Products 06 & 07: Moments
DESC: Product #06 1-species (proton) momenta. Product #07 4-species (proton, He+, alphas, O+) momenta.
HIST: 01-21-93 JLC Created file
01-25-93 JLC Removed table definitions to tbl.asm
04-01-93 JLC modified test program for FM software
05-13-93 JLC Overhauled file to embed into FM/CRTOS.
07-19-93 JLC Finished converting module to product task
08-01-93 JLC Corrected various minor bugs still hangin'round.
08-16-93 JLC Final walk through and commenting
03-03-94 JLC finished re-structuring and mod's per
scientific review
03-09-94 JLC further mod's for new struc debug and
Product 09 support
95-01-30 CAI Fix bug which stopped prod after 1 spin. v1.53
95-08-16 CAI Fix UPD_MOM loop control; fix IT4-7 save
order; add anode efficiency factors. v1.83
95-08-23 DWC Removed single RAM based energy table f(v);
Use opmode sweep selection criteria to select
one of two energy tables from vectors in opmode
table; add energy efficiency term
95-09-30 DWC Change anode eff to separate tables by mass
95-08-31 DWC Change anode eff to separate by hi/lo sens
Offset energy ranges to skip first energy step
95-09-05 CAI Offset energy ranges to skip last e-step. v1.86
95-09-09 CAI Adj sweep A/B index offset in UPD_MOM. v1.88
95-11-13 CAI Update memory use comments.
95-11-22 CAI Fix r12 setup for MS_TIMOUT. v1.92
96-01-13 CAI Implement 16-level prioritized tlm queues. v1.94
96-02-29 CAI Update P09 summation parameters to: 4 sweeps
180 degrees opposite sweep_b_i, and 4 anodes
2, 3, 4, & 5. v2.05
96-03-20 CAI Fix ER_t bug which blocked counts from 3rd energy
range. v2.05
96-03-21 CAI Add tlm pkt timeout error post. v2.05
96-04-22 CAI Update P09 summation parameters to 45x45 deg:
4 sweeps 180 degrees opposite sweep_b_i, and
anodes 3 & 4 (of 0-7). v2.07
96-04-24 CAI Change sweep_b_i to SRP-relative; change P09
beg/end indices from sectors to sweeps. v2.07
96-06-07 AMD Ported the code to ESIC. Introduced interleaved mass
momenta computation (1 mass at time) both for P6/P7
for each 22.5 deg sweep. P7, 4-species, covers the full
phase space after 4 spins. Revised PX_ER_t into a more
general info tables P06_Inf_T / P07_Inf_T.
Code differences were marked by __$$ as usual.
97-01-24 AMD Fixed a bug concerning right energy band updating
97-03-04 AMD Fixed a bug concerning trig tables ptr updtating (r14)
97-22-07 AMD Added odd/even energy computation
97-25-07 AMD Changed the interleaved mass computation into 1mass/1sp
97-03-09 AMD Add dummy burst memory trigger evaluation to MOM_SUBT.
$2.26
97-09-10 AMD Considered odd spin only for SM trigger evaluation $2.27
(see MOM_TRGR)
NOTE: PRODUCT GENERATION
The following Moments are computed across 3 energy ranges
for 4 masses:
* Density (N)
* Bulk Velocity (Vx, Vy, Vz)
* Heat Flux Vector (Hx, Hy, Hz)
* Pressure Tensor (Pxx, Pyy, Pzz, Pxy, Pxz, Pyz)
Which results in 12 (3Ex4M) sets of 13 moment values (156
values) computed and summed in floating point format and
then compressed to 12-bits and packed into 16-bit words
(117 words). Moment products are computed using the
following algorithm:
[ Product 06/07 ]
For sixteen 22.5-degree Energy Sweeps (full spin),
summing 8 anodes
[ Product XX ]
For two 22.5-degree Energy Sweeps when running the
RPA sweeps, summing only anodes TBD
[ both products ]
For Each Energy Step (assigned to three buckets - see P6/7_Inf_T),
Compute phi-based intermediate (IP) values (see below)
For Each Mass (at a specific energy step)
Compute theta-based intermediate (IT) values (see below)
Update Vz (bulk velocity)
and Hz (heat flux vector)
Update Pxz and Pyz (pressure tensor)
Update N (density)
Update Vx, Vy (bulk velocity),
and Hx, Hy (Heat flux vector)
Update Pxx, Pyy, and Pxy (pressure tensor)
Update Pzz (pressure tensor)
Computing the theta-based intermediate values entails
summing the product of each anode counter and a trig
function (depending on moment being computed). Anodes and
corresponding theta angles are shown below:
Anode 0 = 78.75 degress Anode 7 = -78.75 degress
Anode 1 = 56.25 degress Anode 6 = -56.25 degress
Anode 2 = 33.75 degress Anode 5 = -33.75 degress
Anode 3 = 11.25 degress Anode 4 = -11.25 degress
(?? Being changed to floating point with efficiency factors.
