void
cpx_confluent (cpx_t em, cpx_t a, cpx_t b, cpx_t z, unsigned int prec)
{
mpf_t fact;
cpx_t zee, z_n, term;
cpx_t ay, be, poch_a, poch_b;
mpf_init (fact);
cpx_init (zee);
cpx_init (z_n);
cpx_init (term);
cpx_init (ay);
cpx_init (be);
cpx_init (poch_a);
cpx_init (poch_b);
/* Make copy of arguments now! */
cpx_set (zee, z);
cpx_set (z_n, zee);
cpx_set (ay, a);
cpx_set (poch_a, a);
cpx_set (be, b);
cpx_set (poch_b, b);
cpx_set_ui (em, 1, 0);
mpf_set_ui (fact, 1);
mpf_t mag;
mpf_init (mag);
/* Use 10^{-2 * prec} for smallest term in sum */
mpf_t maxterm;
mpf_init (maxterm);
fp_epsilon (maxterm, prec);
mpf_mul (maxterm, maxterm, maxterm);
unsigned int n=1;
while(1)
{
cpx_div_mpf (term, z_n, fact);
cpx_mul (term, term, poch_a);
cpx_div (term, term, poch_b);
cpx_add (em, em, term);
/* Don't go no farther than this */
cpx_mod_sq (mag, term);
if (mpf_cmp (mag, maxterm) < 0) break;
n++;
cpx_mul (z_n, z_n, zee);
mpf_mul_ui (fact, fact, n);
mpf_add_ui (ay[0].re, ay[0].re, 1);
mpf_add_ui (be[0].re, be[0].re, 1);
cpx_mul (poch_a, poch_a, ay);
cpx_mul (poch_b, poch_b, be);
}
mpf_clear (fact);
mpf_clear (mag);
mpf_clear (maxterm);
cpx_clear (zee);
cpx_clear (z_n);
cpx_clear (term);
cpx_clear (ay);
cpx_clear (be);
cpx_clear (poch_a);
cpx_clear (poch_b);
}
bool bbp_pi(bool const & abortTask,
std::string const & digitIndex,
uint32_t const digitStep,
std::string & piSequence)
{
unsigned long const mantissa_bits = 132;
unsigned long const count_offset = 7;
// settings above gives 32 hexadecimal digits
unsigned long count = static_cast<unsigned long>(
floor(log10(pow(2.0, static_cast<double>(mantissa_bits)))));
count -= count_offset;
// starting digit
mpz_t digit;
mpz_init(digit);
if (mpz_set_str(digit, digitIndex.c_str(), 10) < 0)
return false;
mpz_sub_ui(digit, digit, 1); // subtract the 3 digit
mpz_add_ui(digit, digit, digitStep);
mpz_t tmpI[TEMPORARY_INTEGERS];
for (size_t i = 0; i < (sizeof(tmpI) / sizeof(mpz_t)); ++i)
mpz_init(tmpI[i]);
mpf_t tmpF[TEMPORARY_FLOATS];
for (size_t i = 0; i < (sizeof(tmpF) / sizeof(mpf_t)); ++i)
mpf_init2(tmpF[i], mantissa_bits);
// determine epsilon based on the number of digits required
mpf_t epsilon;
mpf_init2(epsilon, mantissa_bits);
mpf_set_ui(epsilon, 10);
mpf_pow_ui(epsilon, epsilon, count + count_offset);
mpf_ui_div(epsilon, 1, epsilon);
// integer constant
mpz_t sixteen;
mpz_init(sixteen);
mpz_set_ui(sixteen, 16);
// determine the series
mpf_t s1, s2, s3, s4;
mpf_init2(s1, mantissa_bits);
mpf_init2(s2, mantissa_bits);
mpf_init2(s3, mantissa_bits);
mpf_init2(s4, mantissa_bits);
series(abortTask, s1, 1, tmpI, tmpF, sixteen, digit, epsilon);
if (abortTask)
return false;
series(abortTask, s2, 4, tmpI, tmpF, sixteen, digit, epsilon);
if (abortTask)
return false;
series(abortTask, s3, 5, tmpI, tmpF, sixteen, digit, epsilon);
if (abortTask)
return false;
series(abortTask, s4, 6, tmpI, tmpF, sixteen, digit, epsilon);
if (abortTask)
return false;
// pid = 4. * s1 - 2. * s2 - s3 - s4;
mpf_mul_ui(s1, s1, 4);
mpf_mul_ui(s2, s2, 2);
mpf_t result;
mpf_init2(result, mantissa_bits);
mpf_sub(result, s1, s2);
mpf_sub(result, result, s3);
mpf_sub(result, result, s4);
// pid = pid - (int) pid + 1.;
mpf_t & tmp1 = tmpF[0];
mpf_floor(tmp1, result);
mpf_sub(result, result, tmp1);
mpf_add_ui(result, result, 1);
mpf_abs(result, result);
// output the result
char resultStr[256];
mp_exp_t exponent;
mpf_get_str(resultStr, &exponent, 16, 254, result);
resultStr[count + 1] = '\0'; // cut off any erroneous bits
piSequence.assign(&resultStr[1]);
// cleanup
for (size_t i = 0; i < (sizeof(tmpI) / sizeof(mpz_t)); ++i)
mpz_clear(tmpI[i]);
for (size_t i = 0; i < (sizeof(tmpF) / sizeof(mpf_t)); ++i)
mpf_clear(tmpF[i]);
mpz_clear(digit);
mpf_clear(epsilon);
mpz_clear(sixteen);
mpf_clear(s1);
mpf_clear(s2);
mpf_clear(s3);
mpf_clear(s4);
mpf_clear(result);
return true;
}
void
mpf_ui_sub (mpf_ptr r, unsigned long int u, mpf_srcptr v)
{
mp_srcptr up, vp;
mp_ptr rp, tp;
mp_size_t usize, vsize, rsize;
mp_size_t prec;
mp_exp_t uexp;
mp_size_t ediff;
int negate;
mp_limb_t ulimb;
TMP_DECL;
vsize = v->_mp_size;
/* Handle special cases that don't work in generic code below. */
if (u == 0)
{
mpf_neg (r, v);
return;
}
if (vsize == 0)
{
mpf_set_ui (r, u);
return;
}
/* If signs of U and V are different, perform addition. */
if (vsize < 0)
{
__mpf_struct v_negated;
v_negated._mp_size = -vsize;
v_negated._mp_exp = v->_mp_exp;
v_negated._mp_d = v->_mp_d;
mpf_add_ui (r, &v_negated, u);
return;
}
TMP_MARK;
/* Signs are now known to be the same. */
ulimb = u;
/* Make U be the operand with the largest exponent. */
if (1 < v->_mp_exp)
{
negate = 1;
usize = ABS (vsize);
vsize = 1;
up = v->_mp_d;
vp = &ulimb;
rp = r->_mp_d;
prec = r->_mp_prec + 1;
uexp = v->_mp_exp;
ediff = uexp - 1;
}
else
{
negate = 0;
usize = 1;
vsize = ABS (vsize);
up = &ulimb;
vp = v->_mp_d;
rp = r->_mp_d;
prec = r->_mp_prec;
uexp = 1;
ediff = 1 - v->_mp_exp;
}
/* Ignore leading limbs in U and V that are equal. Doing
this helps increase the precision of the result. */
if (ediff == 0)
{
/* This loop normally exits immediately. Optimize for that. */
for (;;)
{
usize--;
vsize--;
if (up[usize] != vp[vsize])
break;
uexp--;
if (usize == 0)
goto Lu0;
if (vsize == 0)
goto Lv0;
}
usize++;
vsize++;
/* Note that either operand (but not both operands) might now have
leading zero limbs. It matters only that U is unnormalized if
vsize is now zero, and vice versa. And it is only in that case
that we have to adjust uexp. */
if (vsize == 0)
Lv0:
while (usize != 0 && up[usize - 1] == 0)
usize--, uexp--;
if (usize == 0)
Lu0:
while (vsize != 0 && vp[vsize - 1] == 0)
vsize--, uexp--;
}
/* If U extends beyond PREC, ignore the part that does. */
if (usize > prec)
{
up += usize - prec;
usize = prec;
}
/* If V extends beyond PREC, ignore the part that does.
