2588 lines
88 KiB
C
2588 lines
88 KiB
C
/* Copyright (C) 2007-2019 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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* BID64_to_int32_rnint
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****************************************************************************/
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_to_int32_rnint (int *pres,
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UINT64 *
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px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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_EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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int
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bid64_to_int32_rnint (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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_EXC_INFO_PARAM) {
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#endif
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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 represents x_significand (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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UINT64 C1;
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UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
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UINT128 fstar;
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UINT128 P128;
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// check for NaN or Infinity
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if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_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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BID_RETURN (res);
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}
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// unpack x
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x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
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// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
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C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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if (C1 > 9999999999999999ull) { // non-canonical
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x_exp = 0;
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C1 = 0;
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}
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} else {
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x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
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C1 = x & MASK_BINARY_SIG1;
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}
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// check for zeros (possibly from non-canonical values)
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if (C1 == 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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}
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// x is not special and is not zero
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// q = nr. of decimal digits in x (1 <= q <= 54)
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// determine first the nr. of bits in x
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if (C1 >= 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 >= 0x0000000100000000ull) { // x >= 2^32
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tmp1.d = (double) (C1 >> 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; // 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; // 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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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 >= nr_digits[x_nr_bits - 1].threshold_lo)
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q++;
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}
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exp = x_exp - 398; // unbiased exponent
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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 a signed 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 < -2^31 - 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) > 2^31+1/2
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// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005, 1<=q<=16
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// <=> C * 10^(11-q) > 0x500000005, 1<=q<=16
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if (q <= 11) {
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// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits
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tmp64 = C1 * 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 > 0x500000005ull) {
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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 <= 16 and so -15 <= exp <= -2
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// C * 10^(11-q) > 0x500000005 <=>
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// C > 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 5
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// (scale 2^31+1/2 up)
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// Note: 0x500000005*10^(q-11) has q-1 or q digits, where q <= 16
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tmp64 = 0x500000005ull * ten2k64[q - 11];
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if (C1 > tmp64) {
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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 >= 2^31 - 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) >= 2^31-1/2
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// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=16
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// <=> C * 10^(11-q) >= 0x4fffffffb, 1<=q<=16
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if (q <= 11) {
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// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits
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tmp64 = C1 * 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 >= 0x4fffffffbull) {
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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 <= 16 and so -15 <= exp <= -2
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// C * 10^(11-q) >= 0x4fffffffb <=>
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// C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 5
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// (scale 2^31-1/2 up)
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// Note: 0x4fffffffb*10^(q-11) has q-1 or q digits, where q <= 16
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tmp64 = 0x4fffffffbull * ten2k64[q - 11];
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if (C1 >= tmp64) {
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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: -2^31 - 1/2 <= n < 2^31 - 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
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// res = +/-1
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ind = q - 1;
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if (C1 <= 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 = 0xffffffff; // return -1
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} else { // n > 0
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res = 0x00000001; // return +1
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}
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} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
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// -2^31-1/2 <= x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded
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// to nearest to a 32-bit signed integer
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if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
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ind = -exp; // 1 <= ind <= 15; 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 64 bits
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C1 = C1 + midpoint64[ind - 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 <= 15
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// kx = 10^(-x) = ten2mk64[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 54 bits
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__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
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Cstar = P128.w[1];
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fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
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fstar.w[0] = P128.w[0];
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// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
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// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
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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-64 = shiftright128[ind]
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shift = shiftright128[ind - 1]; // 0 <= shift <= 39
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Cstar = Cstar >> shift;
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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[1] == 0) && fstar.w[0]
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&& (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) {
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// ten2mk128trunc[ind -1].w[1] is identical to
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// ten2mk128[ind -1].w[1]
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// the result is a midpoint; round to nearest
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if (Cstar & 0x01) { // Cstar 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--; // Cstar is now even
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} // else MP in [ODD, EVEN]
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}
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if (x_sign)
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res = -Cstar;
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else
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res = Cstar;
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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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if (x_sign)
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res = -C1;
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else
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res = C1;
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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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if (x_sign)
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res = -C1 * ten2k64[exp];
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else
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res = C1 * ten2k64[exp];
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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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* BID64_to_int32_xrnint
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****************************************************************************/
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_to_int32_xrnint (int *pres,
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UINT64 *
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px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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_EXC_INFO_PARAM) {
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UINT64 x = *px;
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#else
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int
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bid64_to_int32_xrnint (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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_EXC_INFO_PARAM) {
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#endif
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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 represents x_significand (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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UINT64 C1;
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UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
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UINT128 fstar;
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UINT128 P128;
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// check for NaN or Infinity
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if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_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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BID_RETURN (res);
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}
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// unpack x
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x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
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// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
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x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
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C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
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if (C1 > 9999999999999999ull) { // non-canonical
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x_exp = 0;
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C1 = 0;
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}
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} else {
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x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
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C1 = x & MASK_BINARY_SIG1;
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}
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// check for zeros (possibly from non-canonical values)
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if (C1 == 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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}
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// x is not special and is not zero
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// q = nr. of decimal digits in x (1 <= q <= 54)
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// determine first the nr. of bits in x
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if (C1 >= 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 >= 0x0000000100000000ull) { // x >= 2^32
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tmp1.d = (double) (C1 >> 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; // 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; // 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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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 >= nr_digits[x_nr_bits - 1].threshold_lo)
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q++;
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}
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exp = x_exp - 398; // unbiased exponent
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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...
