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Retro68/gcc/libgcc/config/libbid/bid128_to_uint32.c
Wolfgang Thaller 0a883ac4aa upgrade gcc to 6.3.0, binutils to 2.28
2017-04-10 13:32:00 +02:00

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/* Copyright (C) 2007-2016 Free Software Foundation, Inc.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
#include "bid_internal.h"
/*****************************************************************************
* BID128_to_uint32_rnint
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int,
bid128_to_uint32_rnint, x)
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x00000000;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in an unsigned 32-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 <= 10'
if (x_sign) { // if n < 0 and q + exp = 10
// if n < -1/2 then n cannot be converted to uint32 with RN
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x05, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 > 0x05ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 > 0x05 <=>
// C > 0x05 * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 1/2 up)
tmp64 = 0x05ull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
} else { // if n > 0 and q + exp = 10
// if n >= 2^32 - 1/2 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x9fffffffbull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=>
// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 2^32-1/2 up)
tmp64 = 0x9fffffffbull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32: -1/2 <= n < 2^32 - 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 = 0x00000000;
BID_RETURN (res);
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
// if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)
// res = 0
// else if x > 0
// res = +1
// else // if x < 0
// invalid exc
ind = q - 1;
if (ind <= 18) { // 0 <= ind <= 18
if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) {
res = 0x00000000; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x80000000;
*pfpsf |= INVALID_EXCEPTION;
}
} else { // 19 <= ind <= 33
if ((C1.w[1] < midpoint128[ind - 19].w[1])
|| ((C1.w[1] == midpoint128[ind - 19].w[1])
&& (C1.w[0] <= midpoint128[ind - 19].w[0]))) {
res = 0x00000000; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x80000000;
*pfpsf |= INVALID_EXCEPTION;
}
}
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// 1 <= x < 2^32-1/2 so x can be rounded
// to nearest to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
&& (fstar.w[1] || fstar.w[0])
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
// the result is a midpoint; round to nearest
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar.w[0]--; // Cstar.w[0] is now even
} // else MP in [ODD, EVEN]
}
res = Cstar.w[0]; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = C (exact)
res = C1.w[0];
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = C * 10^exp (exact)
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint32_xrnint
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int,
bid128_to_uint32_xrnint, x)
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64, tmp64A;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
unsigned int tmp_inexact = 0;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x00000000;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in an unsigned 32-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 <= 10'
if (x_sign) { // if n < 0 and q + exp = 10
// if n < -1/2 then n cannot be converted to uint32 with RN
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x05, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 > 0x05ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 > 0x05 <=>
// C > 0x05 * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 1/2 up)
tmp64 = 0x05ull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
} else { // if n > 0 and q + exp = 10
// if n >= 2^32 - 1/2 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x9fffffffbull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=>
// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 2^32-1/2 up)
tmp64 = 0x9fffffffbull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32: -1/2 <= n < 2^32 - 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 = 0x00000000;
BID_RETURN (res);
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
// if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)
// res = 0
// else if x > 0
// res = +1
// else // if x < 0
// invalid exc
ind = q - 1;
if (ind <= 18) { // 0 <= ind <= 18
if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) {
res = 0x00000000; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x80000000;
*pfpsf |= INVALID_EXCEPTION;
BID_RETURN (res);
}
} else { // 19 <= ind <= 33
if ((C1.w[1] < midpoint128[ind - 19].w[1])
|| ((C1.w[1] == midpoint128[ind - 19].w[1])
&& (C1.w[0] <= midpoint128[ind - 19].w[0]))) {
res = 0x00000000; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x80000000;
*pfpsf |= INVALID_EXCEPTION;
BID_RETURN (res);
}
}
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// 1 <= x < 2^32-1/2 so x can be rounded
// to nearest to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// determine inexactness of the rounding of C*
