void
test_gc_get_rational (void* data)
{
mpq_t* num = GC_NEW_RATIONAL(runtime);
mpq_t* num2 = GC_NEW_RATIONAL(runtime);
mpq_set_ui(*num, 2, 3);
mpq_set_ui(*num2, 2, 3);
mpq_add(*num, *num, *num2);
tt_assert(mpq_cmp_ui(*num, 4, 3) == 0);
end:;
}
APLRAT PrimFnMonQuoteDotRisR
(APLRAT aplRatRht,
LPPRIMSPEC lpPrimSpec)
{
APLRAT mpqRes = {0};
UINT uRht;
// Check for indeterminates: !N for integer N < 0
if (mpq_integer_p (&aplRatRht)
&& mpq_cmp_ui (&aplRatRht, 0, 1) < 0)
return *mpq_QuadICValue (&aplRatRht, // No left arg
ICNDX_QDOTn,
&aplRatRht,
&mpqRes,
FALSE);
// Check for PosInfinity
if (IsMpqPosInfinity (&aplRatRht))
return mpqPosInfinity;
// If the denominator is 1,
// and the numerator fts in a UINT, ...
if (mpq_integer_p (&aplRatRht)
&& mpz_fits_slong_p (mpq_numref (&aplRatRht)) NE 0)
{
// Initialize the result to 0/1
mpq_init (&mpqRes);
// Extract the numerator
uRht = (UINT) mpz_get_si (mpq_numref (&aplRatRht));
// Compute the factorial
mpz_fac_ui (mpq_numref (&mpqRes), uRht);
} else
RaiseException (EXCEPTION_RESULT_VFP, 0, 0, NULL);
return mpqRes;
} // End PrimFnMonQuoteDotRisR
void
check_n (void)
{
int ret;
/* %n suppressed */
{
int n = 123;
gmp_sscanf (" ", " %*n", &n);
ASSERT_ALWAYS (n == 123);
}
{
int n = 123;
fromstring_gmp_fscanf (" ", " %*n", &n);
ASSERT_ALWAYS (n == 123);
}
#define CHECK_N(type, string) \
do { \
type x[2]; \
char fmt[128]; \
int ret; \
\
x[0] = ~ (type) 0; \
x[1] = ~ (type) 0; \
sprintf (fmt, "abc%%%sn", string); \
ret = gmp_sscanf ("abc", fmt, &x[0]); \
\
ASSERT_ALWAYS (ret == 0); \
\
/* should write whole of x[0] and none of x[1] */ \
ASSERT_ALWAYS (x[0] == 3); \
ASSERT_ALWAYS (x[1] == (type) ~ (type) 0); \
\
} while (0)
CHECK_N (char, "hh");
CHECK_N (long, "l");
#if HAVE_LONG_LONG
CHECK_N (long long, "L");
#endif
#if HAVE_INTMAX_T
CHECK_N (intmax_t, "j");
#endif
#if HAVE_PTRDIFF_T
CHECK_N (ptrdiff_t, "t");
#endif
CHECK_N (short, "h");
CHECK_N (size_t, "z");
/* %Zn */
{
mpz_t x[2];
mpz_init_set_si (x[0], -987L);
mpz_init_set_si (x[1], 654L);
ret = gmp_sscanf ("xyz ", "xyz%Zn", x[0]);
MPZ_CHECK_FORMAT (x[0]);
MPZ_CHECK_FORMAT (x[1]);
ASSERT_ALWAYS (ret == 0);
ASSERT_ALWAYS (mpz_cmp_ui (x[0], 3L) == 0);
ASSERT_ALWAYS (mpz_cmp_ui (x[1], 654L) == 0);
mpz_clear (x[0]);
mpz_clear (x[1]);
}
{
mpz_t x;
mpz_init (x);
ret = fromstring_gmp_fscanf ("xyz ", "xyz%Zn", x);
ASSERT_ALWAYS (ret == 0);
ASSERT_ALWAYS (mpz_cmp_ui (x, 3L) == 0);
mpz_clear (x);
}
/* %Qn */
{
mpq_t x[2];
mpq_init (x[0]);
mpq_init (x[1]);
mpq_set_ui (x[0], -987L, 654L);
mpq_set_ui (x[1], 4115L, 226L);
ret = gmp_sscanf ("xyz ", "xyz%Qn", x[0]);
MPQ_CHECK_FORMAT (x[0]);
MPQ_CHECK_FORMAT (x[1]);
ASSERT_ALWAYS (ret == 0);
