3589 lines
127 KiB
C
3589 lines
127 KiB
C
/* Copyright (C) 2007-2015 Free Software Foundation, Inc.
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This file is part of GCC.
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GCC is free software; you can redistribute it and/or modify it under
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the terms of the GNU General Public License as published by the Free
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Software Foundation; either version 3, or (at your option) any later
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version.
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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#include "bid_internal.h"
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/*****************************************************************************
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* BID128_to_uint32_rnint
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****************************************************************************/
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BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int,
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bid128_to_uint32_rnint, x)
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unsigned int res;
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UINT64 x_sign;
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UINT64 x_exp;
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int exp; // unbiased exponent
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// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
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UINT64 tmp64;
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BID_UI64DOUBLE tmp1;
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unsigned int x_nr_bits;
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int q, ind, shift;
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UINT128 C1, C;
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UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
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UINT256 fstar;
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UINT256 P256;
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// unpack x
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x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
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x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
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C1.w[1] = x.w[1] & MASK_COEFF;
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C1.w[0] = x.w[0];
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// check for NaN or Infinity
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if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
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// x is special
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if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
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if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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} else { // x is QNaN
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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}
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BID_RETURN (res);
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} else { // x is not a NaN, so it must be infinity
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if (!x_sign) { // x is +inf
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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} else { // x is -inf
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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}
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BID_RETURN (res);
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}
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}
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// check for non-canonical values (after the check for special values)
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if ((C1.w[1] > 0x0001ed09bead87c0ull)
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|| (C1.w[1] == 0x0001ed09bead87c0ull
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&& (C1.w[0] > 0x378d8e63ffffffffull))
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|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
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res = 0x00000000;
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BID_RETURN (res);
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} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
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// x is 0
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res = 0x00000000;
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BID_RETURN (res);
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} else { // x is not special and is not zero
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// q = nr. of decimal digits in x
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// determine first the nr. of bits in x
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if (C1.w[1] == 0) {
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if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
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// split the 64-bit value in two 32-bit halves to avoid rounding errors
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if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
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tmp1.d = (double) (C1.w[0] >> 32); // exact conversion
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x_nr_bits =
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33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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} else { // x < 2^32
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tmp1.d = (double) (C1.w[0]); // exact conversion
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x_nr_bits =
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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}
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} else { // if x < 2^53
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tmp1.d = (double) C1.w[0]; // exact conversion
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x_nr_bits =
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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}
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} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
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tmp1.d = (double) C1.w[1]; // exact conversion
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x_nr_bits =
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65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
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}
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q = nr_digits[x_nr_bits - 1].digits;
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if (q == 0) {
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q = nr_digits[x_nr_bits - 1].digits1;
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if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi
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|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi
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&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
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q++;
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}
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exp = (x_exp >> 49) - 6176;
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if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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BID_RETURN (res);
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} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
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// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
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// so x rounded to an integer may or may not fit in an unsigned 32-bit int
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// the cases that do not fit are identified here; the ones that fit
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// fall through and will be handled with other cases further,
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// under '1 <= q + exp <= 10'
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if (x_sign) { // if n < 0 and q + exp = 10
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// if n < -1/2 then n cannot be converted to uint32 with RN
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// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 1/2
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// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x05, 1<=q<=34
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if (q <= 11) {
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tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
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// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
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if (tmp64 > 0x05ull) {
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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BID_RETURN (res);
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}
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// else cases that can be rounded to a 32-bit int fall through
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// to '1 <= q + exp <= 10'
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} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
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// 0.c(0)c(1)...c(q-1) * 10^11 > 0x05 <=>
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// C > 0x05 * 10^(q-11) where 1 <= q - 11 <= 23
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// (scale 1/2 up)
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tmp64 = 0x05ull;
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if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
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__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
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} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
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__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
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}
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if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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BID_RETURN (res);
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}
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// else cases that can be rounded to a 32-bit int fall through
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// to '1 <= q + exp <= 10'
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}
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} else { // if n > 0 and q + exp = 10
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// if n >= 2^32 - 1/2 then n is too large
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// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2
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// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34
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if (q <= 11) {
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tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int
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// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
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if (tmp64 >= 0x9fffffffbull) {
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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BID_RETURN (res);
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}
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// else cases that can be rounded to a 32-bit int fall through
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// to '1 <= q + exp <= 10'
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} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
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// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=>
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// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23
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// (scale 2^32-1/2 up)
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tmp64 = 0x9fffffffbull;
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if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
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__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
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} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
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__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
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}
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if (C1.w[1] > C.w[1]
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|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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BID_RETURN (res);
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}
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// else cases that can be rounded to a 32-bit int fall through
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// to '1 <= q + exp <= 10'
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}
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}
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}
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// n is not too large to be converted to int32: -1/2 <= n < 2^32 - 1/2
