0.04/0.33 WORST_CASE(?,O(n^2)) 0.04/0.33 0.04/0.33 Preprocessing Cost Relations 0.04/0.33 ===================================== 0.04/0.33 0.04/0.33 #### Computed strongly connected components 0.04/0.33 0. recursive : [evalspeedpldi3bb2in/7,evalspeedpldi3bb3in/7,evalspeedpldi3bb4in/7,evalspeedpldi3bb5in/7] 0.04/0.33 1. non_recursive : [evalspeedpldi3stop/5] 0.04/0.33 2. non_recursive : [evalspeedpldi3returnin/5] 0.04/0.33 3. non_recursive : [exit_location/1] 0.04/0.33 4. non_recursive : [evalspeedpldi3bb5in_loop_cont/6] 0.04/0.33 5. non_recursive : [evalspeedpldi3entryin/5] 0.04/0.33 6. non_recursive : [evalspeedpldi3start/5] 0.04/0.33 0.04/0.33 #### Obtained direct recursion through partial evaluation 0.04/0.33 0. SCC is partially evaluated into evalspeedpldi3bb5in/7 0.04/0.33 1. SCC is completely evaluated into other SCCs 0.04/0.33 2. SCC is completely evaluated into other SCCs 0.04/0.33 3. SCC is completely evaluated into other SCCs 0.04/0.33 4. SCC is partially evaluated into evalspeedpldi3bb5in_loop_cont/6 0.04/0.33 5. SCC is partially evaluated into evalspeedpldi3entryin/5 0.04/0.33 6. SCC is partially evaluated into evalspeedpldi3start/5 0.04/0.33 0.04/0.33 Control-Flow Refinement of Cost Relations 0.04/0.33 ===================================== 0.04/0.33 0.04/0.33 ### Specialization of cost equations evalspeedpldi3bb5in/7 0.04/0.33 * CE 8 is refined into CE [11] 0.04/0.33 * CE 7 is refined into CE [12] 0.04/0.33 * CE 5 is refined into CE [13] 0.04/0.33 * CE 6 is refined into CE [14] 0.04/0.33 0.04/0.33 0.04/0.33 ### Cost equations --> "Loop" of evalspeedpldi3bb5in/7 0.04/0.33 * CEs [13] --> Loop 11 0.04/0.33 * CEs [14] --> Loop 12 0.04/0.33 * CEs [11] --> Loop 13 0.04/0.33 * CEs [12] --> Loop 14 0.04/0.33 0.04/0.33 ### Ranking functions of CR evalspeedpldi3bb5in(A,B,C,D,E,F,G) 0.04/0.33 0.04/0.33 #### Partial ranking functions of CR evalspeedpldi3bb5in(A,B,C,D,E,F,G) 0.04/0.33 * Partial RF of phase [11,12]: 0.04/0.33 - RF of loop [11:1]: 0.04/0.33 A-C depends on loops [12:1] 0.04/0.33 B-C-1 depends on loops [12:1] 0.04/0.33 - RF of loop [12:1]: 0.04/0.33 -A+C+1 depends on loops [11:1] 0.04/0.33 B-D 0.04/0.33 C depends on loops [11:1] 0.04/0.33 0.04/0.33 0.04/0.33 ### Specialization of cost equations evalspeedpldi3bb5in_loop_cont/6 0.04/0.33 * CE 10 is refined into CE [15] 0.04/0.33 * CE 9 is refined into CE [16] 0.04/0.33 0.04/0.33 0.04/0.33 ### Cost equations --> "Loop" of evalspeedpldi3bb5in_loop_cont/6 0.04/0.33 * CEs [15] --> Loop 15 0.04/0.33 * CEs [16] --> Loop 16 0.04/0.33 0.04/0.33 ### Ranking functions of CR evalspeedpldi3bb5in_loop_cont(A,B,C,D,E,F) 0.04/0.33 0.04/0.33 #### Partial ranking functions of CR evalspeedpldi3bb5in_loop_cont(A,B,C,D,E,F) 0.04/0.33 0.04/0.33 0.04/0.33 ### Specialization of cost equations evalspeedpldi3entryin/5 0.04/0.33 * CE 3 is refined into CE [17] 0.04/0.33 * CE 4 is refined into CE [18,19,20] 0.04/0.33 * CE 2 is refined into CE [21] 0.04/0.33 0.04/0.33 0.04/0.33 ### Cost equations --> "Loop" of evalspeedpldi3entryin/5 0.04/0.33 * CEs [17] --> Loop 17 0.04/0.33 * CEs [18,19,20] --> Loop 18 0.04/0.33 * CEs [21] --> Loop 19 0.04/0.33 0.04/0.33 ### Ranking functions of CR evalspeedpldi3entryin(A,B,C,D,E) 0.04/0.33 