ASSERT_ALWAYS (mpq_cmp_ui (x[0], 3L, 1L) == 0);
ASSERT_ALWAYS (mpq_cmp_ui (x[1], 4115L, 226L) == 0);
mpq_clear (x[0]);
mpq_clear (x[1]);
}
{
mpq_t x;
mpq_init (x);
ret = fromstring_gmp_fscanf ("xyz ", "xyz%Qn", x);
ASSERT_ALWAYS (ret == 0);
ASSERT_ALWAYS (mpq_cmp_ui (x, 3L, 1L) == 0);
mpq_clear (x);
}
/* %Fn */
{
mpf_t x[2];
mpf_init (x[0]);
mpf_init (x[1]);
mpf_set_ui (x[0], -987L);
mpf_set_ui (x[1], 654L);
ret = gmp_sscanf ("xyz ", "xyz%Fn", x[0]);
MPF_CHECK_FORMAT (x[0]);
MPF_CHECK_FORMAT (x[1]);
ASSERT_ALWAYS (ret == 0);
ASSERT_ALWAYS (mpf_cmp_ui (x[0], 3L) == 0);
ASSERT_ALWAYS (mpf_cmp_ui (x[1], 654L) == 0);
mpf_clear (x[0]);
mpf_clear (x[1]);
}
{
mpf_t x;
mpf_init (x);
ret = fromstring_gmp_fscanf ("xyz ", "xyz%Fn", x);
ASSERT_ALWAYS (ret == 0);
ASSERT_ALWAYS (mpf_cmp_ui (x, 3L) == 0);
mpf_clear (x);
}
}
static void
check_mixed (FILE *fout)
{
int ch = 'a';
signed char sch = -1;
unsigned char uch = 1;
short sh = -1;
unsigned short ush = 1;
int i = -1;
int j = 1;
unsigned int ui = 1;
long lo = -1;
unsigned long ulo = 1;
float f = -1.25;
double d = -1.25;
long double ld = -1.25;
ptrdiff_t p = 1;
size_t sz = 1;
mpz_t mpz;
mpq_t mpq;
mpf_t mpf;
mp_rnd_t rnd = GMP_RNDN;
mp_size_t limb_size = 3;
mp_limb_t limb[3];
mpfr_t mpfr;
mpfr_prec_t prec = 53;
mpz_init (mpz);
mpz_set_ui (mpz, ulo);
mpq_init (mpq);
mpq_set_si (mpq, lo, ulo);
mpf_init (mpf);
mpf_set_q (mpf, mpq);
mpfr_init2 (mpfr, prec);
mpfr_set_f (mpfr, mpf, GMP_RNDN);
limb[0] = limb[1] = limb[2] = ~ (mp_limb_t) 0;
check_vfprintf (fout, "a. %Ra, b. %u, c. %lx%n", mpfr, ui, ulo, &j);
check_length (1, j, 22, d);
check_vfprintf (fout, "a. %c, b. %Rb, c. %u, d. %li%ln", i, mpfr, i,
lo, &ulo);
check_length (2, ulo, 36, lu);
check_vfprintf (fout, "a. %hi, b. %*f, c. %Re%hn", ush, 3, f, mpfr, &ush);
check_length (3, ush, 29, hu);
check_vfprintf (fout, "a. %hi, b. %f, c. %#.2Rf%n", sh, d, mpfr, &i);
check_length (4, i, 29, d);
check_vfprintf (fout, "a. %R*A, b. %Fe, c. %i%zn", rnd, mpfr, mpf, sz,
&sz);
check_length (5, (unsigned long) sz, 34, lu); /* no format specifier "%zu" in C89 */
check_vfprintf (fout, "a. %Pu, b. %c, c. %Zi%Zn", prec, ch, mpz, &mpz);
check_length_with_cmp (6, mpz, 17, mpz_cmp_ui (mpz, 17), Zi);
check_vfprintf (fout, "%% a. %#.0RNg, b. %Qx%Rn, c. %p", mpfr, mpq, &mpfr,
(void *) &i);
check_length_with_cmp (7, mpfr, 15, mpfr_cmp_ui (mpfr, 15), Rg);
#ifndef NPRINTF_T
check_vfprintf (fout, "%% a. %RNg, b. %Qx, c. %td%tn", mpfr, mpq, p, &p);
check_length (8, (long) p, 20, ld); /* no format specifier "%td" in C89 */
#endif
#ifndef NPRINTF_L
check_vfprintf (fout, "a. %RA, b. %Lf, c. %QX%zn", mpfr, ld, mpq, &sz);
check_length (9, (unsigned long) sz, 30, lu); /* no format specifier "%zu" in C89 */
