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Diffstat (limited to 'libgcc/config/libbid/bid64_round_integral.c')
-rw-r--r--libgcc/config/libbid/bid64_round_integral.c534
1 files changed, 290 insertions, 244 deletions
diff --git a/libgcc/config/libbid/bid64_round_integral.c b/libgcc/config/libbid/bid64_round_integral.c
index bbc981e4787..c777ed81195 100644
--- a/libgcc/config/libbid/bid64_round_integral.c
+++ b/libgcc/config/libbid/bid64_round_integral.c
@@ -34,7 +34,7 @@ Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
#if DECIMAL_CALL_BY_REFERENCE
void
-__bid64_round_integral_exact (UINT64 * pres,
+bid64_round_integral_exact (UINT64 * pres,
UINT64 *
px _RND_MODE_PARAM _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
@@ -44,45 +44,53 @@ __bid64_round_integral_exact (UINT64 * pres,
#endif
#else
UINT64
-__bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
+bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
UINT64 res = 0xbaddbaddbaddbaddull;
UINT64 x_sign;
- int exp; // unbiased exponent
+ int exp; // unbiased exponent
// Note: C1 represents the significand (UINT64)
BID_UI64DOUBLE tmp1;
int x_nr_bits;
int q, ind, shift;
UINT64 C1;
// UINT64 res is C* at first - represents up to 16 decimal digits <= 54 bits
- UINT128 fstar = {{ 0x0ull, 0x0ull }};;
+ UINT128 fstar = { {0x0ull, 0x0ull} };
UINT128 P128;
- if ((x & MASK_INF) == MASK_INF) { // x is either INF or NAN
- res = x;
- if ((x & MASK_SNAN) == MASK_SNAN) {
+ x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
+
+ // check for NaNs and infinities
+ if ((x & MASK_NAN) == MASK_NAN) { // check for NaN
+ if ((x & 0x0003ffffffffffffull) > 999999999999999ull)
+ x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
+ else
+ x = x & 0xfe03ffffffffffffull; // clear G6-G12
+ if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
- // return Quiet (SNaN)
+ // return quiet (SNaN)
res = x & 0xfdffffffffffffffull;
+ } else { // QNaN
+ res = x;
}
- // return original input if QNaN or INF, quietize if SNaN
+ BID_RETURN (res);
+ } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
+ res = x_sign | 0x7800000000000000ull;
BID_RETURN (res);
}
// unpack x
- x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
// if the steering bits are 11 (condition will be 0), then
// the exponent is G[0:w+1]
exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398;
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
- if (C1 > 9999999999999999ull) { // non-canonical
- exp = 0;
+ if (C1 > 9999999999999999ull) { // non-canonical
C1 = 0;
}
- } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS)
+ } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS)
exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398;
C1 = (x & MASK_BINARY_SIG1);
}
@@ -139,25 +147,25 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
BID_RETURN (res);
}
break;
- } // end switch ()
+ } // end switch ()
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
- if (C1 >= 0x0020000000000000ull) { // x >= 2^53
+ if (C1 >= 0x0020000000000000ull) { // x >= 2^53
q = 16;
- } else { // if x < 2^53
+ } else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
- q = __bid_nr_digits[x_nr_bits - 1].digits;
+ q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
- q = __bid_nr_digits[x_nr_bits - 1].digits1;
- if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo)
+ q = nr_digits[x_nr_bits - 1].digits1;
+ if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
}
- if (exp >= 0) { // -exp <= 0
+ if (exp >= 0) { // -exp <= 0
// the argument is an integer already
res = x;
BID_RETURN (res);
@@ -165,22 +173,22 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
switch (rnd_mode) {
case ROUNDING_TO_NEAREST:
- if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q
+ if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q
// need to shift right -exp digits from the coefficient; exp will be 0
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits
// FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate
- C1 = C1 + __bid_midpoint64[ind - 1];
+ C1 = C1 + midpoint64[ind - 1];
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
- // __bid_shiftright128[] and __bid_maskhigh128[]
+ // shiftright128[] and maskhigh128[]
// 1 <= x <= 16
- // kx = 10^(-x) = __bid_ten2mk64[ind - 1]
+ // kx = 10^(-x) = ten2mk64[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 64 bits
- __mul_64x64_to_128 (P128, C1, __bid_ten2mk64[ind - 1]);
+ __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
@@ -192,20 +200,20 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
// correct by Property 1)
// n = C* * 10^(e+x)
- if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
+ if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
res = P128.w[1];
fstar.w[1] = 0;
fstar.w[0] = P128.w[0];
- } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
- shift = __bid_shiftright128[ind - 1]; // 3 <= shift <= 63
+ } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
+ shift = shiftright128[ind - 1]; // 3 <= shift <= 63
res = (P128.w[1] >> shift);
- fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1];
+ fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
}
// if (0 < f* < 10^(-x)) then the result is a midpoint
// since round_to_even, subtract 1 if current result is odd
if ((res & 0x0000000000000001ull) && (fstar.w[1] == 0)
- && (fstar.w[0] < __bid_ten2mk64[ind - 1])) {
+ && (fstar.w[0] < ten2mk64[ind - 1])) {
res--;
}
// determine inexactness of the rounding of C*
@@ -217,26 +225,25 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
if (fstar.w[0] > 0x8000000000000000ull) {
// f* > 1/2 and the result may be exact
// fstar.w[0] - 0x8000000000000000ull is f* - 1/2
- if ((fstar.w[0] - 0x8000000000000000ull) > __bid_ten2mk64[ind - 1]) {
+ if ((fstar.w[0] - 0x8000000000000000ull) > ten2mk64[ind - 1]) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
- } // else the result is exact
- } else { // the result is inexact; f2* <= 1/2
+ } // else the result is exact
+ } else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
- } else { // if 3 <= ind - 1 <= 21
- if (fstar.w[1] > __bid_one_half128[ind - 1]
- || (fstar.w[1] == __bid_one_half128[ind - 1]
- && fstar.w[0])) {
+ } else { // if 3 <= ind - 1 <= 21
+ if (fstar.w[1] > onehalf128[ind - 1] ||
+ (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
- if (fstar.w[1] > __bid_one_half128[ind - 1]
- || fstar.w[0] > __bid_ten2mk64[ind - 1]) {
+ if (fstar.w[1] > onehalf128[ind - 1]
+ || fstar.w[0] > ten2mk64[ind - 1]) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
- } // else the result is exact
- } else { // the result is inexact; f2* <= 1/2
+ } // else the result is exact
+ } else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
@@ -244,7 +251,7 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
// set exponent to zero as it was negative before.
res = x_sign | 0x31c0000000000000ull | res;
BID_RETURN (res);
- } else { // if exp < 0 and q + exp < 0
+ } else { // if exp < 0 and q + exp < 0
// the result is +0 or -0
res = x_sign | 0x31c0000000000000ull;
*pfpsf |= INEXACT_EXCEPTION;
@@ -252,22 +259,22 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
}
break;
case ROUNDING_TIES_AWAY:
- if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q
+ if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q
// need to shift right -exp digits from the coefficient; exp will be 0
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits
// FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate
- C1 = C1 + __bid_midpoint64[ind - 1];
+ C1 = C1 + midpoint64[ind - 1];
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
- // __bid_shiftright128[] and __bid_maskhigh128[]
+ // shiftright128[] and maskhigh128[]
// 1 <= x <= 16
- // kx = 10^(-x) = __bid_ten2mk64[ind - 1]
+ // kx = 10^(-x) = ten2mk64[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 64 bits
- __mul_64x64_to_128 (P128, C1, __bid_ten2mk64[ind - 1]);
+ __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);
// if (0 < f* < 10^(-x)) then the result is a midpoint
// C* = floor(C*) - logical right shift; C* has p decimal digits,
@@ -277,14 +284,14 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
// correct by Property 1)
// n = C* * 10^(e+x)
- if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
+ if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
res = P128.w[1];
fstar.w[1] = 0;
fstar.w[0] = P128.w[0];
- } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
- shift = __bid_shiftright128[ind - 1]; // 3 <= shift <= 63
+ } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
+ shift = shiftright128[ind - 1]; // 3 <= shift <= 63
res = (P128.w[1] >> shift);
- fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1];
+ fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
}
// midpoints are already rounded correctly
@@ -297,26 +304,25 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
if (fstar.w[0] > 0x8000000000000000ull) {
// f* > 1/2 and the result may be exact
// fstar.w[0] - 0x8000000000000000ull is f* - 1/2
- if ((fstar.w[0] - 0x8000000000000000ull) > __bid_ten2mk64[ind - 1]) {
+ if ((fstar.w[0] - 0x8000000000000000ull) > ten2mk64[ind - 1]) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
- } // else the result is exact
- } else { // the result is inexact; f2* <= 1/2
+ } // else the result is exact
+ } else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
- } else { // if 3 <= ind - 1 <= 21
- if (fstar.w[1] > __bid_one_half128[ind - 1]
- || (fstar.w[1] == __bid_one_half128[ind - 1]
- && fstar.w[0])) {
+ } else { // if 3 <= ind - 1 <= 21
+ if (fstar.w[1] > onehalf128[ind - 1] ||
+ (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
- if (fstar.w[1] > __bid_one_half128[ind - 1]
- || fstar.w[0] > __bid_ten2mk64[ind - 1]) {
+ if (fstar.w[1] > onehalf128[ind - 1]
+ || fstar.w[0] > ten2mk64[ind - 1]) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
- } // else the result is exact
- } else { // the result is inexact; f2* <= 1/2
+ } // else the result is exact
+ } else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
@@ -324,7 +330,7 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
// set exponent to zero as it was negative before.