|
|
// 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'
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if (x_sign) { // if n < 0 and q + exp = 10
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// if n < -2^31 - 1/2 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31+1/2
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// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005, 1<=q<=16
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// <=> C * 10^(11-q) > 0x500000005, 1<=q<=16
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if (q <= 11) {
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// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits
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tmp64 = C1 * 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 > 0x500000005ull) {
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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'
|
|
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2
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|
// C * 10^(11-q) > 0x500000005 <=>
|
|
// C > 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 5
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// (scale 2^31+1/2 up)
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// Note: 0x500000005*10^(q-11) has q-1 or q digits, where q <= 16
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tmp64 = 0x500000005ull * ten2k64[q - 11];
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if (C1 > tmp64) {
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// set invalid flag
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*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 >= 2^31 - 1/2 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x4fffffffb, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits
|
|
tmp64 = C1 * 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 >= 0x4fffffffbull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x4fffffffb <=>
|
|
// C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31-1/2 up)
|
|
// Note: 0x4fffffffb*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x4fffffffbull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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: -2^31 - 1/2 < n < 2^31 - 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
|
|
// res = +/-1
|
|
ind = q - 1;
|
|
if (C1 <= midpoint64[ind]) {
|
|
res = 0x00000000; // return 0
|
|
} else if (x_sign) { // n < 0
|
|
res = 0xffffffff; // return -1
|
|
} else { // n > 0
|
|
res = 0x00000001; // return +1
|
|
}
|
|
// set inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
|
|
// -2^31-1/2 <= x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded
|
|
// to nearest to a 32-bit signed integer
|
|
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
|
|
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
|
|
// chop off ind digits from the lower part of C1
|
|
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits
|
|
C1 = C1 + midpoint64[ind - 1];
|
|
// calculate C* and f*
|
|
// C* is actually floor(C*) in this case
|
|
// C* and f* need shifting and masking, as shown by
|
|
// shiftright128[] and maskhigh128[]
|
|
// 1 <= x <= 15
|
|
// kx = 10^(-x) = ten2mk64[ind - 1]
|
|
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
|
|
// the approximation of 10^(-x) was rounded up to 54 bits
|
|
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
|
|
Cstar = P128.w[1];
|
|
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
|
|
fstar.w[0] = P128.w[0];
|
|
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
|
|
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
|
|
// if (0 < f* < 10^(-x)) then the result is a midpoint
|
|
// if floor(C*) is even then C* = floor(C*) - logical right
|
|
// shift; C* has p decimal digits, correct by Prop. 1)
|
|
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
|
|
// shift; C* has p decimal digits, correct by Pr. 1)
|
|
// else
|
|
// C* = floor(C*) (logical right shift; C has p decimal digits,
|
|
// correct by Property 1)
|
|
// n = C* * 10^(e+x)
|
|
|
|
// shift right C* by Ex-64 = shiftright128[ind]
|
|
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
|
|
Cstar = Cstar >> shift;
|
|
// determine inexactness of the rounding of C*
|
|
// if (0 < f* - 1/2 < 10^(-x)) then
|
|
// the result is exact
|
|
// else // if (f* - 1/2 > T*) then
|
|
// the result is inexact
|
|
if (ind - 1 <= 2) {
|
|
if (fstar.w[0] > 0x8000000000000000ull) {
|
|
// f* > 1/2 and the result may be exact
|
|
tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2
|
|
if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
} // else the result is exact
|
|
} else { // the result is inexact; f2* <= 1/2
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
}
|
|
} else { // if 3 <= ind - 1 <= 14
|
|
if (fstar.w[1] > onehalf128[ind - 1] ||
|
|
(fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) {
|
|
// f2* > 1/2 and the result may be exact
|
|
// Calculate f2* - 1/2
|
|
tmp64 = fstar.w[1] - onehalf128[ind - 1];
|
|
if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
} // else the result is exact
|
|
} else { // the result is inexact; f2* <= 1/2
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
}
|
|
}
|
|
|
|
// if the result was a midpoint it was rounded away from zero, so
|
|
// it will need a correction
|
|
// check for midpoints
|
|
if ((fstar.w[1] == 0) && fstar.w[0]
|
|
&& (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
// the result is a midpoint; round to nearest
|
|
if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD]
|
|
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
|
|
Cstar--; // Cstar is now even
|
|
} // else MP in [ODD, EVEN]
|
|
}
|
|
if (x_sign)
|
|
res = -Cstar;
|
|
else
|
|
res = Cstar;
|
|
} else if (exp == 0) {
|
|
// 1 <= q <= 10
|
|
// res = +/-C (exact)
|
|
if (x_sign)
|
|
res = -C1;
|
|
else
|
|
res = C1;
|
|
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
|
|
// res = +/-C * 10^exp (exact)
|
|
if (x_sign)
|
|
res = -C1 * ten2k64[exp];
|
|
else
|
|
res = C1 * ten2k64[exp];
|
|
}
|
|
}
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
/*****************************************************************************
|
|
* BID64_to_int32_floor
|
|
****************************************************************************/
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64_to_int32_floor (int *pres,
|
|
UINT64 *
|
|
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 x = *px;
|
|
#else
|
|
int
|
|
bid64_to_int32_floor (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
int res;
|
|
UINT64 x_sign;
|
|
UINT64 x_exp;
|
|
int exp; // unbiased exponent
|
|
// Note: C1 represents x_significand (UINT64)
|
|
UINT64 tmp64;
|
|
BID_UI64DOUBLE tmp1;
|
|
unsigned int x_nr_bits;
|
|
int q, ind, shift;
|
|
UINT64 C1;
|
|
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
|
|
UINT128 fstar;
|
|
UINT128 P128;
|
|
|
|
// check for NaN or Infinity
|
|
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
|
|
// set invalid flag
|
|
*pfpsf |= INVALID_EXCEPTION;
|
|
// return Integer Indefinite
|
|
res = 0x80000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// unpack x
|
|
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
|
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
|
|
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
|
if (C1 > 9999999999999999ull) { // non-canonical
|
|
x_exp = 0;
|
|
C1 = 0;
|
|
}
|
|
} else {
|
|
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
|
|
C1 = x & MASK_BINARY_SIG1;
|
|
}
|
|
|
|
// check for zeros (possibly from non-canonical values)
|
|
if (C1 == 0x0ull) {
|
|
// x is 0
|
|
res = 0x00000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// x is not special and is not zero
|
|
|
|
// q = nr. of decimal digits in x (1 <= q <= 54)
|
|
// determine first the nr. of bits in x
|
|
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
|
|
