/* Test file for mpfr_mul. Copyright 1999, 2001-2018 Free Software Foundation, Inc. Contributed by the AriC and Caramba 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 "mpfr-test.h" #ifdef CHECK_EXTERNAL static int test_mul (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_mul (a, b, c, rnd_mode); if (ok) { printf (" "); mpfr_print_raw (a); printf ("\n"); } return res; } #else #define test_mul mpfr_mul #endif /* checks that xs * ys gives the expected result res */ static void check (const char *xs, const char *ys, mpfr_rnd_t rnd_mode, unsigned int px, unsigned int py, unsigned int pz, const char *res) { mpfr_t xx, yy, zz; mpfr_init2 (xx, px); mpfr_init2 (yy, py); mpfr_init2 (zz, pz); mpfr_set_str1 (xx, xs); mpfr_set_str1 (yy, ys); test_mul(zz, xx, yy, rnd_mode); if (mpfr_cmp_str1 (zz, res) ) { printf ("(1) mpfr_mul failed for x=%s y=%s with rnd=%s\n", xs, ys, mpfr_print_rnd_mode (rnd_mode)); printf ("correct is %s, mpfr_mul gives ", res); mpfr_out_str (stdout, 10, 0, zz, MPFR_RNDN); putchar ('\n'); exit (1); } mpfr_clear (xx); mpfr_clear (yy); mpfr_clear (zz); } static void check53 (const char *xs, const char *ys, mpfr_rnd_t rnd_mode, const char *zs) { mpfr_t xx, yy, zz; mpfr_inits2 (53, xx, yy, zz, (mpfr_ptr) 0); mpfr_set_str1 (xx, xs); mpfr_set_str1 (yy, ys); test_mul (zz, xx, yy, rnd_mode); if (mpfr_cmp_str1 (zz, zs) ) { printf ("(2) mpfr_mul failed for x=%s y=%s with rnd=%s\n", xs, ys, mpfr_print_rnd_mode(rnd_mode)); printf ("correct result is %s,\n mpfr_mul gives ", zs); mpfr_out_str (stdout, 10, 0, zz, MPFR_RNDN); putchar ('\n'); exit (1); } mpfr_clears (xx, yy, zz, (mpfr_ptr) 0); } /* checks that x*y gives the right result with 24 bits of precision */ static void check24 (const char *xs, const char *ys, mpfr_rnd_t rnd_mode, const char *zs) { mpfr_t xx, yy, zz; mpfr_inits2 (24, xx, yy, zz, (mpfr_ptr) 0); mpfr_set_str1 (xx, xs); mpfr_set_str1 (yy, ys); test_mul (zz, xx, yy, rnd_mode); if (mpfr_cmp_str1 (zz, zs) ) { printf ("(3) mpfr_mul failed for x=%s y=%s with " "rnd=%s\n", xs, ys, mpfr_print_rnd_mode(rnd_mode)); printf ("correct result is gives %s, mpfr_mul gives ", zs); mpfr_out_str (stdout, 10, 0, zz, MPFR_RNDN); putchar ('\n'); exit (1); } mpfr_clears (xx, yy, zz, (mpfr_ptr) 0); } /* the following examples come from the paper "Number-theoretic Test Generation for Directed Rounding" from Michael Parks, Table 1 */ static void check_float (void) { check24("8388609.0", "8388609.0", MPFR_RNDN, "70368760954880.0"); check24("16777213.0", "8388609.0", MPFR_RNDN, "140737479966720.0"); check24("8388611.0", "8388609.0", MPFR_RNDN, "70368777732096.0"); check24("12582911.0", "8388610.0", MPFR_RNDN, "105553133043712.0"); check24("12582914.0", "8388610.0", MPFR_RNDN, "105553158209536.0"); check24("13981013.0", "8388611.0", MPFR_RNDN, "117281279442944.0"); check24("11184811.0", "8388611.0", MPFR_RNDN, "93825028587520.0"); check24("11184810.0", "8388611.0", MPFR_RNDN, "93825020198912.0"); check24("13981014.0", "8388611.0", MPFR_RNDN, "117281287831552.0"); check24("8388609.0", "8388609.0", MPFR_RNDZ, "70368760954880.0"); check24("16777213.0", "8388609.0", MPFR_RNDZ, "140737471578112.0"); check24("8388611.0", "8388609.0", MPFR_RNDZ, "70368777732096.0"); check24("12582911.0", "8388610.0", MPFR_RNDZ, "105553124655104.0"); check24("12582914.0", "8388610.0", MPFR_RNDZ, "105553158209536.0"); check24("13981013.0", "8388611.0", MPFR_RNDZ, "117281271054336.0"); check24("11184811.0", "8388611.0", MPFR_RNDZ, "93825028587520.0"); check24("11184810.0", "8388611.0", MPFR_RNDZ, "93825011810304.0"); check24("13981014.0", "8388611.0", MPFR_RNDZ, "117281287831552.0"); check24("8388609.0", "8388609.0", MPFR_RNDU, "70368769343488.0"); check24("16777213.0", "8388609.0", MPFR_RNDU, "140737479966720.0"); check24("8388611.0", "8388609.0", MPFR_RNDU, "70368786120704.0"); check24("12582911.0", "8388610.0", MPFR_RNDU, "105553133043712.0"); check24("12582914.0", "8388610.0", MPFR_RNDU, "105553166598144.0"); check24("13981013.0", "8388611.0", MPFR_RNDU, "117281279442944.0"); check24("11184811.0", "8388611.0", MPFR_RNDU, "93825036976128.0"); check24("11184810.0", "8388611.0", MPFR_RNDU, "93825020198912.0"); check24("13981014.0", "8388611.0", MPFR_RNDU, "117281296220160.0"); check24("8388609.0", "8388609.0", MPFR_RNDD, "70368760954880.0"); check24("16777213.0", "8388609.0", MPFR_RNDD, "140737471578112.0"); check24("8388611.0", "8388609.0", MPFR_RNDD, "70368777732096.0"); check24("12582911.0", "8388610.0", MPFR_RNDD, "105553124655104.0"); check24("12582914.0", "8388610.0", MPFR_RNDD, "105553158209536.0"); check24("13981013.0", "8388611.0", MPFR_RNDD, "117281271054336.0"); check24("11184811.0", "8388611.0", MPFR_RNDD, "93825028587520.0"); check24("11184810.0", "8388611.0", MPFR_RNDD, "93825011810304.0"); check24("13981014.0", "8388611.0", MPFR_RNDD, "117281287831552.0"); } /* check