Note that this may make vsize negative. */
if (vsize + ediff > prec)
{
vp += vsize + ediff - prec;
vsize = prec - ediff;
}
/* Allocate temp space for the result. Allocate
just vsize + ediff later??? */
tp = (mp_ptr) TMP_ALLOC (prec * BYTES_PER_MP_LIMB);
if (ediff >= prec)
{
/* V completely cancelled. */
if (tp != up)
MPN_COPY (rp, up, usize);
rsize = usize;
}
else
{
/* Locate the least significant non-zero limb in (the needed
parts of) U and V, to simplify the code below. */
for (;;)
{
if (vsize == 0)
{
MPN_COPY (rp, up, usize);
rsize = usize;
goto done;
}
if (vp[0] != 0)
break;
vp++, vsize--;
}
for (;;)
{
if (usize == 0)
{
MPN_COPY (rp, vp, vsize);
rsize = vsize;
negate ^= 1;
goto done;
}
if (up[0] != 0)
break;
up++, usize--;
}
/* uuuu | uuuu | uuuu | uuuu | uuuu */
/* vvvvvvv | vv | vvvvv | v | vv */
if (usize > ediff)
{
/* U and V partially overlaps. */
if (ediff == 0)
{
/* Have to compare the leading limbs of u and v
to determine whether to compute u - v or v - u. */
if (usize > vsize)
{
/* uuuu */
/* vv */
int cmp;
cmp = mpn_cmp (up + usize - vsize, vp, vsize);
if (cmp >= 0)
{
mp_size_t size;
size = usize - vsize;
MPN_COPY (tp, up, size);
mpn_sub_n (tp + size, up + size, vp, vsize);
rsize = usize;
}
else
{
/* vv */ /* Swap U and V. */
/* uuuu */
mp_size_t size, i;
size = usize - vsize;
tp[0] = -up[0] & GMP_NUMB_MASK;
for (i = 1; i < size; i++)
tp[i] = ~up[i] & GMP_NUMB_MASK;
mpn_sub_n (tp + size, vp, up + size, vsize);
mpn_sub_1 (tp + size, tp + size, vsize, (mp_limb_t) 1);
negate ^= 1;
rsize = usize;
}
}
else if (usize < vsize)
{
/* uuuu */
/* vvvvvvv */
int cmp;
cmp = mpn_cmp (up, vp + vsize - usize, usize);
if (cmp > 0)
{
mp_size_t size, i;
size = vsize - usize;
tp[0] = -vp[0] & GMP_NUMB_MASK;
for (i = 1; i < size; i++)
tp[i] = ~vp[i] & GMP_NUMB_MASK;
mpn_sub_n (tp + size, up, vp + size, usize);
mpn_sub_1 (tp + size, tp + size, usize, (mp_limb_t) 1);
rsize = vsize;
}
else
{
/* vvvvvvv */ /* Swap U and V. */
/* uuuu */
/* This is the only place we can get 0.0. */
mp_size_t size;
size = vsize - usize;
MPN_COPY (tp, vp, size);
mpn_sub_n (tp + size, vp + size, up, usize);
negate ^= 1;
rsize = vsize;
}
}
else
{
/* uuuu */
/* vvvv */
int cmp;
cmp = mpn_cmp (up, vp + vsize - usize, usize);
if (cmp > 0)
{
mpn_sub_n (tp, up, vp, usize);
rsize = usize;
}
else
{
mpn_sub_n (tp, vp, up, usize);
negate ^= 1;
rsize = usize;
/* can give zero */
}
}
}
else
{
if (vsize + ediff <= usize)
{
/* uuuu */
/* v */
mp_size_t size;
size = usize - ediff - vsize;
MPN_COPY (tp, up, size);
mpn_sub (tp + size, up + size, usize - size, vp, vsize);
rsize = usize;
}
else
{
/* uuuu */
/* vvvvv */
mp_size_t size, i;
size = vsize + ediff - usize;
tp[0] = -vp[0] & GMP_NUMB_MASK;
for (i = 1; i < size; i++)
tp[i] = ~vp[i] & GMP_NUMB_MASK;
mpn_sub (tp + size, up, usize, vp + size, usize - ediff);
mpn_sub_1 (tp + size, tp + size, usize, (mp_limb_t) 1);
rsize = vsize + ediff;
}
}
}
else
{
/* uuuu */
/* vv */
mp_size_t size, i;
size = vsize + ediff - usize;
tp[0] = -vp[0] & GMP_NUMB_MASK;
for (i = 1; i < vsize; i++)
tp[i] = ~vp[i] & GMP_NUMB_MASK;
for (i = vsize; i < size; i++)
tp[i] = GMP_NUMB_MAX;
mpn_sub_1 (tp + size, up, usize, (mp_limb_t) 1);
rsize = size + usize;
}
/* Full normalize. Optimize later. */
while (rsize != 0 && tp[rsize - 1] == 0)
{
rsize--;
uexp--;
}
MPN_COPY (rp, tp, rsize);
}
done:
r->_mp_size = negate ? -rsize : rsize;
r->_mp_exp = uexp;
TMP_FREE;
}
int
main (void)
{
mpf_t f, f0p5;
int got;
const char *expr;
int error = 0;
tests_start ();
mpf_init2 (f, 200L);
mpf_init2 (f0p5, 200L);
/* 0.5 */
mpf_set_ui (f0p5, 1L);
mpf_div_2exp (f0p5, f0p5, 1L);
mpf_set_ui (f, 0L);
expr = "0";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
EXPECT (mpf_fits_ushort_p, 1);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_ui (f, 1L);
expr = "1";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
EXPECT (mpf_fits_ushort_p, 1);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_si (f, -1L);
expr = "-1";
EXPECT (mpf_fits_ulong_p, 0);
EXPECT (mpf_fits_uint_p, 0);
EXPECT (mpf_fits_ushort_p, 0);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_ui (f, (unsigned long) USHRT_MAX);
expr = "USHRT_MAX";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
EXPECT (mpf_fits_ushort_p, 1);
mpf_set_ui (f, (unsigned long) USHRT_MAX);
mpf_add (f, f, f0p5);
expr = "USHRT_MAX + 0.5";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
EXPECT (mpf_fits_ushort_p, 1);
mpf_set_ui (f, (unsigned long) USHRT_MAX);
mpf_add_ui (f, f, 1L);
expr = "USHRT_MAX + 1";
EXPECT (mpf_fits_ushort_p, 0);
mpf_set_ui (f, (unsigned long) UINT_MAX);
expr = "UINT_MAX";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