950817:)
The summing of the trig/counter products is performed in fixed
point math with 17-bits integer and 15 bits fraction. The
theta trig functions are look-up tables with 16-bit fixed
point values - 15 bits of fraction, multiplied by a 16-bit
integer counter value resulting in a 32-bit sum (17-bits
integer, 15 bits fraction. The 16 LS-bits of the integer
portion is then converted to single precision floating point.
"Updating" a moment value entails multiplying the trig/
counter product sum by a phi-based intermediate value
(velocity vector and/or a phi-based trig function
multiplied). All computation after the counter/trig
multiply and addition outlined above is performed in single-
precision floating point.
MOMENT EQUATIONS
The algorithm above uses the following equations for each
moment update:
Density:
N += 1/V * C[t,p,e]
Bulk Velocity:
Vx += cos(p) * SUM( cos(t) * C[t,p,e] )
Vy += sin(p) * SUM( cos(t) * C[t,p,e] )
Vz += SUM( sin(t) * C[t,p,e] )
Heat Flux Vector:
Hx += V^2 * cos(p) * SUM( cos(t) * C[t,p,e] )
Hy += V^2 * sin(p) * SUM( cos(t) * C[t,p,e] )
Hz += V^2 * tSUM( sin(t) * C[t,p,e] )
Pressure Tensor:
Pxx += V * cos^2(p) * SUM( cos^2(t) * C[t,p,e] )
Pyy += V * sin^2(p) * SUM( cos^2(t) * C[t,p,e] )
Pzz += V * SUM( sin^2(t) * C[t,p,e] )
Pxy += V * cos*sin(p) * SUM( cos^2(t) * C[t,p,e] )
Pxz += V * cos(p) * SUM( cos*sin(t) * C[t,p,e] )
Pyz += V * sin(p) * SUM( cos*sin(t) * C[t,p,e] )
Where,
t = theta (anode) angle
p = phi (spin) angle
e = energy step index (0..31)
V = velocity (indexed by energy step number)
C = counter buf (indexed by theta, phi, and energy index)
Multiplied by an anode efficiency factor F(t), and an
energy efficiency factor, F(e,m)
SUM = sum of specified function over all 8 thetas
PHI INTERMEDIATE VALUES
An index into the phi (spin angle) tables is updated
for each energy step of each sweep throughout the entire
spin. The Intermediate Phi products are computed at each
energy step as follows (where e=energy_step_index,
p=phi_spin_angle):
IP0 = V^2[e] * cos(p) IP4 = V[e] * cos(p) * sin(p)
IP1 = V^2[e] * sin(p) IP5 = V[e] * cos(p)
IP2 = V[e] * cos^2(p) IP6 = V[e] * sin(p)
IP3 = V[e] * sin^2(p)
The counters are read every 22.5 degrees.
THETA INTERMEDIATE VALUES
The theta (anode) intermediate values are updated for each
energy step of each sweep throughout the entire spin. These
intermediate values are used by several different moment
calculations.