// if (0 < f* - 1/2 < 10^(-x)) then
// the result is exact
// else // if (f* - 1/2 > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > 0x8000000000000000ull ||
(fstar.w[1] == 0x8000000000000000ull
&& fstar.w[0] > 0x0ull)) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2
if (tmp64 > ten2mk128trunc[ind - 1].w[1]
|| (tmp64 == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
// *pfpsf |= INEXACT_EXCEPTION;
tmp_inexact = 1;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
// *pfpsf |= INEXACT_EXCEPTION;
tmp_inexact = 1;
}
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[3] > 0x0 ||
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
(fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[2] - onehalf128[ind - 1];
tmp64A = fstar.w[3];
if (tmp64 > fstar.w[2])
tmp64A--;
if (tmp64A || tmp64
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
// *pfpsf |= INEXACT_EXCEPTION;
tmp_inexact = 1;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
// *pfpsf |= INEXACT_EXCEPTION;
tmp_inexact = 1;
}
} else { // if 22 <= ind <= 33
if (fstar.w[3] > onehalf128[ind - 1] ||
(fstar.w[3] == onehalf128[ind - 1] &&
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[3] - onehalf128[ind - 1];
if (tmp64 || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
// *pfpsf |= INEXACT_EXCEPTION;
tmp_inexact = 1;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
// *pfpsf |= INEXACT_EXCEPTION;
tmp_inexact = 1;
}
}
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
&& (fstar.w[1] || fstar.w[0])
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
// the result is a midpoint; round to nearest
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar.w[0]--; // Cstar.w[0] is now even
} // else MP in [ODD, EVEN]
}
res = Cstar.w[0]; // the result is positive
if (tmp_inexact)
*pfpsf |= INEXACT_EXCEPTION;
} else if (exp == 0) {
// 1 <= q <= 10
// res = C (exact)
res = C1.w[0];
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = C * 10^exp (exact)
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint32_floor
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int,
bid128_to_uint32_floor, x)
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64, tmp64A;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
int is_inexact_gt_midpoint = 0;
int is_midpoint_lt_even = 0;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x00000000;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
} else { // x is not special and is not zero
// x < 0 is invalid
if (x_sign) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// x > 0 from this point on
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
// n > 0 and q + exp = 10
// if n >= 2^32 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0xa00000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000 <=>
// C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 2^32 up)
tmp64 = 0xa00000000ull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
// n is not too large to be converted to int32: 0 <= n < 2^31
// 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) or n = +0.c(0)c(1)...c(q-1)
// return 0
res = 0x00000000;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
// 1 <= x < 2^32 so x can be rounded down to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// determine inexactness of the rounding of C*
// if (0 < f* - 1/2 < 10^(-x)) then
// the result is exact
// else // if (f* - 1/2 > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > 0x8000000000000000ull ||
(fstar.w[1] == 0x8000000000000000ull
&& fstar.w[0] > 0x0ull)) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2
if (tmp64 > ten2mk128trunc[ind - 1].w[1]
|| (tmp64 == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
is_inexact_gt_midpoint = 1;
}
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[3] > 0x0 ||
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
(fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[2] - onehalf128[ind - 1];
tmp64A = fstar.w[3];
if (tmp64 > fstar.w[2])
tmp64A--;
if (tmp64A || tmp64
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
is_inexact_gt_midpoint = 1;
}
} else { // if 22 <= ind <= 33
if (fstar.w[3] > onehalf128[ind - 1] ||
(fstar.w[3] == onehalf128[ind - 1] &&
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[3] - onehalf128[ind - 1];
if (tmp64 || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
is_inexact_gt_midpoint = 1;
}
}
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
&& (fstar.w[1] || fstar.w[0])
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
// the result is a midpoint; round to nearest
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar.w[0]--; // Cstar.w[0] is now even
is_inexact_gt_midpoint = 0;
} else { // else MP in [ODD, EVEN]
is_midpoint_lt_even = 1;
is_inexact_gt_midpoint = 0;
}
}
// general correction for RM
if (is_midpoint_lt_even || is_inexact_gt_midpoint) {
Cstar.w[0] = Cstar.w[0] - 1;
} else {
; // the result is already correct
}
res = Cstar.w[0];
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1.w[0];
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint32_xfloor
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int,
bid128_to_uint32_xfloor, x)
