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-rw-r--r--mpfr/tests/tgamma.c1069
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diff --git a/mpfr/tests/tgamma.c b/mpfr/tests/tgamma.c
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+++ b/mpfr/tests/tgamma.c
@@ -0,0 +1,1069 @@
+/* mpfr_tgamma -- test file for gamma function
+
+Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 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 <stdio.h>
+#include <stdlib.h>
+
+#include "mpfr-test.h"
+
+/* Note: there could be an incorrect test about suspicious overflow
+ (MPFR_SUSPICIOUS_OVERFLOW) for x = 2^(-emax) = 0.5 * 2^(emin+1) in
+ RNDZ or RNDD, but this case is never tested in the generic tests. */
+#define TEST_FUNCTION mpfr_gamma
+#define RAND_FUNCTION(x) mpfr_random2(x, MPFR_LIMB_SIZE (x), 1, RANDS)
+#include "tgeneric.c"
+
+static void
+special (void)
+{
+ mpfr_t x, y;
+ int inex;
+
+ mpfr_init (x);
+ mpfr_init (y);
+
+ mpfr_set_nan (x);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ if (!mpfr_nan_p (y))
+ {
+ printf ("Error for gamma(NaN)\n");
+ exit (1);
+ }
+
+ mpfr_set_inf (x, -1);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ if (!mpfr_nan_p (y))
+ {
+ printf ("Error for gamma(-Inf)\n");
+ exit (1);
+ }
+
+ mpfr_set_inf (x, 1);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
+ {
+ printf ("Error for gamma(+Inf)\n");
+ exit (1);
+ }
+
+ mpfr_set_ui (x, 0, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
+ {
+ printf ("Error for gamma(+0)\n");
+ exit (1);
+ }
+
+ mpfr_set_ui (x, 0, MPFR_RNDN);
+ mpfr_neg (x, x, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ if (!mpfr_inf_p (y) || mpfr_sgn (y) > 0)
+ {
+ printf ("Error for gamma(-0)\n");
+ exit (1);
+ }
+
+ mpfr_set_ui (x, 1, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ if (mpfr_cmp_ui (y, 1))
+ {
+ printf ("Error for gamma(1)\n");
+ exit (1);
+ }
+
+ mpfr_set_si (x, -1, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ if (!mpfr_nan_p (y))
+ {
+ printf ("Error for gamma(-1)\n");
+ exit (1);
+ }
+
+ mpfr_set_prec (x, 53);
+ mpfr_set_prec (y, 53);
+
+#define CHECK_X1 "1.0762904832837976166"
+#define CHECK_Y1 "0.96134843256452096050"
+
+ mpfr_set_str (x, CHECK_X1, 10, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ mpfr_set_str (x, CHECK_Y1, 10, MPFR_RNDN);
+ if (mpfr_cmp (y, x))
+ {
+ printf ("mpfr_lngamma("CHECK_X1") is wrong:\n"
+ "expected ");
+ mpfr_print_binary (x); putchar ('\n');
+ printf ("got ");
+ mpfr_print_binary (y); putchar ('\n');
+ exit (1);
+ }
+
+#define CHECK_X2 "9.23709516716202383435e-01"
+#define CHECK_Y2 "1.0502315560291053398"
+ mpfr_set_str (x, CHECK_X2, 10, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ mpfr_set_str (x, CHECK_Y2, 10, MPFR_RNDN);
+ if (mpfr_cmp (y, x))
+ {
+ printf ("mpfr_lngamma("CHECK_X2") is wrong:\n"
+ "expected ");
+ mpfr_print_binary (x); putchar ('\n');
+ printf ("got ");
+ mpfr_print_binary (y); putchar ('\n');
+ exit (1);
+ }
+
+ mpfr_set_prec (x, 8);
+ mpfr_set_prec (y, 175);
+ mpfr_set_ui (x, 33, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDU);
+ mpfr_set_prec (x, 175);
+ mpfr_set_str_binary (x, "0.110010101011010101101000010101010111000110011101001000101011000001100010111001101001011E118");
+ if (mpfr_cmp (x, y))
+ {
+ printf ("Error in mpfr_gamma (1)\n");
+ exit (1);
+ }
+
+ mpfr_set_prec (x, 21);
+ mpfr_set_prec (y, 8);
+ mpfr_set_ui (y, 120, MPFR_RNDN);
+ mpfr_gamma (x, y, MPFR_RNDZ);
+ mpfr_set_prec (y, 21);
+ mpfr_set_str_binary (y, "0.101111101110100110110E654");
+ if (mpfr_cmp (x, y))
+ {
+ printf ("Error in mpfr_gamma (120)\n");
+ printf ("Expected "); mpfr_print_binary (y); puts ("");