res = x_sign | 0x31c0000000000000ull | res;
BID_RETURN (res);
- } else { // if exp < 0 and q + exp < 0
+ } else { // if exp < 0 and q + exp < 0
// the result is +0 or -0
res = x_sign | 0x31c0000000000000ull;
*pfpsf |= INEXACT_EXCEPTION;
@@ -332,7 +338,7 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
}
break;
case ROUNDING_DOWN:
- if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q
+ if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q
// need to shift right -exp digits from the coefficient; exp will be 0
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
@@ -340,30 +346,30 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
- // __bid_shiftright128[] and __bid_maskhigh128[]
+ // shiftright128[] and maskhigh128[]
// 1 <= x <= 16
- // kx = 10^(-x) = __bid_ten2mk64[ind - 1]
+ // kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 64 bits
- __mul_64x64_to_128 (P128, C1, __bid_ten2mk64[ind - 1]);
+ __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// if (0 < f* < 10^(-x)) then the result is exact
// n = C* * 10^(e+x)
- if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
+ if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
res = P128.w[1];
fstar.w[1] = 0;
fstar.w[0] = P128.w[0];
- } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
- shift = __bid_shiftright128[ind - 1]; // 3 <= shift <= 63
+ } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
+ shift = shiftright128[ind - 1]; // 3 <= shift <= 63
res = (P128.w[1] >> shift);
- fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1];
+ fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
}
// if (f* > 10^(-x)) then the result is inexact
- if ((fstar.w[1] != 0) || (fstar.w[0] >= __bid_ten2mk64[ind - 1])) {
+ if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) {
if (x_sign) {
// if negative and not exact, increment magnitude
res++;
@@ -373,7 +379,7 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
// set exponent to zero as it was negative before.
res = x_sign | 0x31c0000000000000ull | res;
BID_RETURN (res);
- } else { // if exp < 0 and q + exp <= 0
+ } else { // if exp < 0 and q + exp <= 0
// the result is +0 or -1
if (x_sign) {
res = 0xb1c0000000000001ull;
@@ -385,7 +391,7 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
}
break;
case ROUNDING_UP:
- if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q
+ if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q
// need to shift right -exp digits from the coefficient; exp will be 0
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
@@ -393,30 +399,30 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
- // __bid_shiftright128[] and __bid_maskhigh128[]
+ // shiftright128[] and maskhigh128[]
// 1 <= x <= 16
- // kx = 10^(-x) = __bid_ten2mk64[ind - 1]
+ // kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 64 bits
- __mul_64x64_to_128 (P128, C1, __bid_ten2mk64[ind - 1]);
+ __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// if (0 < f* < 10^(-x)) then the result is exact
// n = C* * 10^(e+x)
- if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
+ if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
res = P128.w[1];
fstar.w[1] = 0;
fstar.w[0] = P128.w[0];
- } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
- shift = __bid_shiftright128[ind - 1]; // 3 <= shift <= 63
+ } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
+ shift = shiftright128[ind - 1]; // 3 <= shift <= 63
res = (P128.w[1] >> shift);
- fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1];
+ fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
}
// if (f* > 10^(-x)) then the result is inexact
- if ((fstar.w[1] != 0) || (fstar.w[0] >= __bid_ten2mk64[ind - 1])) {
+ if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) {
if (!x_sign) {
// if positive and not exact, increment magnitude
res++;
@@ -426,7 +432,7 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
// set exponent to zero as it was negative before.
res = x_sign | 0x31c0000000000000ull | res;
BID_RETURN (res);
- } else { // if exp < 0 and q + exp <= 0
+ } else { // if exp < 0 and q + exp <= 0
// the result is -0 or +1
if (x_sign) {
res = 0xb1c0000000000000ull;
@@ -438,7 +444,7 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
}
break;
case ROUNDING_TO_ZERO:
- if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q
+ if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q
// need to shift right -exp digits from the coefficient; exp will be 0
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
@@ -446,43 +452,43 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
- // __bid_shiftright128[] and __bid_maskhigh128[]
+ // shiftright128[] and maskhigh128[]
// 1 <= x <= 16
- // kx = 10^(-x) = __bid_ten2mk64[ind - 1]
+ // kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 64 bits
- __mul_64x64_to_128 (P128, C1, __bid_ten2mk64[ind - 1]);
+ __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// if (0 < f* < 10^(-x)) then the result is exact
// n = C* * 10^(e+x)
- if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
+ if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
res = P128.w[1];
fstar.w[1] = 0;
fstar.w[0] = P128.w[0];
- } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
- shift = __bid_shiftright128[ind - 1]; // 3 <= shift <= 63
+ } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
+ shift = shiftright128[ind - 1]; // 3 <= shift <= 63
res = (P128.w[1] >> shift);
- fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1];
+ fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
}
// if (f* > 10^(-x)) then the result is inexact
- if ((fstar.w[1] != 0) || (fstar.w[0] >= __bid_ten2mk64[ind - 1])) {
+ if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) {
*pfpsf |= INEXACT_EXCEPTION;
}
// set exponent to zero as it was negative before.