// split the 64-bit value in two 32-bit halves to avoid rounding errors
|
|
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
|
|
tmp1.d = (double) (C1 >> 32); // exact conversion
|
|
x_nr_bits =
|
|
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
} else { // x < 2^32
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
} else { // if x < 2^53
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
q = nr_digits[x_nr_bits - 1].digits;
|
|
if (q == 0) {
|
|
q = nr_digits[x_nr_bits - 1].digits1;
|
|
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
|
|
q++;
|
|
}
|
|
exp = x_exp - 398; // unbiased exponent
|
|
|
|
if ((q + exp) > 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 < -2^31 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x500000000, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000000 has 11 digits
|
|
tmp64 = C1 * 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 > 0x500000000ull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) > 0x500000000 <=>
|
|
// C > 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31+1 up)
|
|
// Note: 0x500000000*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x500000000ull * ten2k64[q - 11];
|
|
if (C1 > tmp64) {
|
|
// 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 >= 2^31 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x500000000, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000000 has 11 digits
|
|
tmp64 = C1 * 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 >= 0x500000000ull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x500000000 <=>
|
|
// C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31-1 up)
|
|
// Note: 0x500000000*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x500000000ull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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: -2^31 <= n < 2^31
|
|
// Note: some of the cases tested for above fall through to this point
|
|
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
|
|
// return -1 or 0
|
|
if (x_sign)
|
|
res = 0xffffffff;
|
|
else
|
|
res = 0x00000000;
|
|
BID_RETURN (res);
|
|
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
|
|
// -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded
|
|
// to nearest to a 32-bit signed integer
|
|
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
|
|
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
|
|
// chop off ind digits from the lower part of C1
|
|
// C1 fits in 64 bits
|
|
// calculate C* and f*
|
|
// C* is actually floor(C*) in this case
|
|
// C* and f* need shifting and masking, as shown by
|
|
// shiftright128[] and maskhigh128[]
|
|
// 1 <= x <= 15
|
|
// kx = 10^(-x) = ten2mk64[ind - 1]
|
|
// C* = C1 * 10^(-x)
|
|
// the approximation of 10^(-x) was rounded up to 54 bits
|
|
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
|
|
Cstar = P128.w[1];
|
|
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
|
|
fstar.w[0] = P128.w[0];
|
|
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
|
|
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
|
|
// C* = floor(C*) (logical right shift; C has p decimal digits,
|
|
// correct by Property 1)
|
|
// n = C* * 10^(e+x)
|
|
|
|
// shift right C* by Ex-64 = shiftright128[ind]
|
|
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
|
|
Cstar = Cstar >> shift;
|
|
// determine inexactness of the rounding of C*
|
|
// if (0 < f* < 10^(-x)) then
|
|
// the result is exact
|
|
// else // if (f* > T*) then
|
|
// the result is inexact
|
|
if (ind - 1 <= 2) {
|
|
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
if (x_sign) { // negative and inexact
|
|
Cstar++;
|
|
}
|
|
} // else the result is exact
|
|
} else { // if 3 <= ind - 1 <= 14
|
|
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
if (x_sign) { // negative and inexact
|
|
Cstar++;
|
|
}
|
|
} // else the result is exact
|
|
}
|
|
|
|
if (x_sign)
|
|
res = -Cstar;
|
|
else
|
|
res = Cstar;
|
|
} else if (exp == 0) {
|
|
// 1 <= q <= 10
|
|
// res = +/-C (exact)
|
|
if (x_sign)
|
|
res = -C1;
|
|
else
|
|
res = C1;
|
|
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
|
|
// res = +/-C * 10^exp (exact)
|
|
if (x_sign)
|
|
res = -C1 * ten2k64[exp];
|
|
else
|
|
res = C1 * ten2k64[exp];
|
|
}
|
|
}
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
/*****************************************************************************
|
|
* BID64_to_int32_xfloor
|
|
****************************************************************************/
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64_to_int32_xfloor (int *pres,
|
|
UINT64 *
|
|
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 x = *px;
|
|
#else
|
|
int
|
|
bid64_to_int32_xfloor (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
int res;
|
|
UINT64 x_sign;
|
|
UINT64 x_exp;
|
|
int exp; // unbiased exponent
|
|
// Note: C1 represents x_significand (UINT64)
|
|
UINT64 tmp64;
|
|
BID_UI64DOUBLE tmp1;
|
|
unsigned int x_nr_bits;
|
|
int q, ind, shift;
|
|
UINT64 C1;
|
|
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
|
|
UINT128 fstar;
|
|
UINT128 P128;
|
|
|
|
// check for NaN or Infinity
|
|
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
|
|
// set invalid flag
|
|
*pfpsf |= INVALID_EXCEPTION;
|
|
// return Integer Indefinite
|
|
res = 0x80000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// unpack x
|
|
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
|
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
|
|
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
|
if (C1 > 9999999999999999ull) { // non-canonical
|
|
x_exp = 0;
|
|
C1 = 0;
|
|
}
|
|
} else {
|
|
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
|
|
C1 = x & MASK_BINARY_SIG1;
|
|
}
|
|
|
|
// check for zeros (possibly from non-canonical values)
|
|
if (C1 == 0x0ull) {
|
|
// x is 0
|
|
res = 0x00000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// x is not special and is not zero
|
|
|
|
// q = nr. of decimal digits in x (1 <= q <= 54)
|
|
// determine first the nr. of bits in x
|
|
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
|
|
// split the 64-bit value in two 32-bit halves to avoid rounding errors
|
|
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
|
|
tmp1.d = (double) (C1 >> 32); // exact conversion
|
|
x_nr_bits =
|
|
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
} else { // x < 2^32
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
} else { // if x < 2^53
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
q = nr_digits[x_nr_bits - 1].digits;
|
|
if (q == 0) {
|
|
q = nr_digits[x_nr_bits - 1].digits1;
|
|
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
|
|
q++;
|
|
}
|
|
exp = x_exp - 398; // unbiased exponent
|
|
|
|
if ((q + exp) > 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 < -2^31 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x500000000, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000000 has 11 digits
|
|
tmp64 = C1 * 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 > 0x500000000ull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) > 0x500000000 <=>
|
|
// C > 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31+1 up)
|
|
// Note: 0x500000000*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x500000000ull * ten2k64[q - 11];
|
|
if (C1 > tmp64) {
|
|
// 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 >= 2^31 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x500000000, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000000 has 11 digits
|
|
tmp64 = C1 * 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 >= 0x500000000ull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x500000000 <=>
|
|
// C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31-1 up)
|
|
// Note: 0x500000000*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x500000000ull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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: -2^31 <= n < 2^31
|
|
// Note: some of the cases tested for above fall through to this point