+ printf ("Got "); mpfr_print_binary (x); puts ("");
+ exit (1);
+ }
+
+ mpfr_set_prec (x, 3);
+ mpfr_set_prec (y, 206);
+ mpfr_set_str_binary (x, "0.110e10");
+ inex = mpfr_gamma (y, x, MPFR_RNDN);
+ mpfr_set_prec (x, 206);
+ mpfr_set_str_binary (x, "0.110111100001000001101010010001000111000100000100111000010011100011011111001100011110101000111101101100110001001100110100001001111110000101010000100100011100010011101110000001000010001100010000101001111E6250");
+ if (mpfr_cmp (x, y))
+ {
+ printf ("Error in mpfr_gamma (768)\n");
+ exit (1);
+ }
+ if (inex <= 0)
+ {
+ printf ("Wrong flag for mpfr_gamma (768)\n");
+ exit (1);
+ }
+
+ /* worst case to exercise retry */
+ mpfr_set_prec (x, 1000);
+ mpfr_set_prec (y, 869);
+ mpfr_const_pi (x, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+
+ mpfr_set_prec (x, 4);
+ mpfr_set_prec (y, 4);
+ mpfr_set_str_binary (x, "-0.1100E-66");
+ mpfr_gamma (y, x, MPFR_RNDN);
+ mpfr_set_str_binary (x, "-0.1011E67");
+ if (mpfr_cmp (x, y))
+ {
+ printf ("Error for gamma(-0.1100E-66)\n");
+ exit (1);
+ }
+
+ mpfr_clear (x);
+ mpfr_clear (y);
+}
+
+static void
+special_overflow (void)
+{
+ mpfr_t x, y;
+ mpfr_exp_t emin, emax;
+ int inex;
+
+ emin = mpfr_get_emin ();
+ emax = mpfr_get_emax ();
+
+ set_emin (-125);
+ set_emax (128);
+
+ mpfr_init2 (x, 24);
+ mpfr_init2 (y, 24);
+ mpfr_set_str_binary (x, "0.101100100000000000110100E7");
+ mpfr_gamma (y, x, MPFR_RNDN);
+ if (!mpfr_inf_p (y))
+ {
+ printf ("Overflow error.\n");
+ mpfr_dump (y);
+ exit (1);
+ }
+
+ /* problem mentioned by Kenneth Wilder, 18 Aug 2005 */
+ mpfr_set_prec (x, 29);
+ mpfr_set_prec (y, 29);
+ mpfr_set_str (x, "-200000000.5", 10, MPFR_RNDN); /* exact */
+ mpfr_gamma (y, x, MPFR_RNDN);
+ if (!(mpfr_zero_p (y) && MPFR_SIGN (y) < 0))
+ {
+ printf ("Error for gamma(-200000000.5)\n");
+ printf ("expected -0");
+ printf ("got ");
+ mpfr_dump (y);
+ exit (1);
+ }
+
+ mpfr_set_prec (x, 53);
+ mpfr_set_prec (y, 53);
+ mpfr_set_str (x, "-200000000.1", 10, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ if (!(mpfr_zero_p (y) && MPFR_SIGN (y) < 0))
+ {
+ printf ("Error for gamma(-200000000.1), prec=53\n");
+ printf ("expected -0");
+ printf ("got ");
+ mpfr_dump (y);
+ exit (1);
+ }
+
+ /* another problem mentioned by Kenneth Wilder, 29 Aug 2005 */
+ mpfr_set_prec (x, 333);
+ mpfr_set_prec (y, 14);
+ mpfr_set_str (x, "-2.0000000000000000000000005", 10, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ mpfr_set_prec (x, 14);
+ mpfr_set_str_binary (x, "-11010011110001E66");
+ if (mpfr_cmp (x, y))
+ {
+ printf ("Error for gamma(-2.0000000000000000000000005)\n");
+ printf ("expected "); mpfr_dump (x);
+ printf ("got "); mpfr_dump (y);
+ exit (1);
+ }
+
+ /* another tests from Kenneth Wilder, 31 Aug 2005 */
+ set_emax (200);
+ set_emin (-200);
+ mpfr_set_prec (x, 38);
+ mpfr_set_prec (y, 54);
+ mpfr_set_str_binary (x, "0.11101111011100111101001001010110101001E-166");
+ mpfr_gamma (y, x, MPFR_RNDN);
+ mpfr_set_prec (x, 54);
+ mpfr_set_str_binary (x, "0.100010001101100001110110001010111111010000100101011E167");
+ if (mpfr_cmp (x, y))
+ {
+ printf ("Error for gamma (test 1)\n");
+ printf ("expected "); mpfr_dump (x);
+ printf ("got "); mpfr_dump (y);
+ exit (1);
+ }
+
+ set_emax (1000);
+ set_emin (-2000);
+ mpfr_set_prec (x, 38);
+ mpfr_set_prec (y, 71);
+ mpfr_set_str_binary (x, "10101011011100001111111000010111110010E-1034");
+ /* 184083777010*2^(-1034) */
+ mpfr_gamma (y, x, MPFR_RNDN);
+ mpfr_set_prec (x, 71);
+ mpfr_set_str_binary (x, "10111111001000011110010001000000000000110011110000000011101011111111100E926");
+ /* 1762885132679550982140*2^926 */
+ if (mpfr_cmp (x, y))
+ {
+ printf ("Error for gamma (test 2)\n");
