/* Test file for mpfr_div (and some mpfr_div_ui, etc. tests). Copyright 1999, 2001-2015 Free Software Foundation, Inc. Contributed by the AriC and Caramel projects, INRIA. This file is part of the GNU MPFR Library. The GNU MPFR 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 MPFR 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 MPFR Library; see the file COPYING.LESSER. If not, see http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ #include #include #include "mpfr-test.h" static void check_equal (mpfr_srcptr a, mpfr_srcptr a2, char *s, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t r) { if ((MPFR_IS_NAN (a) && MPFR_IS_NAN (a2)) || mpfr_equal_p (a, a2)) return; printf ("Error in %s\n", mpfr_print_rnd_mode (r)); printf ("b = "); mpfr_dump (b); printf ("c = "); mpfr_dump (c); printf ("mpfr_div result: "); mpfr_dump (a); printf ("%s result: ", s); mpfr_dump (a2); exit (1); } static int mpfr_all_div (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t r) { mpfr_t a2; unsigned int oldflags, newflags; int inex, inex2; oldflags = __gmpfr_flags; inex = mpfr_div (a, b, c, r); if (a == b || a == c) return inex; newflags = __gmpfr_flags; mpfr_init2 (a2, MPFR_PREC (a)); if (mpfr_integer_p (b) && ! (MPFR_IS_ZERO (b) && MPFR_IS_NEG (b))) { /* b is an integer, but not -0 (-0 is rejected as it becomes +0 when converted to an integer). */ if (mpfr_fits_ulong_p (b, MPFR_RNDA)) { __gmpfr_flags = oldflags; inex2 = mpfr_ui_div (a2, mpfr_get_ui (b, MPFR_RNDN), c, r); MPFR_ASSERTN (SAME_SIGN (inex2, inex)); MPFR_ASSERTN (__gmpfr_flags == newflags); check_equal (a, a2, "mpfr_ui_div", b, c, r); } if (mpfr_fits_slong_p (b, MPFR_RNDA)) { __gmpfr_flags = oldflags; inex2 = mpfr_si_div (a2, mpfr_get_si (b, MPFR_RNDN), c, r); MPFR_ASSERTN (SAME_SIGN (inex2, inex)); MPFR_ASSERTN (__gmpfr_flags == newflags); check_equal (a, a2, "mpfr_si_div", b, c, r); } } if (mpfr_integer_p (c) && ! (MPFR_IS_ZERO (c) && MPFR_IS_NEG (c))) { /* c is an integer, but not -0 (-0 is rejected as it becomes +0 when converted to an integer). */ if (mpfr_fits_ulong_p (c, MPFR_RNDA)) { __gmpfr_flags = oldflags; inex2 = mpfr_div_ui (a2, b, mpfr_get_ui (c, MPFR_RNDN), r); MPFR_ASSERTN (SAME_SIGN (inex2, inex)); MPFR_ASSERTN (__gmpfr_flags == newflags); check_equal (a, a2, "mpfr_div_ui", b, c, r); } if (mpfr_fits_slong_p (c, MPFR_RNDA)) { __gmpfr_flags = oldflags; inex2 = mpfr_div_si (a2, b, mpfr_get_si (c, MPFR_RNDN), r); MPFR_ASSERTN (SAME_SIGN (inex2, inex)); MPFR_ASSERTN (__gmpfr_flags == newflags); check_equal (a, a2, "mpfr_div_si", b, c, r); } } mpfr_clear (a2); return inex; } #ifdef CHECK_EXTERNAL static int test_div (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode) { int res; int ok = rnd_mode == MPFR_RNDN && mpfr_number_p (b) && mpfr_number_p (c); if (ok) { mpfr_print_raw (b); printf (" "); mpfr_print_raw (c); } res = mpfr_all_div (a, b, c, rnd_mode); if (ok) { printf (" "); mpfr_print_raw (a); printf ("\n"); } return res; } #else #define test_div mpfr_all_div #endif #define check53(n, d, rnd, res) check4(n, d, rnd, 53, res) /* return 0 iff a and b are of the same sign */ static int inex_cmp (int a, int b) { if (a > 0) return (b > 0) ? 0 : 1; else if (a == 0) return (b == 0) ? 0 : 1; else return (b < 0) ? 0 : 1; } static void check4 (const char *Ns, const char *Ds, mpfr_rnd_t rnd_mode, int p, const char *Qs) { mpfr_t q, n, d; mpfr_inits2 (p, q, n, d, (mpfr_ptr) 0); mpfr_set_str1 (n, Ns); mpfr_set_str1 (d, Ds); test_div(q, n, d, rnd_mode); if (mpfr_cmp_str (q, Qs, ((p==53) ? 10 : 2), MPFR_RNDN) ) { printf ("mpfr_div failed for n=%s, d=%s, p=%d, rnd_mode=%s\n", Ns, Ds, p, mpfr_print_rnd_mode (rnd_mode)); printf ("got ");mpfr_print_binary(q); mpfr_set_str (q, Qs, ((p==53) ? 