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/* Copyright (C) 2007-2019 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"
/*****************************************************************************
* BID64_to_int64_rnint
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_int64_rnint (SINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
SINT64
bid64_to_int64_rnint (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
SINT64 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 = 0x00000000;
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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...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 a signed 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 <= 19'
if (x_sign) { // if n < 0 and q + exp = 19
// if n < -2^63 - 1/2 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63+1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64+1), 1<=q<=16
// <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000005, 1<=q<=16
// <=> C * 10^(20-q) > 0x50000000000000005, 1<=q<=16
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
// Note: C1 * 10^(11-q) has 19 or 20 digits; 0x50000000000000005, has 20
if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] > 0x05ull)) {
// 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 <= 19'
} else { // if n > 0 and q + exp = 19
// if n >= 2^63 - 1/2 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=16
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=16
// <=> if C * 10^(20-q) >= 0x4fffffffffffffffb, 1<=q<=16
C.w[1] = 0x0000000000000004ull;
C.w[0] = 0xfffffffffffffffbull;
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
if (C.w[1] > 0x04ull ||
(C.w[1] == 0x04ull && 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 <= 19'
} // end else if n > 0 and q + exp = 19
} // end else if ((q + exp) == 19)
// n is not too large to be converted to int64: -2^63-1/2 <= n < 2^63-1/2
// 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
// res = +/-1
ind = q - 1; // 0 <= ind <= 15
if (C1 <= midpoint64[ind]) {
res = 0x0000000000000000ull; // return 0
} else if (x_sign) { // n < 0
res = 0xffffffffffffffffull; // return -1
} else { // n > 0
res = 0x0000000000000001ull; // return +1
}
} else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18)
// -2^63-1/2 <= x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded
// to nearest to a 64-bit signed integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19
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]
}
if (x_sign)
res = -Cstar;
else
res = Cstar;
} else if (exp == 0) {
// 1 <= q <= 16
// res = +/-C (exact)
if (x_sign)
res = -C1;
else
res = C1;
} else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20
// (the upper limit of 20 on q + exp is due to the fact that
// +/-C * 10^exp is guaranteed to fit in 64 bits)
// res = +/-C * 10^exp (exact)
if (x_sign)
res = -C1 * ten2k64[exp];
else
res = C1 * ten2k64[exp];
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_int64_xrnint
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_int64_xrnint (SINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
SINT64
bid64_to_int64_xrnint (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
SINT64 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 = 0x00000000;
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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...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 a signed 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 <= 19'
if (x_sign) { // if n < 0 and q + exp = 19
// if n < -2^63 - 1/2 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63+1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64+1), 1<=q<=16
// <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000005, 1<=q<=16
// <=> C * 10^(20-q) > 0x50000000000000005, 1<=q<=16
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
// Note: C1 * 10^(11-q) has 19 or 20 digits; 0x50000000000000005, has 20
if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] > 0x05ull)) {
// 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 <= 19'
} else { // if n > 0 and q + exp = 19
// if n >= 2^63 - 1/2 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=16
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=16
// <=> if C * 10^(20-q) >= 0x4fffffffffffffffb, 1<=q<=16
C.w[1] = 0x0000000000000004ull;
C.w[0] = 0xfffffffffffffffbull;
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
if (C.w[1] > 0x04ull ||
(C.w[1] == 0x04ull && 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 <= 19'
} // end else if n > 0 and q + exp = 19
} // end else if ((q + exp) == 19)
// n is not too large to be converted to int64: -2^63-1/2 <= n < 2^63-1/2
// 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
// res = +/-1
ind = q - 1; // 0 <= ind <= 15
if (C1 <= midpoint64[ind]) {
res = 0x0000000000000000ull; // return 0
} else if (x_sign) { // n < 0
res = 0xffffffffffffffffull; // return -1
} else { // n > 0
res = 0x0000000000000001ull; // return +1
}
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18)
// -2^63-1/2 <= x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded
// to nearest to a 64-bit signed integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19
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) {
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]
