# Source code for artiq.coredevice.spline

```
from numpy import int32, int64
from artiq.language.core import kernel, portable, delay
from artiq.coredevice.rtio import rtio_output, rtio_output_wide
from artiq.language.types import TInt32, TInt64, TFloat
[docs]class Spline:
r"""Spline interpolating RTIO channel.
One knot of a polynomial basis spline (B-spline) :math:`u(t)`
is defined by the coefficients :math:`u_n` up to order :math:`n = k`.
If the coefficients are evaluated starting at time :math:`t_0`,
the output :math:`u(t)` for :math:`t > t_0, t_0` is:
.. math::
u(t) &= \sum_{n=0}^k \frac{u_n}{n!} (t - t_0)^n \\
&= u_0 + u_1 (t - t_0) + \frac{u_2}{2} (t - t_0)^2 + \dots
This class contains multiple methods to convert spline knot data from SI
to machine units and multiple methods that set the current spline
coefficient data. None of these advance the timeline. The :meth:`smooth`
method is the only method that advances the timeline.
:param width: Width in bits of the quantity that this spline controls
:param time_width: Width in bits of the time counter of this spline
:param channel: RTIO channel number
:param core_device: Core device that this spline is attached to
:param scale: Scale for conversion between machine units and physical
units; to be given as the "full scale physical value".
"""
kernel_invariants = {"channel", "core", "scale", "width",
"time_width", "time_scale"}
def __init__(self, width, time_width, channel, core_device, scale=1.):
self.core = core_device
self.channel = channel
self.width = width
self.scale = float((int64(1) << width) / scale)
self.time_width = time_width
self.time_scale = float((1 << time_width) *
core_device.coarse_ref_period)
[docs] @portable(flags={"fast-math"})
def to_mu(self, value: TFloat) -> TInt32:
"""Convert floating point ``value`` from physical units to 32 bit
integer machine units."""
return int32(round(value*self.scale))
[docs] @portable(flags={"fast-math"})
def from_mu(self, value: TInt32) -> TFloat:
"""Convert 32 bit integer ``value`` from machine units to floating
point physical units."""
return value/self.scale
[docs] @portable(flags={"fast-math"})
def to_mu64(self, value: TFloat) -> TInt64:
"""Convert floating point ``value`` from physical units to 64 bit
integer machine units."""
return int64(round(value*self.scale))
[docs] @kernel
def set_mu(self, value: TInt32):
"""Set spline value (machine units).
:param value: Spline value in integer machine units.
"""
rtio_output(self.channel << 8, value)
[docs] @kernel(flags={"fast-math"})
def set(self, value: TFloat):
"""Set spline value.
:param value: Spline value relative to full-scale.
"""
if self.width > 32:
l = [int32(0)] * 2
self.pack_coeff_mu([self.to_mu64(value)], l)
rtio_output_wide(self.channel << 8, l)
else:
rtio_output(self.channel << 8, self.to_mu(value))
[docs] @kernel
def set_coeff_mu(self, value): # TList(TInt32)
"""Set spline raw values.
:param value: Spline packed raw values.
"""
rtio_output_wide(self.channel << 8, value)
[docs] @portable(flags={"fast-math"})
def pack_coeff_mu(self, coeff, packed): # TList(TInt64), TList(TInt32)
"""Pack coefficients into RTIO data
:param coeff: TList(TInt64) list of machine units spline coefficients.
Lowest (zeroth) order first. The coefficient list is zero-extended
by the RTIO gateware.
:param packed: TList(TInt32) list for packed RTIO data. Must be
pre-allocated. Length in bits is
``n*width + (n - 1)*n//2*time_width``
"""
pos = 0
for i in range(len(coeff)):
wi = self.width + i*self.time_width
ci = coeff[i]
while wi != 0:
j = pos//32
used = pos - 32*j
avail = 32 - used
if avail > wi:
avail = wi
cij = int32(ci)
if avail != 32:
cij &= (1 << avail) - 1
packed[j] |= cij << used
ci >>= avail
wi -= avail
pos += avail
[docs] @portable(flags={"fast-math"})
def coeff_to_mu(self, coeff, coeff64): # TList(TFloat), TList(TInt64)
"""Convert a floating point list of coefficients into a 64 bit
integer (preallocated).