sign of result */ static void check_sign (void) { mpfr_t a, b; mpfr_init2 (a, 53); mpfr_init2 (b, 53); mpfr_set_si (a, -1, MPFR_RNDN); mpfr_set_ui (b, 2, MPFR_RNDN); test_mul(a, b, b, MPFR_RNDN); if (mpfr_cmp_ui (a, 4) ) { printf ("2.0*2.0 gives \n"); mpfr_out_str (stdout, 10, 0, a, MPFR_RNDN); putchar ('\n'); exit (1); } mpfr_clear(a); mpfr_clear(b); } /* checks that the inexact return value is correct */ static void check_exact (void) { mpfr_t a, b, c, d; mpfr_prec_t prec; int i, inexact; mpfr_rnd_t rnd; mpfr_init (a); mpfr_init (b); mpfr_init (c); mpfr_init (d); mpfr_set_prec (a, 17); mpfr_set_prec (b, 17); mpfr_set_prec (c, 32); mpfr_set_str_binary (a, "1.1000111011000100e-1"); mpfr_set_str_binary (b, "1.0010001111100111e-1"); if (test_mul (c, a, b, MPFR_RNDZ)) { printf ("wrong return value (1)\n"); exit (1); } for (prec = MPFR_PREC_MIN; prec < 100; prec++) { mpfr_set_prec (a, prec); mpfr_set_prec (b, prec); /* for prec=1, ensure PREC(c) >= 1 */ mpfr_set_prec (c, 2 * prec - 2 + (prec == 1)); mpfr_set_prec (d, 2 * prec); for (i = 0; i < 1000; i++) { mpfr_urandomb (a, RANDS); mpfr_urandomb (b, RANDS); rnd = RND_RAND (); inexact = test_mul (c, a, b, rnd); if (test_mul (d, a, b, rnd)) /* should be always exact */ { printf ("unexpected inexact return value\n"); exit (1); } if ((inexact == 0) && mpfr_cmp (c, d) && rnd != MPFR_RNDF) { printf ("rnd=%s: inexact=0 but results differ\n", mpfr_print_rnd_mode (rnd)); printf ("a="); mpfr_out_str (stdout, 2, 0, a, rnd); printf ("\nb="); mpfr_out_str (stdout, 2, 0, b, rnd); printf ("\nc="); mpfr_out_str (stdout, 2, 0, c, rnd); printf ("\nd="); mpfr_out_str (stdout, 2, 0, d, rnd); printf ("\n"); exit (1); } else if (inexact && (mpfr_cmp (c, d) == 0) && rnd != MPFR_RNDF) { printf ("inexact!=0 but results agree\n"); printf ("prec=%u rnd=%s a=", (unsigned int) prec, mpfr_print_rnd_mode (rnd)); mpfr_out_str (stdout, 2, 0, a, rnd); printf ("\nb="); mpfr_out_str (stdout, 2, 0, b, rnd); printf ("\nc="); mpfr_out_str (stdout, 2, 0, c, rnd); printf ("\nd="); mpfr_out_str (stdout, 2, 0, d, rnd); printf ("\n"); exit (1); } } } mpfr_clear (a); mpfr_clear (b); mpfr_clear (c); mpfr_clear (d); } static void check_max (void) { mpfr_t xx, yy, zz; mpfr_exp_t emin; int inex; mpfr_init2(xx, 4); mpfr_init2(yy, 4); mpfr_init2(zz, 4); mpfr_set_str1 (xx, "0.68750"); mpfr_mul_2si(xx, xx, MPFR_EMAX_DEFAULT/2, MPFR_RNDN); mpfr_set_str1 (yy, "0.68750"); mpfr_mul_2si(yy, yy, MPFR_EMAX_DEFAULT - MPFR_EMAX_DEFAULT/2 + 1, MPFR_RNDN); mpfr_clear_flags(); test_mul(zz, xx, yy, MPFR_RNDU); if (!(mpfr_overflow_p() && MPFR_IS_INF(zz))) { printf("check_max failed (should be an overflow)\n"); exit(1); } mpfr_clear_flags(); test_mul(zz, xx, yy, MPFR_RNDD); if (mpfr_overflow_p() || MPFR_IS_INF(zz)) { printf("check_max failed (should NOT be an overflow)\n"); exit(1); } mpfr_set_str1 (xx, "0.93750"); mpfr_mul_2si(xx, xx, MPFR_EMAX_DEFAULT, MPFR_RNDN); if (!(MPFR_IS_FP(xx) && MPFR_IS_FP(zz))) { printf("check_max failed (internal error)\n"); exit(1); } if (mpfr_cmp(xx, zz) != 0) { printf("check_max failed: got "); mpfr_out_str(stdout, 2, 0, zz, MPFR_RNDZ); printf(" instead of "); mpfr_out_str(stdout, 2, 0, xx, MPFR_RNDZ); printf("\n"); exit(1); } /* check underflow */ emin = mpfr_get_emin (); set_emin (0); mpfr_set_str_binary (xx, "0.1E0"); mpfr_set_str_binary (yy, "0.1E0"); test_mul (zz, xx, yy, MPFR_RNDN); /* exact result is 0.1E-1, which should round to 0 */ MPFR_ASSERTN(mpfr_cmp_ui (zz, 0) == 0 && MPFR_IS_POS(zz)); set_emin (emin); /* coverage test for mpfr_powerof2_raw */ emin = mpfr_get_emin (); set_emin (0); mpfr_set_prec (xx, mp_bits_per_limb + 1); mpfr_set_str_binary (xx, "0.1E0"); mpfr_nextabove (xx); mpfr_set_str_binary (yy, "0.1E0"); test_mul (zz, xx, yy, MPFR_RNDN); /* exact result is just above 0.1E-1, which should round to minfloat */ MPFR_ASSERTN(mpfr_cmp (zz, yy) == 0); set_emin (emin); /* coverage test for mulders.c, case n > MUL_FFT_THRESHOLD */ mpfr_set_prec (xx, (MUL_FFT_THRESHOLD + 1) * GMP_NUMB_BITS); mpfr_set_prec (yy, (MUL_FFT_THRESHOLD + 1) * GMP_NUMB_BITS); mpfr_set_prec (zz, (MUL_FFT_THRESHOLD + 1) * GMP_NUMB_BITS); mpfr_set_ui (xx, 1, MPFR_RNDN); mpfr_nextbelow (xx); mpfr_set_ui (yy, 1, MPFR_RNDN); mpfr_nextabove (yy); /* xx = 1 - 2^(-p), yy = 1 + 2^(1-p), where p = PREC(x), thus xx * yy should be rounded to 1 */ inex = mpfr_mul (zz, xx, yy, MPFR_RNDN); MPFR_ASSERTN(inex < 0); MPFR_ASSERTN(mpfr_cmp_ui (zz, 1) == 0); mpfr_clear(xx); mpfr_clear(yy); mpfr_clear(zz); } static