_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;
}
decNumber *decNumberAGM(decNumber *res, const decNumber *x, const decNumber *y) {
int n;
decNumber a, g, t, u;
if (decNumberIsNegative(x) || decNumberIsNegative(y))
goto nan;
if (decNumberIsSpecial(x) || decNumberIsSpecial(y)) {
if (decNumberIsNaN(x) || decNumberIsNaN(y))
goto nan;
if (dn_eq0(x) || dn_eq0(y))
goto nan;
return set_inf(res);
}
decNumberCopy(&a, x);
decNumberCopy(&g, y);
for (n=0; n<1000; n++) {
if (relative_error(&a, &g, &const_1e_32))
return decNumberCopy(res, &a);
dn_add(&t, &a, &g);
dn_div2(&u, &t);
dn_multiply(&t, &a, &g);
if (dn_eq0(&t))
return decNumberZero(res);
dn_sqrt(&g, &t);
decNumberCopy(&a, &u);
}
nan: return set_NaN(res);
}
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);
}
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;
}
/**
* convert this number to an int64_t. Truncate if there is a fractional part.
* Return zero if the number cannot be represented.
*/
int64_t DigitList::getInt64() /*const*/ {
if(fHave==kInt64) {
return fUnion.fInt64;
}
// Truncate if non-integer.
// Return 0 if out of range.
// Range of in64_t is -9223372036854775808 to 9223372036854775807 (19 digits)
//
if (fDecNumber->digits + fDecNumber->exponent > 19) {
// Overflow, absolute value too big.
return 0;
}
// The number of integer digits may differ from the number of digits stored
// in the decimal number.
// for 12.345 numIntDigits = 2, number->digits = 5
// for 12E4 numIntDigits = 6, number->digits = 2
// The conversion ignores the fraction digits in the first case,
// and fakes up extra zero digits in the second.
// TODO: It would be faster to store a table of powers of ten to multiply by
// instead of looping over zero digits, multiplying each time.
int32_t numIntDigits = fDecNumber->digits + fDecNumber->exponent;
uint64_t value = 0;
for (int32_t i = 0; i < numIntDigits; i++) {
// Loop is iterating over digits starting with the most significant.
// Numbers are stored with the least significant digit at index zero.
int32_t digitIndex = fDecNumber->digits - i - 1;
int32_t v = (digitIndex >= 0) ? fDecNumber->lsu[digitIndex] : 0;
value = value * (uint64_t)10 + (uint64_t)v;
}
if (decNumberIsNegative(fDecNumber)) {
value = ~value;
value += 1;
}
int64_t svalue = (int64_t)value;
// Check overflow. It's convenient that the MSD is 9 only on overflow, the amount of
// overflow can't wrap too far. The test will also fail -0, but
// that does no harm; the right answer is 0.
if (numIntDigits == 19) {
if (( decNumberIsNegative(fDecNumber) && svalue>0) ||
(!decNumberIsNegative(fDecNumber) && svalue<0)) {
svalue = 0;
}
}
return svalue;
}
static DEC_TYPE
IEEE_FUNCTION_NAME (DEC_TYPE x)
{
decContext context;
decNumber dn_result;
DEC_TYPE result;
decNumber dn_x;
decNumber dn_two;
DEC_TYPE two = DFP_CONSTANT(2.0);
FUNC_CONVERT_TO_DN (&two, &dn_two);
FUNC_CONVERT_TO_DN (&x, &dn_x);
if (decNumberIsNaN (&dn_x))
return x+x;
if (decNumberIsInfinite (&dn_x) )
return decNumberIsNegative (&dn_x) ? DFP_CONSTANT(0.0) : x;
decContextDefault (&context, DEFAULT_CONTEXT);
/* decNumberPow (&dn_result, &dn_two, &dn_x, &context); */
decNumberPower (&dn_result, &dn_two, &dn_x, &context);
FUNC_CONVERT_FROM_DN (&dn_result, &result, &context);
if(context.status & DEC_Overflow)
DFP_EXCEPT (FE_OVERFLOW);
return result;
}
