void zetadk(decNumber *dk, int n, int k, decContext *ctx) {
int i;
decNumber t, r, s, v, sum, const_4;
int_to_dn(&const_4, 4, ctx);
decNumberZero(&sum);
for (i=0; i<=k; i++) {
int_to_dn(&t, n+i-1, ctx);
decNumberFactorial(&s, &t, ctx);
int_to_dn(&t, i, ctx);
decNumberPower(&r, &const_4, &t, ctx);
decNumberMultiply(&v, &s, &r, ctx);
int_to_dn(&t, n-i, ctx);
decNumberFactorial(&s, &t, ctx);
int_to_dn(&t, 2*i, ctx);
decNumberFactorial(&r, &t, ctx);
decNumberMultiply(&t, &r, &s, ctx);
decNumberDivide(&r, &v, &t, ctx);
decNumberAdd(&sum, &sum, &r, ctx);
}
int_to_dn(&t, n, ctx);
#if 1
// Don't bother rounding to int, the conversion in compile_consts
// will do this if required due to the extra precision being carries.
decNumberMultiply(dk, &t, &sum, ctx);
#else
// We can round this to integers this way....
decNumberMultiply(&s, &t, &sum, ctx);
decNumberToIntegralValue(dk, &s, ctx);
#endif
}
_RETURN_TYPE
INTERNAL_FUNCTION_NAME (DEC_TYPE x)
{
DEC_TYPE result;
decContext context;
decNumber dn_result;
decNumber dn_x;
decNumber dn_absx;
decNumber dn_logx;
decNumber dn_one;
decNumber dn_cmp;
enum rounding round;
FUNC_CONVERT_TO_DN (&x, &dn_x);
if (decNumberIsZero (&dn_x))
{
DFP_EXCEPT (FE_INVALID);
DFP_ERRNO (EDOM);
return _FBLOG0;
}
if (decNumberIsInfinite (&dn_x))
{
DFP_EXCEPT (FE_INVALID);
DFP_ERRNO (EDOM);
return decNumberIsNegative (&dn_x) ? _MIN_VALUE : _MAX_VALUE;
}
if (decNumberIsNaN (&dn_x))
{
DFP_EXCEPT (FE_INVALID);
DFP_ERRNO (EDOM);
return _FBLOGNAN;
}
decContextDefault (&context, DEFAULT_CONTEXT);
decNumberAbs (&dn_absx, &dn_x, &context);
/* For DFP, we use radix 10 instead of whatever FLT_RADIX happens to be */
decNumberLog10 (&dn_logx, &dn_absx, &context);
/* Capture the case where truncation will return the wrong result,
by rounding up if -1.0 < x < 1.0 */
round = DEC_ROUND_DOWN;
decNumberFromInt32 (&dn_one, 1);
decNumberCompare (&dn_cmp, &dn_x, &dn_one, &context);
if (-decNumberIsNegative(&dn_cmp))
{
decNumberFromInt32 (&dn_one, -1);
decNumberCompare (&dn_cmp, &dn_x, &dn_one, &context);
if (!decNumberIsNegative(&dn_cmp) && !decNumberIsZero(&dn_cmp))
round = DEC_ROUND_UP;
}
context.round = round;
decNumberToIntegralValue (&dn_result, &dn_logx, &context);
FUNC_CONVERT_FROM_DN (&dn_result, &result, &context);
/* Use _Decimal* to int casting. */
return (_RETURN_TYPE) result;
}
static __ROUND_RETURN_TYPE
IEEE_FUNCTION_NAME (DEC_TYPE x)
{
DEC_TYPE result;
decContext context;
decNumber dn_result;
decNumber dn_x;
FUNC_CONVERT_TO_DN (&x, &dn_x);
if (decNumberIsNaN (&dn_x) || decNumberIsInfinite (&dn_x)
|| x > __MAX_VALUE || x < __MIN_VALUE)
{
DFP_EXCEPT (FE_INVALID);
return (__ROUND_RETURN_TYPE) x;
}
decContextDefault (&context, DEFAULT_CONTEXT);
context.round = __ROUND_MODE;
decNumberToIntegralValue (&dn_result,&dn_x,&context);
FUNC_CONVERT_FROM_DN(&dn_result, &result, &context);
/* Use _Decimal* to __ROUND_RETURN_TYPE casting. */