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64, tmp64A;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
int is_inexact_gt_midpoint = 0;
int is_midpoint_lt_even = 0;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x00000000;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
} else { // x is not special and is not zero
// x < 0 is invalid
if (x_sign) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// x > 0 from this point on
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
// n > 0 and q + exp = 10
// if n >= 2^32 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0xa00000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000 <=>
// C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 2^32 up)
tmp64 = 0xa00000000ull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
// n is not too large to be converted to int32: 0 <= n < 2^31
// 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) or n = +0.c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0
res = 0x00000000;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
// 1 <= x < 2^32 so x can be rounded down to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// determine inexactness of the rounding of C*
// if (0 < f* - 1/2 < 10^(-x)) then
// the result is exact
// else // if (f* - 1/2 > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > 0x8000000000000000ull ||
(fstar.w[1] == 0x8000000000000000ull
&& fstar.w[0] > 0x0ull)) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2
if (tmp64 > ten2mk128trunc[ind - 1].w[1]
|| (tmp64 == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
is_inexact_gt_midpoint = 1;
}
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[3] > 0x0 ||
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
(fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[2] - onehalf128[ind - 1];
tmp64A = fstar.w[3];
if (tmp64 > fstar.w[2])
tmp64A--;
if (tmp64A || tmp64
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
is_inexact_gt_midpoint = 1;
}
} else { // if 22 <= ind <= 33
if (fstar.w[3] > onehalf128[ind - 1] ||
(fstar.w[3] == onehalf128[ind - 1] &&
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[3] - onehalf128[ind - 1];
if (tmp64 || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
is_inexact_gt_midpoint = 1;
}
}
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
&& (fstar.w[1] || fstar.w[0])
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
// the result is a midpoint; round to nearest
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar.w[0]--; // Cstar.w[0] is now even
is_inexact_gt_midpoint = 0;
} else { // else MP in [ODD, EVEN]
is_midpoint_lt_even = 1;
is_inexact_gt_midpoint = 0;
}
}
// general correction for RM
if (is_midpoint_lt_even || is_inexact_gt_midpoint) {
Cstar.w[0] = Cstar.w[0] - 1;
} else {
; // the result is already correct
}
res = Cstar.w[0];
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1.w[0];
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint32_ceil
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int,
bid128_to_uint32_ceil, x)
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64, tmp64A;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
int is_inexact_lt_midpoint = 0;
int is_midpoint_gt_even = 0;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x00000000;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
if (x_sign) { // if n < 0 and q + exp = 10
// if n <= -1 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x0aull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a <=>
// C >= 0x0a * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 1 up)
tmp64 = 0x0aull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
} else { // if n > 0 and q + exp = 10
// if n > 2^32 - 1 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1
// too large if 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 > 0x9fffffff6ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6 <=>
// C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 2^32 up)
tmp64 = 0x9fffffff6ull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32: -2^32-1 < n <= 2^32-1
// 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) or n = +/-0.c(0)c(1)...c(q-1)
// return 0
if (x_sign)
res = 0x00000000;
else
res = 0x00000001;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
// -2^32-1 < x <= -1 or 1 <= x <= 2^32-1 so x can be rounded
// toward positive infinity to a 32-bit signed integer
if (x_sign) { // x <= -1 is invalid
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// x > 0 from this point on
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// determine inexactness of the rounding of C*
// if (0 < f* - 1/2 < 10^(-x)) then
// the result is exact
// else // if (f* - 1/2 > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > 0x8000000000000000ull ||
(fstar.w[1] == 0x8000000000000000ull
&& fstar.w[0] > 0x0ull)) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2
if (tmp64 > ten2mk128trunc[ind - 1].w[1]
|| (tmp64 == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
is_inexact_lt_midpoint = 1;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
;
}
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[3] > 0x0 ||
