static void tcmp2 (double x, double y, int i) { mpfr_t xx, yy; mp_prec_t j; if (i == -1) { if (x == y) i = 53; else i = (int) (__gmpfr_floor_log2 (x) - __gmpfr_floor_log2 (x - y)); } mpfr_init2(xx, 53); mpfr_init2(yy, 53); mpfr_set_d (xx, x, GMP_RNDN); mpfr_set_d (yy, y, GMP_RNDN); j = 0; if (mpfr_cmp2 (xx, yy, &j) == 0) { if (x != y) { printf ("Error in mpfr_cmp2 for\nx="); mpfr_out_str (stdout, 2, 0, xx, GMP_RNDN); printf ("\ny="); mpfr_out_str (stdout, 2, 0, yy, GMP_RNDN); printf ("\ngot sign 0 for x != y\n"); exit (1); } } else if (j != (unsigned) i) { printf ("Error in mpfr_cmp2 for\nx="); mpfr_out_str (stdout, 2, 0, xx, GMP_RNDN); printf ("\ny="); mpfr_out_str (stdout, 2, 0, yy, GMP_RNDN); printf ("\ngot %lu instead of %d\n", j, i); exit (1); } mpfr_clear(xx); mpfr_clear(yy); }
/* agm(x,y) is between x and y, so we don't need to save exponent range */ int mpfr_agm (mpfr_ptr r, mpfr_srcptr op2, mpfr_srcptr op1, mp_rnd_t rnd_mode) { int compare, inexact; mp_size_t s; mp_prec_t p, q; mp_limb_t *up, *vp, *tmpp; mpfr_t u, v, tmp; unsigned long n; /* number of iterations */ unsigned long err = 0; MPFR_ZIV_DECL (loop); MPFR_TMP_DECL(marker); MPFR_LOG_FUNC (("op2[%#R]=%R op1[%#R]=%R rnd=%d", op2,op2,op1,op1,rnd_mode), ("r[%#R]=%R inexact=%d", r, r, inexact)); /* Deal with special values */ if (MPFR_ARE_SINGULAR (op1, op2)) { /* If a or b is NaN, the result is NaN */ if (MPFR_IS_NAN(op1) || MPFR_IS_NAN(op2)) { MPFR_SET_NAN(r); MPFR_RET_NAN; } /* now one of a or b is Inf or 0 */ /* If a and b is +Inf, the result is +Inf. Otherwise if a or b is -Inf or 0, the result is NaN */ else if (MPFR_IS_INF(op1) || MPFR_IS_INF(op2)) { if (MPFR_IS_STRICTPOS(op1) && MPFR_IS_STRICTPOS(op2)) { MPFR_SET_INF(r); MPFR_SET_SAME_SIGN(r, op1); MPFR_RET(0); /* exact */ } else { MPFR_SET_NAN(r); MPFR_RET_NAN; } } else /* a and b are neither NaN nor Inf, and one is zero */ { /* If a or b is 0, the result is +0 since a sqrt is positive */ MPFR_ASSERTD (MPFR_IS_ZERO (op1) || MPFR_IS_ZERO (op2)); MPFR_SET_POS (r); MPFR_SET_ZERO (r); MPFR_RET (0); /* exact */ } } MPFR_CLEAR_FLAGS (r); /* If a or b is negative (excluding -Infinity), the result is NaN */ if (MPFR_UNLIKELY(MPFR_IS_NEG(op1) || MPFR_IS_NEG(op2))) { MPFR_SET_NAN(r); MPFR_RET_NAN; } /* Precision of the following calculus */ q = MPFR_PREC(r); p = q + MPFR_INT_CEIL_LOG2(q) + 15; MPFR_ASSERTD (p >= 7); /* see algorithms.tex */ s = (p - 1) / BITS_PER_MP_LIMB + 1; /* b (op2) and a (op1) are the 2 operands but we want b >= a */ compare = mpfr_cmp (op1, op2); if (MPFR_UNLIKELY( compare == 0 )) { mpfr_set (r, op1, rnd_mode); MPFR_RET (0); /* exact */ } else if (compare > 0) { mpfr_srcptr t = op1; op1 = op2; op2 = t; } /* Now b(=op2) >= a (=op1) */ MPFR_TMP_MARK(marker); /* Main loop */ MPFR_ZIV_INIT (loop, p); for (;;) { mp_prec_t eq; /* Init temporary vars */ MPFR_TMP_INIT (up, u, p, s); MPFR_TMP_INIT (vp, v, p, s); MPFR_TMP_INIT (tmpp, tmp, p, s); /* Calculus of un and vn */ mpfr_mul (u, op1, op2, GMP_RNDN); /* Faster since PREC(op) < PREC(u) */ mpfr_sqrt (u, u, GMP_RNDN); mpfr_add (v, op1, op2, GMP_RNDN); /* add with !