+ printf ("expected "); mpfr_dump (x);
+ printf ("got "); mpfr_dump (y);
+ exit (1);
+ }
+
+ mpfr_set_prec (x, 38);
+ mpfr_set_prec (y, 88);
+ mpfr_set_str_binary (x, "10111100111001010000100001100100100101E-104");
+ /* 202824096037*2^(-104) */
+ mpfr_gamma (y, x, MPFR_RNDN);
+ mpfr_set_prec (x, 88);
+ mpfr_set_str_binary (x, "1010110101111000111010111100010110101010100110111000001011000111000011101100001101110010E-21");
+ /* 209715199999500283894743922*2^(-21) */
+ if (mpfr_cmp (x, y))
+ {
+ printf ("Error for gamma (test 3)\n");
+ printf ("expected "); mpfr_dump (x);
+ printf ("got "); mpfr_dump (y);
+ exit (1);
+ }
+
+ mpfr_set_prec (x, 171);
+ mpfr_set_prec (y, 38);
+ mpfr_set_str (x, "-2993155353253689176481146537402947624254601559176535", 10,
+ MPFR_RNDN);
+ mpfr_div_2exp (x, x, 170, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ mpfr_set_prec (x, 38);
+ mpfr_set_str (x, "201948391737", 10, MPFR_RNDN);
+ mpfr_mul_2exp (x, x, 92, MPFR_RNDN);
+ if (mpfr_cmp (x, y))
+ {
+ printf ("Error for gamma (test 5)\n");
+ printf ("expected "); mpfr_dump (x);
+ printf ("got "); mpfr_dump (y);
+ exit (1);
+ }
+
+ set_emin (-500000);
+ mpfr_set_prec (x, 337);
+ mpfr_set_prec (y, 38);
+ mpfr_set_str (x, "-30000.000000000000000000000000000000000000000000001", 10,
+ MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ mpfr_set_prec (x, 38);
+ mpfr_set_str (x, "-3.623795987425E-121243", 10, MPFR_RNDN);
+ if (mpfr_cmp (x, y))
+ {
+ printf ("Error for gamma (test 7)\n");
+ printf ("expected "); mpfr_dump (x);
+ printf ("got "); mpfr_dump (y);
+ exit (1);
+ }
+
+ /* was producing infinite loop */
+ set_emin (emin);
+ mpfr_set_prec (x, 71);
+ mpfr_set_prec (y, 71);
+ mpfr_set_str (x, "-200000000.1", 10, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ if (!(mpfr_zero_p (y) && MPFR_SIGN (y) < 0))
+ {
+ printf ("Error for gamma (test 8)\n");
+ printf ("expected "); mpfr_dump (x);
+ printf ("got "); mpfr_dump (y);
+ exit (1);
+ }
+
+ set_emax (1073741823);
+ mpfr_set_prec (x, 29);
+ mpfr_set_prec (y, 29);
+ mpfr_set_str (x, "423786866", 10, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
+ {
+ printf ("Error for gamma(423786866)\n");
+ exit (1);
+ }
+
+ /* check exact result */
+ mpfr_set_prec (x, 2);
+ mpfr_set_ui (x, 3, MPFR_RNDN);
+ inex = mpfr_gamma (x, x, MPFR_RNDN);
+ if (inex != 0 || mpfr_cmp_ui (x, 2) != 0)
+ {
+ printf ("Error for gamma(3)\n");
+ exit (1);
+ }
+
+ mpfr_set_emax (1024);
+ mpfr_set_prec (x, 53);
+ mpfr_set_prec (y, 53);
+ mpfr_set_str_binary (x, "101010110100110011111010000110001000111100000110101E-43");
+ mpfr_gamma (x, x, MPFR_RNDU);
+ mpfr_set_str_binary (y, "110000011110001000111110110101011110000100001111111E971");
+ if (mpfr_cmp (x, y) != 0)
+ {
+ printf ("Error for gamma(4)\n");
+ printf ("expected "); mpfr_dump (y);
+ printf ("got "); mpfr_dump (x);
+ exit (1);
+ }
+
+ set_emin (emin);
+ set_emax (emax);
+
+ /* bug found by Kevin Rauch, 26 Oct 2007 */
+ mpfr_set_str (x, "1e19", 10, MPFR_RNDN);
+ inex = mpfr_gamma (x, x, MPFR_RNDN);
+ MPFR_ASSERTN(mpfr_inf_p (x) && inex > 0);
+
+ mpfr_clear (y);
+ mpfr_clear (x);
+}
+
+/* test gamma on some integral values (from Christopher Creutzig). */
+static void
+gamma_integer (void)
+{
+ mpz_t n;
+ mpfr_t x, y;
+ unsigned int i;
+
+ mpz_init (n);
+ mpfr_init2 (x, 149);
+ mpfr_init2 (y, 149);
+
+ for (i = 0; i < 100; i++)
+ {
+ mpz_fac_ui (n, i);
+ mpfr_set_ui (x, i+1, MPFR_RNDN);
+ mpfr_gamma (y, x, MPFR_RNDN);
+ mpfr_set_z (x, n, MPFR_RNDN);
+ if (!mpfr_equal_p (x, y))
+ {
+ printf ("Error for gamma(%u)\n", i+1);
+ printf ("expected "); mpfr_dump (x);
+ printf ("got "); mpfr_dump (y);
+ exit (1);
+ }
+ }