#endif
#ifndef NPRINTF_HH
check_vfprintf (fout, "a. %hhi, b.%RA, c. %hhu%hhn", sch, mpfr, uch, &uch);
check_length (10, (unsigned int) uch, 21, u); /* no format specifier "%hhu" in C89 */
#endif
#if (__GNU_MP_VERSION * 10 + __GNU_MP_VERSION_MINOR) >= 42
/* The 'M' specifier was added in gmp 4.2.0 */
check_vfprintf (fout, "a. %Mx b. %Re%Mn", limb[0], mpfr, &limb[0]);
if (limb[0] != 14 + BITS_PER_MP_LIMB / 4 || limb[1] != ~ (mp_limb_t) 0
|| limb[2] != ~ (mp_limb_t) 0)
{
printf ("Error in test #11: mpfr_vfprintf did not print %d characters"
" as expected\n", 14 + (int) BITS_PER_MP_LIMB / 4);
exit (1);
}
limb[0] = ~ (mp_limb_t) 0;
/* we tell vfprintf that limb array is 2 cells wide
and check it doesn't go through */
check_vfprintf (fout, "a. %Re .b %Nx%Nn", mpfr, limb, limb_size, limb,
limb_size - 1);
if (limb[0] != 14 + 3 * BITS_PER_MP_LIMB / 4 || limb[1] != (mp_limb_t) 0
|| limb[2] != ~ (mp_limb_t) 0)
{
printf ("Error in test #12: mpfr_vfprintf did not print %d characters"
" as expected\n", 14 + (int) BITS_PER_MP_LIMB / 4);
exit (1);
}
#endif
#if defined(HAVE_LONG_LONG) && !defined(NPRINTF_LL)
{
long long llo = -1;
unsigned long long ullo = 1;
check_vfprintf (fout, "a. %Re, b. %llx%Qn", mpfr, ullo, &mpq);
check_length_with_cmp (21, mpq, 16, mpq_cmp_ui (mpq, 16, 1), Qu);
check_vfprintf (fout, "a. %lli, b. %Rf%Fn", llo, mpfr, &mpf);
check_length_with_cmp (22, mpf, 19, mpf_cmp_ui (mpf, 19), Fg);
}
#endif
#if defined(_MPFR_H_HAVE_INTMAX_T) && !defined(NPRINTF_J)
{
intmax_t im = -1;
uintmax_t uim = 1;
check_vfprintf (fout, "a. %*RA, b. %ji%Qn", 10, mpfr, im, &mpq);
check_length_with_cmp (31, mpq, 20, mpq_cmp_ui (mpq, 20, 1), Qu);
check_vfprintf (fout, "a. %.*Re, b. %jx%Fn", 10, mpfr, uim, &mpf);
check_length_with_cmp (32, mpf, 25, mpf_cmp_ui (mpf, 25), Fg);
}
#endif
mpfr_clear (mpfr);
mpf_clear (mpf);
mpq_clear (mpq);
mpz_clear (mpz);
}
static void
check_mixed (void)
{
int ch = 'a';
#ifndef NPRINTF_HH
signed char sch = -1;
unsigned char uch = 1;
#endif
short sh = -1;
unsigned short ush = 1;
int i = -1;
int j = 1;
unsigned int ui = 1;
long lo = -1;
unsigned long ulo = 1;
float f = -1.25;
double d = -1.25;
#if !defined(NPRINTF_T) || !defined(NPRINTF_L)
long double ld = -1.25;
#endif
#ifndef NPRINTF_T
ptrdiff_t p = 1, saved_p;
#endif
size_t sz = 1;
mpz_t mpz;
mpq_t mpq;
mpf_t mpf;
mpfr_rnd_t rnd = MPFR_RNDN;
mpfr_t mpfr;
mpfr_prec_t prec;
mpz_init (mpz);
mpz_set_ui (mpz, ulo);
mpq_init (mpq);
mpq_set_si (mpq, lo, ulo);
mpf_init (mpf);
mpf_set_q (mpf, mpq);
mpfr_init (mpfr);
mpfr_set_f (mpfr, mpf, MPFR_RNDN);
prec = mpfr_get_prec (mpfr);
check_vprintf ("a. %Ra, b. %u, c. %lx%n", mpfr, ui, ulo, &j);
