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#include <config.h>
#include <fpfilter.h>
#if (defined(_Linux_i386_))
#include <fpu_control.h>
#elif ((defined(_SunOS_)) || (defined(_IRIX_)))
#include <ieeefp.h>
#endif
//#include <float.h>
// Are u using Microsoft?!? Sorry I have no idea what a mess they do!
int round_nearest()
{
//#ifdef _Linux_i386_
fpu_control_t w;
_FPU_GETCW(w);
w = w & 0xf3ff | _FPU_RC_NEAREST;
_FPU_SETCW(w);
//#endif
//#ifdef _SunOS_
//
// fp_rnd m = FP_RN;
//
// fpsetround(m);
//
//#endif
//#ifdef _IRIX_
//
// fp_rnd m = FP_RN;
//
// fpsetround(m);
//
//#endif
return 0;
}
int round_down()
{
//#ifdef _Linux_i386_
fpu_control_t w;
_FPU_GETCW(w);
w = w & 0xf3ff | _FPU_RC_DOWN;
_FPU_SETCW(w);
//#endif
//#ifdef _SunOS_
//
// fp_rnd m = FP_RM;
//
// fpsetround(m);
//
//#endif
//#ifdef _IRIX_
//
// fp_rnd m = FP_RM;
//
// fpsetround(m);
//
//#endif
return 0;
}
int round_up()
{
//#ifdef _Linux_i386_
fpu_control_t w;
_FPU_GETCW(w);
w = w & 0xf3ff | _FPU_RC_UP;
_FPU_SETCW(w);
//#endif
//#ifdef _SunOS_
//
// fp_rnd m = FP_RP;
//
// fpsetround(m);
//
//#endif
//#ifdef _IRIX_
//
// fp_rnd m = FP_RP;
//
// fpsetround(m);
//
//#endif
return 0;
}
int round_zero()
{
//#ifdef _Linux_i386_
fpu_control_t w;
_FPU_GETCW(w);
w = w & 0xf3ff | _FPU_RC_ZERO;
_FPU_SETCW(w);
//#endif
//#ifdef _SunOS_
//
// fp_rnd m = FP_RZ;
//
// fpsetround(m);
//
//#endif
//#ifdef _IRIX_
//
// fp_rnd m = FP_RZ;
//
// fpsetround(m);
//
//#endif
return 0;
}
int horner_with_err(const double* const poly,
const unsigned long deg,
const double coeff_err,
const double in_val,
const double in_err,
double& out_val,
double& out_err)
{
unsigned long i;
int f;
double abs_in_val;
double rel_err;
f = finite(in_val);
// 1. Evaluate poly at in_val.
if (f)
f = finite(out_val = poly[0]);
for (i = 1; f && i <= deg; i++)
if (f = finite(out_val *= in_val))
f = finite(out_val += poly[i]);
// 2. Compute a bound on error. We round towards +infinity
// to make sure the bound is sufficient. Since the errors
// on each term could conspire in this way, the error is
// bounded by
// (max per-term error) * (value of abs-val-coeff poly).
// 2-1. Set MPU mode.
round_up();
// 2-2. Evaluate the polynomial whose coeffients are
// the absolute values of the coeffients of poly.
if (f)
if (f = finite(abs_in_val = fabs(in_val)))
f = finite(out_err = fabs(poly[0]));
for (i = 1; f && i <= deg; i++)
if (f = finite(out_err *= abs_in_val))
f = finite(out_err += fabs(poly[i]));
// 2-3. Compute the maximum relative error for any single term.
if (f)
f = finite(rel_err = deg * (2 * DBL_EPSILON + in_err) + coeff_err);
// 2-4. Compute a bound on error.
if (f)
f = finite(out_err *= rel_err);
// 2-5. Retrieve the original rounding mode.
round_nearest();
return f;
}
// int sign_given_err(double val, double err)
// returns some positive value if val is certainly positive,
// some negative value if val is certainly negative, and
// 0 otherwise.
int sign_given_err(const double val, const double err)
{
assert(finite(val));
assert(finite(err));
double v_l, v_h;
if (finite(v_l = val - err) && val > 0.0 && v_l > 0.0)
return 1;
else if (finite(v_h = val + err) && val < 0.0 && v_h < 0.0)
return - 1;
else
return 0;
}
double newton_for_pseudoroot(const double* const poly,
const unsigned long deg,
const double coeff_err,
const double* const deriv,
const double l0,
const double h0)
{
double l, h, l_val, l_err, h_val, h_err, m, p_val, p_err, d_val, d_err;
int l_sign, h_sign, p_sign, d_sign;
l = l0;
horner_with_err(poly, deg, coeff_err, l, 0.0, l_val, l_err);
l_sign = sign_given_err(l_val, l_err);
h = h0;
horner_with_err(poly, deg, coeff_err, h, 0.0, h_val, h_err);
h_sign = sign_given_err(h_val, h_err);
assert(l_sign * h_sign < 0);
m = (l + h) / 2.0;
while (1)
{
horner_with_err(poly, deg, coeff_err, m, 0.0, p_val, p_err);
p_sign = sign_given_err(p_val, p_err);
if (p_sign == 0 || h - l < DBL_EPSILON * h)
return m;
else if (p_sign == l_sign)
l = m;
else
h = m;
horner_with_err(deriv, deg - 1, coeff_err + DBL_EPSILON,
m, 0.0,
d_val, d_err);
m -= p_val / d_val;
if (m <= l || m >= h)
m = (l + h) / 2.0;
}
return 0.0;
}
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