char
_trigreduce(
floatnum x,
int digits)
{
floatstruct tmp;
int expx, save;
signed char sgn;
char odd;
if (float_abscmp(x, &cPi) <= 0)
return 1;
expx = float_getexponent(x);
if (expx > float_getlength(&cPi) - digits)
return 0;
save = float_setprecision(MAXDIGITS);
float_create(&tmp);
sgn = float_getsign(x);
float_abs(x);
float_divmod(&tmp, x, x, &cPi, INTQUOT);
float_setprecision(save);
odd = float_isodd(&tmp);
if (odd)
float_sub(x, x, &cPi, digits+1);
if (sgn < 0)
float_neg(x);
float_free(&tmp);
return 1;
}
char
float_arccosxplus1(
floatnum x,
int digits)
{
if (!chckmathparam(x, digits))
return 0;
if (float_getsign(x) > 0 || float_abscmp(x, &c2) > 0)
return _seterror(x, OutOfDomain);
_arccosxplus1(x, digits);
return 1;
}
char
float_arccos(
floatnum x,
int digits)
{
if (!chckmathparam(x, digits))
return 0;
if (float_abscmp(x, &c1) > 0)
return _seterror(x, OutOfDomain);
_arccos(x, digits);
return 1;
}
/* evaluates arccos (1+x) for -2 <= x <= 0.
The result is in the range 0 <= x <= pi */
void
_arccosxplus1(
floatnum x,
int digits)
{
if (float_abscmp(x, &c1Div2) <= 0)
_arccosxplus1lt0_5(x, digits);
else
{
float_add(x, x, &c1, digits);
_arccos(x, digits);
}
}
/* evaluates arcsin x for -1 <= x <= 1.
The result is in the range -pi/2 <= result <= pi/2
The relative error for a 100 digit result is < 8e-100 */
void
_arcsin(
floatnum x,
int digits)
{
signed char sgn;
if (float_abscmp(x, &c1Div2) <= 0)
_arcsinlt0_5(x, digits);
else
{
sgn = float_getsign(x);
float_abs(x);
_arccos(x, digits);
float_sub(x, &cPiDiv2, x, digits);
float_setsign(x, sgn);
}
}
/* evaluates arctan x for all x. The result is in the
range -pi/2 < result < pi/2
relative error for a 100 digit result is 9e-100 */
void
_arctan(
floatnum x,
int digits)
{
signed char sgn;
if (float_abscmp(x, &c1) > 0)
{
sgn = float_getsign(x);
float_abs(x);
float_reciprocal(x, digits);
_arctanlt1(x, digits);
float_sub(x, &cPiDiv2, x, digits+1);
float_setsign(x, sgn);
}
else
_arctanlt1(x, digits);
}
char
float_artanhxplus1(
floatnum x,
int digits)
{
if (!chckmathparam(x, digits))
return 0;
if (float_getsign(x) >= 0 || float_abscmp(x, &c2) >= 0)
return _seterror(x, OutOfDomain);
if (float_cmp(x, &c1Div2) < 0)
{
float_neg(x);
_artanh1minusx(x, digits);
}
else
{
float_sub(x, &c1, x, digits+1);
_artanh(x, digits);
}
return 1;
}
char
float_tanhminus1(
floatnum x,
int digits)
{
if (!chckmathparam(x, digits))
return 0;
if (float_cmp(x, &c1Div2) >= 0)
return _tanhminus1gt0(x, digits)? 1 : _seterror(x, Underflow);
if (!float_iszero(x))
{
if (float_abscmp(x, &c1Div2) <= 0)
_tanhlt0_5(x, digits);
else
{
float_setsign(x, 1);
_tanhgt0_5(x, digits);
float_setsign(x, -1);
}
}
return float_sub(x, x, &c1, digits);
}