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t_check.pas
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{Main test program for MPArith/mp_int, (c) W.Ehrhardt 2004-2012}
{Many test cases derived from M.J. Fromberger's IMATH }
{Other tests are generated with ARIBAS, Pari/GP, NX and others }
program t_check;
{$x+} {pchar I/O}
{$i STD.INC}
{$i mp_conf.inc}
{$i+} {RTE on I/O error}
{$ifndef FPC}
{$N+}
{$endif}
{$ifdef APPCONS}
{$apptype console}
{$endif}
uses
{$ifdef WINCRT}
WinCRT,
{$endif}
BTypes, mp_types, mp_base,
{$ifdef MPC_Diagnostic}
mp_supp,
{$endif}
mp_prime, mp_modul, mp_numth, mp_pfu, mp_prng, mp_rsa, pfdu, t_check1;
{---------------------------------------------------------------------------}
procedure gcd32_test;
type
t3l= array[1..3] of longint;
const
NTC = 20;
testcase: array[1..NTC] of t3l =
( (0, 0, 0),
(0, 1, 1),
(0, 2, 2),
(0, 3, 3),
(0, 4, 4),
(1, 1, 1),
(1, 2, 1),
(1, 3, 1),
(1, 4, 1),
(2, 2, 2),
(2, 3, 1),
(2, 4, 2),
(3, 3, 3),
(3, 4, 1),
(6,12, 6),
(444444444, 666666666, 222222222),
($40000000, $60000000, $20000000),
(longint($80000000), longint($C0000000), $40000000),
(longint($C6AEA155), longint($84746B8E), 1111111111),
(MaxLongint, -1, 1));
var
i,cnt,f: integer;
TA, TB, TC: longint;
begin
writeln('Test gcd32');
cnt := 0;
f := 0;
for i:=1 to NTC do begin
inc(cnt);
TA := testcase[i][1];
TB := testcase[i][2];
TC := testcase[i][3];
if gcd32u(TA, TB) <> TC then begin
writeln('gcd32u: error for testcase: ',i);
inc(f);
end;
inc(cnt);
if gcd32u(TB, TA) <> TC then begin
writeln('gcd32u: error for swapped testcase: ',i);
inc(f);
end;
if (TA>=0) and (TB>=0) then begin
inc(cnt);
if gcd32(TA, TB) <> TC then begin
writeln('gcd32: error for (++) testcase : ',i);
inc(f);
end;
inc(cnt);
if gcd32(TA, -TB) <> TC then begin
writeln('gcd32: error for (+-) testcase : ',i);
inc(f);
end;
inc(cnt);
if gcd32(-TA, TB) <> TC then begin
writeln('gcd32: error for (-+) testcase : ',i);
inc(f);
end;
inc(cnt);
if gcd32(-TA, -TB) <> TC then begin
writeln('gcd32: error for (--) testcase : ',i);
inc(f);
end;
end;
end;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure xgcd32_test;
var
a,b,u,v,d,c,i: longint;
{$ifdef HAS_INT64}
a64,b64: int64;
{$else}
a64,b64: comp;
{$endif}
f: integer;
begin
writeln('Test xgcd32');
f := 0;
for a:=-100 to 100 do begin
if f<>0 then break;
for b:=-100 to 100 do begin
if f<>0 then break;
xgcd32(a,b,u,v,d);
c := gcd32(a,b);
if c<>d then begin
writeln('GCD diff: a=',a,', b=',b,', d=',d, ', c=',c);
inc(f);
end;
{Here there will be no overflows with |a|,|b| <= 100}
if a*u+b*v<>d then begin
writeln('a*u+b*v<>d for a=',a,', b=',b,', u=',v, ', v=',v, ', d=',d);
inc(f);
end;
end;
end;
for i:=1 to 50000 do begin
if i and $3FF = 0 then write('.');
