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Compute modular inverses of integers faster #2053

Merged
merged 4 commits into from
Jan 9, 2018
Merged

Compute modular inverses of integers faster #2053

merged 4 commits into from
Jan 9, 2018

Commits on Jan 8, 2018

  1. kernel: use AInvInt in some more places

    @fingolfin
    fingolfin committed Jan 8, 2018
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  2. kernel: clang-format InverseModInt

    @fingolfin
    fingolfin committed Jan 8, 2018
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  3. kernel: speed up InverseModInt for small inputs 

    Before (on a 64 bit machine):

gap> q:=3;;n:=7;; for i in [1..2000000] do INVMODINT(q,n); od; time;
360
gap> q:=3;;n:=2^59;; for i in [1..2000000] do INVMODINT(q,n); od; time;
350
gap> q:=3;;n:=2^60;; for i in [1..2000000] do INVMODINT(q,n); od; time;
373
gap> q:=3^60;;n:=7;; for i in [1..2000000] do INVMODINT(q,n); od; time;
380
gap> q:=3^60;;n:=2^59;; for i in [1..2000000] do INVMODINT(q,n); od; time;
1234
gap> q:=3^60;;n:=2^60;; for i in [1..2000000] do INVMODINT(q,n); od; time;
1256
gap> q:=2^6000;;n:=3^6000;; for i in [1..6000] do INVMODINT(q,n); od; time;
637

After:

gap> q:=3;;n:=7;; for i in [1..2000000] do INVMODINT(q,n); od; time;
222
gap> q:=3;;n:=2^59;; for i in [1..2000000] do INVMODINT(q,n); od; time;
219
gap> q:=3;;n:=2^60;; for i in [1..2000000] do INVMODINT(q,n); od; time;
350
gap> q:=3^60;;n:=7;; for i in [1..2000000] do INVMODINT(q,n); od; time;
205
gap> q:=3^60;;n:=2^59;; for i in [1..2000000] do INVMODINT(q,n); od; time;
1193
gap> q:=3^60;;n:=2^60;; for i in [1..2000000] do INVMODINT(q,n); od; time;
1257
gap> q:=2^6000;;n:=3^6000;; for i in [1..6000] do INVMODINT(q,n); od; time;
653
    @fingolfin
    fingolfin committed Jan 8, 2018
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  4. kernel: simplify and sped up ModRat using InverseModInt 

    Before (on a 64 bit machine):

gap> q:=1/3;;n:=7;; for i in [1..2000000] do x:= q mod n; od; time;
258
gap> q:=1/3;;n:=2^59;; for i in [1..2000000] do x:= q mod n; od; time;
295
gap> q:=1/3;;n:=2^60;; for i in [1..2000000] do x:= q mod n; od; time;
569
gap> q:=1/3^60;;n:=7;; for i in [1..2000000] do x:= q mod n; od; time;
537
gap> q:=1/3^60;;n:=2^59;; for i in [1..2000000] do x:= q mod n; od; time;
2364
gap> q:=1/3^60;;n:=2^60;; for i in [1..2000000] do x:= q mod n; od; time;
2821
gap> q:=1/2^6000;;n:=3^6000;; for i in [1..6000] do x:= q mod n; od; time;
19358

After:

gap> q:=1/3;;n:=7;; for i in [1..2000000] do x:= q mod n; od; time;
255
gap> q:=1/3;;n:=2^59;; for i in [1..2000000] do x:= q mod n; od; time;
244
gap> q:=1/3;;n:=2^60;; for i in [1..2000000] do x:= q mod n; od; time;
392
gap> q:=1/3^60;;n:=7;; for i in [1..2000000] do x:= q mod n; od; time;
245
gap> q:=1/3^60;;n:=2^59;; for i in [1..2000000] do x:= q mod n; od; time;
1219
gap> q:=1/3^60;;n:=2^60;; for i in [1..2000000] do x:= q mod n; od; time;
1292
gap> q:=1/2^6000;;n:=3^6000;; for i in [1..6000] do x:= q mod n; od; time;
692
    @fingolfin
    fingolfin committed Jan 8, 2018
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    79ec5f3 View commit details
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