}
if (x_sign)
res = -Cstar;
else
res = Cstar;
} else if (exp == 0) {
// 1 <= q <= 16
// res = +/-C (exact)
if (x_sign)
res = -C1;
else
res = C1;
} else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20
// (the upper limit of 20 on q + exp is due to the fact that
// +/-C * 10^exp is guaranteed to fit in 64 bits)
// res = +/-C * 10^exp (exact)
if (x_sign)
res = -C1 * ten2k64[exp];
else
res = C1 * ten2k64[exp];
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_int64_floor
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_int64_floor (SINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
SINT64
bid64_to_int64_floor (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
SINT64 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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...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 a signed 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 <= 19'
if (x_sign) { // if n < 0 and q + exp = 19
// if n < -2^63 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16
// <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000000, 1<=q<=16
// <=> C * 10^(20-q) > 0x50000000000000000, 1<=q<=16
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
// Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20
if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] != 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 <= 19'
} else { // if n > 0 and q + exp = 19
// if n >= 2^63 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=16
// <=> if C * 10^(20-q) >= 0x50000000000000000, 1<=q<=16
C.w[1] = 0x0000000000000005ull;
C.w[0] = 0x0000000000000000ull;
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
if (C.w[1] >= 0x05ull) {
// actually C.w[1] == 0x05ull && 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 <= 19'
} // end else if n > 0 and q + exp = 19
} // end else if ((q + exp) == 19)
// n is not too large to be converted to int64: -2^63 <= n < 2^63
// 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 -1 or 0
if (x_sign)
res = 0xffffffffffffffffull;
else
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18)
// -2^63 <= x <= -1 or 1 <= x < 2^63 so x can be rounded
// to nearest to a 64-bit signed integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19
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]
if (x_sign) { // negative and inexact
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]
if (x_sign) { // negative and inexact
Cstar++;
}
} // else the result is exact
}
if (x_sign)
res = -Cstar;
else
res = Cstar;
} else if (exp == 0) {
// 1 <= q <= 16
// res = +/-C (exact)
if (x_sign)
res = -C1;
else
res = C1;
} else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20
// (the upper limit of 20 on q + exp is due to the fact that
// +/-C * 10^exp is guaranteed to fit in 64 bits)
// res = +/-C * 10^exp (exact)
if (x_sign)
res = -C1 * ten2k64[exp];
else
res = C1 * ten2k64[exp];
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_int64_xfloor
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_int64_xfloor (SINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
SINT64
bid64_to_int64_xfloor (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
SINT64 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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...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 a signed 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 <= 19'
if (x_sign) { // if n < 0 and q + exp = 19
// if n < -2^63 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16
// <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000000, 1<=q<=16
// <=> C * 10^(20-q) > 0x50000000000000000, 1<=q<=16
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
// Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20
if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] != 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 <= 19'
} else { // if n > 0 and q + exp = 19
// if n >= 2^63 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=16
// <=> if C * 10^(20-q) >= 0x50000000000000000, 1<=q<=16
C.w[1] = 0x0000000000000005ull;
C.w[0] = 0x0000000000000000ull;
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
if (C.w[1] >= 0x05ull) {
// actually C.w[1] == 0x05ull && 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 <= 19'
} // end else if n > 0 and q + exp = 19
} // end else if ((q + exp) == 19)
// n is not too large to be converted to int64: -2^63 <= n < 2^63
// 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 -1 or 0
if (x_sign)
res = 0xffffffffffffffffull;
else
res = 0x0000000000000000ull;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18)
// -2^63 <= x <= -1 or 1 <= x < 2^63 so x can be rounded
// to nearest to a 64-bit signed integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19
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]
if (x_sign) { // negative and inexact
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]
if (x_sign) { // negative and inexact
Cstar++;
}
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
}
if (x_sign)
res = -Cstar;
else
res = Cstar;
} else if (exp == 0) {
// 1 <= q <= 16
// res = +/-C (exact)
if (x_sign)
res = -C1;
else
res = C1;
} else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20
// (the upper limit of 20 on q + exp is due to the fact that