a := mp_random_int;
b := mp_random_int;
xgcd32(a,b,u,v,d);
c := gcd32(a,b);
if c<>d then begin
writeln('GCD diff: a=',a,', b=',b,', d=',d, ', c=',c);
inc(f);
break;
end;
a64 := a;
b64 := b;
if a64*u + b64*v <> d then begin
writeln('a*u+b*v<>d for a=',a,', b=',b,', u=',v, ', v=',v, ', d=',d);
inc(f);
break;
end;
end;
writeln;
writeln('No. of checks failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure IsLong_Test;
var
i,cnt,k,f: word;
xl: longint;
isli, is32: boolean;
begin
f := 0;
cnt := 0;
mp_zero(a);
writeln('Test mp_is_longint: ');
for i:=0 to 64 do begin
isli := mp_is_longint(a,xl);
is32 := mp_bitsize(a)<32;
if isli<>is32 then inc(f)
else begin
if isli then begin
mp_set_int(c,xl);
if mp_is_ne(a,c) then inc(f);
end;
end;
mp_chs(a,b);
isli := mp_is_longint(b,xl);
is32 := mp_bitsize(b)<32;
if isli<>is32 then inc(f)
else begin
if isli then begin
mp_set_int(d,xl);
if mp_is_ne(b,d) then inc(f);
end;
end;
inc(cnt,2);
mp_shl(a,1,a);
mp_inc(a);
end;
for i:=0 to 50 do begin
write('.');
for k:=1 to 1000 do begin
mp_rand_ex(a, 1 + i div DIGIT_BIT, false);
if random(2)=0 then mp_chs(a,a);
isli := mp_is_longint(a,xl);
is32 := mp_bitsize(a)<32;
if isli<>is32 then inc(f)
else begin
if isli then begin
mp_set_int(c,xl);
if mp_is_ne(a,c) then inc(f);
end;
end;
inc(cnt);
end;
end;
writeln;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure TestPrimes16Index;
var
n: word;
i: integer;
OK: boolean;
begin
write('Test Primes16Index ... ');
OK := true;
for i:=1 to NumPrimes16 do begin
if i <> Primes16Index(Primes16[i]) then begin
OK := false;
inc(totalfailed);
writeln('Unstable for i=',i);
continue;
end;
end;
for n:=0 to $FFFF do begin
i := Primes16Index(n);
if i>NumPrimes16 then begin
OK := false;
inc(totalfailed);
writeln('Index too large, n=',n, ', i=',i);
continue;
end;
if i=0 then begin
OK := false;
inc(totalfailed);
writeln('Index 0, n=',n);
continue;
end;
if (n>1) and (Primes16[i]>n) then begin
OK := false;
inc(totalfailed);
writeln('Primes16[i] > n, n=',n);
end;
if (i<NumPrimes16) and (Primes16[i+1]<=n) then begin
OK := false;
inc(totalfailed);
writeln('Primes16[i] not maximal, n=',n, ', i=',i);
end;
end;
if OK then writeln('passed');
writeln;
end;
{---------------------------------------------------------------------------}
procedure test_pi_lphi;
type
ttpprec = record x,a,phi,ppi: longint end;
const
NTC = 13;
tcases: array[1..NTC] of ttpprec = (
(x: 10000; a: 8; phi: 1711; ppi: 1229), {Riesel [40]}
(x: 100000; a: 7; phi: 18053; ppi: 9592), {...}
(x: 15485864; a: 53; phi: 1568715; ppi: 1000000), {Lehmer [39]}
(x: 20000000; a: 58; phi: 1988057; ppi: 1270607), {...}
(x: 25000000; a: 61; phi: 2458751; ppi: 1565927),
(x: 32452845; a: 66; phi: 3140783; ppi: 2000000),