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
(fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[2] - onehalf128[ind - 1];
tmp64A = fstar.w[3];
if (tmp64 > fstar.w[2])
tmp64A--;
if (tmp64A || tmp64
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
is_inexact_lt_midpoint = 1;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
}
} else { // if 22 <= ind <= 33
if (fstar.w[3] > onehalf128[ind - 1] ||
(fstar.w[3] == onehalf128[ind - 1] &&
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[3] - onehalf128[ind - 1];
if (tmp64 || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
is_inexact_lt_midpoint = 1;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
;
}
}
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
&& (fstar.w[1] || fstar.w[0])
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
// the result is a midpoint; round to nearest
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar.w[0]--; // Cstar.w[0] is now even
is_midpoint_gt_even = 1;
is_inexact_lt_midpoint = 0;
} else { // else MP in [ODD, EVEN]
is_inexact_lt_midpoint = 0;
}
}
// general correction for RM
if (is_midpoint_gt_even || is_inexact_lt_midpoint) {
Cstar.w[0] = Cstar.w[0] + 1;
} else {
; // the result is already correct
}
res = Cstar.w[0];
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1.w[0];
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint32_xceil
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int,
bid128_to_uint32_xceil, x)
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64, tmp64A;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
int is_inexact_lt_midpoint = 0;
int is_midpoint_gt_even = 0;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x00000000;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
if (x_sign) { // if n < 0 and q + exp = 10
// if n <= -1 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x0aull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a <=>
// C >= 0x0a * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 1 up)
tmp64 = 0x0aull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
} else { // if n > 0 and q + exp = 10
// if n > 2^32 - 1 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1
// too large if 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 > 0x9fffffff6ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6 <=>
// C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 2^32 up)
tmp64 = 0x9fffffff6ull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32: -2^32-1 < n <= 2^32-1
// 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) or n = +/-0.c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0
if (x_sign)
res = 0x00000000;
else
res = 0x00000001;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
// -2^32-1 < x <= -1 or 1 <= x <= 2^32-1 so x can be rounded
// toward positive infinity to a 32-bit signed integer
if (x_sign) { // x <= -1 is invalid
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// x > 0 from this point on
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// determine inexactness of the rounding of C*
// if (0 < f* - 1/2 < 10^(-x)) then
// the result is exact
// else // if (f* - 1/2 > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > 0x8000000000000000ull ||
(fstar.w[1] == 0x8000000000000000ull
&& fstar.w[0] > 0x0ull)) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2
if (tmp64 > ten2mk128trunc[ind - 1].w[1]
|| (tmp64 == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
is_inexact_lt_midpoint = 1;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[3] > 0x0 ||
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
(fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[2] - onehalf128[ind - 1];
tmp64A = fstar.w[3];
if (tmp64 > fstar.w[2])
tmp64A--;
if (tmp64A || tmp64
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
is_inexact_lt_midpoint = 1;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
} else { // if 22 <= ind <= 33
if (fstar.w[3] > onehalf128[ind - 1] ||
(fstar.w[3] == onehalf128[ind - 1] &&
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[3] - onehalf128[ind - 1];
if (tmp64 || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
is_inexact_lt_midpoint = 1;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
}
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
&& (fstar.w[1] || fstar.w[0])
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
// the result is a midpoint; round to nearest
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar.w[0]--; // Cstar.w[0] is now even
is_midpoint_gt_even = 1;
is_inexact_lt_midpoint = 0;
} else { // else MP in [ODD, EVEN]
is_inexact_lt_midpoint = 0;
}
}
// general correction for RM
if (is_midpoint_gt_even || is_inexact_lt_midpoint) {
Cstar.w[0] = Cstar.w[0] + 1;
} else {
; // the result is already correct
}
res = Cstar.w[0];
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1.w[0];
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint32_int
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int,
bid128_to_uint32_int, x)
int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64, tmp64A;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
int is_inexact_gt_midpoint = 0;
