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/* Copyright (C) 2007-2022 Free Software Foundation, Inc.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
#include "bid_internal.h"
/*****************************************************************************
* BID128_to_uint64_rnint
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
bid128_to_uint64_rnint, x)
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
// in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
// so x rounded to an integer may or may not fit in an unsigned 64-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 20'
if (x_sign) { // if n < 0 and q + exp = 20
// if n < -1/2 then n cannot be converted to uint64 with RN
// too large if c(0)c(1)...c(19).c(20)...c(q-1) > 1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^21 > 0x05, 1<=q<=34
// <=> C * 10^(21-q) > 0x05, 1<=q<=34
if (q == 21) {
// C > 5
if (C1.w[1] != 0 || C1.w[0] > 0x05ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to 64-bit unsigned int fall through
// to '1 <= q + exp <= 20'
} else {
// if 1 <= q <= 20
// C * 10^(21-q) > 5 is true because C >= 1 and 10^(21-q) >= 10
// if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C > 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
} else { // if n > 0 and q + exp = 20
// if n >= 2^64 - 1/2 then n is too large
// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)
// <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34
if (q == 1) {
// C * 10^20 >= 0x9fffffffffffffffb
__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C
if (C.w[1] > 0x09 || (C.w[1] == 0x09
&& C.w[0] >= 0xfffffffffffffffbull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q <= 19) {
// C * 10^(21-q) >= 0x9fffffffffffffffb
__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
if (C.w[1] > 0x09 || (C.w[1] == 0x09
&& C.w[0] >= 0xfffffffffffffffbull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 20) {
// C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff
C.w[0] = C1.w[0] + C1.w[0];
C.w[1] = C1.w[1] + C1.w[1];
if (C.w[0] < C1.w[0])
C.w[1]++;
if (C.w[1] > 0x01 || (C.w[1] == 0x01
&& C.w[0] >= 0xffffffffffffffffull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 21) {
// C >= 0x9fffffffffffffffb
if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
&& C1.w[0] >= 0xfffffffffffffffbull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits
C.w[1] = 0x09;
C.w[0] = 0xfffffffffffffffbull;
__mul_128x64_to_128 (C, ten2k64[q - 21], C);
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
}
}
}
// n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2
// Note: some of the cases tested for above fall through to this point
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
// return 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
// if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)
// res = 0
// else if x > 0
// res = +1
// else // if x < 0
// invalid exc
ind = q - 1;
if (ind <= 18) { // 0 <= ind <= 18
if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) {
res = 0x0000000000000000ull; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x8000000000000000ull;
*pfpsf |= INVALID_EXCEPTION;
}
} else { // 19 <= ind <= 33
if ((C1.w[1] < midpoint128[ind - 19].w[1])
|| ((C1.w[1] == midpoint128[ind - 19].w[1])
&& (C1.w[0] <= midpoint128[ind - 19].w[0]))) {
res = 0x0000000000000000ull; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x8000000000000000ull;
*pfpsf |= INVALID_EXCEPTION;
}
}
} else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
// x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded
// to nearest to a 64-bit unsigned signed integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// 1 <= x < 2^64-1/2 so x can be rounded
// to nearest to a 64-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
&& (fstar.w[1] || fstar.w[0])
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
// the result is a midpoint; round to nearest
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar.w[0]--; // Cstar.w[0] is now even
} // else MP in [ODD, EVEN]
}
res = Cstar.w[0]; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
// res = C (exact)
res = C1.w[0];
} else {
// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
// res = C * 10^exp (exact) - must fit in 64 bits
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint64_xrnint
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
bid128_to_uint64_xrnint, x)
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64, tmp64A;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
// in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
// so x rounded to an integer may or may not fit in an unsigned 64-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 20'
if (x_sign) { // if n < 0 and q + exp = 20
// if n < -1/2 then n cannot be converted to uint64 with RN
// too large if c(0)c(1)...c(19).c(20)...c(q-1) > 1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^21 > 0x05, 1<=q<=34
// <=> C * 10^(21-q) > 0x05, 1<=q<=34
if (q == 21) {
// C > 5
if (C1.w[1] != 0 || C1.w[0] > 0x05ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to 64-bit unsigned int fall through
// to '1 <= q + exp <= 20'
} else {
// if 1 <= q <= 20