|
|
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
|
|
// set inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
// return -1 or 0
|
|
if (x_sign)
|
|
res = 0xffffffff;
|
|
else
|
|
res = 0x00000000;
|
|
BID_RETURN (res);
|
|
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
|
|
// -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded
|
|
// to nearest to a 32-bit signed integer
|
|
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
|
|
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
|
|
// chop off ind digits from the lower part of C1
|
|
// C1 fits in 64 bits
|
|
// calculate C* and f*
|
|
// C* is actually floor(C*) in this case
|
|
// C* and f* need shifting and masking, as shown by
|
|
// shiftright128[] and maskhigh128[]
|
|
// 1 <= x <= 15
|
|
// kx = 10^(-x) = ten2mk64[ind - 1]
|
|
// C* = C1 * 10^(-x)
|
|
// the approximation of 10^(-x) was rounded up to 54 bits
|
|
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
|
|
Cstar = P128.w[1];
|
|
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
|
|
fstar.w[0] = P128.w[0];
|
|
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
|
|
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
|
|
// C* = floor(C*) (logical right shift; C has p decimal digits,
|
|
// correct by Property 1)
|
|
// n = C* * 10^(e+x)
|
|
|
|
// shift right C* by Ex-64 = shiftright128[ind]
|
|
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
|
|
Cstar = Cstar >> shift;
|
|
// determine inexactness of the rounding of C*
|
|
// if (0 < f* < 10^(-x)) then
|
|
// the result is exact
|
|
// else // if (f* > T*) then
|
|
// the result is inexact
|
|
if (ind - 1 <= 2) {
|
|
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
if (x_sign) { // negative and inexact
|
|
Cstar++;
|
|
}
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
} // else the result is exact
|
|
} else { // if 3 <= ind - 1 <= 14
|
|
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
if (x_sign) { // negative and inexact
|
|
Cstar++;
|
|
}
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
} // else the result is exact
|
|
}
|
|
|
|
if (x_sign)
|
|
res = -Cstar;
|
|
else
|
|
res = Cstar;
|
|
} else if (exp == 0) {
|
|
// 1 <= q <= 10
|
|
// res = +/-C (exact)
|
|
if (x_sign)
|
|
res = -C1;
|
|
else
|
|
res = C1;
|
|
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
|
|
// res = +/-C * 10^exp (exact)
|
|
if (x_sign)
|
|
res = -C1 * ten2k64[exp];
|
|
else
|
|
res = C1 * ten2k64[exp];
|
|
}
|
|
}
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
/*****************************************************************************
|
|
* BID64_to_int32_ceil
|
|
****************************************************************************/
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64_to_int32_ceil (int *pres,
|
|
UINT64 *
|
|
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 x = *px;
|
|
#else
|
|
int
|
|
bid64_to_int32_ceil (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
int res;
|
|
UINT64 x_sign;
|
|
UINT64 x_exp;
|
|
int exp; // unbiased exponent
|
|
// Note: C1 represents x_significand (UINT64)
|
|
UINT64 tmp64;
|
|
BID_UI64DOUBLE tmp1;
|
|
unsigned int x_nr_bits;
|
|
int q, ind, shift;
|
|
UINT64 C1;
|
|
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
|
|
UINT128 fstar;
|
|
UINT128 P128;
|
|
|
|
// check for NaN or Infinity
|
|
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
|
|
// set invalid flag
|
|
*pfpsf |= INVALID_EXCEPTION;
|
|
// return Integer Indefinite
|
|
res = 0x80000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// unpack x
|
|
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
|
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
|
|
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
|
if (C1 > 9999999999999999ull) { // non-canonical
|
|
x_exp = 0;
|
|
C1 = 0;
|
|
}
|
|
} else {
|
|
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
|
|
C1 = x & MASK_BINARY_SIG1;
|
|
}
|
|
|
|
// check for zeros (possibly from non-canonical values)
|
|
if (C1 == 0x0ull) {
|
|
// x is 0
|
|
res = 0x00000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// x is not special and is not zero
|
|
|
|
// q = nr. of decimal digits in x (1 <= q <= 54)
|
|
// determine first the nr. of bits in x
|
|
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
|
|
// split the 64-bit value in two 32-bit halves to avoid rounding errors
|
|
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
|
|
tmp1.d = (double) (C1 >> 32); // exact conversion
|
|
x_nr_bits =
|
|
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
} else { // x < 2^32
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
} else { // if x < 2^53
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
q = nr_digits[x_nr_bits - 1].digits;
|
|
if (q == 0) {
|
|
q = nr_digits[x_nr_bits - 1].digits1;
|
|
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
|
|
q++;
|
|
}
|
|
exp = x_exp - 398; // unbiased exponent
|
|
|
|
if ((q + exp) > 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 <= -2^31 - 1 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x50000000a, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x50000000a, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x50000000a has 11 digits
|
|
tmp64 = C1 * 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 >= 0x50000000aull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x50000000a <=>
|
|
// C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31+1 up)
|
|
// Note: 0x50000000a*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x50000000aull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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 > 2^31 - 1 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 - 1
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6, 1<=q<=16
|
|
// <=> C * 10^(11-q) > 0x4fffffff6, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x4fffffff6 has 11 digits
|
|
tmp64 = C1 * 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 > 0x4fffffff6ull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) > 0x4fffffff6 <=>
|
|
// C > 0x4fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31-1 up)
|
|
// Note: 0x4fffffff6*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x4fffffff6ull * ten2k64[q - 11];
|
|
if (C1 > tmp64) {
|
|
// 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: -2^31 - 1 < n <= 2^31 - 1
|
|
// Note: some of the cases tested for above fall through to this point
|
|
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
|
|
// return 0 or 1
|
|
if (x_sign)
|
|
res = 0x00000000;
|
|
else
|
|
res = 0x00000001;
|
|
BID_RETURN (res);
|
|
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
|
|
// -2^31-1 < x <= -1 or 1 <= x <= 2^31-1 so x can be rounded
|
|
// to nearest to a 32-bit signed integer
|
|
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
|
|
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
|
|
// chop off ind digits from the lower part of C1
|
|
// C1 fits in 64 bits
|
|
// calculate C* and f*
|
|
// C* is actually floor(C*) in this case
|
|
// C* and f* need shifting and masking, as shown by
|
|
// shiftright128[] and maskhigh128[]
|
|
// 1 <= x <= 15
|
|
// kx = 10^(-x) = ten2mk64[ind - 1]
|
|
// C* = C1 * 10^(-x)
|
|
// the approximation of 10^(-x) was rounded up to 54 bits
|
|
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
|
|
Cstar = P128.w[1];
|
|
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
|
|
fstar.w[0] = P128.w[0];
|
|
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
|
|
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
|
|
// C* = floor(C*) (logical right shift; C has p decimal digits,
|
|
// correct by Property 1)
|
|
// n = C* * 10^(e+x)
|
|
|
|
// shift right C* by Ex-64 = shiftright128[ind]
|
|
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
|
|
Cstar = Cstar >> shift;
|
|
// determine inexactness of the rounding of C*
|
|
// if (0 < f* < 10^(-x)) then
|
|
// the result is exact