10 : 2), MPFR_RNDN); printf("\nexpected "); mpfr_print_binary(q); putchar('\n'); exit (1); } mpfr_clears (q, n, d, (mpfr_ptr) 0); } static void check24 (const char *Ns, const char *Ds, mpfr_rnd_t rnd_mode, const char *Qs) { mpfr_t q, n, d; mpfr_inits2 (24, q, n, d, (mpfr_ptr) 0); mpfr_set_str1 (n, Ns); mpfr_set_str1 (d, Ds); test_div(q, n, d, rnd_mode); if (mpfr_cmp_str1 (q, Qs) ) { printf ("mpfr_div failed for n=%s, d=%s, prec=24, rnd_mode=%s\n", Ns, Ds, mpfr_print_rnd_mode(rnd_mode)); printf ("expected quotient is %s, got ", Qs); mpfr_out_str(stdout,10,0,q, MPFR_RNDN); putchar('\n'); exit (1); } mpfr_clears (q, n, d, (mpfr_ptr) 0); } /* the following examples come from the paper "Number-theoretic Test Generation for Directed Rounding" from Michael Parks, Table 2 */ static void check_float(void) { check24("70368760954880.0", "8388609.0", MPFR_RNDN, "8.388609e6"); check24("140737479966720.0", "16777213.0", MPFR_RNDN, "8.388609e6"); check24("70368777732096.0", "8388611.0", MPFR_RNDN, "8.388609e6"); check24("105553133043712.0", "12582911.0", MPFR_RNDN, "8.38861e6"); /* the exponent for the following example was forgotten in the Arith'14 version of Parks' paper */ check24 ("12582913.0", "12582910.0", MPFR_RNDN, "1.000000238"); check24 ("105553124655104.0", "12582910.0", MPFR_RNDN, "8388610.0"); check24("140737479966720.0", "8388609.0", MPFR_RNDN, "1.6777213e7"); check24("70368777732096.0", "8388609.0", MPFR_RNDN, "8.388611e6"); check24("105553133043712.0", "8388610.0", MPFR_RNDN, "1.2582911e7"); check24("105553124655104.0", "8388610.0", MPFR_RNDN, "1.258291e7"); check24("70368760954880.0", "8388609.0", MPFR_RNDZ, "8.388608e6"); check24("140737479966720.0", "16777213.0", MPFR_RNDZ, "8.388609e6"); check24("70368777732096.0", "8388611.0", MPFR_RNDZ, "8.388608e6"); check24("105553133043712.0", "12582911.0", MPFR_RNDZ, "8.38861e6"); check24("12582913.0", "12582910.0", MPFR_RNDZ, "1.000000238"); check24 ("105553124655104.0", "12582910.0", MPFR_RNDZ, "8388610.0"); check24("140737479966720.0", "8388609.0", MPFR_RNDZ, "1.6777213e7"); check24("70368777732096.0", "8388609.0", MPFR_RNDZ, "8.38861e6"); check24("105553133043712.0", "8388610.0", MPFR_RNDZ, "1.2582911e7"); check24("105553124655104.0", "8388610.0", MPFR_RNDZ, "1.258291e7"); check24("70368760954880.0", "8388609.0", MPFR_RNDU, "8.388609e6"); check24("140737479966720.0", "16777213.0", MPFR_RNDU, "8.38861e6"); check24("70368777732096.0", "8388611.0", MPFR_RNDU, "8.388609e6"); check24("105553133043712.0", "12582911.0", MPFR_RNDU, "8.388611e6"); check24("12582913.0", "12582910.0", MPFR_RNDU, "1.000000357"); check24 ("105553124655104.0", "12582910.0", MPFR_RNDU, "8388611.0"); check24("140737479966720.0", "8388609.0", MPFR_RNDU, "1.6777214e7"); check24("70368777732096.0", "8388609.0", MPFR_RNDU, "8.388611e6"); check24("105553133043712.0", "8388610.0", MPFR_RNDU, "1.2582912e7"); check24("105553124655104.0", "8388610.0", MPFR_RNDU, "1.2582911e7"); check24("70368760954880.0", "8388609.0", MPFR_RNDD, "8.388608e6"); check24("140737479966720.0", "16777213.0", MPFR_RNDD, "8.388609e6"); check24("70368777732096.0", "8388611.0", MPFR_RNDD, "8.388608e6"); check24("105553133043712.0", "12582911.0", MPFR_RNDD, "8.38861e6"); check24("12582913.0", "12582910.0", MPFR_RNDD, "1.000000238"); check24 ("105553124655104.0", "12582910.0", MPFR_RNDD, "8388610.0"); check24("140737479966720.0", "8388609.0", MPFR_RNDD, "1.6777213e7"); check24("70368777732096.0", "8388609.0", MPFR_RNDD, "8.38861e6"); check24("105553133043712.0", "8388610.0", MPFR_RNDD, "1.2582911e7"); check24("105553124655104.0", "8388610.0", MPFR_RNDD, "1.258291e7"); check24("70368760954880.0", "8388609.0", MPFR_RNDA, "8.388609e6"); } static void