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2478 lines
68 KiB
2478 lines
68 KiB
/* Copyright (c) 2007, 2019, Oracle and/or its affiliates. All rights reserved.
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This library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Library General Public
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License, version 2.0, as published by the Free Software Foundation.
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This library is also distributed with certain software (including
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but not limited to OpenSSL) that is licensed under separate terms,
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as designated in a particular file or component or in included license
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documentation. The authors of MySQL hereby grant you an additional
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permission to link the library and your derivative works with the
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separately licensed software that they have included with MySQL.
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Without limiting anything contained in the foregoing, this file,
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which is part of C Driver for MySQL (Connector/C), is also subject to the
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Universal FOSS Exception, version 1.0, a copy of which can be found at
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http://oss.oracle.com/licenses/universal-foss-exception.
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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Library General Public License, version 2.0, for more details.
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You should have received a copy of the GNU Library General Public
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License along with this library; if not, write to the Free
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Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
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MA 02110-1301 USA */
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/****************************************************************
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This file incorporates work covered by the following copyright and
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permission notice:
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The author of this software is David M. Gay.
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Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
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Permission to use, copy, modify, and distribute this software for any
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purpose without fee is hereby granted, provided that this entire notice
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is included in all copies of any software which is or includes a copy
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or modification of this software and in all copies of the supporting
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documentation for such software.
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THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
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WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
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REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
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OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
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***************************************************************/
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#include "my_config.h"
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#include <limits>
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#include "decimal.h"
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#include "my_inttypes.h"
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#include "my_macros.h"
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#include "my_pointer_arithmetic.h"
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#ifdef HAVE_ENDIAN_H
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#include <endian.h>
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#endif
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#include <errno.h>
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#include <float.h>
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#include <stdlib.h>
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#include <string.h>
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#include "m_string.h"
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#include "my_dbug.h"
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#ifndef EOVERFLOW
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#define EOVERFLOW 84
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#endif
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/**
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Appears to suffice to not call malloc() in most cases.
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@todo
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see if it is possible to get rid of malloc().
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this constant is sufficient to avoid malloc() on all inputs I have tried.
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*/
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#define DTOA_BUFF_SIZE (460 * sizeof(void *))
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/* Magic value returned by dtoa() to indicate overflow */
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#define DTOA_OVERFLOW 9999
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static double my_strtod_int(const char *, const char **, int *, char *, size_t);
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static char *dtoa(double, int, int, int *, int *, char **, char *, size_t);
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static void dtoa_free(char *, char *, size_t);
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/**
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@brief
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Converts a given floating point number to a zero-terminated string
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representation using the 'f' format.
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@details
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This function is a wrapper around dtoa() to do the same as
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sprintf(to, "%-.*f", precision, x), though the conversion is usually more
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precise. The only difference is in handling [-,+]infinity and nan values,
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in which case we print '0\0' to the output string and indicate an overflow.
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@param x the input floating point number.
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@param precision the number of digits after the decimal point.
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All properties of sprintf() apply:
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- if the number of significant digits after the decimal
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point is less than precision, the resulting string is
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right-padded with zeros
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- if the precision is 0, no decimal point appears
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- if a decimal point appears, at least one digit appears
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before it
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@param to pointer to the output buffer. The longest string which
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my_fcvt() can return is FLOATING_POINT_BUFFER bytes
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(including the terminating '\0').
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@param error if not NULL, points to a location where the status of
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conversion is stored upon return.
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false successful conversion
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true the input number is [-,+]infinity or nan.
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The output string in this case is always '0'.
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@param shorten Whether to minimize the number of significant digits. If
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true, write only the minimum number of digits necessary to
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reproduce the double value when parsing the string. If
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false, zeros are added to the end to reach the precision
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limit.
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@return number of written characters (excluding terminating '\0')
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*/
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static size_t my_fcvt_internal(double x, int precision, bool shorten, char *to,
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bool *error) {
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int decpt, sign, len, i;
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char *res, *src, *end, *dst = to;
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char buf[DTOA_BUFF_SIZE];
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DBUG_ASSERT(precision >= 0 && precision < DECIMAL_NOT_SPECIFIED &&
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to != NULL);
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res = dtoa(x, 5, precision, &decpt, &sign, &end, buf, sizeof(buf));
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if (decpt == DTOA_OVERFLOW) {
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dtoa_free(res, buf, sizeof(buf));
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*to++ = '0';
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*to = '\0';
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if (error != NULL) *error = true;
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return 1;
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}
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src = res;
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len = (int)(end - src);
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if (sign) *dst++ = '-';
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if (decpt <= 0) {
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*dst++ = '0';
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*dst++ = '.';
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for (i = decpt; i < 0; i++) *dst++ = '0';
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}
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for (i = 1; i <= len; i++) {
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*dst++ = *src++;
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if (i == decpt && i < len) *dst++ = '.';
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}
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while (i++ <= decpt) *dst++ = '0';
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if (precision > 0 && !shorten) {
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if (len <= decpt) *dst++ = '.';
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for (i = precision - MY_MAX(0, (len - decpt)); i > 0; i--) *dst++ = '0';
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}
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*dst = '\0';
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if (error != NULL) *error = false;
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dtoa_free(res, buf, sizeof(buf));
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return dst - to;
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}
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/**
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@brief
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Converts a given floating point number to a zero-terminated string
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representation using the 'f' format.
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|
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@details
|
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This function is a wrapper around dtoa() to do the same as
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sprintf(to, "%-.*f", precision, x), though the conversion is usually more
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precise. The only difference is in handling [-,+]infinity and nan values,
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in which case we print '0\0' to the output string and indicate an overflow.
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@param x the input floating point number.
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@param precision the number of digits after the decimal point.
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All properties of sprintf() apply:
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- if the number of significant digits after the decimal
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point is less than precision, the resulting string is
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right-padded with zeros
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- if the precision is 0, no decimal point appears
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- if a decimal point appears, at least one digit appears
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before it
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@param to pointer to the output buffer. The longest string which
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my_fcvt() can return is FLOATING_POINT_BUFFER bytes
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(including the terminating '\0').
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@param error if not NULL, points to a location where the status of
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conversion is stored upon return.
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false successful conversion
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true the input number is [-,+]infinity or nan.
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The output string in this case is always '0'.
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@return number of written characters (excluding terminating '\0')
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*/
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size_t my_fcvt(double x, int precision, char *to, bool *error) {
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return my_fcvt_internal(x, precision, false, to, error);
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}
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/**
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@brief
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Converts a given floating point number to a zero-terminated string
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|
representation using the 'f' format.
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|
|
|
@details
|
|
This function is a wrapper around dtoa() to do almost the same as
|
|
sprintf(to, "%-.*f", precision, x), though the conversion is usually more
|
|
precise. The only difference is in handling [-,+]infinity and nan values,
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in which case we print '0\0' to the output string and indicate an overflow.
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The string always contains the minimum number of digits necessary to
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reproduce the same binary double value if the string is parsed back to a
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double value.
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@param x the input floating point number.
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@param to pointer to the output buffer. The longest string which
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my_fcvt() can return is FLOATING_POINT_BUFFER bytes
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(including the terminating '\0').
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@param error if not NULL, points to a location where the status of
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conversion is stored upon return.
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false successful conversion
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true the input number is [-,+]infinity or nan.
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The output string in this case is always '0'.
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@return number of written characters (excluding terminating '\0')
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*/
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size_t my_fcvt_compact(double x, char *to, bool *error) {
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return my_fcvt_internal(x, std::numeric_limits<double>::max_digits10, true,
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to, error);
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}
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/**
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@brief
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Converts a given floating point number to a zero-terminated string
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representation with a given field width using the 'e' format
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(aka scientific notation) or the 'f' one.
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@details
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The format is chosen automatically to provide the most number of significant
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digits (and thus, precision) with a given field width. In many cases, the
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result is similar to that of sprintf(to, "%g", x) with a few notable
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differences:
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- the conversion is usually more precise than C library functions.
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- there is no 'precision' argument. instead, we specify the number of
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characters available for conversion (i.e. a field width).
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- the result never exceeds the specified field width. If the field is too
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short to contain even a rounded decimal representation, my_gcvt()
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indicates overflow and truncates the output string to the specified width.
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- float-type arguments are handled differently than double ones. For a
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float input number (i.e. when the 'type' argument is MY_GCVT_ARG_FLOAT)
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we deliberately limit the precision of conversion by FLT_DIG digits to
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avoid garbage past the significant digits.
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- unlike sprintf(), in cases where the 'e' format is preferred, we don't
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zero-pad the exponent to save space for significant digits. The '+' sign
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for a positive exponent does not appear for the same reason.
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@param x the input floating point number.
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@param type is either MY_GCVT_ARG_FLOAT or MY_GCVT_ARG_DOUBLE.
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Specifies the type of the input number (see notes above).
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@param width field width in characters. The minimal field width to
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hold any number representation (albeit rounded) is 7
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characters ("-Ne-NNN").
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@param to pointer to the output buffer. The result is always
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zero-terminated, and the longest returned string is thus
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'width + 1' bytes.
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@param error if not NULL, points to a location where the status of
|
|
conversion is stored upon return.
|
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false successful conversion
|
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true the input number is [-,+]infinity or nan.
|
|
The output string in this case is always '0'.
|
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@return number of written characters (excluding terminating '\0')
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|
|
@todo
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Check if it is possible and makes sense to do our own rounding on top of
|
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dtoa() instead of calling dtoa() twice in (rare) cases when the resulting
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string representation does not fit in the specified field width and we want
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to re-round the input number with fewer significant digits. Examples:
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|
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my_gcvt(-9e-3, ..., 4, ...);
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my_gcvt(-9e-3, ..., 2, ...);
|
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my_gcvt(1.87e-3, ..., 4, ...);
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my_gcvt(55, ..., 1, ...);
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|
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We do our best to minimize such cases by:
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|
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- passing to dtoa() the field width as the number of significant digits
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|
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- removing the sign of the number early (and decreasing the width before
|
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passing it to dtoa())
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|
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- choosing the proper format to preserve the most number of significant
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digits.