void cmplxAGM(decNumber *rx, decNumber *ry,
const decNumber *a, const decNumber *b,
const decNumber *c, const decNumber *d) {
decNumber x1, x2, y1, y2, t1, t2, u1, u2;
int n;
if (decNumberIsSpecial(a) || decNumberIsSpecial(b) ||
decNumberIsSpecial(c) || decNumberIsSpecial(d)) {
goto nan;
}
cmplxCopy(&x1, &x2, a, b);
cmplxCopy(&y1, &y2, c, d);
for (n=0; n<1000; n++) {
cmplxSubtract(&t1, &t2, &x1, &x2, &y1, &y2);
cmplxR(&u1, &t1, &t2);
dn_compare(&u2, &u1, &const_1e_32);
if (decNumberIsNegative(&u2)) {
cmplxCopy(rx, ry, &x1, &x2);
return;
}
cmplxAdd(&t1, &t2, &x1, &x2, &y1, &y2);
cmplxDiv2(&u1, &u2, &t1, &t2);
cmplxMultiply(&t1, &t2, &x1, &x2, &y1, &y2);
cmplxSqrt(&y1, &y2, &t1, &t2);
cmplxCopy(&x1, &x2, &u1, &u2);
}
nan: cmplx_NaN(rx, ry);
}
static DEC_TYPE
IEEE_FUNCTION_NAME (DEC_TYPE x)
{
decContext context;
decNumber dn_result;
DEC_TYPE result;
decNumber dn_x;
decNumber dn_one;
decNumber dn_exponent;
DEC_TYPE one = DFP_CONSTANT(1.0);
FUNC_CONVERT_TO_DN(&x, &dn_x);
FUNC_CONVERT_TO_DN(&one, &dn_one);
if (decNumberIsNaN (&dn_x))
return x+x;
if (decNumberIsInfinite (&dn_x))
return decNumberIsNegative (&dn_x) ? DFP_CONSTANT(-1.0) : x;
decContextDefault(&context, DEFAULT_CONTEXT);
decNumberExp(&dn_exponent, &dn_x, &context);
decNumberSubtract(&dn_result, &dn_exponent, &dn_one, &context);
FUNC_CONVERT_FROM_DN(&dn_result, &result, &context);
if (context.status & DEC_Overflow)
DFP_EXCEPT (FE_OVERFLOW);
return result;
}
static DEC_TYPE
IEEE_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))
return x+x;
if (decNumberIsZero (&dn_x)) /* If x == 0: Pole Error */
{
DFP_EXCEPT (FE_DIVBYZERO);
return -DFP_HUGE_VAL;
}
if (decNumberIsNegative (&dn_x)) /* If x < 0,: Domain Error */
{
DFP_EXCEPT (FE_INVALID);
return DFP_NAN;
}
if (decNumberIsInfinite (&dn_x))
return x;
decContextDefault (&context, DEFAULT_CONTEXT);
decNumberLn(&dn_result, &dn_x, &context);
FUNC_CONVERT_FROM_DN(&dn_result, &result, &context);
return result;
}
static void
decimal_to_decnumber (const REAL_VALUE_TYPE *r, decNumber *dn)
{
decContext set;
decContextDefault (&set, DEC_INIT_DECIMAL128);
set.traps = 0;
switch (r->cl)
{
case rvc_zero:
decNumberZero (dn);
break;
case rvc_inf:
decNumberFromString (dn, (char *)"Infinity", &set);
break;
case rvc_nan:
if (r->signalling)
decNumberFromString (dn, (char *)"snan", &set);
else
decNumberFromString (dn, (char *)"nan", &set);
break;
case rvc_normal:
gcc_assert (r->decimal);
decimal128ToNumber ((decimal128 *) r->sig, dn);
break;
default:
gcc_unreachable ();
}
/* Fix up sign bit. */
if (r->sign != decNumberIsNegative (dn))
dn->bits ^= DECNEG;
}
static void
decimal_from_decnumber (REAL_VALUE_TYPE *r, decNumber *dn, decContext *context)
{
memset (r, 0, sizeof (REAL_VALUE_TYPE));
r->cl = rvc_normal;
if (decNumberIsZero (dn))
r->cl = rvc_zero;
if (decNumberIsNaN (dn))
r->cl = rvc_nan;
if (decNumberIsInfinite (dn))
r->cl = rvc_inf;
if (context->status & DEC_Overflow)
r->cl = rvc_inf;
if (decNumberIsNegative (dn))
r->sign = 1;
r->decimal = 1;
if (r->cl != rvc_normal)
return;
decContextDefault (context, DEC_INIT_DECIMAL128);
context->traps = 0;
decimal128FromNumber ((decimal128 *) r->sig, dn, context);
}
/* Take a matrix descriptor and return the base register number.
* Optionally return the number of rows and columns in the matrix.
* Optionally return the sign of the initial descriptor as well.