+ mpfr_clear (y);
+ mpfr_clear (x);
+ mpz_clear (n);
+}
+
+/* bug found by Kevin Rauch */
+static void
+test20071231 (void)
+{
+ mpfr_t x;
+ int inex;
+ mpfr_exp_t emin;
+
+ emin = mpfr_get_emin ();
+ mpfr_set_emin (-1000000);
+
+ mpfr_init2 (x, 21);
+ mpfr_set_str (x, "-1000001.5", 10, MPFR_RNDN);
+ inex = mpfr_gamma (x, x, MPFR_RNDN);
+ MPFR_ASSERTN(MPFR_IS_ZERO(x) && MPFR_IS_POS(x) && inex < 0);
+ mpfr_clear (x);
+
+ mpfr_set_emin (emin);
+
+ mpfr_init2 (x, 53);
+ mpfr_set_str (x, "-1000000001.5", 10, MPFR_RNDN);
+ inex = mpfr_gamma (x, x, MPFR_RNDN);
+ MPFR_ASSERTN(MPFR_IS_ZERO(x) && MPFR_IS_POS(x) && inex < 0);
+ mpfr_clear (x);
+}
+
+/* bug found by Stathis in mpfr_gamma, only occurs on 32-bit machines;
+ the second test is for 64-bit machines. This bug reappeared due to
+ r8159. */
+static void
+test20100709 (void)
+{
+ mpfr_t x, y, z;
+ int sign;
+ int inex;
+ mpfr_exp_t emin;
+
+ mpfr_init2 (x, 100);
+ mpfr_init2 (y, 32);
+ mpfr_init2 (z, 32);
+ mpfr_set_str (x, "-4.6308260837372266e+07", 10, MPFR_RNDN);
+ mpfr_set_ui (y, 0, MPFR_RNDN);
+ mpfr_nextabove (y);
+ mpfr_log (y, y, MPFR_RNDD);
+ mpfr_const_log2 (z, MPFR_RNDU);
+ mpfr_sub (y, y, z, MPFR_RNDD); /* log(MIN/2) = log(MIN) - log(2) */
+ mpfr_lgamma (z, &sign, x, MPFR_RNDU);
+ MPFR_ASSERTN (sign == -1);
+ MPFR_ASSERTN (mpfr_less_p (z, y)); /* thus underflow */
+ inex = mpfr_gamma (x, x, MPFR_RNDN);
+ MPFR_ASSERTN (MPFR_IS_ZERO(x) && MPFR_IS_NEG(x) && inex > 0);
+ mpfr_clear (x);
+ mpfr_clear (y);
+ mpfr_clear (z);
+
+ /* Similar test for 64-bit machines (also valid with a 32-bit exponent,
+ but will not trigger the bug). */
+ emin = mpfr_get_emin ();
+ mpfr_set_emin (MPFR_EMIN_MIN);
+ mpfr_init2 (x, 100);
+ mpfr_init2 (y, 32);
+ mpfr_init2 (z, 32);
+ mpfr_set_str (x, "-90.6308260837372266e+15", 10, MPFR_RNDN);
+ mpfr_set_ui (y, 0, MPFR_RNDN);
+ mpfr_nextabove (y);
+ mpfr_log (y, y, MPFR_RNDD);
+ mpfr_const_log2 (z, MPFR_RNDU);
+ mpfr_sub (y, y, z, MPFR_RNDD); /* log(MIN/2) = log(MIN) - log(2) */
+ mpfr_lgamma (z, &sign, x, MPFR_RNDU);
+ MPFR_ASSERTN (sign == -1);
+ MPFR_ASSERTN (mpfr_less_p (z, y)); /* thus underflow */
+ inex = mpfr_gamma (x, x, MPFR_RNDN);
+ MPFR_ASSERTN (MPFR_IS_ZERO(x) && MPFR_IS_NEG(x) && inex > 0);
+ mpfr_clear (x);
+ mpfr_clear (y);
+ mpfr_clear (z);
+ mpfr_set_emin (emin);
+}
+
+/* bug found by Giridhar Tammana */
+static void
+test20120426 (void)
+{
+ mpfr_t xa, xb;
+ int i;
+ mpfr_exp_t emin;
+
+ mpfr_init2 (xa, 53);
+ mpfr_init2 (xb, 53);
+ mpfr_set_d (xb, -168.5, MPFR_RNDN);
+ emin = mpfr_get_emin ();
+ mpfr_set_emin (-1073);
+ i = mpfr_gamma (xa, xb, MPFR_RNDN);
+ i = mpfr_subnormalize (xa, i, MPFR_RNDN); /* new ternary value */
+ mpfr_set_str (xb, "-9.5737343987585366746184749943e-304", 10, MPFR_RNDN);
+ if (!((i > 0) && (mpfr_cmp (xa, xb) == 0)))
+ {
+ printf ("Error in test20120426, i=%d\n", i);
+ printf ("expected ");
+ mpfr_print_binary (xb); putchar ('\n');
+ printf ("got ");
+ mpfr_print_binary (xa); putchar ('\n');
+ exit (1);
+ }
+ mpfr_set_emin (emin);
+ mpfr_clear (xa);
+ mpfr_clear (xb);
+}
+
+static void
+exprange (void)
+{
+ mpfr_exp_t emin, emax;
+ mpfr_t x, y, z;
+ int inex1, inex2;
+ unsigned int flags1, flags2;
+
+ emin = mpfr_get_emin ();
+ emax = mpfr_get_emax ();
+
+ mpfr_init2 (x, 16);
+ mpfr_inits2 (8, y, z, (mpfr_ptr) 0);
+
+ mpfr_set_ui_2exp (x, 5, -1, MPFR_RNDN);
+ mpfr_clear_flags ();
+ inex1 = mpfr_gamma (y, x, MPFR_RNDN);
+ flags1 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ mpfr_set_emin (0);
+ mpfr_clear_flags ();
+ inex2 = mpfr_gamma (z, x, MPFR_RNDN);
+ flags2 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ mpfr_set_emin (emin);