mpf_set_ui (f, (unsigned long) UINT_MAX);
mpf_add (f, f, f0p5);
expr = "UINT_MAX + 0.5";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
mpf_set_ui (f, (unsigned long) UINT_MAX);
mpf_add_ui (f, f, 1L);
expr = "UINT_MAX + 1";
EXPECT (mpf_fits_uint_p, 0);
mpf_set_ui (f, ULONG_MAX);
expr = "ULONG_MAX";
EXPECT (mpf_fits_ulong_p, 1);
mpf_set_ui (f, ULONG_MAX);
mpf_add (f, f, f0p5);
expr = "ULONG_MAX + 0.5";
EXPECT (mpf_fits_ulong_p, 1);
mpf_set_ui (f, ULONG_MAX);
mpf_add_ui (f, f, 1L);
expr = "ULONG_MAX + 1";
EXPECT (mpf_fits_ulong_p, 0);
mpf_set_si (f, (long) SHRT_MAX);
expr = "SHRT_MAX";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_si (f, (long) SHRT_MAX);
expr = "SHRT_MAX + 0.5";
mpf_add (f, f, f0p5);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_si (f, (long) SHRT_MAX);
mpf_add_ui (f, f, 1L);
expr = "SHRT_MAX + 1";
EXPECT (mpf_fits_sshort_p, 0);
mpf_set_si (f, (long) INT_MAX);
expr = "INT_MAX";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
mpf_set_si (f, (long) INT_MAX);
mpf_add (f, f, f0p5);
expr = "INT_MAX + 0.5";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
mpf_set_si (f, (long) INT_MAX);
mpf_add_ui (f, f, 1L);
expr = "INT_MAX + 1";
EXPECT (mpf_fits_sint_p, 0);
mpf_set_si (f, LONG_MAX);
expr = "LONG_MAX";
EXPECT (mpf_fits_slong_p, 1);
mpf_set_si (f, LONG_MAX);
mpf_add (f, f, f0p5);
expr = "LONG_MAX + 0.5";
EXPECT (mpf_fits_slong_p, 1);
mpf_set_si (f, LONG_MAX);
mpf_add_ui (f, f, 1L);
expr = "LONG_MAX + 1";
EXPECT (mpf_fits_slong_p, 0);
mpf_set_si (f, (long) SHRT_MIN);
expr = "SHRT_MIN";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_si (f, (long) SHRT_MIN);
mpf_sub (f, f, f0p5);
expr = "SHRT_MIN - 0.5";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_si (f, (long) SHRT_MIN);
mpf_sub_ui (f, f, 1L);
expr = "SHRT_MIN + 1";
EXPECT (mpf_fits_sshort_p, 0);
mpf_set_si (f, (long) INT_MIN);
expr = "INT_MIN";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
mpf_set_si (f, (long) INT_MIN);
mpf_sub (f, f, f0p5);
expr = "INT_MIN - 0.5";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
mpf_set_si (f, (long) INT_MIN);
mpf_sub_ui (f, f, 1L);
expr = "INT_MIN + 1";
EXPECT (mpf_fits_sint_p, 0);
mpf_set_si (f, LONG_MIN);
expr = "LONG_MIN";
EXPECT (mpf_fits_slong_p, 1);
mpf_set_si (f, LONG_MIN);
mpf_sub (f, f, f0p5);
expr = "LONG_MIN - 0.5";
EXPECT (mpf_fits_slong_p, 1);
mpf_set_si (f, LONG_MIN);
mpf_sub_ui (f, f, 1L);
expr = "LONG_MIN + 1";
EXPECT (mpf_fits_slong_p, 0);
mpf_set_str_or_abort (f, "0.5", 10);
expr = "0.5";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
EXPECT (mpf_fits_ushort_p, 1);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_str_or_abort (f, "-0.5", 10);
expr = "-0.5";
EXPECT (mpf_fits_ulong_p, 0);
EXPECT (mpf_fits_uint_p, 0);
EXPECT (mpf_fits_ushort_p, 0);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_str_or_abort (f, "1.000000000000000000000000000000000001", 16);
expr = "1.000000000000000000000000000000000001 base 16";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
EXPECT (mpf_fits_ushort_p, 1);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_str_or_abort (f, "1@1000", 16);
expr = "1@1000 base 16";
EXPECT (mpf_fits_ulong_p, 0);
EXPECT (mpf_fits_uint_p, 0);
EXPECT (mpf_fits_ushort_p, 0);
EXPECT (mpf_fits_slong_p, 0);
EXPECT (mpf_fits_sint_p, 0);
EXPECT (mpf_fits_sshort_p, 0);
mpf_set_ui (f, 1L);
mpf_mul_2exp (f, f, BITS_PER_ULONG + 1);
mpf_sub_ui (f, f, 1L);
expr = "2^(BITS_PER_ULONG+1) - 1";
EXPECT (mpf_fits_ulong_p, 0);
EXPECT (mpf_fits_uint_p, 0);
EXPECT (mpf_fits_ushort_p, 0);
EXPECT (mpf_fits_slong_p, 0);
EXPECT (mpf_fits_sint_p, 0);
EXPECT (mpf_fits_sshort_p, 0);
mpf_set_ui (f, 1L);
mpf_mul_2exp (f, f, BITS_PER_ULONG + 1);
mpf_sub_ui (f, f, 1L);
mpf_neg (f, f);
expr = "- (2^(BITS_PER_ULONG+1) - 1)";
EXPECT (mpf_fits_ulong_p, 0);
EXPECT (mpf_fits_uint_p, 0);
EXPECT (mpf_fits_ushort_p, 0);
EXPECT (mpf_fits_slong_p, 0);
EXPECT (mpf_fits_sint_p, 0);
EXPECT (mpf_fits_sshort_p, 0);
mpf_set_ui (f, 1L);
mpf_mul_2exp (f, f, BITS_PER_ULONG + 5);
mpf_sub_ui (f, f, 1L);
expr = "2^(BITS_PER_ULONG+5) - 1";
EXPECT (mpf_fits_ulong_p, 0);
EXPECT (mpf_fits_uint_p, 0);
EXPECT (mpf_fits_ushort_p, 0);
EXPECT (mpf_fits_slong_p, 0);
EXPECT (mpf_fits_sint_p, 0);
EXPECT (mpf_fits_sshort_p, 0);
if (error)
abort ();
mpf_clear (f);
mpf_clear (f0p5);
tests_end ();
exit (0);
}
long int julia(const mpf_t x, const mpf_t xr, long int xres, const mpf_t y, const mpf_t yr, long int yres, mpf_t *c, int flag, long int max_iteration,
float *iterations, int my_rank, int p, MPI_Comm comm)
{
double t0 = MPI_Wtime();
int i,j;
// Find how many rows per process.