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*/
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size_t my_gcvt(double x, my_gcvt_arg_type type, int width, char *to,
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bool *error) {
|
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int decpt, sign, len, exp_len;
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char *res, *src, *end, *dst = to, *dend = dst + width;
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char buf[DTOA_BUFF_SIZE];
|
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bool have_space, force_e_format;
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DBUG_ASSERT(width > 0 && to != NULL);
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|
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/* We want to remove '-' from equations early */
|
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if (x < 0.) width--;
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res = dtoa(x, 4, type == MY_GCVT_ARG_DOUBLE ? width : MY_MIN(width, FLT_DIG),
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&decpt, &sign, &end, buf, sizeof(buf));
|
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if (decpt == DTOA_OVERFLOW) {
|
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dtoa_free(res, buf, sizeof(buf));
|
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*to++ = '0';
|
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*to = '\0';
|
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if (error != NULL) *error = true;
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return 1;
|
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}
|
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|
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if (error != NULL) *error = false;
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|
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src = res;
|
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len = (int)(end - res);
|
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|
|
/*
|
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Number of digits in the exponent from the 'e' conversion.
|
|
The sign of the exponent is taken into account separetely, we don't need
|
|
to count it here.
|
|
*/
|
|
exp_len = 1 + (decpt >= 101 || decpt <= -99) + (decpt >= 11 || decpt <= -9);
|
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|
|
/*
|
|
Do we have enough space for all digits in the 'f' format?
|
|
Let 'len' be the number of significant digits returned by dtoa,
|
|
and F be the length of the resulting decimal representation.
|
|
Consider the following cases:
|
|
1. decpt <= 0, i.e. we have "0.NNN" => F = len - decpt + 2
|
|
2. 0 < decpt < len, i.e. we have "NNN.NNN" => F = len + 1
|
|
3. len <= decpt, i.e. we have "NNN00" => F = decpt
|
|
*/
|
|
have_space =
|
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(decpt <= 0 ? len - decpt + 2
|
|
: decpt > 0 && decpt < len ? len + 1 : decpt) <= width;
|
|
/*
|
|
The following is true when no significant digits can be placed with the
|
|
specified field width using the 'f' format, and the 'e' format
|
|
will not be truncated.
|
|
*/
|
|
force_e_format = (decpt <= 0 && width <= 2 - decpt && width >= 3 + exp_len);
|
|
/*
|
|
Assume that we don't have enough space to place all significant digits in
|
|
the 'f' format. We have to choose between the 'e' format and the 'f' one
|
|
to keep as many significant digits as possible.
|
|
Let E and F be the lengths of decimal representaion in the 'e' and 'f'
|
|
formats, respectively. We want to use the 'f' format if, and only if F <= E.
|
|
Consider the following cases:
|
|
1. decpt <= 0.
|
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F = len - decpt + 2 (see above)
|
|
E = len + (len > 1) + 1 + 1 (decpt <= -99) + (decpt <= -9) + 1
|
|
("N.NNe-MMM")
|
|
(F <= E) <=> (len == 1 && decpt >= -1) || (len > 1 && decpt >= -2)
|
|
We also need to ensure that if the 'f' format is chosen,
|
|
the field width allows us to place at least one significant digit
|
|
(i.e. width > 2 - decpt). If not, we prefer the 'e' format.
|
|
2. 0 < decpt < len
|
|
F = len + 1 (see above)
|
|
E = len + 1 + 1 + ... ("N.NNeMMM")
|
|
F is always less than E.
|
|
3. len <= decpt <= width
|
|
In this case we have enough space to represent the number in the 'f'
|
|
format, so we prefer it with some exceptions.
|
|
4. width < decpt
|
|
The number cannot be represented in the 'f' format at all, always use
|
|
the 'e' 'one.
|
|
*/
|
|
if ((have_space ||
|
|
/*
|
|
Not enough space, let's see if the 'f' format provides the most number
|
|
of significant digits.
|
|
*/
|
|
((decpt <= width &&
|
|
(decpt >= -1 || (decpt == -2 && (len > 1 || !force_e_format)))) &&
|
|
!force_e_format)) &&
|
|
|
|
/*
|
|
Use the 'e' format in some cases even if we have enough space for the
|
|
'f' one. See comment for MAX_DECPT_FOR_F_FORMAT.
|
|
*/
|
|
(!have_space || (decpt >= -MAX_DECPT_FOR_F_FORMAT + 1 &&
|
|
(decpt <= MAX_DECPT_FOR_F_FORMAT || len > decpt)))) {
|
|
/* 'f' format */
|
|
int i;
|
|
|
|
width -= (decpt < len) + (decpt <= 0 ? 1 - decpt : 0);
|
|
|
|
/* Do we have to truncate any digits? */
|
|
if (width < len) {
|
|
if (width < decpt) {
|
|
if (error != NULL) *error = true;
|
|
width = decpt;
|
|
}
|
|
|
|
/*
|
|
We want to truncate (len - width) least significant digits after the
|
|
decimal point. For this we are calling dtoa with mode=5, passing the
|
|
number of significant digits = (len-decpt) - (len-width) = width-decpt
|
|
*/
|
|
dtoa_free(res, buf, sizeof(buf));
|
|
res = dtoa(x, 5, width - decpt, &decpt, &sign, &end, buf, sizeof(buf));
|
|
src = res;
|
|
len = (int)(end - res);
|
|
}
|
|
|
|
if (len == 0) {
|
|
/* Underflow. Just print '0' and exit */
|
|
*dst++ = '0';
|
|
goto end;
|
|
}
|
|
|
|
/*
|
|
At this point we are sure we have enough space to put all digits
|
|
returned by dtoa
|
|
*/
|
|
if (sign && dst < dend) *dst++ = '-';
|
|
if (decpt <= 0) {
|
|
if (dst < dend) *dst++ = '0';
|
|
if (len > 0 && dst < dend) *dst++ = '.';
|
|
for (; decpt < 0 && dst < dend; decpt++) *dst++ = '0';
|
|
}
|
|
|
|
for (i = 1; i <= len && dst < dend; i++) {
|
|
*dst++ = *src++;
|
|
if (i == decpt && i < len && dst < dend) *dst++ = '.';
|
|
}
|
|
while (i++ <= decpt && dst < dend) *dst++ = '0';
|
|
} else {
|
|
/* 'e' format */
|
|
int decpt_sign = 0;
|
|
|
|
if (--decpt < 0) {
|
|
decpt = -decpt;
|
|
width--;
|
|
decpt_sign = 1;
|
|
}
|
|
width -= 1 + exp_len; /* eNNN */
|
|
|
|
if (len > 1) width--;
|
|
|
|
if (width <= 0) {
|
|
/* Overflow */
|
|
if (error != NULL) *error = true;
|
|
width = 0;
|
|
}
|
|
|
|
/* Do we have to truncate any digits? */
|
|
if (width < len) {
|
|
/* Yes, re-convert with a smaller width */
|
|
dtoa_free(res, buf, sizeof(buf));
|
|
res = dtoa(x, 4, width, &decpt, &sign, &end, buf, sizeof(buf));
|
|
src = res;
|
|
len = (int)(end - res);
|
|
if (--decpt < 0) decpt = -decpt;
|
|
}
|
|
/*
|
|
At this point we are sure we have enough space to put all digits
|
|
returned by dtoa
|
|
*/
|
|
if (sign && dst < dend) *dst++ = '-';
|
|
if (dst < dend) *dst++ = *src++;
|
|
if (len > 1 && dst < dend) {
|
|
*dst++ = '.';
|
|
while (src < end && dst < dend) *dst++ = *src++;
|
|
}
|
|
if (dst < dend) *dst++ = 'e';
|
|
if (decpt_sign && dst < dend) *dst++ = '-';
|
|
|
|
if (decpt >= 100 && dst < dend) {
|
|
*dst++ = decpt / 100 + '0';
|
|
decpt %= 100;
|
|
if (dst < dend) *dst++ = decpt / 10 + '0';
|
|
} else if (decpt >= 10 && dst < dend)
|
|
*dst++ = decpt / 10 + '0';
|
|
if (dst < dend) *dst++ = decpt % 10 + '0';
|
|
}
|
|
|
|
end:
|
|
dtoa_free(res, buf, sizeof(buf));
|
|
*dst = '\0';
|
|
|
|
return dst - to;
|
|
}
|
|
|
|
/**
|
|
@brief
|
|
Converts string to double (string does not have to be zero-terminated)
|
|
|
|
@details
|
|
This is a wrapper around dtoa's version of strtod().
|
|
|
|
@param str input string
|
|
@param end address of a pointer to the first character after the input
|
|
string. Upon return the pointer is set to point to the first
|
|
rejected character.
|
|
@param error Upon return is set to EOVERFLOW in case of underflow or
|
|
overflow.
|
|
|
|
@return The resulting double value. In case of underflow, 0.0 is
|
|
returned. In case overflow, signed DBL_MAX is returned.
|
|
*/
|
|
|
|
double my_strtod(const char *str, const char **end, int *error) {
|
|
char buf[DTOA_BUFF_SIZE];
|
|
double res;
|
|
DBUG_ASSERT(
|
|
end != NULL &&
|
|
((str != NULL && *end != NULL) || (str == NULL && *end == NULL)) &&
|
|
error != NULL);
|
|
|
|
res = my_strtod_int(str, end, error, buf, sizeof(buf));
|
|
return (*error == 0) ? res : (res < 0 ? -DBL_MAX : DBL_MAX);
|
|
}
|
|
|
|
double my_atof(const char *nptr) {
|
|
int error;
|
|
const char *end = nptr + 65535; /* Should be enough */
|
|
return (my_strtod(nptr, &end, &error));
|
|
}
|
|
|
|
/****************************************************************
|
|
*
|
|
* The author of this software is David M. Gay.
|
|
*
|
|
* Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
|
|
*
|
|
* Permission to use, copy, modify, and distribute this software for any
|
|
* purpose without fee is hereby granted, provided that this entire notice
|
|
* is included in all copies of any software which is or includes a copy
|
|
* or modification of this software and in all copies of the supporting
|
|
* documentation for such software.