(x: 33000000; a: 66; phi: 3193726; ppi: 2031667),
(x: 37000000; a: 67; phi: 3569832; ppi: 2261623),
(x: 40000000; a: 68; phi: 3847872; ppi: 2433654),
(x: 90000000; a: 25; phi: 10826326; ppi: 5216954),
(x: 100000000; a: 90; phi: 9110819; ppi: 5761455),
(x: 999000000; a: 40; phi: 107108994; ppi: 50799577),
(x:1000000000; a: 40; phi: 107216231; ppi: 50847534));
var
i,cnt,f: integer;
tphi, tpi: longint;
begin
write('Test primepi32 / lsumphi32 ');
cnt := 0;
f := 0;
for i:=1 to NTC do with tcases[i] do begin
write('.');
tpi := primepi32(x);
tphi := lsumphi32(x,a);
inc(cnt,2);
if tpi<>ppi then begin
inc(f);
writeln('Failure primepi32 for i =', i);
end;
if tphi<>phi then begin
inc(f);
writeln('Failure lphi for i =', i);
end;
end;
writeln;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure test_prime32;
const {http://primes.utm.edu/nthprime/index.php#nth}
p10: array[0..8] of longint = (2,29,541,7919,104729,1299709,15485863,
179424673,2038074743);
var
i,cnt,f: integer;
p,k: longint;
begin
write('Test prime32 ... ');
cnt := 0;
f := 0;
k := 1;
for i:=0 to 8 do begin
if i<>0 then k := 10*k;
p := prime32(k);
inc(cnt);
if p<>p10[i] then begin
inc(f);
writeln('Failure for k =', k);
end;
end;
writeln;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure test_4sq;
{$ifdef BIT16}
const
BITSI = 4;
{$else}
const
BITSI = 8;
{$endif}
var
i,bits,cnt,f: integer;
begin
f := 0;
cnt := 0;
write('mp_4sq test ');
for i:=1 to 100 do begin
if odd(i) then bits := 50*BITSI
else begin
bits := i*BITSI;
write('.');
end;
mp_rand_bits_ex(e,bits,false);
if random(4)=0 then mp_shl(e,random(10),e);
case random(3) of
0: mp_4sq(e,a,b,c,d);
1: mp_4sq_sa(e,a,b,c,d);
2: mp_4sq(e,a,b,c,d);
end;
inc(cnt);
mp_sqr(a,s);
mp_sqr(b,t); mp_add(s,t,s);
mp_sqr(c,t); mp_add(s,t,s);
mp_sqr(d,t); mp_add(s,t,s);
if mp_is_ne(s,e) then begin
mp_writeln('e = ',e);
mp_writeln('s = ',s);
mp_writeln('a = ',a);
mp_writeln('b = ',b);
mp_writeln('c = ',c);
mp_writeln('d = ',d);
inc(f);
end;
end;
writeln;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{$ifndef BIT16}
{---------------------------------------------------------------------------}
procedure astr_test;
var
i,cnt,f: integer;
bits: longint;
r: word;
s: ansistring;
begin
f := 0;
cnt := 0;
writeln('mp_(read)_radix_astr test: ');
for i:=1 to 100 do begin
if i and 2 = 0 then write('.');
r := 2+random(MaxRadix-1);
mp_show_plus := random(2)=0;
bits := sqr(longint(i))*10;
mp_rand_bits_ex(a,bits,false);
if random(2)=0 then mp_chs(a,a);
s := mp_radix_astr(a,r);
mp_read_radix_astr(b,s,r);
inc(cnt);
if mp_is_ne(a,b) then begin
writeln('Failed for i/bits/radix=',i,'/',bits,'/',r);
inc(f);
end;
end;
writeln;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{$endif}