|
|
// else // if (f* > T*) then
|
|
// the result is inexact
|
|
if (ind - 1 <= 2) {
|
|
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
if (!x_sign) { // positive and inexact
|
|
Cstar++;
|
|
}
|
|
} // else the result is exact
|
|
} else { // if 3 <= ind - 1 <= 14
|
|
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
if (!x_sign) { // positive and inexact
|
|
Cstar++;
|
|
}
|
|
} // else the result is exact
|
|
}
|
|
|
|
if (x_sign)
|
|
res = -Cstar;
|
|
else
|
|
res = Cstar;
|
|
} else if (exp == 0) {
|
|
// 1 <= q <= 10
|
|
// res = +/-C (exact)
|
|
if (x_sign)
|
|
res = -C1;
|
|
else
|
|
res = C1;
|
|
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
|
|
// res = +/-C * 10^exp (exact)
|
|
if (x_sign)
|
|
res = -C1 * ten2k64[exp];
|
|
else
|
|
res = C1 * ten2k64[exp];
|
|
}
|
|
}
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
/*****************************************************************************
|
|
* BID64_to_int32_xceil
|
|
****************************************************************************/
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64_to_int32_xceil (int *pres,
|
|
UINT64 *
|
|
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 x = *px;
|
|
#else
|
|
int
|
|
bid64_to_int32_xceil (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
int res;
|
|
UINT64 x_sign;
|
|
UINT64 x_exp;
|
|
int exp; // unbiased exponent
|
|
// Note: C1 represents x_significand (UINT64)
|
|
UINT64 tmp64;
|
|
BID_UI64DOUBLE tmp1;
|
|
unsigned int x_nr_bits;
|
|
int q, ind, shift;
|
|
UINT64 C1;
|
|
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
|
|
UINT128 fstar;
|
|
UINT128 P128;
|
|
|
|
// check for NaN or Infinity
|
|
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
|
|
// set invalid flag
|
|
*pfpsf |= INVALID_EXCEPTION;
|
|
// return Integer Indefinite
|
|
res = 0x80000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// unpack x
|
|
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
|
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
|
|
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
|
if (C1 > 9999999999999999ull) { // non-canonical
|
|
x_exp = 0;
|
|
C1 = 0;
|
|
}
|
|
} else {
|
|
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
|
|
C1 = x & MASK_BINARY_SIG1;
|
|
}
|
|
|
|
// check for zeros (possibly from non-canonical values)
|
|
if (C1 == 0x0ull) {
|
|
// x is 0
|
|
res = 0x00000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// x is not special and is not zero
|
|
|
|
// q = nr. of decimal digits in x (1 <= q <= 54)
|
|
// determine first the nr. of bits in x
|
|
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
|
|
// split the 64-bit value in two 32-bit halves to avoid rounding errors
|
|
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
|
|
tmp1.d = (double) (C1 >> 32); // exact conversion
|
|
x_nr_bits =
|
|
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
} else { // x < 2^32
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
} else { // if x < 2^53
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
q = nr_digits[x_nr_bits - 1].digits;
|
|
if (q == 0) {
|
|
q = nr_digits[x_nr_bits - 1].digits1;
|
|
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
|
|
q++;
|
|
}
|
|
exp = x_exp - 398; // unbiased exponent
|
|
|
|
if ((q + exp) > 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 <= -2^31 - 1 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x50000000a, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x50000000a, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x50000000a has 11 digits
|
|
tmp64 = C1 * 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 >= 0x50000000aull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x50000000a <=>
|
|
// C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31+1 up)
|
|
// Note: 0x50000000a*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x50000000aull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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 > 2^31 - 1 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 - 1
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6, 1<=q<=16
|
|
// <=> C * 10^(11-q) > 0x4fffffff6, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x4fffffff6 has 11 digits
|
|
tmp64 = C1 * 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 > 0x4fffffff6ull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) > 0x4fffffff6 <=>
|
|
// C > 0x4fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31-1 up)
|
|
// Note: 0x4fffffff6*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x4fffffff6ull * ten2k64[q - 11];
|
|
if (C1 > tmp64) {
|
|
// 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: -2^31 - 1 < n <= 2^31 - 1
|
|
// Note: some of the cases tested for above fall through to this point
|
|
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
|
|
// set inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
// return 0 or 1
|
|
if (x_sign)
|
|
res = 0x00000000;
|
|
else
|
|
res = 0x00000001;
|
|
BID_RETURN (res);
|
|
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
|
|
// -2^31-1 < x <= -1 or 1 <= x <= 2^31-1 so x can be rounded
|
|
// to nearest to a 32-bit signed integer
|
|
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
|
|
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
|
|
// chop off ind digits from the lower part of C1
|
|
// C1 fits in 64 bits
|
|
// calculate C* and f*
|
|
// C* is actually floor(C*) in this case
|
|
// C* and f* need shifting and masking, as shown by
|
|
// shiftright128[] and maskhigh128[]
|
|
// 1 <= x <= 15
|
|
// kx = 10^(-x) = ten2mk64[ind - 1]
|
|
// C* = C1 * 10^(-x)
|
|
// the approximation of 10^(-x) was rounded up to 54 bits
|
|
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
|
|
Cstar = P128.w[1];
|
|
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
|
|
fstar.w[0] = P128.w[0];
|
|
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
|
|
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
|
|
// C* = floor(C*) (logical right shift; C has p decimal digits,
|
|
// correct by Property 1)
|
|
// n = C* * 10^(e+x)
|
|
|
|
// shift right C* by Ex-64 = shiftright128[ind]
|
|
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
|
|
Cstar = Cstar >> shift;
|
|
// determine inexactness of the rounding of C*
|
|
// if (0 < f* < 10^(-x)) then
|
|
// the result is exact
|
|
// else // if (f* > T*) then
|
|
// the result is inexact
|
|
if (ind - 1 <= 2) {
|
|
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
if (!x_sign) { // positive and inexact
|
|
Cstar++;
|
|
}
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
} // else the result is exact
|
|
} else { // if 3 <= ind - 1 <= 14
|
|
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
if (!x_sign) { // positive and inexact
|
|
Cstar++;
|
|
}
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
} // else the result is exact
|
|
}
|
|
|
|
if (x_sign)
|
|
res = -Cstar;
|
|
else
|
|
res = Cstar;
|
|
} else if (exp == 0) {
|
|
// 1 <= q <= 10
|
|
// res = +/-C (exact)
|
|
if (x_sign)
|
|
res = -C1;
|
|
else
|
|
res = C1;
|
|
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
|
|
// res = +/-C * 10^exp (exact)
|
|
if (x_sign)
|
|
res = -C1 * ten2k64[exp];
|
|
else
|
|
res = C1 * ten2k64[exp];
|
|
}
|
|
}
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
/*****************************************************************************
|
|
* BID64_to_int32_int
|
|
****************************************************************************/
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64_to_int32_int (int *pres,
|
|
UINT64 *
|
|
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 x = *px;
|
|
#else
|
|
int
|
|
bid64_to_int32_int (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
int res;
|
|
UINT64 x_sign;
|
|
UINT64 x_exp;
|
|
int exp; // unbiased exponent
|
|
// Note: C1 represents x_significand (UINT64)
|
|
UINT64 tmp64;
|
|
BID_UI64DOUBLE tmp1;
|
|
unsigned int x_nr_bits;
|
|
int q, ind, shift;