res = x_sign | 0x31c0000000000000ull | res;
BID_RETURN (res);
- } else { // if exp < 0 and q + exp < 0
+ } else { // if exp < 0 and q + exp < 0
// the result is +0 or -0
res = x_sign | 0x31c0000000000000ull;
*pfpsf |= INEXACT_EXCEPTION;
BID_RETURN (res);
}
break;
- } // end switch ()
+ } // end switch ()
BID_RETURN (res);
}
@@ -492,20 +498,20 @@ __bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
#if DECIMAL_CALL_BY_REFERENCE
void
-__bid64_round_integral_nearest_even (UINT64 * pres,
+bid64_round_integral_nearest_even (UINT64 * pres,
UINT64 *
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
-__bid64_round_integral_nearest_even (UINT64 x _EXC_FLAGS_PARAM
+bid64_round_integral_nearest_even (UINT64 x _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
- UINT64 res = 0x0ull;
+ UINT64 res = 0xbaddbaddbaddbaddull;
UINT64 x_sign;
- int exp; // unbiased exponent
+ int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
BID_UI64DOUBLE tmp1;
int x_nr_bits;
@@ -514,29 +520,37 @@ __bid64_round_integral_nearest_even (UINT64 x _EXC_FLAGS_PARAM
UINT128 fstar;
UINT128 P128;
- if ((x & MASK_INF) == MASK_INF) { // x is either INF or NAN
- res = x;
- if ((x & MASK_SNAN) == MASK_SNAN) {
- // set invalid flag
+ x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
+
+ // check for NaNs and infinities
+ if ((x & MASK_NAN) == MASK_NAN) { // check for NaN
+ if ((x & 0x0003ffffffffffffull) > 999999999999999ull)
+ x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
+ else
+ x = x & 0xfe03ffffffffffffull; // clear G6-G12
+ if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN
+ // set invalid flag
*pfpsf |= INVALID_EXCEPTION;
- // return Quiet (SNaN)
+ // return quiet (SNaN)
res = x & 0xfdffffffffffffffull;
+ } else { // QNaN
+ res = x;
}
- // return original input if QNaN or INF, quietize if SNaN
+ BID_RETURN (res);
+ } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
+ res = x_sign | 0x7800000000000000ull;
BID_RETURN (res);
}
// unpack x
- x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
// if the steering bits are 11 (condition will be 0), then
// the exponent is G[0:w+1]
exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398;
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
- if (C1 > 9999999999999999ull) { // non-canonical
- exp = 0;
+ if (C1 > 9999999999999999ull) { // non-canonical
C1 = 0;
}
- } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS)
+ } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS)
exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398;
C1 = (x & MASK_BINARY_SIG1);
}
@@ -557,40 +571,40 @@ __bid64_round_integral_nearest_even (UINT64 x _EXC_FLAGS_PARAM
}
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
- if (C1 >= 0x0020000000000000ull) { // x >= 2^53
+ if (C1 >= 0x0020000000000000ull) { // x >= 2^53
q = 16;
- } else { // if x < 2^53
+ } else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
- q = __bid_nr_digits[x_nr_bits - 1].digits;
+ q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
- q = __bid_nr_digits[x_nr_bits - 1].digits1;
- if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo)
+ q = nr_digits[x_nr_bits - 1].digits1;
+ if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
}
- if (exp >= 0) { // -exp <= 0
+ if (exp >= 0) { // -exp <= 0
// the argument is an integer already
res = x;
BID_RETURN (res);
- } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q
+ } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q
// need to shift right -exp digits from the coefficient; the exp will be 0
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits
// FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate
- C1 = C1 + __bid_midpoint64[ind - 1];
+ C1 = C1 + midpoint64[ind - 1];
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
- // __bid_shiftright128[] and __bid_maskhigh128[]
+ // shiftright128[] and maskhigh128[]
// 1 <= x <= 16
- // kx = 10^(-x) = __bid_ten2mk64[ind - 1]
+ // kx = 10^(-x) = ten2mk64[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 64 bits
- __mul_64x64_to_128 (P128, C1, __bid_ten2mk64[ind - 1]);
+ __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
@@ -602,26 +616,26 @@ __bid64_round_integral_nearest_even (UINT64 x _EXC_FLAGS_PARAM
// correct by Property 1)
// n = C* * 10^(e+x)
- if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
+ if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
res = P128.w[1];
fstar.w[1] = 0;
fstar.w[0] = P128.w[0];
- } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
- shift = __bid_shiftright128[ind - 1]; // 3 <= shift <= 63
+ } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
+ shift = shiftright128[ind - 1]; // 3 <= shift <= 63
res = (P128.w[1] >> shift);
- fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1];
+ fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
}
// if (0 < f* < 10^(-x)) then the result is a midpoint
// since round_to_even, subtract 1 if current result is odd
if ((res & 0x0000000000000001ull) && (fstar.w[1] == 0)
- && (fstar.w[0] < __bid_ten2mk64[ind - 1])) {
+ && (fstar.w[0] < ten2mk64[ind - 1])) {
res--;
}
// set exponent to zero as it was negative before.