0.04/0.33 #### Partial ranking functions of CR evalspeedpldi3entryin(A,B,C,D,E) 0.04/0.33 0.04/0.33 0.04/0.33 ### Specialization of cost equations evalspeedpldi3start/5 0.04/0.33 * CE 1 is refined into CE [22,23,24] 0.04/0.33 0.04/0.33 0.04/0.33 ### Cost equations --> "Loop" of evalspeedpldi3start/5 0.04/0.33 * CEs [24] --> Loop 20 0.04/0.33 * CEs [23] --> Loop 21 0.04/0.33 * CEs [22] --> Loop 22 0.04/0.33 0.04/0.33 ### Ranking functions of CR evalspeedpldi3start(A,B,C,D,E) 0.04/0.33 0.04/0.33 #### Partial ranking functions of CR evalspeedpldi3start(A,B,C,D,E) 0.04/0.33 0.04/0.33 0.04/0.33 Computing Bounds 0.04/0.33 ===================================== 0.04/0.33 0.04/0.33 #### Cost of chains of evalspeedpldi3bb5in(A,B,C,D,E,F,G): 0.04/0.33 * Chain [[11,12],14]: 1*it(11)+1*it(12)+0 0.04/0.33 Such that:aux(19) =< B 0.04/0.33 aux(4) =< B-C 0.04/0.33 it(12) =< B-D 0.04/0.33 aux(3) =< it(12)*aux(19) 0.04/0.33 it(11) =< aux(3)+aux(4) 0.04/0.33 0.04/0.33 with precondition: [E=2,F=0,B=G,A>=1,C>=0,D>=0,B>=A+1,B>=D+1] 0.04/0.33 0.04/0.33 * Chain [[11,12],13]: 1*it(11)+1*it(12)+0 0.04/0.33 Such that:aux(19) =< B 0.04/0.33 aux(4) =< B-C 0.04/0.33 it(12) =< B-D 0.04/0.33 aux(3) =< it(12)*aux(19) 0.04/0.33 it(11) =< aux(3)+aux(4) 0.04/0.33 0.04/0.33 with precondition: [E=3,A>=1,C>=0,D>=0,B>=A+1,B>=D+1] 0.04/0.33 0.04/0.33 * Chain [13]: 0 0.04/0.33 with precondition: [E=3,A>=1,C>=0,D>=0,B>=A+1] 0.04/0.33 0.04/0.33 0.04/0.33 #### Cost of chains of evalspeedpldi3bb5in_loop_cont(A,B,C,D,E,F): 0.04/0.33 * Chain [16]: 0 0.04/0.33 with precondition: [A=2,B>=1,C>=B+1] 0.04/0.33 0.04/0.33 * Chain [15]: 0 0.04/0.33 with precondition: [A=3,B>=1,C>=B+1] 0.04/0.33 0.04/0.33 0.04/0.33 #### Cost of chains of evalspeedpldi3entryin(A,B,C,D,E): 0.04/0.33 * Chain [19]: 0 0.04/0.33 with precondition: [0>=A] 0.04/0.33 0.04/0.33 * Chain [18]: 2*s(3)+2*s(5)+0 0.04/0.33 Such that:aux(24) =< B 0.04/0.33 s(3) =< aux(24) 0.04/0.33 s(4) =< s(3)*aux(24) 0.04/0.33 s(5) =< s(4)+aux(24) 0.04/0.33 0.04/0.33 with precondition: [A>=1,B>=A+1] 0.04/0.33 0.04/0.33 * Chain [17]: 0 0.04/0.33 with precondition: [A>=B] 0.04/0.33 0.04/0.33 0.04/0.33 #### Cost of chains of evalspeedpldi3start(A,B,C,D,E): 0.04/0.33 * Chain [22]: 0 0.04/0.33 with precondition: [0>=A] 0.04/0.33 0.04/0.33 * Chain [21]: 2*s(12)+2*s(14)+0 0.04/0.33 Such that:s(11) =< B 0.04/0.33 s(12) =< s(11) 0.04/0.33 s(13) =< s(12)*s(11) 0.04/0.33 s(14) =< s(13)+s(11) 0.04/0.33 0.04/0.33 with precondition: [A>=1,B>=A+1] 0.04/0.33 0.04/0.33 * Chain [20]: 0 0.04/0.33 with precondition: [A>=B] 0.04/0.33 0.04/0.33 0.04/0.33 Closed-form bounds of evalspeedpldi3start(A,B,C,D,E): 0.04/0.33 ------------------------------------- 0.04/0.33 * Chain [22] with precondition: [0>=A] 0.04/0.33 - Upper bound: 0 0.04/0.33 - Complexity: constant 0.04/0.33 * Chain [21] with precondition: [A>=1,B>=A+1] 0.04/0.33 - Upper bound: 2*B*B+4*B 0.04/0.33 - Complexity: n^2 0.04/0.33 * Chain [20] with precondition: [A>=B] 0.04/0.33 - Upper bound: 0 0.04/0.33 - Complexity: constant 0.04/0.33 0.04/0.33 ### Maximum cost of evalspeedpldi3start(A,B,C,D,E): nat(B)*2*nat(B)+nat(B)*4 0.04/0.33 Asymptotic class: n^2 0.04/0.33 * Total analysis performed in 252 ms. 0.04/0.33 0.04/0.43 EOF