// C * 10^(21-q) > 5 is true because C >= 1 and 10^(21-q) >= 10
// if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C > 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
} else { // if n > 0 and q + exp = 20
// if n >= 2^64 - 1/2 then n is too large
// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)
// <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34
if (q == 1) {
// C * 10^20 >= 0x9fffffffffffffffb
__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C
if (C.w[1] > 0x09 || (C.w[1] == 0x09
&& C.w[0] >= 0xfffffffffffffffbull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q <= 19) {
// C * 10^(21-q) >= 0x9fffffffffffffffb
__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
if (C.w[1] > 0x09 || (C.w[1] == 0x09
&& C.w[0] >= 0xfffffffffffffffbull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 20) {
// C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff
C.w[0] = C1.w[0] + C1.w[0];
C.w[1] = C1.w[1] + C1.w[1];
if (C.w[0] < C1.w[0])
C.w[1]++;
if (C.w[1] > 0x01 || (C.w[1] == 0x01
&& C.w[0] >= 0xffffffffffffffffull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 21) {
// C >= 0x9fffffffffffffffb
if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
&& C1.w[0] >= 0xfffffffffffffffbull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits
C.w[1] = 0x09;
C.w[0] = 0xfffffffffffffffbull;
__mul_128x64_to_128 (C, ten2k64[q - 21], C);
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
}
}
}
// n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2
// Note: some of the cases tested for above fall through to this point
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
// if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)
// res = 0
// else if x > 0
// res = +1
// else // if x < 0
// invalid exc
ind = q - 1;
if (ind <= 18) { // 0 <= ind <= 18
if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) {
res = 0x0000000000000000ull; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x8000000000000000ull;
*pfpsf |= INVALID_EXCEPTION;
BID_RETURN (res);
}
} else { // 19 <= ind <= 33
if ((C1.w[1] < midpoint128[ind - 19].w[1])
|| ((C1.w[1] == midpoint128[ind - 19].w[1])
&& (C1.w[0] <= midpoint128[ind - 19].w[0]))) {
res = 0x0000000000000000ull; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x8000000000000000ull;
*pfpsf |= INVALID_EXCEPTION;
BID_RETURN (res);
}
}
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
// x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded
// to nearest to a 64-bit unsigned signed integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// 1 <= x < 2^64-1/2 so x can be rounded
// to nearest to a 64-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// determine inexactness of the rounding of C*
// if (0 < f* - 1/2 < 10^(-x)) then
// the result is exact
// else // if (f* - 1/2 > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > 0x8000000000000000ull ||
(fstar.w[1] == 0x8000000000000000ull
&& fstar.w[0] > 0x0ull)) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2
if (tmp64 > ten2mk128trunc[ind - 1].w[1]
|| (tmp64 == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[3] > 0x0 ||
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
(fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[2] - onehalf128[ind - 1];
tmp64A = fstar.w[3];
if (tmp64 > fstar.w[2])
tmp64A--;
if (tmp64A || tmp64
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
} else { // if 22 <= ind <= 33
if (fstar.w[3] > onehalf128[ind - 1] ||
(fstar.w[3] == onehalf128[ind - 1] &&
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[3] - onehalf128[ind - 1];
if (tmp64 || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
}
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
&& (fstar.w[1] || fstar.w[0])
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
// the result is a midpoint; round to nearest
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar.w[0]--; // Cstar.w[0] is now even
} // else MP in [ODD, EVEN]
}
res = Cstar.w[0]; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
// res = C (exact)
res = C1.w[0];
} else {
// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
// res = C * 10^exp (exact) - must fit in 64 bits
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint64_floor
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
bid128_to_uint64_floor, x)
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 P256;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // x is not special and is not zero
// if n < 0 then n cannot be converted to uint64 with RM
if (x_sign) { // if n < 0 and q + exp = 20
// too large if c(0)c(1)...c(19).c(20)...c(q-1) > 0
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
// in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
// so x rounded to an integer may or may not fit in an unsigned 64-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 20'
// if n > 0 and q + exp = 20
// if n >= 2^64 then n is too large
// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65
// <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34
if (q == 1) {
// C * 10^20 >= 0xa0000000000000000
__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C
if (C.w[1] >= 0x0a) {
// actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q <= 19) {
// C * 10^(21-q) >= 0xa0000000000000000
__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
if (C.w[1] >= 0x0a) {
// actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 20) {
// C >= 0x10000000000000000
if (C1.w[1] >= 0x01) {
// actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 21) {
// C >= 0xa0000000000000000
if (C1.w[1] >= 0x0a) {
// actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits
C.w[1] = 0x0a;
C.w[0] = 0x0000000000000000ull;
__mul_128x64_to_128 (C, ten2k64[q - 21], C);
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
}
}
// n is not too large to be converted to int64 if 0 <= n < 2^64
// Note: some of the cases tested for above fall through to this point
if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1)
// return 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
// 1 <= x < 2^64 so x can be rounded
// down to a 64-bit unsigned signed integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 127 bits
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
res = Cstar.w[0]; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
// res = C (exact)
res = C1.w[0];
} else {
// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
// res = C * 10^exp (exact) - must fit in 64 bits
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint64_xfloor
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
bid128_to_uint64_xfloor, x)
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // x is not special and is not zero
// if n < 0 then n cannot be converted to uint64 with RM
if (x_sign) { // if n < 0 and q + exp = 20
// too large if c(0)c(1)...c(19).c(20)...c(q-1) > 0
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
// in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
// so x rounded to an integer may or may not fit in an unsigned 64-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 20'
// if n > 0 and q + exp = 20
// if n >= 2^64 then n is too large
// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65
// <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34
if (q == 1) {
// C * 10^20 >= 0xa0000000000000000
__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C
if (C.w[1] >= 0x0a) {
// actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q <= 19) {
// C * 10^(21-q) >= 0xa0000000000000000
__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
if (C.w[1] >= 0x0a) {
// actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 20) {
// C >= 0x10000000000000000
if (C1.w[1] >= 0x01) {
// actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 21) {
// C >= 0xa0000000000000000
if (C1.w[1] >= 0x0a) {
// actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits
C.w[1] = 0x0a;
C.w[0] = 0x0000000000000000ull;
__mul_128x64_to_128 (C, ten2k64[q - 21], C);
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
}
}
// n is not too large to be converted to int64 if 0 <= n < 2^64
// Note: some of the cases tested for above fall through to this point
if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
// 1 <= x < 2^64 so x can be rounded
// down to a 64-bit unsigned signed integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 127 bits
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// determine inexactness of the rounding of C*
// if (0 < f* < 10^(-x)) then
// the result is exact
// else // if (f* > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1] ||
(fstar.w[1] == ten2mk128trunc[ind - 1].w[1] &&
fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // if 22 <= ind <= 33
if (fstar.w[3] || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
}
res = Cstar.w[0]; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
// res = C (exact)
res = C1.w[0];
} else {
// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
// res = C * 10^exp (exact) - must fit in 64 bits
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint64_ceil
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, bid128_to_uint64_ceil,
x)
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
// in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
// so x rounded to an integer may or may not fit in an unsigned 64-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 20'
if (x_sign) { // if n < 0 and q + exp = 20
// if n <= -1 then n cannot be converted to uint64 with RZ
// too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1
// <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34
// <=> C * 10^(21-q) >= 0x0a, 1<=q<=34
if (q == 21) {
// C >= a
if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to 64-bit unsigned int fall through
// to '1 <= q + exp <= 20'
} else {
// if 1 <= q <= 20
// C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10
// if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
} else { // if n > 0 and q + exp = 20
// if n > 2^64 - 1 then n is too large
// <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 > 10 * (2^64 - 1)
// <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=34
if (q == 1) {
// C * 10^20 > 0x9fffffffffffffff6
__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C
if (C.w[1] > 0x09 || (C.w[1] == 0x09
