Index

L2-norm, 361-norm, 211-scaling, 21 z transform, 8

Algorithm ALAP, 118 Algorithm ArchSynth, 121 Algorithm ASAP, 118 Algorithm ChvatalHeur, 133 Algorithm IncompSched, 129 Algorithm LatencyBounds, 125 Algorithm Levy–Low, 19 Algorithm ResBindWLSel, 135

Algorithm Scale Non-Recurse, 16 Algorithm ScaleCondition, 85 Algorithm SSet, 132

Algorithm WLCondition, 32 Algorithm WLRefine, 138 Algorithm Word-LengthFalling, 52 AlgorithmCombinedOptHeur, 102 AlgorithmSlackReduce, 97 analytic peak estimation, 15 annotated computation graph, 13 architectural synthesis, 111

area models, 42

as-late-as-possible (ALAP) scheduling, 118

as-soon-as-possible (ASAP) scheduling, 118

bound critical path, 137

Cauchy-Schwartz inequality, 94 Chvatal’s heuristic, 133

computable computation graphs, 12 computation graph, 9, 10 conditioning, 29

conditioning: saturating systems, 85 convexity of constraint space, 45 convolution, 9

critical path, 137 cross-correlation function, 84

data range propagation, 22 di erentiable nonlinear systems, 38

error estimation, 27

feasible clique, 133 Field-Programmable Gate Array, 6 FPGA, 6

heuristic for word-length optimization, 51

high-level synthesis, 111

inclusion monotonic interval extension, 23

interval extension, 23

Levy-Low algorithm, 19 limit cycles, 75 linearization, 39

maximal clique, 132 maximum clique, 132

MILP-based word-length optimization, 53

monotonicity of constraint space, 45

164 Index

multiple word-length, 12

multiple word-length architectural synthesis, problem definition, 114

noise model: linear time-invariant systems, 32

nonlinear systems, 38

optimum word-length, 53

peak value estimation, 15 perturbation analysis, 38 propagation of wordlengths, 29

resource binding, 111

saturated Gaussian distribution, 85 saturation arithmetic, 79 saturation computation graph, 84 saturation nonlinearity, 83

saturation system, 84 saturator, 81 scheduling, 111

scheduling with incomplete information, 127

second-order section, 20 sequencing graph, 113

set covering, problem definition, 133 signum function, 21

slackness, of saturation error bound, 94 spectral bounds on noise, 36

transfer function calculation, 16

well-conditioned computation graph, 32 well-connected computation graph, 12 word-length compatibility graph, 122 word-length optimization, 27 word-length optimization, definition of,

45