*/
static int matrix_decompose(const decNumber *x, int *rows, int *cols, int *up) {
decNumber ax, y;
unsigned int n, base;
int r, c, u;
if (decNumberIsNegative(x)) {
dn_abs(&ax, x);
x = &ax;
u = 0;
} else
u = 1;
if (up) *up = u;
dn_mulpow10(&y, x, 4);
n = dn_to_int(&y);
base = n / 10000;
c = n % 100;
r = (n / 100) % 100;
if (c == 0)
c = r;
if (! matrix_range_check(base, r, c))
return -1;
if (c == 0) {
err(ERR_BAD_PARAM);
return -1;
}
if (rows) *rows = r;
if (cols) *cols = c;
return base;
}
static inline int
dfp_compare_op (dfp_binary_func op, DFP_C_TYPE arg_a, DFP_C_TYPE arg_b)
{
IEEE_TYPE a, b;
decContext context;
decNumber arg1, arg2, res;
int result;
HOST_TO_IEEE (arg_a, &a);
HOST_TO_IEEE (arg_b, &b);
decContextDefault (&context, CONTEXT_INIT);
context.round = CONTEXT_ROUND;
TO_INTERNAL (&a, &arg1);
TO_INTERNAL (&b, &arg2);
/* Perform the comparison. */
op (&res, &arg1, &arg2, &context);
if (CONTEXT_TRAPS && CONTEXT_ERRORS (context))
DFP_RAISE (0);
if (decNumberIsNegative (&res))
result = -1;
else if (decNumberIsZero (&res))
result = 0;
else
result = 1;
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);
decContextDefault (&context, DEFAULT_CONTEXT);
if (decNumberIsInfinite (&dn_x))
{
if (decNumberIsNegative (&dn_x))
result = -M_PI_2dl;
else
result = M_PI_2dl;
}
else
{
decNumberAtan (&dn_result, &dn_x, &context);
FUNC_CONVERT_FROM_DN (&dn_result, &result, &context);
}
return result;
}
static void
decimal_to_decnumber (const REAL_VALUE_TYPE *r, decNumber *dn)
{
decContext set;
decContextDefault (&set, DEC_INIT_DECIMAL128);
set.traps = 0;
switch (r->cl)
{
case rvc_zero:
decNumberZero (dn);
break;
case rvc_inf:
decNumberFromString (dn, "Infinity", &set);
break;
case rvc_nan:
if (r->signalling)
decNumberFromString (dn, "snan", &set);
else
decNumberFromString (dn, "nan", &set);
break;
case rvc_normal:
if (!r->decimal)
{
/* dconst{1,2,m1,half} are used in various places in
the middle-end and optimizers, allow them here
as an exception by converting them to decimal. */
if (memcmp (r, &dconst1, sizeof (*r)) == 0)
{
decNumberFromString (dn, "1", &set);
break;
}
if (memcmp (r, &dconst2, sizeof (*r)) == 0)
{
decNumberFromString (dn, "2", &set);
break;
}
if (memcmp (r, &dconstm1, sizeof (*r)) == 0)
{
decNumberFromString (dn, "-1", &set);
break;
}
if (memcmp (r, &dconsthalf, sizeof (*r)) == 0)
{
decNumberFromString (dn, "0.5", &set);
break;
}
gcc_unreachable ();
}
decimal128ToNumber ((const decimal128 *) r->sig, dn);
break;
default:
gcc_unreachable ();
}
/* Fix up sign bit. */
if (r->sign != decNumberIsNegative (dn))
dn->bits ^= DECNEG;
}
/**
* Currently, getDouble() depends on atof() to do its conversion.
*
* WARNING!!
* This is an extremely costly function. ~1/2 of the conversion time
* can be linked to this function.
*/
double
DigitList::getDouble() const
{
// TODO: fix thread safety. Can probably be finessed some by analyzing
// what public const functions can see which DigitLists.
// Like precompute fDouble for DigitLists coming in from a parse
// or from a Formattable::set(), but not for any others.
if (fHaveDouble) {
return fDouble;
}
DigitList *nonConstThis = const_cast<DigitList *>(this);
if (isZero()) {
nonConstThis->fDouble = 0.0;
if (decNumberIsNegative(fDecNumber)) {
nonConstThis->fDouble /= -1;
}
} else if (isInfinite()) {
if (std::numeric_limits<double>::has_infinity) {
nonConstThis->fDouble = std::numeric_limits<double>::infinity();
} else {
nonConstThis->fDouble = std::numeric_limits<double>::max();
}
if (!isPositive()) {
nonConstThis->fDouble = -fDouble;
}
} else {
MaybeStackArray<char, MAX_DBL_DIGITS+18> s;
// Note: 14 is a magic constant from the decNumber library documentation,
// the max number of extra characters beyond the number of digits
// needed to represent the number in string form. Add a few more
// for the additional digits we retain.
