### Table 4: Fixed-Point Configurations

"... In PAGE 7: ... Vertex-II Implementation of Floating-Point Adder B. Tested formats and implementation details The formats chosen for comparison are illustrated in Table4 and Table 5 for fixed and floating point formats respectively. They have in- teger ranges [-32, +32].... In PAGE 7: ...Table4... In PAGE 7: ... C. Comparison of various formats space requirements Table 6 and Table 7 show the space requirements of all formats im- plemented as detailed in Table4 and Table 5. Note that fixed format fix1 - fix5 have comparable range and pre- cision to floating formats float1 - float5.... ..."

### Table 1: An Example of Fixed-Point Addition

"... In PAGE 5: ... Detailed implementation of the Fixed-Point adder based on a Ripple Carry Adder and a Carry Lookahead architecture are shown in Figure 12 and Figure 13 respectively. Table1 gives an exam- ple of this parameterized adder. The term parameterized indicates that the length of integer part and fractional part can be set through two generic variables: int lens and frac lens for the length of integer part and fractional part separately.... ..."

### Table 3. The overloaded operators in fixed point

"... In PAGE 2: ... Our approach is very similar to the FixPt C++ class library. We overloaded the basic math operators ( Table3 ), analyz- ing the dynamic range of each internal variables. The pro- cess of profiling starts defining an identifier for each real variable: Id = trace( realvar ) The occurrences of realvar after calculation will be stored in a custom list: traceid(Id, realvar) Such profiling procedure produces the required IWL for each considered real variable.... ..."

### Table 1. First 32 Fixed Points of Michael

"... In PAGE 10: ...8 GHz, and the pro- gram only takes 2-3 minutes to decide whether there exists a xed point for a given Ri. We provide the rst 32 xed points found by using our method in Table1 (Numbers are hexadecimal and listed in increasing or- der according to Ri). A more complete table is provided in the Appendix... ..."

### Table 2: Fixed-point DSPs.

"... In PAGE 2: ... The control from a microprocessor can be achieved via a host in- terface with a word-length of 8 bits. An overview of xed-point DSPs with respect to word-length and cycle time is shown in Table2 . Ba- sically, the precision of the arithmetic can be dou- bled if quantization a ects the stability and numeric precision of the applied algorithm.... ..."

### Table 1: Construction of the fixed-point

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"... In PAGE 3: ...Table1... ..."

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### TABLE IV FIXED POINT PARAMETERSUPDATED IN EACH ITERATION

2003

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