void _asinrat( PRAT *px, int32_t precision)
{
CREATETAYLOR();
DUPRAT(pret,*px);
DUPRAT(thisterm,*px);
DUPNUM(n2,num_one);
do
{
NEXTTERM(xx,MULNUM(n2) MULNUM(n2)
INC(n2) DIVNUM(n2) INC(n2) DIVNUM(n2), precision);
}
while ( !SMALL_ENOUGH_RAT( thisterm, precision) );
DESTROYTAYLOR();
}
void _acosrat( PRAT *px, int32_t precision)
{
CREATETAYLOR();
createrat(thisterm);
thisterm->pp=longtonum( 1L, BASEX );
thisterm->pq=longtonum( 1L, BASEX );
DUPNUM(n2,num_one);
do
{
NEXTTERM(xx,MULNUM(n2) MULNUM(n2)
INC(n2) DIVNUM(n2) INC(n2) DIVNUM(n2), precision);
}
while ( !SMALL_ENOUGH_RAT( thisterm, precision) );
DESTROYTAYLOR();
}
void _sinhrat(PRAT* px, int32_t precision)
{
if (!IsValidForHypFunc(*px, precision))
{
// Don't attempt exp of anything large or small
throw(CALC_E_DOMAIN);
}
CREATETAYLOR();
DUPRAT(pret, *px);
DUPRAT(thisterm, pret);
DUPNUM(n2, num_one);
do
{
NEXTTERM(xx, INC(n2) DIVNUM(n2) INC(n2) DIVNUM(n2), precision);
} while (!SMALL_ENOUGH_RAT(thisterm, precision));
DESTROYTAYLOR();
}
void _gamma( PRAT *pn, uint32_t radix, int32_t precision)
{
PRAT factorial= nullptr;
PNUMBER count= nullptr;
PRAT tmp= nullptr;
PRAT one_pt_five= nullptr;
PRAT a= nullptr;
PRAT a2= nullptr;
PRAT term= nullptr;
PRAT sum= nullptr;
PRAT err= nullptr;
PRAT mpy= nullptr;
PRAT ratprec = nullptr;
PRAT ratRadix = nullptr;
long oldprec;
// Set up constants and initial conditions
oldprec = precision;
ratprec = longtorat( oldprec );
// Find the best 'A' for convergence to the required precision.
a=longtorat( radix );
lograt(&a, precision);
mulrat(&a, ratprec, precision);
// Really is -ln(n)+1, but -ln(n) will be < 1
// if we scale n between 0.5 and 1.5
addrat(&a, rat_two, precision);
DUPRAT(tmp,a);
lograt(&tmp, precision);
mulrat(&tmp, *pn, precision);
addrat(&a, tmp, precision);
addrat(&a, rat_one, precision);
// Calculate the necessary bump in precision and up the precision.
// The following code is equivalent to
// precision += ln(exp(a)*pow(a,n+1.5))-ln(radix));
DUPRAT(tmp,*pn);
one_pt_five=longtorat( 3L );
divrat( &one_pt_five, rat_two, precision);
addrat( &tmp, one_pt_five, precision);
DUPRAT(term,a);
powratcomp( &term, tmp, radix, precision);
DUPRAT( tmp, a );
exprat( &tmp, radix, precision);
mulrat( &term, tmp, precision);
lograt( &term, precision);
ratRadix = longtorat(radix);
DUPRAT(tmp,ratRadix);
lograt( &tmp, precision);
subrat( &term, tmp, precision);
precision += rattolong( term, radix, precision);
// Set up initial terms for series, refer to series in above comment block.
DUPRAT(factorial,rat_one); // Start factorial out with one
count = longtonum( 0L, BASEX );
DUPRAT(mpy,a);
powratcomp(&mpy,*pn, radix, precision);
// a2=a^2
DUPRAT(a2,a);
mulrat(&a2, a, precision);
// sum=(1/n)-(a/(n+1))
DUPRAT(sum,rat_one);
divrat(&sum, *pn, precision);
DUPRAT(tmp,*pn);
addrat(&tmp, rat_one, precision);
DUPRAT(term,a);
divrat(&term, tmp, precision);
subrat(&sum, term, precision);
DUPRAT(err,ratRadix);
NEGATE(ratprec);
powratcomp(&err,ratprec, radix, precision);
divrat(&err, ratRadix, precision);
// Just get something not tiny in term
DUPRAT(term, rat_two );
// Loop until precision is reached, or asked to halt.
while ( !zerrat( term ) && rat_gt( term, err, precision) )
{
addrat(pn, rat_two, precision);
// WARNING: mixing numbers and rationals here.
// for speed and efficiency.
INC(count);
mulnumx(&(factorial->pp),count);
INC(count)
mulnumx(&(factorial->pp),count);
divrat(&factorial, a2, precision);
DUPRAT(tmp,*pn);
addrat( &tmp, rat_one, precision);
destroyrat(term);
createrat(term);
DUPNUM(term->pp,count);
DUPNUM(term->pq,num_one);
addrat( &term, rat_one, precision);
mulrat( &term, tmp, precision);
DUPRAT(tmp,a);
divrat( &tmp, term, precision);
DUPRAT(term,rat_one);
divrat( &term, *pn, precision);
subrat( &term, tmp, precision);
divrat (&term, factorial, precision);
addrat( &sum, term, precision);
ABSRAT(term);
}
// Multiply by factor.
mulrat( &sum, mpy, precision);
// And cleanup
precision = oldprec;
destroyrat(ratprec);
destroyrat(err);
destroyrat(term);
destroyrat(a);
destroyrat(a2);
destroyrat(tmp);
destroyrat(one_pt_five);
destroynum(count);
destroyrat(factorial);
destroyrat(*pn);
DUPRAT(*pn,sum);
destroyrat(sum);
}
