/* Test file for mpfr_fma. Copyright 2001-2021 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 https://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" /* When a * b is exact, the FMA is equivalent to the separate operations. */ static void test_exact (void) { const char *val[] = { "@NaN@", "-@Inf@", "-2", "-1", "-0", "0", "1", "2", "@Inf@" }; int sv = numberof (val); int i, j, k; int rnd; mpfr_t a, b, c, r1, r2; mpfr_inits2 (8, a, b, c, r1, r2, (mpfr_ptr) 0); for (i = 0; i < sv; i++) for (j = 0; j < sv; j++) for (k = 0; k < sv; k++) RND_LOOP (rnd) { if (mpfr_set_str (a, val[i], 10, MPFR_RNDN) || mpfr_set_str (b, val[j], 10, MPFR_RNDN) || mpfr_set_str (c, val[k], 10, MPFR_RNDN) || mpfr_mul (r1, a, b, (mpfr_rnd_t) rnd) || mpfr_add (r1, r1, c, (mpfr_rnd_t) rnd)) { if (rnd == MPFR_RNDF) continue; printf ("test_exact internal error for (%d,%d,%d,%d,%s)\n", i, j, k, rnd, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); exit (1); } if (mpfr_fma (r2, a, b, c, (mpfr_rnd_t) rnd)) { printf ("test_exact(%d,%d,%d,%d): mpfr_fma should be exact\n", i, j, k, rnd); exit (1); } if (MPFR_IS_NAN (r1)) { if (MPFR_IS_NAN (r2)) continue; printf ("test_exact(%d,%d,%d,%d): mpfr_fma should be NaN\n", i, j, k, rnd); exit (1); } if (! mpfr_equal_p (r1, r2) || MPFR_SIGN (r1) != MPFR_SIGN (r2)) { printf ("test_exact(%d,%d,%d,%d):\nexpected ", i, j, k, rnd); mpfr_out_str (stdout, 10, 0, r1, MPFR_RNDN); printf ("\n got "); mpfr_out_str (stdout, 10, 0, r2, MPFR_RNDN); printf ("\n"); exit (1); } } mpfr_clears (a, b, c, r1, r2, (mpfr_ptr) 0); } static void test_overflow1 (void) { mpfr_t x, y, z, r; int inex; mpfr_inits2 (8, x, y, z, r, (mpfr_ptr) 0); MPFR_SET_POS (x); mpfr_setmax (x, mpfr_get_emax ()); /* x = 2^emax - ulp */ mpfr_set_ui (y, 2, MPFR_RNDN); /* y = 2 */ mpfr_neg (z, x, MPFR_RNDN); /* z = -x = -(2^emax - ulp) */ mpfr_clear_flags (); /* The intermediate multiplication x * y overflows, but x * y + z = x is representable. */ inex = mpfr_fma (r, x, y, z, MPFR_RNDN); if (inex || ! mpfr_equal_p (r, x)) { printf ("Error in test_overflow1\nexpected "); mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN); printf (" with inex = 0\n got "); mpfr_out_str (stdout, 2, 0, r, MPFR_RNDN); printf (" with inex = %d\n", inex); exit (1); } if (mpfr_overflow_p ()) { printf ("Error in test_overflow1: overflow flag set\n"); exit (1); } mpfr_clears (x, y, z, r, (mpfr_ptr) 0); } static void test_overflow2 (void) { mpfr_t x, y, z, r; int i, inex, rnd, err = 0; mpfr_inits2 (8, x, y, z, r, (mpfr_ptr) 0); MPFR_SET_POS (x); mpfr_setmin (x, mpfr_get_emax ()); /* x = 0.1@emax */ mpfr_set_si (y, -2, MPFR_RNDN); /* y = -2 */ /* The intermediate multiplication x * y will overflow. */ for (i = -9; i <= 9; i++) RND_LOOP_NO_RNDF (rnd) { int inf, overflow; inf = rnd == MPFR_RNDN || rnd == MPFR_RNDD || rnd == MPFR_RNDA; overflow = inf || i <= 0; inex = mpfr_set_si_2exp (z, i, mpfr_get_emin (), MPFR_RNDN); MPFR_ASSERTN (inex == 0); mpfr_clear_flags (); /* One has: x * y = -1@emax exactly (but not representable). */ inex = mpfr_fma (r, x, y, z, (mpfr_rnd_t) rnd); if (overflow ^ (mpfr_overflow_p () != 0)) { printf ("Error in test_overflow2 (i = %d, %s): wrong overflow" " flag (should be %d)\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd), overflow); err = 1; } if (mpfr_nanflag_p ()) { printf ("Error in test_overflow2 (i = %d, %s): NaN flag should" " not be set\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); err = 1; } if (mpfr_nan_p (r)) { printf ("Error in test_overflow2 (i = %d, %s): got NaN\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); err = 1; } else if (MPFR_IS_POS (r)) { printf ("Error in test_overflow2 (i = %d, %s): wrong sign " "(+ instead of -)\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); err = 1; } else if (inf && ! mpfr_inf_p (r)) { printf ("Error in test_overflow2 (i = %d, %s): expected -Inf," " got\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); mpfr_dump (r); err = 1; } else if (!inf && (mpfr_inf_p (r) || (mpfr_nextbelow (r), ! mpfr_inf_p (r)))) { printf ("Error in test_overflow2 (i = %d, %s): expected -MAX," " got\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); mpfr_dump (r); err = 1; } if (inf ? inex >= 0 : inex <= 0) { printf ("Error in test_overflow2 (i = %d, %s): wrong inexact" " flag (got %d)\n", i, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd), inex); err = 1; } } if (err) exit (1); mpfr_clears (x, y, z, r, (mpfr_ptr) 0); } static void test_overflow3 (void) { mpfr_t x, y, z, r; int inex; mpfr_prec_t p = 8; mpfr_flags_t ex_flags = MPFR_FLAGS_OVERFLOW | MPFR_FLAGS_INEXACT, flags; int i, j, k; unsigned int neg; mpfr_inits2 (p, x, y, z, (mpfr_ptr) 0); for (i = 0; i < 2; i++) { mpfr_init2 (r, 2 * p + i); mpfr_set_ui_2exp (x, 1, mpfr_get_emax () - 1, MPFR_RNDN); mpfr_set_ui (y, 2, MPFR_RNDN); /* y = 2 */ for (j = 1; j <= 2; j++) for (k = 0; k <= 1; k++) { mpfr_set_si_2exp (z, -1, mpfr_get_emax () - mpfr_get_prec (r) - j, MPFR_RNDN); if (k) mpfr_nextabove (z); for (neg = 0; neg <= 3; neg++) { mpfr_clear_flags (); /* (The following applies for neg = 0 or 2, all the signs need to be reversed for neg = 1 or 3.) We have x*y = 2^emax and z = - 2^(emax-2p-i-j) * (1-k*2^(-p)), thus x*y+z = 2^emax - 2^(emax-2p-i-j) + k*2^(emax-3p-i-j) should overflow. Indeed it is >= the midpoint of 2^emax - 2^(emax-2p-i) and 2^emax, the midpoint being obtained for j = 1 and k = 0. */ inex = mpfr_fma (r, x, y, z, MPFR_RNDN); flags = __gmpfr_flags; if (! mpfr_inf_p (r) || flags != ex_flags || ((neg & 1) == 0 ? (inex <= 0 || MPFR_IS_NEG (r)) : (inex >= 0 || MPFR_IS_POS (r)))) { printf ("Error in test_overflow3 for " "i=%d j=%d k=%d neg=%u\n", i, j, k, neg); printf ("Expected %c@Inf@\n with inex %c 0 and flags:", (neg & 1) == 0 ? '+' : '-', (neg & 1) == 0 ? '>' : '<'); flags_out (ex_flags); printf ("Got "); mpfr_dump (r); printf (" with inex = %d and flags:", inex); flags_out (flags); exit (1); } if (neg == 0 || neg == 2) mpfr_neg (x, x, MPFR_RNDN); if (neg == 1 || neg == 3) mpfr_neg (y, y, MPFR_RNDN); mpfr_neg (z, z, MPFR_RNDN); } /* neg */ } /* k */ mpfr_clear (r); } /* i */ mpfr_clears (x, y, z, (mpfr_ptr) 0); } static void test_overflow4 (void) { mpfr_t x, y, z, r1, r2; mpfr_exp_t emax, e; mpfr_prec_t px; mpfr_flags_t flags1, flags2; int inex1, inex2; int ei, i, j; int below; unsigned int neg; emax = mpfr_get_emax (); mpfr_init2 (y, MPFR_PREC_MIN); mpfr_set_ui (y, 2, MPFR_RNDN); /* y = 2 */ mpfr_init2 (z, 8); for (px = 17; px < 256; px *= 2) { mpfr_init2 (x, px); mpfr_inits2 (px - 8, r1, r2, (mpfr_ptr) 0); for (ei = 0; ei <= 1; ei++) { e = ei ? emax : 0; mpfr_set_ui_2exp (x, 1, e - 1, MPFR_RNDN); mpfr_nextabove (x); /* x = 2^(e - 1) + 2^(e - px) */ /* x*y = 2^e + 2^(e - px + 1), which internally overflows when e = emax. */ for (i = -4; i <= 4; i++) for (j = 2; j <= 3; j++) { mpfr_set_si_2exp (z, -j, e - px + i, MPFR_RNDN); /* If |z| <= 2^(e - px + 1), then x*y + z >= 2^e and RZ(x*y + z) = 2^e with an unbounded exponent range. If |z| > 2^(e - px + 1), then RZ(x*y + z) is the predecessor of 2^e (since |z| < ulp(r)/2); this occurs when i > 0 and when i = 0 and j > 2 */ mpfr_set_ui_2exp (r1, 1, e - 1, MPFR_RNDN); below = i > 0 || (i == 0 && j > 2); if (below) mpfr_nextbelow (r1); mpfr_clear_flags (); inex1 = mpfr_mul_2ui (r1, r1, 1, MPFR_RNDZ); if (below || e < emax) { inex1 = i == 0 && j == 2 ? 