+ if (inex1 != inex2 || flags1 != flags2 || ! mpfr_equal_p (y, z))
+ {
+ printf ("Error in exprange (test1)\n");
+ printf ("x = ");
+ mpfr_dump (x);
+ printf ("Expected inex1 = %d, flags1 = %u, ", SIGN (inex1), flags1);
+ mpfr_dump (y);
+ printf ("Got inex2 = %d, flags2 = %u, ", SIGN (inex2), flags2);
+ mpfr_dump (z);
+ exit (1);
+ }
+
+ mpfr_set_ui_2exp (x, 32769, -60, MPFR_RNDN);
+ mpfr_clear_flags ();
+ inex1 = mpfr_gamma (y, x, MPFR_RNDD);
+ flags1 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ mpfr_set_emax (45);
+ mpfr_clear_flags ();
+ inex2 = mpfr_gamma (z, x, MPFR_RNDD);
+ flags2 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ mpfr_set_emax (emax);
+ if (inex1 != inex2 || flags1 != flags2 || ! mpfr_equal_p (y, z))
+ {
+ printf ("Error in exprange (test2)\n");
+ printf ("x = ");
+ mpfr_dump (x);
+ printf ("Expected inex1 = %d, flags1 = %u, ", SIGN (inex1), flags1);
+ mpfr_dump (y);
+ printf ("Got inex2 = %d, flags2 = %u, ", SIGN (inex2), flags2);
+ mpfr_dump (z);
+ exit (1);
+ }
+
+ mpfr_set_emax (44);
+ mpfr_clear_flags ();
+ inex1 = mpfr_check_range (y, inex1, MPFR_RNDD);
+ flags1 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ mpfr_clear_flags ();
+ inex2 = mpfr_gamma (z, x, MPFR_RNDD);
+ flags2 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ mpfr_set_emax (emax);
+ if (inex1 != inex2 || flags1 != flags2 || ! mpfr_equal_p (y, z))
+ {
+ printf ("Error in exprange (test3)\n");
+ printf ("x = ");
+ mpfr_dump (x);
+ printf ("Expected inex1 = %d, flags1 = %u, ", SIGN (inex1), flags1);
+ mpfr_dump (y);
+ printf ("Got inex2 = %d, flags2 = %u, ", SIGN (inex2), flags2);
+ mpfr_dump (z);
+ exit (1);
+ }
+
+ mpfr_set_ui_2exp (x, 1, -60, MPFR_RNDN);
+ mpfr_clear_flags ();
+ inex1 = mpfr_gamma (y, x, MPFR_RNDD);
+ flags1 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ mpfr_set_emax (60);
+ mpfr_clear_flags ();
+ inex2 = mpfr_gamma (z, x, MPFR_RNDD);
+ flags2 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ mpfr_set_emax (emax);
+ if (inex1 != inex2 || flags1 != flags2 || ! mpfr_equal_p (y, z))
+ {
+ printf ("Error in exprange (test4)\n");
+ printf ("x = ");
+ mpfr_dump (x);
+ printf ("Expected inex1 = %d, flags1 = %u, ", SIGN (inex1), flags1);
+ mpfr_dump (y);
+ printf ("Got inex2 = %d, flags2 = %u, ", SIGN (inex2), flags2);
+ mpfr_dump (z);
+ exit (1);
+ }
+
+ MPFR_ASSERTN (MPFR_EMIN_MIN == - MPFR_EMAX_MAX);
+ mpfr_set_emin (MPFR_EMIN_MIN);
+ mpfr_set_emax (MPFR_EMAX_MAX);
+ mpfr_set_ui (x, 0, MPFR_RNDN);
+ mpfr_nextabove (x); /* x = 2^(emin - 1) */
+ mpfr_set_inf (y, 1);
+ inex1 = 1;
+ flags1 = MPFR_FLAGS_INEXACT | MPFR_FLAGS_OVERFLOW;
+ mpfr_clear_flags ();
+ /* MPFR_RNDU: overflow, infinity since 1/x = 2^(emax + 1) */
+ inex2 = mpfr_gamma (z, x, MPFR_RNDU);
+ flags2 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ if (inex1 != inex2 || flags1 != flags2 || ! mpfr_equal_p (y, z))
+ {
+ printf ("Error in exprange (test5)\n");
+ printf ("x = ");
+ mpfr_dump (x);
+ printf ("Expected inex1 = %d, flags1 = %u, ", SIGN (inex1), flags1);
+ mpfr_dump (y);
+ printf ("Got inex2 = %d, flags2 = %u, ", SIGN (inex2), flags2);
+ mpfr_dump (z);
+ exit (1);
+ }
+ mpfr_clear_flags ();
+ /* MPFR_RNDN: overflow, infinity since 1/x = 2^(emax + 1) */
+ inex2 = mpfr_gamma (z, x, MPFR_RNDN);
+ flags2 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ if (inex1 != inex2 || flags1 != flags2 || ! mpfr_equal_p (y, z))
+ {
+ printf ("Error in exprange (test6)\n");
+ printf ("x = ");
+ mpfr_dump (x);
+ printf ("Expected inex1 = %d, flags1 = %u, ", SIGN (inex1), flags1);
+ mpfr_dump (y);
+ printf ("Got inex2 = %d, flags2 = %u, ", SIGN (inex2), flags2);
+ mpfr_dump (z);
+ exit (1);
+ }
+ mpfr_nextbelow (y);