{---------------------------------------------------------------------------}
procedure test_catalan;
var
i,cnt,f: integer;
p: word;
n,am,bm: longint;
{$ifdef MP_16BIT}
{$ifdef BIT16}
const imax=30;
{$else}
const imax=35;
{$endif}
{$else}
const imax=40;
{$endif}
const
NSC = 19;
sc: array[0..NSC] of longint = {http://oeis.org/A000108}
(1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012,
742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190);
begin
f := 0;
cnt := 0;
writeln('mp_catalan test: ');
for i:=0 to NSC do begin
inc(cnt);
mp_catalan(i,a);
mp_sub_int(a,sc[i],a);
if not mp_is0(a) then begin
inc(f);
writeln('Small check failed for i=',i);
end;
end;
for i:=2 to imax do begin
inc(cnt);
{Check: (1/2)*Catalan((p^2-1)/2) mod p^2 = 2^p-1 mod p^2}
p := primes16[2*i];
n := sqr(longint(p));
mp_catalan((n-1) div 2, a);
mp_shr1(a);
mp_mersenne(p,b);
mp_mod_int(a,n,am);
mp_mod_int(b,n,bm);
if am<>bm then begin
inc(f);
writeln('Failed for p=',p);
end;
if odd(i) then write('.');
end;
{check C(n) = sum(C(i)*C(n-1-i), i=0..n-1}
mp_catalan(1000,a);
for i:=0 to 999 do begin
if i and 63 = 0 then write('+');
mp_catalan(i,b);
mp_catalan(999-i,c);
mp_mul(b,c,d);
mp_sub(a,d,a);
end;
inc(cnt);
if not mp_is0(a) then begin
inc(f);
writeln('Summation check failed');
end;
writeln;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure test_poch_perm;
var
i,n,cnt,f: integer;
const
tpoch : array[-6..6, 0..7] of longint = (
( 1, -6, 30, -120, 360, -720, 720, 0 ),
( 1, -5, 20, -60, 120, -120, 0, 0 ),
( 1, -4, 12, -24, 24, 0, 0, 0 ),
( 1, -3, 6, -6, 0, 0, 0, 0 ),
( 1, -2, 2, 0, 0, 0, 0, 0 ),
( 1, -1, 0, 0, 0, 0, 0, 0 ),
( 1, 0, 0, 0, 0, 0, 0, 0 ),
( 1, 1, 2, 6, 24, 120, 720, 5040 ),
( 1, 2, 6, 24, 120, 720, 5040, 40320 ),
( 1, 3, 12, 60, 360, 2520, 20160, 181440 ),
( 1, 4, 20, 120, 840, 6720, 60480, 604800 ),
( 1, 5, 30, 210, 1680, 15120, 151200, 1663200 ),
( 1, 6, 42, 336, 3024, 30240, 332640, 3991680 ));
const
tperm : array[0..8, 0..8] of word = (
( 1, 0, 0, 0, 0, 0, 0, 0, 0 ),
( 1, 1, 0, 0, 0, 0, 0, 0, 0 ),
( 1, 2, 2, 0, 0, 0, 0, 0, 0 ),
( 1, 3, 6, 6, 0, 0, 0, 0, 0 ),
( 1, 4, 12, 24, 24, 0, 0, 0, 0 ),
( 1, 5, 20, 60, 120, 120, 0, 0, 0 ),
( 1, 6, 30, 120, 360, 720, 720, 0, 0 ),
( 1, 7, 42, 210, 840, 2520, 5040, 5040, 0 ),
( 1, 8, 56, 336, 1680, 6720, 20160, 40320, 40320 ));
{$ifdef BIT16}
const
ifmax = 8;
{$else}
const
ifmax = 14;
{$endif}
begin
f := 0;
cnt := 0;
write('Test mp_product / mp_poch / mp_perm ');
for n:=-6 to 6 do begin
write('.');
for i:=0 to 7 do begin
inc(cnt);
mp_poch(n,i,a);
mp_sub_int(a,tpoch[n,i],b);
if not mp_iszero(b) then begin
writeln('mp_poch tab fail n,i =',n,',',i);
inc(f);
end;
end;
end;
inc(cnt,2);