return (__ROUND_RETURN_TYPE)result;
/* return (__ROUND_RETURN_TYPE)decNumberToInteger (&dn_result); */
}
INT_TYPE
DFP_TO_INT (DFP_C_TYPE x)
{
/* decNumber's decimal* types have the same format as C's _Decimal*
types, but they have different calling conventions. */
IEEE_TYPE s;
char buf[BUFMAX];
char *pos;
decNumber qval, n1, n2;
decContext context;
decContextDefault (&context, CONTEXT_INIT);
/* Need non-default rounding mode here. */
context.round = DEC_ROUND_DOWN;
HOST_TO_IEEE (x, &s);
TO_INTERNAL (&s, &n1);
/* Rescale if the exponent is less than zero. */
decNumberToIntegralValue (&n2, &n1, &context);
/* Get a value to use for the quantize call. */
decNumberFromString (&qval, (char *) "1.0", &context);
/* Force the exponent to zero. */
decNumberQuantize (&n1, &n2, &qval, &context);
/* This is based on text in N1107 section 5.1; it might turn out to be
undefined behavior instead. */
if (context.status & DEC_Invalid_operation)
{
#if defined (L_sd_to_si) || defined (L_dd_to_si) || defined (L_td_to_si)
if (decNumberIsNegative(&n2))
return INT_MIN;
else
return INT_MAX;
#elif defined (L_sd_to_di) || defined (L_dd_to_di) || defined (L_td_to_di)
if (decNumberIsNegative(&n2))
/* Find a defined constant that will work here. */
return (-9223372036854775807LL - 1LL);
else
/* Find a defined constant that will work here. */
return 9223372036854775807LL;
#elif defined (L_sd_to_usi) || defined (L_dd_to_usi) || defined (L_td_to_usi)
return UINT_MAX;
#elif defined (L_sd_to_udi) || defined (L_dd_to_udi) || defined (L_td_to_udi)
/* Find a defined constant that will work here. */
return 18446744073709551615ULL;
#endif
}
/* Get a string, which at this point will not include an exponent. */
decNumberToString (&n1, buf);
/* Ignore the fractional part. */
pos = strchr (buf, '.');
if (pos)
*pos = 0;
/* Use a C library function to convert to the integral type. */
return STR_TO_INT (buf, NULL, 10);
}
void* decSingleToIntegralValue (decSingle* _0, const decSingle* _1, decContext* ctx, int32_t rnd) noexcept
{
decNumber _0num;
decNumber _1num;
decSingleToNumber (_1, &_1num);
enum rounding prev_rnd = ctx->round;
ctx->round = (enum rounding)rnd;
decNumberToIntegralValue (&_0num, &_1num, ctx);
ctx->round = prev_rnd;
return decSingleFromNumber (_0, &_0num, ctx);
}
DEC_TYPE
INTERNAL_FUNCTION_NAME (DEC_TYPE x)
{
decContext context;
decNumber dn_result;
DEC_TYPE result;
decNumber dn_x;
FUNC_CONVERT_TO_DN (&x, &dn_x);
decContextDefault (&context, DEFAULT_CONTEXT);
decContextDefault (&context, DEFAULT_CONTEXT);
context.round = DEC_ROUND_HALF_EVEN;
decNumberToIntegralValue (&dn_result, &dn_x, &context);
decNumberToIntegralValue (&dn_result, &dn_x, &context);
FUNC_CONVERT_FROM_DN (&dn_result, &result, &context);
return result;
}
DEC_TYPE
INTERNAL_FUNCTION_NAME (DEC_TYPE x)
{
decContext context;
decNumber dn_result;
DEC_TYPE result;
decNumber dn_x;