// +/-C * 10^exp is guaranteed to fit in 64 bits)
// res = +/-C * 10^exp (exact)
if (x_sign)
res = -C1 * ten2k64[exp];
else
res = C1 * ten2k64[exp];
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_int64_ceil
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_int64_ceil (SINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM)
{
UINT64 x = *px;
#else
SINT64
bid64_to_int64_ceil (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM)
{
#endif
SINT64 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 = 0x00000000;
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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...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 a signed 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 <= 19'
if (x_sign) { // if n < 0 and q + exp = 19
// if n <= -2^63 - 1 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=16
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=16
// <=> C * 10^(20-q) >= 0x5000000000000000a, 1<=q<=16
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
// Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20
if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x0aull)) {
// 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 <= 19'
} else { // if n > 0 and q + exp = 19
// if n > 2^63 - 1 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 - 1
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64-2), 1<=q<=16
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 0x4fffffffffffffff6, 1<=q<=16
// <=> if C * 10^(20-q) > 0x4fffffffffffffff6, 1<=q<=16
C.w[1] = 0x0000000000000004ull;
C.w[0] = 0xfffffffffffffff6ull;
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
if (C.w[1] > 0x04ull ||
(C.w[1] == 0x04ull && 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 <= 19'
} // end else if n > 0 and q + exp = 19
} // end else if ((q + exp) == 19)
// n is not too large to be converted to int64: -2^63-1 < n < 2^63
// 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 or 1
if (x_sign)
res = 0x00000000;
else
res = 0x00000001;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18)
// -2^63-1 < x <= -1 or 1 <= x <= 2^63 - 1 so x can be rounded
// to nearest to a 64-bit signed integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19
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]
if (!x_sign) { // positive and inexact
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]
if (!x_sign) { // positive and inexact
Cstar++;
}
} // else the result is exact
}
if (x_sign)
res = -Cstar;
else
res = Cstar;
} else if (exp == 0) {
// 1 <= q <= 16
// res = +/-C (exact)
if (x_sign)
res = -C1;
else
res = C1;
} else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20
// (the upper limit of 20 on q + exp is due to the fact that
// +/-C * 10^exp is guaranteed to fit in 64 bits)
// res = +/-C * 10^exp (exact)
if (x_sign)
res = -C1 * ten2k64[exp];
else
res = C1 * ten2k64[exp];
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_int64_xceil
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_int64_xceil (SINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
SINT64
bid64_to_int64_xceil (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
SINT64 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 = 0x00000000;
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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...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 a signed 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 <= 19'
if (x_sign) { // if n < 0 and q + exp = 19
// if n <= -2^63 - 1 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=16
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=16
// <=> C * 10^(20-q) >= 0x5000000000000000a, 1<=q<=16
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
// Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20
if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x0aull)) {
// 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 <= 19'
} else { // if n > 0 and q + exp = 19
// if n > 2^63 - 1 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 - 1
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64-2), 1<=q<=16
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 0x4fffffffffffffff6, 1<=q<=16
// <=> if C * 10^(20-q) > 0x4fffffffffffffff6, 1<=q<=16
C.w[1] = 0x0000000000000004ull;
C.w[0] = 0xfffffffffffffff6ull;
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
if (C.w[1] > 0x04ull ||
(C.w[1] == 0x04ull && 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 <= 19'
} // end else if n > 0 and q + exp = 19
} // end else if ((q + exp) == 19)
// n is not too large to be converted to int64: -2^63-1 < n < 2^63
// 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 or 1
if (x_sign)
res = 0x00000000;
else
res = 0x00000001;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18)
// -2^63-1 < x <= -1 or 1 <= x <= 2^63 - 1 so x can be rounded
// to nearest to a 64-bit signed integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19
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]
if (!x_sign) { // positive and inexact
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]
if (!x_sign) { // positive and inexact
Cstar++;
}
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
}
if (x_sign)
res = -Cstar;
else
res = Cstar;
} else if (exp == 0) {
// 1 <= q <= 16
// res = +/-C (exact)
if (x_sign)
res = -C1;
else
res = C1;
