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phaser: use misoc cordic

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Robert Jördens 2016-11-13 17:29:38 +01:00
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artiq/gateware/dsp/cordic.py
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# Copyright 2014-2015 Robert Jordens <jordens@gmail.com>
#
# This file is part of redpid.
#
# redpid is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# redpid is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with redpid. If not, see <http://www.gnu.org/licenses/>.
from math import atan, atanh, log, sqrt, pi
from migen import *
class TwoQuadrantCordic(Module):
"""Coordinate rotation digital computer
Trigonometric, and arithmetic functions implemented using
additions/subtractions and shifts.
http://eprints.soton.ac.uk/267873/1/tcas1_cordic_review.pdf
http://www.andraka.com/files/crdcsrvy.pdf
http://zatto.free.fr/manual/Volder_CORDIC.pdf
The way the CORDIC is executed is controlled by `eval_mode`.
If `"iterative"` the stages are iteratively evaluated, one per clock
cycle. This mode uses the least amount of registers, but has the
lowest throughput and highest latency. If `"pipelined"` all stages
are executed in every clock cycle but separated by registers. This
mode has full throughput but uses many registers and has large
latency. If `"combinatorial"`, there are no registers, throughput is
maximal and latency is zero. `"pipelined"` and `"combinatorial"` use
the same number of shifters and adders.
The type of trigonometric/arithmetic function is determined by
`cordic_mode` and `func_mode`. :math:`g` is the gain of the CORDIC.
* rotate-circular: rotate the vector `(xi, yi)` by an angle `zi`.
Used to calculate trigonometric functions, `sin(), cos(),
tan() = sin()/cos()`, or to perform polar-to-cartesian coordinate
transformation:
.. math::
x_o = g \\cos(z_i) x_i - g \\sin(z_i) y_i
y_o = g \\sin(z_i) x_i + g \\cos(z_i) y_i
* vector-circular: determine length and angle of the vector
`(xi, yi)`. Used to calculate `arctan(), sqrt()` or
to perform cartesian-to-polar transformation:
.. math::
x_o = g\\sqrt{x_i^2 + y_i^2}
z_o = z_i + \\tan^{-1}(y_i/x_i)
* rotate-hyperbolic: hyperbolic functions of `zi`. Used to
calculate hyperbolic functions, `sinh, cosh, tanh = cosh/sinh,
exp = cosh + sinh`:
.. math::
x_o = g \\cosh(z_i) x_i + g \\sinh(z_i) y_i
y_o = g \\sinh(z_i) x_i + g \\cosh(z_i) z_i
* vector-hyperbolic: natural logarithm `ln(), arctanh()`, and
`sqrt()`. Use `x_i = a + b` and `y_i = a - b` to obtain `2*
sqrt(a*b)` and `ln(a/b)/2`:
.. math::
x_o = g\\sqrt{x_i^2 - y_i^2}
z_o = z_i + \\tanh^{-1}(y_i/x_i)
* rotate-linear: multiply and accumulate (not a very good
multiplier implementation):
.. math::
y_o = g(y_i + x_i z_i)
* vector-linear: divide and accumulate:
.. math::
z_o = g(z_i + y_i/x_i)
Parameters
----------
width : int
Bit width of the input and output signals. Defaults to 16. Input
and output signals are signed.
widthz : int
Bit with of `zi` and `zo`. Defaults to the `width`.
stages : int or None
Number of CORDIC incremental rotation stages. Defaults to
`width + min(1, guard)`.
guard : int or None
Add guard bits to the intermediate signals. If `None`,
defaults to `guard = log2(width)` which guarantees accuracy
to `width` bits.
eval_mode : str, {"iterative", "pipelined", "combinatorial"}
cordic_mode : str, {"rotate", "vector"}
func_mode : str, {"circular", "linear", "hyperbolic"}
Evaluation and arithmetic mode. See above.