// Round down to appx. double precision, if the number is longer than that.
// Copy the number first, so that we don't modify the original.
if (getCount() > MAX_DBL_DIGITS + 3) {
DigitList numToConvert(*this);
numToConvert.reduce(); // Removes any trailing zeros, so that digit count is good.
numToConvert.round(MAX_DBL_DIGITS+3);
uprv_decNumberToString(numToConvert.fDecNumber, s);
// TODO: how many extra digits should be included for an accurate conversion?
} else {
uprv_decNumberToString(this->fDecNumber, s);
}
U_ASSERT(uprv_strlen(&s[0]) < MAX_DBL_DIGITS+18);
loadDecimalChar();
if (gDecimal != '.') {
char *decimalPt = strchr(s, '.');
if (decimalPt != NULL) {
*decimalPt = gDecimal;
}
}
char *end = NULL;
nonConstThis->fDouble = uprv_strtod(s, &end);
}
nonConstThis->fHaveDouble = TRUE;
return fDouble;
}
int
INTERNAL_FUNCTION_NAME (DEC_TYPE x, DEC_TYPE y)
{
decNumber dn_x;
decNumber dn_y;
decNumber dn_result;
decContext context;
FUNC_CONVERT_TO_DN(&x, &dn_x);
FUNC_CONVERT_TO_DN(&y, &dn_y);
if(decNumberIsNaN(&dn_x) || decNumberIsNaN(&dn_y))
return 0;
decNumberCompare (&dn_result, &dn_x, &dn_y, &context);
return (-decNumberIsNegative (&dn_result)) ||
(!decNumberIsNegative (&dn_result) && !decNumberIsZero (&dn_result));
}
DEC_TYPE
INTERNAL_FUNCTION_NAME (DEC_TYPE x, DEC_TYPE y)
{
decContext context;
DEC_TYPE result;
decNumber dn_x;
decNumber dn_y;
FUNC_CONVERT_TO_DN (&x, &dn_x);
FUNC_CONVERT_TO_DN (&y, &dn_y);
if(decNumberIsNegative (&dn_x) != decNumberIsNegative (&dn_y))
decNumberNegate (&dn_x);
decContextDefault (&context, DEFAULT_CONTEXT);
FUNC_CONVERT_FROM_DN (&dn_x, &result, &context);
return result;
}
int64_t DigitList::getInt64() /*const*/ {
// Round if non-integer. (Truncate or round?)
// Return 0 if out of range.
// Range of in64_t is -9223372036854775808 to 9223372036854775807 (19 digits)
//
if (fDecNumber->digits + fDecNumber->exponent > 19) {
// Overflow, absolute value too big.
return 0;
}
decNumber *workingNum = fDecNumber;
if (fDecNumber->exponent != 0) {
// Force to an integer, with zero exponent, rounding if necessary.
DigitList copy(*this);
DigitList zero;
uprv_decNumberQuantize(copy.fDecNumber, copy.fDecNumber, zero.fDecNumber, &fContext);
workingNum = copy.fDecNumber;
}
uint64_t value = 0;
int32_t numDigits = workingNum->digits;
for (int i = numDigits-1; i>=0 ; --i) {
int v = workingNum->lsu[i];
value = value * (uint64_t)10 + (uint64_t)v;
}
if (decNumberIsNegative(workingNum)) {
value = ~value;
value += 1;
}
int64_t svalue = (int64_t)value;
// Check overflow. It's convenient that the MSD is 9 only on overflow, the amount of
// overflow can't wrap too far. The test will also fail -0, but
// that does no harm; the right answer is 0.
if (numDigits == 19) {
if (( decNumberIsNegative(fDecNumber) && svalue>0) ||
(!decNumberIsNegative(fDecNumber) && svalue<0)) {
svalue = 0;
}
}
return svalue;
}
/**
* Currently, getDouble() depends on strtod() to do its conversion.
*
* WARNING!!
* This is an extremely costly function. ~1/2 of the conversion time
* can be linked to this function.
*/
double
DigitList::getDouble() const
{
{
Mutex mutex;
if (fHave == kDouble) {
return fUnion.fDouble;
}
}
double tDouble = 0.0;
if (isZero()) {
tDouble = 0.0;
if (decNumberIsNegative(fDecNumber)) {
tDouble /= -1;
}
} else if (isInfinite()) {
if (std::numeric_limits<double>::has_infinity) {
tDouble = std::numeric_limits<double>::infinity();
} else {
tDouble = std::numeric_limits<double>::max();
}
if (!isPositive()) {
tDouble = -tDouble; //this was incorrectly "-fDouble" originally.