&& C.w[0] > 0xfffffffffffffff6ull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q <= 19) {
// C * 10^(21-q) > 0x9fffffffffffffff6
__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
if (C.w[1] > 0x09 || (C.w[1] == 0x09
&& C.w[0] > 0xfffffffffffffff6ull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 20) {
// C > 0xffffffffffffffff
if (C1.w[1]) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 21) {
// C > 0x9fffffffffffffff6
if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
&& C1.w[0] > 0xfffffffffffffff6ull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C > 10^(q-21) * 0x9fffffffffffffff6 max 44 bits x 68 bits
C.w[1] = 0x09;
C.w[0] = 0xfffffffffffffff6ull;
__mul_128x64_to_128 (C, ten2k64[q - 21], C);
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
}
}
}
// n is not too large to be converted to int64 if -1 < n <= 2^64 - 1
// Note: some of the cases tested for above fall through to this point
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
// return 0 or 1
if (x_sign)
res = 0x0000000000000000ull;
else
res = 0x0000000000000001ull;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
// x <= -1 or 1 <= x < 2^64 so if positive x can be rounded
// to zero to a 64-bit unsigned signed integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// 1 <= x <= 2^64 - 1 so x can be rounded
// to zero to a 64-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 127 bits
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// if the result is positive and inexact, need to add 1 to it
// determine inexactness of the rounding of C*
// if (0 < f* < 10^(-x)) then
// the result is exact
// else // if (f* > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
if (!x_sign) { // positive and inexact
Cstar.w[0]++;
if (Cstar.w[0] == 0x0)
Cstar.w[1]++;
}
} // else the result is exact
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
if (!x_sign) { // positive and inexact
Cstar.w[0]++;
if (Cstar.w[0] == 0x0)
Cstar.w[1]++;
}
} // else the result is exact
} else { // if 22 <= ind <= 33
if (fstar.w[3] || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
if (!x_sign) { // positive and inexact
Cstar.w[0]++;
if (Cstar.w[0] == 0x0)
Cstar.w[1]++;
}
} // else the result is exact
}
res = Cstar.w[0]; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
// res = C (exact)
res = C1.w[0];
} else {
// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
// res = C * 10^exp (exact) - must fit in 64 bits
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint64_xceil
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
bid128_to_uint64_xceil, x)
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
// in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
// so x rounded to an integer may or may not fit in an unsigned 64-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 20'
if (x_sign) { // if n < 0 and q + exp = 20
// if n <= -1 then n cannot be converted to uint64 with RZ
// too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1
// <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34
// <=> C * 10^(21-q) >= 0x0a, 1<=q<=34
if (q == 21) {
// C >= a
if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to 64-bit unsigned int fall through
// to '1 <= q + exp <= 20'
} else {
// if 1 <= q <= 20
// C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10
// if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
} else { // if n > 0 and q + exp = 20
// if n > 2^64 - 1 then n is too large
// <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 > 10 * (2^64 - 1)
// <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=34
if (q == 1) {
// C * 10^20 > 0x9fffffffffffffff6
__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C
if (C.w[1] > 0x09 || (C.w[1] == 0x09
&& C.w[0] > 0xfffffffffffffff6ull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q <= 19) {
// C * 10^(21-q) > 0x9fffffffffffffff6
__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
if (C.w[1] > 0x09 || (C.w[1] == 0x09
&& C.w[0] > 0xfffffffffffffff6ull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 20) {
// C > 0xffffffffffffffff
if (C1.w[1]) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 21) {
// C > 0x9fffffffffffffff6
if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
&& C1.w[0] > 0xfffffffffffffff6ull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C > 10^(q-21) * 0x9fffffffffffffff6 max 44 bits x 68 bits
C.w[1] = 0x09;
C.w[0] = 0xfffffffffffffff6ull;
__mul_128x64_to_128 (C, ten2k64[q - 21], C);
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
}
}
}
// n is not too large to be converted to int64 if -1 < n <= 2^64 - 1
// Note: some of the cases tested for above fall through to this point
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0 or 1
if (x_sign)
res = 0x0000000000000000ull;
else
res = 0x0000000000000001ull;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
// x <= -1 or 1 <= x < 2^64 so if positive x can be rounded
// to zero to a 64-bit unsigned signed integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// 1 <= x <= 2^64 - 1 so x can be rounded
// to zero to a 64-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 127 bits
