char
_lngamma(
floatnum x,
int digits)
{
floatstruct factor;
int infinity;
char result;
if (float_cmp(x, &c1) == 0 || float_cmp(x, &c2) == 0)
return _setzero(x);
float_create(&factor);
result = _lngamma_prim(x, &factor, &infinity, digits)
&& infinity == 0;
if (result)
{
float_abs(&factor);
_ln(&factor, digits + 1);
result = float_sub(x, x, &factor, digits+1);
}
float_free(&factor);
if (infinity != 0)
return _seterror(x, ZeroDivide);
if (!result)
float_setnan(x);
return result;
}
/* evaluates tan x for |x| <= pi.
A return value of 0 indicates
that x = +/- pi/2 within
small tolerances, so that tan x
cannot be reliable computed */
char
_tan(
floatnum x,
int digits)
{
signed char sgn;
sgn = float_getsign(x);
float_abs(x);
if (float_cmp(x, &cPiDiv2) > 0)
{
float_sub(x, &cPi, x, digits+1);
sgn = -sgn;
}
if (float_cmp(x, &cPiDiv4) <= 0)
_tanltPiDiv4(x, digits);
else
{
float_sub(x, &cPiDiv2, x, digits+1);
if (float_iszero(x) || float_getexponent(x) < -digits)
return 0;
_tanltPiDiv4(x, digits);
float_reciprocal(x, digits);
}
float_setsign(x, sgn);
return 1;
}
Error float_out(
p_otokens tokens,
floatnum x,
int scale,
signed char base,
char outmode)
{
t_number_desc n;
_emptytokens(tokens);
/* do some sanity checks first */
if (!_validmode(outmode) || scale < 0 || !_isvalidbase(base))
return InvalidParam;
_clearnumber(&n);
if (float_iszero(x))
n.prefix.base = IO_BASE_ZERO;
else if (!float_isnan(x))
n.prefix.base = base;
if (!_isvalidbase(n.prefix.base))
/* NaN and 0 are handled here */
return desc2str(tokens, &n, 0);
n.prefix.sign = float_getsign(x);
float_abs(x);
switch (outmode)
{
case IO_MODE_FIXPOINT:
return _outfixp(tokens, x, &n, scale);
case IO_MODE_ENG:
return _outeng(tokens, x, &n, scale);
case IO_MODE_COMPLEMENT:
return _outcompl(tokens, x, &n, 0);
default:
return _outsci(tokens, x, &n, scale);
}
}
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;
}
void
_cos(
floatnum x,
int digits)
{
signed char sgn;
float_abs(x);
sgn = 1;
if (float_cmp(x, &cPiDiv2) > 0)
{
sgn = -1;
float_sub(x, &cPi, x, digits+1);
}
if (float_cmp(x, &cPiDiv4) <= 0)
{
if (2*float_getexponent(x)+2 < - digits)
float_setzero(x);
else
_cosminus1ltPiDiv4(x, digits);
float_add(x, x, &c1, digits);
}
else
{
float_sub(x, &cPiDiv2, x, digits+1);
_sinltPiDiv4(x, digits);
}
float_setsign(x, sgn);
}
char
_cosminus1ltPiDiv4(
floatnum x,
int digits)
{
floatstruct tmp;
int reductions;
if (float_iszero(x))
return 1;
float_abs(x);
reductions = 0;
while(float_getexponent(x) >= -2)
{
float_mul(x, x, &c1Div2, digits+1);
++reductions;
}
if (!cosminus1near0(x, digits) && reductions == 0)
return !float_iszero(x);
float_create(&tmp);
for(; reductions-- > 0;)
{
float_mul(&tmp, x, x, digits);
float_add(x, x, x, digits+2);
float_add(x, x, &tmp, digits+2);
float_add(x, x, x, digits+2);
}
float_free(&tmp);
return 1;
}
/* evaluates cos x - 1 for |x| <= pi.
This function may underflow, which
is indicated by the return value 0 */
char
_cosminus1(
floatnum x,
int digits)
{
float_abs(x);
if (float_cmp(x, &cPiDiv4) <= 0)
return _cosminus1ltPiDiv4(x, digits);
_cos(x, digits);
float_sub(x, x, &c1, digits);
return 1;
}
char
float_tanh(
floatnum x,
int digits)
{
signed char sgn;
if (!chckmathparam(x, digits))
return 0;
sgn = float_getsign(x);
float_abs(x);
if (float_cmp(x, &c1Div2) >= 0)
_tanhgt0_5(x, digits);
else
_tanhlt0_5(x, digits);
float_setsign(x, sgn);
return 1;
}
/* 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);
}
}
char
float_raise(
floatnum power,
cfloatnum base,
cfloatnum exponent,
int digits)
{
signed char sgn;
if (float_isnan(exponent) || float_isnan(base))
return _seterror(power, NoOperand);
if (digits <= 0 || digits > MATHPRECISION)
return _seterror(power, InvalidPrecision);
if (float_iszero(base))
{
switch(float_getsign(exponent))
{
case 0:
return _seterror(power, OutOfDomain);
case -1:
return _seterror(power, ZeroDivide);
}
return _setzero(power);
}
sgn = float_getsign(base);
if (sgn < 0)
{
if (!float_isinteger(exponent))
return _seterror(power, OutOfDomain);
if ((float_getdigit(exponent, float_getexponent(exponent)) & 1) == 0)
sgn = 1;
}
float_copy(power, base, digits+1);
float_abs(power);
if (!_raise(power, exponent, digits))
{
float_seterror(Overflow);
if (float_getexponent(base) * float_getsign(exponent) < 0)
float_seterror(Underflow);
return _setnan(power);
}
float_setsign(power, sgn);
return 1;
}
/* 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);
}
/* evaluate sin x for |x| <= pi/4,
using |sin x| = sqrt((1-cos x)*(2 + cos x-1))
relative error for 100 digit results is < 6e-100*/
void
_sinltPiDiv4(
floatnum x,
int digits)
{
floatstruct tmp;
signed char sgn;
if (2*float_getexponent(x)+2 < -digits)
/* for small x: sin x approx.== x */
return;
float_create(&tmp);
sgn = float_getsign(x);
_cosminus1ltPiDiv4(x, digits);
float_add(&tmp, x, &c2, digits+1);
float_mul(x, x, &tmp, digits+1);
float_abs(x);
float_sqrt(x, digits);
float_setsign(x, sgn);
float_free(&tmp);
}
/* evaluates arccos x for -1 <= x <= 1.
The result is in the range 0 <= result <= pi.
The relative error for a 100 digit result is < 5e-100 */
void
_arccos(
floatnum x,
int digits)
{
signed char sgn;
sgn = float_getsign(x);
float_abs(x);
if (float_cmp(x, &c1Div2) > 0)
{
float_sub(x, x, &c1, digits+1);
_arccosxplus1lt0_5(x, digits);
}
else
{
_arcsinlt0_5(x, digits);
float_sub(x, &cPiDiv2, x, digits+1);
}
if (sgn < 0)
float_sub(x, &cPi, x, digits+1);
}
int main()
{
printf("%d \n",int_abs(-5));
printf("%d",float_abs(-5.123));
return 0;
}