}
} else {
MaybeStackArray<char, MAX_DBL_DIGITS+18> s;
// Note: 14 is a magic constant from the decNumber library documentation,
// the max number of extra characters beyond the number of digits
// needed to represent the number in string form. Add a few more
// for the additional digits we retain.
// Round down to appx. double precision, if the number is longer than that.
// Copy the number first, so that we don't modify the original.
if (getCount() > MAX_DBL_DIGITS + 3) {
DigitList numToConvert(*this);
numToConvert.reduce(); // Removes any trailing zeros, so that digit count is good.
numToConvert.round(MAX_DBL_DIGITS+3);
uprv_decNumberToString(numToConvert.fDecNumber, s.getAlias());
// TODO: how many extra digits should be included for an accurate conversion?
} else {
uprv_decNumberToString(this->fDecNumber, s.getAlias());
}
U_ASSERT(uprv_strlen(&s[0]) < MAX_DBL_DIGITS+18);
char *end = NULL;
tDouble = decimalStrToDouble(s.getAlias(), &end);
}
{
Mutex mutex;
DigitList *nonConstThis = const_cast<DigitList *>(this);
nonConstThis->internalSetDouble(tDouble);
}
return tDouble;
}
/* Convert a decimal real to a date.
* We have to honour the current date mode and make sure that things
* don't go out of range.
*/
static int extract_date(const decNumber *x, int *year, int *month, int *day) {
int ip, fp, y, m, d;
decNumber z, a;
int neg = 1;
if (is_intmode())
return 1;
if (decNumberIsNegative(x)) {
dn_minus(&z, x);
neg = -1;
} else {
decNumberCopy(&z, x);
}
decNumberTrunc(&a, &z); // a = iii z = iii.ffrrrr
ip = dn_to_int(&a);
dn_subtract(&a, &z, &a); // a = .ffrrrr
dn_mul100(&z, &a); // z = ff.rrrr
decNumberTrunc(&a, &z); // a = ff
fp = dn_to_int(&a);
dn_subtract(&z, &z, &a); // z = .rrrr
switch (UState.date_mode) {
default:
case DATE_YMD:
y = ip;
m = fp;
dn_mul100(&a, &z);
decNumberTrunc(&z, &a);
d = dn_to_int(&z);
break;
case DATE_DMY:
d = ip;
m = fp;
goto year;
case DATE_MDY:
m = ip;
d = fp;
year: dn_mulpow10(&a, &z, 4);
decNumberTrunc(&z, &a);
y = dn_to_int(&z);
break;
}
/* Make sense of things
*/
y *= neg;
if (year != NULL)
*year = y;
if (month != NULL)
*month = m;
if (day != NULL)
*day = d;
return check_date(y, m, d);
}
static DEC_TYPE
IEEE_FUNCTION_NAME (DEC_TYPE x)
{
decContext context;
decNumber dn_result;
DEC_TYPE result, one, temp;
decNumber dn_x, dn_temp, dn_one;
/* int comp;*/
one=DFP_CONSTANT(1.0);
FUNC_CONVERT_TO_DN (&one, &dn_one);
FUNC_CONVERT_TO_DN (&x, &dn_x);
/* Handle NaN and early exit for x==0 */
if (decNumberIsNaN (&dn_x) || decNumberIsZero (&dn_x))
return x + x;
decContextDefault (&context, DEFAULT_CONTEXT);
decNumberAbs (&dn_temp, &dn_x, &context);
FUNC_CONVERT_FROM_DN (&dn_temp, &temp, &context);
if(temp==one) {
/* |x| == 1 -> Pole Error */
DFP_EXCEPT (FE_DIVBYZERO);
return decNumberIsNegative(&dn_x) ? -DFP_HUGE_VAL:DFP_HUGE_VAL;
} else if (temp>one) {
/* |x| > 1 -> Domain Error (this handles +-Inf too) */
DFP_EXCEPT (FE_INVALID);
return DFP_NAN;
}
// comp = decCompare (&dn_temp, &dn_one);
// switch (comp)
// {
// case 0: /* |x| == 1 -> Pole Error */
// DFP_EXCEPT (FE_DIVBYZERO);
// return decNumberIsNegative(&dn_x) ? -DFP_HUGE_VAL:DFP_HUGE_VAL;
// case 1: /* |x| > 1 -> Domain Error (this handles +-Inf too) */
// DFP_EXCEPT (FE_INVALID);
// return DFP_NAN;
// }
/* Using trig identity: atanh(x) = 1/2 * log((1+x)/(1-x)) */
decNumberAdd (&dn_result, &dn_one, &dn_x, &context);
decNumberSubtract (&dn_temp, &dn_one, &dn_x, &context);
decNumberDivide (&dn_result, &dn_result, &dn_temp, &context);
decNumberLn (&dn_result, &dn_result, &context);
decNumberAdd (&dn_temp, &dn_one, &dn_one, &context); /* 2 */