|
|
*
|
|
* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
|
|
* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
|
|
* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
|
|
* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
|
|
*
|
|
***************************************************************/
|
|
/* Please send bug reports to David M. Gay (dmg at acm dot org,
|
|
* with " at " changed at "@" and " dot " changed to "."). */
|
|
|
|
/*
|
|
Original copy of the software is located at http://www.netlib.org/fp/dtoa.c
|
|
It was adjusted to serve MySQL server needs:
|
|
* strtod() was modified to not expect a zero-terminated string.
|
|
It now honors 'se' (end of string) argument as the input parameter,
|
|
not just as the output one.
|
|
* in dtoa(), in case of overflow/underflow/NaN result string now contains "0";
|
|
decpt is set to DTOA_OVERFLOW to indicate overflow.
|
|
* support for VAX, IBM mainframe and 16-bit hardware removed
|
|
* we always assume that 64-bit integer type is available
|
|
* support for Kernigan-Ritchie style headers (pre-ANSI compilers)
|
|
removed
|
|
* all gcc warnings ironed out
|
|
* we always assume multithreaded environment, so we had to change
|
|
memory allocation procedures to use stack in most cases;
|
|
malloc is used as the last resort.
|
|
* pow5mult rewritten to use pre-calculated pow5 list instead of
|
|
the one generated on the fly.
|
|
*/
|
|
|
|
/*
|
|
On a machine with IEEE extended-precision registers, it is
|
|
necessary to specify double-precision (53-bit) rounding precision
|
|
before invoking strtod or dtoa. If the machine uses (the equivalent
|
|
of) Intel 80x87 arithmetic, the call
|
|
_control87(PC_53, MCW_PC);
|
|
does this with many compilers. Whether this or another call is
|
|
appropriate depends on the compiler; for this to work, it may be
|
|
necessary to #include "float.h" or another system-dependent header
|
|
file.
|
|
*/
|
|
|
|
/*
|
|
#define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
|
|
and dtoa should round accordingly.
|
|
#define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
|
|
and Honor_FLT_ROUNDS is not #defined.
|
|
|
|
TODO: check if we can get rid of the above two
|
|
*/
|
|
|
|
typedef int32 Long;
|
|
typedef uint32 ULong;
|
|
typedef int64 LLong;
|
|
typedef uint64 ULLong;
|
|
|
|
typedef union {
|
|
double d;
|
|
ULong L[2];
|
|
} U;
|
|
|
|
#if defined(WORDS_BIGENDIAN) || \
|
|
(defined(__FLOAT_WORD_ORDER) && (__FLOAT_WORD_ORDER == __BIG_ENDIAN))
|
|
#define word0(x) (x)->L[0]
|
|
#define word1(x) (x)->L[1]
|
|
#else
|
|
#define word0(x) (x)->L[1]
|
|
#define word1(x) (x)->L[0]
|
|
#endif
|
|
|
|
#define dval(x) (x)->d
|
|
|
|
/* #define P DBL_MANT_DIG */
|
|
/* Ten_pmax= floor(P*log(2)/log(5)) */
|
|
/* Bletch= (highest power of 2 < DBL_MAX_10_EXP) / 16 */
|
|
/* Quick_max= floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
|
|
/* Int_max= floor(P*log(FLT_RADIX)/log(10) - 1) */
|
|
|
|
#define Exp_shift 20
|
|
#define Exp_shift1 20
|
|
#define Exp_msk1 0x100000
|
|
#define Exp_mask 0x7ff00000
|
|
#define P 53
|
|
#define Bias 1023
|
|
#define Emin (-1022)
|
|
#define Exp_1 0x3ff00000
|
|
#define Exp_11 0x3ff00000
|
|
#define Ebits 11
|
|
#define Frac_mask 0xfffff
|
|
#define Frac_mask1 0xfffff
|
|
#define Ten_pmax 22
|
|
#define Bletch 0x10
|
|
#define Bndry_mask 0xfffff
|
|
#define Bndry_mask1 0xfffff
|
|
#define LSB 1
|
|
#define Sign_bit 0x80000000
|
|
#define Log2P 1
|
|
#define Tiny1 1
|
|
#define Quick_max 14
|
|
#define Int_max 14
|
|
|
|
#ifndef Flt_Rounds
|
|
#ifdef FLT_ROUNDS
|
|
#define Flt_Rounds FLT_ROUNDS
|
|
#else
|
|
#define Flt_Rounds 1
|
|
#endif
|
|
#endif /*Flt_Rounds*/
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
#define Rounding rounding
|
|
#undef Check_FLT_ROUNDS
|
|
#define Check_FLT_ROUNDS
|
|
#endif
|
|
|
|
#define rounded_product(a, b) a *= b
|
|
#define rounded_quotient(a, b) a /= b
|
|
|
|
#define Big0 (Frac_mask1 | Exp_msk1 * (DBL_MAX_EXP + Bias - 1))
|
|
#define Big1 0xffffffff
|
|
#define FFFFFFFF 0xffffffffUL
|
|
|
|
/* This is tested to be enough for dtoa */
|
|
|
|
#define Kmax 15
|
|
|
|
#define Bcopy(x, y) \
|
|
memcpy((char *)&x->sign, (char *)&y->sign, \
|
|
2 * sizeof(int) + y->wds * sizeof(ULong))
|
|
|
|
/* Arbitrary-length integer */
|
|
|
|
typedef struct Bigint {
|
|
union {
|
|
ULong *x; /* points right after this Bigint object */
|
|
struct Bigint *next; /* to maintain free lists */
|
|
} p;
|
|
int k; /* 2^k = maxwds */
|
|
int maxwds; /* maximum length in 32-bit words */
|
|
int sign; /* not zero if number is negative */
|
|
int wds; /* current length in 32-bit words */
|
|
} Bigint;
|
|
|
|
/* A simple stack-memory based allocator for Bigints */
|
|
|
|
typedef struct Stack_alloc {
|
|
char *begin;
|
|
char *free;
|
|
char *end;
|
|
/*
|
|
Having list of free blocks lets us reduce maximum required amount
|
|
of memory from ~4000 bytes to < 1680 (tested on x86).
|
|
*/
|
|
Bigint *freelist[Kmax + 1];
|
|
} Stack_alloc;
|
|
|
|
/*
|
|
Try to allocate object on stack, and resort to malloc if all
|
|
stack memory is used. Ensure allocated objects to be aligned by the pointer
|
|
size in order to not break the alignment rules when storing a pointer to a
|
|
Bigint.
|
|
*/
|
|
|
|
static Bigint *Balloc(int k, Stack_alloc *alloc) {
|
|
Bigint *rv;
|
|
DBUG_ASSERT(k <= Kmax);
|
|
if (k <= Kmax && alloc->freelist[k]) {
|
|
rv = alloc->freelist[k];
|
|
alloc->freelist[k] = rv->p.next;
|
|
} else {
|
|
int x, len;
|
|
|
|
x = 1 << k;
|
|
len = MY_ALIGN(sizeof(Bigint) + x * sizeof(ULong), SIZEOF_CHARP);
|
|
|
|
if (alloc->free + len <= alloc->end) {
|
|
rv = (Bigint *)alloc->free;
|
|
alloc->free += len;
|
|
} else
|
|
rv = (Bigint *)malloc(len);
|
|
|
|
rv->k = k;
|
|
rv->maxwds = x;
|
|
}
|
|
rv->sign = rv->wds = 0;
|
|
rv->p.x = (ULong *)(rv + 1);
|
|
return rv;
|
|
}
|
|
|
|
/*
|
|
If object was allocated on stack, try putting it to the free
|
|
list. Otherwise call free().
|
|
*/
|
|
|
|
static void Bfree(Bigint *v, Stack_alloc *alloc) {
|
|
char *gptr = (char *)v; /* generic pointer */
|
|
if (gptr < alloc->begin || gptr >= alloc->end)
|
|
free(gptr);
|
|
else if (v->k <= Kmax) {
|
|
/*
|
|
Maintain free lists only for stack objects: this way we don't
|
|
have to bother with freeing lists in the end of dtoa;
|
|
heap should not be used normally anyway.
|
|
*/
|
|
v->p.next = alloc->freelist[v->k];
|
|
alloc->freelist[v->k] = v;
|
|
}
|
|
}
|
|
|
|
/*
|
|
This is to place return value of dtoa in: tries to use stack
|
|
as well, but passes by free lists management and just aligns len by
|
|
the pointer size in order to not break the alignment rules when storing a
|
|
pointer to a Bigint.
|
|
*/
|
|
|
|
static char *dtoa_alloc(int i, Stack_alloc *alloc) {
|
|
char *rv;
|
|
int aligned_size = MY_ALIGN(i, SIZEOF_CHARP);
|
|
if (alloc->free + aligned_size <= alloc->end) {
|
|
rv = alloc->free;
|
|
alloc->free += aligned_size;
|
|
} else
|
|
rv = static_cast<char *>(malloc(i));
|
|
return rv;
|
|
}
|
|
|
|
/*
|
|
dtoa_free() must be used to free values s returned by dtoa()
|
|
This is the counterpart of dtoa_alloc()
|
|
*/
|
|
|
|
static void dtoa_free(char *gptr, char *buf, size_t buf_size) {
|
|
if (gptr < buf || gptr >= buf + buf_size) free(gptr);
|
|
}
|
|
|
|
/* Bigint arithmetic functions */
|
|
|
|
/* Multiply by m and add a */
|
|
|
|
static Bigint *multadd(Bigint *b, int m, int a, Stack_alloc *alloc) {
|
|
int i, wds;
|
|
ULong *x;
|
|
ULLong carry, y;
|
|
Bigint *b1;
|
|
|
|
wds = b->wds;
|
|
x = b->p.x;
|
|
i = 0;
|
|
carry = a;
|
|
do {
|
|
y = *x * (ULLong)m + carry;
|
|
carry = y >> 32;
|
|
*x++ = (ULong)(y & FFFFFFFF);
|
|
} while (++i < wds);
|
|
if (carry) {
|
|
if (wds >= b->maxwds) {
|
|
b1 = Balloc(b->k + 1, alloc);
|
|
Bcopy(b1, b);
|
|
Bfree(b, alloc);
|
|
b = b1;
|
|
}
|
|
b->p.x[wds++] = (ULong)carry;
|
|
b->wds = wds;
|
|
}
|
|
return b;
|
|
}
|
|
|
|
/**
|
|
Converts a string to Bigint.