|
|
UINT64 C1;
|
|
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
|
|
UINT128 P128;
|
|
|
|
// check for NaN or Infinity
|
|
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
|
|
// set invalid flag
|
|
*pfpsf |= INVALID_EXCEPTION;
|
|
// return Integer Indefinite
|
|
res = 0x80000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// unpack x
|
|
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
|
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
|
|
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
|
if (C1 > 9999999999999999ull) { // non-canonical
|
|
x_exp = 0;
|
|
C1 = 0;
|
|
}
|
|
} else {
|
|
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
|
|
C1 = x & MASK_BINARY_SIG1;
|
|
}
|
|
|
|
// check for zeros (possibly from non-canonical values)
|
|
if (C1 == 0x0ull) {
|
|
// x is 0
|
|
res = 0x00000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// x is not special and is not zero
|
|
|
|
// q = nr. of decimal digits in x (1 <= q <= 54)
|
|
// determine first the nr. of bits in x
|
|
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
|
|
// split the 64-bit value in two 32-bit halves to avoid rounding errors
|
|
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
|
|
tmp1.d = (double) (C1 >> 32); // exact conversion
|
|
x_nr_bits =
|
|
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
} else { // x < 2^32
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
} else { // if x < 2^53
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
q = nr_digits[x_nr_bits - 1].digits;
|
|
if (q == 0) {
|
|
q = nr_digits[x_nr_bits - 1].digits1;
|
|
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
|
|
q++;
|
|
}
|
|
exp = x_exp - 398; // unbiased exponent
|
|
|
|
if ((q + exp) > 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 <= -2^31 - 1 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x50000000a, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x50000000a, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x50000000a has 11 digits
|
|
tmp64 = C1 * 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 >= 0x50000000aull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x50000000a <=>
|
|
// C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31+1 up)
|
|
// Note: 0x50000000a*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x50000000aull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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 >= 2^31 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x500000000, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000000 has 11 digits
|
|
tmp64 = C1 * 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 >= 0x500000000ull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x500000000 <=>
|
|
// C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31-1 up)
|
|
// Note: 0x500000000*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x500000000ull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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: -2^31 - 1 < n < 2^31
|
|
// Note: some of the cases tested for above fall through to this point
|
|
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
|
|
// return 0
|
|
res = 0x00000000;
|
|
BID_RETURN (res);
|
|
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
|
|
// -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded
|
|
// to nearest to a 32-bit signed integer
|
|
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
|
|
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
|
|
// chop off ind digits from the lower part of C1
|
|
// C1 fits in 64 bits
|
|
// calculate C* and f*
|
|
// C* is actually floor(C*) in this case
|
|
// C* and f* need shifting and masking, as shown by
|
|
// shiftright128[] and maskhigh128[]
|
|
// 1 <= x <= 15
|
|
// kx = 10^(-x) = ten2mk64[ind - 1]
|
|
// C* = C1 * 10^(-x)
|
|
// the approximation of 10^(-x) was rounded up to 54 bits
|
|
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
|
|
Cstar = P128.w[1];
|
|
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
|
|
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
|
|
// C* = floor(C*) (logical right shift; C has p decimal digits,
|
|
// correct by Property 1)
|
|
// n = C* * 10^(e+x)
|
|
|
|
// shift right C* by Ex-64 = shiftright128[ind]
|
|
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
|
|
Cstar = Cstar >> shift;
|
|
if (x_sign)
|
|
res = -Cstar;
|
|
else
|
|
res = Cstar;
|
|
} else if (exp == 0) {
|
|
// 1 <= q <= 10
|
|
// res = +/-C (exact)
|
|
if (x_sign)
|
|
res = -C1;
|
|
else
|
|
res = C1;
|
|
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
|
|
// res = +/-C * 10^exp (exact)
|
|
if (x_sign)
|
|
res = -C1 * ten2k64[exp];
|
|
else
|
|
res = C1 * ten2k64[exp];
|
|
}
|
|
}
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
/*****************************************************************************
|
|
* BID64_to_int32_xint
|
|
****************************************************************************/
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64_to_int32_xint (int *pres,
|
|
UINT64 *
|
|
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 x = *px;
|
|
#else
|
|
int
|
|
bid64_to_int32_xint (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
int res;
|
|
UINT64 x_sign;
|
|
UINT64 x_exp;
|
|
int exp; // unbiased exponent
|
|
// Note: C1 represents x_significand (UINT64)
|
|
UINT64 tmp64;
|
|
BID_UI64DOUBLE tmp1;
|
|
unsigned int x_nr_bits;
|
|
int q, ind, shift;
|
|
UINT64 C1;
|
|
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
|
|
UINT128 fstar;
|
|
UINT128 P128;
|
|
|
|
// check for NaN or Infinity
|
|
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
|
|
// set invalid flag
|
|
*pfpsf |= INVALID_EXCEPTION;
|
|
// return Integer Indefinite
|
|
res = 0x80000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// unpack x
|
|
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
|
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
|
|
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
|
if (C1 > 9999999999999999ull) { // non-canonical
|
|
x_exp = 0;
|
|
C1 = 0;
|
|
}
|
|
} else {
|
|
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
|
|
C1 = x & MASK_BINARY_SIG1;
|
|
}
|
|
|
|
// check for zeros (possibly from non-canonical values)
|
|
if (C1 == 0x0ull) {
|
|
// x is 0
|
|
res = 0x00000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// x is not special and is not zero
|
|
|
|
// q = nr. of decimal digits in x (1 <= q <= 54)
|
|
// determine first the nr. of bits in x
|
|
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
|
|
// split the 64-bit value in two 32-bit halves to avoid rounding errors
|
|
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
|
|
tmp1.d = (double) (C1 >> 32); // exact conversion
|
|
x_nr_bits =
|
|
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
} else { // x < 2^32
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
} else { // if x < 2^53
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
q = nr_digits[x_nr_bits - 1].digits;
|
|
if (q == 0) {
|
|
q = nr_digits[x_nr_bits - 1].digits1;
|
|
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
|
|
q++;
|
|
}
|
|
exp = x_exp - 398; // unbiased exponent
|
|
|
|
if ((q + exp) > 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 <= -2^31 - 1 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x50000000a, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x50000000a, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x50000000a has 11 digits
|
|
tmp64 = C1 * 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 >= 0x50000000aull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x50000000a <=>
|
|
// C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31+1 up)
|
|
// Note: 0x50000000a*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x50000000aull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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 >= 2^31 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x500000000, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000000 has 11 digits
