### TABLE 2 MEAN COEFFICIENTS FOR THE TRANSFORMATION EQUATIONS

### Table 4. The transformation equations determine the relative and absolute location of cells

in Algebraic Semantics Based Behavioural Views of Configuration Relocation in Reconfigurable Computing

"... In PAGE 14: ....6. An Illustration With the ability to do the three basic movements of V, H, and R90 and the operations of vertical offset and horizontal offset, any reconfiguration of a cell mapping is possible in our idealised FPGA. Table4 details the transformation equations for relocating that configuration following their relative and absolute locations. Old Location New Location Vertical flip S( i n i R row g184 g611 , j m j R col g184 g611 ) lt;r,c gt; S( g40g41rev j m j i n i R V col R V row ) ( ), ( 1 1 g184 g61 g184 g61 ) lt;maxrow-r,c gt; Horizontal flip S( i n i R row g184 g611 , j m j R col g184 g611 ) lt;r,c gt; S( g40g41 ) ( , ) ( 1 1 j m j rev i n i R H col R H row g184 g61 g184 g61 ) lt;r,maxcol-c gt; Rotate 90o S( i n i R row g184 g611 , j m j R col g184 g611 ) lt;r,c gt; S( g40g41 ) ( 90 , ) ( 90 1 1 j m j rev i n i R R row R R col g184 g61 g184 g61 ) ... ..."

### TABLE 1 EQUATIONS THAT TRANSFORM A KERNEL LOCATED AT (yz, zv) FROM WORLD SPACE (y, z) INTO PERSPECTIVE SPACE (yp, zp = z)

### Table 3: Simplified cost equations for local transformations (when the system cost function is SUM).

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### Table 3: Equivalents Under the Tanh Transformation

"... In PAGE 13: ... (Hunter[17] solved these problems only in the asymptotic limit jXj!1.) Table3 collects the various identities which are helpful in transforming to the new coordinate z and then back again. Unfortunately, it was not possible to flnd complete explicit inner solutions at third and higher order.... ..."

### Table 2.4: Transforming an update equation for system identification into one for inverse mod- eling by using the matrix-inversion lemma, and vice versa.

2000

### Table 2.4: Transforming an update equation for system identification into one for inverse mod- eling by using the matrix-inversion lemma, and vice versa.

2000

### Table 1: The PERFECT Club Benchmark Suite terminations of molecular electronic structure. The two-electron integral transformation transforms the electron repul- sion integrals from the atomic orbital (AO) basis set to the molecular orbital (MO) basis set according to a fourth-order tensor transformation equation. The evaluation of the integral transformation is formulated as a series of matrix multiplications.

1989

"... In PAGE 18: ... The Fortran 77 language standard that was adopted by the PERFECT Club (after a few porting iterations) can be classi ed into ve categories: syntax, documentation, declarations, In- put/Output (I/O), and general programming techniques. The modi cation of the original Fortran 77 program in Table1 according to the following guidelines insured a successful run on the machines in Table 2. We note that many of the requirements re ect well-known ANSI Fortran 77 standards1.... In PAGE 22: ... is the maximum allowable relative error. Since the outputs of a few of the benchmark programs in Table1 are quite sensitive to machine round-o errors2, a large relative error (e.... In PAGE 22: ... 4.3 Performance Measures The fundamental measurements that were recorded for each of the programs in Table1 on the machines in Table 2 were the CPU time and wall-clock times. Initially, these measures were taken on the original (or baseline) code without any manual optimization by the programmer using 64-bit arithmetic3.... In PAGE 25: ... Identifying di erences in the type and the impact of software transformations used in these diaries should lead to a better understanding of the performance behavior of supercomputers, in general. 5 Results In this section, we present the baseline (compiler-optimized only) and hand- optimized measurements for the PERFECT benchmark suite ( Table1 ) on the machines listed in Table 2. Figures 1 through 6 illustrate the range of performance obtained when the PERFECT Club benchmarks are simply ported and compiler-optimized on each machine.... In PAGE 42: ... 5.3 MDG Although many of the diaries recorded for a particular benchmark program in Table1 were unique to the respective machines in Table 2, the molecu- lar dynamics benchmark, MDG, provides one example in which practically the same transformations were chosen for optimization on the Alliant FX/8, CRAY X-MP/416, IBM 3090-600S, and NEC SX-2. Diaries for MDG on the iPSC/1, MARK III, and NCUBE/10 machines are not included in our comparison.... In PAGE 44: ... Redundant array operations removed. (CSHIFT, INTERF, POTENG) 2 1 Microtask (parallelize) outermost loops and (INTERF, POTENG) Table1 1: Diary entries for MDG on the Alliant FX/8 and CRAY X-MP/416.... In PAGE 45: ... (INTERF) 3 4,11,14 Unrolled inner-most loop and expanded scalar variables for vector operations. (POTENG) Table1 2: Diary entries for MDG on IBM 3090-600S and NEC SX-2.... In PAGE 54: ...3.0 Table1 3: Machines used by PERFECT Club Members . Descriptor Machine NEC SX-2 NCUBE/10 iPSC/1 Mark III Location HARC Cal.... In PAGE 54: ...20A V2.4 Table1 4: Machines used by PERFECT Club Members .... ..."

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### Table 7. Appropriateness of the automatic diagnosis for incorrect expansions, reductions and transformations on equations (i.e., when it is judged appropriate by the analyst). Class Type Number Appropriate Ratio

2005

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