int *rows;
rows = (int*)malloc(sizeof(int)*p);
for (i=0; i < p; i++)
rows[i] = yres/p;
for (i=0; i < yres % p; i++)
rows[i]++;
//allocate memory for each processor
if(my_rank > 0){
iterations = (float*)malloc( sizeof(float) * xres * rows[my_rank]);
assert(iterations);
}
//------------julia gmp
const double maxRadius = 4.0;
mpf_t xi, yi, x_min, x_max, y_min, y_max, savex, savex2, savey, radius, xgap, ygap, savex_a, savex_b, savey_a, savey_b, tmp, tmp1;
mpf_init(xi);
mpf_init(yi);
mpf_init(x_min);
mpf_init(x_max);
mpf_init(y_min);
mpf_init(y_max);
mpf_init(savex);
mpf_init(savex2);
mpf_init(savey);
mpf_init(radius);
mpf_init(xgap);
mpf_init(ygap);
mpf_init(savex_a);
mpf_init(savex_b);
mpf_init(savey_a);
mpf_init(savey_b);
mpf_init(tmp);
mpf_init(tmp1);
//double x_min = x - xr;
mpf_sub(x_min, x, xr);
//double x_max = x + xr;
mpf_add(x_max, x, xr);
//double y_min = y - yr;
mpf_sub(y_min, y, yr);
//double y_max = y + yr;
mpf_add(y_max, y, yr);
// spaceing between x and y points
//double xgap = (x_max - x_min) / xres;
mpf_sub(xgap, x_max, x_min);
mpf_div_ui(xgap, xgap, xres);
//double ygap = (y_max - y_min) / yres;
mpf_sub(ygap, y_max, y_min);
mpf_div_ui(ygap, ygap, yres);
//----------------------------
long long int iteration;
long long int total_number_iterations = 0;
int k = 0;
for (j = my_rank; j < yres; j+=p){
if(my_rank==0)
k = j; //needed for root
for (i = 0; i < xres; i++){
//xi = x_min + i * xgap;
mpf_mul_ui(tmp, xgap, i);
mpf_add(xi, x_min, tmp);
//yi = y_min + j * ygap;
mpf_mul_ui(tmp, ygap, j);
mpf_add(yi, y_min, tmp);
//flag betwee[n julia or mandelbrot
//savex = flag * c[0] + (1 - flag) * xi;
mpf_mul_ui(savex_a, c[0], flag);
mpf_mul_ui(savex_b, xi, (1-flag));
mpf_add(savex, savex_a, savex_b);
//savey = flag * c[1] + (1 - flag) * yi;
mpf_mul_ui(savey_a, c[1], flag);
mpf_mul_ui(savey_b, yi, (1-flag));
mpf_add(savey, savey_a, savey_b);
//radius = 0;
mpf_set_ui(radius, 0);
iteration = 0;
//while ((radius <= maxRadius) && (iteration < max_iteration)){
while ((mpf_cmp_d(radius, maxRadius)<=0) && (iteration < max_iteration)){
//savex2 = xi;
mpf_add_ui(savex2, xi, 0);
//xi = xi * xi - yi * yi + savex;
mpf_mul(xi, xi, xi);
mpf_mul(tmp, yi, yi);
mpf_sub(xi, xi, tmp);
mpf_add(xi, xi, savex);
//yi = 2.0f * savex2 * yi + savey;
mpf_mul_ui(tmp, savex2, 2);
mpf_mul(yi, yi, tmp);
mpf_add(yi, yi, savey);
//radius = xi * xi + yi * yi;
mpf_mul(tmp, xi, xi);
mpf_mul(tmp1, yi, yi);
mpf_add(radius, tmp, tmp1);
iteration++;
}
total_number_iterations += iteration;
float *p = iterations + k*xres + i;
//if (radius > maxRadius){
if (mpf_cmp_d(radius, maxRadius)>0){
//float zn = sqrt(xi*xi + yi*yi);
mpf_t zn;
mpf_init(zn);
mpf_mul(tmp, xi, xi);
mpf_mul(tmp1, yi, yi);
mpf_add(zn, tmp, tmp1);
mpf_sqrt(zn, zn);
double n = mpf_get_d(zn);
//float nu = log(log(zn) / log(2))/log(2);
double nu = log(log(n) / log(2))/log(2);
//the point has escaped at iteration at any of the iterations 0,1,2,3...
*p = iteration + 1 - nu;
}
else
// zij stays within the region up to max_iteration
{
assert(iteration==max_iteration);
*p = -1;
}
}
k++;
}
//collect various data
MPI_Status status;
if(my_rank == 0){
int i,j;
for(i = 1; i < p; i++){
for(j = 0; j < rows[i]; j++){
MPI_Recv((iterations + (i + j * p) * xres), xres, MPI_FLOAT, i, 0, comm, &status);
//MPI_Irecv((iterations + (i + j * p) * xres), xres, MPI_FLOAT, i, 0, comm, NULL);
}
}
}
else{
int i;
for(i = 0; i < rows[my_rank]; i++)
MPI_Send((iterations + i *xres), xres, MPI_FLOAT, 0, 0, comm);
}
//reduce max iteration count
long long int total_reduced_iterations = -1;
//printf("rank: %i, total_reduced_iterations: %i\n", my_rank, total_number_iterations);
MPI_Reduce(&total_number_iterations, &total_reduced_iterations, 1, MPI_LONG_LONG_INT, MPI_SUM, 0, comm);
double t4 = MPI_Wtime();
double max_reduced_time = -1;
double total_time = t4 - t0;
MPI_Reduce(&total_time, &max_reduced_time, 1, MPI_DOUBLE, MPI_MAX, 0, comm);
if(my_rank == 0){
printf("np: %i, time: %f , iterations: %lld\n",p, max_reduced_time, total_reduced_iterations);
//printf("%i\t%.2e\n", p, max_reduced_time);
}
//clear
//printf("proc: %i, total time: %lf sec, init: %lf sec, calc: %lf sec, collect: %lf\n", my_rank, t4-t0, t1-t0, t2-t1, t3-t2);
return total_reduced_iterations;
}
void
check_rand (int argc, char **argv)
{
mp_size_t size;
mp_exp_t exp;
int reps = 20000;
int i;
mpf_t u, v, w, wref;
mp_size_t bprec = 100;
mpf_t rerr, max_rerr, limit_rerr;
gmp_randstate_t rands;
if (argc > 1)
{
reps = strtol (argv[1], 0, 0);
if (argc > 2)
bprec = strtol (argv[2], 0, 0);
}
mpf_set_default_prec (bprec);
gmp_randinit_default(rands);
mpf_init_set_ui (limit_rerr, 1);
mpf_div_2exp (limit_rerr, limit_rerr, bprec);