check_length (1, j, 22, d);
check_vprintf ("a. %c, b. %Rb, c. %u, d. %li%ln", i, mpfr, i, lo, &ulo);
check_length (2, ulo, 36, lu);
check_vprintf ("a. %hi, b. %*f, c. %Re%hn", ush, 3, f, mpfr, &ush);
check_length (3, ush, 29, hu);
check_vprintf ("a. %hi, b. %f, c. %#.2Rf%n", sh, d, mpfr, &i);
check_length (4, i, 29, d);
check_vprintf ("a. %R*A, b. %Fe, c. %i%zn", rnd, mpfr, mpf, sz, &sz);
check_length (5, (unsigned long) sz, 34, lu); /* no format specifier '%zu' in C89 */
check_vprintf ("a. %Pu, b. %c, c. %RUG, d. %Zi%Zn", prec, ch, mpfr, mpz, &mpz);
check_length_with_cmp (6, mpz, 24, mpz_cmp_ui (mpz, 24), Zi);
check_vprintf ("%% a. %#.0RNg, b. %Qx%Rn c. %p",
mpfr, mpq, &mpfr, (void *) &i);
check_length_with_cmp (7, mpfr, 15, mpfr_cmp_ui (mpfr, 15), Rg);
#ifndef NPRINTF_T
saved_p = p;
check_vprintf ("%% a. %RNg, b. %Qx, c. %td%tn", mpfr, mpq, p, &p);
if (p != 20)
mpfr_fprintf (stderr, "Error in test 8, got '%% a. %RNg, b. %Qx, c. %td'\n", mpfr, mpq, saved_p);
check_length (8, (long) p, 20, ld); /* no format specifier '%td' in C89 */
#endif
#ifndef NPRINTF_L
check_vprintf ("a. %RA, b. %Lf, c. %QX%zn", mpfr, ld, mpq, &sz);
check_length (9, (unsigned long) sz, 30, lu); /* no format specifier '%zu' in C89 */
#endif
#ifndef NPRINTF_HH
check_vprintf ("a. %hhi, b. %Ra, c. %hhu%hhn", sch, mpfr, uch, &uch);
check_length (10, (unsigned int) uch, 22, u); /* no format specifier '%hhu' in C89 */
#endif
#if defined(HAVE_LONG_LONG) && !defined(NPRINTF_LL)
{
long long llo = -1;
unsigned long long ullo = 1;
check_vprintf ("a. %Re, b. %llx%Qn", mpfr, ullo, &mpq);
check_length_with_cmp (11, mpq, 16, mpq_cmp_ui (mpq, 16, 1), Qu);
check_vprintf ("a. %lli, b. %Rf%lln", llo, mpfr, &ullo);
check_length (12, ullo, 19, llu);
}
#endif
#if defined(_MPFR_H_HAVE_INTMAX_T) && !defined(NPRINTF_J)
{
intmax_t im = -1;
uintmax_t uim = 1;
check_vprintf ("a. %*RA, b. %ji%Fn", 10, mpfr, im, &mpf);
check_length_with_cmp (31, mpf, 20, mpf_cmp_ui (mpf, 20), Fg);
check_vprintf ("a. %.*Re, b. %jx%jn", 10, mpfr, uim, &im);
check_length (32, (long) im, 25, li); /* no format specifier "%ji" in C89 */
}
#endif
mpfr_clear (mpfr);
mpf_clear (mpf);
mpq_clear (mpq);
mpz_clear (mpz);
}
void setup_polynomial(polynomial *F, int numVars, FILE *IN, int polyNumber)
/***************************************************************\
* USAGE: setup the next polynomial described in IN *
\***************************************************************/
{
int i, j, rV, max, base = 10;
// initialize the number of variables, degree & isReal
F->numVariables = numVars;
F->degree = 0;
F->isReal = 1;
// read in the number of terms
fscanf(IN, "%d\n", &F->numTerms);
// error checking - want number of terms >= 0