|
|
|
|
Now we have nd0 digits, starting at s, followed by a
|
|
decimal point, followed by nd-nd0 digits.
|
|
Unless nd0 == nd, in which case we have a number of the form:
|
|
".xxxxxx" or "xxxxxx."
|
|
|
|
@param s Input string, already partially parsed by my_strtod_int().
|
|
@param nd0 Number of digits before decimal point.
|
|
@param nd Total number of digits.
|
|
@param y9 Pre-computed value of the first nine digits.
|
|
@param alloc Stack allocator for Bigints.
|
|
*/
|
|
static Bigint *s2b(const char *s, int nd0, int nd, ULong y9,
|
|
Stack_alloc *alloc) {
|
|
Bigint *b;
|
|
int i, k;
|
|
Long x, y;
|
|
|
|
x = (nd + 8) / 9;
|
|
for (k = 0, y = 1; x > y; y <<= 1, k++)
|
|
;
|
|
b = Balloc(k, alloc);
|
|
b->p.x[0] = y9;
|
|
b->wds = 1;
|
|
|
|
i = 9;
|
|
if (9 < nd0) {
|
|
s += 9;
|
|
do
|
|
b = multadd(b, 10, *s++ - '0', alloc);
|
|
while (++i < nd0);
|
|
s++; /* skip '.' */
|
|
} else
|
|
s += 10;
|
|
/* now do the fractional part */
|
|
for (; i < nd; i++) b = multadd(b, 10, *s++ - '0', alloc);
|
|
return b;
|
|
}
|
|
|
|
static int hi0bits(ULong x) {
|
|
int k = 0;
|
|
|
|
if (!(x & 0xffff0000)) {
|
|
k = 16;
|
|
x <<= 16;
|
|
}
|
|
if (!(x & 0xff000000)) {
|
|
k += 8;
|
|
x <<= 8;
|
|
}
|
|
if (!(x & 0xf0000000)) {
|
|
k += 4;
|
|
x <<= 4;
|
|
}
|
|
if (!(x & 0xc0000000)) {
|
|
k += 2;
|
|
x <<= 2;
|
|
}
|
|
if (!(x & 0x80000000)) {
|
|
k++;
|
|
if (!(x & 0x40000000)) return 32;
|
|
}
|
|
return k;
|
|
}
|
|
|
|
static int lo0bits(ULong *y) {
|
|
int k;
|
|
ULong x = *y;
|
|
|
|
if (x & 7) {
|
|
if (x & 1) return 0;
|
|
if (x & 2) {
|
|
*y = x >> 1;
|
|
return 1;
|
|
}
|
|
*y = x >> 2;
|
|
return 2;
|
|
}
|
|
k = 0;
|
|
if (!(x & 0xffff)) {
|
|
k = 16;
|
|
x >>= 16;
|
|
}
|
|
if (!(x & 0xff)) {
|
|
k += 8;
|
|
x >>= 8;
|
|
}
|
|
if (!(x & 0xf)) {
|
|
k += 4;
|
|
x >>= 4;
|
|
}
|
|
if (!(x & 0x3)) {
|
|
k += 2;
|
|
x >>= 2;
|
|
}
|
|
if (!(x & 1)) {
|
|
k++;
|
|
x >>= 1;
|
|
if (!x) return 32;
|
|
}
|
|
*y = x;
|
|
return k;
|
|
}
|
|
|
|
/* Convert integer to Bigint number */
|
|
|
|
static Bigint *i2b(int i, Stack_alloc *alloc) {
|
|
Bigint *b;
|
|
|
|
b = Balloc(1, alloc);
|
|
b->p.x[0] = i;
|
|
b->wds = 1;
|
|
return b;
|
|
}
|
|
|
|
/* Multiply two Bigint numbers */
|
|
|
|
static Bigint *mult(Bigint *a, Bigint *b, Stack_alloc *alloc) {
|
|
Bigint *c;
|
|
int k, wa, wb, wc;
|
|
ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
|
|
ULong y;
|
|
ULLong carry, z;
|
|
|
|
if (a->wds < b->wds) {
|
|
c = a;
|
|
a = b;
|
|
b = c;
|
|
}
|
|
k = a->k;
|
|
wa = a->wds;
|
|
wb = b->wds;
|
|
wc = wa + wb;
|
|
if (wc > a->maxwds) k++;
|
|
c = Balloc(k, alloc);
|
|
for (x = c->p.x, xa = x + wc; x < xa; x++) *x = 0;
|
|
xa = a->p.x;
|
|
xae = xa + wa;
|
|
xb = b->p.x;
|
|
xbe = xb + wb;
|
|
xc0 = c->p.x;
|
|
for (; xb < xbe; xc0++) {
|
|
if ((y = *xb++)) {
|
|
x = xa;
|
|
xc = xc0;
|
|
carry = 0;
|
|
do {
|
|
z = *x++ * (ULLong)y + *xc + carry;
|
|
carry = z >> 32;
|
|
*xc++ = (ULong)(z & FFFFFFFF);
|
|
} while (x < xae);
|
|
*xc = (ULong)carry;
|
|
}
|
|
}
|
|
for (xc0 = c->p.x, xc = xc0 + wc; wc > 0 && !*--xc; --wc)
|
|
;
|
|
c->wds = wc;
|
|
return c;
|
|
}
|
|
|
|
/*
|
|
Precalculated array of powers of 5: tested to be enough for
|
|
vasting majority of dtoa_r cases.
|
|
*/
|
|
|
|
static ULong powers5[] = {
|
|
625UL,
|
|
|
|
390625UL,
|
|
|
|
2264035265UL, 35UL,
|
|
|
|
2242703233UL, 762134875UL, 1262UL,
|
|
|
|
3211403009UL, 1849224548UL, 3668416493UL, 3913284084UL, 1593091UL,
|
|
|
|
781532673UL, 64985353UL, 253049085UL, 594863151UL, 3553621484UL,
|
|
3288652808UL, 3167596762UL, 2788392729UL, 3911132675UL, 590UL,
|
|
|
|
2553183233UL, 3201533787UL, 3638140786UL, 303378311UL, 1809731782UL,
|
|
3477761648UL, 3583367183UL, 649228654UL, 2915460784UL, 487929380UL,
|
|
1011012442UL, 1677677582UL, 3428152256UL, 1710878487UL, 1438394610UL,
|
|
2161952759UL, 4100910556UL, 1608314830UL, 349175UL};
|
|
|
|
static Bigint p5_a[] = {
|
|
/* { x } - k - maxwds - sign - wds */
|
|
{{powers5}, 1, 1, 0, 1}, {{powers5 + 1}, 1, 1, 0, 1},
|
|
{{powers5 + 2}, 1, 2, 0, 2}, {{powers5 + 4}, 2, 3, 0, 3},
|
|
{{powers5 + 7}, 3, 5, 0, 5}, {{powers5 + 12}, 4, 10, 0, 10},
|
|
{{powers5 + 22}, 5, 19, 0, 19}};
|
|
|
|
#define P5A_MAX (sizeof(p5_a) / sizeof(*p5_a) - 1)
|
|
|
|
static Bigint *pow5mult(Bigint *b, int k, Stack_alloc *alloc) {
|
|
Bigint *b1, *p5, *p51 = NULL;
|
|
int i;
|
|
static int p05[3] = {5, 25, 125};
|
|
bool overflow = false;
|
|
|
|
if ((i = k & 3)) b = multadd(b, p05[i - 1], 0, alloc);
|
|
|
|
if (!(k >>= 2)) return b;
|
|
p5 = p5_a;
|
|
for (;;) {
|
|
if (k & 1) {
|
|
b1 = mult(b, p5, alloc);
|
|
Bfree(b, alloc);
|
|
b = b1;
|
|
}
|
|
if (!(k >>= 1)) break;
|
|
/* Calculate next power of 5 */
|
|
if (overflow) {
|
|
p51 = mult(p5, p5, alloc);
|
|
Bfree(p5, alloc);
|
|
p5 = p51;
|
|
} else if (p5 < p5_a + P5A_MAX)
|
|
++p5;
|
|
else if (p5 == p5_a + P5A_MAX) {
|
|
p5 = mult(p5, p5, alloc);
|
|
overflow = true;
|
|
}
|
|
}
|
|
if (p51) Bfree(p51, alloc);
|
|
return b;
|
|
}
|
|
|
|
static Bigint *lshift(Bigint *b, int k, Stack_alloc *alloc) {
|
|
int i, k1, n, n1;
|
|
Bigint *b1;
|
|
ULong *x, *x1, *xe, z;
|
|
|
|
n = k >> 5;
|
|
k1 = b->k;
|
|
n1 = n + b->wds + 1;
|
|
for (i = b->maxwds; n1 > i; i <<= 1) k1++;
|
|
b1 = Balloc(k1, alloc);
|
|
x1 = b1->p.x;
|
|
for (i = 0; i < n; i++) *x1++ = 0;
|
|
x = b->p.x;
|
|
xe = x + b->wds;
|
|
if (k &= 0x1f) {
|
|
k1 = 32 - k;
|
|
z = 0;
|
|
do {
|
|
*x1++ = *x << k | z;
|
|
z = *x++ >> k1;
|
|
} while (x < xe);
|
|
if ((*x1 = z)) ++n1;
|
|
} else
|
|
do
|
|
*x1++ = *x++;
|
|
while (x < xe);
|
|
b1->wds = n1 - 1;
|
|
Bfree(b, alloc);
|
|
return b1;
|
|
}
|
|
|
|
static int cmp(Bigint *a, Bigint *b) {
|
|
ULong *xa, *xa0, *xb, *xb0;
|
|
int i, j;
|
|
|
|
i = a->wds;
|
|
j = b->wds;
|
|
if (i -= j) return i;
|
|
xa0 = a->p.x;
|
|
xa = xa0 + j;
|
|
xb0 = b->p.x;
|
|
xb = xb0 + j;
|
|
for (;;) {
|
|
if (*--xa != *--xb) return *xa < *xb ? -1 : 1;
|
|
if (xa <= xa0) break;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
static Bigint *diff(Bigint *a, Bigint *b, Stack_alloc *alloc) {
|
|
Bigint *c;
|
|
int i, wa, wb;
|
|
ULong *xa, *xae, *xb, *xbe, *xc;
|
|
ULLong borrow, y;
|
|
|
|
i = cmp(a, b);
|
|
if (!i) {
|
|
c = Balloc(0, alloc);
|
|
c->wds = 1;
|
|
c->p.x[0] = 0;
|
|
return c;
|
|
}
|
|
if (i < 0) {
|
|
c = a;
|
|
a = b;
|
|
b = c;
|
|
i = 1;
|
|