int is_midpoint_lt_even = 0;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x00000000;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
if (x_sign) { // if n < 0 and q + exp = 10
// if n <= -1 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x0aull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit uint fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a <=>
// C >= 0x0a * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 1 up)
tmp64 = 0x0aull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
} else { // if n > 0 and q + exp = 10
// if n >= 2^32 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0xa00000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit uint fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000 <=>
// C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 2^32 up)
tmp64 = 0xa00000000ull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to uint32: -2^32 < n < 2^32
// 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) or n = +/-0.c(0)c(1)...c(q-1)
// return 0
res = 0x00000000;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
// x = d(0)...d(k).d(k+1)..., k >= 0, d(0) != 0
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// x > 0 from this point on
// 1 <= x < 2^32 so x can be rounded to zero to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// determine inexactness of the rounding of C*
// if (0 < f* - 1/2 < 10^(-x)) then
// the result is exact
// else // if (f* - 1/2 > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > 0x8000000000000000ull ||
(fstar.w[1] == 0x8000000000000000ull
&& fstar.w[0] > 0x0ull)) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2
if (tmp64 > ten2mk128trunc[ind - 1].w[1]
|| (tmp64 == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
is_inexact_gt_midpoint = 1;
}
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[3] > 0x0 ||
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
(fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[2] - onehalf128[ind - 1];
tmp64A = fstar.w[3];
if (tmp64 > fstar.w[2])
tmp64A--;
if (tmp64A || tmp64
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
is_inexact_gt_midpoint = 1;
}
} else { // if 22 <= ind <= 33
if (fstar.w[3] > onehalf128[ind - 1] ||
(fstar.w[3] == onehalf128[ind - 1] &&
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[3] - onehalf128[ind - 1];
if (tmp64 || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
is_inexact_gt_midpoint = 1;
}
}
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
&& (fstar.w[1] || fstar.w[0])
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
// the result is a midpoint; round to nearest
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar.w[0]--; // Cstar.w[0] is now even
is_inexact_gt_midpoint = 0;
} else { // else MP in [ODD, EVEN]
is_midpoint_lt_even = 1;
is_inexact_gt_midpoint = 0;
}
}
// general correction for RZ
if (is_midpoint_lt_even || is_inexact_gt_midpoint) {
Cstar.w[0] = Cstar.w[0] - 1;
} else {
; // exact, the result is already correct
}
res = Cstar.w[0];
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1.w[0];
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint32_xint
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int,
bid128_to_uint32_xint, x)
int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64, tmp64A;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
int is_inexact_gt_midpoint = 0;
int is_midpoint_lt_even = 0;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x00000000;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
if (x_sign) { // if n < 0 and q + exp = 10
// if n <= -1 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x0aull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit uint fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a <=>
// C >= 0x0a * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 1 up)
tmp64 = 0x0aull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
} else { // if n > 0 and q + exp = 10
// if n >= 2^32 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0xa00000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit uint fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000 <=>
// C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 2^32 up)
tmp64 = 0xa00000000ull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to uint32: -2^32 < n < 2^32
// 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) or n = +/-0.c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0
res = 0x00000000;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
// x = d(0)...d(k).d(k+1)..., k >= 0, d(0) != 0
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// x > 0 from this point on
// 1 <= x < 2^32 so x can be rounded to zero to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// determine inexactness of the rounding of C*
// if (0 < f* - 1/2 < 10^(-x)) then
// the result is exact
// else // if (f* - 1/2 > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > 0x8000000000000000ull ||
(fstar.w[1] == 0x8000000000000000ull
&& fstar.w[0] > 0x0ull)) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2
if (tmp64 > ten2mk128trunc[ind - 1].w[1]
|| (tmp64 == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
is_inexact_gt_midpoint = 1;
