"... In PAGE 4: ...n the other names. Processes which di er by -conversion, , are identi ed. The actions that a process can perform, ranged over by , are de ned by the following syntax: ::= x(z) xy x(z): Names x and y are free names of , (fn( )), whereas z is a bound name (bn( )); moreover n( ) = fn( ) [ bn( ). The transitions for the late oper- ational semantics are de ned by the rules of Table1 (rules SUMr, PARr, COMr and CLOSEr have been omitted). In transition p x(y) ?! p0 (resp.... In PAGE 7: ... Rules for 7?! and 7?! appear in Table 2 (rules SUMr f , SUMr b , PARr f, PARr b, COMr and CLOSEr have been omitted). Notice that some of the rules of Table1 have two counterparts, according to whether they refer to free or bound transitions. Some comments on the rules of Table 2 are in... In PAGE 8: ... This happens, for instance, in rule COM: in this case, the target s of the input transition is applied to the name y, which is the message of the output transition. Consider now rules RES: in Table1 these rules have a side-condition; namely a transition of p with label can be performed also by ( x)p provided x does not appear among the names of . This side-condition is expressed in the LF encoding by requiring that the process px perform the transition independently from the name x, which is chosen to instantiate abstraction p.... In PAGE 8: ... In this way, the variable x, being bound, behaves as \generic quot; hence di erent from all the names in . Rule OPEN is similar; in this case, however, according to Table1 , the value of the free output has to coincide with the name of the restriction. The free output becomes a bound output, so the restriction is removed in the target state, which then becomes an abstraction.... ..."

"... In PAGE 11: ...7% zebra 89.1% In Table2 we show the number of dynamic constraint store insertions and deletions for these benchmarks. The number of insertions and and the number of deletions saved out by late storage analysis is of course identical.... ..."

"... In PAGE 11: ...7% zebra 89.1% In Table2 we show the number of dynamic constraint store insertions and deletions for these benchmarks. The number of insertions and and the number of deletions saved out by late storage analysis is of course identical.... ..."

"... In PAGE 11: ...7% zebra 89.1% In Table2 we show the number of dynamic constraint store insertions and deletions for these benchmarks. The number of insertions and and the number of deletions saved out by late storage analysis is of course identical.... ..."

"... In PAGE 2: ... a42a43a8 is the angle of rotation at each iteration and is set by the coordinate system used. As each iteration of the CORDIC equations is performed, either a39 (rotation mode) or a25 (vectoring mode) is driven to 0 and the equations in Table1 are generated. Each coordinate system is useful for computing different functions.... In PAGE 2: ... For the functions of interest, the circular and hyperbolic sys- tems are used. Table1 describes the equations generated after a54 iterations for each coordinate system and mode of operation. Table 1 also provides the equations for a59 a8 .... In PAGE 2: ... The circular coordinate system is used for all of the trigonometric functions. From Table1 , by setting a25a11a60 to zero the equations reduce to: a7a9a8a61a14 a59 a8a63a62a58a7a64a60 a56a58a57a11a51 a39a65a60 (4) a25 a8 a14 a59 a8 a62a66a7 a60 a51a53a52a67a54 a39 a60 (5) Therefore, with a7a64a60 = 1/a59 a8 , after n iterations of equations 1, 2 and 3, a7 a8 a14 a56a66a57a11a51 a39 a60 and a25 a8 a14 a51a53a52a67a54 a39 a60 . 2.... In PAGE 3: ...Table1 : CORDIC equations[11] Coordinate rotation vectoring scale rotation System mode mode factor, a59 a8 angle, a42a43a8 m = 1 a7a9a8a75a14 a59 a8 a44 a7a9a60 a56a66a57a11a51 a39a65a60a15a18a21a25a11a60 a51a66a52a67a54 a39a65a60a53a48 a7a17a8a75a14 a59 a8a78a77 a44 a7a17a79 a60 a35a37a25a26a79 a60 a48 a80a50a81 a8a11a82a78a60a84a83 a85 a35a86a27 a29 a79 a8 (circular) a25a31a8a75a14 a59 a8 a44 a25a11a60 a56a58a57a11a51 a7a64a60a76a35a37a7a64a60 a51a53a52a55a54 a39a65a60a53a48 a25a31a8a75a14a88a87 a69a72a71 a54 a29 a12 a27 a29 a8 a39a65a8a75a14a40a87 a39a43a8a89a14a88a39a65a60a90a35a91a69a72a71 a54 a29 a12 a25a11a60a43a73a74a7a64a60 a92 1.64676 (n = 0 to a93 ) m = 0 a7 a8 a14a34a7 a60 a7 a8 a14a34a7 a60 no scale (linear) a25a24a8a89a14a88a25a11a60a90a35a37a7a64a60a65a25a11a60 a25a31a8a75a14a88a87 factor a27 a29 a12 a39a65a8a75a14a40a87 a39a43a8a75a14a88a39a65a60a90a35a37a25a11a60a43a73a74a7a64a60 m = -1 a7 a8 a14 a59 a8 a44 a7 a60 a56a58a57a11a51a43a94 a39 a60 a35a37a25 a60 a51a66a52a67a54a46a94 a39 a60 a48 a7 a8 a14 a59 a8 a77 a44 a7 a79 a60 a18a21a25 a79 a60 a48 a80 a81 a8a11a82a32a12 a83 a85 a35a86a27 a29 a79 a8 (hyperbolic) a25 a8 a14 a59 a8 a44 a25 a60 a56a58a57a11a51a43a94 a7 a60 a35a37a7 a60 a51a66a52a67a54 a39 a60 a48 a25 a8 a14a88a87 a69a72a71 a54a46a94 a29 a12 a27 a29 a8 a39 a8 a14a40a87 a39 a8 a14a34a39 a60 a35a37a69a72a71 a54a46a94 a29 a12 a25 a60 a73a74a7 a60 a92 0.... In PAGE 3: ...terations must also be repeated (n = 4, 13,40,...,k,3k+1,...) or the vector will not converge. This generates the hyperbolic equations in Table1 for each mode of operation. As can be seen, the same methods can be used to calculate a51a53a52a67a54a46a94 , a56a66a57a11a51a65a94 and a69a72a71 a54a46a94 a29 a12 as were used for a51a53a52a67a54 , a56a66a57a11a51 and a69a72a71 a54 a29 a12 .... In PAGE 3: ... As can be seen, the same methods can be used to calculate a51a53a52a67a54a46a94 , a56a66a57a11a51a65a94 and a69a72a71 a54a46a94 a29 a12 as were used for a51a53a52a67a54 , a56a66a57a11a51 and a69a72a71 a54 a29 a12 . From [10]: a83 a105 a14 a77 a44 a7 a79 a18a21a25 a79 a48 (9) where a7 a60 = a105 + 1/4 and a25 a60 = a105 - 1/4 and, a106 a54 a105 a14a88a27a107a62a53a69a72a71 a54a46a94 a29 a12a11a108 a25 a60 a73a43a7 a60a58a109 (10) where a7a64a60 = a105 + 1 and a25a11a60 = a105 - 1 By using the vectoring mode of operation from Table1 , the square root and natural log can be directly computed. The square root of a value (a105 ) is generated by setting a7 a60 a14 a105 a35 a85 a73 a108 a110 a59 a79 a8 a109 and a25a31a60a111a14 a105 a18 a85 a73 a108 a110 a59 a79 a8 a109 .... ..."