decNumberDivide (&dn_result, &dn_result, &dn_temp, &context);
FUNC_CONVERT_FROM_DN (&dn_result, &result, &context);
return result;
}
// 60 bytes
decNumber *decNumberSign(decNumber *r, const decNumber *x) {
const decNumber *z;
if (decNumberIsNaN(x))
z = x;
else if (dn_eq0(x))
z = &const_0;
else if (decNumberIsNegative(x))
z = &const__1;
else
z = &const_1;
return decNumberCopy(r, z);
}
static DEC_TYPE
IEEE_FUNCTION_NAME (DEC_TYPE x)
{
decContext context;
decNumber dn_result;
DEC_TYPE result;
decNumber dn_x;
decNumber dn_sum;
decNumber dn_one;
DEC_TYPE one = DFP_CONSTANT(1.0);
FUNC_CONVERT_TO_DN (&x, &dn_x);
FUNC_CONVERT_TO_DN (&one, &dn_one);
/* For NaN, 0, or +Inf, just return x */
if (decNumberIsNaN (&dn_x) || decNumberIsZero (&dn_x) ||
(decNumberIsInfinite (&dn_x) && !decNumberIsNegative (&dn_x)))
return x+x;
decContextDefault(&context, DEFAULT_CONTEXT);
decNumberAdd(&dn_sum, &dn_x, &dn_one, &context);
if (decNumberIsZero(&dn_sum)) /* Pole Error if x was -1 */
{
DFP_EXCEPT (FE_DIVBYZERO);
return -DFP_HUGE_VAL;
}
if (decNumberIsNegative(&dn_sum)) /* Domain Error if x < -1 */
{
DFP_EXCEPT (FE_INVALID);
return DFP_NAN;
}
decNumberLn(&dn_result, &dn_sum, &context);
FUNC_CONVERT_FROM_DN(&dn_result, &result, &context);
return result;
}
int
PREFIXED_FUNCTION_NAME (DEC_TYPE x, DEC_TYPE y)
{
decNumber dn_x, dn_y, result;
decContext context;
decContextDefault(&context, DEFAULT_CONTEXT);
FUNC_CONVERT_TO_DN(&x, &dn_x);
FUNC_CONVERT_TO_DN(&y, &dn_y);
if(decNumberIsNaN(&dn_x) || decNumberIsNaN(&dn_y))
return -1;
decNumberCompare(&result, &dn_x, &dn_y, &context);
return !decNumberIsNegative(&result) && !decNumberIsZero(&result);
}
void convertToIntX<int64>(const decNumber* pDecNum, decContext* pContext, int64& result)
{
static const uint64 s_arrPowerOfTen[19] = {
1, 10, 100, 1000, 10000, 100000, 1000000,
10000000, 100000000, 1000000000, 10000000000ULL,
100000000000ULL, 1000000000000ULL, 10000000000000ULL,
100000000000000ULL, 1000000000000000ULL, 10000000000000000ULL,
100000000000000000ULL, 1000000000000000000ULL };
if (decNumberIsSpecial(pDecNum))
{
char sNumber[1024];
throw("Attempt to get an integer from invalid number");
}
else if (pDecNum->exponent != 0)
{
char sNumber[1024];
// FTHROW(InvalidArgumentException, "Unsupported exponent %d, only zero exponent is supported, number %s", pDecNum->exponent, decNumberToString(pDecNum, sNumber));
throw("Unsupported exponent , only zero exponent is supported, number ");
}
else if (pDecNum->digits > (int)(sizeof(s_arrPowerOfTen)/sizeof(*s_arrPowerOfTen)))
{
char sNumber[1024];
// FTHROW(InvalidArgumentException, "Overflow during conversion, number of digits is %d, number %s", pDecNum->digits, decNumberToString(pDecNum, sNumber));
throw("Overflow during conversion, number of digits is number ");
}
const decNumberUnit* pDigit = pDecNum->lsu;
uint64 nUnsignedResult = 0;
const bool isNegative = decNumberIsNegative(pDecNum);
const uint64 nMaxValue = isNegative ? -std::numeric_limits<int64>::min() : std::numeric_limits<int64>::max();
for (int i = 0; i < pDecNum->digits; ++pDigit, i += DECDPUN)
{
const uint64 nPrev = nUnsignedResult; // to be able to check on 'overflow'
nUnsignedResult += *pDigit * s_arrPowerOfTen[i];
if ((nUnsignedResult < nPrev) || (nUnsignedResult > nMaxValue))
{
char sNumber[1024];
throw("Overflow during conversion, step");
// FTHROW(InvalidArgumentException, "Overflow during conversion, step %d (%llu, %llu, %llu), number %s",
// i, nUnsignedResult, nPrev, nMaxValue, decNumberToString(pDecNum, sNumber));
}
}
result = isNegative ? -((int64)nUnsignedResult) : (int64)nUnsignedResult;
}
/* Compute a factorial.