} else
|
|
i = 0;
|
|
c = Balloc(a->k, alloc);
|
|
c->sign = i;
|
|
wa = a->wds;
|
|
xa = a->p.x;
|
|
xae = xa + wa;
|
|
wb = b->wds;
|
|
xb = b->p.x;
|
|
xbe = xb + wb;
|
|
xc = c->p.x;
|
|
borrow = 0;
|
|
do {
|
|
y = (ULLong)*xa++ - *xb++ - borrow;
|
|
borrow = y >> 32 & (ULong)1;
|
|
*xc++ = (ULong)(y & FFFFFFFF);
|
|
} while (xb < xbe);
|
|
while (xa < xae) {
|
|
y = *xa++ - borrow;
|
|
borrow = y >> 32 & (ULong)1;
|
|
*xc++ = (ULong)(y & FFFFFFFF);
|
|
}
|
|
while (!*--xc) wa--;
|
|
c->wds = wa;
|
|
return c;
|
|
}
|
|
|
|
static double ulp(U *x) {
|
|
Long L;
|
|
U u;
|
|
|
|
L = (word0(x) & Exp_mask) - (P - 1) * Exp_msk1;
|
|
word0(&u) = L;
|
|
word1(&u) = 0;
|
|
return dval(&u);
|
|
}
|
|
|
|
static double b2d(Bigint *a, int *e) {
|
|
ULong *xa, *xa0, w, y, z;
|
|
int k;
|
|
U d;
|
|
#define d0 word0(&d)
|
|
#define d1 word1(&d)
|
|
|
|
xa0 = a->p.x;
|
|
xa = xa0 + a->wds;
|
|
y = *--xa;
|
|
k = hi0bits(y);
|
|
*e = 32 - k;
|
|
if (k < Ebits) {
|
|
d0 = Exp_1 | y >> (Ebits - k);
|
|
w = xa > xa0 ? *--xa : 0;
|
|
d1 = y << ((32 - Ebits) + k) | w >> (Ebits - k);
|
|
goto ret_d;
|
|
}
|
|
z = xa > xa0 ? *--xa : 0;
|
|
if (k -= Ebits) {
|
|
d0 = Exp_1 | y << k | z >> (32 - k);
|
|
y = xa > xa0 ? *--xa : 0;
|
|
d1 = z << k | y >> (32 - k);
|
|
} else {
|
|
d0 = Exp_1 | y;
|
|
d1 = z;
|
|
}
|
|
ret_d:
|
|
#undef d0
|
|
#undef d1
|
|
return dval(&d);
|
|
}
|
|
|
|
static Bigint *d2b(U *d, int *e, int *bits, Stack_alloc *alloc) {
|
|
Bigint *b;
|
|
int de, k;
|
|
ULong *x, y, z;
|
|
int i;
|
|
#define d0 word0(d)
|
|
#define d1 word1(d)
|
|
|
|
b = Balloc(1, alloc);
|
|
x = b->p.x;
|
|
|
|
z = d0 & Frac_mask;
|
|
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
|
|
if ((de = (int)(d0 >> Exp_shift))) z |= Exp_msk1;
|
|
if ((y = d1)) {
|
|
if ((k = lo0bits(&y))) {
|
|
x[0] = y | z << (32 - k);
|
|
z >>= k;
|
|
} else
|
|
x[0] = y;
|
|
i = b->wds = (x[1] = z) ? 2 : 1;
|
|
} else {
|
|
k = lo0bits(&z);
|
|
x[0] = z;
|
|
i = b->wds = 1;
|
|
k += 32;
|
|
}
|
|
if (de) {
|
|
*e = de - Bias - (P - 1) + k;
|
|
*bits = P - k;
|
|
} else {
|
|
*e = de - Bias - (P - 1) + 1 + k;
|
|
*bits = 32 * i - hi0bits(x[i - 1]);
|
|
}
|
|
return b;
|
|
#undef d0
|
|
#undef d1
|
|
}
|
|
|
|
static double ratio(Bigint *a, Bigint *b) {
|
|
U da, db;
|
|
int k, ka, kb;
|
|
|
|
dval(&da) = b2d(a, &ka);
|
|
dval(&db) = b2d(b, &kb);
|
|
k = ka - kb + 32 * (a->wds - b->wds);
|
|
if (k > 0)
|
|
word0(&da) += k * Exp_msk1;
|
|
else {
|
|
k = -k;
|
|
word0(&db) += k * Exp_msk1;
|
|
}
|
|
return dval(&da) / dval(&db);
|
|
}
|
|
|
|
static const double tens[] = {1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7,
|
|
1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15,
|
|
1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22};
|
|
|
|
static const double bigtens[] = {1e16, 1e32, 1e64, 1e128, 1e256};
|
|
static const double tinytens[] = {
|
|
1e-16, 1e-32, 1e-64, 1e-128,
|
|
9007199254740992. * 9007199254740992.e-256 /* = 2^106 * 1e-53 */
|
|
};
|
|
/*
|
|
The factor of 2^53 in tinytens[4] helps us avoid setting the underflow
|
|
flag unnecessarily. It leads to a song and dance at the end of strtod.
|
|
*/
|
|
#define Scale_Bit 0x10
|
|
#define n_bigtens 5
|
|
|
|
/*
|
|
strtod for IEEE--arithmetic machines.
|
|
|
|
This strtod returns a nearest machine number to the input decimal
|
|
string (or sets errno to EOVERFLOW). Ties are broken by the IEEE round-even
|
|
rule.
|
|
|
|
Inspired loosely by William D. Clinger's paper "How to Read Floating
|
|
Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
|
|
|
|
Modifications:
|
|
|
|
1. We only require IEEE (not IEEE double-extended).
|
|
2. We get by with floating-point arithmetic in a case that
|
|
Clinger missed -- when we're computing d * 10^n
|
|
for a small integer d and the integer n is not too
|
|
much larger than 22 (the maximum integer k for which
|
|
we can represent 10^k exactly), we may be able to
|
|
compute (d*10^k) * 10^(e-k) with just one roundoff.
|
|
3. Rather than a bit-at-a-time adjustment of the binary
|
|
result in the hard case, we use floating-point
|
|
arithmetic to determine the adjustment to within
|
|
one bit; only in really hard cases do we need to
|
|
compute a second residual.
|
|
4. Because of 3., we don't need a large table of powers of 10
|
|
for ten-to-e (just some small tables, e.g. of 10^k
|
|
for 0 <= k <= 22).
|
|
*/
|
|
|
|
static double my_strtod_int(const char *s00, const char **se, int *error,
|
|
char *buf, size_t buf_size) {
|
|
int scale;
|
|
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c = 0, dsign, e, e1, esign, i, j, k,
|
|
nd, nd0, nf, nz, nz0, sign;
|
|
const char *s, *s0, *s1, *end = *se;
|
|
double aadj, aadj1;
|
|
U aadj2, adj, rv, rv0;
|
|
Long L;
|
|
ULong y, z;
|
|
Bigint *bb = NULL, *bb1, *bd = NULL, *bd0, *bs = NULL, *delta = NULL;
|
|
#ifdef Honor_FLT_ROUNDS
|
|
int rounding;
|
|
#endif
|
|
Stack_alloc alloc;
|
|
|
|
*error = 0;
|
|
|
|
alloc.begin = alloc.free = buf;
|
|
alloc.end = buf + buf_size;
|
|
memset(alloc.freelist, 0, sizeof(alloc.freelist));
|
|
|
|
sign = nz0 = nz = 0;
|
|
dval(&rv) = 0.;
|
|
for (s = s00; s < end; s++) switch (*s) {
|
|
case '-':
|
|
sign = 1;
|
|
// Fall through.
|
|
case '+':
|
|
s++;
|
|
goto break2;
|
|
case '\t':
|
|
case '\n':
|
|
case '\v':
|
|
case '\f':
|
|
case '\r':
|
|
case ' ':
|
|
continue;
|
|
default:
|
|
goto break2;
|
|
}
|
|
break2:
|
|
if (s >= end) goto ret0;
|
|
|
|
if (*s == '0') {
|
|
nz0 = 1;
|
|
while (++s < end && *s == '0')
|
|
;
|
|
if (s >= end) goto ret;
|
|
}
|
|
s0 = s;
|
|
y = z = 0;
|
|
for (nd = nf = 0; s < end && (c = *s) >= '0' && c <= '9'; nd++, s++)
|
|
if (nd < 9)
|
|
y = 10 * y + c - '0';
|
|
else if (nd < 16)
|
|
z = 10 * z + c - '0';
|
|
nd0 = nd;
|
|
if (s < end && c == '.') {
|
|
if (++s < end) c = *s;
|
|
if (!nd) {
|
|
for (; s < end; ++s) {
|
|
c = *s;
|
|
if (c != '0') break;
|
|
nz++;
|
|
}
|
|
if (s < end && c > '0' && c <= '9') {
|
|
s0 = s;
|
|
nf += nz;
|
|
nz = 0;
|
|
} else
|
|
goto dig_done;
|
|
}
|
|
for (; s < end; ++s) {
|
|
c = *s;
|
|
if (c < '0' || c > '9') break;
|
|
/*
|
|
Here we are parsing the fractional part.
|
|
We can stop counting digits after a while: the extra digits
|
|
will not contribute to the actual result produced by s2b().
|
|
We have to continue scanning, in case there is an exponent part.