res = x_sign | 0x31c0000000000000ull | res;
BID_RETURN (res);
- } else { // if exp < 0 and q + exp < 0
+ } else { // if exp < 0 and q + exp < 0
// the result is +0 or -0
res = x_sign | 0x31c0000000000000ull;
BID_RETURN (res);
@@ -634,20 +648,20 @@ __bid64_round_integral_nearest_even (UINT64 x _EXC_FLAGS_PARAM
#if DECIMAL_CALL_BY_REFERENCE
void
-__bid64_round_integral_negative (UINT64 * pres,
+bid64_round_integral_negative (UINT64 * pres,
UINT64 *
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
-__bid64_round_integral_negative (UINT64 x _EXC_FLAGS_PARAM
+bid64_round_integral_negative (UINT64 x _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
- UINT64 res = 0x0ull;
+ UINT64 res = 0xbaddbaddbaddbaddull;
UINT64 x_sign;
- int exp; // unbiased exponent
+ int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
BID_UI64DOUBLE tmp1;
int x_nr_bits;
@@ -657,29 +671,37 @@ __bid64_round_integral_negative (UINT64 x _EXC_FLAGS_PARAM
UINT128 fstar;
UINT128 P128;
- if ((x & MASK_INF) == MASK_INF) { // x is either INF or NAN
- res = x;
- if ((x & MASK_SNAN) == MASK_SNAN) {
- // set invalid flag
+ x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
+
+ // check for NaNs and infinities
+ if ((x & MASK_NAN) == MASK_NAN) { // check for NaN
+ if ((x & 0x0003ffffffffffffull) > 999999999999999ull)
+ x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
+ else
+ x = x & 0xfe03ffffffffffffull; // clear G6-G12
+ if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN
+ // set invalid flag
*pfpsf |= INVALID_EXCEPTION;
- // return Quiet (SNaN)
+ // return quiet (SNaN)
res = x & 0xfdffffffffffffffull;
+ } else { // QNaN
+ res = x;
}
- // return original input if QNaN or INF, quietize if SNaN
+ BID_RETURN (res);
+ } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
+ res = x_sign | 0x7800000000000000ull;
BID_RETURN (res);
}
// unpack x
- x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
// if the steering bits are 11 (condition will be 0), then
// the exponent is G[0:w+1]
exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398;
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
- if (C1 > 9999999999999999ull) { // non-canonical
- exp = 0;
+ if (C1 > 9999999999999999ull) { // non-canonical
C1 = 0;
}
- } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS)
+ } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS)
exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398;
C1 = (x & MASK_BINARY_SIG1);
}
@@ -704,25 +726,25 @@ __bid64_round_integral_negative (UINT64 x _EXC_FLAGS_PARAM
}
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
- if (C1 >= 0x0020000000000000ull) { // x >= 2^53
+ if (C1 >= 0x0020000000000000ull) { // x >= 2^53
q = 16;
- } else { // if x < 2^53
+ } else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
- q = __bid_nr_digits[x_nr_bits - 1].digits;
+ q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
- q = __bid_nr_digits[x_nr_bits - 1].digits1;
- if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo)
+ q = nr_digits[x_nr_bits - 1].digits1;
+ if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
}
- if (exp >= 0) { // -exp <= 0
+ if (exp >= 0) { // -exp <= 0
// the argument is an integer already
res = x;
BID_RETURN (res);
- } else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q
+ } else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q
// need to shift right -exp digits from the coefficient; the exp will be 0
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
@@ -730,38 +752,38 @@ __bid64_round_integral_negative (UINT64 x _EXC_FLAGS_PARAM
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
- // __bid_shiftright128[] and __bid_maskhigh128[]
+ // shiftright128[] and maskhigh128[]
// 1 <= x <= 16
- // kx = 10^(-x) = __bid_ten2mk64[ind - 1]
+ // kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 64 bits
- __mul_64x64_to_128 (P128, C1, __bid_ten2mk64[ind - 1]);
+ __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// if (0 < f* < 10^(-x)) then the result is exact
// n = C* * 10^(e+x)
- if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
+ if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
res = P128.w[1];
fstar.w[1] = 0;
fstar.w[0] = P128.w[0];
- } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
- shift = __bid_shiftright128[ind - 1]; // 3 <= shift <= 63
+ } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
+ shift = shiftright128[ind - 1]; // 3 <= shift <= 63
res = (P128.w[1] >> shift);
- fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1];
+ fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
}
// if (f* > 10^(-x)) then the result is inexact
if (x_sign
- && ((fstar.w[1] != 0) || (fstar.w[0] >= __bid_ten2mk64[ind - 1]))) {
+ && ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1]))) {
// if negative and not exact, increment magnitude
res++;
}
// set exponent to zero as it was negative before.