}
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[3] > 0x0 ||
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
(fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[2] - onehalf128[ind - 1];
tmp64A = fstar.w[3];
if (tmp64 > fstar.w[2])
tmp64A--;
if (tmp64A || tmp64
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
is_inexact_gt_midpoint = 1;
}
} else { // if 22 <= ind <= 33
if (fstar.w[3] > onehalf128[ind - 1] ||
(fstar.w[3] == onehalf128[ind - 1] &&
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[3] - onehalf128[ind - 1];
if (tmp64 || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
is_inexact_gt_midpoint = 1;
}
}
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
&& (fstar.w[1] || fstar.w[0])
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
// the result is a midpoint; round to nearest
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar.w[0]--; // Cstar.w[0] is now even
is_inexact_gt_midpoint = 0;
} else { // else MP in [ODD, EVEN]
is_midpoint_lt_even = 1;
is_inexact_gt_midpoint = 0;
}
}
// general correction for RZ
if (is_midpoint_lt_even || is_inexact_gt_midpoint) {
Cstar.w[0] = Cstar.w[0] - 1;
} else {
; // exact, the result is already correct
}
res = Cstar.w[0];
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1.w[0];
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint32_rninta
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int,
bid128_to_uint32_rninta, x)
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 P256;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x00000000;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
if (x_sign) { // if n < 0 and q + exp = 10
// if n <= -1/2 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x05, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x05ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x05 <=>
// C >= 0x05 * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 1/2 up)
tmp64 = 0x05ull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
} else { // if n > 0 and q + exp = 10
// if n >= 2^32 - 1/2 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x9fffffffbull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=>
// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 2^32-1/2 up)
tmp64 = 0x9fffffffbull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32: -1/2 < n < 2^32 - 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 = 0x00000000;
BID_RETURN (res);
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
// if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1)
// res = 0
// else if x > 0
// res = +1
// else // if x < 0
// invalid exc
ind = q - 1;
if (ind <= 18) { // 0 <= ind <= 18
if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) {
res = 0x00000000; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x80000000;
*pfpsf |= INVALID_EXCEPTION;
}
} else { // 19 <= ind <= 33
if ((C1.w[1] < midpoint128[ind - 19].w[1])
|| ((C1.w[1] == midpoint128[ind - 19].w[1])
&& (C1.w[0] < midpoint128[ind - 19].w[0]))) {
res = 0x00000000; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x80000000;
*pfpsf |= INVALID_EXCEPTION;
}
}
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// 1 <= x < 2^31-1/2 so x can be rounded
// to nearest-away to a 32-bit signed integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// if the result was a midpoint, it was already rounded away from zero
res = Cstar.w[0]; // always positive
// no need to check for midpoints - already rounded away from zero!
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1.w[0];
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID128_to_uint32_xrninta
****************************************************************************/
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int,
bid128_to_uint32_xrninta, x)
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
UINT64 tmp64, tmp64A;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT128 C1, C;
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
UINT256 fstar;
UINT256 P256;
unsigned int tmp_inexact = 0;
// unpack x
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
C1.w[1] = x.w[1] & MASK_COEFF;
C1.w[0] = x.w[0];
// check for NaN or Infinity
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
// x is special
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is QNaN
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
} else { // x is not a NaN, so it must be infinity
if (!x_sign) { // x is +inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
} else { // x is -inf
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
}
BID_RETURN (res);
}
}
// check for non-canonical values (after the check for special values)
if ((C1.w[1] > 0x0001ed09bead87c0ull)
|| (C1.w[1] == 0x0001ed09bead87c0ull
&& (C1.w[0] > 0x378d8e63ffffffffull))
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
res = 0x00000000;
BID_RETURN (res);
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
} else { // x is not special and is not zero
// q = nr. of decimal digits in x
// determine first the nr. of bits in x
if (C1.w[1] == 0) {
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) (C1.w[0]); // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1.w[0]; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