0 : -1; flags1 = inex1 ? MPFR_FLAGS_INEXACT : 0; } else { MPFR_ASSERTN (inex1 < 0); flags1 = MPFR_FLAGS_INEXACT | MPFR_FLAGS_OVERFLOW; MPFR_ASSERTN (flags1 == __gmpfr_flags); } for (neg = 0; neg <= 3; neg++) { mpfr_clear_flags (); inex2 = mpfr_fma (r2, x, y, z, MPFR_RNDZ); flags2 = __gmpfr_flags; if (! (mpfr_equal_p (r1, r2) && SAME_SIGN (inex1, inex2) && flags1 == flags2)) { printf ("Error in test_overflow4 for " "px=%d ei=%d i=%d j=%d neg=%u\n", (int) px, ei, i, j, neg); printf ("Expected "); mpfr_dump (r1); printf ("with inex = %d and flags:", inex1); flags_out (flags1); printf ("Got "); mpfr_dump (r2); printf ("with inex = %d and flags:", inex2); flags_out (flags2); exit (1); } if (neg == 0 || neg == 2) mpfr_neg (x, x, MPFR_RNDN); if (neg == 1 || neg == 3) mpfr_neg (y, y, MPFR_RNDN); mpfr_neg (z, z, MPFR_RNDN); mpfr_neg (r1, r1, MPFR_RNDN); inex1 = - inex1; } } } mpfr_clears (x, r1, r2, (mpfr_ptr) 0); } mpfr_clears (y, z, (mpfr_ptr) 0); } static void test_overflow5 (void) { mpfr_t x, y, z, r1, r2; mpfr_exp_t emax; int inex1, inex2; int i, rnd; unsigned int neg, negr; emax = mpfr_get_emax (); mpfr_init2 (x, 123); mpfr_init2 (y, 45); mpfr_init2 (z, 67); mpfr_inits2 (89, r1, r2, (mpfr_ptr) 0); mpfr_set_ui_2exp (x, 1, emax - 1, MPFR_RNDN); for (i = 3; i <= 17; i++) { mpfr_set_ui (y, i, MPFR_RNDN); mpfr_set_ui_2exp (z, 1, emax - 1, MPFR_RNDN); for (neg = 0; neg < 8; neg++) { mpfr_setsign (x, x, neg & 1, MPFR_RNDN); mpfr_setsign (y, y, neg & 2, MPFR_RNDN); mpfr_setsign (z, z, neg & 4, MPFR_RNDN); /* |x*y + z| = (i +/- 1) * 2^(emax - 1) >= 2^emax (overflow) and x*y + z has the same sign as x*y. */ negr = (neg ^ (neg >> 1)) & 1; RND_LOOP (rnd) { mpfr_set_inf (r1, 1); if (MPFR_IS_LIKE_RNDZ ((mpfr_rnd_t) rnd, negr)) { mpfr_nextbelow (r1); inex1 = -1; } else inex1 = 1; if (negr) { mpfr_neg (r1, r1, MPFR_RNDN); inex1 = - inex1; } mpfr_clear_flags (); inex2 = mpfr_fma (r2, x, y, z, (mpfr_rnd_t) rnd); MPFR_ASSERTN (__gmpfr_flags == (MPFR_FLAGS_INEXACT | MPFR_FLAGS_OVERFLOW)); if (! (mpfr_equal_p (r1, r2) && SAME_SIGN (inex1, inex2))) { printf ("Error in test_overflow5 for i=%d neg=%u %s\n", i, neg, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); printf ("Expected "); mpfr_dump (r1); printf ("with inex = %d\n", inex1); printf ("Got "); mpfr_dump (r2); printf ("with inex = %d\n", inex2); exit (1); } } /* rnd */ } /* neg */ } /* i */ mpfr_clears (x, y, z, r1, r2, (mpfr_ptr) 0); } static void test_underflow1 (void) { mpfr_t x, y, z, r; int inex, signy, signz, rnd, err = 0; mpfr_inits2 (8, x, y, z, r, (mpfr_ptr) 0); MPFR_SET_POS (x); mpfr_setmin (x, mpfr_get_emin ()); /* x = 0.1@emin */ for (signy = -1; signy <= 1; signy += 2) { mpfr_set_si_2exp (y, signy, -1, MPFR_RNDN); /* |y| = 1/2 */ for (signz = -3; signz <= 3; signz += 2) { RND_LOOP (rnd) { mpfr_set_si (z, signz, MPFR_RNDN); if (ABS (signz) != 1) mpfr_setmax (z, mpfr_get_emax ()); /* |z| = 1 or 2^emax - ulp */ mpfr_clear_flags (); inex = mpfr_fma (r, x, y, z, (mpfr_rnd_t) rnd); #define STRTU1 "Error in test_underflow1 (signy = %d, signz = %d, %s)\n " if (mpfr_nanflag_p ()) { printf (STRTU1 "NaN flag is set\n", signy, signz, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); err = 1; } if (signy < 0 && MPFR_IS_LIKE_RNDD(rnd, signz)) mpfr_nextbelow (z); if (signy > 0 && MPFR_IS_LIKE_RNDU(rnd, signz)) mpfr_nextabove (z); if ((mpfr_overflow_p () != 0) ^ (mpfr_inf_p (z) != 0)) { printf (STRTU1 "wrong overflow flag\n", signy, signz, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); err = 1; } if (mpfr_underflow_p ()) { printf (STRTU1 "underflow flag is set\n", signy, signz, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); err = 1; } if (! mpfr_equal_p (r, z)) { printf (STRTU1 "got ", signy, signz, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); mpfr_dump (r); printf (" instead of "); mpfr_dump (z); err = 1; } if (inex >= 0 && (rnd == MPFR_RNDD || (rnd == MPFR_RNDZ && signz > 0) || (rnd == MPFR_RNDN && signy > 0))) { printf (STRTU1 "ternary value = %d instead of < 0\n", signy, signz, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd), inex); err = 1; } if (inex <= 0 && (rnd == MPFR_RNDU || (rnd == MPFR_RNDZ && signz < 0) || (rnd == MPFR_RNDN && signy < 0))) { printf (STRTU1 "ternary value = %d instead of > 0\n", signy, signz, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd), inex); err = 1; } } } } if (err) exit (1); mpfr_clears (x, y, z, r, (mpfr_ptr) 0); } static void test_underflow2 (void) { mpfr_t x, y, z, r1, r2; int e, b, i, prec = 32, pz, inex; unsigned int neg; mpfr_init2 (x, MPFR_PREC_MIN); mpfr_inits2 (prec, y, z, r1, r2, (mpfr_ptr) 0); mpfr_set_si_2exp (x, 1, mpfr_get_emin () - 1, MPFR_RNDN); /* x = 2^(emin-1) */ for (e = -1; e <= prec + 2; e++) { mpfr_set (z, x, MPFR_RNDN); /* z = x = 2^(emin+e) */ for (b = 0; b <= 1; b++) { for (pz = prec - 4 * (b == 0); pz <= prec + 4; pz++) { inex = mpfr_prec_round (z, pz, MPFR_RNDZ); MPFR_ASSERTN (inex == 0); for (i = 15; i <= 17; i++) { mpfr_flags_t flags1, flags2; int inex1, inex2; mpfr_set_si_2exp (y, i, -4 - prec, MPFR_RNDN); /* <--- r ---> * z = 1.000...00b with b = 0 or 1 * xy = 01111 (i = 15) * or 10000 (i = 16) * or 10001 (i = 17) * * x, y, and z will be modified to test the different sign * combinations. In the case b = 0 (i.e. |z| is a power of * 2) and x*y has a different sign from z, then y will be * divided by 2, so that i = 16 corresponds to a midpoint. */ for (neg = 0; neg < 8; neg++) { int xyneg, prev_binade; mpfr_setsign (x, x, neg & 1, MPFR_RNDN); mpfr_setsign (y, y, neg & 2, MPFR_RNDN); mpfr_setsign (z, z, neg & 4, MPFR_RNDN); xyneg = (neg ^ (neg >> 1)) & 1; /* true iff x*y < 0 */ /* If a change of binade occurs by adding x*y to z exactly, then take into account the fact that the midpoint has a different exponent. */ prev_binade = b == 0 && (xyneg ^ MPFR_IS_NEG (z)); if (prev_binade) mpfr_div_2ui (y, y, 1, MPFR_RNDN); mpfr_set (r1, z, MPFR_RNDN); flags1 = MPFR_FLAGS_INEXACT; if (e == -1 && i == 17 && b == 0 && (xyneg ^ (neg >> 2)) != 0) { /* Special underflow case. */ flags1 |= MPFR_FLAGS_UNDERFLOW; inex1 = xyneg ? 1 : -1; } else if (i == 15 || (i == 16 && b == 0)) { /* round toward z */ inex1 = xyneg ? 1 : -1; } else if (xyneg) { /* round away from z, with x*y < 0 */ mpfr_nextbelow (r1); inex1 = -1; } else { /* round away from z, with x*y > 0 */ mpfr_nextabove (r1); inex1 = 1; } mpfr_clear_flags (); inex2 = mpfr_fma (r2, x, y, z, MPFR_RNDN); flags2 = __gmpfr_flags; if (! (mpfr_equal_p (r1, r2) && SAME_SIGN (inex1, inex2) && flags1 == flags2)) { printf ("Error in test_underflow2 for " "e=%d b=%d pz=%d i=%d neg=%u\n", e, b, pz, i, neg); printf ("Expected "); mpfr_dump (r1); printf ("with inex = %d and flags:", inex1); flags_out (flags1); printf ("Got "); mpfr_dump (r2); printf ("with inex = %d and flags:", inex2); flags_out (flags2); exit (1); } /* Restore y. */ if (prev_binade) mpfr_mul_2ui (y, y, 1, MPFR_RNDN); } /* neg */ } /* i */ } /* pz */ inex = mpfr_prec_round (z, prec, MPFR_RNDZ); MPFR_ASSERTN (inex == 0); MPFR_SET_POS (z); mpfr_nextabove (z); } /* b */ mpfr_mul_2ui (x, x, 1, MPFR_RNDN); } /* e */ mpfr_clears (x, y, z, r1, r2, (mpfr_ptr) 0); } static void test_underflow3 (int n) { mpfr_t x, y, z, t1, t2; int sign, k, s, rnd, inex1, inex2; mpfr_exp_t e; mpfr_flags_t flags1, flags2; mpfr_inits2 (4, x, z, t1, t2, (mpfr_ptr) 0); mpfr_init2 (y, 6); e = mpfr_get_emin () - 1; for (sign = 1; sign >= -1; sign -= 2) for (k = 1; k <= 7; k++) for (s = -1; s <= 1; s++) { mpfr_set_si_2exp (x, sign, e, MPFR_RNDN); mpfr_set_si_2exp (y, 8*k+s, -6, MPFR_RNDN); mpfr_neg (z, x, MPFR_RNDN); /* x = sign * 2^(emin-1) y = (8 * k + s) * 2^(-6) = k / 8 + s * 2^(-6) z = -x = -sign * 2^(emin-1) FMA(x,y,z) = sign * ((k-8) * 2^(emin-4) + s * 2^(emin-7)) exactly. Note: The purpose of the s * 2^(emin-7) term is to yield double rounding when scaling for k = 4, s != 0, MPFR_RNDN. */ RND_LOOP_NO_RNDF (rnd) { mpfr_clear_flags (); inex1 = mpfr_set_si_2exp (t1, sign * (8*k+s-64), e-6, (mpfr_rnd_t) rnd); flags1 = __gmpfr_flags; mpfr_clear_flags (); inex2 = mpfr_fma (t2, x, y, z, (mpfr_rnd_t) rnd); flags2 = __gmpfr_flags; if (! (mpfr_equal_p (t1, t2) && SAME_SIGN (inex1, inex2) && flags1 == flags2)) { printf ("Error in test_underflow3, n = %d, sign = %d," " k = %d, s = %d, %s\n", n, sign, k, s, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); printf ("Expected "); mpfr_dump (t1); printf (" with inex ~ %d, flags =", inex1); flags_out (flags1); printf ("Got "); mpfr_dump (t2); printf (" with inex ~ %d, flags =", inex2); flags_out (flags2); exit (1); } } } mpfr_clears (x, y, z, t1, t2, (mpfr_ptr) 0); } /* Test s = x*y + z with PREC(z) > PREC(s) + 1, x*y underflows, where z + x*y and z + sign(x*y) * 2^(emin-1) do not give the same result. x = 2^emin y = 2^(-8) z = 2^emin * (2^PREC(s) + k - 2^(-1)) with k = 3 for MPFR_RNDN and k = 2 for the directed rounding modes. Also test the opposite versions with neg != 0. */ static void test_underflow4 (void) { mpfr_t x, y, z, s1, s2; mpfr_prec_t ps = 32; int inex, rnd; mpfr_inits2 (MPFR_PREC_MIN, x, y, (mpfr_ptr) 0); mpfr_inits2 (ps, s1, s2, (mpfr_ptr) 0); mpfr_init2 (z, ps + 2); inex = mpfr_set_si_2exp (x, 1, mpfr_get_emin (), MPFR_RNDN); MPFR_ASSERTN (inex == 0); inex = mpfr_set_si_2exp (y, 1, -8, MPFR_RNDN); MPFR_ASSERTN (inex == 0); RND_LOOP_NO_RNDF (rnd) { mpfr_flags_t flags1, flags2; int inex1, inex2; unsigned int neg; inex = mpfr_set_si_2exp (z, 1 << 1, ps, MPFR_RNDN); MPFR_ASSERTN (inex == 0); inex = mpfr_sub_ui (z, z, 1, MPFR_RNDN); MPFR_ASSERTN (inex == 0); inex = mpfr_div_2ui (z, z, 1, MPFR_RNDN); MPFR_ASSERTN (inex == 0); inex = mpfr_add_ui (z, z, rnd == MPFR_RNDN ? 3 : 2, MPFR_RNDN); MPFR_ASSERTN (inex == 0); inex = mpfr_mul (z, z, x, MPFR_RNDN); MPFR_ASSERTN (inex == 0); for (neg = 0; neg <= 3; neg++) { inex1 = mpfr_set (s1, z, (mpfr_rnd_t) rnd); flags1 = MPFR_FLAGS_INEXACT; mpfr_clear_flags (); inex2 = mpfr_fma (s2, x, y, z, (mpfr_rnd_t) rnd); flags2 = __gmpfr_flags; if (! (mpfr_equal_p (s1, s2) && SAME_SIGN (inex1, inex2) && flags1 == flags2)) { printf ("Error in test_underflow4 for neg=%u %s\n", neg, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); printf ("Expected "); mpfr_dump (s1); printf (" with inex ~ %d, flags =", inex1); flags_out (flags1); printf ("Got "); mpfr_dump (s2); printf (" with inex ~ %d, flags =", inex2); flags_out (flags2); exit (1); } if (neg == 0 || neg == 2) mpfr_neg (x, x, MPFR_RNDN); if (neg == 1 || neg == 3) mpfr_neg (y, y, MPFR_RNDN); mpfr_neg (z, z, MPFR_RNDN); } } mpfr_clears (x, y, z, s1, s2, (mpfr_ptr) 0); } /* Test s = x*y + z on: x = +/- 2^emin y = +/- 2^(-3) z = +/- 2^(emin + PREC(s)) and MPFR numbers close to this value. with PREC(z) from PREC(s) - 2 to PREC(s) + 8. */ static void test_underflow5 (void) { mpfr_t w, x, y, z, s1, s2, t; mpfr_exp_t emin; mpfr_prec_t ps = 32; int inex, i, j, rnd; unsigned int neg; mpfr_inits2 (MPFR_PREC_MIN, w, x, y, (mpfr_ptr) 0); mpfr_inits2 (ps, s1, s2, (mpfr_ptr) 0); mpfr_init2 (t, ps + 9); emin = mpfr_get_emin (); inex = mpfr_set_si_2exp (w, 1, emin, MPFR_RNDN); /* w = 2^emin */ MPFR_ASSERTN (inex == 0); inex = mpfr_set_si (x, 1, MPFR_RNDN); MPFR_ASSERTN (inex == 0); inex = mpfr_set_si_2exp (y, 1, -3, MPFR_RNDN); MPFR_ASSERTN (inex == 0); for (i = -2; i <= 8; i++) { mpfr_init2 (z, ps + i); inex = mpfr_set_si_2exp (z, 1, ps, MPFR_RNDN); MPFR_ASSERTN (inex == 0); for (j = 1; j <= 32; j++) mpfr_nextbelow (z); for (j = -32; j <= 32; j++) { for (neg = 0; neg < 8; neg++) { mpfr_setsign (x, x, neg & 1, MPFR_RNDN); mpfr_setsign (y, y, neg & 2, MPFR_RNDN); mpfr_setsign (z, z, neg & 4, MPFR_RNDN); inex = mpfr_fma (t, x, y, z, MPFR_RNDN); MPFR_ASSERTN (inex == 0); inex = mpfr_mul (x, x, w, MPFR_RNDN); MPFR_ASSERTN (inex == 0); inex = mpfr_mul (z, z, w, MPFR_RNDN); MPFR_ASSERTN (inex == 0); RND_LOOP_NO_RNDF (rnd) { mpfr_flags_t flags1, flags2; int inex1, inex2; mpfr_clear_flags (); inex1 = mpfr_mul (s1, w, t, (mpfr_rnd_t) rnd); flags1 = __gmpfr_flags; mpfr_clear_flags (); inex2 = mpfr_fma (s2, x, y, z, (mpfr_rnd_t) rnd); flags2 = __gmpfr_flags; if (! (mpfr_equal_p (s1, s2) && SAME_SIGN (inex1, inex2) && flags1 == flags2)) { printf ("Error in test_underflow5 on " "i=%d j=%d neg=%u %s\n", i, j, neg, mpfr_print_rnd_mode ((mpfr_rnd_t) rnd)); printf ("Expected "); mpfr_dump (s1); printf (" with inex ~ %d, flags =", inex1); flags_out (flags1); printf ("Got "); mpfr_dump (s2); printf (" with inex ~ %d, flags =", inex2); flags_out (flags2); exit (1); } } /* rnd */ inex = mpfr_div (x, x, w, MPFR_RNDN); MPFR_ASSERTN (inex == 0); inex = mpfr_div (z, z, w, MPFR_RNDN); MPFR_ASSERTN (inex == 0); } /* neg */ MPFR_SET_POS (z); /* restore the value before the loop on neg */ mpfr_nextabove (z); } /* j */ mpfr_clear (z); } /* i */ mpfr_clears (w, x, y, s1, s2, t, (mpfr_ptr) 0); } static void bug20101018 (void) { mpfr_t x, y, z, t, u; int i; mpfr_init2 (x, 64); mpfr_init2 (y, 64); mpfr_init2 (z, 64); mpfr_init2 (t, 64); mpfr_init2 (u, 64); mpfr_set_str (x, "0xf.fffffffffffffffp-14766", 16, MPFR_RNDN); mpfr_set_str (y, "-0xf.fffffffffffffffp+317", 16, MPFR_RNDN); mpfr_set_str (z, "0x8.3ffffffffffe3ffp-14443", 16, MPFR_RNDN); mpfr_set_str (t, "0x8.7ffffffffffc7ffp-14444", 16, MPFR_RNDN); i = mpfr_fma (u, x, y, z, MPFR_RNDN); if (! mpfr_equal_p (u, t)) { printf ("Wrong result in bug20101018 (a)\n"); printf ("Expected "); mpfr_out_str (stdout, 16, 0, t, MPFR_RNDN); printf ("\nGot "); mpfr_out_str (stdout, 16, 0, u, MPFR_RNDN); printf ("\n"); exit (1); } if (i <= 0) { printf ("Wrong ternary value in bug20101018 (a)\n"); printf ("Expected > 0\n"); printf ("Got %d\n", i); exit (1); } mpfr_set_str (x, "-0xf.fffffffffffffffp-11420", 16, MPFR_RNDN); mpfr_set_str (y, "0xf.fffffffffffffffp+9863", 16, MPFR_RNDN); mpfr_set_str (z, "0x8.fffff80ffffffffp-1551", 16, MPFR_RNDN); mpfr_set_str (t, "0x9.fffff01ffffffffp-1552", 16, MPFR_RNDN); i = mpfr_fma (u, x, y, z, MPFR_RNDN); if (! mpfr_equal_p (u, t)) { printf ("Wrong result in bug20101018 (b)\n"); printf ("Expected "); mpfr_out_str (stdout, 16, 0, t, MPFR_RNDN); printf ("\nGot "); mpfr_out_str (stdout, 16, 0, u, MPFR_RNDN); printf ("\n"); exit (1); } if (i <= 0) { printf ("Wrong ternary value in bug20101018 (b)\n"); printf ("Expected > 0\n"); printf ("Got %d\n", i); exit (1); } mpfr_set_str (x, "0xf.fffffffffffffffp-2125", 16, MPFR_RNDN); mpfr_set_str (y, "-0xf.fffffffffffffffp-6000", 16, MPFR_RNDN); mpfr_set_str (z, "0x8p-8119", 16, MPFR_RNDN); mpfr_set_str (t, "0x8.000000000000001p-8120", 16, MPFR_RNDN); i = mpfr_fma (u, x, y, z, MPFR_RNDN); if (! mpfr_equal_p (u, t)) { printf ("Wrong result in bug20101018 (c)\n"); printf ("Expected "); mpfr_out_str (stdout, 16, 0, t, MPFR_RNDN); printf ("\nGot "); mpfr_out_str (stdout, 16, 0, u, MPFR_RNDN); printf ("\n"); exit (1); } if (i <= 0) { printf ("Wrong ternary value in bug20101018 (c)\n"); printf ("Expected > 0\n"); printf ("Got %d\n", i); exit (1); } mpfr_clear (x); mpfr_clear (y); mpfr_clear (z); mpfr_clear (t); mpfr_clear (u); } /* bug found with GMP_CHECK_RANDOMIZE=1514407719 */ static void bug20171219 (void) { mpfr_t x, y, z, t, u; int i; mpfr_init2 (x, 60); mpfr_init2 (y, 60); mpfr_init2 (z, 60); mpfr_init2 (t, 68); mpfr_init2 (u, 68); mpfr_set_ui (x, 1, MPFR_RNDN); mpfr_set_ui (y, 1, MPFR_RNDN); mpfr_set_ui (z, 1, MPFR_RNDN); mpfr_set_ui (t, 2, MPFR_RNDN); i = mpfr_fma (u, x, y, z, MPFR_RNDA); if (! mpfr_equal_p (u, t)) { printf ("Wrong result in bug20171219 (a)\n"); printf ("Expected "); mpfr_out_str (stdout, 16, 0, t, MPFR_RNDN); printf ("\nGot "); mpfr_out_str (stdout, 16, 0, u, MPFR_RNDN); printf ("\n"); exit (1); } if (i != 0) { printf ("Wrong ternary value in bug20171219\n"); printf ("Expected 0\n"); printf ("Got %d\n", i); exit (1); } mpfr_clear (x); mpfr_clear (y); mpfr_clear (z); mpfr_clear (t); mpfr_clear (u); } /* coverage test for mpfr_set_1_2, case prec < GMP_NUMB_BITS, inex > 0, rb <> 0, sb = 0 */ static void coverage (void) { mpfr_t x, y, z, s; int inex; mpfr_exp_t emax; mpfr_inits2 (GMP_NUMB_BITS - 1, x, y, z, s, (mpfr_ptr) 0); /* set x to 2^(GMP_NUMB_BITS/2) + 1, y to 2^(GMP_NUMB_BITS/2) - 1 */ MPFR_ASSERTN((GMP_NUMB_BITS % 2) == 0); mpfr_set_ui_2exp (x, 1, GMP_NUMB_BITS / 2, MPFR_RNDN); mpfr_sub_ui (y, x, 1, MPFR_RNDN); mpfr_add_ui (x, x, 1, MPFR_RNDN); /* we have x*y = 2^GMP_NUMB_BITS - 1, thus has exponent GMP_NUMB_BITS */ /* set z to 2^(1-GMP_NUMB_BITS), with exponent 2-GMP_NUMB_BITS */ mpfr_set_ui_2exp (z, 1, 1 - GMP_NUMB_BITS, MPFR_RNDN); inex = mpfr_fms (s, x, y, z, MPFR_RNDN); /* s should be 2^GMP_NUMB_BITS-2 */ MPFR_ASSERTN(inex < 0); inex = mpfr_add_ui (s, s, 2, MPFR_RNDN); MPFR_ASSERTN(mpfr_cmp_ui_2exp (s, 1, GMP_NUMB_BITS) == 0); /* same example, but with overflow */ emax = mpfr_get_emax (); set_emax (GMP_NUMB_BITS + 1); mpfr_set_ui_2exp (z, 1, mpfr_get_emax () - 1, MPFR_RNDZ); mpfr_clear_flags (); inex = mpfr_fma (s, x, y, z, MPFR_RNDN); /* x*y = 2^GMP_NUMB_BITS - 1, z = 2^GMP_NUMB_BITS, thus x*y+z = 2^(GMP_NUMB_BITS+1) - 1 should round to 2^(GMP_NUMB_BITS+1), thus give an overflow */ MPFR_ASSERTN(inex > 0); MPFR_ASSERTN(mpfr_inf_p (s) && mpfr_sgn (s) > 0); MPFR_ASSERTN(mpfr_overflow_p ()); set_emax (emax); mpfr_clear (x); mpfr_clear (y); mpfr_clear (z); mpfr_clear (s); } int main (int argc, char *argv[]) { mpfr_t x, y, z, s; mpfr_exp_t emin, emax; int i; tests_start_mpfr (); coverage (); emin = mpfr_get_emin (); emax = mpfr_get_emax (); bug20171219 (); bug20101018 (); mpfr_init (x); mpfr_init (s); mpfr_init (y); mpfr_init (z); /* check special cases */ mpfr_set_prec (x, 2); mpfr_set_prec (y, 2); mpfr_set_prec (z, 2); mpfr_set_prec (s, 2); mpfr_set_str (x, "-0.75", 10, MPFR_RNDN); mpfr_set_str (y, "0.5", 10, MPFR_RNDN); mpfr_set_str (z, "0.375", 10, MPFR_RNDN); mpfr_fma (s, x, y, z, MPFR_RNDU); /* result is 0 */ if (mpfr_cmp_ui (s, 0)) { printf ("Error: -0.75 * 0.5 + 0.375 should be equal to 0 for prec=2\n"); printf ("got instead "); mpfr_dump (s); exit (1); } mpfr_set_prec (x, 27); mpfr_set_prec (y, 27); mpfr_set_prec (z, 27); mpfr_set_prec (s, 27); mpfr_set_str_binary (x, "1.11111111111111111111111111e-1"); mpfr_set (y, x, MPFR_RNDN); mpfr_set_str_binary (z, "-1.00011110100011001011001001e-1"); if (mpfr_fma (s, x, y, z, MPFR_RNDN) >= 0) { printf ("Wrong inexact flag for x=y=1-2^(-27)\n"); exit (1); } mpfr_set_nan (x); mpfr_urandomb (y, RANDS); mpfr_urandomb (z, RANDS); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_nan_p (s)) { printf ("evaluation of function in x=NAN does not return NAN\n"); exit (1); } mpfr_set_nan (y); mpfr_urandomb (x, RANDS); mpfr_urandomb (z, RANDS); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_nan_p(s)) { printf ("evaluation of function in y=NAN does not return NAN\n"); exit (1); } mpfr_set_nan (z); mpfr_urandomb (y, RANDS); mpfr_urandomb (x, RANDS); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_nan_p (s)) { printf ("evaluation of function in z=NAN does not return NAN\n"); exit (1); } mpfr_set_inf (x, 1); mpfr_set_inf (y, 1); mpfr_set_inf (z, 1); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_inf_p (s) || mpfr_sgn (s) < 0) { printf ("Error for (+inf) * (+inf) + (+inf)\n"); exit (1); } mpfr_set_inf (x, -1); mpfr_set_inf (y, -1); mpfr_set_inf (z, 1); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_inf_p (s) || mpfr_sgn (s) < 0) { printf ("Error for (-inf) * (-inf) + (+inf)\n"); exit (1); } mpfr_set_inf (x, 1); mpfr_set_inf (y, -1); mpfr_set_inf (z, -1); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_inf_p (s) || mpfr_sgn (s) > 0) { printf ("Error for (+inf) * (-inf) + (-inf)\n"); exit (1); } mpfr_set_inf (x, -1); mpfr_set_inf (y, 1); mpfr_set_inf (z, -1); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_inf_p (s) || mpfr_sgn (s) > 0) { printf ("Error for (-inf) * (+inf) + (-inf)\n"); exit (1); } mpfr_set_inf (x, 1); mpfr_set_ui (y, 0, MPFR_RNDN); mpfr_urandomb (z, RANDS); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_nan_p (s)) { printf ("evaluation of function in x=INF y=0 does not return NAN\n"); exit (1); } mpfr_set_inf (y, 1); mpfr_set_ui (x, 0, MPFR_RNDN); mpfr_urandomb (z, RANDS); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_nan_p (s)) { printf ("evaluation of function in x=0 y=INF does not return NAN\n"); exit (1); } mpfr_set_inf (x, 1); mpfr_urandomb (y, RANDS); /* always positive */ mpfr_set_inf (z, -1); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_nan_p (s)) { printf ("evaluation of function in x=INF y>0 z=-INF does not return NAN\n"); exit (1); } mpfr_set_inf (y, 1); mpfr_urandomb (x, RANDS); mpfr_set_inf (z, -1); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_nan_p (s)) { printf ("evaluation of function in x>0 y=INF z=-INF does not return NAN\n"); exit (1); } mpfr_set_inf (x, 1); do mpfr_urandomb (y, RANDS); while (MPFR_IS_ZERO(y)); mpfr_urandomb (z, RANDS); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_inf_p (s) || mpfr_sgn (s) < 0) { printf ("evaluation of function in x=INF does not return INF\n"); exit (1); } mpfr_set_inf (y, 1); do mpfr_urandomb (x, RANDS); while (MPFR_IS_ZERO(x)); mpfr_urandomb (z, RANDS); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_inf_p (s) || mpfr_sgn (s) < 0) { printf ("evaluation of function at y=INF does not return INF\n"); exit (1); } mpfr_set_inf (z, 1); mpfr_urandomb (x, RANDS); mpfr_urandomb (y, RANDS); mpfr_fma (s, x, y, z, MPFR_RNDN); if (!mpfr_inf_p (s) || mpfr_sgn (s) < 0) { printf ("evaluation of function in z=INF does not return INF\n"); exit (1); } mpfr_set_ui (x, 0, MPFR_RNDN); mpfr_urandomb (y, RANDS); mpfr_urandomb (z, RANDS); mpfr_fma (s, x, y, z, MPFR_RNDN); if (! mpfr_equal_p (s, z)) { printf ("evaluation of function in x=0 does not return z\n"); exit (1); } mpfr_set_ui (y, 0, MPFR_RNDN); mpfr_urandomb (x, RANDS); mpfr_urandomb (z, RANDS); mpfr_fma (s, x, y, z, MPFR_RNDN); if (! mpfr_equal_p (s, z)) { printf ("evaluation of function in y=0 does not return z\n"); exit (1); } { mpfr_prec_t prec; mpfr_t t, slong; mpfr_rnd_t rnd; int inexact, compare; unsigned int n; mpfr_prec_t p0 = 2, p1 = 200; unsigned int N = 200; mpfr_init (t); mpfr_init (slong); /* generic test */ for (prec = p0; prec <= p1; prec++) { mpfr_set_prec (x, prec); mpfr_set_prec (y, prec); mpfr_set_prec (z, prec); mpfr_set_prec (s, prec); mpfr_set_prec (t, prec); for (n = 0; n < N; n++) { mpfr_urandomb (x, RANDS); mpfr_urandomb (y, RANDS); mpfr_urandomb (z, RANDS); if (randlimb () % 2) mpfr_neg (x, x, MPFR_RNDN); if (randlimb () % 2) mpfr_neg (y, y, MPFR_RNDN); if (randlimb () % 2) mpfr_neg (z, z, MPFR_RNDN); rnd = RND_RAND_NO_RNDF (); mpfr_set_prec (slong, 2 * prec); if (mpfr_mul (slong, x, y, rnd)) { printf ("x*y should be exact\n"); exit (1); } compare = mpfr_add (t, slong, z, rnd); inexact = mpfr_fma (s, x, y, z, rnd); if (! mpfr_equal_p (s, t)) { printf ("results differ for\n"); printf (" x="); mpfr_dump (x); printf (" y="); mpfr_dump (y); printf (" z="); mpfr_dump (z); printf (" with prec=%u rnd_mode=%s\n", (unsigned int) prec, mpfr_print_rnd_mode (rnd)); printf ("got "); mpfr_dump (s); printf ("expected "); mpfr_dump (t); printf ("approx "); mpfr_dump (slong); exit (1); } if (! SAME_SIGN (inexact, compare)) { printf ("Wrong inexact flag for rnd=%s: expected %d, got %d\n", mpfr_print_rnd_mode (rnd), compare, inexact); printf (" x="); mpfr_dump (x); printf (" y="); mpfr_dump (y); printf (" z="); mpfr_dump (z); printf (" s="); mpfr_dump (s); exit (1); } } } mpfr_clear (t); mpfr_clear (slong); } mpfr_clear (x); mpfr_clear (y); mpfr_clear (z); mpfr_clear (s); test_exact (); for (i = 0; i <= 2; i++) { if (i == 0) { /* corresponds to the generic code + mpfr_check_range */ set_emin (-1024); set_emax (1024); } else if (i == 1) { set_emin (MPFR_EMIN_MIN); set_emax (MPFR_EMAX_MAX); } else { MPFR_ASSERTN (i == 2); if (emin == MPFR_EMIN_MIN && emax == MPFR_EMAX_MAX) break; set_emin (emin); set_emax (emax); } test_overflow1 (); test_overflow2 (); test_overflow3 (); test_overflow4 (); test_overflow5 (); test_underflow1 (); test_underflow2 (); test_underflow3 (i); test_underflow4 (); test_underflow5 (); } tests_end_mpfr (); return 0; }