res = x_sign | 0x31c0000000000000ull | res;
BID_RETURN (res);
- } else { // if exp < 0 and q + exp <= 0
+ } else { // if exp < 0 and q + exp <= 0
// the result is +0 or -1
if (x_sign) {
res = 0xb1c0000000000001ull;
@@ -778,20 +800,20 @@ __bid64_round_integral_negative (UINT64 x _EXC_FLAGS_PARAM
#if DECIMAL_CALL_BY_REFERENCE
void
-__bid64_round_integral_positive (UINT64 * pres,
+bid64_round_integral_positive (UINT64 * pres,
UINT64 *
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
-__bid64_round_integral_positive (UINT64 x _EXC_FLAGS_PARAM
+bid64_round_integral_positive (UINT64 x _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
- UINT64 res = 0x0ull;
+ UINT64 res = 0xbaddbaddbaddbaddull;
UINT64 x_sign;
- int exp; // unbiased exponent
+ int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
BID_UI64DOUBLE tmp1;
int x_nr_bits;
@@ -801,29 +823,37 @@ __bid64_round_integral_positive (UINT64 x _EXC_FLAGS_PARAM
UINT128 fstar;
UINT128 P128;
- if ((x & MASK_INF) == MASK_INF) { // x is either INF or NAN
- res = x;
- if ((x & MASK_SNAN) == MASK_SNAN) {
- // set invalid flag
+ x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
+
+ // check for NaNs and infinities
+ if ((x & MASK_NAN) == MASK_NAN) { // check for NaN
+ if ((x & 0x0003ffffffffffffull) > 999999999999999ull)
+ x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
+ else
+ x = x & 0xfe03ffffffffffffull; // clear G6-G12
+ if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN
+ // set invalid flag
*pfpsf |= INVALID_EXCEPTION;
- // return Quiet (SNaN)
+ // return quiet (SNaN)
res = x & 0xfdffffffffffffffull;
+ } else { // QNaN
+ res = x;
}
- // return original input if QNaN or INF, quietize if SNaN
+ BID_RETURN (res);
+ } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
+ res = x_sign | 0x7800000000000000ull;
BID_RETURN (res);
}
// unpack x
- x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
// if the steering bits are 11 (condition will be 0), then
// the exponent is G[0:w+1]
exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398;
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
- if (C1 > 9999999999999999ull) { // non-canonical
- exp = 0;
+ if (C1 > 9999999999999999ull) { // non-canonical
C1 = 0;
}
- } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS)
+ } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS)
exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398;
C1 = (x & MASK_BINARY_SIG1);
}
@@ -848,25 +878,25 @@ __bid64_round_integral_positive (UINT64 x _EXC_FLAGS_PARAM
}
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
- if (C1 >= 0x0020000000000000ull) { // x >= 2^53
+ if (C1 >= 0x0020000000000000ull) { // x >= 2^53
q = 16;
- } else { // if x < 2^53
+ } else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
- q = __bid_nr_digits[x_nr_bits - 1].digits;
+ q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
- q = __bid_nr_digits[x_nr_bits - 1].digits1;
- if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo)
+ q = nr_digits[x_nr_bits - 1].digits1;
+ if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
}
- if (exp >= 0) { // -exp <= 0
+ if (exp >= 0) { // -exp <= 0
// the argument is an integer already
res = x;
BID_RETURN (res);
- } else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q
+ } else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q
// need to shift right -exp digits from the coefficient; the exp will be 0
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
@@ -874,38 +904,38 @@ __bid64_round_integral_positive (UINT64 x _EXC_FLAGS_PARAM
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
- // __bid_shiftright128[] and __bid_maskhigh128[]
+ // shiftright128[] and maskhigh128[]
// 1 <= x <= 16
- // kx = 10^(-x) = __bid_ten2mk64[ind - 1]
+ // kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 64 bits
- __mul_64x64_to_128 (P128, C1, __bid_ten2mk64[ind - 1]);
+ __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// if (0 < f* < 10^(-x)) then the result is exact
// n = C* * 10^(e+x)
- if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
+ if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
res = P128.w[1];
fstar.w[1] = 0;
fstar.w[0] = P128.w[0];
- } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
- shift = __bid_shiftright128[ind - 1]; // 3 <= shift <= 63
+ } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
+ shift = shiftright128[ind - 1]; // 3 <= shift <= 63
res = (P128.w[1] >> shift);
- fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1];
+ fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
}
// if (f* > 10^(-x)) then the result is inexact
if (!x_sign
- && ((fstar.w[1] != 0) || (fstar.w[0] >= __bid_ten2mk64[ind - 1]))) {
+ && ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1]))) {
// if positive and not exact, increment magnitude
res++;
}
// set exponent to zero as it was negative before.