The symmetry of the trig multiplication and summations then
allow the software to save half of the potential 16x32
multiplies per energy step. The IT Values are:
ODD: EVEN:
----------------- -----------------
IT0 = Ctr0 - Ctr7 IT4 = Ctr0 + Ctr7
IT1 = Ctr1 - Ctr6 IT5 = Ctr1 + Ctr6
IT2 = Ctr2 - Ctr5 IT6 = Ctr2 + Ctr5
IT3 = Ctr3 - Ctr4 IT7 = Ctr3 + Ctr4
Thus, counter summations of the form:
(Sin(+78)*Ctr0) + (Sin(-78)*Ctr7) +
(Sin(+56)*Ctr1) + (Sin(-56)*Ctr6) + ...
can be simplified to:
(Sin(+78)*(Ctr0-Ctr7)) + (Sin(+56)*(Ctr1-Ctr6)) + ...
or:
Sin(78)*IT0 + Sin(56)*IT1 + ...
which has half as many multiplies. The difference between
IT0 and IT4, or IT1 and IT5 ,..., is the symmetry of the
trig function. Odd trig functions use IT0 through IT3,
and even functions use IT4 through IT7.
COUNTER BUFFER
The counter buffer (ctr_b) supplied by the code in cis.asm
is structured as 32 energy sets of 4 mass sets of 8 theta
values, as follows:
Buffer Theta
Offset E-Step Mass (Anode)
------ ------ ---- -----
0 0 0 0
1 0 0 1
2 0 0 2
... ... ... ...
7 0 0 7 Masses #1 and #2
8 0 2 0 <--- are out of numer-
9 0 2 1 | ical order in the
... ... ... ... |- buffer. This is
15 0 2 7 | caused by the
16 0 1 0 <--- comparator/counter
17 0 1 1 wiring.
... ... ... ...
30 0 3 6
31 0 3 7
32 1 0 0
33 1 0 1
... ... ... ...
1021 31 3 5
1022 31 3 6
1023 31 3 7
MEMORY USE
The summation buffer memory is reused for the telemetry
packet buffer. In addition four words are allocated just
before the summation buffer for a 2-word packet handling
structure and 2-word packet header. Memory use is:
Length
(words) Description
------ ---------------
2 packet handling structure
2 packet header
312 summation buffer
------
316 total per product buffer
53 product variables
27 sub-task tss
------
396 Allocation for 1st buffer
27 task tss (at prod task creation)
------
423 Total allocation for 1-buffer product
316 Allocation for 2nd buffer
------
739 Total allocation for 2-buffer product
SAMPLING MODESMass Interleaved mode: up to Ver. $2.23The on-board software is able to compute one mass momenta contribute per
sweep for each momenta product P6 or P7. Therefore, in case of P7, just a quarter
of the phase space is covered in one spin if all together the 4 species are considered.Being 16 (sweeps) a multiple of 4 (species) is necessary to change once per spin the selected mass on which the moments are computed, otherwise some azimuthal gap will appear in the azimuthal coverage.
This is controlled by a dedicated mass modulo 4 counter which is reset at P7 creation and next incremented for each sweep. As soon as 16 (one spin) is reached the current mass # is incremented by 2 insted of one.Odd/even energies mode: since Ver. $ 2.24Due to the lack of computational resource computations have been modified to be able to perform the momenta computations by skipping odd/even energy ac- cording to the spin number at the time of the data collection starting. The dedicated var SPIN_EOV will be reset to 1 or 0 according to the LSB bit of the spin. During each spin collection the bit will be toggled. The status of the bit will correspond to odd (1) energies or (0) energies steps collection. Note that this collection is independently from the entry energy step put in the energy range tables P6_Inf_T or P7_Inf_T.Mass inteleaved mode suppression: since Ver $ 2.27Full one mass per spin computation has been preferred for P7. Note that this
has been simply achieved by placing a comment to the mass register setting instruction which holds the selected mass to be updated. A 'nop' instruct. has been left in the code to be able to switch back to the previous interleaved mode which performs the mass average over 4 spins by a simple S/W patch.
MOMENT SUM BUFFER ALLOCATION SIZEThe moment summation buffer size is 156 (3x4x13) floating values, or 312 words. This memory space is reused for the packet data to conserve RAM use. Thus 4 additional words must be allocated to store a 2-word packet processing structure plus a 2-word packet header just before the sum buffer.
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