* Currently, only for positive integer arguments. Needs to be extended
* to a full gamma function.
*/
decNumber *decNumberFactorial(decNumber *r, const decNumber *x, decContext *ctx) {
decNumber y, const_1;
int_to_dn(&const_1, 1, ctx);
decNumberCopy(&y, x);
if (!decNumberIsNegative(x) || decNumberIsZero(x)) {
decNumberCopy(r, &const_1);
for (;;) {
if (decNumberIsZero(&y))
break;
if (decNumberIsInfinite(r))
break;
decNumberMultiply(r, r, &y, ctx);
decNumberSubtract(&y, &y, &const_1, ctx);
}
}
return r;
}
/**
* Currently, getDouble() depends on strtod() to do its conversion.
*
* WARNING!!
* This is an extremely costly function. ~1/2 of the conversion time
* can be linked to this function.
*/
double
DigitList::getDouble() const
{
static char gDecimal = 0;
char decimalSeparator;
{
Mutex mutex;
if (fHave == kDouble) {
return fUnion.fDouble;
} else if(fHave == kInt64) {
return (double)fUnion.fInt64;
}
decimalSeparator = gDecimal;
}
if (decimalSeparator == 0) {
// We need to know the decimal separator character that will be used with strtod().
// Depends on the C runtime global locale.
// Most commonly is '.'
// TODO: caching could fail if the global locale is changed on the fly.
char rep[MAX_DIGITS];
sprintf(rep, "%+1.1f", 1.0);
decimalSeparator = rep[2];
}
double tDouble = 0.0;
if (isZero()) {
tDouble = 0.0;
if (decNumberIsNegative(fDecNumber)) {
tDouble /= -1;
}
} else if (isInfinite()) {
if (std::numeric_limits<double>::has_infinity) {
tDouble = std::numeric_limits<double>::infinity();
} else {
tDouble = std::numeric_limits<double>::max();
}
if (!isPositive()) {
tDouble = -tDouble; //this was incorrectly "-fDouble" originally.
}
} else {
MaybeStackArray<char, MAX_DBL_DIGITS+18> s;
// Note: 14 is a magic constant from the decNumber library documentation,
// the max number of extra characters beyond the number of digits
// needed to represent the number in string form. Add a few more
// for the additional digits we retain.
// Round down to appx. double precision, if the number is longer than that.
// Copy the number first, so that we don't modify the original.
if (getCount() > MAX_DBL_DIGITS + 3) {
DigitList numToConvert(*this);
numToConvert.reduce(); // Removes any trailing zeros, so that digit count is good.
numToConvert.round(MAX_DBL_DIGITS+3);
uprv_decNumberToString(numToConvert.fDecNumber, s);
// TODO: how many extra digits should be included for an accurate conversion?