|
|
*/
|
|
if (nd < 2 * DBL_DIG) {
|
|
nz++;
|
|
if (c -= '0') {
|
|
nf += nz;
|
|
for (i = 1; i < nz; i++)
|
|
if (nd++ < 9)
|
|
y *= 10;
|
|
else if (nd <= DBL_DIG + 1)
|
|
z *= 10;
|
|
if (nd++ < 9)
|
|
y = 10 * y + c;
|
|
else if (nd <= DBL_DIG + 1)
|
|
z = 10 * z + c;
|
|
nz = 0;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
dig_done:
|
|
e = 0;
|
|
if (s < end && (c == 'e' || c == 'E')) {
|
|
if (!nd && !nz && !nz0) goto ret0;
|
|
s00 = s;
|
|
esign = 0;
|
|
if (++s < end) switch (c = *s) {
|
|
case '-':
|
|
esign = 1;
|
|
// Fall through.
|
|
case '+':
|
|
if (++s < end) c = *s;
|
|
}
|
|
if (s < end && c >= '0' && c <= '9') {
|
|
while (s < end && c == '0') c = *++s;
|
|
if (s < end && c > '0' && c <= '9') {
|
|
L = c - '0';
|
|
s1 = s;
|
|
// Avoid overflow in loop body below.
|
|
while (++s < end && (c = *s) >= '0' && c <= '9' &&
|
|
L < (std::numeric_limits<Long>::max() - 255) / 10) {
|
|
L = 10 * L + c - '0';
|
|
}
|
|
if (s - s1 > 8 || L > 19999)
|
|
/* Avoid confusion from exponents
|
|
* so large that e might overflow.
|
|
*/
|
|
e = 19999; /* safe for 16 bit ints */
|
|
else
|
|
e = (int)L;
|
|
if (esign) e = -e;
|
|
} else
|
|
e = 0;
|
|
} else
|
|
s = s00;
|
|
}
|
|
if (!nd) {
|
|
if (!nz && !nz0) {
|
|
ret0:
|
|
s = s00;
|
|
sign = 0;
|
|
}
|
|
goto ret;
|
|
}
|
|
e1 = e -= nf;
|
|
|
|
/*
|
|
Now we have nd0 digits, starting at s0, followed by a
|
|
decimal point, followed by nd-nd0 digits. The number we're
|
|
after is the integer represented by those digits times
|
|
10**e
|
|
*/
|
|
|
|
if (!nd0) nd0 = nd;
|
|
k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
|
|
dval(&rv) = y;
|
|
if (k > 9) {
|
|
dval(&rv) = tens[k - 9] * dval(&rv) + z;
|
|
}
|
|
bd0 = 0;
|
|
if (nd <= DBL_DIG
|
|
#ifndef Honor_FLT_ROUNDS
|
|
&& Flt_Rounds == 1
|
|
#endif
|
|
) {
|
|
if (!e) goto ret;
|
|
if (e > 0) {
|
|
if (e <= Ten_pmax) {
|
|
#ifdef Honor_FLT_ROUNDS
|
|
/* round correctly FLT_ROUNDS = 2 or 3 */
|
|
if (sign) {
|
|
rv.d = -rv.d;
|
|
sign = 0;
|
|
}
|
|
#endif
|
|
/* rv = */ rounded_product(dval(&rv), tens[e]);
|
|
goto ret;
|
|
}
|
|
i = DBL_DIG - nd;
|
|
if (e <= Ten_pmax + i) {
|
|
/*
|
|
A fancier test would sometimes let us do
|
|
this for larger i values.
|
|
*/
|
|
#ifdef Honor_FLT_ROUNDS
|
|
/* round correctly FLT_ROUNDS = 2 or 3 */
|
|
if (sign) {
|
|
rv.d = -rv.d;
|
|
sign = 0;
|
|
}
|
|
#endif
|
|
e -= i;
|
|
dval(&rv) *= tens[i];
|
|
/* rv = */ rounded_product(dval(&rv), tens[e]);
|
|
goto ret;
|
|
}
|
|
}
|
|
#ifndef Inaccurate_Divide
|
|
else if (e >= -Ten_pmax) {
|
|
#ifdef Honor_FLT_ROUNDS
|
|
/* round correctly FLT_ROUNDS = 2 or 3 */
|
|
if (sign) {
|
|
rv.d = -rv.d;
|
|
sign = 0;
|
|
}
|
|
#endif
|
|
/* rv = */ rounded_quotient(dval(&rv), tens[-e]);
|
|
goto ret;
|
|
}
|
|
#endif
|
|
}
|
|
e1 += nd - k;
|
|
|
|
scale = 0;
|
|
#ifdef Honor_FLT_ROUNDS
|
|
if ((rounding = Flt_Rounds) >= 2) {
|
|
if (sign)
|
|
rounding = rounding == 2 ? 0 : 2;
|
|
else if (rounding != 2)
|
|
rounding = 0;
|
|
}
|
|
#endif
|
|
|
|
/* Get starting approximation = rv * 10**e1 */
|
|
|
|
if (e1 > 0) {
|
|
if ((i = e1 & 15)) dval(&rv) *= tens[i];
|
|
if (e1 &= ~15) {
|
|
if (e1 > DBL_MAX_10_EXP) {
|
|
ovfl:
|
|
*error = EOVERFLOW;
|
|
/* Can't trust HUGE_VAL */
|
|
#ifdef Honor_FLT_ROUNDS
|
|
switch (rounding) {
|
|
case 0: /* toward 0 */
|
|
case 3: /* toward -infinity */
|
|
word0(&rv) = Big0;
|
|
word1(&rv) = Big1;
|
|
break;
|
|
default:
|
|
word0(&rv) = Exp_mask;
|
|
word1(&rv) = 0;
|
|
}
|
|
#else /*Honor_FLT_ROUNDS*/
|
|
word0(&rv) = Exp_mask;
|
|
word1(&rv) = 0;
|
|
#endif /*Honor_FLT_ROUNDS*/
|
|
if (bd0) goto retfree;
|
|
goto ret;
|
|
}
|
|
e1 >>= 4;
|
|
for (j = 0; e1 > 1; j++, e1 >>= 1)
|
|
if (e1 & 1) dval(&rv) *= bigtens[j];
|
|
/* The last multiplication could overflow. */
|
|
word0(&rv) -= P * Exp_msk1;
|
|
dval(&rv) *= bigtens[j];
|
|
if ((z = word0(&rv) & Exp_mask) > Exp_msk1 * (DBL_MAX_EXP + Bias - P))
|
|
goto ovfl;
|
|
if (z > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P)) {
|
|
/* set to largest number (Can't trust DBL_MAX) */
|
|
word0(&rv) = Big0;
|
|
word1(&rv) = Big1;
|
|
} else
|
|
word0(&rv) += P * Exp_msk1;
|
|
}
|
|
} else if (e1 < 0) {
|
|
e1 = -e1;
|
|
if ((i = e1 & 15)) dval(&rv) /= tens[i];
|
|
if ((e1 >>= 4)) {
|
|
if (e1 >= 1 << n_bigtens) goto undfl;
|
|
if (e1 & Scale_Bit) scale = 2 * P;
|
|
for (j = 0; e1 > 0; j++, e1 >>= 1)
|
|
if (e1 & 1) dval(&rv) *= tinytens[j];
|
|
if (scale &&
|
|
(j = 2 * P + 1 - ((word0(&rv) & Exp_mask) >> Exp_shift)) > 0) {
|
|
/* scaled rv is denormal; zap j low bits */
|
|
if (j >= 32) {
|
|
word1(&rv) = 0;
|
|
if (j >= 53)
|
|
word0(&rv) = (P + 2) * Exp_msk1;
|
|
else
|
|
word0(&rv) &= 0xffffffff << (j - 32);
|
|
} else
|
|
word1(&rv) &= 0xffffffff << j;
|
|
}
|
|
if (!dval(&rv)) {
|
|
undfl:
|
|
dval(&rv) = 0.;
|
|
if (bd0) goto retfree;
|
|
goto ret;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Now the hard part -- adjusting rv to the correct value.*/
|
|
|
|
/* Put digits into bd: true value = bd * 10^e */
|
|
|
|
bd0 = s2b(s0, nd0, nd, y, &alloc);
|
|
|
|
for (;;) {
|
|
bd = Balloc(bd0->k, &alloc);
|
|
Bcopy(bd, bd0);
|
|
bb = d2b(&rv, &bbe, &bbbits, &alloc); /* rv = bb * 2^bbe */
|
|
bs = i2b(1, &alloc);
|
|
|
|
if (e >= 0) {
|
|
bb2 = bb5 = 0;
|
|
bd2 = bd5 = e;
|
|
} else {
|
|
bb2 = bb5 = -e;
|
|
bd2 = bd5 = 0;
|
|
}
|
|
if (bbe >= 0)
|
|
bb2 += bbe;
|
|
else
|
|
bd2 -= bbe;
|
|
bs2 = bb2;
|
|
#ifdef Honor_FLT_ROUNDS
|
|
if (rounding != 1) bs2++;
|
|
#endif
|
|
j = bbe - scale;
|
|
i = j + bbbits - 1; /* logb(rv) */
|
|
if (i < Emin) /* denormal */
|
|
j += P - Emin;
|
|
else
|
|
j = P + 1 - bbbits;
|
|
bb2 += j;
|
|
bd2 += j;
|
|
bd2 += scale;
|
|
i = bb2 < bd2 ? bb2 : bd2;
|
|
if (i > bs2) i = bs2;
|
|
if (i > 0) {
|
|
bb2 -= i;
|
|
bd2 -= i;
|
|
bs2 -= i;
|
|
}
|
|
if (bb5 > 0) {
|
|
bs = pow5mult(bs, bb5, &alloc);
|
|
bb1 = mult(bs, bb, &alloc);
|
|
Bfree(bb, &alloc);
|
|
bb = bb1;
|
|
}
|
|
if (bb2 > 0) bb = lshift(bb, bb2, &alloc);
|
|
if (bd5 > 0) bd = pow5mult(bd, bd5, &alloc);
|
|
if (bd2 > 0) bd = lshift(bd, bd2, &alloc);
|
|
if (bs2 > 0) bs = lshift(bs, bs2, &alloc);
|
|
delta = diff(bb, bd, &alloc);
|
|
dsign = delta->sign;
|
|
delta->sign = 0;
|
|
i = cmp(delta, bs);
|
|
#ifdef Honor_FLT_ROUNDS
|
|
if (rounding != 1) {
|
|
if (i < 0) {
|
|
/* Error is less than an ulp */
|
|
if (!delta->p.x[0] && delta->wds <= 1) {
|
|
/* exact */
|
|
break;
|
|
}
|
|
if (rounding) {
|
|
if (dsign) {
|
|
adj.d = 1.;
|
|
goto apply_adj;
|
|
}
|
|
} else if (!dsign) {
|
|
adj.d = -1.;
|
|
if (!word1(&rv) && !(word0(&rv) & Frac_mask)) {
|
|
y = word0(&rv) & Exp_mask;
|
|
if (!scale || y > 2 * P * Exp_msk1) {
|
|
delta = lshift(delta, Log2P, &alloc);
|
|
if (cmp(delta, bs) <= 0) adj.d = -0.5;
|
|
}
|
|
}
|
|
apply_adj:
|
|
if (scale && (y = word0(&rv) & Exp_mask) <= 2 * P * Exp_msk1)
|
|
word0(&adj) += (2 * P + 1) * Exp_msk1 - y;
|
|
dval(&rv) += adj.d * ulp(&rv);
|
|
}
|
|
break;
|
|
}
|
|
adj.d = ratio(delta, bs);
|
|
if (adj.d < 1.) adj.d = 1.;
|
|
if (adj.d <= 0x7ffffffe) {
|
|
/* adj = rounding ? ceil(adj) : floor(adj); */
|
|
y = adj.d;
|
|
if (y != adj.d) {
|
|
if (!((rounding >> 1) ^ dsign)) y++;
|
|
adj.d = y;
|
|
}
|
|
}
|
|
if (scale && (y = word0(&rv) & Exp_mask) <= 2 * P * Exp_msk1)
|
|
word0(&adj) += (2 * P + 1) * Exp_msk1 - y;
|
|
adj.d *= ulp(&rv);
|
|
if (dsign)
|
|
dval(&rv) += adj.d;
|
|
else
|
|
dval(&rv) -= adj.d;
|
|
goto cont;
|
|
}
|
|
#endif /*Honor_FLT_ROUNDS*/
|
|
|
|
if (i < 0) {
|
|
/*
|
|
Error is less than half an ulp -- check for special case of mantissa
|
|
a power of two.