check_double(void) { check53("0.0", "1.0", MPFR_RNDZ, "0.0"); check53("-7.4988969224688591e63", "4.8816866450288732e306", MPFR_RNDD, "-1.5361282826510687291e-243"); check53("-1.33225773037748601769e+199", "3.63449540676937123913e+79", MPFR_RNDZ, "-3.6655920045905428978e119"); check53("9.89438396044940256501e-134", "5.93472984109987421717e-67",MPFR_RNDU, "1.6672003992376663654e-67"); check53("9.89438396044940256501e-134", "5.93472984109987421717e-67",MPFR_RNDA, "1.6672003992376663654e-67"); check53("9.89438396044940256501e-134", "-5.93472984109987421717e-67", MPFR_RNDU, "-1.6672003992376663654e-67"); check53("-4.53063926135729747564e-308", "7.02293374921793516813e-84", MPFR_RNDD, "-6.4512060388748850857e-225"); check53("6.25089225176473806123e-01","-2.35527154824420243364e-230", MPFR_RNDD, "-2.6540006635008291192e229"); check53("6.25089225176473806123e-01","-2.35527154824420243364e-230", MPFR_RNDA, "-2.6540006635008291192e229"); check53("6.52308934689126e15", "-1.62063546601505417497e273", MPFR_RNDN, "-4.0250194961676020848e-258"); check53("1.04636807108079349236e-189", "3.72295730823253012954e-292", MPFR_RNDZ, "2.810583051186143125e102"); /* problems found by Kevin under HP-PA */ check53 ("2.861044553323177e-136", "-1.1120354257068143e+45", MPFR_RNDZ, "-2.5727998292003016e-181"); check53 ("-4.0559157245809205e-127", "-1.1237723844524865e+77", MPFR_RNDN, "3.6091968273068081e-204"); check53 ("-1.8177943561493235e-93", "-8.51233984260364e-104", MPFR_RNDU, "2.1354814184595821e+10"); } static void check_64(void) { mpfr_t x,y,z; mpfr_inits2 (64, x, y, z, (mpfr_ptr) 0); mpfr_set_str_binary(x, "1.00100100110110101001010010101111000001011100100101010000000000E54"); mpfr_set_str_binary(y, "1.00000000000000000000000000000000000000000000000000000000000000E584"); test_div(z, x, y, MPFR_RNDU); if (mpfr_cmp_str (z, "0.1001001001101101010010100101011110000010111001001010100000000000E-529", 2, MPFR_RNDN)) { printf("Error for tdiv for MPFR_RNDU and p=64\nx="); mpfr_print_binary(x); printf("\ny="); mpfr_print_binary(y); printf("\ngot "); mpfr_print_binary(z); printf("\nexpected 0.1001001001101101010010100101011110000010111001001010100000000000E-529\n"); exit(1); } mpfr_clears (x, y, z, (mpfr_ptr) 0); } static void check_convergence (void) { mpfr_t x, y; int i, j; mpfr_init2(x, 130); mpfr_set_str_binary(x, "0.1011111101011010101000001010011111101000011100011101010011111011000011001010000000111100100111110011001010110100100001001000111001E6944"); mpfr_init2(y, 130); mpfr_set_ui(y, 5, MPFR_RNDN); test_div(x, x, y, MPFR_RNDD); /* exact division */ mpfr_set_prec(x, 64); mpfr_set_prec(y, 64); mpfr_set_str_binary(x, "0.10010010011011010100101001010111100000101110010010101E55"); mpfr_set_str_binary(y, "0.1E585"); test_div(x, x, y, MPFR_RNDN); mpfr_set_str_binary(y, "0.10010010011011010100101001010111100000101110010010101E-529"); if (mpfr_cmp (x, y)) { printf ("Error in mpfr_div for prec=64, rnd=MPFR_RNDN\n"); printf ("got "); mpfr_print_binary(x); puts (""); printf ("instead of "); mpfr_print_binary(y); puts (""); exit(1); } for (i=32; i<=64; i+=32) { mpfr_set_prec(x, i); mpfr_set_prec(y, i); mpfr_set_ui(x, 1, MPFR_RNDN); RND_LOOP(j) { mpfr_set_ui (y, 1, MPFR_RNDN); test_div (y, x, y, (mpfr_rnd_t) j); if (mpfr_cmp_ui (y, 1)) { printf ("mpfr_div failed for x=1.0, y=1.0, prec=%d rnd=%s\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) j)); printf ("got "); mpfr_print_binary(y); puts (""); exit (1); } } } mpfr_clear (x); mpfr_clear (y); } #define KMAX 10000 /* given y = o(x/u), x, u, find the inexact flag by multiplying y by u */ static int get_inexact (mpfr_t y, mpfr_t x, mpfr_t u) { mpfr_t xx; int inex; mpfr_init2 (xx, mpfr_get_prec (y) + mpfr_get_prec (u)); mpfr_mul (xx, y, u, MPFR_RNDN); /* exact */ inex = mpfr_cmp (xx, x); mpfr_clear (xx); return