static Error
_pack2frac(
floatnum x,
p_ext_seq_desc n,
int digits)
{
floatstruct tmp;
int exp;
Error result;
n->seq.digits -= n->seq.trailing0;
n->seq.trailing0 = 0;
switch(n->seq.base)
{
case IO_BASE_NAN:
float_setnan(x);
break;
case IO_BASE_ZERO:
float_setzero(x);
break;
default:
if ((result = _pack2int(x, n)) != Success)
return result;
float_create(&tmp);
float_setinteger(&tmp, n->seq.base);
_raiseposi(&tmp, &exp, n->seq.digits, digits+2);
float_div(x, x, &tmp, digits + 2);
float_setexponent(x, float_getexponent(x) - exp);
float_free(&tmp);
}
n->seq.digits += n->seq.trailing0;
return Success;
}
static Error
_packdec2int(
floatnum x,
p_ext_seq_desc n)
{
int ofs;
int exp;
int bufsz;
int i;
char buf[DECPRECISION];
float_setnan(x);
ofs = n->seq.leadingSignDigits;
exp = n->seq.trailing0;
bufsz = n->seq.digits - ofs - exp;
if (bufsz > DECPRECISION)
return IOBufferOverflow;
if (bufsz == 0)
float_setzero(x);
else
for (i = -1; ++i < bufsz;)
buf[i] = n->getdigit(ofs++, &n->seq) + '0';
float_setsignificand(x, NULL, buf, bufsz);
float_setexponent(x, exp + bufsz - 1);
return Success;
}
/* series expansion of cos/cosh - 1 used for small x,
|x| <= 0.01.
The function returns 0, if an underflow occurs.
The relative error seems to be less than 5e-100 for
a 100-digit calculation with |x| < 0.01 */
char
cosminus1series(
floatnum x,
int digits,
char alternating)
{
floatstruct sum, smd;
int expsqrx, pwrsz, addsz, i;
expsqrx = 2 * float_getexponent(x);
float_setexponent(x, 0);
float_mul(x, x, x, digits+1);
float_mul(x, x, &c1Div2, digits+1);
float_setsign(x, alternating? -1 : 1);
expsqrx += float_getexponent(x);
if (float_iszero(x) || expsqrx < EXPMIN)
{
/* underflow */
float_setzero(x);
return expsqrx == 0;
}
float_setexponent(x, expsqrx);
pwrsz = digits + expsqrx + 2;
if (pwrsz <= 0)
/* for very small x, cos/cosh(x) - 1 = (-/+)0.5*x*x */
return 1;
addsz = pwrsz;
float_create(&sum);
float_create(&smd);
float_copy(&smd, x, pwrsz);
float_setzero(&sum);
i = 2;
while (pwrsz > 0)
{
float_mul(&smd, &smd, x, pwrsz+1);
float_divi(&smd, &smd, i*(2*i-1), pwrsz);
float_add(&sum, &sum, &smd, addsz);
++i;
pwrsz = digits + float_getexponent(&smd);
}
float_add(x, x, &sum, digits+1);
float_free(&sum);
float_free(&smd);
return 1;
}
static Error
_outscidec(
p_otokens tokens,
floatnum x,
p_number_desc n,
int scale)
{
float_checkedround(x, scale + 1);
n->exp = float_getexponent(x);
float_setexponent(x, 0);
_setfndesc(n, x);
return desc2str(tokens, n, scale);
}
static Error
_outengdec(
p_otokens tokens,
floatnum x,
p_number_desc n,
int scale)
{
int shift;
float_checkedround(x, scale + 1);
n->exp = float_getexponent(x);
if (n->exp < 0)
shift = 2 - (-n->exp-1) % 3;
else
shift = n->exp % 3;
float_setexponent(x, shift);
n->exp -= shift;
_setfndesc(n, x);
return desc2str(tokens, n, scale - shift);
}
char
float_lg(
floatnum x,
int digits)
{
floatstruct tmp;
int expx;
if (!chckmathparam(x, digits))
return 0;
if (float_getsign(x) <= 0)
return _seterror(x, OutOfDomain);
float_create(&tmp);
expx = float_getexponent(x);
float_setexponent(x, 0);
_ln(x, digits);
float_div(x, x, &cLn10, digits);
float_setinteger(&tmp, expx);
float_add(x, x, &tmp, digits);
float_free(&tmp);
return 1;
}