Attributes
----------
xi, yi, zi : Signal(width), in
Input values, signed.
xo, yo, zo : Signal(width), out
Output values, signed.
new_out : Signal(1), out
Asserted if output values are freshly updated in the current
cycle.
new_in : Signal(1), out
Asserted if new input values are being read in the next cycle.
zmax : float
`zi` and `zo` normalization factor. Floating point `zmax`
corresponds to `1<<(widthz - 1)`. `x` and `y` are scaled such
that floating point `1` corresponds to `1<<(width - 1)`.
gain : float
Cumulative, intrinsic gain and scaling factor. In circular mode
`sqrt(xi**2 + yi**2)` should be no larger than `2**(width - 1)/gain`
to prevent overflow. Additionally, in hyperbolic and linear mode,
the operation itself can cause overflow.
interval : int
Output interval in clock cycles. Inverse throughput.
latency : int
Input-to-output latency. The result corresponding to the inputs
appears at the outputs `latency` cycles later.
Notes
-----
Each stage `i` in the CORDIC performs the following operation:
.. math::
x_{i+1} = x_i - m d_i y_i r^{-s_{m,i}},
y_{i+1} = y_i + d_i x_i r^{-s_{m,i}},
z_{i+1} = z_i - d_i a_{m,i},
where:
* :math:`d_i`: clockwise or counterclockwise, determined by
`sign(z_i)` in rotate mode or `sign(-y_i)` in vector mode.
* :math:`r`: radix of the number system (2)
* :math:`m`: 1: circular, 0: linear, -1: hyperbolic
* :math:`s_{m,i}`: non decreasing integer shift sequence
* :math:`a_{m,i}`: elemetary rotation angle: :math:`a_{m,i} =
\\tan^{-1}(\\sqrt{m} s_{m,i})/\\sqrt{m}`.
"""
def __init__(self, width=16, widthz=None, stages=None, guard=0,
eval_mode="iterative", cordic_mode="rotate",
func_mode="circular"):
# validate parameters
assert eval_mode in ("combinatorial", "pipelined", "iterative")
assert cordic_mode in ("rotate", "vector")
assert func_mode in ("circular", "linear", "hyperbolic")
self.cordic_mode = cordic_mode
self.func_mode = func_mode
if guard is None:
# guard bits to guarantee "width" accuracy
guard = int(log(width)/log(2))
if widthz is None:
widthz = width
if stages is None:
stages = width + min(1, guard) # cuts error below LSB
# input output interface
self.xi = Signal((width, True))
self.yi = Signal((width, True))
self.zi = Signal((widthz, True))
self.xo = Signal((width, True))
self.yo = Signal((width, True))
self.zo = Signal((widthz, True))
self.new_in = Signal()
self.new_out = Signal()
###
a, s, self.zmax, self.gain = self._constants(stages, widthz + guard)
stages = len(a) # may have increased due to repetitions
if eval_mode == "iterative":
num_sig = 3
self.interval = stages + 1
self.latency = stages + 2
else:
num_sig = stages + 1
self.interval = 1
if eval_mode == "pipelined":
self.latency = stages
else: # combinatorial
self.latency = 0
# inter-stage signals
x = [Signal((width + guard, True)) for i in range(num_sig)]
y = [Signal((width + guard, True)) for i in range(num_sig)]
z = [Signal((widthz + guard, True)) for i in range(num_sig)]
# hook up inputs and outputs to the first and last inter-stage
# signals
self.comb += [
x[0].eq(self.xi << guard),
y[0].eq(self.yi << guard),
z[0].eq(self.zi << guard),
self.xo.eq(x[-1] >> guard),
self.yo.eq(y[-1] >> guard),
self.zo.eq(z[-1] >> guard),
]
if eval_mode == "iterative":