inex; } static void check_hard (void) { mpfr_t u, v, q, q2; mpfr_prec_t precu, precv, precq; int rnd; int inex, inex2, i, j; mpfr_init (q); mpfr_init (q2); mpfr_init (u); mpfr_init (v); for (precq = MPFR_PREC_MIN; precq <= 64; precq ++) { mpfr_set_prec (q, precq); mpfr_set_prec (q2, precq + 1); for (j = 0; j < 2; j++) { if (j == 0) { do { mpfr_urandomb (q2, RANDS); } while (mpfr_cmp_ui (q2, 0) == 0); } else /* use q2=1 */ mpfr_set_ui (q2, 1, MPFR_RNDN); for (precv = precq; precv <= 10 * precq; precv += precq) { mpfr_set_prec (v, precv); do { mpfr_urandomb (v, RANDS); } while (mpfr_cmp_ui (v, 0) == 0); for (precu = precq; precu <= 10 * precq; precu += precq) { mpfr_set_prec (u, precu); mpfr_mul (u, v, q2, MPFR_RNDN); mpfr_nextbelow (u); for (i = 0; i <= 2; i++) { RND_LOOP(rnd) { inex = test_div (q, u, v, (mpfr_rnd_t) rnd); inex2 = get_inexact (q, u, v); if (inex_cmp (inex, inex2)) { printf ("Wrong inexact flag for rnd=%s: expected %d, got %d\n", mpfr_print_rnd_mode ((mpfr_rnd_t) rnd), inex2, inex); printf ("u= "); mpfr_dump (u); printf ("v= "); mpfr_dump (v); printf ("q= "); mpfr_dump (q); mpfr_set_prec (q2, precq + precv); mpfr_mul (q2, q, v, MPFR_RNDN); printf ("q*v="); mpfr_dump (q2); exit (1); } } mpfr_nextabove (u); } } } } } mpfr_clear (q); mpfr_clear (q2); mpfr_clear (u); mpfr_clear (v); } static void check_lowr (void) { mpfr_t x, y, z, z2, z3, tmp; int k, c, c2; mpfr_init2 (x, 1000); mpfr_init2 (y, 100); mpfr_init2 (tmp, 850); mpfr_init2 (z, 10); mpfr_init2 (z2, 10); mpfr_init2 (z3, 50); for (k = 1; k < KMAX; k++) { do { mpfr_urandomb (z, RANDS); } while (mpfr_cmp_ui (z, 0) == 0); do { mpfr_urandomb (tmp, RANDS); } while (mpfr_cmp_ui (tmp, 0) == 0); mpfr_mul (x, z, tmp, MPFR_RNDN); /* exact */ c = test_div (z2, x, tmp, MPFR_RNDN); if (c || mpfr_cmp (z2, z)) { printf ("Error in mpfr_div rnd=MPFR_RNDN\n"); printf ("got "); mpfr_print_binary(z2); puts (""); printf ("instead of "); mpfr_print_binary(z); puts (""); printf ("inex flag = %d, expected 0\n", c); exit (1); } } /* x has still precision 1000, z precision 10, and tmp prec 850 */ mpfr_set_prec (z2, 9); for (k = 1; k < KMAX; k++) { mpfr_urandomb (z, RANDS); do { mpfr_urandomb (tmp, RANDS); } while (mpfr_cmp_ui (tmp, 0) == 0); mpfr_mul (x, z, tmp, MPFR_RNDN); /* exact */ c = test_div (z2, x, tmp, MPFR_RNDN); /* since z2 has one less bit that z, either the division is exact if z is representable on 9 bits, or we have an even round case */ c2 = get_inexact (z2, x, tmp); if ((mpfr_cmp (z2, z) == 0 && c) || inex_cmp (c, c2)) { printf ("Error in mpfr_div rnd=MPFR_RNDN\n"); printf ("got "); mpfr_print_binary(z2); puts (""); printf ("instead of "); mpfr_print_binary(z); puts (""); printf ("inex flag = %d, expected %d\n", c, c2); exit (1); } else if (c == 2) { mpfr_nexttoinf (z); if (mpfr_cmp(z2, z)) { printf ("Error in mpfr_div [even rnd?] rnd=MPFR_RNDN\n"); printf ("Dividing "); printf ("got "); mpfr_print_binary(z2); puts (""); printf ("instead of "); mpfr_print_binary(z); puts (""); printf ("inex flag = %d\n", 1); exit (1); } } else if (c == -2) { mpfr_nexttozero (z); if (mpfr_cmp(z2, z)) { printf ("Error in mpfr_div [even rnd?] rnd=MPFR_RNDN\n"); printf ("Dividing "); printf ("got "); mpfr_print_binary(z2); puts (""); printf ("instead of "); mpfr_print_binary(z); puts (""); printf ("inex flag = %d\n", 1); exit (1); } } } mpfr_set_prec(x, 1000); mpfr_set_prec(y, 100); mpfr_set_prec(tmp, 850); mpfr_set_prec(z, 10); mpfr_set_prec(z2, 10); /* almost exact divisions */ for (k = 1; k < KMAX; k++) { do { mpfr_urandomb (z, RANDS); } while (mpfr_cmp_ui (z, 0) == 0); do { mpfr_urandomb (tmp, RANDS); } while (mpfr_cmp_ui (tmp, 0) == 0); mpfr_mul(x, z, tmp, MPFR_RNDN); mpfr_set(y, tmp, MPFR_RNDD); mpfr_nexttoinf (x); c = test_div(z2, x, y, MPFR_RNDD); test_div(z3, x, y, MPFR_RNDD); mpfr_set(z, z3, MPFR_RNDD); if (c != -1 || mpfr_cmp(z2, z)) { printf ("Error in mpfr_div rnd=MPFR_RNDD\n"); printf ("got "); mpfr_print_binary(z2); puts (""); printf ("instead of "); mpfr_print_binary(z); puts (""); printf ("inex flag = %d\n", c); exit (1); } mpfr_set (y, tmp, MPFR_RNDU); test_div (z3, x, y, MPFR_RNDU); mpfr_set (z, z3, MPFR_RNDU); c = test_div (z2, x, y, MPFR_RNDU); if (c != 1 || mpfr_cmp (z2, z)) { printf ("Error in mpfr_div rnd=MPFR_RNDU\n"); printf ("u="); mpfr_dump (x); printf ("v="); mpfr_dump (y); printf ("got "); mpfr_print_binary (z2); puts (""); printf ("instead of "); mpfr_print_binary (z); puts (""); printf ("inex flag = %d\n", c); exit (1); } } mpfr_clear (x); mpfr_clear (y); mpfr_clear (z); mpfr_clear (z2); mpfr_clear (z3); mpfr_clear (tmp); } #define MAX_PREC 128 static void check_inexact (void) { mpfr_t x, y, z, u; mpfr_prec_t px, py, pu; int inexact, cmp; mpfr_rnd_t rnd; mpfr_init (x); mpfr_init (y); mpfr_init (z); mpfr_init (u); mpfr_set_prec (x, 28); mpfr_set_prec (y, 28); mpfr_set_prec (z, 1023); mpfr_set_str_binary (x, "0.1000001001101101111100010011E0"); mpfr_set_str (z, "48284762641021308813686974720835219181653367326353400027913400579340343320519877153813133510034402932651132854764198688352364361009429039801248971901380781746767119334993621199563870113045276395603170432175354501451429471578325545278975153148347684600400321033502982713296919861760382863826626093689036010394", 10, MPFR_RNDN); mpfr_div (x, x, z, MPFR_RNDN); mpfr_set_str_binary (y, "0.1111001011001101001001111100E-1023"); if (mpfr_cmp (x, y)) { printf ("Error in mpfr_div for prec=28, RNDN\n"); printf ("Expected "); mpfr_dump (y); printf ("Got "); mpfr_dump (x); exit (1); } mpfr_set_prec (x, 53); mpfr_set_str_binary (x, "0.11101100110010100011011000000100001111011111110010101E0"); mpfr_set_prec (u, 127); mpfr_set_str_binary (u, "0.1000001100110110110101110110101101111000110000001111111110000000011111001010110100110010111111111101000001011011101011101101000E-2"); mpfr_set_prec (y, 95); inexact = test_div (y, x, u, MPFR_RNDN); if (inexact != (cmp = get_inexact (y, x, u))) { printf ("Wrong inexact flag (0): expected %d, got %d\n", cmp, inexact); printf ("x="); mpfr_out_str (stdout, 10, 99, x, MPFR_RNDN); printf ("\n"); printf ("u="); mpfr_out_str (stdout, 10, 99, u, MPFR_RNDN); printf ("\n"); printf ("y="); mpfr_out_str (stdout, 10, 99, y, MPFR_RNDN); printf ("\n"); exit (1); } mpfr_set_prec (x, 33); mpfr_set_str_binary (x, "0.101111100011011101010011101100001E0"); mpfr_set_prec (u, 2); mpfr_set_str_binary (u, "0.1E0"); mpfr_set_prec (y, 28); if ((inexact = test_div (y, x, u, MPFR_RNDN) >= 0)) { printf ("Wrong inexact flag (1): expected -1, got %d\n", inexact); exit (1); } mpfr_set_prec (x, 129); mpfr_set_str_binary (x, "0.111110101111001100000101011100101100110011011101010001000110110101100101000010000001110110100001101010001010100010001111001101010E-2"); mpfr_set_prec (u, 15); mpfr_set_str_binary (u, "0.101101000001100E-1"); mpfr_set_prec (y, 92); if ((inexact = test_div (y, x, u, MPFR_RNDN)) <= 0) { printf ("Wrong inexact flag for rnd=MPFR_RNDN(1): expected 1, got %d\n", inexact); mpfr_dump (x); mpfr_dump (u); mpfr_dump (y); exit (1); } for (px=2; px 0) && (cmp <= 0)) || ((inexact < 0) && (cmp >= 0))) { printf ("Wrong inexact flag for rnd=%s\n", mpfr_print_rnd_mode(rnd)); printf ("expected %d, got %d\n", cmp, inexact); printf ("x="); mpfr_print_binary (x); puts (""); printf ("u="); mpfr_print_binary (u); puts (""); printf ("y="); mpfr_print_binary (y); puts (""); printf ("y*u="); mpfr_print_binary (z); puts (""); exit (1); } } } } } mpfr_clear (x); mpfr_clear (y); mpfr_clear (z); mpfr_clear (u); } static void check_special (void) { mpfr_t a, d, q; mpfr_exp_t emax, emin; int i; mpfr_init2 (a, 100L); mpfr_init2 (d, 100L); mpfr_init2 (q, 100L); /* 1/nan == nan */ mpfr_set_ui (a, 1L, MPFR_RNDN); MPFR_SET_NAN (d); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN); /* nan/1 == nan */ MPFR_SET_NAN (a); mpfr_set_ui (d, 1L, MPFR_RNDN); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN); /* +inf/1 == +inf */ MPFR_SET_INF (a); MPFR_SET_POS (a); mpfr_set_ui (d, 1L, MPFR_RNDN); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_inf_p (q)); MPFR_ASSERTN (mpfr_sgn (q) > 0); MPFR_ASSERTN (__gmpfr_flags == 0); /* +inf/-1 == -inf */ MPFR_SET_INF (a); MPFR_SET_POS (a); mpfr_set_si (d, -1, MPFR_RNDN); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_inf_p (q)); MPFR_ASSERTN (mpfr_sgn (q) < 0); MPFR_ASSERTN (__gmpfr_flags == 0); /* -inf/1 == -inf */ MPFR_SET_INF (a); MPFR_SET_NEG (a); mpfr_set_ui (d, 1L, MPFR_RNDN); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_inf_p (q)); MPFR_ASSERTN (mpfr_sgn (q) < 0); MPFR_ASSERTN (__gmpfr_flags == 0); /* -inf/-1 == +inf */ MPFR_SET_INF (a); MPFR_SET_NEG (a); mpfr_set_si (d, -1, MPFR_RNDN); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_inf_p (q)); MPFR_ASSERTN (mpfr_sgn (q) > 0); MPFR_ASSERTN (__gmpfr_flags == 0); /* 1/+inf == +0 */ mpfr_set_ui (a, 1L, MPFR_RNDN); MPFR_SET_INF (d); MPFR_SET_POS (d); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_number_p (q)); MPFR_ASSERTN (mpfr_sgn (q) == 0); MPFR_ASSERTN (MPFR_IS_POS (q)); MPFR_ASSERTN (__gmpfr_flags == 0); /* 1/-inf == -0 */ mpfr_set_ui (a, 1L, MPFR_RNDN); MPFR_SET_INF (d); MPFR_SET_NEG (d); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_number_p (q)); MPFR_ASSERTN (mpfr_sgn (q) == 0); MPFR_ASSERTN (MPFR_IS_NEG (q)); MPFR_ASSERTN (__gmpfr_flags == 0); /* -1/+inf == -0 */ mpfr_set_si (a, -1, MPFR_RNDN); MPFR_SET_INF (d); MPFR_SET_POS (d); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_number_p (q)); MPFR_ASSERTN (mpfr_sgn (q) == 0); MPFR_ASSERTN (MPFR_IS_NEG (q)); MPFR_ASSERTN (__gmpfr_flags == 0); /* -1/-inf == +0 */ mpfr_set_si (a, -1, MPFR_RNDN); MPFR_SET_INF (d); MPFR_SET_NEG (d); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_number_p (q)); MPFR_ASSERTN (mpfr_sgn (q) == 0); MPFR_ASSERTN (MPFR_IS_POS (q)); MPFR_ASSERTN (__gmpfr_flags == 0); /* 0/0 == nan */ mpfr_set_ui (a, 0L, MPFR_RNDN); mpfr_set_ui (d, 0L, MPFR_RNDN); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN); /* +inf/+inf == nan */ MPFR_SET_INF (a); MPFR_SET_POS (a); MPFR_SET_INF (d); MPFR_SET_POS (d); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_NAN); /* 1/+0 = +inf */ mpfr_set_ui (a, 1, MPFR_RNDZ); mpfr_set_ui (d, 0, MPFR_RNDZ); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0); MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0); /* 1/-0 = -inf */ mpfr_set_ui (a, 1, MPFR_RNDZ); mpfr_set_ui (d, 0, MPFR_RNDZ); mpfr_neg (d, d, MPFR_RNDZ); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0); MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0); /* -1/+0 = -inf */ mpfr_set_si (a, -1, MPFR_RNDZ); mpfr_set_ui (d, 0, MPFR_RNDZ); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0); MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0); /* -1/-0 = +inf */ mpfr_set_si (a, -1, MPFR_RNDZ); mpfr_set_ui (d, 0, MPFR_RNDZ); mpfr_neg (d, d, MPFR_RNDZ); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0); MPFR_ASSERTN (__gmpfr_flags == MPFR_FLAGS_DIVBY0); /* +inf/+0 = +inf */ MPFR_SET_INF (a); MPFR_SET_POS (a); mpfr_set_ui (d, 0, MPFR_RNDZ); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0); MPFR_ASSERTN (__gmpfr_flags == 0); /* +inf/-0 = -inf */ MPFR_SET_INF (a); MPFR_SET_POS (a); mpfr_set_ui (d, 0, MPFR_RNDZ); mpfr_neg (d, d, MPFR_RNDZ); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0); MPFR_ASSERTN (__gmpfr_flags == 0); /* -inf/+0 = -inf */ MPFR_SET_INF (a); MPFR_SET_NEG (a); mpfr_set_ui (d, 0, MPFR_RNDZ); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0); MPFR_ASSERTN (__gmpfr_flags == 0); /* -inf/-0 = +inf */ MPFR_SET_INF (a); MPFR_SET_NEG (a); mpfr_set_ui (d, 0, MPFR_RNDZ); mpfr_neg (d, d, MPFR_RNDZ); mpfr_clear_flags (); MPFR_ASSERTN (test_div (q, a, d, MPFR_RNDZ) == 0); /* exact */ MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0); MPFR_ASSERTN (__gmpfr_flags == 0); /* check overflow */ emax = mpfr_get_emax (); set_emax (1); mpfr_set_ui (a, 1, MPFR_RNDZ); mpfr_set_ui (d, 1, MPFR_RNDZ); mpfr_div_2exp (d, d, 1, MPFR_RNDZ); mpfr_clear_flags (); test_div (q, a, d, MPFR_RNDU); /* 1 / 0.5 = 2 -> overflow */ MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0); MPFR_ASSERTN (__gmpfr_flags == (MPFR_FLAGS_OVERFLOW | MPFR_FLAGS_INEXACT)); set_emax (emax); /* check underflow */ emin = mpfr_get_emin (); set_emin (-1); mpfr_set_ui (a, 1, MPFR_RNDZ); mpfr_div_2exp (a, a, 2, MPFR_RNDZ); mpfr_set_prec (d, mpfr_get_prec (q) + 8); for (i = -1; i <= 1; i++) { int sign; /* Test 2^(-2) / (+/- (2 + eps)), with eps < 0, eps = 0, eps > 0. -> underflow. With div.c r5513, this test fails for eps > 0 in MPFR_RNDN. */ mpfr_set_ui (d, 2, MPFR_RNDZ); if (i < 0) mpfr_nextbelow (d); if (i > 0) mpfr_nextabove (d); for (sign = 0; sign <= 1; sign++) { mpfr_clear_flags (); test_div (q, a, d, MPFR_RNDZ); /* result = 0 */ MPFR_ASSERTN (__gmpfr_flags == (MPFR_FLAGS_UNDERFLOW | MPFR_FLAGS_INEXACT)); MPFR_ASSERTN (sign ? MPFR_IS_NEG (q) : MPFR_IS_POS (q)); MPFR_ASSERTN (MPFR_IS_ZERO (q)); mpfr_clear_flags (); test_div (q, a, d, MPFR_RNDN); /* result = 0 iff eps >= 0 */ MPFR_ASSERTN (__gmpfr_flags == (MPFR_FLAGS_UNDERFLOW | MPFR_FLAGS_INEXACT)); MPFR_ASSERTN (sign ? MPFR_IS_NEG (q) : MPFR_IS_POS (q)); if (i < 0) mpfr_nexttozero (q); MPFR_ASSERTN (MPFR_IS_ZERO (q)); mpfr_neg (d, d, MPFR_RNDN); } } set_emin (emin); mpfr_clear (a); mpfr_clear (d); mpfr_clear (q); } static void consistency (void) { mpfr_t x, y, z1, z2; int i; mpfr_inits (x, y, z1, z2, (mpfr_ptr) 0); for (i = 0; i < 10000; i++) { mpfr_rnd_t rnd; mpfr_prec_t px, py, pz, p; int inex1, inex2; rnd = RND_RAND (); px = (randlimb () % 256) + 2; py = (randlimb () % 128) + 2; pz = (randlimb () % 256) + 2; mpfr_set_prec (x, px); mpfr_set_prec (y, py); mpfr_set_prec (z1, pz); mpfr_set_prec (z2, pz); mpfr_urandomb (x, RANDS); do mpfr_urandomb (y, RANDS); while (mpfr_zero_p (y)); inex1 = mpfr_div (z1, x, y, rnd); MPFR_ASSERTN (!MPFR_IS_NAN (z1)); p = MAX (MAX (px, py), pz); if (mpfr_prec_round (x, p, MPFR_RNDN) != 0 || mpfr_prec_round (y, p, MPFR_RNDN) != 0) { printf ("mpfr_prec_round error for i = %d\n", i); exit (1); } inex2 = mpfr_div (z2, x, y, rnd); MPFR_ASSERTN (!MPFR_IS_NAN (z2)); if (inex1 != inex2 || mpfr_cmp (z1, z2) != 0) { printf ("Consistency error for i = %d\n", i); exit (1); } } mpfr_clears (x, y, z1, z2, (mpfr_ptr) 0); } /* Reported by Carl Witty on 2007-06-03 */ static void test_20070603 (void) { mpfr_t n, d, q, c; mpfr_init2 (n, 128); mpfr_init2 (d, 128); mpfr_init2 (q, 31); mpfr_init2 (c, 31); mpfr_set_str (n, "10384593717069655257060992206846485", 10, MPFR_RNDN); mpfr_set_str (d, "10384593717069655257060992206847132", 10, MPFR_RNDN); mpfr_div (q, n, d, MPFR_RNDU); mpfr_set_ui (c, 1, MPFR_RNDN); if (mpfr_cmp (q, c) != 0) { printf ("Error in test_20070603\nGot "); mpfr_dump (q); printf ("instead of "); mpfr_dump (c); exit (1); } /* same for 64-bit machines */ mpfr_set_prec (n, 256); mpfr_set_prec (d, 256); mpfr_set_prec (q, 63); mpfr_set_str (n, "822752278660603021077484591278675252491367930877209729029898240", 10, MPFR_RNDN); mpfr_set_str (d, "822752278660603021077484591278675252491367930877212507873738752", 