tmp1.d = (double) C1.w[1]; // exact conversion
x_nr_bits =
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
q++;
}
exp = (x_exp >> 49) - 6176;
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
if (x_sign) { // if n < 0 and q + exp = 10
// if n <= -1/2 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x05, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x05ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x05 <=>
// C >= 0x05 * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 1/2 up)
tmp64 = 0x05ull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
} else { // if n > 0 and q + exp = 10
// if n >= 2^32 - 1/2 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34
if (q <= 11) {
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x9fffffffbull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=>
// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23
// (scale 2^32-1/2 up)
tmp64 = 0x9fffffffbull;
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
}
if (C1.w[1] > C.w[1]
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32: -1/2 < n < 2^32 - 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 = 0x00000000;
BID_RETURN (res);
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
// if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1)
// res = 0
// else if x > 0
// res = +1
// else // if x < 0
// invalid exc
ind = q - 1;
if (ind <= 18) { // 0 <= ind <= 18
if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) {
res = 0x00000000; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x80000000;
*pfpsf |= INVALID_EXCEPTION;
BID_RETURN (res);
}
} else { // 19 <= ind <= 33
if ((C1.w[1] < midpoint128[ind - 19].w[1])
|| ((C1.w[1] == midpoint128[ind - 19].w[1])
&& (C1.w[0] < midpoint128[ind - 19].w[0]))) {
res = 0x00000000; // return 0
} else if (!x_sign) { // n > 0
res = 0x00000001; // return +1
} else {
res = 0x80000000;
*pfpsf |= INVALID_EXCEPTION;
BID_RETURN (res);
}
}
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// 1 <= x < 2^31-1/2 so x can be rounded
// to nearest-away to a 32-bit signed integer
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
tmp64 = C1.w[0];
if (ind <= 19) {
C1.w[0] = C1.w[0] + midpoint64[ind - 1];
} else {
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
}
if (C1.w[0] < tmp64)
C1.w[1]++;
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 33
// kx = 10^(-x) = ten2mk128[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 118 bits
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[1] = P256.w[3];
Cstar.w[0] = P256.w[2];
fstar.w[3] = 0;
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
} else { // 22 <= ind - 1 <= 33
Cstar.w[1] = 0;
Cstar.w[0] = P256.w[3];
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
fstar.w[2] = P256.w[2];
fstar.w[1] = P256.w[1];
fstar.w[0] = P256.w[0];
}
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-128 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 102
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
Cstar.w[0] =
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
} else { // 22 <= ind - 1 <= 33
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
}
// if the result was a midpoint, it was already rounded away from zero
// determine inexactness of the rounding of C*
// if (0 < f* - 1/2 < 10^(-x)) then
// the result is exact
// else // if (f* - 1/2 > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[1] > 0x8000000000000000ull ||
(fstar.w[1] == 0x8000000000000000ull
&& fstar.w[0] > 0x0ull)) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2
if (tmp64 > ten2mk128trunc[ind - 1].w[1]
|| (tmp64 == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
// *pfpsf |= INEXACT_EXCEPTION;
tmp_inexact = 1;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
// *pfpsf |= INEXACT_EXCEPTION;
tmp_inexact = 1;
}
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
if (fstar.w[3] > 0x0 ||
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
(fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[2] - onehalf128[ind - 1];
tmp64A = fstar.w[3];
if (tmp64 > fstar.w[2])
tmp64A--;
if (tmp64A || tmp64
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
// *pfpsf |= INEXACT_EXCEPTION;
tmp_inexact = 1;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
// *pfpsf |= INEXACT_EXCEPTION;
tmp_inexact = 1;
}
} else { // if 22 <= ind <= 33
if (fstar.w[3] > onehalf128[ind - 1] ||
(fstar.w[3] == onehalf128[ind - 1] &&
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[3] - onehalf128[ind - 1];
if (tmp64 || fstar.w[2]
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
// set the inexact flag
// *pfpsf |= INEXACT_EXCEPTION;
tmp_inexact = 1;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
// *pfpsf |= INEXACT_EXCEPTION;
tmp_inexact = 1;
}
}
// no need to check for midpoints - already rounded away from zero!
res = Cstar.w[0]; // the result is positive
if (tmp_inexact)
*pfpsf |= INEXACT_EXCEPTION;
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1.w[0];
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1.w[0] * ten2k64[exp];
}
}
}
BID_RETURN (res);
}
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