+ inex1 = -1;
+ mpfr_clear_flags ();
+ /* MPFR_RNDD: overflow, maxnum since 1/x = 2^(emax + 1) */
+ inex2 = mpfr_gamma (z, x, MPFR_RNDD);
+ flags2 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ if (inex1 != inex2 || flags1 != flags2 || ! mpfr_equal_p (y, z))
+ {
+ printf ("Error in exprange (test7)\n");
+ printf ("x = ");
+ mpfr_dump (x);
+ printf ("Expected inex1 = %d, flags1 = %u, ", SIGN (inex1), flags1);
+ mpfr_dump (y);
+ printf ("Got inex2 = %d, flags2 = %u, ", SIGN (inex2), flags2);
+ mpfr_dump (z);
+ exit (1);
+ }
+ mpfr_mul_2ui (x, x, 1, MPFR_RNDN); /* x = 2^emin */
+ mpfr_set_inf (y, 1);
+ inex1 = 1;
+ flags1 = MPFR_FLAGS_INEXACT | MPFR_FLAGS_OVERFLOW;
+ mpfr_clear_flags ();
+ /* MPFR_RNDU: overflow, infinity since 1/x = 2^emax */
+ inex2 = mpfr_gamma (z, x, MPFR_RNDU);
+ flags2 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ if (inex1 != inex2 || flags1 != flags2 || ! mpfr_equal_p (y, z))
+ {
+ printf ("Error in exprange (test8)\n");
+ printf ("x = ");
+ mpfr_dump (x);
+ printf ("Expected inex1 = %d, flags1 = %u, ", SIGN (inex1), flags1);
+ mpfr_dump (y);
+ printf ("Got inex2 = %d, flags2 = %u, ", SIGN (inex2), flags2);
+ mpfr_dump (z);
+ exit (1);
+ }
+ mpfr_clear_flags ();
+ /* MPFR_RNDN: overflow, infinity since 1/x = 2^emax */
+ inex2 = mpfr_gamma (z, x, MPFR_RNDN);
+ flags2 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ if (inex1 != inex2 || flags1 != flags2 || ! mpfr_equal_p (y, z))
+ {
+ printf ("Error in exprange (test9)\n");
+ printf ("x = ");
+ mpfr_dump (x);
+ printf ("Expected inex1 = %d, flags1 = %u, ", SIGN (inex1), flags1);
+ mpfr_dump (y);
+ printf ("Got inex2 = %d, flags2 = %u, ", SIGN (inex2), flags2);
+ mpfr_dump (z);
+ exit (1);
+ }
+ mpfr_nextbelow (y);
+ inex1 = -1;
+ flags1 = MPFR_FLAGS_INEXACT;
+ mpfr_clear_flags ();
+ /* MPFR_RNDD: no overflow, maxnum since 1/x = 2^emax and euler > 0 */
+ inex2 = mpfr_gamma (z, x, MPFR_RNDD);
+ flags2 = __gmpfr_flags;
+ MPFR_ASSERTN (mpfr_inexflag_p ());
+ if (inex1 != inex2 || flags1 != flags2 || ! mpfr_equal_p (y, z))
+ {
+ printf ("Error in exprange (test10)\n");
+ printf ("x = ");
+ mpfr_dump (x);
+ printf ("Expected inex1 = %d, flags1 = %u, ", SIGN (inex1), flags1);
+ mpfr_dump (y);
+ printf ("Got inex2 = %d, flags2 = %u, ", SIGN (inex2), flags2);
+ mpfr_dump (z);
+ exit (1);
+ }
+ mpfr_set_emin (emin);
+ mpfr_set_emax (emax);
+
+ mpfr_clears (x, y, z, (mpfr_ptr) 0);
+}
+
+static int
+tiny_aux (int stop, mpfr_exp_t e)
+{
+ mpfr_t x, y, z;
+ int r, s, spm, inex, err = 0;
+ int expected_dir[2][5] = { { 1, -1, 1, -1, 1 }, { 1, 1, 1, -1, -1 } };
+ mpfr_exp_t saved_emax;
+
+ saved_emax = mpfr_get_emax ();
+
+ mpfr_init2 (x, 32);
+ mpfr_inits2 (8, y, z, (mpfr_ptr) 0);
+
+ mpfr_set_ui_2exp (x, 1, e, MPFR_RNDN);
+ spm = 1;
+ for (s = 0; s < 2; s++)
+ {
+ RND_LOOP(r)
+ {
+ mpfr_rnd_t rr = (mpfr_rnd_t) r;
+ mpfr_exp_t exponent, emax;
+
+ /* Exponent of the rounded value in unbounded exponent range. */
+ exponent = expected_dir[s][r] < 0 && s == 0 ? - e : 1 - e;
+
+ for (emax = exponent - 1; emax <= exponent; emax++)
+ {
+ unsigned int flags, expected_flags = MPFR_FLAGS_INEXACT;
+ int overflow, expected_inex = expected_dir[s][r];
+
+ if (emax > MPFR_EMAX_MAX)
+ break;
+ mpfr_set_emax (emax);
+
+ mpfr_clear_flags ();
+ inex = mpfr_gamma (y, x, rr);
+ flags = __gmpfr_flags;
+ mpfr_clear_flags ();
+ mpfr_set_si_2exp (z, spm, - e, MPFR_RNDU);
+ overflow = mpfr_overflow_p ();
+ /* z is 1/x - euler rounded toward +inf */
+
+ if (overflow && rr == MPFR_RNDN && s == 1)
+ expected_inex = -1;
+
+ if (expected_inex < 0)
+ mpfr_nextbelow (z); /* 1/x - euler rounded toward -inf */
+
+ if (exponent > emax)
