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gcc/libgcc/config/libbid/bid64_to_uint64.c

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/* Copyright (C) 2007 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 2, or (at your option) any later
version.
In addition to the permissions in the GNU General Public License, the
Free Software Foundation gives you unlimited permission to link the
compiled version of this file into combinations with other programs,
and to distribute those combinations without any restriction coming
from the use of this file. (The General Public License restrictions
do apply in other respects; for example, they cover modification of
the file, and distribution when not linked into a combine
executable.)
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.
You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING. If not, write to the Free
Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA. */
#include "bid_internal.h"
/*****************************************************************************
* BID64_to_uint64_rnint
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint64_rnint (UINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
bid64_to_uint64_rnint (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT128 C;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((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 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
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 then x is much less than -1/2
// => 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<=16
if (q == 1) {
// C * 10^20 >= 0x9fffffffffffffffb
__mul_128x64_to_128 (C, C1, 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 (2 <= q <= 16) => 5 <= 21 - q <= 19
// Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb
// has 21 digits
__mul_64x64_to_128MACH (C, C1, 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'
}
}
}
// 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; // 0 <= ind <= 15
if (C1 <= midpoint64[ind]) {
res = 0x0000000000000000ull; // return 0
} else if (!x_sign) { // n > 0
res = 0x0000000000000001ull; // return +1
} else { // if n < 0
res = 0x8000000000000000ull;
*pfpsf |= INVALID_EXCEPTION;
BID_RETURN (res);
}
} else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= 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 <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 15; 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 64 bits
C1 = C1 + midpoint64[ind - 1];
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// 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-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[1] == 0) && fstar.w[0] &&
(fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// the result is a midpoint; round to nearest
if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar--; // Cstar is now even
} // else MP in [ODD, EVEN]
}
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint64_xrnint
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint64_xrnint (UINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
bid64_to_uint64_xrnint (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT128 C;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((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 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
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 then x is much less than -1/2
// => 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<=16
if (q == 1) {
// C * 10^20 >= 0x9fffffffffffffffb
__mul_128x64_to_128 (C, C1, 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 (2 <= q <= 16) => 5 <= 21 - q <= 19
// Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb
// has 21 digits
__mul_64x64_to_128MACH (C, C1, 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'
}
}
}
// 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; // 0 <= ind <= 15
if (C1 <= midpoint64[ind]) {
res = 0x0000000000000000ull; // return 0
} else if (!x_sign) { // n > 0
res = 0x0000000000000001ull; // return +1
} else { // if n < 0
res = 0x8000000000000000ull;
*pfpsf |= INVALID_EXCEPTION;
BID_RETURN (res);
}
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= 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 <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 15; 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 64 bits
C1 = C1 + midpoint64[ind - 1];
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// 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-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// 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) { // fstar.w[1] is 0
if (fstar.w[0] > 0x8000000000000000ull) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2
if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// 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 3 <= ind - 1 <= 14
if (fstar.w[1] > onehalf128[ind - 1] ||
(fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[1] - onehalf128[ind - 1];
if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// 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[1] == 0) && fstar.w[0] &&
(fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// the result is a midpoint; round to nearest
if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar--; // Cstar is now even
} // else MP in [ODD, EVEN]
}
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint64_floor
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint64_floor (UINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
bid64_to_uint64_floor (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT128 C;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
}
// x is not special and is not zero
if (x_sign) { // if n < 0 the conversion is invalid
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((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 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
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'
// 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<=16
if (q == 1) {
// C * 10^20 >= 0xa0000000000000000
__mul_128x64_to_128 (C, C1, 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 (2 <= q <= 16) => 5 <= 21 - q <= 19
// Note: C * 10^(21-q) has 20 or 21 digits; 0xa0000000000000000
// has 21 digits
__mul_64x64_to_128MACH (C, C1, 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'
}
}
// 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 <= 16, -15 <= exp <= 19)
// 1 <= x < 2^64 so x can be rounded
// to nearest to a 64-bit unsigned signed integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 64 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 <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// 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-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint64_xfloor
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint64_xfloor (UINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
bid64_to_uint64_xfloor (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT128 C;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
}
// x is not special and is not zero
if (x_sign) { // if n < 0 the conversion is invalid
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((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 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
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'
// 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<=16
if (q == 1) {
// C * 10^20 >= 0xa0000000000000000
__mul_128x64_to_128 (C, C1, 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 (2 <= q <= 16) => 5 <= 21 - q <= 19
// Note: C * 10^(21-q) has 20 or 21 digits; 0xa0000000000000000
// has 21 digits
__mul_64x64_to_128MACH (C, C1, 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'
}
}
// 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 <= 16, -15 <= exp <= 19)
// 1 <= x < 2^64 so x can be rounded
// to nearest to a 64-bit unsigned signed integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 64 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 <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// 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-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// 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) { // fstar.w[1] is 0
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // if 3 <= ind - 1 <= 14
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
}
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint64_ceil
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint64_ceil (UINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
bid64_to_uint64_ceil (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT128 C;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((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 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
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 then x is much less than -1
// => 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 >= 5*(2^65 - 2)
// <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=16
if (q == 1) {
// C * 10^20 > 0x9fffffffffffffff6
__mul_128x64_to_128 (C, C1, 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 (2 <= q <= 16) => 5 <= 21 - q <= 19
// Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffff6
// has 21 digits
__mul_64x64_to_128MACH (C, C1, 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'
}
}
}
// 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 or 1
if (x_sign)
res = 0x0000000000000000ull;
else
res = 0x0000000000000001ull;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19)
// x <= -1 or 1 <= x <= 2^64 - 1 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 so x can be rounded