#if VERBOSE
mpf_dump (limit_rerr);
#endif
mpf_init (rerr);
mpf_init_set_ui (max_rerr, 0);
mpf_init (u);
mpf_init (v);
mpf_init (w);
mpf_init (wref);
for (i = 0; i < reps; i++)
{
size = urandom (rands) % (2 * SIZE) - SIZE;
exp = urandom (rands) % SIZE;
mpf_rrandomb (u, rands, size, exp);
size = urandom (rands) % (2 * SIZE) - SIZE;
exp = urandom (rands) % SIZE;
mpf_rrandomb (v, rands, size, exp);
if ((urandom (rands) & 1) != 0)
mpf_add_ui (u, v, 1);
else if ((urandom (rands) & 1) != 0)
mpf_sub_ui (u, v, 1);
mpf_sub (w, u, v);
refmpf_sub (wref, u, v);
mpf_reldiff (rerr, w, wref);
if (mpf_cmp (rerr, max_rerr) > 0)
{
mpf_set (max_rerr, rerr);
#if VERBOSE
mpf_dump (max_rerr);
#endif
if (mpf_cmp (rerr, limit_rerr) > 0)
{
printf ("ERROR after %d tests\n", i);
printf (" u = ");
mpf_dump (u);
printf (" v = ");
mpf_dump (v);
printf ("wref = ");
mpf_dump (wref);
printf (" w = ");
mpf_dump (w);
abort ();
}
}
}
mpf_clear (limit_rerr);
mpf_clear (rerr);
mpf_clear (max_rerr);
mpf_clear (u);
mpf_clear (v);
mpf_clear (w);
mpf_clear (wref);
gmp_randclear(rands);
}
int main() {
pthread_t thread_a, thread_b; /* My threads*/
int i;
FILE *filePi, *fileTime;
clock_t start, end;
double cpu_time_used;
mpf_set_default_prec(BITS_PER_DIGIT * 11000000);
/* Borwein Variable Initialization */
for(i=0; i<2; i++)
for(j=0; j<2; j++)
mpf_init(params[i][j]);
mpf_init(real_pi);
mpf_init(y0Aux);
mpf_init(y0Aux2);
mpf_init(a0Aux);
mpf_init(a0Aux2);
mpf_init(pi[0]);
mpf_init(pi[1]);
mpf_init_set_str(error, "1e-10000000", 10);
/* Initial value setting */
mpf_sqrt_ui(params[A][0], 2.0); /* a0 = sqrt(2)*/
mpf_mul_ui(params[A][0], params[A][0], 4.0); /* a0 = 4 * sqrt(2) */
mpf_ui_sub(params[A][0], 6.0, params[A][0]); /* a0 = 6 - 4 * sqrt(2) */
mpf_sqrt_ui(params[Y][0], 2.0); /* y0 = sqrt(2) */
mpf_sub_ui(params[Y][0], params[Y][0], 1.0); /* y0 = sqrt(2) - 1 */
mpf_set_ui(pi[0], 0);
mpf_set_ui(pi[1], 0);
i = 1;
j = 1;
iteracoes = 0;
x = 0;
/* Load the reals digits of pi */
filePi = fopen("pi.txt", "r");
gmp_fscanf(filePi, "%Ff", real_pi);
fclose(filePi);
start = clock();
while(1){
/* y = ( 1 - (1 - y0 ^ 4) ^ 0.25 ) / ( 1 + ( 1 - y0 ^ 4) ^ 0.25 ) */
mpf_pow_ui(y0Aux, params[Y][0], 4);
mpf_ui_sub(y0Aux, 1.0, y0Aux);
mpf_sqrt(y0Aux, y0Aux);
mpf_sqrt(y0Aux, y0Aux);
mpf_add_ui(y0Aux2, y0Aux, 1.0);
mpf_ui_sub(y0Aux, 1.0, y0Aux);
mpf_div(params[Y][1], y0Aux, y0Aux2);
/* a = a0 * ( 1 + params[Y][1] ) ^ 4 - 2 ^ ( 2 * i + 3 ) * params[Y][1] * ( 1 + params[Y][1] + params[Y][1] ^ 2 ) */
/* Threads creation */
pthread_create(&thread_a, NULL, calc_a, NULL);
pthread_create(&thread_b, NULL, calc_b, NULL);
pthread_join(thread_a, NULL);
pthread_join(thread_b, NULL);
/* 2 ^ ( 2 * i + 3 ) * params[Y][1] * ( 1 + params[Y][1] + params[Y][1] ^ 2 ) */
mpf_mul(a0Aux, a0Aux, a0Aux2);
/*a0 * ( 1 + params[Y][1] ) ^ 4*/
mpf_add_ui(a0Aux2, params[Y][1], 1);
mpf_pow_ui(a0Aux2, a0Aux2, 4);
mpf_mul(a0Aux2, params[A][0], a0Aux2);
/* form the entire expression */
mpf_sub(params[A][1], a0Aux2, a0Aux);
mpf_set(params[A][0], params[A][1]);
mpf_set(params[Y][0], params[Y][1]);
mpf_ui_div(pi[j], 1, params[A][0]);
gmp_printf("\nIteracao %d | pi = %.25Ff", iteracoes, pi[j]);
/* Calculate the error */
mpf_sub(pi[(j+1)%2], real_pi, pi[j]);
mpf_abs(pi[(j+1) % 2], pi[(j+1) % 2]);
if(mpf_cmp(pi[(j+1)%2], error) < 0){
printf("\n%d iteracoes para alcancar 10 milhoes de digitos de corretos.", iteracoes);
break;
}
j = (j+1) % 2;
iteracoes++;
i++;
}
end = clock();
cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
fileTime = fopen("execution_time.txt", "w");
fprintf(fileTime, "Execution time: %f\n", cpu_time_used);
fclose(fileTime);
/* Clean up*/
for(i=0; i<2; i++)
for(j=0; j<2; j++)
mpf_clear(params[i][j]);
mpf_clear(pi[0]);
mpf_clear(pi[1]);
mpf_clear(real_pi);
mpf_clear(error);
return 0;
}
void
check_various (void)
{
mpf_t src, trunc, ceil, floor;
int n, i;
mpf_init2 (src, 512L);
mpf_init2 (trunc, 256L);
mpf_init2 (ceil, 256L);
mpf_init2 (floor, 256L);
/* 0 */
mpf_set_ui (src, 0L);
mpf_set_ui (trunc, 0L);
mpf_set_ui (ceil, 0L);
mpf_set_ui (floor, 0L);
check_all (src, trunc, ceil, floor);
/* 1 */
mpf_set_ui (src, 1L);
mpf_set_ui (trunc, 1L);
mpf_set_ui (ceil, 1L);
mpf_set_ui (floor, 1L);
check_all (src, trunc, ceil, floor);
/* 2^1024 */
mpf_set_ui (src, 1L);
mpf_mul_2exp (src, src, 1024L);
mpf_set (trunc, src);
mpf_set (ceil, src);
mpf_set (floor, src);
check_all (src, trunc, ceil, floor);
/* 1/2^1024, fraction only */
mpf_set_ui (src, 1L);
mpf_div_2exp (src, src, 1024L);
mpf_set_si (trunc, 0L);
mpf_set_si (ceil, 1L);
mpf_set_si (floor, 0L);
check_all (src, trunc, ceil, floor);
/* 1/2 */
mpf_set_ui (src, 1L);
mpf_div_2exp (src, src, 1L);