+ expected_flags |= MPFR_FLAGS_OVERFLOW;
+
+ if (!(mpfr_equal_p (y, z) && flags == expected_flags
+ && SAME_SIGN (inex, expected_inex)))
+ {
+ printf ("Error in tiny for s = %d, r = %s, emax = %"
+ MPFR_EXP_FSPEC "d%s\n on ",
+ s, mpfr_print_rnd_mode (rr), emax,
+ exponent > emax ? " (overflow)" : "");
+ mpfr_dump (x);
+ printf (" expected inex = %2d, ", expected_inex);
+ mpfr_dump (z);
+ printf (" got inex = %2d, ", SIGN (inex));
+ mpfr_dump (y);
+ printf (" expected flags = %u, got %u\n",
+ expected_flags, flags);
+ if (stop)
+ exit (1);
+ err = 1;
+ }
+ }
+ }
+ mpfr_neg (x, x, MPFR_RNDN);
+ spm = - spm;
+ }
+
+ mpfr_clears (x, y, z, (mpfr_ptr) 0);
+ mpfr_set_emax (saved_emax);
+ return err;
+}
+
+static void
+tiny (int stop)
+{
+ mpfr_exp_t emin;
+ int err = 0;
+
+ emin = mpfr_get_emin ();
+
+ /* Note: in r7499, exponent -17 will select the generic code (in
+ tiny_aux, x has precision 32), while the other exponent values
+ will select special code for tiny values. */
+ err |= tiny_aux (stop, -17);
+ err |= tiny_aux (stop, -999);
+ err |= tiny_aux (stop, mpfr_get_emin ());
+
+ if (emin != MPFR_EMIN_MIN)
+ {
+ mpfr_set_emin (MPFR_EMIN_MIN);
+ err |= tiny_aux (stop, MPFR_EMIN_MIN);
+ mpfr_set_emin (emin);
+ }
+
+ if (err)
+ exit (1);
+}
+
+/* Test mpfr_gamma in precision p1 by comparing it with exp(lgamma(x))
+ computing with a working precision p2. Assume that x is not an
+ integer <= 2. */
+static void
+exp_lgamma (mpfr_t x, mpfr_prec_t p1, mpfr_prec_t p2)
+{
+ mpfr_t yd, yu, zd, zu;
+ int inexd, inexu, sign;
+ int underflow = -1, overflow = -1; /* -1: we don't know */
+ int got_underflow, got_overflow;
+
+ if (mpfr_integer_p (x) && mpfr_cmp_si (x, 2) <= 0)
+ {
+ printf ("Warning! x is an integer <= 2 in exp_lgamma: ");
+ mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
+ return;
+ }
+ mpfr_inits2 (p2, yd, yu, (mpfr_ptr) 0);
+ inexd = mpfr_lgamma (yd, &sign, x, MPFR_RNDD);
+ mpfr_set (yu, yd, MPFR_RNDN); /* exact */
+ if (inexd)
+ mpfr_nextabove (yu);
+ mpfr_clear_flags ();
+ mpfr_exp (yd, yd, MPFR_RNDD);
+ if (! mpfr_underflow_p ())
+ underflow = 0;
+ if (mpfr_overflow_p ())
+ overflow = 1;
+ mpfr_clear_flags ();
+ mpfr_exp (yu, yu, MPFR_RNDU);
+ if (mpfr_underflow_p ())
+ underflow = 1;
+ if (! mpfr_overflow_p ())
+ overflow = 0;
+ if (sign < 0)
+ {
+ mpfr_neg (yd, yd, MPFR_RNDN); /* exact */
+ mpfr_neg (yu, yu, MPFR_RNDN); /* exact */
+ mpfr_swap (yd, yu);
+ }
+ /* yd < Gamma(x) < yu (strict inequalities since x != 1 and x != 2) */
+ mpfr_inits2 (p1, zd, zu, (mpfr_ptr) 0);
+ mpfr_clear_flags ();
+ inexd = mpfr_gamma (zd, x, MPFR_RNDD); /* zd <= Gamma(x) < yu */
+ got_underflow = underflow == -1 ? -1 : !! mpfr_underflow_p ();
+ got_overflow = overflow == -1 ? -1 : !! mpfr_overflow_p ();
+ if (! mpfr_less_p (zd, yu) || inexd > 0 ||
+ got_underflow != underflow ||
+ got_overflow != overflow)
+ {
+ printf ("Error in exp_lgamma on x = ");
+ mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
+ printf ("yu = ");
+ mpfr_dump (yu);
+ printf ("zd = ");
+ mpfr_dump (zd);
+ printf ("got inexd = %d, expected <= 0\n", inexd);
+ printf ("got underflow = %d, expected %d\n", got_underflow, underflow);
+ printf ("got overflow = %d, expected %d\n", got_overflow, overflow);
+ exit (1);
+ }
+ mpfr_clear_flags ();
+ inexu = mpfr_gamma (zu, x, MPFR_RNDU); /* zu >= Gamma(x) > yd */
+ got_underflow = underflow == -1 ? -1 : !! mpfr_underflow_p ();
+ got_overflow = overflow == -1 ? -1 : !! mpfr_overflow_p ();
+ if (! mpfr_greater_p (zu, yd) || inexu < 0 ||
+ got_underflow != underflow ||
+ got_overflow != overflow)
+ {
+ printf ("Error in exp_lgamma on x = ");
+ mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