} else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20
// (the upper limit of 20 on q + exp is due to the fact that
// +/-C * 10^exp is guaranteed to fit in 64 bits)
// res = +/-C * 10^exp (exact)
if (x_sign)
res = -C1 * ten2k64[exp];
else
res = C1 * ten2k64[exp];
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_int64_int
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_int64_int (SINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
UINT64 x = *px;
#else
SINT64
bid64_to_int64_int (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
SINT64 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 = 0x00000000;
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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...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 a signed 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 <= 19'
if (x_sign) { // if n < 0 and q + exp = 19
// if n <= -2^63 - 1 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=16
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=16
// <=> C * 10^(20-q) >= 0x5000000000000000a, 1<=q<=16
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
// Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20
if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x0aull)) {
// 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 <= 19'
} else { // if n > 0 and q + exp = 19
// if n >= 2^63 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=16
// <=> if C * 10^(20-q) >= 0x50000000000000000, 1<=q<=16
C.w[1] = 0x0000000000000005ull;
C.w[0] = 0x0000000000000000ull;
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
if (C.w[1] >= 0x05ull) {
// actually C.w[1] == 0x05ull && 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 <= 19'
} // end else if n > 0 and q + exp = 19
} // end else if ((q + exp) == 19)
// n is not too large to be converted to int64: -2^63-1 < n < 2^63
// 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 (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18)
// -2^63-1 < x <= -1 or 1 <= x < 2^63 so x can be rounded
// to nearest to a 64-bit signed integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19
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;
if (x_sign)
res = -Cstar;
else
res = Cstar;
} else if (exp == 0) {
// 1 <= q <= 16
// res = +/-C (exact)
if (x_sign)
res = -C1;
else
res = C1;
} else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20
// (the upper limit of 20 on q + exp is due to the fact that
// +/-C * 10^exp is guaranteed to fit in 64 bits)
// res = +/-C * 10^exp (exact)
if (x_sign)
res = -C1 * ten2k64[exp];
else
res = C1 * ten2k64[exp];
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_int64_xint
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_int64_xint (SINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM)
{
UINT64 x = *px;
#else
SINT64
bid64_to_int64_xint (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM)
{
#endif
SINT64 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 = 0x00000000;
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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...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 a signed 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 <= 19'
if (x_sign) { // if n < 0 and q + exp = 19
// if n <= -2^63 - 1 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=16
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=16
// <=> C * 10^(20-q) >= 0x5000000000000000a, 1<=q<=16
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
// Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20
if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x0aull)) {
// 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 <= 19'
} else { // if n > 0 and q + exp = 19
// if n >= 2^63 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=16
// <=> if C * 10^(20-q) >= 0x50000000000000000, 1<=q<=16
C.w[1] = 0x0000000000000005ull;
C.w[0] = 0x0000000000000000ull;
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
if (C.w[1] >= 0x05ull) {
// actually C.w[1] == 0x05ull && 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 <= 19'
} // end else if n > 0 and q + exp = 19
} // end else if ((q + exp) == 19)
// n is not too large to be converted to int64: -2^63-1 < n < 2^63
// 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 (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18)
// -2^63-1 < x <= -1 or 1 <= x < 2^63 so x can be rounded
// to nearest to a 64-bit signed integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19
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
}
if (x_sign)
res = -Cstar;
else
res = Cstar;
} else if (exp == 0) {
// 1 <= q <= 16
// res = +/-C (exact)
if (x_sign)
res = -C1;
else
res = C1;
} else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20
// (the upper limit of 20 on q + exp is due to the fact that
// +/-C * 10^exp is guaranteed to fit in 64 bits)
// res = +/-C * 10^exp (exact)
if (x_sign)
res = -C1 * ten2k64[exp];
else
res = C1 * ten2k64[exp];
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_int64_rninta
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_int64_rninta (SINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
SINT64
bid64_to_int64_rninta (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
SINT64 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 = 0x00000000;