mpf_set_si (trunc, 0L);
mpf_set_si (ceil, 1L);
mpf_set_si (floor, 0L);
check_all (src, trunc, ceil, floor);
/* 123+1/2^64 */
mpf_set_ui (src, 1L);
mpf_div_2exp (src, src, 64L);
mpf_add_ui (src, src, 123L);
mpf_set_si (trunc, 123L);
mpf_set_si (ceil, 124L);
mpf_set_si (floor, 123L);
check_all (src, trunc, ceil, floor);
/* integer of full prec+1 limbs, unchanged */
n = PREC(trunc)+1;
ASSERT_ALWAYS (n <= PREC(src)+1);
EXP(src) = n;
SIZ(src) = n;
for (i = 0; i < SIZ(src); i++)
PTR(src)[i] = i+100;
mpf_set (trunc, src);
mpf_set (ceil, src);
mpf_set (floor, src);
check_all (src, trunc, ceil, floor);
/* full prec+1 limbs, 1 trimmed for integer */
n = PREC(trunc)+1;
ASSERT_ALWAYS (n <= PREC(src)+1);
EXP(src) = n-1;
SIZ(src) = n;
for (i = 0; i < SIZ(src); i++)
PTR(src)[i] = i+200;
EXP(trunc) = n-1;
SIZ(trunc) = n-1;
for (i = 0; i < SIZ(trunc); i++)
PTR(trunc)[i] = i+201;
mpf_set (floor, trunc);
mpf_add_ui (ceil, trunc, 1L);
check_all (src, trunc, ceil, floor);
/* prec+3 limbs, 2 trimmed for size */
n = PREC(trunc)+3;
ASSERT_ALWAYS (n <= PREC(src)+1);
EXP(src) = n;
SIZ(src) = n;
for (i = 0; i < SIZ(src); i++)
PTR(src)[i] = i+300;
EXP(trunc) = n;
SIZ(trunc) = n-2;
for (i = 0; i < SIZ(trunc); i++)
PTR(trunc)[i] = i+302;
mpf_set (floor, trunc);
mpf_set (ceil, trunc);
PTR(ceil)[0]++;
check_all (src, trunc, ceil, floor);
/* prec+4 limbs, 2 trimmed for size, 1 trimmed for integer */
n = PREC(trunc)+4;
ASSERT_ALWAYS (n <= PREC(src)+1);
EXP(src) = n-1;
SIZ(src) = n;
for (i = 0; i < SIZ(src); i++)
PTR(src)[i] = i+400;
EXP(trunc) = n-1;
SIZ(trunc) = n-3;
for (i = 0; i < SIZ(trunc); i++)
PTR(trunc)[i] = i+403;
mpf_set (floor, trunc);
mpf_set (ceil, trunc);
PTR(ceil)[0]++;
check_all (src, trunc, ceil, floor);
/* F.F, carry out of ceil */
EXP(src) = 1;
SIZ(src) = 2;
PTR(src)[0] = GMP_NUMB_MAX;
PTR(src)[1] = GMP_NUMB_MAX;
EXP(trunc) = 1;
SIZ(trunc) = 1;
PTR(trunc)[0] = GMP_NUMB_MAX;
mpf_set (floor, trunc);
EXP(ceil) = 2;
SIZ(ceil) = 1;
PTR(ceil)[0] = 1;
check_all (src, trunc, ceil, floor);
/* FF.F, carry out of ceil */
EXP(src) = 2;
SIZ(src) = 3;
PTR(src)[0] = GMP_NUMB_MAX;
PTR(src)[1] = GMP_NUMB_MAX;
PTR(src)[2] = GMP_NUMB_MAX;
EXP(trunc) = 2;
SIZ(trunc) = 2;
PTR(trunc)[0] = GMP_NUMB_MAX;
PTR(trunc)[1] = GMP_NUMB_MAX;
mpf_set (floor, trunc);
EXP(ceil) = 3;
SIZ(ceil) = 1;
PTR(ceil)[0] = 1;
check_all (src, trunc, ceil, floor);
mpf_clear (src);
mpf_clear (trunc);
mpf_clear (ceil);
mpf_clear (floor);
}
bool sum_test(double xf, int prec)
{
bool fail = false;
int k;
mpf_t a_k, x, xn, term, sum, sino, low_bound;
mpf_init(a_k);
mpf_init(x);
mpf_init(xn);
mpf_init(term);
mpf_init(sum);
mpf_init(sino);
mpf_init(low_bound);
long nbits = (long) floor (3.321 * prec);
mpf_set_ui(x, 1);
mpf_div_2exp(low_bound, x, nbits+32);
// Sum the series sum_k=1^\infty a_k x^k
// It should equal sin(2pi/(1+x))
mpf_set_d(x, xf);
mpf_set_ui(sum, 0);
mpf_set(xn, x);
for (k=1; k<100000; k++)
{
topsin_series(a_k, k, prec);
mpf_mul(term, a_k, xn);
mpf_add(sum, sum, term);
// If the term is small enough, we are done.
mpf_abs(term, term);
if (mpf_cmp(term, low_bound) < 0) break;
mpf_mul(xn, xn, x);
}
// Now compute sin(2pi/(1+x))
mpf_add_ui(term, x, 1);
fp_two_pi(sino, prec);
mpf_div(term, sino, term);
fp_sine(sino, term, prec);
// the sum and the sine should be equal
mpf_sub(term, sino, sum);
double zero = mpf_get_d(term);
double lim = pow(10.0, -prec);
if (fabs(zero) > lim)
{
printf("Error: Expecting precision 1.0e-%d got %g at x=%f\n", prec, zero, xf);
fail = true;
}
mpf_clear(a_k);
mpf_clear(x);
mpf_clear(xn);
mpf_clear(term);
mpf_clear(sum);
mpf_clear(sino);
mpf_clear(low_bound);
return fail;
}
void jarvis_hypercube_approximation
(int C, /* Number of types of customers*/
int N, /* Number of servers */
mpf_t *lambda, /* arrive rate according to a Poisson process per type */
mpf_t **Tao, /* expected service time for service i and customer of node m */
int **a, /* for customers of type m, the list of preferred servers */
mpf_t **f) {
mpf_t Lambda;
mpf_t Rho;
mpf_t tao;
mpf_t *rho;
mpf_t *new_rho;
mpf_t *Q_N_rho;
mpf_t max_change;
mpf_t tmp;
mpf_init(Lambda);
rho = new mpf_t [N];
for (int i = 0; i < N;i++)
mpf_init(rho[i]);
mpf_init(tao);
mpf_init_set_ui(P__0,1);
mpf_init_set_ui(P__N,1);
Q_N_rho = new mpf_t [N];
for (int i = 0;i < N;i++)
mpf_init(Q_N_rho[i]);
new_rho = new mpf_t [N];
for (int i = 0;i < N;i++)
mpf_init(new_rho[i]);
mpf_init(Rho);
mpf_init(max_change);
mpf_init(tmp);
/* INITIALIZE: */
for (int m = 0;m < C;m++)
mpf_add(Lambda,Lambda,lambda[m]);
/* Busy probability rho_i */
for (int i = 0; i < N;i++) {
for (int m = 0; m < C;m++) {
if (a[m][0] == i) {
mpf_mul(tmp,lambda[m],Tao[i][m]);
mpf_add(rho[i],rho[i],tmp);