mp_read_decimal_str(b,'6729457515998774705268610104629483525487942150402731785206632546304000000000');
mp_poch(60,40,a);
if mp_is_ne(a,b) then begin
writeln('mp_poch(60,40) failed');
inc(f);
end;
mp_read_decimal_str(b,'45159067006671175434518243598614826795313039459718126370816000000000');
mp_poch(-70,40,a);
if mp_is_ne(a,b) then begin
writeln('mp_poch(-70,40) failed');
inc(f);
end;
for n:=0 to 8 do begin
write('.');
for i:=0 to 8 do begin
inc(cnt);
mp_perm(n,i,a);
mp_sub_int(a,tperm[n,i],b);
if not mp_iszero(b) then begin
writeln('mp_perm tab fail n,i = ',n,',',i);
inc(f);
end;
end;
end;
inc(cnt);
mp_read_decimal_str(b,'3420189997285434351598365756849270130350567547616624640000000000');
mp_perm(60,40,a);
if mp_is_ne(a,b) then begin
writeln('mp_perm(60,40) failed');
inc(f);
end;
for i:=0 to ifmax do begin
write('.');
inc(cnt);
n := 1000*i;
mp_fact(n,a);
mp_product(b,1,n);
if mp_is_ne(a,b) then begin
writeln('mp_product failed for i = ',i);
inc(f);
end;
end;
writeln;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure test_EulerPhi;
const
NE1=200;
ea: array[0..NE1] of byte = {with(numtheory): [seq(phi(i),i=0..200)];}
(0,1,1,2,2,4,2,6,4,6,4,10,4,12,6,8,8,16,6,18,8,
12,10,22,8,20,12,18,12,28,8,30,16,20,16,24,12,36,
18,24,16,40,12,42,20,24,22,46,16,42,20,32,24,52,
18,40,24,36,28,58,16,60,30,36,32,48,20,66,32,44,
24,70,24,72,36,40,36,60,24,78,32,54,40,82,24,64,
42,56,40,88,24,72,44,60,46,72,32,96,42,60,40,100,
32,102,48,48,52,106,36,108,40,72,48,112,36,88,56,
72,58,96,32,110,60,80,60,100,36,126,64,84,48,130,
40,108,66,72,64,136,44,138,48,92,70,120,48,112,72,
84,72,148,40,150,72,96,60,120,48,156,78,104,64,132,
54,162,80,80,82,166,48,156,64,108,84,172,56,120,80,
116,88,178,48,180,72,120,88,144,60,160,92,108,72,
190,64,192,96,96,84,196,60,198,80);
const
NE2=10;
nl: array[1..NE2] of longint = ({random values and 2^30}
35690018,1809741004,112970497,1577004683,1997451014,
1419616041,862708834,403211554,2113914896,$40000000);
el: array[1..NE2] of longint = (
13374720,904870500,112970496,1508439240,920131488,
946148112,398173152,201605776,1056571776,$20000000);
var
i,cnt,f: integer;
begin
f := 0;
cnt := 0;
writeln('Test EulerPhi32 ...');
for i:=0 to NE1 do begin
inc(cnt);
if EulerPhi32(i) <> ea[i] then begin
writeln('Failed for i = ',i);
inc(f);
end;
end;
for i:=1 to NE2 do begin
inc(cnt);
if EulerPhi32(nl[i]) <> el[i] then begin
writeln('Failed for ', nl[i]);
inc(f);
end;
end;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure test_carmichael;
const
NC1=200;
ca: array[0..NC1] of byte = {with(numtheory): [seq(lambda(n), n=0..200)];}
(0,1,1,2,2,4,2,6,2,6,4,10,2,12,6,4,4,16,6,18,4,6,
10,22,2,20,12,18,6,28,4,30,8,10,16,12,6,36,18,12,
4,40,6,42,10,12,22,46,4,42,20,16,12,52,18,20,6,
18,28,58,4,60,30,6,16,12,10,66,16,22,12,70,6,72,