res = x_sign | 0x31c0000000000000ull | res;
BID_RETURN (res);
- } else { // if exp < 0 and q + exp <= 0
+ } else { // if exp < 0 and q + exp <= 0
// the result is -0 or +1
if (x_sign) {
res = 0xb1c0000000000000ull;
@@ -922,20 +952,20 @@ __bid64_round_integral_positive (UINT64 x _EXC_FLAGS_PARAM
#if DECIMAL_CALL_BY_REFERENCE
void
-__bid64_round_integral_zero (UINT64 * pres,
+bid64_round_integral_zero (UINT64 * pres,
UINT64 *
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
-__bid64_round_integral_zero (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+bid64_round_integral_zero (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
- UINT64 res = 0x0ull;
+ UINT64 res = 0xbaddbaddbaddbaddull;
UINT64 x_sign;
- int exp; // unbiased exponent
+ int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
BID_UI64DOUBLE tmp1;
int x_nr_bits;
@@ -944,29 +974,37 @@ __bid64_round_integral_zero (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
// UINT64 res is C* at first - represents up to 34 decimal digits ~ 113 bits
UINT128 P128;
- if ((x & MASK_INF) == MASK_INF) { // x is either INF or NAN
- res = x;
- if ((x & MASK_SNAN) == MASK_SNAN) {
- // set invalid flag
+ x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
+
+ // check for NaNs and infinities
+ if ((x & MASK_NAN) == MASK_NAN) { // check for NaN
+ if ((x & 0x0003ffffffffffffull) > 999999999999999ull)
+ x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
+ else
+ x = x & 0xfe03ffffffffffffull; // clear G6-G12
+ if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN
+ // set invalid flag
*pfpsf |= INVALID_EXCEPTION;
- // return Quiet (SNaN)
+ // return quiet (SNaN)
res = x & 0xfdffffffffffffffull;
+ } else { // QNaN
+ res = x;
}
- // return original input if QNaN or INF, quietize if SNaN
+ BID_RETURN (res);
+ } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
+ res = x_sign | 0x7800000000000000ull;
BID_RETURN (res);
}
// unpack x
- x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
// if the steering bits are 11 (condition will be 0), then
// the exponent is G[0:w+1]
exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398;
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
- if (C1 > 9999999999999999ull) { // non-canonical
- exp = 0;
+ if (C1 > 9999999999999999ull) { // non-canonical
C1 = 0;
}
- } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS)
+ } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS)
exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398;
C1 = (x & MASK_BINARY_SIG1);
}
@@ -987,25 +1025,25 @@ __bid64_round_integral_zero (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
}
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
- if (C1 >= 0x0020000000000000ull) { // x >= 2^53
+ if (C1 >= 0x0020000000000000ull) { // x >= 2^53
q = 16;
- } else { // if x < 2^53
+ } else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
- q = __bid_nr_digits[x_nr_bits - 1].digits;
+ q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
- q = __bid_nr_digits[x_nr_bits - 1].digits1;
- if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo)
+ q = nr_digits[x_nr_bits - 1].digits1;
+ if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
}
- if (exp >= 0) { // -exp <= 0
+ if (exp >= 0) { // -exp <= 0
// the argument is an integer already
res = x;
BID_RETURN (res);
- } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q
+ } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q
// need to shift right -exp digits from the coefficient; the exp will be 0
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
@@ -1013,36 +1051,36 @@ __bid64_round_integral_zero (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
- // __bid_shiftright128[] and __bid_maskhigh128[]
+ // shiftright128[] and maskhigh128[]
// 1 <= x <= 16
- // kx = 10^(-x) = __bid_ten2mk64[ind - 1]
+ // kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 64 bits
- __mul_64x64_to_128 (P128, C1, __bid_ten2mk64[ind - 1]);
+ __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// if (0 < f* < 10^(-x)) then the result is exact
// n = C* * 10^(e+x)
- if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
+ if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
res = P128.w[1];
// redundant fstar.w[1] = 0;
// redundant fstar.w[0] = P128.w[0];
- } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
- shift = __bid_shiftright128[ind - 1]; // 3 <= shift <= 63
+ } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
+ shift = shiftright128[ind - 1]; // 3 <= shift <= 63
res = (P128.w[1] >> shift);
- // redundant fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1];
+ // redundant fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
// redundant fstar.w[0] = P128.w[0];
}
// if (f* > 10^(-x)) then the result is inexact
- // if ((fstar.w[1] != 0) || (fstar.w[0] >= __bid_ten2mk64[ind-1])){
+ // if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind-1])){
// // redundant
// }
// set exponent to zero as it was negative before.
