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,
  14   can be synthesised using Ztrans)
  15 * **Ztrigpi**: trig. xxx-pi sinpi cospi tanpi
  16 * **Ztrignpi**: trig non-xxx-pi sin cos tan
  17 * **Zarctrigpi**: arc-trig. a-xxx-pi: atan2pi asinpi acospi
  18 * **Zarctrignpi**: arc-trig. non-a-xxx-pi: atan2, asin, acos
  19 * **Zfhyp**: hyperbolic/inverse-hyperbolic.  sinh, cosh, tanh, asinh,
  20   acosh, atanh (can be synthesised - see below)
  21 * **ZftransAdv**: much more complex to implement in hardware
  22
  23 Minimum recommended requirements for 3D: Zftrans, Ztrigpi, Zarctrigpi,
  24 Zarctrignpi
  25
  26 [[!toc levels=2]]
  27
  28 # TODO:
  29
  30 * Decision on accuracy
  31 <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002355.html>
  32 * Errors **MUST** be repeatable.
  33 * How about three Platform Specifications? 3D, UNIX and Embedded?
  34 <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002361.html>
  35
  36 # List of 2-arg opcodes
  37
  38 [[!table  data="""
  39 opcode    | Description           | pseudo-code                | Extension |
  40 FATAN2    | atan2 arc tangent     | rd = atan2(rs2, rs1)       | Zarctrignpi |
  41 FATAN2PI  | atan arc tangent / pi | rd = atan2(rs2, rs1) / pi  | Zarctrigpi |
  42 FPOW      | x power of y          | rd = pow(rs1, rs2)         | ZftransAdv |
  43 FROOT     | x power 1/y           | rd = pow(rs1, 1/rs2)       | ZftransAdv |
  44 FHYPOT    | hypotenuse            | rd = sqrt(rs1^2 + rs2^2)       | Zftrans    |
  45 """]]
  46
  47 # List of 1-arg transcendental opcodes
  48
  49 [[!table  data="""
  50 opcode   | Description              | pseudo-code             | Extension |
  51 FCBRT    | Cube Root                | rd = pow(rs1, 3)        | Zftrans    |
  52 FEXP2    | power-of-2               | rd = pow(2, rs1)        | Zftrans    |
  53 FLOG2    | log2                     | rd = log2(rs1)          | Zftrans    |
  54 FEXPM1   | exponent minus 1         | rd = pow(e, rs1) - 1.0  | Zftrans    |
  55 FLOG1P   | log plus 1               | rd = log(e, 1 + rs1)    | Zftrans    |
  56 FEXP     | exponent                 | rd = pow(e, rs1)        | ZftransExt |
  57 FLOG     | natural log (base e)     | rd = log(e, rs1)        | ZftransExt |
  58 FEXP10   | power-of-10              | rd = pow(10, rs1)       | ZftransExt |
  59 FLOG10   | log base 10              | rd = log10(rs1)         | ZftransExt |
  60 """]]
  61
  62 # List of 1-arg trigonometric opcodes
  63
  64 [[!table  data="""
  65 opcode   | Description              | pseudo-code             | Extension |
  66 FSIN     | sin (radians)            | rd = sin(rs1)           | Ztrignpi    |
  67 FCOS     | cos (radians)            | rd = cos(rs1)           | Ztrignpi    |
  68 FTAN     | tan (radians)            | rd = tan(rs1)           | Ztrignpi    |
  69 FASIN    | arcsin (radians)         | rd = asin(rs1)          | Zarctrignpi |
  70 FACOS    | arccos (radians)         | rd = acos(rs1)          | Zarctrignpi |
  71 FSINPI   | sin times pi             | rd = sin(pi * rs1)      | Ztrigpi |
  72 FCOSPI   | cos times pi             | rd = cos(pi * rs1)      | Ztrigpi |
  73 FTANPI   | tan times pi             | rd = tan(pi * rs1)      | Ztrigpi |
  74 FASINPI  | arcsin times pi          | rd = asin(pi * rs1)     | Zarctrigpi |
  75 FACOSPI  | arccos times pi          | rd = acos(pi * rs1)     | Zarctrigpi |
  76 FATANPI  | arctan times pi          | rd = atan(pi * rs1)     | Zarctrigpi |
  77 FSINH    | hyperbolic sin (radians) | rd = sinh(rs1)          | Zfhyp |
  78 FCOSH    | hyperbolic cos (radians) | rd = cosh(rs1)          | Zfhyp |
  79 FTANH    | hyperbolic tan (radians) | rd = tanh(rs1)          | Zfhyp |
  80 FASINH   | inverse hyperbolic sin   | rd = asinh(rs1)         | Zfhyp |
  81 FACOSH   | inverse hyperbolic cos   | rd = acosh(rs1)         | Zfhyp |
  82 FATANH   | inverse hyperbolic tan   | rd = atanh(rs1)         | Zfhyp |
  83 """]]
  84
  85 # Synthesis, Pseudo-code ops and macro-ops
  86
  87 The pseudo-ops are best left up to the compiler rather than being actual
  88 pseudo-ops, by allocating one scalar FP register for use as a constant
  89 (loop invariant) set to "1.0" at the beginning of a function or other
  90 suitable code block.
  91
  92 * FRCP rd, rs1 - pseudo-code alias for rd = 1.0 / rs1
  93 * FATAN - pseudo-code alias for rd = atan2(rs1, 1.0) - FATAN2
  94 * FATANPI - pseudo alias for rd = atan2pi(rs1, 1.0) - FATAN2PI
  95 * FSINCOS - fused macro-op between FSIN and FCOS (issued in that order).
  96 * FSINCOSPI - fused macro-op between FSINPI and FCOSPI (issued in that order).
  97
  98 FATANPI example pseudo-code:
  99
 100     lui t0, 0x3F800 // upper bits of f32 1.0
 101     fmv.x.s ft0, t0
 102     fatan2pi.s rd, rs1, ft0
 103
 104 Hypotenuse example (obviates need for Zfhyp except for high-performance):
 105
 106     ASINH( x ) = ln( x + SQRT(x**2+1)
 107
 108 LOG / LOGP1 example:
 109
 110     LOG(x) = LOGP1(x) + 1.0
 111     EXP(x) = EXPM1(x-1.0)
 112
 113 # To evaluate: should LOG be replaced with LOG1P (and EXP with EXPM1)?
 114
 115 RISC principle says "exclude LOG because it's covered by LOGP1 plus an ADD".
 116 Research needed to ensure that implementors are not compromised by such
 117 a decision
 118 <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002358.html>