if (F->numTerms <= 0)
{ // error
printf("ERROR: The number of terms (%d) must be positive.\n", F->numTerms);
// close file and exit
fclose(IN);
errExit(ERROR_INPUT_SYSTEM);
}
// allocate memory
mpq_init(F->norm_sqr);
F->coeff = (rational_complex_number *)errMalloc(F->numTerms * sizeof(rational_complex_number));
F->exponents = (int **)errMalloc(F->numTerms * sizeof(int *));
// setup the terms
for (i = 0; i < F->numTerms; i++)
{ // allocate & initialize memory
F->exponents[i] = (int *)errMalloc(numVars * sizeof(int));
initialize_rational_number(F->coeff[i]);
// read in exponents, compute degree, and perform error checking - want exponents >= 0
max = 0;
for (j = 0; j < numVars; j++)
{
fscanf(IN, "%d", &F->exponents[i][j]);
if (F->exponents[i][j] < 0)
{ // error
printf("ERROR: The exponent for variable %d in monomial %d of polynomial %d must be nonnegative (%d).\n", j+1, i+1, polyNumber+1, F->exponents[i][j]);
// close file and exit
fclose(IN);
errExit(ERROR_INPUT_SYSTEM);
}
max += F->exponents[i][j];
}
// update degree, if needed
if (max > F->degree)
F->degree = max;
// read in real & imaginary part of coefficient
rV = mpq_inp_str(F->coeff[i]->re, IN, base);
if (rV == 0)
{ // error in reading the coefficient
printf("ERROR: There appears to be an error when reading in the real part of the\n coefficient for monomial %d of polynomial %d.\n", i+1, polyNumber+1);
// close file and exit
fclose(IN);
errExit(ERROR_INPUT_SYSTEM);
}
rV = mpq_inp_str(F->coeff[i]->im, IN, base);
if (rV == 0)
{ // error in reading the coefficient
printf("ERROR: There appears to be an error when reading in the imaginary part of the\n coefficient for monomial %d of polynomial %d.\n", i+1, polyNumber+1);
// close file and exit
fclose(IN);
errExit(ERROR_INPUT_SYSTEM);
}
// setup in canonical form
mpq_canonicalize(F->coeff[i]->re);
mpq_canonicalize(F->coeff[i]->im);
// update isReal, if needed
if (F->isReal && mpq_cmp_ui(F->coeff[i]->im, 0, 1) != 0)
F->isReal = 0;
}
// compute norm_sqr
norm_sqr_polynomial(F->norm_sqr, F);
return;
}
void setup_exponential(exponential *F, int numVars, FILE *IN, int expNumber, int yIndex)
/***************************************************************\
* USAGE: setup the next exponential described in IN *
\***************************************************************/
{
int rV, base = 10;
// read in the x variable index
rV = fscanf(IN, "%d", &F->xIndex);
if (rV == 0)
{ // error in reading the x variable index
printf("ERROR: There appears to be an error when reading in the variable index\n for exponential %d.\n", expNumber+1);
// close file and exit
fclose(IN);
errExit(ERROR_INPUT_SYSTEM);
}