10, MPFR_RNDN); mpfr_div (q, n, d, MPFR_RNDU); if (mpfr_cmp (q, c) != 0) { printf ("Error in test_20070603\nGot "); mpfr_dump (q); printf ("instead of "); mpfr_dump (c); exit (1); } mpfr_clear (n); mpfr_clear (d); mpfr_clear (q); mpfr_clear (c); } /* Bug found while adding tests for mpfr_cot */ static void test_20070628 (void) { mpfr_exp_t old_emax; mpfr_t x, y; int inex, err = 0; old_emax = mpfr_get_emax (); if (mpfr_set_emax (256)) { printf ("Can't change exponent range\n"); exit (1); } mpfr_inits2 (53, x, y, (mpfr_ptr) 0); mpfr_set_si (x, -1, MPFR_RNDN); mpfr_set_si_2exp (y, 1, -256, MPFR_RNDN); mpfr_clear_flags (); inex = mpfr_div (x, x, y, MPFR_RNDD); if (MPFR_SIGN (x) >= 0 || ! mpfr_inf_p (x)) { printf ("Error in test_20070628: expected -Inf, got\n"); mpfr_dump (x); err++; } if (inex >= 0) { printf ("Error in test_20070628: expected inex < 0, got %d\n", inex); err++; } if (! mpfr_overflow_p ()) { printf ("Error in test_20070628: overflow flag is not set\n"); err++; } mpfr_clears (x, y, (mpfr_ptr) 0); mpfr_set_emax (old_emax); } #define TEST_FUNCTION test_div #define TWO_ARGS #define RAND_FUNCTION(x) mpfr_random2(x, MPFR_LIMB_SIZE (x), randlimb () % 100, RANDS) #include "tgeneric.c" static void test_extreme (void) { mpfr_t x, y, z; mpfr_exp_t emin, emax; mpfr_prec_t p[4] = { 8, 32, 64, 256 }; int xi, yi, zi, j, r; unsigned int flags, ex_flags; emin = mpfr_get_emin (); emax = mpfr_get_emax (); mpfr_set_emin (MPFR_EMIN_MIN); mpfr_set_emax (MPFR_EMAX_MAX); for (xi = 0; xi < 4; xi++) { mpfr_init2 (x, p[xi]); mpfr_setmax (x, MPFR_EMAX_MAX); MPFR_ASSERTN (mpfr_check (x)); for (yi = 0; yi < 4; yi++) { mpfr_init2 (y, p[yi]); mpfr_setmin (y, MPFR_EMIN_MIN); for (j = 0; j < 2; j++) { MPFR_ASSERTN (mpfr_check (y)); for (zi = 0; zi < 4; zi++) { mpfr_init2 (z, p[zi]); RND_LOOP (r) { mpfr_clear_flags (); mpfr_div (z, x, y, (mpfr_rnd_t) r); flags = __gmpfr_flags; MPFR_ASSERTN (mpfr_check (z)); ex_flags = MPFR_FLAGS_OVERFLOW | MPFR_FLAGS_INEXACT; if (flags != ex_flags) { printf ("Bad flags in test_extreme on z = a/b" " with %s and\n", mpfr_print_rnd_mode ((mpfr_rnd_t) r)); printf ("a = "); mpfr_dump (x); printf ("b = "); mpfr_dump (y); printf ("Expected flags:"); flags_out (ex_flags); printf ("Got flags: "); flags_out (flags); printf ("z = "); mpfr_dump (z); exit (1); } mpfr_clear_flags (); mpfr_div (z, y, x, (mpfr_rnd_t) r); flags = __gmpfr_flags; MPFR_ASSERTN (mpfr_check (z)); ex_flags = MPFR_FLAGS_UNDERFLOW | MPFR_FLAGS_INEXACT; if (flags != ex_flags) { printf ("Bad flags in test_extreme on z = a/b" " with %s and\n", mpfr_print_rnd_mode ((mpfr_rnd_t) r)); printf ("a = "); mpfr_dump (y); printf ("b = "); mpfr_dump (x); printf ("Expected flags:"); flags_out (ex_flags); printf ("Got flags: "); flags_out (flags); printf ("z = "); mpfr_dump (z); exit (1); } } mpfr_clear (z); } /* zi */ mpfr_nextabove (y); } /* j */ mpfr_clear (y); } /* yi */ mpfr_clear (x); } /* xi */ set_emin (emin); set_emax (emax); } int main (int argc, char *argv[]) { tests_start_mpfr (); check_inexact (); check_hard (); check_special (); check_lowr (); check_float (); /* checks single precision */ check_double (); check_convergence (); check_64 (); check4("4.0","4.503599627370496e15", MPFR_RNDZ, 62, "0.10000000000000000000000000000000000000000000000000000000000000E-49"); check4("1.0","2.10263340267725788209e+187", MPFR_RNDU, 65, "0.11010011111001101011111001100111110100000001101001111100111000000E-622"); check4("2.44394909079968374564e-150", "2.10263340267725788209e+187",MPFR_RNDU, 65, "0.11010011111001101011111001100111110100000001101001111100111000000E-1119"); consistency (); test_20070603 (); test_20070628 (); test_generic (2, 800, 50); test_extreme (); tests_end_mpfr (); return 0; }