res = x_sign | 0x31c0000000000000ull | res;
BID_RETURN (res);
- } else { // if exp < 0 and q + exp < 0
+ } else { // if exp < 0 and q + exp < 0
// the result is +0 or -0
res = x_sign | 0x31c0000000000000ull;
BID_RETURN (res);
@@ -1055,20 +1093,20 @@ __bid64_round_integral_zero (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
#if DECIMAL_CALL_BY_REFERENCE
void
-__bid64_round_integral_nearest_away (UINT64 * pres,
+bid64_round_integral_nearest_away (UINT64 * pres,
UINT64 *
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
-__bid64_round_integral_nearest_away (UINT64 x _EXC_FLAGS_PARAM
+bid64_round_integral_nearest_away (UINT64 x _EXC_FLAGS_PARAM
_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
- UINT64 res = 0x0ull;
+ UINT64 res = 0xbaddbaddbaddbaddull;
UINT64 x_sign;
- int exp; // unbiased exponent
+ int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
BID_UI64DOUBLE tmp1;
int x_nr_bits;
@@ -1076,29 +1114,37 @@ __bid64_round_integral_nearest_away (UINT64 x _EXC_FLAGS_PARAM
UINT64 C1;
UINT128 P128;
- if ((x & MASK_INF) == MASK_INF) { // x is either INF or NAN
- res = x;
- if ((x & MASK_SNAN) == MASK_SNAN) {
- // set invalid flag
+ x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
+
+ // check for NaNs and infinities
+ if ((x & MASK_NAN) == MASK_NAN) { // check for NaN
+ if ((x & 0x0003ffffffffffffull) > 999999999999999ull)
+ x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits
+ else
+ x = x & 0xfe03ffffffffffffull; // clear G6-G12
+ if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN
+ // set invalid flag
*pfpsf |= INVALID_EXCEPTION;
- // return Quiet (SNaN)
+ // return quiet (SNaN)
res = x & 0xfdffffffffffffffull;
+ } else { // QNaN
+ res = x;
}
- // return original input if QNaN or INF, quietize if SNaN
+ BID_RETURN (res);
+ } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity
+ res = x_sign | 0x7800000000000000ull;
BID_RETURN (res);
}
// unpack x
- x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
// if the steering bits are 11 (condition will be 0), then
// the exponent is G[0:w+1]
exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398;
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
- if (C1 > 9999999999999999ull) { // non-canonical
- exp = 0;
+ if (C1 > 9999999999999999ull) { // non-canonical
C1 = 0;
}
- } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS)
+ } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS)
exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398;
C1 = (x & MASK_BINARY_SIG1);
}
@@ -1119,40 +1165,40 @@ __bid64_round_integral_nearest_away (UINT64 x _EXC_FLAGS_PARAM
}
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
- if (C1 >= 0x0020000000000000ull) { // x >= 2^53
+ if (C1 >= 0x0020000000000000ull) { // x >= 2^53
q = 16;
- } else { // if x < 2^53
+ } else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
- q = __bid_nr_digits[x_nr_bits - 1].digits;
+ q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
- q = __bid_nr_digits[x_nr_bits - 1].digits1;
- if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo)
+ q = nr_digits[x_nr_bits - 1].digits1;
+ if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
}
- if (exp >= 0) { // -exp <= 0
+ if (exp >= 0) { // -exp <= 0
// the argument is an integer already
res = x;
BID_RETURN (res);
- } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q
+ } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q
// need to shift right -exp digits from the coefficient; the exp will be 0
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits
// FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate
- C1 = C1 + __bid_midpoint64[ind - 1];
+ C1 = C1 + midpoint64[ind - 1];
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
- // __bid_shiftright128[] and __bid_maskhigh128[]
+ // shiftright128[] and maskhigh128[]
// 1 <= x <= 16
- // kx = 10^(-x) = __bid_ten2mk64[ind - 1]
+ // kx = 10^(-x) = ten2mk64[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 64 bits
- __mul_64x64_to_128 (P128, C1, __bid_ten2mk64[ind - 1]);
+ __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);
// if (0 < f* < 10^(-x)) then the result is a midpoint
// C* = floor(C*) - logical right shift; C* has p decimal digits,
@@ -1162,17 +1208,17 @@ __bid64_round_integral_nearest_away (UINT64 x _EXC_FLAGS_PARAM
// correct by Property 1)
// n = C* * 10^(e+x)
- if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
+ if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0
res = P128.w[1];
- } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
- shift = __bid_shiftright128[ind - 1]; // 3 <= shift <= 63
+ } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63
+ shift = shiftright128[ind - 1]; // 3 <= shift <= 63
res = (P128.w[1] >> shift);
}
// midpoints are already rounded correctly
// set exponent to zero as it was negative before.
res = x_sign | 0x31c0000000000000ull | res;
BID_RETURN (res);
- } else { // if exp < 0 and q + exp < 0
+ } else { // if exp < 0 and q + exp < 0
// the result is +0 or -0
res = x_sign | 0x31c0000000000000ull;
BID_RETURN (res);
generated by cgit v1.2.3 (git 2.25.1) at 2024-06-16 15:37:11 +0000