+ printf ("yd = ");
+ mpfr_dump (yd);
+ printf ("zu = ");
+ mpfr_dump (zu);
+ printf ("got inexu = %d, expected >= 0\n", inexu);
+ printf ("got underflow = %d, expected %d\n", got_underflow, underflow);
+ printf ("got overflow = %d, expected %d\n", got_overflow, overflow);
+ exit (1);
+ }
+ if (mpfr_equal_p (zd, zu))
+ {
+ if (inexd != 0 || inexu != 0)
+ {
+ printf ("Error in exp_lgamma on x = ");
+ mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
+ printf ("zd = zu, thus exact, but inexd = %d and inexu = %d\n",
+ inexd, inexu);
+ exit (1);
+ }
+ MPFR_ASSERTN (got_underflow == 0);
+ MPFR_ASSERTN (got_overflow == 0);
+ }
+ else if (inexd == 0 || inexu == 0)
+ {
+ printf ("Error in exp_lgamma on x = ");
+ mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
+ printf ("zd != zu, thus inexact, but inexd = %d and inexu = %d\n",
+ inexd, inexu);
+ exit (1);
+ }
+ mpfr_clears (yd, yu, zd, zu, (mpfr_ptr) 0);
+}
+
+static void
+exp_lgamma_tests (void)
+{
+ mpfr_t x;
+ mpfr_exp_t emin, emax;
+ int i;
+
+ emin = mpfr_get_emin ();
+ emax = mpfr_get_emax ();
+ set_emin (MPFR_EMIN_MIN);
+ set_emax (MPFR_EMAX_MAX);
+
+ mpfr_init2 (x, 96);
+ for (i = 3; i <= 8; i++)
+ {
+ mpfr_set_ui (x, i, MPFR_RNDN);
+ exp_lgamma (x, 53, 64);
+ mpfr_nextbelow (x);
+ exp_lgamma (x, 53, 64);
+ mpfr_nextabove (x);
+ mpfr_nextabove (x);
+ exp_lgamma (x, 53, 64);
+ }
+ mpfr_set_str (x, "1.7", 10, MPFR_RNDN);
+ exp_lgamma (x, 53, 64);
+ mpfr_set_str (x, "-4.6308260837372266e+07", 10, MPFR_RNDN);
+ exp_lgamma (x, 53, 64);
+ mpfr_set_str (x, "-90.6308260837372266e+15", 10, MPFR_RNDN);
+ exp_lgamma (x, 53, 64);
+ /* The following test gives a large positive result < +Inf */
+ mpfr_set_str (x, "1.2b13fc45a92dea1@14", 16, MPFR_RNDN);
+ exp_lgamma (x, 53, 64);
+ /* Idem for a large negative result > -Inf */
+ mpfr_set_str (x, "-1.2b13fc45a92de81@14", 16, MPFR_RNDN);
+ exp_lgamma (x, 53, 64);
+ /* The following two tests trigger an endless loop in r8186
+ on 64-bit machines (64-bit exponent). The second one (due
+ to undetected overflow) is a direct consequence of the
+ first one, due to the call of Gamma(2-x) if x < 1. */
+ mpfr_set_str (x, "1.2b13fc45a92dec8@14", 16, MPFR_RNDN);
+ exp_lgamma (x, 53, 64);
+ mpfr_set_str (x, "-1.2b13fc45a92dea8@14", 16, MPFR_RNDN);
+ exp_lgamma (x, 53, 64);
+ /* Similar tests (overflow threshold) for 32-bit machines. */
+ mpfr_set_str (x, "2ab68d8.657542f855111c61", 16, MPFR_RNDN);
+ exp_lgamma (x, 12, 64);
+ mpfr_set_str (x, "-2ab68d6.657542f855111c61", 16, MPFR_RNDN);
+ exp_lgamma (x, 12, 64);
+ /* The following test is an overflow on 32-bit and 64-bit machines.
+ Revision r8189 fails on 64-bit machines as the flag is unset. */
+ mpfr_set_str (x, "1.2b13fc45a92ded8@14", 16, MPFR_RNDN);
+ exp_lgamma (x, 53, 64);
+ /* On the following tests, with r8196, one gets an underflow on
+ 32-bit machines, while a normal result is expected (see FIXME
+ in gamma.c:382). */
+ mpfr_set_str (x, "-2ab68d6.657542f855111c6104", 16, MPFR_RNDN);
+ exp_lgamma (x, 12, 64); /* failure on 32-bit machines */
+ mpfr_set_str (x, "-12b13fc45a92deb.1c6c5bc964", 16, MPFR_RNDN);
+ exp_lgamma (x, 12, 64); /* failure on 64-bit machines */
+ mpfr_clear (x);
+
+ set_emin (emin);
+ set_emax (emax);
+}
+
+int
+main (int argc, char *argv[])
+{
+ tests_start_mpfr ();
+
+ special ();
+ special_overflow ();
+ exprange ();
+ tiny (argc == 1);
+ test_generic (2, 100, 2);
+ gamma_integer ();
+ test20071231 ();
+ test20100709 ();
+ test20120426 ();
+ exp_lgamma_tests ();
+
+ data_check ("data/gamma", mpfr_gamma, "mpfr_gamma");
+
+ tests_end_mpfr ();
+ return 0;
+}
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