X-Git-Url: https://oss.titaniummirror.com/gitweb?a=blobdiff_plain;f=gmp%2Ftests%2Fmpz%2Ft-jac.c;fp=gmp%2Ftests%2Fmpz%2Ft-jac.c;h=1b3e092888aa64354961fd09d0e1d54a6c50da36;hb=6fed43773c9b0ce596dca5686f37ac3fc0fa11c0;hp=0000000000000000000000000000000000000000;hpb=27b11d56b743098deb193d510b337ba22dc52e5c;p=msp430-gcc.git diff --git a/gmp/tests/mpz/t-jac.c b/gmp/tests/mpz/t-jac.c new file mode 100644 index 00000000..1b3e0928 --- /dev/null +++ b/gmp/tests/mpz/t-jac.c @@ -0,0 +1,747 @@ +/* Exercise mpz_*_kronecker_*() and mpz_jacobi() functions. + +Copyright 1999, 2000, 2001, 2002, 2003, 2004 Free Software Foundation, Inc. + +This file is part of the GNU MP Library. + +The GNU MP Library is free software; you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation; either version 3 of the License, or (at your +option) any later version. + +The GNU MP Library is distributed in the hope that it will be useful, but +WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY +or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public +License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ + + +/* With no arguments the various Kronecker/Jacobi symbol routines are + checked against some test data and a lot of derived data. + + To check the test data against PARI-GP, run + + t-jac -p | gp -q + + It takes a while because the output from "t-jac -p" is big. + + + Enhancements: + + More big test cases than those given by check_squares_zi would be good. */ + + +#include +#include +#include + +#include "gmp.h" +#include "gmp-impl.h" +#include "tests.h" + + +#ifdef _LONG_LONG_LIMB +#define LL(l,ll) ll +#else +#define LL(l,ll) l +#endif + + +int option_pari = 0; + + +unsigned long +mpz_mod4 (mpz_srcptr z) +{ + mpz_t m; + unsigned long ret; + + mpz_init (m); + mpz_fdiv_r_2exp (m, z, 2); + ret = mpz_get_ui (m); + mpz_clear (m); + return ret; +} + +int +mpz_fits_ulimb_p (mpz_srcptr z) +{ + return (SIZ(z) == 1 || SIZ(z) == 0); +} + +mp_limb_t +mpz_get_ulimb (mpz_srcptr z) +{ + if (SIZ(z) == 0) + return 0; + else + return PTR(z)[0]; +} + + +void +try_base (mp_limb_t a, mp_limb_t b, int answer) +{ + int got; + + if ((b & 1) == 0 || b == 1 || a > b) + return; + + got = mpn_jacobi_base (a, b, 0); + if (got != answer) + { + printf (LL("mpn_jacobi_base (%lu, %lu) is %d should be %d\n", + "mpn_jacobi_base (%llu, %llu) is %d should be %d\n"), + a, b, got, answer); + abort (); + } +} + + +void +try_zi_ui (mpz_srcptr a, unsigned long b, int answer) +{ + int got; + + got = mpz_kronecker_ui (a, b); + if (got != answer) + { + printf ("mpz_kronecker_ui ("); + mpz_out_str (stdout, 10, a); + printf (", %lu) is %d should be %d\n", b, got, answer); + abort (); + } +} + + +void +try_zi_si (mpz_srcptr a, long b, int answer) +{ + int got; + + got = mpz_kronecker_si (a, b); + if (got != answer) + { + printf ("mpz_kronecker_si ("); + mpz_out_str (stdout, 10, a); + printf (", %ld) is %d should be %d\n", b, got, answer); + abort (); + } +} + + +void +try_ui_zi (unsigned long a, mpz_srcptr b, int answer) +{ + int got; + + got = mpz_ui_kronecker (a, b); + if (got != answer) + { + printf ("mpz_ui_kronecker (%lu, ", a); + mpz_out_str (stdout, 10, b); + printf (") is %d should be %d\n", got, answer); + abort (); + } +} + + +void +try_si_zi (long a, mpz_srcptr b, int answer) +{ + int got; + + got = mpz_si_kronecker (a, b); + if (got != answer) + { + printf ("mpz_si_kronecker (%ld, ", a); + mpz_out_str (stdout, 10, b); + printf (") is %d should be %d\n", got, answer); + abort (); + } +} + + +/* Don't bother checking mpz_jacobi, since it only differs for b even, and + we don't have an actual expected answer for it. tests/devel/try.c does + some checks though. */ +void +try_zi_zi (mpz_srcptr a, mpz_srcptr b, int answer) +{ + int got; + + got = mpz_kronecker (a, b); + if (got != answer) + { + printf ("mpz_kronecker ("); + mpz_out_str (stdout, 10, a); + printf (", "); + mpz_out_str (stdout, 10, b); + printf (") is %d should be %d\n", got, answer); + abort (); + } +} + + +void +try_pari (mpz_srcptr a, mpz_srcptr b, int answer) +{ + printf ("try("); + mpz_out_str (stdout, 10, a); + printf (","); + mpz_out_str (stdout, 10, b); + printf (",%d)\n", answer); +} + + +void +try_each (mpz_srcptr a, mpz_srcptr b, int answer) +{ + if (option_pari) + { + try_pari (a, b, answer); + return; + } + + if (mpz_fits_ulimb_p (a) && mpz_fits_ulimb_p (b)) + try_base (mpz_get_ulimb (a), mpz_get_ulimb (b), answer); + + if (mpz_fits_ulong_p (b)) + try_zi_ui (a, mpz_get_ui (b), answer); + + if (mpz_fits_slong_p (b)) + try_zi_si (a, mpz_get_si (b), answer); + + if (mpz_fits_ulong_p (a)) + try_ui_zi (mpz_get_ui (a), b, answer); + + if (mpz_fits_sint_p (a)) + try_si_zi (mpz_get_si (a), b, answer); + + try_zi_zi (a, b, answer); +} + + +/* Try (a/b) and (a/-b). */ +void +try_pn (mpz_srcptr a, mpz_srcptr b_orig, int answer) +{ + mpz_t b; + + mpz_init_set (b, b_orig); + try_each (a, b, answer); + + mpz_neg (b, b); + if (mpz_sgn (a) < 0) + answer = -answer; + + try_each (a, b, answer); + + mpz_clear (b); +} + + +/* Try (a+k*p/b) for various k, using the fact (a/b) is periodic in a with + period p. For b>0, p=b if b!=2mod4 or p=4*b if b==2mod4. */ + +void +try_periodic_num (mpz_srcptr a_orig, mpz_srcptr b, int answer) +{ + mpz_t a, a_period; + int i; + + if (mpz_sgn (b) <= 0) + return; + + mpz_init_set (a, a_orig); + mpz_init_set (a_period, b); + if (mpz_mod4 (b) == 2) + mpz_mul_ui (a_period, a_period, 4); + + /* don't bother with these tests if they're only going to produce + even/even */ + if (mpz_even_p (a) && mpz_even_p (b) && mpz_even_p (a_period)) + goto done; + + for (i = 0; i < 6; i++) + { + mpz_add (a, a, a_period); + try_pn (a, b, answer); + } + + mpz_set (a, a_orig); + for (i = 0; i < 6; i++) + { + mpz_sub (a, a, a_period); + try_pn (a, b, answer); + } + + done: + mpz_clear (a); + mpz_clear (a_period); +} + + +/* Try (a/b+k*p) for various k, using the fact (a/b) is periodic in b of + period p. + + period p + a==0,1mod4 a + a==2mod4 4*a + a==3mod4 and b odd 4*a + a==3mod4 and b even 8*a + + In Henri Cohen's book the period is given as 4*a for all a==2,3mod4, but + a counterexample would seem to be (3/2)=-1 which with (3/14)=+1 doesn't + have period 4*a (but rather 8*a with (3/26)=-1). Maybe the plain 4*a is + to