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phaser: use misoc cordic
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# Copyright 2014-2015 Robert Jordens <jordens@gmail.com>
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#
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# This file is part of redpid.
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#
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# redpid is free software: you can redistribute it and/or modify
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# it under the terms of the GNU General Public License as published by
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# the Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# redpid is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU General Public License for more details.
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#
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# You should have received a copy of the GNU General Public License
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# along with redpid. If not, see <http://www.gnu.org/licenses/>.
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from math import atan, atanh, log, sqrt, pi
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from migen import *
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class TwoQuadrantCordic(Module):
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"""Coordinate rotation digital computer
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Trigonometric, and arithmetic functions implemented using
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additions/subtractions and shifts.
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http://eprints.soton.ac.uk/267873/1/tcas1_cordic_review.pdf
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http://www.andraka.com/files/crdcsrvy.pdf
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http://zatto.free.fr/manual/Volder_CORDIC.pdf
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The way the CORDIC is executed is controlled by `eval_mode`.
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If `"iterative"` the stages are iteratively evaluated, one per clock
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cycle. This mode uses the least amount of registers, but has the
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lowest throughput and highest latency. If `"pipelined"` all stages
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are executed in every clock cycle but separated by registers. This
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mode has full throughput but uses many registers and has large
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latency. If `"combinatorial"`, there are no registers, throughput is
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maximal and latency is zero. `"pipelined"` and `"combinatorial"` use
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the same number of shifters and adders.
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The type of trigonometric/arithmetic function is determined by
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`cordic_mode` and `func_mode`. :math:`g` is the gain of the CORDIC.
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* rotate-circular: rotate the vector `(xi, yi)` by an angle `zi`.
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Used to calculate trigonometric functions, `sin(), cos(),
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tan() = sin()/cos()`, or to perform polar-to-cartesian coordinate
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transformation:
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.. math::
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x_o = g \\cos(z_i) x_i - g \\sin(z_i) y_i
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y_o = g \\sin(z_i) x_i + g \\cos(z_i) y_i
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* vector-circular: determine length and angle of the vector
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`(xi, yi)`. Used to calculate `arctan(), sqrt()` or
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to perform cartesian-to-polar transformation:
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.. math::
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x_o = g\\sqrt{x_i^2 + y_i^2}
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z_o = z_i + \\tan^{-1}(y_i/x_i)
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* rotate-hyperbolic: hyperbolic functions of `zi`. Used to
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calculate hyperbolic functions, `sinh, cosh, tanh = cosh/sinh,
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exp = cosh + sinh`:
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.. math::
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x_o = g \\cosh(z_i) x_i + g \\sinh(z_i) y_i
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y_o = g \\sinh(z_i) x_i + g \\cosh(z_i) z_i
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* vector-hyperbolic: natural logarithm `ln(), arctanh()`, and
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`sqrt()`. Use `x_i = a + b` and `y_i = a - b` to obtain `2*
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sqrt(a*b)` and `ln(a/b)/2`:
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.. math::
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x_o = g\\sqrt{x_i^2 - y_i^2}
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z_o = z_i + \\tanh^{-1}(y_i/x_i)
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* rotate-linear: multiply and accumulate (not a very good
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multiplier implementation):
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.. math::
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y_o = g(y_i + x_i z_i)
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* vector-linear: divide and accumulate:
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.. math::
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z_o = g(z_i + y_i/x_i)
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Parameters
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----------
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width : int
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Bit width of the input and output signals. Defaults to 16. Input
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and output signals are signed.
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widthz : int
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Bit with of `zi` and `zo`. Defaults to the `width`.
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stages : int or None
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Number of CORDIC incremental rotation stages. Defaults to
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`width + min(1, guard)`.
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guard : int or None
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Add guard bits to the intermediate signals. If `None`,
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defaults to `guard = log2(width)` which guarantees accuracy
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to `width` bits.
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eval_mode : str, {"iterative", "pipelined", "combinatorial"}
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cordic_mode : str, {"rotate", "vector"}
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func_mode : str, {"circular", "linear", "hyperbolic"}
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Evaluation and arithmetic mode. See above.
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Attributes
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----------
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xi, yi, zi : Signal(width), in
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Input values, signed.
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xo, yo, zo : Signal(width), out
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Output values, signed.