=prec is still good*/ mpfr_div_2ui (v, v, 1, GMP_RNDN); n = 1; while (mpfr_cmp2 (u, v, &eq) != 0 && eq <= p - 2) { mpfr_add (tmp, u, v, GMP_RNDN); mpfr_div_2ui (tmp, tmp, 1, GMP_RNDN); /* See proof in algorithms.tex */ if (4*eq > p) { mpfr_t w; /* tmp = U(k) */ mpfr_init2 (w, (p + 1) / 2); mpfr_sub (w, v, u, GMP_RNDN); /* e = V(k-1)-U(k-1) */ mpfr_sqr (w, w, GMP_RNDN); /* e = e^2 */ mpfr_div_2ui (w, w, 4, GMP_RNDN); /* e*= (1/2)^2*1/4 */ mpfr_div (w, w, tmp, GMP_RNDN); /* 1/4*e^2/U(k) */ mpfr_sub (v, tmp, w, GMP_RNDN); err = MPFR_GET_EXP (tmp) - MPFR_GET_EXP (v); /* 0 or 1 */ mpfr_clear (w); break; } mpfr_mul (u, u, v, GMP_RNDN); mpfr_sqrt (u, u, GMP_RNDN); mpfr_swap (v, tmp); n ++; } /* the error on v is bounded by (18n+51) ulps, or twice if there was an exponent loss in the final subtraction */ err += MPFR_INT_CEIL_LOG2(18 * n + 51); /* 18n+51 should not overflow since n is about log(p) */ /* we should have n+2 <= 2^(p/4) [see algorithms.tex] */ if (MPFR_LIKELY (MPFR_INT_CEIL_LOG2(n + 2) <= p / 4 && MPFR_CAN_ROUND (v, p - err, q, rnd_mode))) break; /* Stop the loop */ /* Next iteration */ MPFR_ZIV_NEXT (loop, p); s = (p - 1) / BITS_PER_MP_LIMB + 1; } MPFR_ZIV_FREE (loop); /* Setting of the result */ inexact = mpfr_set (r, v, rnd_mode); /* Let's clean */ MPFR_TMP_FREE(marker); return inexact; /* agm(u,v) can be exact for u, v rational only for u=v. Proof (due to Nicolas Brisebarre): it suffices to consider u=1 and v<1. Then 1/AGM(1,v) = 2F1(1/2,1/2,1;1-v^2), and a theorem due to G.V. Chudnovsky states that for x a non-zero algebraic number with |x|<1, then 2F1(1/2,1/2,1;x) and 2F1(-1/2,1/2,1;x) are algebraically independent over Q. */ }
int main (void) { double x, y; mpfr_t xx, yy; int c; long i; mpfr_prec_t p; tests_start_mpfr (); mpfr_init (xx); mpfr_init (yy); mpfr_set_prec (xx, 2); mpfr_set_prec (yy, 2); mpfr_set_str_binary(xx, "-0.10E0"); mpfr_set_str_binary(yy, "-0.10E0"); if ((mpfr_cmp) (xx, yy)) { printf ("mpfr_cmp (xx, yy) returns non-zero for prec=2\n"); exit (1); } mpfr_set_prec (xx, 65); mpfr_set_prec (yy, 65); mpfr_set_str_binary(xx, "0.10011010101000110101010000000011001001001110001011101011111011101E623"); mpfr_set_str_binary(yy, "0.10011010101000110101010000000011001001001110001011101011111011100E623"); p = 0; if (mpfr_cmp2 (xx, yy, &p) <= 0 || p != 64) { printf ("Error (1) in mpfr_cmp2\n"); exit (1); } mpfr_set_str_binary(xx, "0.10100010001110110111000010001000010011111101000100011101000011100"); mpfr_set_str_binary(yy, "0.10100010001110110111000010001000010011111101000100011101000011011"); p = 0; if (mpfr_cmp2 (xx, yy, &p) <= 0 || p != 64) { printf ("Error (2) in mpfr_cmp2\n"); exit (1); } mpfr_set_prec (xx, 160); mpfr_set_prec (yy, 160); mpfr_set_str_binary (xx, "0.1E1"); mpfr_set_str_binary (yy, "0.1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111100000110001110100"); p = 0; if (mpfr_cmp2 (xx, yy, &p) <= 0 || p != 144) { printf ("Error (3) in mpfr_cmp2\n"); exit (1); } mpfr_set_prec (xx, 53); mpfr_set_prec (yy, 200); mpfr_set_ui (xx, 1, (mpfr_rnd_t) 0); mpfr_set_ui (yy, 1, (mpfr_rnd_t) 0); if (mpfr_cmp (xx, yy) != 0) { printf ("Error in mpfr_cmp: 1.0 != 1.0\n"); exit (1); } mpfr_set_prec (yy, 31); mpfr_set_str (xx, "1.0000000002", 10, (mpfr_rnd_t) 0); mpfr_set_ui (yy, 1, (mpfr_rnd_t) 0); if (!(mpfr_cmp (xx,yy)>0)) { printf ("Error in mpfr_cmp: not 1.0000000002 > 1.0\n"); exit (1); } mpfr_set_prec (yy, 53); /* bug found by Gerardo Ballabio */ mpfr_set_ui(xx, 0, MPFR_RNDN); mpfr_set_str (yy, "0.1", 10, MPFR_RNDN); if ((c = mpfr_cmp (xx, yy)) >= 0) { printf ("Error in mpfr_cmp(0.0, 0.1), gives %d\n", c); exit (1); } mpfr_set_inf (xx, 1); mpfr_set_str (yy, "-23489745.0329", 10, MPFR_RNDN); if ((c = mpfr_cmp (xx, yy)) <= 0) { printf ("Error in mpfr_cmp(Infp, 23489745.0329), gives %d\n", c); exit (1); } mpfr_set_inf (xx, 1); mpfr_set_inf (yy, -1); if ((c = mpfr_cmp (xx, yy)) <= 0) { printf ("Error in mpfr_cmp(Infp, Infm), gives %d\n", c); exit (1); } mpfr_set_inf (xx, -1); mpfr_set_inf (yy, 1); if ((c = mpfr_cmp (xx, yy)) >= 0) { printf ("Error in mpfr_cmp(Infm, Infp), gives %d\n", c); exit (1); } mpfr_set_inf (xx, 1); mpfr_set_inf (yy, 1); if ((c = mpfr_cmp (xx, yy)) != 0) { printf ("Error in mpfr_cmp(Infp, Infp), gives %d\n", c); exit (1); } mpfr_set_inf (xx, -1); mpfr_set_inf (yy, -1); if ((c = mpfr_cmp (xx, yy)) != 0) { printf ("Error in mpfr_cmp(Infm, Infm), gives %d\n", c); exit (1); } mpfr_set_inf (xx, -1); mpfr_set_str (yy, "2346.09234", 10, MPFR_RNDN); if ((c = mpfr_cmp (xx, yy)) >= 0) { printf ("Error in mpfr_cmp(Infm, 2346.09234), gives %d\n", c); exit (1); } mpfr_set_ui (xx, 0, MPFR_RNDN); mpfr_set_ui (yy, 1, MPFR_RNDN); if ((c = mpfr_cmp3 (xx, yy, 1)) >= 0) { printf ("Error: mpfr_cmp3 (0, 1, 1) gives %d instead of" " a negative value\n", c); exit (1); } if ((c = mpfr_cmp3 (xx, yy, -1)) <= 0) { printf ("Error: mpfr_cmp3 (0, 1, -1) gives %d instead of" " a positive value\n", c); exit (1); } for (i=0; i<500000; ) { x = DBL_RAND (); y = DBL_RAND (); if (!Isnan(x) && !Isnan(y)) { i++; mpfr_set_d (xx, x, MPFR_RNDN); mpfr_set_d (yy, y, MPFR_RNDN); c = mpfr_cmp (xx,yy); if ((c>0 && x<=y) || (c==0 && x!=y) || (c<0 && x>=y)) { printf ("Error in mpfr_cmp with x=%1.20e, y=%1.20e" " mpfr_cmp(x,y)=%d\n", x, y, c); exit (1); } } } /* Check for NAN */ mpfr_set_nan (xx); mpfr_clear_erangeflag (); c = (mpfr_cmp) (xx, yy); if (c != 0 || !mpfr_erangeflag_p () ) { printf ("NAN error (1)\n"); exit (1); } mpfr_clear_erangeflag (); c = (mpfr_cmp) (yy, xx); if (c != 0 || !mpfr_erangeflag_p () ) { printf ("NAN error (2)\n"); exit (1); } mpfr_clear_erangeflag (); c = (mpfr_cmp) (xx, xx); if (c != 0 || !mpfr_erangeflag_p () ) { printf ("NAN error (3)\n"); exit (1); } mpfr_clear (xx); mpfr_clear (yy); tests_end_mpfr (); return 0; }