void check_min(void) { mpfr_t xx, yy, zz; mpfr_init2(xx, 4); mpfr_init2(yy, 4); mpfr_init2(zz, 3); mpfr_set_str1(xx, "0.9375"); mpfr_mul_2si(xx, xx, MPFR_EMIN_DEFAULT/2, MPFR_RNDN); mpfr_set_str1(yy, "0.9375"); mpfr_mul_2si(yy, yy, MPFR_EMIN_DEFAULT - MPFR_EMIN_DEFAULT/2 - 1, MPFR_RNDN); test_mul(zz, xx, yy, MPFR_RNDD); if (MPFR_NOTZERO (zz)) { printf("check_min failed: got "); mpfr_out_str(stdout, 2, 0, zz, MPFR_RNDZ); printf(" instead of 0\n"); exit(1); } test_mul(zz, xx, yy, MPFR_RNDU); mpfr_set_str1 (xx, "0.5"); mpfr_mul_2si(xx, xx, MPFR_EMIN_DEFAULT, MPFR_RNDN); if (mpfr_sgn(xx) <= 0) { printf("check_min failed (internal error)\n"); exit(1); } if (mpfr_cmp(xx, zz) != 0) { printf("check_min failed: got "); mpfr_out_str(stdout, 2, 0, zz, MPFR_RNDZ); printf(" instead of "); mpfr_out_str(stdout, 2, 0, xx, MPFR_RNDZ); printf("\n"); exit(1); } mpfr_clear(xx); mpfr_clear(yy); mpfr_clear(zz); } static void check_nans (void) { mpfr_t p, x, y; mpfr_init2 (x, 123L); mpfr_init2 (y, 123L); mpfr_init2 (p, 123L); /* nan * 0 == nan */ mpfr_set_nan (x); mpfr_set_ui (y, 0L, MPFR_RNDN); test_mul (p, x, y, MPFR_RNDN); MPFR_ASSERTN (mpfr_nan_p (p)); /* 1 * nan == nan */ mpfr_set_ui (x, 1L, MPFR_RNDN); mpfr_set_nan (y); test_mul (p, x, y, MPFR_RNDN); MPFR_ASSERTN (mpfr_nan_p (p)); /* 0 * +inf == nan */ mpfr_set_ui (x, 0L, MPFR_RNDN); mpfr_set_nan (y); test_mul (p, x, y, MPFR_RNDN); MPFR_ASSERTN (mpfr_nan_p (p)); /* +1 * +inf == +inf */ mpfr_set_ui (x, 1L, MPFR_RNDN); mpfr_set_inf (y, 1); test_mul (p, x, y, MPFR_RNDN); MPFR_ASSERTN (mpfr_inf_p (p)); MPFR_ASSERTN (mpfr_sgn (p) > 0); /* -1 * +inf == -inf */ mpfr_set_si (x, -1L, MPFR_RNDN); mpfr_set_inf (y, 1); test_mul (p, x, y, MPFR_RNDN); MPFR_ASSERTN (mpfr_inf_p (p)); MPFR_ASSERTN (mpfr_sgn (p) < 0); mpfr_clear (x); mpfr_clear (y); mpfr_clear (p); } #define BUFSIZE 1552 static void get_string (char *s, FILE *fp) { int c, n = BUFSIZE; while ((c = getc (fp)) != '\n') { if (c == EOF) { printf ("Error in get_string: end of file\n"); exit (1); } *(unsigned char *)s++ = c; if (--n == 0) { printf ("Error in get_string: buffer is too small\n"); exit (1); } } *s = '\0'; } static void check_regression (void) { mpfr_t x, y, z; int i; FILE *fp; char s[BUFSIZE]; mpfr_inits2 (6177, x, y, z, (mpfr_ptr) 0); /* we read long strings from a file since ISO C90 does not support strings of length > 509 */ fp = src_fopen ("tmul.dat", "r"); if (fp == NULL) { fprintf (stderr, "Error, cannot open tmul.dat in srcdir\n"); exit (1); } get_string (s, fp); mpfr_set_str (y, s, 16, MPFR_RNDN); get_string (s, fp); mpfr_set_str (z, s, 16, MPFR_RNDN); i = mpfr_mul (x, y, z, MPFR_RNDN); get_string (s, fp); if (mpfr_cmp_str (x, s, 16, MPFR_RNDN) != 0 || i != -1) { printf ("Regression test 1 failed (i=%d, expected -1)\nx=", i); mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n'); exit (1); } fclose (fp); mpfr_set_prec (x, 606); mpfr_set_prec (y, 606); mpfr_set_prec (z, 606); mpfr_set_str (y, "-f.ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff92daefc3f8052ca9f58736564d9e93e62d324@-1", 16, MPFR_RNDN); mpfr_set_str (z, "-f.ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff92daefc3f8052ca9f58736564d9e93e62d324@-1", 16, MPFR_RNDN); i = mpfr_mul (x, y, z, MPFR_RNDU); mpfr_set_str (y, "f.ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff25b5df87f00a5953eb0e6cac9b3d27cc5a64c@-1", 16, MPFR_RNDN); if (mpfr_cmp (x, y) || i <= 0) { printf ("Regression test (2) failed! (i=%d - Expected 1)\n", i); mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n'); exit (1); } mpfr_set_prec (x, 184); mpfr_set_prec (y, 92); mpfr_set_prec (z, 1023); mpfr_set_str (y, "6.9b8c8498882770d8038c3b0@-1", 16, MPFR_RNDN); mpfr_set_str (z, "7.44e24b986e7fb296f1e936ce749fec3504cbf0d5ba769466b1c9f1578115efd5d29b4c79271191a920a99280c714d3a657ad6e3afbab77ffce9d697e9bb9110e26d676069afcea8b69f1d1541f2365042d80a97c21dcccd8ace4f1bb58b49922003e738e6f37bb82ef653cb2e87f763974e6ae50ae54e7724c38b80653e3289@255", 16, MPFR_RNDN); i = mpfr_mul (x, y, z, MPFR_RNDU); mpfr_set_prec (y, 184); mpfr_set_str (y, "3.0080038f2ac5054e3e71ccbb95f76aaab2221715025a28@255", 16, MPFR_RNDN); if (mpfr_cmp (x, y) || i <= 0) { printf ("Regression test (4) failed! (i=%d - expected 1)\n", i); printf ("Ref: 3.0080038f2ac5054e3e71ccbb95f76aaab2221715025a28@255\n" "Got: "); mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); printf ("\n"); exit (1); } mpfr_set_prec (x, 908); mpfr_set_prec (y, 908); mpfr_set_prec (z, 908); mpfr_set_str (y, "-f.fffffffffffffffffffffffffffffffffffffffffffffffffffffff" "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff" "ffffffffffffffffffffffffffffffffffffffffffffffffffffff99be91f83ec6f0ed28a3d42" "e6e9a327230345ea6@-1", 