}
}
}
/* mean service time 'tao' */
for (int m = 0;m < C;m++) {
mpf_mul(tmp,lambda[m],Tao[a[m][0]][m]);
mpf_add(tao,tao,tmp);
}
mpf_div(tao,tao,Lambda);
/* Define intial values for P__0 and P__N */
for (int i = 0;i < N;i++) {
mpf_ui_sub(tmp,1,rho[i]);
mpf_mul(P__0,P__0,tmp);
}
for (int i = 0;i < N;i++)
mpf_mul(P__N,P__N,rho[i]);
/* ITERATION: */
do {
/*
cout << "'rho_i':";
for (int i = 0;i < N;i++) cout << " " << mpf_get_d(rho[i]);
cout << endl;
*/
/* traffic intensity */
mpf_mul(Rho,Lambda,tao);
mpf_div_ui(Rho,Rho,N);
/* Compute Q(N,'rho',k) */
for (int k = 0;k < N;k++)
correction_factor_Q(Q_N_rho[k],N,Rho,k);
/* Compute f_{im} */
mpf_t rho_a_ml;
mpf_init(rho_a_ml);
for (int i = 0;i < N;i++) {
for (int m = 0;m < C;m++) {
mpf_set_ui(rho_a_ml,1);
for (int k = 0;k < N;k++) {
if (a[m][k] == i) {
mpf_ui_sub(tmp,1,rho[i]);
mpf_mul(tmp,tmp,rho_a_ml);
mpf_mul(f[i][m],tmp,Q_N_rho[k]);
break;
}
mpf_mul(rho_a_ml,rho_a_ml,rho[a[m][k]]);
}
}
}
mpf_clear(rho_a_ml);
/* Aproximation of 'rho'_i */
mpf_t Vi;
mpf_init(Vi);
mpf_init(rho_a_ml);
for (int i = 0;i < N;i++) {
mpf_set_ui(Vi,0);
for (int m = 0;m < C;m++) {
mpf_set_ui(rho_a_ml,1);
for (int k = 0;k < N;k++) {
if (a[m][k] == i) {
mpf_mul(tmp,lambda[m],Tao[i][m]);
mpf_mul(tmp,tmp,Q_N_rho[k]);
mpf_mul(tmp,tmp,rho_a_ml);
mpf_add(Vi,Vi,tmp);
/* Vi += lambda[m] * Tao[i][m] * Q_N_rho[k] * rho_a_ml */
break;
}
mpf_mul(rho_a_ml,rho_a_ml,rho[a[m][k]]);
}
}
mpf_add_ui(tmp,Vi,1);
mpf_div(new_rho[i],Vi,tmp);
}
mpf_clear(rho_a_ml);
mpf_clear(Vi);
/* Convergence criterion */
mpf_set_ui(max_change,0);
for (int i = 0;i < N;i++) {
mpf_sub(tmp,rho[i],new_rho[i]);
mpf_abs(tmp,tmp);
if (mpf_cmp(tmp,max_change) > 0)
mpf_set(max_change,tmp);
}
/*
cout << "max change = " << mpf_get_d(max_change);
if (mpf_cmp_d(max_change,JARVIS_EPSILON) < 0)
cout << " **STOP**" << endl;
else
cout << "\r";
*/
if (mpf_cmp_d(max_change,JARVIS_EPSILON) < 0) break; /* STOP */
for (int i = 0;i < N;i++)
mpf_set(rho[i],new_rho[i]);
/* Compute P__0 */
mpf_set_ui(P__0,1);
for (int i = 0;i < N;i++) {
mpf_ui_sub(tmp,1,rho[i]);
mpf_mul(P__0,P__0,tmp);
}
/* Compute P__N */
mpf_t s_rho;
mpf_init(s_rho);
for (int i = 0;i < N;i++)
mpf_add(s_rho,s_rho,rho[i]);
mpf_div_ui(tmp,s_rho,N);
mpf_div(tmp,tmp,Rho);
mpf_ui_sub(P__N,1,tmp);
/* Compute mean service time 'tao' */
mpf_t aux;
mpf_set_ui(tao,0);
mpf_init(aux);
for (int m = 0;m < C;m++) {
mpf_set_ui(tmp,0);
for (int i = 0;i < N;i++) {
mpf_mul(aux,Tao[i][m],f[i][m]);
mpf_add(tmp,tmp,aux);
}
mpf_mul(tmp,lambda[m],tmp);
mpf_add(tao,tao,tmp);
}
mpf_div(tao,tao,Lambda); // / Lambda
mpf_ui_sub(aux,1,P__N); // 1 - P__N
mpf_div(tao,tao,aux); // / (1 - P__N)
mpf_clear(aux);
} while (1);
/*
cout << "finsh jarvis" << endl;
for (int i = 0;i < N;i++) {
for (int m = 0;m < C;m++) {
cout << mpf_get_d(f[i][m]) << " ";
}
cout << endl;
}
*/
mpf_clear(tmp);
mpf_clear(max_change);
mpf_clear(Rho);
for (int i = 0;i < N;i++)
mpf_clear(new_rho[i]);
delete [] new_rho;
for (int i = 0;i < N;i++)
mpf_clear(Q_N_rho[i]);
delete [] Q_N_rho;
mpf_clear(P__N);
mpf_clear(P__0);
mpf_clear(tao);
for (int i = 0;i < N;i++)
mpf_clear(rho[i]);
delete [] rho;
mpf_clear(Lambda);
}
void
check_random (long reps)
{
unsigned long test;
gmp_randstate_ptr rands = RANDS;
mpf_t a, b, x;
mpz_t ds;
int hibits, lshift1, lshift2;
int xtra;
#define HIBITS 10
#define LSHIFT1 10
#define LSHIFT2 10
mpf_set_default_prec ((1 << HIBITS) + (1 << LSHIFT1) + (1 << LSHIFT2));
mpz_init (ds);
mpf_inits (a, b, x, NULL);
for (test = 0; test < reps; test++)
{
mpz_urandomb (ds, rands, HIBITS);
hibits = mpz_get_ui (ds) + 1;
mpz_urandomb (ds, rands, hibits);
mpz_setbit (ds, hibits - 1); /* make sure msb is set */
mpf_set_z (a, ds);
mpf_set_z (b, ds);
mpz_urandomb (ds, rands, LSHIFT1);
lshift1 = mpz_get_ui (ds);
mpf_mul_2exp (a, a, lshift1 + 1);
mpf_mul_2exp (b, b, lshift1 + 1);
mpf_add_ui (a, a, 1); /* make a one-bit difference */
mpz_urandomb (ds, rands, LSHIFT2);
lshift2 = mpz_get_ui (ds);
mpf_mul_2exp (a, a, lshift2);
mpf_mul_2exp (b, b, lshift2);
mpz_urandomb (ds, rands, lshift2);
mpf_set_z (x, ds);
mpf_add (a, a, x);
mpf_add (b, b, x);
insert_random_low_zero_limbs (a, rands);
insert_random_low_zero_limbs (b, rands);
if (mpf_eq (a, b, lshift1 + hibits) == 0 ||
mpf_eq (b, a, lshift1 + hibits) == 0)
{
dump_abort (a, b, lshift1 + hibits, lshift1, lshift2, hibits, 1, test);
}
for (xtra = 1; xtra < 100; xtra++)
if (mpf_eq (a, b, lshift1 + hibits + xtra) != 0 ||
mpf_eq (b, a, lshift1 + hibits + xtra) != 0)
{
dump_abort (a, b, lshift1 + hibits + xtra, lshift1, lshift2, hibits, 0, test);
}
}
mpf_clears (a, b, x, NULL);
mpz_clear (ds);
}
/**
* Algoritmo de Borwein
*
* a1 se aproxima do valor de 1/PI.
