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 * **Zfrsqrt**: Reciprocal square-root.
  23
  24 Minimum recommended requirements for 3D: Zftrans, Ztrigpi, Zarctrigpi,
  25 Zarctrignpi
  26
  27 [[!toc levels=2]]
  28
  29 # TODO:
  30
  31 * Decision on accuracy
  32 <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002355.html>
  33 * Errors **MUST** be repeatable.
  34 * How about three Platform Specifications? 3D, UNIX and Embedded?
  35 <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002361.html>
  36 * Reciprocal Square-root is in its own separate extension (Zfrsqrt) as
  37   it is desirable on its own by other implementors.  This to be evaluated.
  38
  39
  40 # List of 2-arg opcodes
  41
  42 [[!table  data="""
  43 opcode    | Description           | pseudo-code                | Extension |
  44 FATAN2    | atan2 arc tangent     | rd = atan2(rs2, rs1)       | Zarctrignpi |
  45 FATAN2PI  | atan arc tangent / pi | rd = atan2(rs2, rs1) / pi  | Zarctrigpi |
  46 FPOW      | x power of y          | rd = pow(rs1, rs2)         | ZftransAdv |
  47 FROOT     | x power 1/y           | rd = pow(rs1, 1/rs2)       | ZftransAdv |
  48 FHYPOT    | hypotenuse            | rd = sqrt(rs1^2 + rs2^2)       | Zftrans    |
  49 """]]
  50
  51 # List of 1-arg transcendental opcodes
  52
  53 [[!table  data="""
  54 opcode   | Description              | pseudo-code             | Extension |
  55 FRSQRT   | Reciprocal Square-root   | rd = sqrt(rs1)          | Zfrsqrt    |
  56 FCBRT    | Cube Root                | rd = pow(rs1, 3)        | Zftrans    |
  57 FEXP2    | power-of-2               | rd = pow(2, rs1)        | Zftrans    |
  58 FLOG2    | log2                     | rd = log2(rs1)          | Zftrans    |
  59 FEXPM1   | exponent minus 1         | rd = pow(e, rs1) - 1.0  | Zftrans    |
  60 FLOG1P   | log plus 1               | rd = log(e, 1 + rs1)    | Zftrans    |
  61 FEXP     | exponent                 | rd = pow(e, rs1)        | ZftransExt |
  62 FLOG     | natural log (base e)     | rd = log(e, rs1)        | ZftransExt |
  63 FEXP10   | power-of-10              | rd = pow(10, rs1)       | ZftransExt |
  64 FLOG10   | log base 10              | rd = log10(rs1)         | ZftransExt |
  65 """]]
  66
  67 # List of 1-arg trigonometric opcodes
  68
  69 [[!table  data="""
  70 opcode   | Description              | pseudo-code             | Extension |
  71 FSIN     | sin (radians)            | rd = sin(rs1)           | Ztrignpi    |
  72 FCOS     | cos (radians)            | rd = cos(rs1)           | Ztrignpi    |
  73 FTAN     | tan (radians)            | rd = tan(rs1)           | Ztrignpi    |
  74 FASIN    | arcsin (radians)         | rd = asin(rs1)          | Zarctrignpi |
  75 FACOS    | arccos (radians)         | rd = acos(rs1)          | Zarctrignpi |
  76 FSINPI   | sin times pi             | rd = sin(pi * rs1)      | Ztrigpi |
  77 FCOSPI   | cos times pi             | rd = cos(pi * rs1)      | Ztrigpi |
  78 FTANPI   | tan times pi             | rd = tan(pi * rs1)      | Ztrigpi |
  79 FASINPI  | arcsin times pi          | rd = asin(pi * rs1)     | Zarctrigpi |
  80 FACOSPI  | arccos times pi          | rd = acos(pi * rs1)     | Zarctrigpi |
  81 FATANPI  | arctan times pi          | rd = atan(pi * rs1)     | Zarctrigpi |
  82 FSINH    | hyperbolic sin (radians) | rd = sinh(rs1)          | Zfhyp |
  83 FCOSH    | hyperbolic cos (radians) | rd = cosh(rs1)          | Zfhyp |
  84 FTANH    | hyperbolic tan (radians) | rd = tanh(rs1)          | Zfhyp |
  85 FASINH   | inverse hyperbolic sin   | rd = asinh(rs1)         | Zfhyp |
  86 FACOSH   | inverse hyperbolic cos   | rd = acosh(rs1)         | Zfhyp |
  87 FATANH   | inverse hyperbolic tan   | rd = atanh(rs1)         | Zfhyp |
  88 """]]
  89
  90 # Synthesis, Pseudo-code ops and macro-ops
  91
  92 The pseudo-ops are best left up to the compiler rather than being actual
  93 pseudo-ops, by allocating one scalar FP register for use as a constant
  94 (loop invariant) set to "1.0" at the beginning of a function or other
  95 suitable code block.
  96
  97 * FRCP rd, rs1 - pseudo-code alias for rd = 1.0 / rs1
  98 * FATAN - pseudo-code alias for rd = atan2(rs1, 1.0) - FATAN2
  99 * FATANPI - pseudo alias for rd = atan2pi(rs1, 1.0) - FATAN2PI
 100 * FSINCOS - fused macro-op between FSIN and FCOS (issued in that order).
 101 * FSINCOSPI - fused macro-op between FSINPI and FCOSPI (issued in that order).
 102
 103 FATANPI example pseudo-code:
 104
 105     lui t0, 0x3F800 // upper bits of f32 1.0
 106     fmv.x.s ft0, t0
 107     fatan2pi.s rd, rs1, ft0
 108
 109 Hypotenuse example (obviates need for Zfhyp except for high-performance):
 110
 111     ASINH( x ) = ln( x + SQRT(x**2+1)
 112
 113 LOG / LOGP1 example:
 114
 115     LOG(x) = LOGP1(x) + 1.0
 116     EXP(x) = EXPM1(x-1.0)
 117
 118 # To evaluate: should LOG be replaced with LOG1P (and EXP with EXPM1)?
 119
 120 RISC principle says "exclude LOG because it's covered by LOGP1 plus an ADD".
 121 Research needed to ensure that implementors are not compromised by such
 122 a decision
 123 <http://lists.libre-riscv.org/pipermail/libre-riscv-dev/2019-August/002358.html>