// error checking - want variable index to be in 1,2,..,numVars
if (F->xIndex < 1 || F->xIndex > numVars)
{ // error
printf("ERROR: The variable index for exponential %d must be between 1 and %d.\n", expNumber+1, numVars);
// close file and exit
fclose(IN);
errExit(ERROR_INPUT_SYSTEM);
}
// setup x & y variable index
F->xIndex--;
F->yIndex = yIndex;
// read in the type of exponential function: exp, sin, or cos
rV = readInExpFunction(IN, &F->expFunction, &F->isHyperbolic);
if (rV == 0)
{ // error in reading the exponential function
printf("ERROR: There appears to be an error when reading in the exponential function\n for exponential %d.\n", expNumber+1);
// close file and exit
fclose(IN);
errExit(ERROR_INPUT_SYSTEM);
}
// error checking
if (F->expFunction != 'X' && F->expFunction != 'S' && F->expFunction != 'C')
{ // error
printf("ERROR: The exponential function for exponential %d appears to be incorrect.\n", expNumber+1);
// close file and exit
fclose(IN);
errExit(ERROR_INPUT_SYSTEM);
}
// read in real & imaginary part of beta
initialize_rational_number(F->beta);
rV = mpq_inp_str(F->beta->re, IN, base);
if (rV == 0)
{ // error in reading the coefficient
printf("ERROR: There appears to be an error when reading in the real part of the\n exponential constant for exponential %d.\n", expNumber+1);
// close file and exit
fclose(IN);
errExit(ERROR_INPUT_SYSTEM);
}
rV = mpq_inp_str(F->beta->im, IN, base);
if (rV == 0)
{ // error in reading the coefficient
printf("ERROR: There appears to be an error when reading in the imaginary part of the\n exponential constant exponential %d.\n", expNumber+1);
// close file and exit
fclose(IN);
errExit(ERROR_INPUT_SYSTEM);
}
// setup in canonical form
mpq_canonicalize(F->beta->re);
mpq_canonicalize(F->beta->im);
// update isReal
F->isReal = !mpq_cmp_ui(F->beta->im, 0, 1);
return;
}
int print_coeff(FILE *OUT, rational_complex_number z, int somethingPrinted)
/***************************************************************\
* USAGE: prints z to OUT in user-friendly way *
\***************************************************************/
{
int rV = -2; // 0 if z is zero (nothing printed), 1 if z is one (nothing printed), -1 if z is -1 (nothing printed), -2 otherwise (something printed)
int base = 10;
if (mpq_cmp_ui(z->re, 0, 1) == 0)
{ // real part is zero
if (mpq_cmp_ui(z->im, 0, 1) == 0)
{ // imag part is zero
rV = 0;
}
else
{ // imag part is nonzero
if (somethingPrinted && mpq_sgn(z->im) >= 0)
fprintf(OUT, "+");
if (mpq_cmp_ui(z->im, 1, 1) == 0)
fprintf(OUT, "I");
else if (mpq_cmp_si(z->im, -1, 1) == 0)
fprintf(OUT, "-I");
else
{
mpq_out_str(OUT, base, z->im);
fprintf(OUT, "*I");
}
}
}
else
{ // real part is nonzero