* Cada iteração quadruplica o número de dígitos corretos.
*
*/
void gmp_borwein()
{
/*variáveis para calculo com respectivos valores iniciais*/
mpf_t a0, a1, y0, y1, aux1, aux2;
/*contador de iterações*/
long unsigned int k=0;
//mpf_set_default_prec(33220); /*define a precisao do float em bits*/
mpf_set_default_prec(33219280);//(33219280); /*define a precisao do float em bits*/
mpf_init(a0),mpf_init(a1),mpf_init(y0),mpf_init(y1),mpf_init(aux1),mpf_init(aux2); /*Inicializa as variáveis em 0*/
/*seta os valores inicias das váriaveis de precisão variável*/
/*a0 = 6-4*sqrt(2)*/
mpf_set_ui(aux1,2);
mpf_sqrt(aux1,aux1); /*sqrt(2)*/
mpf_mul_ui(a0,aux1,4);
mpf_ui_sub(a0,6,a0);
//mpf_set_d(a0, 6-4*sqrt(2));
mpf_sub_ui(y0,aux1,1); /*y0 = sqrt(2)-1*/
while(k<12)
{
/*y1 = (1-sqrt(sqrt((1-pow(y0,4))))) / (1+sqrt(sqrt(1-pow(y0,4))));*/
mpf_pow_ui(y1,y0,4); /*y1 = pow(y0,4)*/
mpf_ui_sub(y1,1,y1); /*y1 = 1 - y1*/
mpf_sqrt(y1,y1);
mpf_sqrt(y1,y1);
mpf_ui_sub(aux1,1,y1);
mpf_add_ui(aux2,y1,1);
mpf_div(y1,aux1,aux2);
/*a1 = a0*pow(1 + y1,4) - pow(2,2*k+3)*y1*(1+y1+pow(y1,2));*/
mpf_add_ui(a1,y1,1); /*a1 = y1+1*/
mpf_pow_ui(a1,a1,4); /*a1 = a1^4*/
mpf_mul(a1,a0,a1); /*a1 = a0*a1*/
mpf_pow_ui(aux2,y1,2); /*aux2 = pow(y1,2)*/
mpf_add(aux2,aux2,y1); /*aux2 += y1*/
mpf_add_ui(aux2,aux2,1); /*aux2++*/
mpf_mul(aux2,aux2,y1); /*aux2 *= y1*/
mpf_set_ui(aux1,2); /* aux1=2 */
mpf_pow_ui(aux1,aux1,2*k+3); /* aux1 = pow(aux1,2*k+3)*/
mpf_mul(aux1,aux1,aux2); /*aux1 = aux1*aux2*/
mpf_sub(a1,a1,aux1);
/*troca os valores das variáveis de maneira eficiente*/
mpf_swap(a0,a1);
mpf_swap(y0,y1);
k++;
/*gmp_printf("k=%ld, y1=%.*Ff, 1/PI=%.*Ff\n", k, 20, y1, 20, a1);
gmp_printf("a0=%.*Ff, y0=%.*Ff\n", 20, a0, 20, y0);*/
}
mpf_ui_div(a1,1,a1); /*PI=1/a1*/
gmp_printf("%.*Ff\n",10000000,a1);
mpf_clear(a0),mpf_clear(a1),mpf_clear(y0),mpf_clear(y1),mpf_clear(aux1),mpf_clear(aux2); /*Limpa as variáveis da memória*/
}
int main ()
{
int i = 0; /*Contador de iterações*/
int k = 8; /*Fator de multiplicação*/
mpf_t pi_pas, pi_novo;
mpf_t a_pas, a_novo;
mpf_t y_pas, y_novo;
mpf_t temp1, temp2;
mpf_t e;
FILE *fileTime; /*Ponteiro do arquivo de saída*/
clock_t start, end;
double cpu_time_used;
mpf_set_default_prec(BITS_PER_DIGIT * 11000000); /*Precisão default*/
/*Inicialização das variáveis*/
mpf_init(pi_pas);
mpf_init(pi_novo);
mpf_init(a_pas);
mpf_init(y_pas);
mpf_init(temp1);
mpf_init(temp2);
mpf_init_set_d(a_novo, 32.0);
mpf_sqrt(a_novo, a_novo);
mpf_ui_sub(a_novo, 6, a_novo);
mpf_init_set_d(y_novo, 2.0);
mpf_sqrt(y_novo, y_novo);
mpf_sub_ui(y_novo, y_novo, 1);
mpf_init_set_str(e, "1e-10000000", 10);
mpf_ui_div(pi_novo, 1, a_novo);
start = clock();
/*Calcula as iterações*/
do
{
mpf_swap(pi_pas, pi_novo);
mpf_swap(a_pas, a_novo);
mpf_swap(y_pas, y_novo);
mpf_pow_ui(y_pas, y_pas, 4);
mpf_ui_sub(y_pas, 1, y_pas);
mpf_sqrt(y_pas, y_pas);
mpf_sqrt(y_pas, y_pas);
mpf_add_ui(temp1, y_pas, 1);
mpf_ui_sub(y_novo, 1, y_pas);
mpf_div(y_novo, y_novo, temp1);
mpf_add_ui(temp1, y_novo, 1);
mpf_pow_ui(temp2, y_novo, 2);
mpf_add(temp2, temp2, temp1);
mpf_mul(temp2, temp2, y_novo);
mpf_mul_ui(temp2, temp2, k);
k *= 4;
mpf_pow_ui(temp1, temp1, 4);
mpf_mul(temp1, temp1, a_pas);
mpf_sub(a_novo, temp1, temp2);
mpf_ui_div(pi_novo, 1, a_novo);
mpf_sub(pi_pas, pi_novo, pi_pas);
mpf_abs(pi_pas, pi_pas);
gmp_printf("\nIteracao %d | pi = %.25Ff", i, pi_novo);
i++;
} while ( mpf_cmp(e, pi_pas) < 0 );
end = clock();
cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
fileTime = fopen("execution_time.txt", "w");
fprintf(fileTime, "Execution time: %f\n", cpu_time_used);
fclose(fileTime);
/*Libera espaço de memória*/
mpf_clear(pi_pas);
mpf_clear(pi_novo);
mpf_clear(a_pas);
mpf_clear(a_novo);
mpf_clear(y_pas);
mpf_clear(y_novo);
mpf_clear(temp1);
mpf_clear(temp2);
mpf_clear(e);
return 0;
}