be read as applying to a plain Jacobi symbol with b odd, rather than + the Kronecker extension to b even. */ + +void +try_periodic_den (mpz_srcptr a, mpz_srcptr b_orig, int answer) +{ + mpz_t b, b_period; + int i; + + if (mpz_sgn (a) == 0 || mpz_sgn (b_orig) == 0) + return; + + mpz_init_set (b, b_orig); + + mpz_init_set (b_period, a); + if (mpz_mod4 (a) == 3 && mpz_even_p (b)) + mpz_mul_ui (b_period, b_period, 8L); + else if (mpz_mod4 (a) >= 2) + mpz_mul_ui (b_period, b_period, 4L); + + /* don't bother with these tests if they're only going to produce + even/even */ + if (mpz_even_p (a) && mpz_even_p (b) && mpz_even_p (b_period)) + goto done; + + for (i = 0; i < 6; i++) + { + mpz_add (b, b, b_period); + try_pn (a, b, answer); + } + + mpz_set (b, b_orig); + for (i = 0; i < 6; i++) + { + mpz_sub (b, b, b_period); + try_pn (a, b, answer); + } + + done: + mpz_clear (b); + mpz_clear (b_period); +} + + +static const unsigned long ktable[] = { + 0, 1, 2, 3, 4, 5, 6, 7, + GMP_NUMB_BITS-1, GMP_NUMB_BITS, GMP_NUMB_BITS+1, + 2*GMP_NUMB_BITS-1, 2*GMP_NUMB_BITS, 2*GMP_NUMB_BITS+1, + 3*GMP_NUMB_BITS-1, 3*GMP_NUMB_BITS, 3*GMP_NUMB_BITS+1 +}; + + +/* Try (a/b*2^k) for various k. */ +void +try_2den (mpz_srcptr a, mpz_srcptr b_orig, int answer) +{ + mpz_t b; + int kindex; + int answer_a2, answer_k; + unsigned long k; + + /* don't bother when b==0 */ + if (mpz_sgn (b_orig) == 0) + return; + + mpz_init_set (b, b_orig); + + /* (a/2) is 0 if a even, 1 if a==1 or 7 mod 8, -1 if a==3 or 5 mod 8 */ + answer_a2 = (mpz_even_p (a) ? 0 + : (((SIZ(a) >= 0 ? PTR(a)[0] : -PTR(a)[0]) + 2) & 7) < 4 ? 1 + : -1); + + for (kindex = 0; kindex < numberof (ktable); kindex++) + { + k = ktable[kindex]; + + /* answer_k = answer*(answer_a2^k) */ + answer_k = (answer_a2 == 0 && k != 0 ? 0 + : (k & 1) == 1 && answer_a2 == -1 ? -answer + : answer); + + mpz_mul_2exp (b, b_orig, k); + try_pn (a, b, answer_k); + } + + mpz_clear (b); +} + + +/* Try (a*2^k/b) for various k. If it happens mpz_ui_kronecker() gets (2/b) + wrong it will show up as wrong answers demanded. */ +void +try_2num (mpz_srcptr a_orig, mpz_srcptr b, int answer) +{ + mpz_t a; + int kindex; + int answer_2b, answer_k; + unsigned long k; + + /* don't bother when a==0 */ + if (mpz_sgn (a_orig) == 0) + return; + + mpz_init (a); + + /* (2/b) is 0 if b even, 1 if b==1 or 7 mod 8, -1 if b==3 or 5 mod 8 */ + answer_2b = (mpz_even_p (b) ? 0 + : (((SIZ(b) >= 0 ? PTR(b)[0] : -PTR(b)[0]) + 2) & 7) < 4 ? 1 + : -1); + + for (kindex = 0; kindex < numberof (ktable); kindex++) + { + k = ktable[kindex]; + + /* answer_k = answer*(answer_2b^k) */ + answer_k = (answer_2b == 0 && k != 0 ? 0 + : (k & 1) == 1 && answer_2b == -1 ? -answer + : answer); + + mpz_mul_2exp (a, a_orig, k); + try_pn (a, b, answer_k); + } + + mpz_clear (a); +} + + +/* The try_2num() and try_2den() routines don't in turn call + try_periodic_num() and try_periodic_den() because it hugely increases the + number of tests performed, without obviously increasing coverage. + + Useful extra derived cases can be added here. */ + +void +try_all (mpz_t a, mpz_t b, int answer) +{ + try_pn (a, b, answer); + try_periodic_num (a, b, answer); + try_periodic_den (a, b, answer); + try_2num (a, b, answer); + try_2den (a, b, answer); +} + + +void +check_data (void) +{ + static const struct { + const char *a; + const char *b; + int answer; + + } data[] = { + + /* Note that the various derived checks in try_all() reduce the cases + that need to be given here. */ + + /* some zeros */ + { "0", "0", 0 }, + { "0", "2", 0 }, + { "0", "6", 0 }, + { "5", "0", 0 }, + { "24", "60", 0 }, + + /* (a/1) = 1, any a + In particular note (0/1)=1 so that (a/b)=(a mod b/b). */ + { "0", "1", 1 }, + { "1", "1", 1 }, + { "2", "1", 1 }, + { "3", "1", 1 }, + { "4", "1", 1 }, + { "5", "1", 1 }, + + /* (0/b) = 0, b != 1 */ + { "0", "3", 0 }, + { "0", "5", 0 }, + { "0", "7", 0 }, + { "0", "9", 0 }, + { "0", "11", 0 }, + { "0", "13", 0 }, + { "0", "15", 0 }, + + /* (1/b) = 1 */ + { "1", "1", 1 }, + { "1", "3", 1 }, + { "1", "5", 1 }, + { "1", "7", 1 }, + { "1", "9", 1 }, + { "1", "11", 1 }, + + /* (-1/b) = (-1)^((b-1)/2) which is -1 for b==3 mod 4 */ + { "-1", "1", 1 }, + { "-1", "3", -1 }, + { "-1", "5", 1 }, + { "-1", "7", -1 }, + { "-1", "9", 1 }, + { "-1", "11", -1 }, + { "-1", "13", 1 }, + { "-1", "15", -1 }, + { "-1", "17", 1 }, + { "-1", "19", -1 }, + + /* (2/b) = (-1)^((b^2-1)/8) which is -1 for b==3,5 mod 8. + try_2num() will exercise multiple powers of 2 in the numerator. */ + { "2", "1", 1 }, + { "2", "3", -1 }, + { "2", "5", -1 }, + { "2", "7", 1 }, + { "2", "9", 1 }, + { "2", "11", -1 }, + { "2", "13", -1 }, + { "2", "15", 1 }, + { "2", "17", 1 }, + + /* (-2/b) = (-1)^((b^2-1)/8)*(-1)^((b-1)/2) which is -1 for b==5,7mod8. + try_2num() will exercise multiple powers of 2 in the numerator, which + will test that the shift in mpz_si_kronecker() uses unsigned not + signed. */ + { "-2", "1", 1 }, + { "-2", "3", 1 }, + { "-2", "5", -1 }, + { "-2", "7", -1 }, + { "-2", "9", 1 }, + { "-2", "11", 1 }, + { "-2", "13", -1 }, + { "-2", "15", -1 }, + { "-2", "17", 1 }, + + /* (a/2)=(2/a). + try_2den() will exercise multiple powers of 2 in the denominator. */ + { "3", "2", -1 }, + { "5", "2", -1 }, + { "7", "2", 1 }, + { "9", "2", 1 }, + { "11", "2", -1 }, + + /* Harriet Griffin, "Elementary Theory of Numbers", page 155, various + examples. */ + { "2", "135", 1 }, + { "135", "19", -1 }, + { "2", "19", -1 }, + { "19", "135", 1 }, + { "173", "135", 1 }, + { "38", "135", 1 }, + { "135", "173", 1 }, + { "173", "5", -1 }, + { "3", "5", -1 }, + { "5", "173", -1 }, + { "173", "3", -1 }, + { "2", "3", -1 }, + { "3", "173", -1 }, + { "253", "21", 1 }, + { "1", "21", 1 }, + { "21", "253", 1 }, + { "21", "11", -1 }, + { "-1", "11", -1 }, + + /* Griffin page 147 */ + { "-1", "17", 1 }, + { "2", "17", 1 }, + { "-2", "17", 1 }, + { "-1", "89", 1 }, + { "2", "89", 1 }, + + /* Griffin page 148 */ + { "89", "11", 1 }, + { "1", "11", 1 }, + { "89", "3", -1 }, + { "2", "3", -1 }, + { "3", "89", -1 }, + { "11", "89", 1 }, + { "33", "89", -1 }, + + /* H. Davenport, "The Higher Arithmetic", page 65, the quadratic + residues and non-residues mod 19. */ + { "1", "19", 1 }, + { "4", "19", 1 }, + { "5", "19", 1 }, + { "6", "19", 1 }, + { "7", "19", 