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new_out : Signal(1), out
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Asserted if output values are freshly updated in the current
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cycle.
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new_in : Signal(1), out
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Asserted if new input values are being read in the next cycle.
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zmax : float
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`zi` and `zo` normalization factor. Floating point `zmax`
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corresponds to `1<<(widthz - 1)`. `x` and `y` are scaled such
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that floating point `1` corresponds to `1<<(width - 1)`.
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gain : float
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Cumulative, intrinsic gain and scaling factor. In circular mode
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`sqrt(xi**2 + yi**2)` should be no larger than `2**(width - 1)/gain`
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to prevent overflow. Additionally, in hyperbolic and linear mode,
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the operation itself can cause overflow.
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interval : int
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Output interval in clock cycles. Inverse throughput.
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latency : int
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Input-to-output latency. The result corresponding to the inputs
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appears at the outputs `latency` cycles later.
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Notes
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-----
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Each stage `i` in the CORDIC performs the following operation:
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.. math::
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x_{i+1} = x_i - m d_i y_i r^{-s_{m,i}},
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y_{i+1} = y_i + d_i x_i r^{-s_{m,i}},
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z_{i+1} = z_i - d_i a_{m,i},
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where:
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* :math:`d_i`: clockwise or counterclockwise, determined by
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`sign(z_i)` in rotate mode or `sign(-y_i)` in vector mode.
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* :math:`r`: radix of the number system (2)
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* :math:`m`: 1: circular, 0: linear, -1: hyperbolic
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* :math:`s_{m,i}`: non decreasing integer shift sequence
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* :math:`a_{m,i}`: elemetary rotation angle: :math:`a_{m,i} =
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\\tan^{-1}(\\sqrt{m} s_{m,i})/\\sqrt{m}`.
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"""
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def __init__(self, width=16, widthz=None, stages=None, guard=0,
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eval_mode="iterative", cordic_mode="rotate",
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func_mode="circular"):
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# validate parameters
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assert eval_mode in ("combinatorial", "pipelined", "iterative")
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assert cordic_mode in ("rotate", "vector")
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assert func_mode in ("circular", "linear", "hyperbolic")
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self.cordic_mode = cordic_mode
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self.func_mode = func_mode
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if guard is None:
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# guard bits to guarantee "width" accuracy
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guard = int(log(width)/log(2))
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if widthz is None:
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widthz = width
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if stages is None:
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stages = width + min(1, guard) # cuts error below LSB
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# input output interface
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self.xi = Signal((width, True))
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self.yi = Signal((width, True))
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self.zi = Signal((widthz, True))
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self.xo = Signal((width, True))
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self.yo = Signal((width, True))
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self.zo = Signal((widthz, True))
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self.new_in = Signal()
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self.new_out = Signal()
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###
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a, s, self.zmax, self.gain = self._constants(stages, widthz + guard)
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stages = len(a) # may have increased due to repetitions
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if eval_mode == "iterative":
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num_sig = 3
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self.interval = stages + 1
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self.latency = stages + 2
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else:
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num_sig = stages + 1
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self.interval = 1
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if eval_mode == "pipelined":
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self.latency = stages
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else: # combinatorial
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self.latency = 0
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# inter-stage signals
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x = [Signal((width + guard, True)) for i in range(num_sig)]
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y = [Signal((width + guard, True)) for i in range(num_sig)]
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z = [Signal((widthz + guard, True)) for i in range(num_sig)]
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# hook up inputs and outputs to the first and last inter-stage
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# signals
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self.comb += [
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x[0].eq(self.xi << guard),
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y[0].eq(self.yi << guard),
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z[0].eq(self.zi << guard),
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self.xo.eq(x[-1] >> guard),
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self.yo.eq(y[-1] >> guard),
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self.zo.eq(z[-1] >> guard),
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]
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if eval_mode == "iterative":
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# We afford one additional iteration for in/out.