# We afford one additional iteration for in/out.
i = Signal(max=stages + 1)
self.comb += [
self.new_in.eq(i == stages),
self.new_out.eq(i == 1),
]
ai = Signal((widthz + guard, True))
self.sync += ai.eq(Array(a)[i])
if range(stages) == s:
si = i - 1 # shortcut if no stage repetitions
else:
si = Signal(max=stages + 1)
self.sync += si.eq(Array(s)[i])
xi, yi, zi = x[1], y[1], z[1]
self.sync += [
self._stage(xi, yi, zi, xi, yi, zi, si, ai),
i.eq(i + 1),
If(i == stages,
i.eq(0),
),
If(i == 0,
x[2].eq(xi), y[2].eq(yi), z[2].eq(zi),
xi.eq(x[0]), yi.eq(y[0]), zi.eq(z[0]),
)
]
else:
self.comb += [
self.new_out.eq(1),
self.new_in.eq(1),
]
for i, si in enumerate(s):
stmt = self._stage(x[i], y[i], z[i],
x[i + 1], y[i + 1], z[i + 1],
si, a[i])
if eval_mode == "pipelined":
self.sync += stmt
else: # combinatorial
self.comb += stmt
def _constants(self, stages, bits):
if self.func_mode == "circular":
s = range(stages)
a = [atan(2**-i) for i in s]
g = [sqrt(1 + 2**(-2*i)) for i in s]
#zmax = sum(a)
# use pi anyway as the input z can cause overflow
# and we need the range for quadrant mapping
zmax = pi
elif self.func_mode == "linear":
s = range(stages)
a = [2**-i for i in s]
g = [1 for i in s]
#zmax = sum(a)
# use 2 anyway as this simplifies a and scaling
zmax = 2.
else: # hyperbolic
s = []
# need to repeat some stages:
j = 4
for i in range(stages):
if i == j:
s.append(j)
j = 3*j + 1
s.append(i + 1)
a = [atanh(2**-i) for i in s]
g = [sqrt(1 - 2**(-2*i)) for i in s]
zmax = sum(a)*2
# round here helps the width=2**i - 1 case but hurts the
# important width=2**i case
cast = int
if log(bits)/log(2) % 1:
cast = round
a = [cast(ai*2**(bits - 1)/zmax) for ai in a]
gain = 1.
for gi in g:
gain *= gi
return a, s, zmax, gain
def _stage(self, xi, yi, zi, xo, yo, zo, i, ai):
dir = Signal()
if self.cordic_mode == "rotate":
self.comb += dir.eq(zi < 0)
else: # vector
self.comb += dir.eq(yi >= 0)
dx = yi >> i
dy = xi >> i
dz = ai
if self.func_mode == "linear":
dx = 0
elif self.func_mode == "hyperbolic":
dx = -dx
stmt = [
xo.eq(xi + Mux(dir, dx, -dx)),
yo.eq(yi + Mux(dir, -dy, dy)),
zo.eq(zi + Mux(dir, dz, -dz))
]
return stmt
class Cordic(TwoQuadrantCordic):
"""Four-quadrant CORDIC
Same as :class:`TwoQuadrantCordic` but with support and convergence
for `abs(zi) > pi/2 in circular rotate mode or `xi < 0` in circular
vector mode.
"""
def __init__(self, **kwargs):
TwoQuadrantCordic.__init__(self, **kwargs)
if self.func_mode != "circular":
return # no need to remap quadrants
cxi, cyi, czi = self.xi, self.yi, self.zi
self.xi = xi = Signal.like(cxi)
self.yi = yi = Signal.like(cyi)
self.zi = zi = Signal.like(czi)
###
q = Signal()
if self.cordic_mode == "rotate":
self.comb += q.eq(zi[-2] ^ zi[-1])
else: # vector
self.comb += q.eq(xi < 0)
self.comb += [
If(q,
Cat(cxi, cyi, czi).eq(
Cat(-xi, -yi, zi + (1 << len(zi) - 1)))
).Else(
Cat(cxi, cyi, czi).eq(Cat(xi, yi, zi))
)
]

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artiq/gateware/dsp/sawg.py
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from migen import * from migen import *
from misoc.interconnect.stream import Endpoint from misoc.interconnect.stream import Endpoint
from misoc.cores.cordic import Cordic
from .cordic import Cordic
from .accu import PhasedAccu from .accu import PhasedAccu
from .tools import eqh from .tools import eqh