1 }, + { "9", "19", 1 }, + { "11", "19", 1 }, + { "16", "19", 1 }, + { "17", "19", 1 }, + { "2", "19", -1 }, + { "3", "19", -1 }, + { "8", "19", -1 }, + { "10", "19", -1 }, + { "12", "19", -1 }, + { "13", "19", -1 }, + { "14", "19", -1 }, + { "15", "19", -1 }, + { "18", "19", -1 }, + + /* Residues and non-residues mod 13 */ + { "0", "13", 0 }, + { "1", "13", 1 }, + { "2", "13", -1 }, + { "3", "13", 1 }, + { "4", "13", 1 }, + { "5", "13", -1 }, + { "6", "13", -1 }, + { "7", "13", -1 }, + { "8", "13", -1 }, + { "9", "13", 1 }, + { "10", "13", 1 }, + { "11", "13", -1 }, + { "12", "13", 1 }, + + /* various */ + { "5", "7", -1 }, + { "15", "17", 1 }, + { "67", "89", 1 }, + + /* special values inducing a==b==1 at the end of jac_or_kron() */ + { "0x10000000000000000000000000000000000000000000000001", + "0x10000000000000000000000000000000000000000000000003", 1 }, + }; + + int i; + mpz_t a, b; + + mpz_init (a); + mpz_init (b); + + for (i = 0; i < numberof (data); i++) + { + mpz_set_str_or_abort (a, data[i].a, 0); + mpz_set_str_or_abort (b, data[i].b, 0); + try_all (a, b, data[i].answer); + } + + mpz_clear (a); + mpz_clear (b); +} + + +/* (a^2/b)=1 if gcd(a,b)=1, or (a^2/b)=0 if gcd(a,b)!=1. + This includes when a=0 or b=0. */ +void +check_squares_zi (void) +{ + gmp_randstate_ptr rands = RANDS; + mpz_t a, b, g; + int i, answer; + mp_size_t size_range, an, bn; + mpz_t bs; + + mpz_init (bs); + mpz_init (a); + mpz_init (b); + mpz_init (g); + + for (i = 0; i < 50; i++) + { + mpz_urandomb (bs, rands, 32); + size_range = mpz_get_ui (bs) % 10 + 2; + + mpz_urandomb (bs, rands, size_range); + an = mpz_get_ui (bs); + mpz_rrandomb (a, rands, an); + + mpz_urandomb (bs, rands, size_range); + bn = mpz_get_ui (bs); + mpz_rrandomb (b, rands, bn); + + mpz_gcd (g, a, b); + if (mpz_cmp_ui (g, 1L) == 0) + answer = 1; + else + answer = 0; + + mpz_mul (a, a, a); + + try_all (a, b, answer); + } + + mpz_clear (bs); + mpz_clear (a); + mpz_clear (b); + mpz_clear (g); +} + + +/* Check the handling of asize==0, make sure it isn't affected by the low + limb. */ +void +check_a_zero (void) +{ + mpz_t a, b; + + mpz_init_set_ui (a, 0); + mpz_init (b); + + mpz_set_ui (b, 1L); + PTR(a)[0] = 0; + try_all (a, b, 1); /* (0/1)=1 */ + PTR(a)[0] = 1; + try_all (a, b, 1); /* (0/1)=1 */ + + mpz_set_si (b, -1L); + PTR(a)[0] = 0; + try_all (a, b, 1); /* (0/-1)=1 */ + PTR(a)[0] = 1; + try_all (a, b, 1); /* (0/-1)=1 */ + + mpz_set_ui (b, 0); + PTR(a)[0] = 0; + try_all (a, b, 0); /* (0/0)=0 */ + PTR(a)[0] = 1; + try_all (a, b, 0); /* (0/0)=0 */ + + mpz_set_ui (b, 2); + PTR(a)[0] = 0; + try_all (a, b, 0); /* (0/2)=0 */ + PTR(a)[0] = 1; + try_all (a, b, 0); /* (0/2)=0 */ + + mpz_clear (a); + mpz_clear (b); +} + + +int +main (int argc, char *argv[]) +{ + tests_start (); + + if (argc >= 2 && strcmp (argv[1], "-p") == 0) + { + option_pari = 1; + + printf ("\ +try(a,b,answer) =\n\ +{\n\ + if (kronecker(a,b) != answer,\n\ + print(\"wrong at \", a, \",\", b,\n\ + \" expected \", answer,\n\ + \" pari says \", kronecker(a,b)))\n\ +}\n"); + } + + check_data (); + check_squares_zi (); + check_a_zero (); + + tests_end (); + exit (0); +}