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// Note: some of the cases tested for above fall through to this point
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if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
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// return 0
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res = 0x00000000;
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BID_RETURN (res);
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} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
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// if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)
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// res = 0
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// else if x > 0
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// res = +1
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// else // if x < 0
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// invalid exc
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ind = q - 1;
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if (ind <= 18) { // 0 <= ind <= 18
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if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) {
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res = 0x00000000; // return 0
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} else if (!x_sign) { // n > 0
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res = 0x00000001; // return +1
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} else {
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res = 0x80000000;
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*pfpsf |= INVALID_EXCEPTION;
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}
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} else { // 19 <= ind <= 33
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if ((C1.w[1] < midpoint128[ind - 19].w[1])
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|| ((C1.w[1] == midpoint128[ind - 19].w[1])
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&& (C1.w[0] <= midpoint128[ind - 19].w[0]))) {
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res = 0x00000000; // return 0
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} else if (!x_sign) { // n > 0
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res = 0x00000001; // return +1
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} else {
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res = 0x80000000;
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*pfpsf |= INVALID_EXCEPTION;
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}
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}
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} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
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if (x_sign) { // x <= -1
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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BID_RETURN (res);
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}
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// 1 <= x < 2^32-1/2 so x can be rounded
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// to nearest to a 32-bit unsigned integer
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if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
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ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
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// chop off ind digits from the lower part of C1
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// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits
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tmp64 = C1.w[0];
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if (ind <= 19) {
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C1.w[0] = C1.w[0] + midpoint64[ind - 1];
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} else {
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C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
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C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
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}
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if (C1.w[0] < tmp64)
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C1.w[1]++;
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// calculate C* and f*
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// C* is actually floor(C*) in this case
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// C* and f* need shifting and masking, as shown by
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// shiftright128[] and maskhigh128[]
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// 1 <= x <= 33
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// kx = 10^(-x) = ten2mk128[ind - 1]
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// C* = (C1 + 1/2 * 10^x) * 10^(-x)
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// the approximation of 10^(-x) was rounded up to 118 bits
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__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
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if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
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Cstar.w[1] = P256.w[3];
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Cstar.w[0] = P256.w[2];
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fstar.w[3] = 0;
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fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
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fstar.w[1] = P256.w[1];
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fstar.w[0] = P256.w[0];
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} else { // 22 <= ind - 1 <= 33
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Cstar.w[1] = 0;
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Cstar.w[0] = P256.w[3];
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fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
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fstar.w[2] = P256.w[2];
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fstar.w[1] = P256.w[1];
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fstar.w[0] = P256.w[0];
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}
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// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
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// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
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// if (0 < f* < 10^(-x)) then the result is a midpoint
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// if floor(C*) is even then C* = floor(C*) - logical right
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// shift; C* has p decimal digits, correct by Prop. 1)
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// else if floor(C*) is odd C* = floor(C*)-1 (logical right
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// shift; C* has p decimal digits, correct by Pr. 1)
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// else
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// C* = floor(C*) (logical right shift; C has p decimal digits,
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// correct by Property 1)
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// n = C* * 10^(e+x)
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// shift right C* by Ex-128 = shiftright128[ind]
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shift = shiftright128[ind - 1]; // 0 <= shift <= 102
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if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21
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Cstar.w[0] =
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(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
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// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
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} else { // 22 <= ind - 1 <= 33
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Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38
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}
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// if the result was a midpoint it was rounded away from zero, so
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// it will need a correction
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// check for midpoints
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if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
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&& (fstar.w[1] || fstar.w[0])
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&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
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|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
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&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
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// the result is a midpoint; round to nearest
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if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD]
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// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
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Cstar.w[0]--; // Cstar.w[0] is now even
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} // else MP in [ODD, EVEN]
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}
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res = Cstar.w[0]; // the result is positive
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} else if (exp == 0) {
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// 1 <= q <= 10
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// res = C (exact)
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res = C1.w[0];
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} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
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// res = C * 10^exp (exact)
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res = C1.w[0] * ten2k64[exp];
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}
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}
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}
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BID_RETURN (res);
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}
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/*****************************************************************************
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* BID128_to_uint32_xrnint
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****************************************************************************/
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BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int,
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bid128_to_uint32_xrnint, x)
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unsigned int res;
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UINT64 x_sign;
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UINT64 x_exp;
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int exp; // unbiased exponent
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// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
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UINT64 tmp64, tmp64A;
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BID_UI64DOUBLE tmp1;
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unsigned int x_nr_bits;
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int q, ind, shift;
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UINT128 C1, C;
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UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits
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UINT256 fstar;
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UINT256 P256;
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unsigned int tmp_inexact = 0;
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// unpack x
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x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
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x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions
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C1.w[1] = x.w[1] & MASK_COEFF;
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C1.w[0] = x.w[0];
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// check for NaN or Infinity
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if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
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// x is special
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if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
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if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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} else { // x is QNaN
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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}
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BID_RETURN (res);
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} else { // x is not a NaN, so it must be infinity
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if (!x_sign) { // x is +inf
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// set invalid flag
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*pfpsf |= INVALID_EXCEPTION;
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// return Integer Indefinite
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res = 0x80000000;
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} 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);
|
|
}
|