decNumber dn_tmp;
decNumber dn_log10;
decNumber dn_one;
decNumber dn_cmp;
enum rounding round;
FUNC_CONVERT_TO_DN (&x, &dn_x);
if (decNumberIsNaN (&dn_x))
return x+x;
if (decNumberIsInfinite (&dn_x)) /* +-Inf: Inf */
return DEC_INFINITY;
if (decNumberIsZero (&dn_x)) /* Pole Error if x==0 */
{
DFP_ERRNO (ERANGE);
DFP_EXCEPT (FE_DIVBYZERO);
return -DFP_HUGE_VAL;
}
if (decNumberIsInfinite (&dn_x) && decNumberIsNegative (&dn_x))
return -x;
decContextDefault (&context, DEFAULT_CONTEXT);
decNumberAbs (&dn_tmp, &dn_x, &context);
/* For DFP, we use radix 10 instead of whatever FLT_RADIX
happens to be */
decNumberLog10 (&dn_log10, &dn_tmp, &context);
/* Capture the case where truncation will return the wrong result,
by rounding up if -1.0 < x < 1.0 */
round = DEC_ROUND_DOWN;
decNumberFromInt32 (&dn_one, 1);
decNumberCompare (&dn_cmp, &dn_x, &dn_one, &context);
if (-decNumberIsNegative(&dn_cmp))
{
decNumberFromInt32 (&dn_one, -1);
decNumberCompare (&dn_cmp, &dn_x, &dn_one, &context);
if (!decNumberIsNegative(&dn_cmp) && !decNumberIsZero(&dn_cmp))
round = DEC_ROUND_UP;
}
context.round = round;
decNumberToIntegralValue (&dn_result, &dn_log10, &context);
FUNC_CONVERT_FROM_DN (&dn_result, &result, &context);
return result;
}
DEC_TYPE
INTERNAL_FUNCTION_NAME (DEC_TYPE x)
{
decContext context;
decNumber dn_result;
DEC_TYPE result;
decNumber dn_x;
FUNC_CONVERT_TO_DN (&x, &dn_x);
if (decNumberIsNaN (&dn_x) || decNumberIsInfinite (&dn_x) ||
decNumberIsZero (&dn_x))
return x+x;
decContextDefault (&context, DEFAULT_CONTEXT);
context.round = __ROUND_MODE;
decNumberToIntegralValue (&dn_result, &dn_x, &context);
FUNC_CONVERT_FROM_DN (&dn_result, &result, &context);
if (context.status & DEC_Overflow)
DFP_EXCEPT (FE_OVERFLOW);
return result;
}
/* decNumber doesn't provide support for conversions to 64-bit integer
types, so do it the hard way. */
INT_TYPE
DFP_TO_INT (DFP_C_TYPE x)
{
/* decNumber's decimal* types have the same format as C's _Decimal*
types, but they have different calling conventions. */
/* TODO: Decimal float to integer conversions should raise FE_INVALID
if the result value does not fit into the result type. */
IEEE_TYPE s;
char buf[BUFMAX];
char *pos;
decNumber qval, n1, n2;
decContext context;
/* Use a large context to avoid losing precision. */
decContextDefault (&context, DEC_INIT_DECIMAL128);
/* Need non-default rounding mode here. */
context.round = DEC_ROUND_DOWN;
HOST_TO_IEEE (x, &s);
TO_INTERNAL (&s, &n1);
/* Rescale if the exponent is less than zero. */
decNumberToIntegralValue (&n2, &n1, &context);
/* Get a value to use for the quantize call. */
decNumberFromString (&qval, (char *) "1.", &context);
/* Force the exponent to zero. */
decNumberQuantize (&n1, &n2, &qval, &context);
/* Get a string, which at this point will not include an exponent. */
decNumberToString (&n1, buf);
/* Ignore the fractional part. */