16, MPFR_RNDN); mpfr_set_str (z, "-f.fffffffffffffffffffffffffffffffffffffffffffffffffffffff" "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff" "ffffffffffffffffffffffffffffffffffffffffffffffffffffff99be91f83ec6f0ed28a3d42" "e6e9a327230345ea6@-1", 16, MPFR_RNDN); i = mpfr_mul (x, y, z, MPFR_RNDU); mpfr_set_str (y, "f.ffffffffffffffffffffffffffffffffffffffffffffffffffffffff" "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff" "fffffffffffffffffffffffffffffffffffffffffffffffffffff337d23f07d8de1da5147a85c" "dd3464e46068bd4d@-1", 16, MPFR_RNDN); if (mpfr_cmp (x, y) || i <= 0) { printf ("Regression test (5) failed! (i=%d - expected 1)\n", i); mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); printf ("\n"); exit (1); } mpfr_set_prec (x, 50); mpfr_set_prec (y, 40); mpfr_set_prec (z, 53); mpfr_set_str (y, "4.1ffffffff8", 16, MPFR_RNDN); mpfr_set_str (z, "4.2000000ffe0000@-4", 16, MPFR_RNDN); i = mpfr_mul (x, y, z, MPFR_RNDN); if (mpfr_cmp_str (x, "1.104000041d6c0@-3", 16, MPFR_RNDN) != 0 || i <= 0) { printf ("Regression test (6) failed! (i=%d - expected 1)\nx=", i); mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); printf ("\nMore prec="); mpfr_set_prec (x, 93); mpfr_mul (x, y, z, MPFR_RNDN); mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); printf ("\n"); exit (1); } mpfr_set_prec (x, 439); mpfr_set_prec (y, 393); mpfr_set_str (y, "-1.921fb54442d18469898cc51701b839a252049c1114cf98e804177d" "4c76273644a29410f31c6809bbdf2a33679a748636600", 16, MPFR_RNDN); i = mpfr_mul (x, y, y, MPFR_RNDU); if (mpfr_cmp_str (x, "2.77a79937c8bbcb495b89b36602306b1c2159a8ff834288a19a08" "84094f1cda3dc426da61174c4544a173de83c2500f8bfea2e0569e3698", 16, MPFR_RNDN) != 0 || i <= 0) { printf ("Regression test (7) failed! (i=%d - expected 1)\nx=", i); mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); printf ("\n"); exit (1); } mpfr_set_prec (x, 1023); mpfr_set_prec (y, 1023); mpfr_set_prec (z, 511); mpfr_set_ui (x, 17, MPFR_RNDN); mpfr_set_ui (y, 42, MPFR_RNDN); i = mpfr_mul (z, x, y, MPFR_RNDN); if (mpfr_cmp_ui (z, 17*42) != 0 || i != 0) { printf ("Regression test (8) failed! (i=%d - expected 0)\nz=", i); mpfr_out_str (stdout, 16, 0, z, MPFR_RNDN); printf ("\n"); exit (1); } mpfr_clears (x, y, z, (mpfr_ptr) 0); } #define TEST_FUNCTION test_mul #define TWO_ARGS #define RAND_FUNCTION(x) mpfr_random2(x, MPFR_LIMB_SIZE (x), randlimb () % 100, RANDS) #include "tgeneric.c" /* multiplies x by 53-bit approximation of Pi */ static int mpfr_mulpi (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t r) { mpfr_t z; int inex; mpfr_init2 (z, 53); mpfr_set_str_binary (z, "11.001001000011111101101010100010001000010110100011"); inex = mpfr_mul (y, x, z, r); mpfr_clear (z); return inex; } static void valgrind20110503 (void) { mpfr_t a, b, c; mpfr_init2 (a, 2); mpfr_init2 (b, 2005); mpfr_init2 (c, 2); mpfr_set_ui (b, 5, MPFR_RNDN); mpfr_nextabove (b); mpfr_set_ui (c, 1, MPFR_RNDN); mpfr_mul (a, b, c, MPFR_RNDZ); /* After the call to mpfr_mulhigh_n, valgrind complains: Conditional jump or move depends on uninitialised value(s) */ mpfr_clears (a, b, c, (mpfr_ptr) 0); } static void testall_rndf (mpfr_prec_t pmax) { mpfr_t a, b, c, d; mpfr_prec_t pa, pb, pc; for (pa = MPFR_PREC_MIN; pa <= pmax; pa++) { mpfr_init2 (a, pa); mpfr_init2 (d, pa); for (pb = MPFR_PREC_MIN; pb <= pmax; pb++) { mpfr_init2 (b, pb); mpfr_set_ui (b, 1, MPFR_RNDN); while (mpfr_cmp_ui (b, 2) < 0) { for (pc = MPFR_PREC_MIN; pc <= pmax; pc++) { mpfr_init2 (c, pc); mpfr_set_ui (c, 1, MPFR_RNDN); while (mpfr_cmp_ui (c, 2) < 0) { mpfr_mul (a, b, c, MPFR_RNDF); mpfr_mul (d, b, c, MPFR_RNDD); if (!mpfr_equal_p (a, d)) { mpfr_mul (d, b, c, MPFR_RNDU); if (!mpfr_equal_p (a, d)) { printf ("Error: mpfr_mul(a,b,c,RNDF) does not " "match RNDD/RNDU\n"); printf ("b="); mpfr_dump (b); printf ("c="); mpfr_dump (c); printf ("a="); mpfr_dump (a); exit (1); } } mpfr_nextabove (c); } mpfr_clear (c); } mpfr_nextabove (b); } mpfr_clear (b); } mpfr_clear (a); mpfr_clear (d); } } /* Check underflow flag corresponds to *after* rounding. * * More precisely, we want to test mpfr_mul on inputs b and c such that * EXP(b*c) < emin but EXP(round(b*c, p, rnd)) = emin. Thus an underflow * must not be generated. */ static void test_underflow (mpfr_prec_t pmax) { mpfr_exp_t emin; mpfr_prec_t p; mpfr_t a0, a, b, c; int inex; mpfr_init2 (a0, MPFR_PREC_MIN); emin = mpfr_get_emin (); mpfr_setmin (a0, emin); /* 0.5 * 2^emin */ /* for RNDN, we want b*c < 0.5 * 2^emin but RNDN(b*c, p) = 0.5 * 2^emin, thus b*c >= (0.5 - 1/4 * ulp_p(0.5)) * 2^emin */ for (p = MPFR_PREC_MIN; p <= pmax; p++) { mpfr_init2 (a, p + 1); mpfr_init2 (b, p + 10); mpfr_init2 (c, p + 10); do mpfr_urandomb (b, RANDS); while (MPFR_IS_ZERO (b)); inex = mpfr_set_ui_2exp (a, 1, -1, MPFR_RNDZ); /* a = 0.5 */ MPFR_ASSERTN (inex == 0); mpfr_nextbelow (a); /* 0.5 - 1/2*ulp_{p+1}(0.5) = 0.5 - 1/4*ulp_p(0.5) */ inex = mpfr_div (c, a, b, MPFR_RNDU); /* 0.5 - 1/4 * ulp_p(0.5) = a <= b*c < 0.5 */ mpfr_mul_2si (b, b, emin / 2, MPFR_RNDZ); mpfr_mul_2si (c, c, (emin - 1) / 2, MPFR_RNDZ); /* now (0.5 - 1/4 * ulp_p(0.5)) * 2^emin <= b*c < 0.5 * 2^emin, thus b*c should be rounded to 0.5 * 2^emin */ mpfr_set_prec (a, p); mpfr_clear_underflow (); mpfr_mul (a, b, c, MPFR_RNDN); if (mpfr_underflow_p () || ! mpfr_equal_p (a, a0)) { printf ("Error, b*c incorrect or underflow flag incorrectly set" " for emin=%" MPFR_EXP_FSPEC "d, rnd=%s\n", (mpfr_eexp_t) emin, mpfr_print_rnd_mode (MPFR_RNDN)); printf ("b="); mpfr_dump (b); printf ("c="); mpfr_dump (c); printf ("a="); mpfr_dump (a); mpfr_set_prec (a, mpfr_get_prec (b) + mpfr_get_prec (c)); mpfr_mul_2exp (b, b, 1, MPFR_RNDN); inex = mpfr_mul (a, b, c, MPFR_RNDN); MPFR_ASSERTN (inex == 0); printf ("Exact 2*a="); mpfr_dump (a); exit (1); } mpfr_clear (a); mpfr_clear (b); mpfr_clear (c); } /* for RNDU, we want b*c < 0.5*2^emin but RNDU(b*c, p) = 0.5*2^emin thus b*c > (0.5 - 1/2 * ulp_p(0.5)) * 2^emin */ for (p = MPFR_PREC_MIN; p <= pmax; p++) { mpfr_init2 (a, p); mpfr_init2 (b, p + 10); mpfr_init2 (c, p + 10); do mpfr_urandomb (b, RANDS); while (MPFR_IS_ZERO (b)); inex = mpfr_set_ui_2exp (a, 1, -1, MPFR_RNDZ); /* a = 0.5 */ MPFR_ASSERTN (inex == 0); mpfr_nextbelow (a); /* 0.5 - 1/2 * ulp_p(0.5) */ inex = mpfr_div (c, a, b, MPFR_RNDU); /* 0.5 - 1/2 * ulp_p(0.5) <= b*c < 0.5 */ mpfr_mul_2si (b, b, emin / 2, MPFR_RNDZ); mpfr_mul_2si (c, c, (emin - 1) / 2, MPFR_RNDZ); if (inex == 0) mpfr_nextabove (c); /* ensures b*c > (0.5 - 1/2 * ulp_p(0.5)) * 2^emin. Warning: for p=1, 0.5 - 1/2 * ulp_p(0.5) = 0.25, thus b*c > 2^(emin-2), which should also be rounded up with p=1 to 0.5 * 2^emin with an unbounded exponent range. */ mpfr_clear_underflow (); mpfr_mul (a, b, c, MPFR_RNDU); if (mpfr_underflow_p () || ! mpfr_equal_p (a, a0)) { printf ("Error, b*c incorrect or underflow flag incorrectly set" " for emin=%" MPFR_EXP_FSPEC "d, rnd=%s\n", (mpfr_eexp_t) emin, mpfr_print_rnd_mode (MPFR_RNDU)); printf ("b="); mpfr_dump (b); printf ("c="); mpfr_dump (c); printf ("a="); mpfr_dump (a); mpfr_set_prec (a, mpfr_get_prec (b) + mpfr_get_prec (c)); mpfr_mul_2exp (b, b, 1, MPFR_RNDN); inex = mpfr_mul (a, b, c, MPFR_RNDN); MPFR_ASSERTN (inex == 0); printf ("Exact 2*a="); mpfr_dump (a); exit (1); } mpfr_clear (a); mpfr_clear (b); mpfr_clear (c); } mpfr_clear (a0); } /* checks special case where no underflow should occur */ static void bug20161209 (void) { mpfr_exp_t emin; mpfr_t x, y, z; emin = mpfr_get_emin (); set_emin (-1); /* test for mpfr_mul_1 for 64-bit limb, mpfr_mul_2 for 32-bit limb */ mpfr_init2 (x, 53); mpfr_init2 (y, 53); mpfr_init2 (z, 53); mpfr_set_str_binary (x, "0.101000001E-1"); /* x = 321/2^10 */ mpfr_set_str_binary (y, "0.110011000010100101111000011011000111011000001E-1"); /* y = 28059810762433/2^46 */ /* x * y = (2^53+1)/2^56 = 0.001...000[1]000..., and should round to 0.25 */ mpfr_mul (z, x, y, MPFR_RNDN); MPFR_ASSERTN(mpfr_cmp_ui_2exp (z, 1, -2) == 0); /* test for mpfr_mul_2 for 64-bit limb */ mpfr_set_prec (x, 65); mpfr_set_prec (y, 65); mpfr_set_prec (z, 65); mpfr_set_str_binary (x, "0.101101000010010110100001E-1"); /* 11806113/2^25 */ mpfr_set_str_binary (y, "0.101101011110010101011010001111111001100001E-1"); /* y = 3124947910241/2^43 */ /* x * y = (2^65+1)/2^68 = 0.001...000[1]000..., and should round to 0.25 */ mpfr_mul (z, x, y, MPFR_RNDN); MPFR_ASSERTN(mpfr_cmp_ui_2exp (z, 1, -2) == 0); /* test for the generic code */ mpfr_set_prec (x, 54); mpfr_set_prec (y, 55); mpfr_set_prec (z, 53); mpfr_set_str_binary (x, "0.101000001E-1"); mpfr_set_str_binary (y, "0.110011000010100101111000011011000111011000001E-1"); mpfr_mul (z, x, y, MPFR_RNDN); MPFR_ASSERTN(mpfr_cmp_ui_2exp (z, 1, -2) == 0); /* another test for the generic code */ mpfr_set_prec (x, 66); mpfr_set_prec (y, 67); mpfr_set_prec (z, 65); mpfr_set_str_binary (x, "0.101101000010010110100001E-1"); mpfr_set_str_binary (y, "0.101101011110010101011010001111111001100001E-1"); mpfr_mul (z, x, y, MPFR_RNDN); MPFR_ASSERTN(mpfr_cmp_ui_2exp (z, 1, -2) == 0); mpfr_clear (x); mpfr_clear (y); mpfr_clear (z); set_emin (emin); } /* test for case in mpfr_mul_1() where: ax = __gmpfr_emin - 1 ap[0] == ~mask rnd_mode = MPFR_RNDZ. Whatever the values of rb and sb, we should round to zero (underflow). */ static void bug20161209a (void) { mpfr_exp_t emin; mpfr_t x, y, z; emin = mpfr_get_emin (); set_emin (-1); mpfr_init2 (x, 53); mpfr_init2 (y, 53); mpfr_init2 (z, 53); /* case rb = sb = 0 */ mpfr_set_str_binary (x, "0.11010010100110000110110011111E-1"); mpfr_set_str_binary (y, "0.1001101110011000110100001"); /* x = 441650591/2^30, y = 20394401/2^25 */ /* x * y = (2^53-1)/2^55 = 0.00111...111[0]000..., and should round to 0 */ mpfr_mul (z, x, y, MPFR_RNDZ); MPFR_ASSERTN(mpfr_zero_p (z)); /* case rb = 1, sb = 0 */ mpfr_set_str_binary (x, "0.111111111000000000000000000111111111E-1"); mpfr_set_str_binary (y, "0.1000000001000000001"); /* x = 68585259519/2^37, y = 262657/2^19 */ /* x * y = (2^54-1)/2^56 = 0.00111...111[1]000..., and should round to 0 */ mpfr_mul (z, x, y, MPFR_RNDZ); MPFR_ASSERTN(mpfr_zero_p (z)); /* case rb = 0, sb = 1 */ mpfr_set_str_binary (x, "0.110010011001011110001100100001000001E-1"); mpfr_set_str_binary (y, "0.10100010100010111101"); /* x = 541144371852^37, y = 665789/2^20 */ /* x * y = (2^55-3)/2^57 = 0.00111...111[0]100..., and should round to 0 */ mpfr_mul (z, x, y, MPFR_RNDZ); MPFR_ASSERTN(mpfr_zero_p (z)); /* case rb = sb = 1 */ mpfr_set_str_binary (x, "0.10100110001001001010001111110010100111E-1"); mpfr_set_str_binary (y, "0.110001010011101001"); /* x = 178394823847/2^39, y = 201961/2^18 */ /* x * y = (2^55-1)/2^57 = 0.00111...111[1]100..., and should round to 0 */ mpfr_mul (z, x, y, MPFR_RNDZ); MPFR_ASSERTN(mpfr_zero_p (z)); /* similar test for mpfr_mul_2 (we only check rb = sb = 1 here) */ mpfr_set_prec (x, 65); mpfr_set_prec (y, 65); mpfr_set_prec (z, 65); /* 2^67-1 = 193707721 * 761838257287 */ mpfr_set_str_binary (x, "0.1011100010111011111011001001E-1"); mpfr_set_str_binary (y, "0.1011000101100001000110010100010010000111"); mpfr_mul (z, x, y, MPFR_RNDZ); MPFR_ASSERTN(mpfr_zero_p (z)); mpfr_clear (x); mpfr_clear (y); mpfr_clear (z); set_emin (emin); } /* bug for RNDF */ static void bug20170602 (void) { mpfr_t x, u, y, yd, yu; mpfr_init2 (x, 493); mpfr_init2 (u, 493); mpfr_init2 (y, 503); mpfr_init2 (yd, 503); mpfr_init2 (yu, 503); mpfr_set_str_binary (x, "0.1111100000000000001111111110000000001111111111111000000000000000000011111111111111111111111000000000000000000001111111111111111111111111111111111111111000000000011111111111111111111000000000011111111111111000000000000001110000000000000000000000000000000000000000011111111111110011111111111100000000000000011111111111111111110000000011111111111111111110011111111111110000000000001111111111111111000000000000000000000000000000000000111111111111111111111111111111011111111111111111111111111111100E44"); mpfr_set_str_binary (u, "0.1110000000000000001111111111111111111111111111111111111000000000111111111111111111111111111111000000000000000000001111111000000000000000011111111111111111111111111111111111111111111111111111111000000000000000011111111111111000000011111111111111111110000000000000001111111111111111111111111111111111111110000000000001111111111111111111111111111111111111000000000000000000000000000000000001111111111111000000000000000000001111111111100000000000000011111111111111111111111111111111111111111111111E35"); mpfr_mul (y, x, u, MPFR_RNDF); mpfr_mul (yd, x, u, MPFR_RNDD); mpfr_mul (yu, x, u, MPFR_RNDU); if (mpfr_cmp (y, yd) != 0 && mpfr_cmp (y, yu) != 0) { printf ("RNDF is neither RNDD nor RNDU\n"); printf ("x"); mpfr_dump (x); printf ("u"); mpfr_dump (u); printf ("y(RNDF)="); mpfr_dump (y); printf ("y(RNDD)="); mpfr_dump (yd); printf ("y(RNDU)="); mpfr_dump (yu); exit (1); } mpfr_clear (x); mpfr_clear (u); mpfr_clear (y); mpfr_clear (yd); mpfr_clear (yu); } /* Test for 1 to 3 limbs. */ static void small_prec (void) { mpfr_exp_t emin, emax; mpfr_t x, y, z1, z2, zz; int xq, yq, zq; mpfr_rnd_t rnd; mpfr_flags_t flags1, flags2; int inex1, inex2; int i, j, r, s, ediff; emin = mpfr_get_emin (); emax = mpfr_get_emax (); /* The mpfr_mul implementation doesn't extend the exponent range, so that it is OK to reduce it here for the test to make sure that mpfr_mul_2si can be used. */ set_emin (-1000); set_emax (1000); mpfr_inits2 (3 * GMP_NUMB_BITS, x, y, z1, z2, (mpfr_ptr) 0); mpfr_init2 (zz, 6 * GMP_NUMB_BITS); for (i = 0; i < 3; i++) for (j = 0; j < 10000; j++) { xq = i * GMP_NUMB_BITS + 1 + randlimb () % GMP_NUMB_BITS; mpfr_set_prec (x, xq); yq = i * GMP_NUMB_BITS + 1 + randlimb () % GMP_NUMB_BITS; mpfr_set_prec (y, yq); zq = i * GMP_NUMB_BITS + 1 + randlimb () % (GMP_NUMB_BITS-1); mpfr_set_prec (z1, zq); mpfr_set_prec (z2, zq); s = r = randlimb () & 0x7f; do mpfr_urandomb (x, RANDS); while (mpfr_zero_p (x)); if (s & 1) mpfr_neg (x, x, MPFR_RNDN); s >>= 1; if (s & 1) { do mpfr_urandomb (y, RANDS); while (mpfr_zero_p (y)); } else { mpfr_ui_div (y, 1, x, MPFR_RNDN); mpfr_set_exp (y, 0); } s >>= 1; if (s & 1) mpfr_neg (y, y, MPFR_RNDN); s >>= 1; rnd = RND_RAND_NO_RNDF (); inex1 = mpfr_mul (zz, x, y, MPFR_RNDN); MPFR_ASSERTN (inex1 == 0); if (s == 0) { ediff = __gmpfr_emin - MPFR_EXP (x); mpfr_set_exp (x, __gmpfr_emin); } else if (s == 1) { ediff = __gmpfr_emax - MPFR_EXP (x) + 1; mpfr_set_exp (x, __gmpfr_emax); mpfr_mul_2ui (y, y, 1, MPFR_RNDN); } else ediff = 0; mpfr_clear_flags (); inex1 = mpfr_mul_2si (z1, zz, ediff, rnd); flags1 = __gmpfr_flags; mpfr_clear_flags (); inex2 = mpfr_mul (z2, x, y, rnd); flags2 = __gmpfr_flags; if (!