|
|
tmp64 = C1 * 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 >= 0x500000000ull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x500000000 <=>
|
|
// C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31-1 up)
|
|
// Note: 0x500000000*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x500000000ull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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: -2^31 - 1 < n < 2^31
|
|
// Note: some of the cases tested for above fall through to this point
|
|
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
|
|
// set inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
// return 0
|
|
res = 0x00000000;
|
|
BID_RETURN (res);
|
|
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
|
|
// -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded
|
|
// to nearest to a 32-bit signed integer
|
|
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
|
|
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
|
|
// chop off ind digits from the lower part of C1
|
|
// C1 fits in 64 bits
|
|
// calculate C* and f*
|
|
// C* is actually floor(C*) in this case
|
|
// C* and f* need shifting and masking, as shown by
|
|
// shiftright128[] and maskhigh128[]
|
|
// 1 <= x <= 15
|
|
// kx = 10^(-x) = ten2mk64[ind - 1]
|
|
// C* = C1 * 10^(-x)
|
|
// the approximation of 10^(-x) was rounded up to 54 bits
|
|
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
|
|
Cstar = P128.w[1];
|
|
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
|
|
fstar.w[0] = P128.w[0];
|
|
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
|
|
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
|
|
// C* = floor(C*) (logical right shift; C has p decimal digits,
|
|
// correct by Property 1)
|
|
// n = C* * 10^(e+x)
|
|
|
|
// shift right C* by Ex-64 = shiftright128[ind]
|
|
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
|
|
Cstar = Cstar >> shift;
|
|
// determine inexactness of the rounding of C*
|
|
// if (0 < f* < 10^(-x)) then
|
|
// the result is exact
|
|
// else // if (f* > T*) then
|
|
// the result is inexact
|
|
if (ind - 1 <= 2) {
|
|
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
} // else the result is exact
|
|
} else { // if 3 <= ind - 1 <= 14
|
|
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
} // else the result is exact
|
|
}
|
|
|
|
if (x_sign)
|
|
res = -Cstar;
|
|
else
|
|
res = Cstar;
|
|
} else if (exp == 0) {
|
|
// 1 <= q <= 10
|
|
// res = +/-C (exact)
|
|
if (x_sign)
|
|
res = -C1;
|
|
else
|
|
res = C1;
|
|
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
|
|
// res = +/-C * 10^exp (exact)
|
|
if (x_sign)
|
|
res = -C1 * ten2k64[exp];
|
|
else
|
|
res = C1 * ten2k64[exp];
|
|
}
|
|
}
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
/*****************************************************************************
|
|
* BID64_to_int32_rninta
|
|
****************************************************************************/
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64_to_int32_rninta (int *pres,
|
|
UINT64 *
|
|
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 x = *px;
|
|
#else
|
|
int
|
|
bid64_to_int32_rninta (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
int res;
|
|
UINT64 x_sign;
|
|
UINT64 x_exp;
|
|
int exp; // unbiased exponent
|
|
// Note: C1 represents x_significand (UINT64)
|
|
UINT64 tmp64;
|
|
BID_UI64DOUBLE tmp1;
|
|
unsigned int x_nr_bits;
|
|
int q, ind, shift;
|
|
UINT64 C1;
|
|
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
|
|
UINT128 P128;
|
|
|
|
// check for NaN or Infinity
|
|
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
|
|
// set invalid flag
|
|
*pfpsf |= INVALID_EXCEPTION;
|
|
// return Integer Indefinite
|
|
res = 0x80000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// unpack x
|
|
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
|
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
|
|
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
|
if (C1 > 9999999999999999ull) { // non-canonical
|
|
x_exp = 0;
|
|
C1 = 0;
|
|
}
|
|
} else {
|
|
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
|
|
C1 = x & MASK_BINARY_SIG1;
|
|
}
|
|
|
|
// check for zeros (possibly from non-canonical values)
|
|
if (C1 == 0x0ull) {
|
|
// x is 0
|
|
res = 0x00000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// x is not special and is not zero
|
|
|
|
// q = nr. of decimal digits in x (1 <= q <= 54)
|
|
// determine first the nr. of bits in x
|
|
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
|
|
// split the 64-bit value in two 32-bit halves to avoid rounding errors
|
|
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
|
|
tmp1.d = (double) (C1 >> 32); // exact conversion
|
|
x_nr_bits =
|
|
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
} else { // x < 2^32
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
} else { // if x < 2^53
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
q = nr_digits[x_nr_bits - 1].digits;
|
|
if (q == 0) {
|
|
q = nr_digits[x_nr_bits - 1].digits1;
|
|
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
|
|
q++;
|
|
}
|
|
exp = x_exp - 398; // unbiased exponent
|
|
|
|
if ((q + exp) > 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 <= -2^31 - 1/2 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1/2
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x500000005, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits
|
|
tmp64 = C1 * 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 >= 0x500000005ull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x500000005 <=>
|
|
// C >= 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31+1/2 up)
|
|
// Note: 0x500000005*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x500000005ull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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 >= 2^31 - 1/2 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x4fffffffb, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits
|
|
tmp64 = C1 * 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 >= 0x4fffffffbull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x4fffffffb <=>
|
|
// C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31-1/2 up)
|
|
// Note: 0x4fffffffb*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x4fffffffbull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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: -2^31 - 1/2 < n < 2^31 - 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
|
|
// res = +/-1
|
|
ind = q - 1;
|
|
if (C1 < midpoint64[ind]) {
|
|
res = 0x00000000; // return 0
|
|
} else if (x_sign) { // n < 0
|
|
res = 0xffffffff; // return -1
|
|
} else { // n > 0
|
|
res = 0x00000001; // return +1
|
|
}
|
|
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
|
|
// -2^31-1/2 <= x <= -1 or 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 <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
|
|
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
|
|
// chop off ind digits from the lower part of C1
|
|
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits
|
|
C1 = C1 + midpoint64[ind - 1];
|
|
// calculate C* and f*
|
|
// C* is actually floor(C*) in this case
|
|
// C* and f* need shifting and masking, as shown by
|
|
// shiftright128[] and maskhigh128[]
|
|
// 1 <= x <= 15
|
|
// kx = 10^(-x) = ten2mk64[ind - 1]
|
|
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
|
|
// the approximation of 10^(-x) was rounded up to 54 bits
|
|
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
|
|
Cstar = P128.w[1];
|
|
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
|
|
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
|
|
// C* = floor(C*)-1 (logical right shift; C* has p decimal digits,
|
|
// correct by Pr. 1)
|
|
// n = C* * 10^(e+x)
|
|
|
|
// shift right C* by Ex-64 = shiftright128[ind]
|
|