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// if the result is positive and inexact, need to add 1 to it
// determine inexactness of the rounding of C*
// if (0 < f* < 10^(-x)) then
// the result is exact
// else // if (f* > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
if (!x_sign) { // positive and inexact
Cstar.w[0]++;
if (Cstar.w[0] == 0x0)
Cstar.w[1]++;
}
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
if (!x_sign) { // positive and inexact
Cstar.w[0]++;
if (Cstar.w[0] == 0x0)
Cstar.w[1]++;
}
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // if 22 <= ind <= 33
if (fstar.w[3] || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
if (!x_sign) { // positive and inexact
Cstar.w[0]++;
if (Cstar.w[0] == 0x0)
Cstar.w[1]++;
}
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
}
res = Cstar.w[0]; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
// res = C (exact)
res = C1.w[0];
} else {
// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
// res = C * 10^exp (exact) - must fit in 64 bits
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint64_int
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, bid128_to_uint64_int,
x)
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 P256;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
// in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
// so x rounded to an integer may or may not fit in an unsigned 64-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 20'
if (x_sign) { // if n < 0 and q + exp = 20
// if n <= -1 then n cannot be converted to uint64 with RZ
// too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1
// <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34
// <=> C * 10^(21-q) >= 0x0a, 1<=q<=34
if (q == 21) {
// C >= a
if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to 64-bit unsigned int fall through
// to '1 <= q + exp <= 20'
} else {
// if 1 <= q <= 20
// C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10
// if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
} else { // if n > 0 and q + exp = 20
// if n >= 2^64 then n is too large
// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65
// <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34
if (q == 1) {
// C * 10^20 >= 0xa0000000000000000
__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C
if (C.w[1] >= 0x0a) {
// actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q <= 19) {
// C * 10^(21-q) >= 0xa0000000000000000
__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
if (C.w[1] >= 0x0a) {
// actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 20) {
// C >= 0x10000000000000000
if (C1.w[1] >= 0x01) {
// actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 21) {
// C >= 0xa0000000000000000
if (C1.w[1] >= 0x0a) {
// actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits
C.w[1] = 0x0a;
C.w[0] = 0x0000000000000000ull;
__mul_128x64_to_128 (C, ten2k64[q - 21], C);
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
}
}
}
// n is not too large to be converted to int64 if -1 < n < 2^64
// Note: some of the cases tested for above fall through to this point
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
// return 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
// x <= -1 or 1 <= x < 2^64 so if positive x can be rounded
// to zero to a 64-bit unsigned signed integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// 1 <= x < 2^64 so x can be rounded
// to zero to a 64-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 127 bits
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
res = Cstar.w[0]; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
// res = C (exact)
res = C1.w[0];
} else {
// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
// res = C * 10^exp (exact) - must fit in 64 bits
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint64_xint
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, bid128_to_uint64_xint,
x)
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
// in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
// so x rounded to an integer may or may not fit in an unsigned 64-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 20'
if (x_sign) { // if n < 0 and q + exp = 20
// if n <= -1 then n cannot be converted to uint64 with RZ
// too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1
// <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34
// <=> C * 10^(21-q) >= 0x0a, 1<=q<=34
if (q == 21) {
// C >= a
if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to 64-bit unsigned int fall through
// to '1 <= q + exp <= 20'
} else {
// if 1 <= q <= 20
// C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10
// if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
} else { // if n > 0 and q + exp = 20
// if n >= 2^64 then n is too large
// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65
// <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34
if (q == 1) {
// C * 10^20 >= 0xa0000000000000000
__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C
if (C.w[1] >= 0x0a) {
// actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q <= 19) {
// C * 10^(21-q) >= 0xa0000000000000000
__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
if (C.w[1] >= 0x0a) {
// actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 20) {
// C >= 0x10000000000000000
if (C1.w[1] >= 0x01) {
// actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 21) {
// C >= 0xa0000000000000000
if (C1.w[1] >= 0x0a) {
// actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits
C.w[1] = 0x0a;
C.w[0] = 0x0000000000000000ull;
__mul_128x64_to_128 (C, ten2k64[q - 21], C);
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
}
}
}
// n is not too large to be converted to int64 if -1 < n < 2^64
// Note: some of the cases tested for above fall through to this point
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
// x <= -1 or 1 <= x < 2^64 so if positive x can be rounded
// to zero to a 64-bit unsigned signed integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// 1 <= x < 2^64 so x can be rounded
// to zero to a 64-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 127 bits
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// determine inexactness of the rounding of C*
// if (0 < f* < 10^(-x)) then
// the result is exact
// else // if (f* > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // if 22 <= ind <= 33
if (fstar.w[3] || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
}
res = Cstar.w[0]; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
// res = C (exact)
res = C1.w[0];
} else {
// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
// res = C * 10^exp (exact) - must fit in 64 bits
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint64_rninta
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
bid128_to_uint64_rninta, x)
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 P256;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
// in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
// so x rounded to an integer may or may not fit in an unsigned 64-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 20'
if (x_sign) { // if n < 0 and q + exp = 20
// if n <= -1/2 then n cannot be converted to uint64 with RN
// too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x05, 1<=q<=34
// <=> C * 10^(21-q) >= 0x05, 1<=q<=34
if (q == 21) {
// C >= 5
if (C1.w[1] != 0 || C1.w[0] >= 0x05ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to 64-bit unsigned int fall through
// to '1 <= q + exp <= 20'
} else {
// if 1 <= q <= 20
// C * 10^(21-q) >= 5 is true because C >= 1 and 10^(21-q) >= 10
// if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
} else { // if n > 0 and q + exp = 20
// if n >= 2^64 - 1/2 then n is too large
// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)
// <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34
if (q == 1) {
// C * 10^20 >= 0x9fffffffffffffffb
__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C
if (C.w[1] > 0x09 || (C.w[1] == 0x09
&& C.w[0] >= 0xfffffffffffffffbull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q <= 19) {
// C * 10^(21-q) >= 0x9fffffffffffffffb
__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
if (C.w[1] > 0x09 || (C.w[1] == 0x09
&& C.w[0] >= 0xfffffffffffffffbull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 20) {
// C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff
C.w[0] = C1.w[0] + C1.w[0];
C.w[1] = C1.w[1] + C1.w[1];
if (C.w[0] < C1.w[0])
C.w[1]++;
if (C.w[1] > 0x01 || (C.w[1] == 0x01
&& C.w[0] >= 0xffffffffffffffffull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 21) {
// C >= 0x9fffffffffffffffb
if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
&& C1.w[0] >= 0xfffffffffffffffbull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits
C.w[1] = 0x09;
C.w[0] = 0xfffffffffffffffbull;
__mul_128x64_to_128 (C, ten2k64[q - 21], C);
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
}
}
}
// n is not too large to be converted to int64 if -1/2 < n < 2^64 - 1/2
// Note: some of the cases tested for above fall through to this point
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
// return 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
// if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1)
// res = 0
// else if x > 0
// res = +1
// else // if x < 0
// invalid exc
ind = q - 1;
if (ind <= 18) { // 0 <= ind <= 18
if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) {
res = 0x0000000000000000ull; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
} else { // 19 <= ind <= 33
if ((C1.w[1] < midpoint128[ind - 19].w[1])
|| ((C1.w[1] == midpoint128[ind - 19].w[1])
&& (C1.w[0] < midpoint128[ind - 19].w[0]))) {
res = 0x0000000000000000ull; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
}
} else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
// x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded
// to nearest to a 64-bit unsigned signed integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// 1 <= x < 2^64-1/2 so x can be rounded
// to nearest to a 64-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// if the result was a midpoint it was rounded away from zero
res = Cstar.w[0]; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
// res = C (exact)
res = C1.w[0];
} else {
// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
// res = C * 10^exp (exact) - must fit in 64 bits
