mirror of
https://github.com/m-labs/artiq.git
synced 2024-12-19 00:16:29 +08:00
phaser: use misoc cordic
This commit is contained in:
parent
2e482505c6
commit
70a70320bd
@ -1,358 +0,0 @@
|
||||
# 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))
|
||||
)
|
||||
]
|
||||
@ -1,7 +1,7 @@
|
||||
from migen import *
|
||||
from misoc.interconnect.stream import Endpoint
|
||||
from misoc.cores.cordic import Cordic
|
||||
|
||||
from .cordic import Cordic
|
||||
from .accu import PhasedAccu
|
||||
from .tools import eqh
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user