/* check that for x = 1.u 1 v 0^k low(x) y = 1.u 0 v 1^k low(y) mpfr_cmp2 (x, y) returns 1 + |u| + |v| + k for low(x) >= low(y), and 1 + |u| + |v| + k + 1 otherwise */ static void worst_cases (void) { mpfr_t x, y; unsigned int i, j, k, b, expected; mp_prec_t l; mpfr_init2 (x, 200); mpfr_init2 (y, 200); mpfr_set_ui (y, 1, GMP_RNDN); for (i=1; i<MPFR_PREC(x); i++) { mpfr_set_ui (x, 1, GMP_RNDN); mpfr_div_2exp (y, y, 1, GMP_RNDN); /* y = 1/2^i */ l = 0; if (mpfr_cmp2 (x, y, &l) <= 0 || l != 1) { printf ("Error in mpfr_cmp2:\nx="); mpfr_out_str (stdout, 2, 0, x, GMP_RNDN); printf ("\ny="); mpfr_out_str (stdout, 2, 0, y, GMP_RNDN); printf ("\ngot %lu instead of %u\n", l, 1); exit (1); } mpfr_add (x, x, y, GMP_RNDN); /* x = 1 + 1/2^i */ l = 0; if (mpfr_cmp2 (x, y, &l) <= 0 || l != 0) { printf ("Error in mpfr_cmp2:\nx="); mpfr_out_str (stdout, 2, 0, x, GMP_RNDN); printf ("\ny="); mpfr_out_str (stdout, 2, 0, y, GMP_RNDN); printf ("\ngot %lu instead of %u\n", l, 0); exit (1); } } for (i=0; i<64; i++) /* |u| = i */ { mpfr_random (x); mpfr_set (y, x, GMP_RNDN); set_bit (x, i + 1, 1); set_bit (y, i + 1, 0); for (j=0; j<64; j++) /* |v| = j */ { b = randlimb () % 2; set_bit (x, i + j + 2, b); set_bit (y, i + j + 2, b); for (k=0; k<64; k++) { if (k) set_bit (x, i + j + k + 1, 0); if (k) set_bit (y, i + j + k + 1, 1); set_bit (x, i + j + k + 2, 1); set_bit (y, i + j + k + 2, 0); l = 0; mpfr_cmp2 (x, y, &l); expected = i + j + k + 1; if (l != expected) { printf ("Error in mpfr_cmp2:\nx="); mpfr_out_str (stdout, 2, 0, x, GMP_RNDN); printf ("\ny="); mpfr_out_str (stdout, 2, 0, y, GMP_RNDN); printf ("\ngot %lu instead of %u\n", l, expected); exit (1); } set_bit (x, i + j + k + 2, 0); set_bit (x, i + j + k + 3, 0); set_bit (y, i + j + k + 3, 1); l = 0; mpfr_cmp2 (x, y, &l); expected = i + j + k + 2; if (l != expected) { printf ("Error in mpfr_cmp2:\nx="); mpfr_out_str (stdout, 2, 0, x, GMP_RNDN); printf ("\ny="); mpfr_out_str (stdout, 2, 0, y, GMP_RNDN); printf ("\ngot %lu instead of %u\n", l, expected); exit (1); } } } } mpfr_clear (x); mpfr_clear (y); }
static void special (void) { mpfr_t x, y; mp_prec_t j; mpfr_init (x); mpfr_init (y); /* bug found by Nathalie Revol, 21 March 2001 */ mpfr_set_prec (x, 65); mpfr_set_prec (y, 65); mpfr_set_str_binary (x, "0.10000000000000000000000000000000000001110010010110100110011110000E1"); mpfr_set_str_binary (y, "0.11100100101101001100111011111111110001101001000011101001001010010E-35"); j = 0; if (mpfr_cmp2 (x, y, &j) <= 0 || j != 1) { printf ("Error in mpfr_cmp2:\n"); printf ("x="); mpfr_print_binary (x); puts (""); printf ("y="); mpfr_print_binary (y); puts (""); printf ("got %lu, expected 1\n", j); exit (1); } mpfr_set_prec(x, 127); mpfr_set_prec(y, 