} else {
uprv_decNumberToString(this->fDecNumber, s);
}
U_ASSERT(uprv_strlen(&s[0]) < MAX_DBL_DIGITS+18);
if (decimalSeparator != '.') {
char *decimalPt = strchr(s, '.');
if (decimalPt != NULL) {
*decimalPt = decimalSeparator;
}
}
char *end = NULL;
tDouble = uprv_strtod(s, &end);
}
{
Mutex mutex;
DigitList *nonConstThis = const_cast<DigitList *>(this);
nonConstThis->internalSetDouble(tDouble);
gDecimal = decimalSeparator;
}
return tDouble;
}
/* Smart CDF helper routine that return three values */
void cdf_Q_helper(enum nilop op) {
decNumber a, b, t, u, x2, d, absx, x;
int i;
getX(&x);
dn_abs(&absx, &x);
if (dn_lt(&absx, &const_2_326)) {
decNumberSquare(&x2, &absx);
decNumberCopy(&t, &absx);
decNumberCopy(&a, &absx);
decNumberCopy(&d, &const_3);
for (i=0;i<500; i++) {
dn_multiply(&u, &t, &x2);
dn_divide(&t, &u, &d);
dn_add(&u, &a, &t);
if (dn_eq(&u, &a))
break;
decNumberCopy(&a, &u);
dn_p2(&d, &d);
}
decNumberCopy(&b, &const_0_5);
if (decNumberIsNegative(&x))
dn_minus(&a, &a);
} else {
const decNumber *nom, *extra, *sub;
//dn_minus(&x2, &absx);
//n = ceil(extra + nom / (|x| - sub))
if (is_usrdblmode()) {
sub = &const_1_5;
nom = &const_300;
extra = &const_8;
}
else {
sub = &const_1_3;
nom = &const_100;
extra = &const_4;
}
dn_subtract(&b, &absx, sub);
dn_divide(&t, nom, &b);
dn_add(&u, &t, extra);
decNumberCeil(&b, &u);
decNumberZero(&t);
do {
dn_add(&u, &x, &t);
dn_divide(&t, &b, &u);
dn_dec(&b);
} while (! dn_eq0(&b));
dn_add(&u, &t, &x);
decNumberRecip(&a, &u);
if (decNumberIsNegative(&a)) {
dn_minus(&a, &a);
decNumberZero(&b);
} else {
dn_1(&b);
dn_minus(&a, &a);
}
}
pdf_Q(&t, &x);
setXYZ(&t, &a, &b);
}
void dn_elliptic(decNumber *sn, decNumber *cn, decNumber *dn, const decNumber *u, const decNumber *m) {
decNumber a, b, e, f, g;
decNumber s_n, c_n, d_n;
decNumber MU[ELLIPTIC_N], NU[ELLIPTIC_N], C[ELLIPTIC_N], D[ELLIPTIC_N];
decNumber sin_umu, cos_umu, t, r;
int n = 0;
#define mu(n) (MU + (n))
#define nu(n) (NU + (n))
#define c(n) (C + (n))
#define d(n) (D + (n))
if (sn == NULL) sn = &s_n;
if (cn == NULL) cn = &c_n;
if (dn == NULL) dn = &d_n;
dn_abs(&a, m);
if (dn_lt(&const_1, &a)) {
cmplx_NaN(sn, cn);
set_NaN(dn);
return;
}
if (dn_lt(&a, &const_1e_32)) {
dn_sincos(u, sn, cn);
dn_1(dn);
return;
}
dn_m1(&a, m);
if (dn_abs_lt(&a, &const_1e_32)) {
dn_sinhcosh(u, &a, &b);
decNumberRecip(cn, &b);
dn_multiply(sn, &a, cn);
decNumberCopy(dn, cn);
return;
}
dn_1(mu(0));
dn_1m(&a, m);
dn_sqrt(nu(0), &a);
for (;;) {
dn_add(&g, mu(n), nu(n));
dn_abs(&a, &g);
dn_mulpow10(&b, &a, 32);
dn_mul2(&a, &b);
dn_subtract(&e, mu(n), nu(n));
dn_abs(&f, &e);
if (dn_gt(&a, &f))
break;
dn_div2(mu(n+1), &g);
dn_multiply(&a, mu(n), nu(n));
dn_sqrt(nu(n+1), &a);
n++;
if (n >= ELLIPTIC_N-1)
break;
}
dn_multiply(&a, u, mu(n));
dn_sincos(&a, &sin_umu, &cos_umu);
if (dn_abs_lt(&sin_umu, dn_abs(&b, &cos_umu)))
dn_divide(&t, &sin_umu, &cos_umu);
else
dn_divide(&t, &cos_umu, &sin_umu);
dn_multiply(c(n), mu(n), &t);
dn_1(d(n));
while (n > 0) {
n--;
dn_multiply(c(n), d(n+1), c(n+1));
decNumberSquare(&a, c(n+1));
dn_divide(&r, &a, mu(n+1));
dn_add(&a, &r, nu(n));
dn_add(&b, &r, mu(n));
dn_divide(d(n), &a, &b);
}
cmplxAbs(&f, &b, &const_1, c(0));
if (decNumberIsNegative(&e)) {
dn_1m(&a, m);
dn_sqrt(&g, &a);
dn_divide(dn, &g, d(0));
dn_divide(cn, dn, &f);
if (decNumberIsNegative(&cos_umu))
dn_minus(cn, cn);
dn_divide(&a, c(0), &g);
dn_multiply(sn, cn, &a);
} else {
decNumberCopy(dn, d(0));
dn_divide(sn, &const_1, &f);
if (decNumberIsNegative(&sin_umu))
dn_minus(sn, sn);
dn_multiply(cn, c(0), sn);
}
#undef mu
#undef nu
#undef c
#undef d
}