(mpfr_equal_p (z1, z2) && SAME_SIGN (inex1, inex2) && flags1 == flags2)) { printf ("Error in small_prec on i = %d, j = %d\n", i, j); printf ("r = 0x%x, xq = %d, yq = %d, zq = %d, rnd = %s\n", r, xq, yq, zq, mpfr_print_rnd_mode (rnd)); printf ("x = "); mpfr_dump (x); printf ("y = "); mpfr_dump (y); printf ("ediff = %d\n", ediff); printf ("zz = "); mpfr_dump (zz); printf ("Expected "); mpfr_dump (z1); printf ("with inex = %d and flags =", inex1); flags_out (flags1); printf ("Got "); mpfr_dump (z2); printf ("with inex = %d and flags =", inex2); flags_out (flags2); exit (1); } } mpfr_clears (x, y, z1, z2, zz, (mpfr_ptr) 0); set_emin (emin); set_emax (emax); } /* check ax < __gmpfr_emin with rnd_mode == MPFR_RNDN, rb = 0 and sb <> 0 */ static void test_underflow2 (void) { mpfr_t x, y, z; mpfr_exp_t emin; emin = mpfr_get_emin (); mpfr_set_emin (0); mpfr_init2 (x, 24); mpfr_init2 (y, 24); mpfr_init2 (z, 24); mpfr_set_ui_2exp (x, 12913, -14, MPFR_RNDN); mpfr_set_ui_2exp (y, 5197, -13, MPFR_RNDN); mpfr_clear_underflow (); /* x*y = 0.0111111111111111111111111[01] thus underflow */ mpfr_mul (z, y, x, MPFR_RNDN); MPFR_ASSERTN(mpfr_cmp_ui_2exp (z, 1, -1) == 0); MPFR_ASSERTN(mpfr_underflow_p ()); mpfr_set_prec (x, 65); mpfr_set_prec (y, 65); mpfr_set_prec (z, 65); mpfr_set_str_binary (x, "0.10011101000110111011111100101001111"); mpfr_set_str_binary (y, "0.110100001001000111000011011110011"); mpfr_clear_underflow (); /* x*y = 0.011111111111111111111111111111111111111111111111111111111111111111[01] thus underflow */ mpfr_mul (z, y, x, MPFR_RNDN); MPFR_ASSERTN(mpfr_cmp_ui_2exp (z, 1, -1) == 0); MPFR_ASSERTN(mpfr_underflow_p ()); mpfr_clear (y); mpfr_clear (x); mpfr_clear (z); mpfr_set_emin (emin); } static void coverage (mpfr_prec_t pmax) { mpfr_t a, b, c; mpfr_prec_t p; int inex; for (p = MPFR_PREC_MIN; p <= pmax; p++) { mpfr_init2 (a, p); mpfr_init2 (b, p); mpfr_init2 (c, p); /* exercise case b*c = 2^(emin-2), which is just in the middle between 0 and the smallest positive number 0.5*2^emin */ mpfr_set_ui_2exp (b, 1, mpfr_get_emin (), MPFR_RNDN); mpfr_set_ui_2exp (c, 1, -2, MPFR_RNDN); mpfr_clear_flags (); inex = mpfr_mul (a, b, c, MPFR_RNDN); MPFR_ASSERTN(inex < 0); MPFR_ASSERTN(mpfr_zero_p (a) && mpfr_signbit (a) == 0); MPFR_ASSERTN(mpfr_underflow_p ()); if (p == 1) goto end_of_loop; /* case b*c > 2^(emin-2): b = (1-2^(-p))*2^emin, c = 0.25*(1+2^(1-p)), thus b*c = (1+2^(-p)-2^(1-2p))*2^(emin-2) should be rounded to 2^(emin-1) for RNDN */ mpfr_nextbelow (b); mpfr_nextabove (c); mpfr_clear_flags (); inex = mpfr_mul (a, b, c, MPFR_RNDN); MPFR_ASSERTN(inex > 0); MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0); MPFR_ASSERTN(mpfr_underflow_p ()); /* b = (1-2^(1-p))*2^emin, c = 0.25*(1+2^(1-p)), thus b*c = (1-2^(2-2p))*2^(emin-2) should be rounded to 0 */ mpfr_nextbelow (b); mpfr_clear_flags (); inex = mpfr_mul (a, b, c, MPFR_RNDN); MPFR_ASSERTN(inex < 0); MPFR_ASSERTN(mpfr_zero_p (a) && mpfr_signbit (a) == 0); MPFR_ASSERTN(mpfr_underflow_p ()); /* special case where b*c is in [nextbelow(0.5*2^emin),0.5*2^emin[ */ if ((p % 2) == 0) { /* the middle of the interval [nextbelow(0.5*2^emin),0.5*2^emin[ is (1-2^(-p-1))*2^(emin-1) = (1-2^(-p/2))*(1+2^(-p/2))*2^(emin-1) */ mpfr_set_si_2exp (b, -1, -p/2, MPFR_RNDN); mpfr_add_ui (b, b, 1, MPFR_RNDN); mpfr_set_si_2exp (c, 1, -p/2, MPFR_RNDN); mpfr_add_ui (c, c, 1, MPFR_RNDN); MPFR_ASSERTN(mpfr_get_emin () < 0); mpfr_mul_2si (b, b, (mpfr_get_emin () - 1) / 2, MPFR_RNDN); mpfr_mul_2si (c, c, (mpfr_get_emin () - 2) / 2, MPFR_RNDN); mpfr_clear_flags (); inex = mpfr_mul (a, b, c, MPFR_RNDN); MPFR_ASSERTN(inex > 0); MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0); MPFR_ASSERTN(mpfr_underflow_p ()); mpfr_clear_flags (); inex = mpfr_mul (a, b, c, MPFR_RNDU); MPFR_ASSERTN(inex > 0); MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0); MPFR_ASSERTN(mpfr_underflow_p ()); mpfr_clear_flags (); inex = mpfr_mul (a, b, c, MPFR_RNDD); MPFR_ASSERTN(inex < 0); MPFR_ASSERTN(mpfr_zero_p (a) && mpfr_signbit (a) == 0); MPFR_ASSERTN(mpfr_underflow_p ()); } else /* p is odd: b = (1-2^(-(p+1)/2))*2^... c = (1+2^(-(p+1)/2))*2^... */ { mpfr_set_si_2exp (b, -1, -(p+1)/2, MPFR_RNDN); mpfr_add_ui (b, b, 1, MPFR_RNDN); mpfr_set_si_2exp (c, 1, -(p+1)/2, MPFR_RNDN); mpfr_add_ui (c, c, 1, MPFR_RNDN); MPFR_ASSERTN(mpfr_get_emin () < 0); mpfr_mul_2si (b, b, (mpfr_get_emin () - 1) / 2, MPFR_RNDN); mpfr_mul_2si (c, c, (mpfr_get_emin () - 2) / 2, MPFR_RNDN); mpfr_clear_flags (); inex = mpfr_mul (a, b, c, MPFR_RNDN); MPFR_ASSERTN(inex > 0); MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0); MPFR_ASSERTN(!mpfr_underflow_p ()); mpfr_clear_flags (); inex = mpfr_mul (a, b, c, MPFR_RNDU); MPFR_ASSERTN(inex > 0); MPFR_ASSERTN(mpfr_cmp_ui_2exp (a, 1, mpfr_get_emin () - 1) == 0); MPFR_ASSERTN(!mpfr_underflow_p ()); mpfr_clear_flags (); inex = mpfr_mul (a, b, c, MPFR_RNDD); MPFR_ASSERTN(inex < 0); MPFR_ASSERTN(mpfr_zero_p (a) && mpfr_signbit (a) == 0); MPFR_ASSERTN(mpfr_underflow_p ()); } if (p <= 2) /* for p=2, 1+2^(-ceil((p+1)/2)) = 1 + 2^(-2) is not exactly representable */ goto end_of_loop; /* b = 1-2^(-ceil((p+1)/2)) c = 1+2^(-ceil((p+1)/2)) For p odd, b*c = 1-2^(p+1) should round to 1; for p even, b*c = 1-2^(p+2) should round to 1 too. */ mpfr_set_si_2exp (b, -1, -(p+2)/2, MPFR_RNDN); mpfr_add_ui (b, b, 1, MPFR_RNDN); mpfr_set_si_2exp (c, 1, -(p+2)/2, MPFR_RNDN); mpfr_add_ui (c, c, 1, MPFR_RNDN); inex = mpfr_mul (a, b, c, MPFR_RNDN); MPFR_ASSERTN(inex > 0); MPFR_ASSERTN(mpfr_cmp_ui (a, 1) == 0); /* For RNDU, b*c should round to 1 */ inex = mpfr_mul (a, b, c, MPFR_RNDU); MPFR_ASSERTN(inex > 0); MPFR_ASSERTN(mpfr_cmp_ui (a, 1) == 0); /* For RNDD, b*c should round to 1-2^(-p) */ inex = mpfr_mul (a, b, c, MPFR_RNDD); MPFR_ASSERTN(inex < 0); mpfr_nextabove (a); MPFR_ASSERTN(mpfr_cmp_ui (a, 1) == 0); /* same as above, but near emax, to exercise the case where a carry produces an overflow */ mpfr_set_si_2exp (b, -1, -(p+2)/2, MPFR_RNDN); mpfr_add_ui (b, b, 1, MPFR_RNDN); mpfr_mul_2si (b, b, mpfr_get_emax (), MPFR_RNDN); mpfr_set_si_2exp (c, 1, -(p+2)/2, MPFR_RNDN); mpfr_add_ui (c, c, 1, MPFR_RNDN); /* b*c should round to 2^emax */ mpfr_clear_flags (); inex = mpfr_mul (a, b, c, MPFR_RNDN); MPFR_ASSERTN(inex > 0); MPFR_ASSERTN(mpfr_inf_p (a) && mpfr_sgn (a) > 0); MPFR_ASSERTN(mpfr_overflow_p ()); /* idem for RNDU */ mpfr_clear_flags (); inex = mpfr_mul (a, b, c, MPFR_RNDU); MPFR_ASSERTN(inex > 0); MPFR_ASSERTN(mpfr_inf_p (a) && mpfr_sgn (a) > 0); MPFR_ASSERTN(mpfr_overflow_p ()); /* For RNDD, b*c should round to (1-2^(-p))*2^emax */ mpfr_clear_flags (); inex = mpfr_mul (a, b, c, MPFR_RNDD); MPFR_ASSERTN(inex < 0); MPFR_ASSERTN(!mpfr_inf_p (a)); MPFR_ASSERTN(!mpfr_overflow_p ()); mpfr_nextabove (a); MPFR_ASSERTN(mpfr_inf_p (a) && mpfr_sgn (a) > 0); end_of_loop: mpfr_clear (a); mpfr_clear (b); mpfr_clear (c); } } int main (int argc, char *argv[]) { tests_start_mpfr (); coverage (1024); testall_rndf (9); check_nans (); check_exact (); check_float (); check53("6.9314718055994530941514e-1", "0.0", MPFR_RNDZ, "0.0"); check53("0.0", "6.9314718055994530941514e-1", MPFR_RNDZ, "0.0"); check_sign(); check53("-4.165000000e4", "-0.00004801920768307322868063274915", MPFR_RNDN, "2.0"); check53("2.71331408349172961467e-08", "-6.72658901114033715233e-165", MPFR_RNDZ, "-1.8251348697787782844e-172"); check53("2.71331408349172961467e-08", "-6.72658901114033715233e-165", MPFR_RNDA, "-1.8251348697787786e-172"); check53("0.31869277231188065", "0.88642843322303122", MPFR_RNDZ, "2.8249833483992453642e-1"); check("8.47622108205396074254e-01", "3.24039313247872939883e-01", MPFR_RNDU, 28, 45, 2, "0.375"); check("8.47622108205396074254e-01", "3.24039313247872939883e-01", MPFR_RNDA, 28, 45, 2, "0.375"); check("2.63978122803639081440e-01", "6.8378615379333496093e-1", MPFR_RNDN, 34, 23, 31, "0.180504585267044603"); check("1.0", "0.11835170935876249132", MPFR_RNDU, 6, 41, 36, "0.1183517093595583"); check53("67108865.0", "134217729.0", MPFR_RNDN, "9.007199456067584e15"); check("1.37399642157394197284e-01", "2.28877275604219221350e-01", MPFR_RNDN, 49, 15, 32, "0.0314472340833162888"); check("4.03160720978664954828e-01", "5.854828e-1" /*"5.85483042917246621073e-01"*/, MPFR_RNDZ, 51, 22, 32, "0.2360436821472831"); check("3.90798504668055102229e-14", "9.85394674650308388664e-04", MPFR_RNDN, 46, 22, 12, "0.385027296503914762e-16"); check("4.58687081072827851358e-01", "2.20543551472118792844e-01", MPFR_RNDN, 49, 3, 2, "0.09375"); check_max(); check_min(); small_prec (); check_regression (); test_generic (MPFR_PREC_MIN, 500, 100); data_check ("data/mulpi", mpfr_mulpi, "mpfr_mulpi"); valgrind20110503 (); test_underflow (128); bug20161209 (); bug20161209a (); bug20170602 (); test_underflow2 (); tests_end_mpfr (); return 0; }