  87 * FATAN - pseudo-code alias for rd = atan2(rs1, 1.0) - FATAN2
  88 * FATANPI - pseudo alias for rd = atan2pi(rs1, 1.0) - FATAN2PI
  89 * FSINCOS - fused macro-op between FSIN and FCOS (issued in that order).
  90 * FSINCOSPI - fused macro-op between FSINPI and FCOSPI (issued in that order).
  91
  92 FATANPI example pseudo-code:
  93
  94     lui t0, 0x3F800 // upper bits of f32 1.0
  95     fmv.x.s ft0, t0
  96     fatan2pi.s rd, rs1, ft0
  97
  98 Hypotenuse example (obviates need for Zfhyp except for high-performance):
  99
 100     ASINH( x ) = ln( x + SQRT(x**2+1)
 101
 102 # To evaluate: should LOG be replaced with LOG1P (and EXP with EXPM1)?
 103
 104     LOG(x) = LOGP1(x) + 1.0
 105     EXP(x) = EXPM1(x-1.0)
 106
 107 RISC principle says "exclude LOG because it's covered by LOGP1 plus an ADD".
 108 Research needed to ensure that implementors are not compromised by such
 109 a decision
 110 <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002358.html>