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
|
|
Cstar = Cstar >> shift;
|
|
|
|
// if the result was a midpoint it was rounded away from zero
|
|
if (x_sign)
|
|
res = -Cstar;
|
|
else
|
|
res = Cstar;
|
|
} else if (exp == 0) {
|
|
// 1 <= q <= 10
|
|
// res = +/-C (exact)
|
|
if (x_sign)
|
|
res = -C1;
|
|
else
|
|
res = C1;
|
|
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
|
|
// res = +/-C * 10^exp (exact)
|
|
if (x_sign)
|
|
res = -C1 * ten2k64[exp];
|
|
else
|
|
res = C1 * ten2k64[exp];
|
|
}
|
|
}
|
|
BID_RETURN (res);
|
|
}
|
|
|
|
/*****************************************************************************
|
|
* BID64_to_int32_xrninta
|
|
****************************************************************************/
|
|
|
|
#if DECIMAL_CALL_BY_REFERENCE
|
|
void
|
|
bid64_to_int32_xrninta (int *pres,
|
|
UINT64 *
|
|
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
UINT64 x = *px;
|
|
#else
|
|
int
|
|
bid64_to_int32_xrninta (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
|
|
_EXC_INFO_PARAM) {
|
|
#endif
|
|
int res;
|
|
UINT64 x_sign;
|
|
UINT64 x_exp;
|
|
int exp; // unbiased exponent
|
|
// Note: C1 represents x_significand (UINT64)
|
|
UINT64 tmp64;
|
|
BID_UI64DOUBLE tmp1;
|
|
unsigned int x_nr_bits;
|
|
int q, ind, shift;
|
|
UINT64 C1;
|
|
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
|
|
UINT128 fstar;
|
|
UINT128 P128;
|
|
|
|
// check for NaN or Infinity
|
|
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
|
|
// set invalid flag
|
|
*pfpsf |= INVALID_EXCEPTION;
|
|
// return Integer Indefinite
|
|
res = 0x80000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// unpack x
|
|
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
|
|
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
|
|
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
|
|
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
|
|
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
|
|
if (C1 > 9999999999999999ull) { // non-canonical
|
|
x_exp = 0;
|
|
C1 = 0;
|
|
}
|
|
} else {
|
|
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
|
|
C1 = x & MASK_BINARY_SIG1;
|
|
}
|
|
|
|
// check for zeros (possibly from non-canonical values)
|
|
if (C1 == 0x0ull) {
|
|
// x is 0
|
|
res = 0x00000000;
|
|
BID_RETURN (res);
|
|
}
|
|
// x is not special and is not zero
|
|
|
|
// q = nr. of decimal digits in x (1 <= q <= 54)
|
|
// determine first the nr. of bits in x
|
|
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
|
|
// split the 64-bit value in two 32-bit halves to avoid rounding errors
|
|
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
|
|
tmp1.d = (double) (C1 >> 32); // exact conversion
|
|
x_nr_bits =
|
|
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
} else { // x < 2^32
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
} else { // if x < 2^53
|
|
tmp1.d = (double) C1; // exact conversion
|
|
x_nr_bits =
|
|
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
|
|
}
|
|
q = nr_digits[x_nr_bits - 1].digits;
|
|
if (q == 0) {
|
|
q = nr_digits[x_nr_bits - 1].digits1;
|
|
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
|
|
q++;
|
|
}
|
|
exp = x_exp - 398; // unbiased exponent
|
|
|
|
if ((q + exp) > 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 <= -2^31 - 1/2 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1/2
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x500000005, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits
|
|
tmp64 = C1 * 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 >= 0x500000005ull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x500000005 <=>
|
|
// C >= 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31+1/2 up)
|
|
// Note: 0x500000005*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x500000005ull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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 >= 2^31 - 1/2 then n is too large
|
|
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2
|
|
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=16
|
|
// <=> C * 10^(11-q) >= 0x4fffffffb, 1<=q<=16
|
|
if (q <= 11) {
|
|
// Note: C * 10^(11-q) has 10 or 11 digits; 0x500000005 has 11 digits
|
|
tmp64 = C1 * 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 >= 0x4fffffffbull) {
|
|
// 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 <= 16 and so -15 <= exp <= -2
|
|
// C * 10^(11-q) >= 0x4fffffffb <=>
|
|
// C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 5
|
|
// (scale 2^31-1/2 up)
|
|
// Note: 0x4fffffffb*10^(q-11) has q-1 or q digits, where q <= 16
|
|
tmp64 = 0x4fffffffbull * ten2k64[q - 11];
|
|
if (C1 >= tmp64) {
|
|
// 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: -2^31 - 1/2 < n < 2^31 - 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
|
|
// res = +/-1
|
|
ind = q - 1;
|
|
if (C1 < midpoint64[ind]) {
|
|
res = 0x00000000; // return 0
|
|
} else if (x_sign) { // n < 0
|
|
res = 0xffffffff; // return -1
|
|
} else { // n > 0
|
|
res = 0x00000001; // return +1
|
|
}
|
|
// set inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
|
|
// -2^31-1/2 <= x <= -1 or 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 <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
|
|
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
|
|
// chop off ind digits from the lower part of C1
|
|
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits
|
|
C1 = C1 + midpoint64[ind - 1];
|
|
// calculate C* and f*
|
|
// C* is actually floor(C*) in this case
|
|
// C* and f* need shifting and masking, as shown by
|
|
// shiftright128[] and maskhigh128[]
|
|
// 1 <= x <= 15
|
|
// kx = 10^(-x) = ten2mk64[ind - 1]
|
|
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
|
|
// the approximation of 10^(-x) was rounded up to 54 bits
|
|
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
|
|
Cstar = P128.w[1];
|
|
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
|
|
fstar.w[0] = P128.w[0];
|
|
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
|
|
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
|
|
// C* = floor(C*)-1 (logical right shift; C* has p decimal digits,
|
|
// correct by Pr. 1)
|
|
// n = C* * 10^(e+x)
|
|
|
|
// shift right C* by Ex-64 = shiftright128[ind]
|
|
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
|
|
Cstar = Cstar >> shift;
|
|
// determine inexactness of the rounding of C*
|
|
// if (0 < f* - 1/2 < 10^(-x)) then
|
|
// the result is exact
|
|
// else // if (f* - 1/2 > T*) then
|
|
// the result is inexact
|
|
if (ind - 1 <= 2) {
|
|
if (fstar.w[0] > 0x8000000000000000ull) {
|
|
// f* > 1/2 and the result may be exact
|
|
tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2
|
|
if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
} // else the result is exact
|
|
} else { // the result is inexact; f2* <= 1/2
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
}
|
|
} else { // if 3 <= ind - 1 <= 14
|
|
if (fstar.w[1] > onehalf128[ind - 1] ||
|
|
(fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) {
|
|
// f2* > 1/2 and the result may be exact
|
|
// Calculate f2* - 1/2
|
|
tmp64 = fstar.w[1] - onehalf128[ind - 1];
|
|
if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
|
|
// ten2mk128trunc[ind -1].w[1] is identical to
|
|
// ten2mk128[ind -1].w[1]
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
} // else the result is exact
|
|
} else { // the result is inexact; f2* <= 1/2
|
|
// set the inexact flag
|
|
*pfpsf |= INEXACT_EXCEPTION;
|
|
}
|
|
}
|
|
|
|
// if the result was a midpoint it was rounded away from zero
|
|
if (x_sign)
|
|
res = -Cstar;
|
|
else
|
|
res = Cstar;
|
|
} else if (exp == 0) {
|
|
// 1 <= q <= 10
|
|
// res = +/-C (exact)
|
|
if (x_sign)
|
|
res = -C1;
|
|
else
|
|
res = C1;
|
|
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
|
|
// res = +/-C * 10^exp (exact)
|
|
if (x_sign)
|
|
res = -C1 * ten2k64[exp];
|
|
else
|
|
res = C1 * ten2k64[exp];
|
|
}
|
|
}
|
|
BID_RETURN (res);
|
|
}
|