:param coeff: TList(TFloat) list of coefficients in physical units.
:param coeff64: TList(TInt64) preallocated list of coefficients in
machine units.
"""
for i in range(len(coeff)):
vi = coeff[i] * self.scale
for j in range(i):
vi *= self.time_scale
ci = int64(round(vi))
coeff64[i] = ci
# artiq.wavesynth.coefficients.discrete_compensate:
if i == 2:
coeff64[1] += ci >> self.time_width + 1
elif i == 3:
coeff64[2] += ci >> self.time_width
coeff64[1] += ci // 6 >> 2*self.time_width
[docs] def coeff_as_packed_mu(self, coeff64):
"""Pack 64 bit integer machine units coefficients into 32 bit integer
RTIO data list.
This is a host-only method that can be used to generate packed
spline coefficient data to be frozen into kernels at compile time.
"""
n = len(coeff64)
width = n*self.width + (n - 1)*n//2*self.time_width
packed = [int32(0)] * ((width + 31)//32)
self.pack_coeff_mu(coeff64, packed)
return packed
[docs] def coeff_as_packed(self, coeff):
"""Convert floating point spline coefficients into 32 bit integer
packed data.
This is a host-only method that can be used to generate packed
spline coefficient data to be frozen into kernels at compile time.
"""
coeff64 = [int64(0)] * len(coeff)
self.coeff_to_mu(coeff, coeff64)
return self.coeff_as_packed_mu(coeff64)
[docs] @kernel(flags={"fast-math"})
def set_coeff(self, coeff): # TList(TFloat)
"""Set spline coefficients.
Missing coefficients (high order) are zero-extended byt the RTIO
gateware.
If more coefficients are supplied than the gateware supports the extra
coefficients are ignored.
:param value: List of floating point spline coefficients,
lowest order (constant) coefficient first. Units are the
unit of this spline's value times increasing powers of 1/s.
"""
n = len(coeff)
coeff64 = [int64(0)] * n
self.coeff_to_mu(coeff, coeff64)
width = n*self.width + (n - 1)*n//2*self.time_width
packed = [int32(0)] * ((width + 31)//32)
self.pack_coeff_mu(coeff64, packed)
self.set_coeff_mu(packed)
[docs] @kernel(flags={"fast-math"})
def smooth(self, start: TFloat, stop: TFloat, duration: TFloat,
order: TInt32):
"""Initiate an interpolated value change.
For zeroth order (step) interpolation, the step is at
``start + duration/2``.
First order interpolation corresponds to a linear value ramp from
``start`` to ``stop`` over ``duration``.
The third order interpolation is constrained to have zero first
order derivative at both `start` and `stop`.
For first order and third order interpolation (linear and cubic)
the interpolator needs to be stopped explicitly at the stop time
(e.g. by setting spline coefficient data or starting a new
:meth:`smooth` interpolation).
This method advances the timeline by ``duration``.
:param start: Initial value of the change. In physical units.
:param stop: Final value of the change. In physical units.
:param duration: Duration of the interpolation. In physical units.
:param order: Order of the interpolation. Only 0, 1,
and 3 are valid: step, linear, cubic.
"""
if order == 0:
delay(duration/2.)
self.set_coeff([stop])
delay(duration/2.)
elif order == 1:
self.set_coeff([start, (stop - start)/duration])
delay(duration)
elif order == 3:
v2 = 6.*(stop - start)/(duration*duration)
self.set_coeff([start, 0., v2, -2.*v2/duration])
delay(duration)
else:
raise ValueError("Invalid interpolation order. "
"Supported orders are: 0, 1, 3.")
```