127); mpfr_set_str_binary(x, "0.1011010000110111111000000101011110110001000101101011011110010010011110010000101101000010011001100110010000000010110000101000101E6"); mpfr_set_str_binary(y, "0.1011010000110111111000000101011011111100011101000011001111000010100010100110110100110010011001100110010000110010010110000010110E6"); j = 0; if (mpfr_cmp2(x, y, &j) <= 0 || j != 32) { printf ("Error in mpfr_cmp2:\n"); printf ("x="); mpfr_print_binary(x); puts (""); printf ("y="); mpfr_print_binary(y); puts (""); printf ("got %lu, expected 32\n", j); exit (1); } mpfr_set_prec (x, 128); mpfr_set_prec (y, 239); mpfr_set_str_binary (x, "0.10001000110110000111011000101011111100110010010011001101000011111010010110001000000010100110100111111011011010101100100000000000E167"); mpfr_set_str_binary (y, "0.10001000110110000111011000101011111100110010010011001101000011111010010110001000000010100110100111111011011010101100011111111111111111111111111111111111111111111111011111100101011100011001101000100111000010000000000101100110000111111000101E167"); j = 0; if (mpfr_cmp2(x, y, &j) <= 0 || j != 164) { printf ("Error in mpfr_cmp2:\n"); printf ("x="); mpfr_print_binary(x); puts (""); printf ("y="); mpfr_print_binary(y); puts (""); printf ("got %lu, expected 164\n", j); exit (1); } /* bug found by Nathalie Revol, 29 March 2001 */ mpfr_set_prec (x, 130); mpfr_set_prec (y, 130); mpfr_set_str_binary (x, "0.1100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E2"); mpfr_set_str_binary (y, "0.1011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111100E2"); j = 0; if (mpfr_cmp2(x, y, &j) <= 0 || j != 127) { printf ("Error in mpfr_cmp2:\n"); printf ("x="); mpfr_print_binary(x); puts (""); printf ("y="); mpfr_print_binary(y); puts (""); printf ("got %lu, expected 127\n", j); exit (1); } /* bug found by Nathalie Revol, 2 Apr 2001 */ mpfr_set_prec (x, 65); mpfr_set_prec (y, 65); mpfr_set_ui (x, 5, GMP_RNDN); mpfr_set_str_binary (y, "0.10011111111111111111111111111111111111111111111111111111111111101E3"); j = 0; if (mpfr_cmp2(x, y, &j) <= 0 || j != 63) { printf ("Error in mpfr_cmp2:\n"); printf ("x="); mpfr_print_binary(x); puts (""); printf ("y="); mpfr_print_binary(y); puts (""); printf ("got %lu, expected 63\n", j); exit (1); } /* bug found by Nathalie Revol, 2 Apr 2001 */ mpfr_set_prec (x, 65); mpfr_set_prec (y, 65); mpfr_set_str_binary (x, "0.10011011111000101001110000000000000000000000000000000000000000000E-69"); mpfr_set_str_binary (y, "0.10011011111000101001101111111111111111111111111111111111111111101E-69"); j = 0; if (mpfr_cmp2(x, y, &j) <= 0 || j != 63) { printf ("Error in mpfr_cmp2:\n"); printf ("x="); mpfr_print_binary(x); puts (""); printf ("y="); mpfr_print_binary(y); puts (""); printf ("got %lu, expected 63\n", j); exit (1); } mpfr_set_prec (x, 65); mpfr_set_prec (y, 32); mpfr_set_str_binary (x, "1.1110111011110001110111011111111111101000011001011100101100101101"); mpfr_set_str_binary (y, "0.11101110111100011101110111111111"); if (mpfr_cmp2 (x, y, &j) <= 0 || j != 0) { printf ("Error in mpfr_cmp2 (1)\n"); exit (1); } mpfr_clear (x); mpfr_clear (y); }