pos = strchr (buf, '.');
if (pos)
*pos = 0;
/* Use a C library function to convert to the integral type. */
return STR_TO_INT (buf, NULL, 10);
}
static DEC_TYPE
IEEE_FUNCTION_NAME (DEC_TYPE x, DEC_TYPE y)
{
decContext context;
decNumber dn_result;
DEC_TYPE result;
DEC_TYPE absx;
decNumber dn_x;
decNumber dn_absx;
decNumber dn_y;
decNumber dn_one;
decNumber dn_two;
decNumber dn_temp;
decNumber dn_temp2;
decNumber dn_temp3;
int y_is_int;
int y_is_oddint=0;
int abs_x_vs_1;
DEC_TYPE one = DFP_CONSTANT(1.0);
DEC_TYPE two = DFP_CONSTANT(2.0);
FUNC_CONVERT_TO_DN (&x, &dn_x);
FUNC_CONVERT_TO_DN (&y, &dn_y);
FUNC_CONVERT_TO_DN (&one, &dn_one);
decContextDefault (&context, DEFAULT_CONTEXT);
if (decNumberIsZero (&dn_y))
return one;
if (decNumberIsNaN (&dn_x))
return x+x;
decNumberAbs (&dn_absx, &dn_x, &context);
FUNC_CONVERT_FROM_DN (&dn_absx, &absx, &context);
if(absx<one)
abs_x_vs_1 = -1;
else if (absx==one)
abs_x_vs_1 = 0;
else
abs_x_vs_1 = 1;
/* abs_x_vs_1 = decCompare(&dn_absx, &dn_one); */
if(abs_x_vs_1 == 0 && !decNumberIsNegative (&dn_x)) /* If x == +1 */
return one;
if (decNumberIsNaN (&dn_y))
return y+y;
/* Detect if y is odd/an integer */
decNumberToIntegralValue (&dn_temp, &dn_y, &context);
decNumberSubtract (&dn_temp2, &dn_temp, &dn_y, &context);
y_is_int = decNumberIsZero (&dn_temp2);
if (y_is_int)
{
FUNC_CONVERT_TO_DN (&two, &dn_two);
decNumberDivide (&dn_temp, &dn_y, &dn_two, &context);
decNumberToIntegralValue (&dn_temp2, &dn_temp, &context);
decNumberSubtract (&dn_temp3, &dn_temp2, &dn_temp, &context);
y_is_oddint = !decNumberIsZero (&dn_temp3);
}
/* Handle all special cases for which x = +-0 */
if (decNumberIsZero (&dn_x))
{
if(decNumberIsNegative (&dn_y))
{
if (decNumberIsInfinite (&dn_y)) /* +-0^-Inf = +Inf */
return -y;
/* Pole Error for x = +-0, y < 0 */
DFP_EXCEPT (FE_DIVBYZERO);
return decNumberIsNegative(&dn_x) && y_is_oddint ?
-DFP_HUGE_VAL : DFP_HUGE_VAL;
}
return decNumberIsNegative(&dn_x) && y_is_oddint ?
-DFP_CONSTANT(0.0) : DFP_CONSTANT(0.0);
}
/* Handle remaining special cases for x = +-Inf or y = +-Inf */
if (decNumberIsInfinite (&dn_x) || decNumberIsInfinite (&dn_y))
{
if (abs_x_vs_1 == 0) /* If (-1)^(+-Inf) */
return one;
if (abs_x_vs_1 < 0) /* x^(+-Inf), where 0<x<1 */
return decNumberIsNegative (&dn_y) ? DFP_HUGE_VAL
: DFP_CONSTANT(0.0);
if (decNumberIsNegative (&dn_y))
result = DFP_CONSTANT(0.0);
else
result = (DEC_TYPE)DEC_INFINITY;
if (y_is_oddint && decNumberIsNegative(&dn_x))
result = -result;
return result;
}
/* Domain Error: x < 0 && y is a finite non-int */
if (decNumberIsNegative (&dn_x) && !y_is_int)
{
DFP_EXCEPT (FE_INVALID);
return DFP_NAN;
}
decNumberPower (&dn_result, &dn_x, &dn_y, &context);
FUNC_CONVERT_FROM_DN (&dn_result, &result, &context);
if (context.status & DEC_Overflow)
DFP_EXCEPT (FE_OVERFLOW);
if (context.status & DEC_Underflow)
DFP_EXCEPT (FE_UNDERFLOW);
return result;
}