|
|
*/
|
|
if (dsign || word1(&rv) || word0(&rv) & Bndry_mask ||
|
|
(word0(&rv) & Exp_mask) <= (2 * P + 1) * Exp_msk1) {
|
|
break;
|
|
}
|
|
if (!delta->p.x[0] && delta->wds <= 1) {
|
|
/* exact result */
|
|
break;
|
|
}
|
|
delta = lshift(delta, Log2P, &alloc);
|
|
if (cmp(delta, bs) > 0) goto drop_down;
|
|
break;
|
|
}
|
|
if (i == 0) {
|
|
/* exactly half-way between */
|
|
if (dsign) {
|
|
if ((word0(&rv) & Bndry_mask1) == Bndry_mask1 &&
|
|
word1(&rv) ==
|
|
((scale && (y = word0(&rv) & Exp_mask) <= 2 * P * Exp_msk1)
|
|
? (0xffffffff &
|
|
(0xffffffff << (2 * P + 1 - (y >> Exp_shift))))
|
|
: 0xffffffff)) {
|
|
/*boundary case -- increment exponent*/
|
|
word0(&rv) = (word0(&rv) & Exp_mask) + Exp_msk1;
|
|
word1(&rv) = 0;
|
|
dsign = 0;
|
|
break;
|
|
}
|
|
} else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) {
|
|
drop_down:
|
|
/* boundary case -- decrement exponent */
|
|
if (scale) {
|
|
L = word0(&rv) & Exp_mask;
|
|
if (L <= (2 * P + 1) * Exp_msk1) {
|
|
if (L > (P + 2) * Exp_msk1) /* round even ==> accept rv */
|
|
break;
|
|
/* rv = smallest denormal */
|
|
goto undfl;
|
|
}
|
|
}
|
|
L = (word0(&rv) & Exp_mask) - Exp_msk1;
|
|
word0(&rv) = L | Bndry_mask1;
|
|
word1(&rv) = 0xffffffff;
|
|
break;
|
|
}
|
|
if (!(word1(&rv) & LSB)) break;
|
|
if (dsign)
|
|
dval(&rv) += ulp(&rv);
|
|
else {
|
|
dval(&rv) -= ulp(&rv);
|
|
if (!dval(&rv)) goto undfl;
|
|
}
|
|
dsign = 1 - dsign;
|
|
break;
|
|
}
|
|
if ((aadj = ratio(delta, bs)) <= 2.) {
|
|
if (dsign)
|
|
aadj = aadj1 = 1.;
|
|
else if (word1(&rv) || word0(&rv) & Bndry_mask) {
|
|
if (word1(&rv) == Tiny1 && !word0(&rv)) goto undfl;
|
|
aadj = 1.;
|
|
aadj1 = -1.;
|
|
} else {
|
|
/* special case -- power of FLT_RADIX to be rounded down... */
|
|
if (aadj < 2. / FLT_RADIX)
|
|
aadj = 1. / FLT_RADIX;
|
|
else
|
|
aadj *= 0.5;
|
|
aadj1 = -aadj;
|
|
}
|
|
} else {
|
|
aadj *= 0.5;
|
|
aadj1 = dsign ? aadj : -aadj;
|
|
#ifdef Check_FLT_ROUNDS
|
|
switch (Rounding) {
|
|
case 2: /* towards +infinity */
|
|
aadj1 -= 0.5;
|
|
break;
|
|
case 0: /* towards 0 */
|
|
case 3: /* towards -infinity */
|
|
aadj1 += 0.5;
|
|
}
|
|
#else
|
|
if (Flt_Rounds == 0) aadj1 += 0.5;
|
|
#endif /*Check_FLT_ROUNDS*/
|
|
}
|
|
y = word0(&rv) & Exp_mask;
|
|
|
|
/* Check for overflow */
|
|
|
|
if (y == Exp_msk1 * (DBL_MAX_EXP + Bias - 1)) {
|
|
dval(&rv0) = dval(&rv);
|
|
word0(&rv) -= P * Exp_msk1;
|
|
adj.d = aadj1 * ulp(&rv);
|
|
dval(&rv) += adj.d;
|
|
if ((word0(&rv) & Exp_mask) >= Exp_msk1 * (DBL_MAX_EXP + Bias - P)) {
|
|
if (word0(&rv0) == Big0 && word1(&rv0) == Big1) goto ovfl;
|
|
word0(&rv) = Big0;
|
|
word1(&rv) = Big1;
|
|
goto cont;
|
|
} else
|
|
word0(&rv) += P * Exp_msk1;
|
|
} else {
|
|
if (scale && y <= 2 * P * Exp_msk1) {
|
|
if (aadj <= 0x7fffffff) {
|
|
if ((z = (ULong)aadj) <= 0) z = 1;
|
|
aadj = z;
|
|
aadj1 = dsign ? aadj : -aadj;
|
|
}
|
|
dval(&aadj2) = aadj1;
|
|
word0(&aadj2) += (2 * P + 1) * Exp_msk1 - y;
|
|
aadj1 = dval(&aadj2);
|
|
adj.d = aadj1 * ulp(&rv);
|
|
dval(&rv) += adj.d;
|
|
if (rv.d == 0.) goto undfl;
|
|
} else {
|
|
adj.d = aadj1 * ulp(&rv);
|
|
dval(&rv) += adj.d;
|
|
}
|
|
}
|
|
z = word0(&rv) & Exp_mask;
|
|
if (!scale)
|
|
if (y == z) {
|
|
/* Can we stop now? */
|
|
L = (Long)aadj;
|
|
aadj -= L;
|
|
/* The tolerances below are conservative. */
|
|
if (dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
|
|
if (aadj < .4999999 || aadj > .5000001) break;
|
|
} else if (aadj < .4999999 / FLT_RADIX)
|
|
break;
|
|
}
|
|
cont:
|
|
Bfree(bb, &alloc);
|
|
Bfree(bd, &alloc);
|
|
Bfree(bs, &alloc);
|
|
Bfree(delta, &alloc);
|
|
}
|
|
if (scale) {
|
|
word0(&rv0) = Exp_1 - 2 * P * Exp_msk1;
|
|
word1(&rv0) = 0;
|
|
dval(&rv) *= dval(&rv0);
|
|
}
|
|
retfree:
|
|
Bfree(bb, &alloc);
|
|
Bfree(bd, &alloc);
|
|
Bfree(bs, &alloc);
|
|
Bfree(bd0, &alloc);
|
|
Bfree(delta, &alloc);
|
|
ret:
|
|
*se = s;
|
|
return sign ? -dval(&rv) : dval(&rv);
|
|
}
|
|
|
|
static int quorem(Bigint *b, Bigint *S) {
|
|
int n;
|
|
ULong *bx, *bxe, q, *sx, *sxe;
|
|
ULLong borrow, carry, y, ys;
|
|
|
|
n = S->wds;
|
|
if (b->wds < n) return 0;
|
|
sx = S->p.x;
|
|
sxe = sx + --n;
|
|
bx = b->p.x;
|
|
bxe = bx + n;
|
|
q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
|
|
if (q) {
|
|
borrow = 0;
|
|
carry = 0;
|
|
do {
|
|
ys = *sx++ * (ULLong)q + carry;
|
|
carry = ys >> 32;
|
|
y = *bx - (ys & FFFFFFFF) - borrow;
|
|
borrow = y >> 32 & (ULong)1;
|
|
*bx++ = (ULong)(y & FFFFFFFF);
|
|
} while (sx <= sxe);
|
|
if (!*bxe) {
|
|
bx = b->p.x;
|
|
while (--bxe > bx && !*bxe) --n;
|
|
b->wds = n;
|
|
}
|
|
}
|
|
if (cmp(b, S) >= 0) {
|
|
q++;
|
|
borrow = 0;
|
|
carry = 0;
|
|
bx = b->p.x;
|
|
sx = S->p.x;
|
|
do {
|
|
ys = *sx++ + carry;
|
|
carry = ys >> 32;
|
|
y = *bx - (ys & FFFFFFFF) - borrow;
|
|
borrow = y >> 32 & (ULong)1;
|
|
*bx++ = (ULong)(y & FFFFFFFF);
|
|
} while (sx <= sxe);
|
|
bx = b->p.x;
|
|
bxe = bx + n;
|
|
if (!*bxe) {
|
|
while (--bxe > bx && !*bxe) --n;
|
|
b->wds = n;
|
|
}
|
|
}
|
|
return q;
|
|
}
|
|
|
|
/*
|
|
dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
|
|
|
|
Inspired by "How to Print Floating-Point Numbers Accurately" by
|
|
Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
|
|
|
|
Modifications:
|
|
1. Rather than iterating, we use a simple numeric overestimate
|
|
to determine k= floor(log10(d)). We scale relevant
|
|
quantities using O(log2(k)) rather than O(k) multiplications.