// to nearest to a 64-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 64 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 <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// 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-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// 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) { // fstar.w[1] is 0
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
Cstar++;
} // else the result is exact
} else { // if 3 <= ind - 1 <= 14
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
Cstar++;
} // else the result is exact
}
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint64_xceil
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint64_xceil (UINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
bid64_to_uint64_xceil (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT128 C;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((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 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
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 then x is much less than -1
// => 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 >= 5*(2^65 - 2)
// <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=16
if (q == 1) {
// C * 10^20 > 0x9fffffffffffffff6
__mul_128x64_to_128 (C, C1, 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 (2 <= q <= 16) => 5 <= 21 - q <= 19
// Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffff6
// has 21 digits
__mul_64x64_to_128MACH (C, C1, 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'
}
}
}
// 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 or 1
if (x_sign)
res = 0x0000000000000000ull;
else
res = 0x0000000000000001ull;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19)
// x <= -1 or 1 <= x <= 2^64 - 1 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 so x can be rounded
// to nearest to a 64-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 64 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 <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// 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-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// 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) { // fstar.w[1] is 0
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
Cstar++;
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // if 3 <= ind - 1 <= 14
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
Cstar++;
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
}
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint64_int
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint64_int (UINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM)
{
UINT64 x = *px;
#else
UINT64
bid64_to_uint64_int (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM)
{
#endif
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT128 C;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((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 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
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 then x is much less than -1
// => 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<=16
if (q == 1) {
// C * 10^20 >= 0xa0000000000000000
__mul_128x64_to_128 (C, C1, 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 (2 <= q <= 16) => 5 <= 21 - q <= 19
// Note: C * 10^(21-q) has 20 or 21 digits; 0xa0000000000000000
// has 21 digits
__mul_64x64_to_128MACH (C, C1, 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'
}
}
}
// 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 <= 16, -15 <= exp <= 19)
// x <= -1 or 1 <= x < 2^64 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 so x can be rounded
// to nearest to a 64-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 64 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 <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// 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-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint64_xint
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint64_xint (UINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
bid64_to_uint64_xint (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT128 C;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((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 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
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 then x is much less than -1
// => 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<=16
if (q == 1) {
// C * 10^20 >= 0xa0000000000000000
__mul_128x64_to_128 (C, C1, 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 (2 <= q <= 16) => 5 <= 21 - q <= 19
// Note: C * 10^(21-q) has 20 or 21 digits; 0xa0000000000000000
// has 21 digits
__mul_64x64_to_128MACH (C, C1, 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'
}
}
}
// 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 <= 16, -15 <= exp <= 19)
// x <= -1 or 1 <= x < 2^64 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 so x can be rounded
// to nearest to a 64-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 64 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 <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// 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-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// 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) { // fstar.w[1] is 0
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // if 3 <= ind - 1 <= 14
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
}
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint64_rninta
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint64_rninta (UINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
bid64_to_uint64_rninta (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT128 C;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((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 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
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 then x is much less than -1/2
// => 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<=16
if (q == 1) {
// C * 10^20 >= 0x9fffffffffffffffb
__mul_128x64_to_128 (C, C1, 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 (2 <= q <= 16) => 5 <= 21 - q <= 19
// Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb
// has 21 digits
__mul_64x64_to_128MACH (C, C1, 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'
}
}
}
// 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; // 0 <= ind <= 15
if (C1 < midpoint64[ind]) {
res = 0x0000000000000000ull; // return 0
} else if (!x_sign) { // n > 0
res = 0x0000000000000001ull; // return +1
} else { // if n < 0
res = 0x8000000000000000ull;
*pfpsf |= INVALID_EXCEPTION;
BID_RETURN (res);
}
} else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= 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 <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 15; 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 64 bits
C1 = C1 + midpoint64[ind - 1];
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// 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-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// if the result was a midpoint it was rounded away from zero
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint64_xrninta
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint64_xrninta (UINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
UINT64
bid64_to_uint64_xrninta (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
UINT64 res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT128 C;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x0000000000000000ull;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((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 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
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 then x is much less than -1/2
// => 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<=16
if (q == 1) {
// C * 10^20 >= 0x9fffffffffffffffb
__mul_128x64_to_128 (C, C1, 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 (2 <= q <= 16) => 5 <= 21 - q <= 19
// Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb
// has 21 digits
__mul_64x64_to_128MACH (C, C1, 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'
}
}
}
// 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; // 0 <= ind <= 15
if (C1 < midpoint64[ind]) {
res = 0x0000000000000000ull; // return 0
} else if (!x_sign) { // n > 0
res = 0x0000000000000001ull; // return +1
} else { // if n < 0
res = 0x8000000000000000ull;
*pfpsf |= INVALID_EXCEPTION;
BID_RETURN (res);
}
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= 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 <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20
ind = -exp; // 1 <= ind <= 15; 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 64 bits
C1 = C1 + midpoint64[ind - 1];
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// 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-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// 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) { // fstar.w[1] is 0
if (fstar.w[0] > 0x8000000000000000ull) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2
if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// 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 3 <= ind - 1 <= 14
if (fstar.w[1] > onehalf128[ind - 1] ||
(fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[1] - onehalf128[ind - 1];
if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// 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; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
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