if (mpq_cmp_ui(z->im, 0, 1) == 0)
{ // imag part is zero
if (mpq_cmp_ui(z->re, 1, 1) == 0)
{ // value is 1
rV = 1;
}
else if (mpq_cmp_si(z->re, -1, 1) == 0)
{ // value is -1
rV = -1;
}
else
{
if (somethingPrinted && mpq_sgn(z->re) >= 0)
fprintf(OUT, "+");
mpq_out_str(OUT, base, z->re);
}
}
else
{ // imag part is nonzero
if (somethingPrinted)
fprintf(OUT, "+");
fprintf(OUT, "(");
mpq_out_str(OUT, base, z->re);
if (mpq_sgn(z->im) >= 0)
fprintf(OUT, "+");
mpq_out_str(OUT, base, z->im);
fprintf(OUT, "*I)");
}
}
return rV;
}
void
check_n (void)
{
{
int n = -1;
check_one ("blah", "%nblah", &n);
ASSERT_ALWAYS (n == 0);
}
{
int n = -1;
check_one ("hello ", "hello %n", &n);
ASSERT_ALWAYS (n == 6);
}
{
int n = -1;
check_one ("hello world", "hello %n world", &n);
ASSERT_ALWAYS (n == 6);
}
#define CHECK_N(type, string) \
do { \
type x[2]; \
char fmt[128]; \
\
x[0] = ~ (type) 0; \
x[1] = ~ (type) 0; \
sprintf (fmt, "%%d%%%sn%%d", string); \
check_one ("123456", fmt, 123, &x[0], 456); \
\
/* should write whole of x[0] and none of x[1] */ \
ASSERT_ALWAYS (x[0] == 3); \
ASSERT_ALWAYS (x[1] == (type) ~ (type) 0); \
\
} while (0)
CHECK_N (mp_limb_t, "M");
CHECK_N (char, "hh");
CHECK_N (long, "l");
#if HAVE_LONG_LONG
CHECK_N (long long, "L");
#endif
#if HAVE_INTMAX_T
CHECK_N (intmax_t, "j");
#endif
#if HAVE_PTRDIFF_T
CHECK_N (ptrdiff_t, "t");
#endif
CHECK_N (short, "h");
CHECK_N (size_t, "z");
{
mpz_t x[2];
mpz_init_set_si (x[0], -987L);
mpz_init_set_si (x[1], 654L);
check_one ("123456", "%d%Zn%d", 123, x[0], 456);
MPZ_CHECK_FORMAT (x[0]);
MPZ_CHECK_FORMAT (x[1]);
ASSERT_ALWAYS (mpz_cmp_ui (x[0], 3L) == 0);
ASSERT_ALWAYS (mpz_cmp_ui (x[1], 654L) == 0);
mpz_clear (x[0]);
mpz_clear (x[1]);
}
{
mpq_t x[2];
mpq_init (x[0]);
mpq_init (x[1]);
mpq_set_ui (x[0], -987L, 654L);
mpq_set_ui (x[1], 4115L, 226L);
check_one ("123456", "%d%Qn%d", 123, x[0], 456);
MPQ_CHECK_FORMAT (x[0]);
MPQ_CHECK_FORMAT (x[1]);
ASSERT_ALWAYS (mpq_cmp_ui (x[0], 3L, 1L) == 0);
ASSERT_ALWAYS (mpq_cmp_ui (x[1], 4115L, 226L) == 0);
mpq_clear (x[0]);
mpq_clear (x[1]);
}
{
mpf_t x[2];
mpf_init (x[0]);
mpf_init (x[1]);
mpf_set_ui (x[0], -987L);
mpf_set_ui (x[1], 654L);
check_one ("123456", "%d%Fn%d", 123, x[0], 456);
MPF_CHECK_FORMAT (x[0]);
MPF_CHECK_FORMAT (x[1]);
ASSERT_ALWAYS (mpf_cmp_ui (x[0], 3L) == 0);
ASSERT_ALWAYS (mpf_cmp_ui (x[1], 654L) == 0);
mpf_clear (x[0]);
mpf_clear (x[1]);
}
{
mp_limb_t a[5];
mp_limb_t a_want[numberof(a)];
mp_size_t i;
a[0] = 123;
check_one ("blah", "bl%Nnah", a, (mp_size_t) 0);
ASSERT_ALWAYS (a[0] == 123);
MPN_ZERO (a_want, numberof (a_want));
for (i = 1; i < numberof (a); i++)
{
check_one ("blah", "bl%Nnah", a, i);
a_want[0] = 2;