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i = Signal(max=stages + 1)
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self.comb += [
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self.new_in.eq(i == stages),
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self.new_out.eq(i == 1),
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]
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ai = Signal((widthz + guard, True))
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self.sync += ai.eq(Array(a)[i])
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if range(stages) == s:
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si = i - 1 # shortcut if no stage repetitions
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else:
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si = Signal(max=stages + 1)
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self.sync += si.eq(Array(s)[i])
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xi, yi, zi = x[1], y[1], z[1]
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self.sync += [
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self._stage(xi, yi, zi, xi, yi, zi, si, ai),
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i.eq(i + 1),
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If(i == stages,
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i.eq(0),
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),
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If(i == 0,
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x[2].eq(xi), y[2].eq(yi), z[2].eq(zi),
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xi.eq(x[0]), yi.eq(y[0]), zi.eq(z[0]),
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)
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]
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else:
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self.comb += [
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self.new_out.eq(1),
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self.new_in.eq(1),
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]
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for i, si in enumerate(s):
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stmt = self._stage(x[i], y[i], z[i],
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x[i + 1], y[i + 1], z[i + 1],
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si, a[i])
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if eval_mode == "pipelined":
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self.sync += stmt
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else: # combinatorial
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self.comb += stmt
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def _constants(self, stages, bits):
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if self.func_mode == "circular":
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s = range(stages)
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a = [atan(2**-i) for i in s]
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g = [sqrt(1 + 2**(-2*i)) for i in s]
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#zmax = sum(a)
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# use pi anyway as the input z can cause overflow
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# and we need the range for quadrant mapping
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zmax = pi
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elif self.func_mode == "linear":
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s = range(stages)
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a = [2**-i for i in s]
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g = [1 for i in s]
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#zmax = sum(a)
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# use 2 anyway as this simplifies a and scaling
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zmax = 2.
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else: # hyperbolic
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s = []
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# need to repeat some stages:
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j = 4
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for i in range(stages):
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if i == j:
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s.append(j)
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j = 3*j + 1
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s.append(i + 1)
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a = [atanh(2**-i) for i in s]
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g = [sqrt(1 - 2**(-2*i)) for i in s]
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zmax = sum(a)*2
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# round here helps the width=2**i - 1 case but hurts the
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# important width=2**i case
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cast = int
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if log(bits)/log(2) % 1:
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cast = round
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a = [cast(ai*2**(bits - 1)/zmax) for ai in a]
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gain = 1.
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for gi in g:
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gain *= gi
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return a, s, zmax, gain
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def _stage(self, xi, yi, zi, xo, yo, zo, i, ai):
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dir = Signal()
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if self.cordic_mode == "rotate":
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self.comb += dir.eq(zi < 0)
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else: # vector
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self.comb += dir.eq(yi >= 0)
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dx = yi >> i
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dy = xi >> i
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dz = ai
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if self.func_mode == "linear":
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dx = 0
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elif self.func_mode == "hyperbolic":
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dx = -dx
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stmt = [
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xo.eq(xi + Mux(dir, dx, -dx)),
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yo.eq(yi + Mux(dir, -dy, dy)),
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zo.eq(zi + Mux(dir, dz, -dz))
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]
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return stmt
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class Cordic(TwoQuadrantCordic):
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"""Four-quadrant CORDIC
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Same as :class:`TwoQuadrantCordic` but with support and convergence
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for `abs(zi) > pi/2 in circular rotate mode or `xi < 0` in circular
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vector mode.
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"""
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def __init__(self, **kwargs):
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TwoQuadrantCordic.__init__(self, **kwargs)
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if self.func_mode != "circular":
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return # no need to remap quadrants
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cxi, cyi, czi = self.xi, self.yi, self.zi
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self.xi = xi = Signal.like(cxi)
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self.yi = yi = Signal.like(cyi)
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self.zi = zi = Signal.like(czi)
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###
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q = Signal()
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if self.cordic_mode == "rotate":
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self.comb += q.eq(zi[-2] ^ zi[-1])
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else: # vector
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self.comb += q.eq(xi < 0)
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self.comb += [
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If(q,
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Cat(cxi, cyi, czi).eq(
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Cat(-xi, -yi, zi + (1 << len(zi) - 1)))
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).Else(
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Cat(cxi, cyi, czi).eq(Cat(xi, yi, zi))
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)
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]
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@ -1,7 +1,7 @@
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from migen import *
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from misoc.interconnect.stream import Endpoint
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from misoc.cores.cordic import Cordic
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from .cordic import Cordic
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from .accu import PhasedAccu
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from .tools import eqh
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