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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...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 a signed 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 <= 19'
if (x_sign) { // if n < 0 and q + exp = 19
// if n <= -2^63 - 1/2 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+1), 1<=q<=16
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000005, 1<=q<=16
// <=> C * 10^(20-q) >= 0x50000000000000005, 1<=q<=16
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
// Note: C1 * 10^(11-q) has 19 or 20 digits; 0x50000000000000005, has 20
if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x05ull)) {
// 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 <= 19'
} else { // if n > 0 and q + exp = 19
// if n >= 2^63 - 1/2 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=16
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=16
// <=> if C * 10^(20-q) >= 0x4fffffffffffffffb, 1<=q<=16
C.w[1] = 0x0000000000000004ull;
C.w[0] = 0xfffffffffffffffbull;
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
if (C.w[1] > 0x04ull ||
(C.w[1] == 0x04ull && 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 <= 19'
} // end else if n > 0 and q + exp = 19
} // end else if ((q + exp) == 19)
// n is not too large to be converted to int64: -2^63-1/2 < n < 2^63-1/2
// 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
// res = +/-1
ind = q - 1; // 0 <= ind <= 15
if (C1 < midpoint64[ind]) {
res = 0x0000000000000000ull; // return 0
} else if (x_sign) { // n < 0
res = 0xffffffffffffffffull; // return -1
} else { // n > 0
res = 0x0000000000000001ull; // return +1
}
} else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18)
// -2^63-1/2 < x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded
// to nearest to a 64-bit signed integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19
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
if (x_sign)
res = -Cstar;
else
res = Cstar;
} else if (exp == 0) {
// 1 <= q <= 16
// res = +/-C (exact)
if (x_sign)
res = -C1;
else
res = C1;
} else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20
// (the upper limit of 20 on q + exp is due to the fact that
// +/-C * 10^exp is guaranteed to fit in 64 bits)
// res = +/-C * 10^exp (exact)
if (x_sign)
res = -C1 * ten2k64[exp];
else
res = C1 * ten2k64[exp];
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_int64_xrninta
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_int64_xrninta (SINT64 * pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
SINT64
bid64_to_int64_xrninta (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
SINT64 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 = 0x00000000;
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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x8000000000000000ull;
BID_RETURN (res);
} else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...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 a signed 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 <= 19'
if (x_sign) { // if n < 0 and q + exp = 19
// if n <= -2^63 - 1/2 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+1), 1<=q<=16
// <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000005, 1<=q<=16
// <=> C * 10^(20-q) >= 0x50000000000000005, 1<=q<=16
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
// Note: C1 * 10^(11-q) has 19 or 20 digits; 0x50000000000000005, has 20
if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x05ull)) {
// 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 <= 19'
} else { // if n > 0 and q + exp = 19
// if n >= 2^63 - 1/2 then n is too large
// too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=16
// <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=16
// <=> if C * 10^(20-q) >= 0x4fffffffffffffffb, 1<=q<=16
C.w[1] = 0x0000000000000004ull;
C.w[0] = 0xfffffffffffffffbull;
// 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1
__mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]);
if (C.w[1] > 0x04ull ||
(C.w[1] == 0x04ull && 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 <= 19'
} // end else if n > 0 and q + exp = 19
} // end else if ((q + exp) == 19)
// n is not too large to be converted to int64: -2^63-1/2 < n < 2^63-1/2
// 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
// res = +/-1
ind = q - 1; // 0 <= ind <= 15
if (C1 < midpoint64[ind]) {
res = 0x0000000000000000ull; // return 0
} else if (x_sign) { // n < 0
res = 0xffffffffffffffffull; // return -1
} else { // n > 0
res = 0x0000000000000001ull; // return +1
}
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18)
// -2^63-1/2 < x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded
// to nearest to a 64-bit signed integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19
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) {
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
if (x_sign)
res = -Cstar;
else
res = Cstar;
} else if (exp == 0) {
// 1 <= q <= 16
// res = +/-C (exact)
if (x_sign)
res = -C1;
else
res = C1;
} else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20
// (the upper limit of 20 on q + exp is due to the fact that
// +/-C * 10^exp is guaranteed to fit in 64 bits)
// res = +/-C * 10^exp (exact)
if (x_sign)
res = -C1 * ten2k64[exp];
else
res = C1 * ten2k64[exp];
}
}
BID_RETURN (res);
}