ASSERT_ALWAYS (mpn_cmp (a, a_want, i) == 0);
}
}
}
int sqrt_upper(mpq_t sqrt_x, mpq_t x, int digits)
/***************************************************************\
* USAGE: compute a certified rational upper bound on the sqrt(x)*
* that is within 10^-digits of the true value 0-good,1-error *
\***************************************************************/
{
int rV = 0, sign = mpq_sgn(x);
// verify digits >= 0
if (digits < 0)
{ // error
printf("ERROR: The number of digits must be nonnegative!\n");
errExit(ERROR_CONFIGURATION);
}
// check the sign of x
if (sign == -1)
{ // x is negative - return error
rV = 1;
}
else if (sign == 0)
{ // x is zero - sqrt(x) = 0
mpq_set_ui(sqrt_x, 0, 1);
rV = 0;
}
else
{ // x is positive - compute sqrt(x)
int prec;
mpfr_t sqrt_x_float;
mpf_t tempMPF;
mpq_t sqrt_x_temp, tempMPQ;
// determine the precision to use to get an approximation
if (digits <= 16)
prec = 64;
else
{ // determine the precision needed
prec = (int) ceil((digits + 0.5) / (32 * log10(2.0)));
if (prec <= 2)
prec = 64;
else
prec *= 32;
}
// initialize
mpfr_init2(sqrt_x_float, prec);
mpf_init2(tempMPF, prec);
mpq_init(sqrt_x_temp);
mpq_init(tempMPQ);
// approximate sqrt(x) - round up!
mpfr_set_q(sqrt_x_float, x, GMP_RNDU);
mpfr_sqrt(sqrt_x_float, sqrt_x_float, GMP_RNDU);
// convert to rational
mpfr_get_f(tempMPF, sqrt_x_float, GMP_RNDU);
mpq_set_f(sqrt_x_temp, tempMPF);
// verify that sqrt_x_temp is an upper bound
mpq_mul(tempMPQ, sqrt_x_temp, sqrt_x_temp);
if (mpq_cmp(tempMPQ, x) >= 0)
{ // we have an upper bound - refine & certify it
refine_sqrt_upper(sqrt_x_temp, x, digits);
// copy to sqrt_x
mpq_set(sqrt_x, sqrt_x_temp);
rV = 0;
}
else
{ // try again with 2*x (Newton iterations still converge quadratically!)
mpq_add(tempMPQ, x, x);
mpfr_set_q(sqrt_x_float, tempMPQ, GMP_RNDU);
mpfr_sqrt(sqrt_x_float, sqrt_x_float, GMP_RNDU);
// convert to rational
mpfr_get_f(tempMPF, sqrt_x_float, GMP_RNDU);
mpq_set_f(sqrt_x_temp, tempMPF);
// verify that sqrt_x_temp is an upper bound
mpq_mul(tempMPQ, sqrt_x_temp, sqrt_x_temp);
if (mpq_cmp(tempMPQ, x) >= 0)
{ // we have an upper bound - refine & certify it
refine_sqrt_upper(sqrt_x_temp, x, digits);
// copy to sqrt_x
mpq_set(sqrt_x, sqrt_x_temp);
rV = 0;
}
else
{ // take any upper bound
if (mpq_cmp_ui(x, 1, 1) <= 0)
{ // 1 is an upper bound for sqrt(x)
mpq_set_ui(sqrt_x_temp, 1, 1);
}
else
{ // x is an upper bound for sqrt(x)
mpq_set(sqrt_x_temp, x);
}
// we have an upper bound - refine & certify it
refine_sqrt_upper(sqrt_x_temp, x, digits);
// copy to sqrt_x
mpq_set(sqrt_x, sqrt_x_temp);
rV = 0;
}
}
// clear
mpfr_clear(sqrt_x_float);
mpf_clear(tempMPF);
mpq_clear(sqrt_x_temp);
mpq_clear(tempMPQ);
}
return rV;
}