36,20,18,30,12,78,4,54,40,82,6,16,42,28,10,88,12,
12,22,30,46,36,8,96,42,30,20,100,16,102,12,12,52,
106,18,108,20,36,12,112,18,44,28,12,58,48,4,110,60,
40,30,100,6,126,32,42,12,130,10,18,66,36,16,136,22,
138,12,46,70,60,12,28,72,42,36,148,20,150,18,48,30,
60,12,156,78,52,8,66,54,162,40,20,82,166,6,156,16,
18,42,172,28,60,20,58,88,178,12,180,12,60,22,36,30,
80,46,18,36,190,16,192,96,12,42,196,30,198,20);
const
NC2=10;
nl: array[1..NC2] of longint = ( {random values and 2^30}
35690018,1809741004,112970497,1577004683,1997451014,
1419616041,862708834,403211554,2113914896, $40000000);
cl: array[1..NC2] of longint = (
30960,452435250,112970496,68565420,12779604,
236537028,99543288,201605776,33017868, $10000000);
var
i,cnt,f: integer;
begin
f := 0;
cnt := 0;
writeln('Test Carmichael32 ...');
for i:=0 to NC1 do begin
inc(cnt);
if Carmichael32(i) <> ca[i] then begin
writeln('Failed for i = ',i);
inc(f);
end;
end;
for i:=1 to NC2 do begin
inc(cnt);
if Carmichael32(nl[i]) <> cl[i] then begin
writeln('Failed for ', nl[i]);
inc(f);
end;
end;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure test_is_carmichael;
var
cnt,f: integer;
begin
f := 0;
cnt := 8;
writeln('Test mp_is_pcarmichael ...');
mp_read_decimal(a,'2140699681');
if not mp_is_pcarmichael(a) then begin
writeln('Failed for ', mp_decimal(a));
inc(f);
end;
mp_read_decimal(a,'2135039017');
if mp_is_pcarmichael(a) then begin
writeln('Failed for ', mp_decimal(a));
inc(f);
end;
mp_read_decimal(a,'725849475559');
if mp_is_pcarmichael(a) then begin
writeln('Failed for ', mp_decimal(a));
inc(f);
end;
mp_read_decimal(a,'9487582789999');
if mp_is_pcarmichael(a) then begin
writeln('Failed for ', mp_decimal(a));
inc(f);
end;
mp_read_decimal(a,'4954039956700380001');
if not mp_is_pcarmichael(a) then begin
writeln('Failed for ', mp_decimal(a));
inc(f);
end;
mp_read_decimal(a,'3887636054124102392503405910694993617809');
if not mp_is_pcarmichael(a) then begin
writeln('Failed for ', mp_decimal(a));
inc(f);
end;
mp_read_decimal(a,'388764511027199999999999999414113587204032640000000000'+
'2943194650080514478879999999507163017775414944305441');
if not mp_is_pcarmichael(a) then begin
writeln('Failed for ', mp_decimal(a));
inc(f);
end;
mp_nextprime(a);
if mp_is_pcarmichael(a) then begin
writeln('Failed for ', mp_decimal(a));
inc(f);
end;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure test_moebius;
const
NM1=200;
ma: array[1..NM1] of shortint = {with(numtheory): [[seq(mobius(x),x=1..200)];}
(1,-1,-1,0,-1,1,-1,0,0,1,-1,0,-1,1,1,0,-1,0,
-1,0,1,1,-1,0,0,1,0,0,-1,-1,-1,0,1,1,1,0,-1,
1,1,0,-1,-1,-1,0,0,1,-1,0,0,0,1,0,-1,0,1,0,
1,1,-1,0,-1,1,0,0,1,-1,-1,0,1,-1,-1,0,-1,1,
0,0,1,-1,-1,0,0,1,-1,0,1,1,1,0,-1,0,1,0,1,