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint64_xrninta
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
bid128_to_uint64_xrninta, x)
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64, tmp64A;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
// in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
// so x rounded to an integer may or may not fit in an unsigned 64-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 20'
if (x_sign) { // if n < 0 and q + exp = 20
// if n <= -1/2 then n cannot be converted to uint64 with RN
// too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x05, 1<=q<=34
// <=> C * 10^(21-q) >= 0x05, 1<=q<=34
if (q == 21) {
// C >= 5
if (C1.w[1] != 0 || C1.w[0] >= 0x05ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to 64-bit unsigned int fall through
// to '1 <= q + exp <= 20'
} else {
// if 1 <= q <= 20
// C * 10^(21-q) >= 5 is true because C >= 1 and 10^(21-q) >= 10
// if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
} else { // if n > 0 and q + exp = 20
// if n >= 2^64 - 1/2 then n is too large
// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2
// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)
// <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34
if (q == 1) {
// C * 10^20 >= 0x9fffffffffffffffb
__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C
if (C.w[1] > 0x09 || (C.w[1] == 0x09
&& C.w[0] >= 0xfffffffffffffffbull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q <= 19) {
// C * 10^(21-q) >= 0x9fffffffffffffffb
__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
if (C.w[1] > 0x09 || (C.w[1] == 0x09
&& C.w[0] >= 0xfffffffffffffffbull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 20) {
// C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff
C.w[0] = C1.w[0] + C1.w[0];
C.w[1] = C1.w[1] + C1.w[1];
if (C.w[0] < C1.w[0])
C.w[1]++;
if (C.w[1] > 0x01 || (C.w[1] == 0x01
&& C.w[0] >= 0xffffffffffffffffull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else if (q == 21) {
// C >= 0x9fffffffffffffffb
if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
&& C1.w[0] >= 0xfffffffffffffffbull)) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
// C >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits
C.w[1] = 0x09;
C.w[0] = 0xfffffffffffffffbull;
__mul_128x64_to_128 (C, ten2k64[q - 21], C);
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// else cases that can be rounded to a 64-bit int fall through
// to '1 <= q + exp <= 20'
}
}
}
// n is not too large to be converted to int64 if -1/2 < n < 2^64 - 1/2
// Note: some of the cases tested for above fall through to this point
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0
res = 0x0000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
// if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1)
// res = 0
// else if x > 0
// res = +1
// else // if x < 0
// invalid exc
ind = q - 1;
if (ind <= 18) { // 0 <= ind <= 18
if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) {
res = 0x0000000000000000ull; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x8000000000000000ull;
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
} else { // 19 <= ind <= 33
if ((C1.w[1] < midpoint128[ind - 19].w[1])
|| ((C1.w[1] == midpoint128[ind - 19].w[1])
&& (C1.w[0] < midpoint128[ind - 19].w[0]))) {
res = 0x0000000000000000ull; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x8000000000000000ull;
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
}
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
// x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded
// to nearest to a 64-bit unsigned signed integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// 1 <= x < 2^64-1/2 so x can be rounded
// to nearest to a 64-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// determine inexactness of the rounding of C*
// if (0 < f* - 1/2 < 10^(-x)) then
// the result is exact
// else // if (f* - 1/2 > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > 0x8000000000000000ull ||
(fstar.w[1] == 0x8000000000000000ull
&& fstar.w[0] > 0x0ull)) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2
if (tmp64 > ten2mk128trunc[ind - 1].w[1]
|| (tmp64 == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[3] > 0x0 ||
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
(fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[2] - onehalf128[ind - 1];
tmp64A = fstar.w[3];
if (tmp64 > fstar.w[2])
tmp64A--;
if (tmp64A || tmp64
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
} else { // if 22 <= ind <= 33
if (fstar.w[3] > onehalf128[ind - 1] ||
(fstar.w[3] == onehalf128[ind - 1] &&
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[3] - onehalf128[ind - 1];
if (tmp64 || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
}
// if the result was a midpoint it was rounded away from zero
res = Cstar.w[0]; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
// res = C (exact)
res = C1.w[0];
} else {
// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
// res = C * 10^exp (exact) - must fit in 64 bits
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
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