void factrat(PRAT* px, uint32_t radix, int32_t precision)
{
PRAT fact = nullptr;
PRAT frac = nullptr;
PRAT neg_rat_one = nullptr;
if (rat_gt(*px, rat_max_fact, precision) || rat_lt(*px, rat_min_fact, precision))
{
// Don't attempt factorial of anything too large or small.
throw CALC_E_OVERFLOW;
}
DUPRAT(fact, rat_one);
DUPRAT(neg_rat_one, rat_one);
neg_rat_one->pp->sign *= -1;
DUPRAT(frac, *px);
fracrat(&frac, radix, precision);
// Check for negative integers and throw an error.
if ((zerrat(frac) || (LOGRATRADIX(frac) <= -precision)) && (SIGN(*px) == -1))
{
throw CALC_E_DOMAIN;
}
while (rat_gt(*px, rat_zero, precision) && (LOGRATRADIX(*px) > -precision))
{
mulrat(&fact, *px, precision);
subrat(px, rat_one, precision);
}
// Added to make numbers 'close enough' to integers use integer factorial.
if (LOGRATRADIX(*px) <= -precision)
{
DUPRAT((*px), rat_zero);
intrat(&fact, radix, precision);
}
while (rat_lt(*px, neg_rat_one, precision))
{
addrat(px, rat_one, precision);
divrat(&fact, *px, precision);
}
if (rat_neq(*px, rat_zero, precision))
{
addrat(px, rat_one, precision);
_gamma(px, radix, precision);
mulrat(px, fact, precision);
}
else
{
DUPRAT(*px, fact);
}
destroyrat(fact);
destroyrat(frac);
destroyrat(neg_rat_one);
}
void asinrat( PRAT *px, uint32_t radix, int32_t precision)
{
long sgn;
PRAT pret= nullptr;
PRAT phack= nullptr;
sgn = (*px)->pp->sign* (*px)->pq->sign;
(*px)->pp->sign = 1;
(*px)->pq->sign = 1;
// Avoid the really bad part of the asin curve near +/-1.
DUPRAT(phack,*px);
subrat(&phack, rat_one, precision);
// Since *px might be epsilon near zero we must set it to zero.
if ( rat_le(phack, rat_smallest, precision) && rat_ge(phack, rat_negsmallest, precision) )
{
destroyrat(phack);
DUPRAT( *px, pi_over_two );
}
else
{
destroyrat(phack);
if ( rat_gt( *px, pt_eight_five, precision) )
{
if ( rat_gt( *px, rat_one, precision) )
{
subrat( px, rat_one, precision);
if ( rat_gt( *px, rat_smallest, precision) )
{
throw( CALC_E_DOMAIN );
}
else
{
DUPRAT(*px,rat_one);
}
}
DUPRAT(pret,*px);
mulrat( px, pret, precision);
(*px)->pp->sign *= -1;
addrat( px, rat_one, precision);
rootrat( px, rat_two, radix, precision);
_asinrat( px, precision);
(*px)->pp->sign *= -1;
addrat( px, pi_over_two, precision);
destroyrat(pret);
}
else
{
_asinrat( px, precision);
}
}
(*px)->pp->sign = sgn;
(*px)->pq->sign = 1;
}
void atanrat( PRAT *px, uint32_t radix, int32_t precision)
{
long sgn;
PRAT tmpx= nullptr;
sgn = (*px)->pp->sign * (*px)->pq->sign;
(*px)->pp->sign = 1;
(*px)->pq->sign = 1;
if ( rat_gt( (*px), pt_eight_five, precision) )
{
if ( rat_gt( (*px), rat_two, precision) )
{
(*px)->pp->sign = sgn;
(*px)->pq->sign = 1;
DUPRAT(tmpx,rat_one);
divrat(&tmpx, (*px), precision);
_atanrat(&tmpx, precision);
tmpx->pp->sign = sgn;
tmpx->pq->sign = 1;
DUPRAT(*px,pi_over_two);
subrat(px, tmpx, precision);
destroyrat( tmpx );
}
else
{
(*px)->pp->sign = sgn;
DUPRAT(tmpx,*px);
mulrat( &tmpx, *px, precision);
addrat( &tmpx, rat_one, precision);
rootrat( &tmpx, rat_two, radix, precision);
divrat( px, tmpx, precision);
destroyrat( tmpx );
asinrat( px, radix, precision);
(*px)->pp->sign = sgn;
(*px)->pq->sign = 1;
}
}
else
{
(*px)->pp->sign = sgn;
(*px)->pq->sign = 1;
_atanrat( px, precision);
}
if ( rat_gt( *px, pi_over_two, precision) )
{
subrat( px, pi, precision);
}
}
void coshrat(PRAT* px, uint32_t radix, int32_t precision)
{
PRAT tmpx = nullptr;
(*px)->pp->sign = 1;
(*px)->pq->sign = 1;
if (rat_ge(*px, rat_one, precision))
{
DUPRAT(tmpx, *px);
exprat(px, radix, precision);
tmpx->pp->sign *= -1;
exprat(&tmpx, radix, precision);
addrat(px, tmpx, precision);
divrat(px, rat_two, precision);
destroyrat(tmpx);
}
else
{
_coshrat(px, radix, precision);
}
// Since *px might be epsilon below 1 due to TRIMIT
// we need this trick here.
if (rat_lt(*px, rat_one, precision))
{
DUPRAT(*px, rat_one);
}
}
void tanhrat(PRAT* px, uint32_t radix, int32_t precision)
{
PRAT ptmp = nullptr;
DUPRAT(ptmp, *px);
sinhrat(px, radix, precision);
coshrat(&ptmp, radix, precision);
mulnumx(&((*px)->pp), ptmp->pq);
mulnumx(&((*px)->pq), ptmp->pp);
destroyrat(ptmp);
}
bool IsValidForHypFunc(PRAT px, int32_t precision)
{
PRAT ptmp = nullptr;
bool bRet = true;
DUPRAT(ptmp, rat_min_exp);
divrat(&ptmp, rat_ten, precision);
if (rat_lt(px, ptmp, precision))
{
bRet = false;
}
destroyrat(ptmp);
return bRet;
}
void sinhrat(PRAT* px, uint32_t radix, int32_t precision)
{
PRAT tmpx = nullptr;
if (rat_ge(*px, rat_one, precision))
{
DUPRAT(tmpx, *px);
exprat(px, radix, precision);
tmpx->pp->sign *= -1;
exprat(&tmpx, radix, precision);
subrat(px, tmpx, precision);
divrat(px, rat_two, precision);
destroyrat(tmpx);
}
else
{
_sinhrat(px, precision);
}
}
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);
}