1,1,0,-1,0,0,0,-1,-1,-1,0,-1,1,-1,0,-1,-1,1,
0,-1,-1,1,0,0,1,1,0,0,1,1,0,0,0,-1,0,1,-1,
-1,0,1,1,0,0,-1,-1,-1,0,1,1,1,0,1,1,0,0,-1,
0,-1,0,0,-1,1,0,-1,1,1,0,1,0,-1,0,-1,1,-1,0,
0,-1,0,0,-1,-1,0,0,1,1,-1,0,-1,-1,1,0,1,-1,
1,0,0,-1,-1,0,-1,1,-1,0,-1,0,-1,0);
const
NM2=10;
nl: array[1..NM2] of longint = ({random values and 2^30}
35690018,1809741004,112970497,1577004683,1997451014,
1419616041,862708834,403211554,2113914896, $40000000);
ml: array[1..NM2] of shortint = (-1, 0, -1, 1, 1, -1, 0, 1, 0, 0);
var
i,cnt,f: integer;
begin
f := 0;
cnt := 0;
writeln('Test Moebius32 ...');
for i:=1 to NM1 do begin
inc(cnt);
if Moebius32(i) <> ma[i] then begin
writeln('Failed for i = ',i);
inc(f);
end;
end;
for i:=1 to NM2 do begin
inc(cnt);
if Moebius32(nl[i]) <> ml[i] then begin
writeln('Failed for ', nl[i]);
inc(f);
end;
end;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure test_primroot;
const
NR1=200;
ra: array[2..NR1] of byte = ( {with(numtheory): [[seq(primroot(x),x=2..200)];}
1,2,3,2,5,3,0,2,3,2,0,2,3,0,0,3,5,2,0,0,7,5,0,2,7,2,0,2,0,
3,0,0,3,0,0,2,3,0,0,6,0,3,0,0,5,5,0,3,3,0,0,2,5,0,0,0,3,2,
0,2,3,0,0,0,0,2,0,0,0,7,0,5,5,0,0,0,0,3,0,2,7,2,0,0,3,0,0,
3,0,0,0,0,5,0,0,5,3,0,0,2,0,5,0,0,3,2,0,6,0,0,0,3,0,0,0,0,
11,0,0,2,7,0,0,2,0,3,0,0,0,2,0,0,7,0,0,3,0,2,0,0,7,0,0,0,
5,0,0,2,0,6,0,0,0,0,0,5,3,0,0,0,5,2,0,0,5,5,0,2,0,0,0,2,0,
0,0,0,3,2,0,2,0,0,0,0,0,0,0,0,0,19,0,5,5,0,0,2,0,3,0);
const
NM2=10;
nl: array[1..NM2] of longint = ( {random values}
112970497, 403211554, 2113914896, 1799212189, 31134751,
607067782, 917676758, 2031081119, 1505450647, 29179441);
ml: array[1..NM2] of byte = (5, 3, 0, 2, 6, 11, 15, 7, 3, 13);
var
i,cnt,f: integer;
begin
f := 0;
cnt := 0;
writeln('Test primroot32 ...');
for i:=2 to NR1 do begin
inc(cnt);
if primroot32(i) <> ra[i] then begin
writeln('Failed for i = ',i);
inc(f);
end;
end;
for i:=1 to NM2 do begin
inc(cnt);
if primroot32(nl[i]) <> ml[i] then begin
writeln('Failed for ', nl[i]);
inc(f);
end;
end;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure test_order32;
const
N1 = 100;
M1 = 101;
O1 : array[1..N1] of byte = ( {[seq(order(i,101),i=1..100)];}
1,100,100,50,25,10,100,100,50,4,100,100,50,10,100,25,
10,100,25,50,50,50,50,25,25,100,100,100,100,50,25,
20,50,100,100,5,25,100,20,100,20,100,50,20,50,100,
50,100,50,100,100,25,100,25,100,25,20,25,100,20,100,
20,100,50,10,100,100,25,20,50,25,100,100,100,100,50,
50,25,25,25,25,50,100,5,50,100,5,25,100,100,4,25,
100,100,5,50,25,100,100,2);
N2 = 97;
M2 = 13*17;
O2 : array[0..N2] of byte = ( {[seq(order(i,13*17),i=0..97)];}
0,1,24,48,12,16,48,48,8,24,48,48,16,0,16,24,6,
0,4,24,48,4,48,48,48,8,0,16,48,48,12,16,24,
12,0,3,24,48,4,0,16,48,24,24,16,48,48,4,48,
24,12,0,0,8,48,12,48,16,48,24,8,48,48,48,4,
0,8,12,0,6,8,48,12,16,48,48,24,8,0,16,48,12,
48,8,12,0,4,24,48,12,16,0,16,24,24,48,16,48);
var
i,n: longint;
cnt,f: integer;
begin
f := 0;
cnt := 0;
writeln('Test order32 ...');
for i:=low(O1) to high(O1) do begin
inc(cnt);
n := order32(i,M1);
if n <> O1[i] then begin
inc(f);
writeln('O1 failed: ',i);
end;
end;
for i:=low(O2) to high(O2) do begin
inc(cnt);
n := order32(i,M2);
if n <> O2[i] then begin
inc(f);
writeln('O2 failed: ',i);
writeln(i);
end;
end;
for i:=2 to 2000 do begin
inc(cnt,2);
n := sqr(i);
if 2<>order32(i,i+1) then begin
inc(f);
writeln('Order 2 failed: ',i);
end;
if 4<>order32(i,n+1) then begin
inc(f);
writeln('Order 4 failed: ',i);
end;
end;
writeln('No. of checks: ',cnt,', failed: ',f);
inc(totalfailed,f);
writeln;
end;
{---------------------------------------------------------------------------}
procedure test_sigmak;
var
i,cnt,f: integer;
const
sigma_0: array[1..15] of byte = ( {http://oeis.org/A000005}
1,2,2,3,2,4,2,4,3,4,2,6,2,4,4);
sigma_1: array[1..15] of byte = ( {http://oeis.org/A000203}
1,3,4,7,6,12,8,15,13,18,12,28,14,24,24);
sigma_2: array[1..15] of word = ( { http://oeis.org/A001157}
1,5,10,21,26,50,50,85,91,130,122,210,170,250,260);
sigma_3: array[1..15] of word = ( { http://oeis.org/A001158}
1,9,28,73,126,252,344,585,757,1134,1332,2044,2198,3096,3528);
sigma_4: array[1..15] of word = ( { http://oeis.org/A001159}
1,17,82,273,626,1394,2402,4369,6643,10642,14642,22386,28562,40834,51332);
sigma_5: array[1..15] of longint = ( { http://oeis.org/A001160}
1,33,244,1057,3126,8052,16808,33825,59293,103158,161052,257908,371294,554664,762744);
const {Pari: sigma(n,k)}
s11 = '2017807491561102999631484340618436673467747480392679929996';
s12 = '2911221654831869466363023287520284782191148555791577871102530352168390412613776';
s13 = '1547729197788406436578232909486595843792561058208796001316378245478351358596333115611712045580793104620576';
s17 = '3595461272557299653174091079336363772054784552910504170610996694917'
+'45365420254055103594069576816820962820097287171393649148064062176676896';
s42 = '150130937545330708181211458454834608908702699731083721027349152152500';
begin
f := 0;
cnt := 0;
writeln('Test mp_sigmak ...');
for i:=1 to 15 do begin
inc(cnt);
mp_sigmak(0,i,a);
if mp_cmp_int(a, sigma_0[i])<>MP_EQ then begin
inc(f);
writeln('Fail sigma_0: ',i);
end;
inc(cnt);
mp_sigmak(1,i,a);
if mp_cmp_int(a, sigma_1[i])<>MP_EQ then begin
inc(f);
writeln('Fail sigma_1: ',i);
end;
inc(cnt);
mp_sigmak(2,i,a);
if mp_cmp_int(a, sigma_2[i])<>MP_EQ then begin
inc(f);
writeln('Fail sigma_2: ',i);
end;
inc(cnt);
mp_sigmak(3,i,a);
if mp_cmp_int(a, sigma_3[i])<>MP_EQ then begin
inc(f);
writeln('Fail sigma_3: ',i);
end;
inc(cnt);
mp_sigmak(4,i,a);