|
|
2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
|
|
try to generate digits strictly left to right. Instead, we
|
|
compute with fewer bits and propagate the carry if necessary
|
|
when rounding the final digit up. This is often faster.
|
|
3. Under the assumption that input will be rounded nearest,
|
|
mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
|
|
That is, we allow equality in stopping tests when the
|
|
round-nearest rule will give the same floating-point value
|
|
as would satisfaction of the stopping test with strict
|
|
inequality.
|
|
4. We remove common factors of powers of 2 from relevant
|
|
quantities.
|
|
5. When converting floating-point integers less than 1e16,
|
|
we use floating-point arithmetic rather than resorting
|
|
to multiple-precision integers.
|
|
6. When asked to produce fewer than 15 digits, we first try
|
|
to get by with floating-point arithmetic; we resort to
|
|
multiple-precision integer arithmetic only if we cannot
|
|
guarantee that the floating-point calculation has given
|
|
the correctly rounded result. For k requested digits and
|
|
"uniformly" distributed input, the probability is
|
|
something like 10^(k-15) that we must resort to the Long
|
|
calculation.
|
|
*/
|
|
|
|
static char *dtoa(double dd, int mode, int ndigits, int *decpt, int *sign,
|
|
char **rve, char *buf, size_t buf_size) {
|
|
/*
|
|
Arguments ndigits, decpt, sign are similar to those
|
|
of ecvt and fcvt; trailing zeros are suppressed from
|
|
the returned string. If not null, *rve is set to point
|
|
to the end of the return value. If d is +-Infinity or NaN,
|
|
then *decpt is set to DTOA_OVERFLOW.
|
|
|
|
mode:
|
|
0 ==> shortest string that yields d when read in
|
|
and rounded to nearest.
|
|
1 ==> like 0, but with Steele & White stopping rule;
|
|
e.g. with IEEE P754 arithmetic , mode 0 gives
|
|
1e23 whereas mode 1 gives 9.999999999999999e22.
|
|
2 ==> max(1,ndigits) significant digits. This gives a
|
|
return value similar to that of ecvt, except
|
|
that trailing zeros are suppressed.
|
|
3 ==> through ndigits past the decimal point. This
|
|
gives a return value similar to that from fcvt,
|
|
except that trailing zeros are suppressed, and
|
|
ndigits can be negative.
|
|
4,5 ==> similar to 2 and 3, respectively, but (in
|
|
round-nearest mode) with the tests of mode 0 to
|
|
possibly return a shorter string that rounds to d.
|
|
With IEEE arithmetic and compilation with
|
|
-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
|
|
as modes 2 and 3 when FLT_ROUNDS != 1.
|
|
6-9 ==> Debugging modes similar to mode - 4: don't try
|
|
fast floating-point estimate (if applicable).
|
|
|
|
Values of mode other than 0-9 are treated as mode 0.
|
|
|
|
Sufficient space is allocated to the return value
|
|
to hold the suppressed trailing zeros.
|
|
*/
|
|
|
|
int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0, j, j1, k, k0,
|
|
k_check, leftright, m2, m5, s2, s5,
|
|
spec_case, try_quick;
|
|
Long L;
|
|
int denorm;
|
|
ULong x;
|
|
Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
|
|
U d2, eps, u;
|
|
double ds;
|
|
char *s, *s0;
|
|
#ifdef Honor_FLT_ROUNDS
|
|
int rounding;
|
|
#endif
|
|
Stack_alloc alloc;
|
|
|
|
alloc.begin = alloc.free = buf;
|
|
alloc.end = buf + buf_size;
|
|
memset(alloc.freelist, 0, sizeof(alloc.freelist));
|
|
|
|
u.d = dd;
|
|
if (word0(&u) & Sign_bit) {
|
|
/* set sign for everything, including 0's and NaNs */
|
|
*sign = 1;
|
|
word0(&u) &= ~Sign_bit; /* clear sign bit */
|
|
} else
|
|
*sign = 0;
|
|
|
|
/* If infinity, set decpt to DTOA_OVERFLOW, if 0 set it to 1 */
|
|
if (((word0(&u) & Exp_mask) == Exp_mask && (*decpt = DTOA_OVERFLOW)) ||
|
|
(!dval(&u) && (*decpt = 1))) {
|
|
/* Infinity, NaN, 0 */
|
|
char *res = (char *)dtoa_alloc(2, &alloc);
|
|
res[0] = '0';
|
|
res[1] = '\0';
|
|
if (rve) *rve = res + 1;
|
|
return res;
|
|
}
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
if ((rounding = Flt_Rounds) >= 2) {
|
|
if (*sign)
|
|
rounding = rounding == 2 ? 0 : 2;
|
|
else if (rounding != 2)
|
|
rounding = 0;
|
|
}
|
|
#endif
|
|
|
|
b = d2b(&u, &be, &bbits, &alloc);
|
|
if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask >> Exp_shift1)))) {
|
|
dval(&d2) = dval(&u);
|
|
word0(&d2) &= Frac_mask1;
|
|
word0(&d2) |= Exp_11;
|
|
|
|
/*
|
|
log(x) ~=~ log(1.5) + (x-1.5)/1.5
|
|
log10(x) = log(x) / log(10)
|
|
~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
|
|
log10(d)= (i-Bias)*log(2)/log(10) + log10(d2)
|
|
|
|
This suggests computing an approximation k to log10(d) by
|
|
|
|
k= (i - Bias)*0.301029995663981
|
|
+ ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
|
|
|
|
We want k to be too large rather than too small.
|
|
The error in the first-order Taylor series approximation
|
|
is in our favor, so we just round up the constant enough
|
|
to compensate for any error in the multiplication of
|
|
(i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
|
|
and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
|
|
adding 1e-13 to the constant term more than suffices.
|
|
Hence we adjust the constant term to 0.1760912590558.
|
|
(We could get a more accurate k by invoking log10,
|
|
but this is probably not worthwhile.)
|
|
*/
|
|
|
|
i -= Bias;
|
|
denorm = 0;
|
|
} else {
|
|
/* d is denormalized */
|
|
|
|
i = bbits + be + (Bias + (P - 1) - 1);
|
|
x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32)
|
|
: word1(&u) << (32 - i);
|
|
dval(&d2) = x;
|
|
word0(&d2) -= 31 * Exp_msk1; /* adjust exponent */
|
|
i -= (Bias + (P - 1) - 1) + 1;
|
|
denorm = 1;
|
|
}
|
|
ds = (dval(&d2) - 1.5) * 0.289529654602168 + 0.1760912590558 +
|
|
i * 0.301029995663981;
|
|
k = (int)ds;
|
|
if (ds < 0. && ds != k) k--; /* want k= floor(ds) */
|
|
k_check = 1;
|
|
if (k >= 0 && k <= Ten_pmax) {
|
|
if (dval(&u) < tens[k]) k--;
|
|
k_check = 0;
|
|
}
|
|
j = bbits - i - 1;
|
|
if (j >= 0) {
|
|
b2 = 0;
|
|
s2 = j;
|
|
} else {
|
|
b2 = -j;
|
|
s2 = 0;
|
|
}
|
|
if (k >= 0) {
|
|
b5 = 0;
|
|
s5 = k;
|
|
s2 += k;
|
|
} else {
|
|
b2 -= k;
|
|
b5 = -k;
|
|
s5 = 0;
|
|
}
|
|
if (mode < 0 || mode > 9) mode = 0;
|
|
|
|
#ifdef Check_FLT_ROUNDS
|
|
try_quick = Rounding == 1;
|
|
#else
|
|
try_quick = 1;
|
|
#endif
|
|
|
|
if (mode > 5) {
|
|
mode -= 4;
|
|
try_quick = 0;
|
|
}
|
|
leftright = 1;
|
|
switch (mode) {
|
|
case 0:
|
|
case 1:
|
|
ilim = ilim1 = -1;
|
|
i = 18;
|
|
ndigits = 0;
|
|
break;
|
|
case 2:
|
|
leftright = 0;
|
|
// Fall through.
|
|
case 4:
|
|
if (ndigits <= 0) ndigits = 1;
|
|
ilim = ilim1 = i = ndigits;
|
|
break;
|
|
case 3:
|
|
leftright = 0;
|
|
// Fall through.
|
|
case 5:
|
|
i = ndigits + k + 1;
|
|
ilim = i;
|
|
ilim1 = i - 1;
|
|
if (i <= 0) i = 1;
|
|
}
|
|
s = s0 = dtoa_alloc(i, &alloc);
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
if (mode > 1 && rounding != 1) leftright = 0;
|
|
#endif
|
|
|
|
if (ilim >= 0 && ilim <= Quick_max && try_quick) {
|
|
/* Try to get by with floating-point arithmetic. */
|
|
i = 0;
|
|
dval(&d2) = dval(&u);
|
|
k0 = k;
|
|
ilim0 = ilim;
|
|
ieps = 2; /* conservative */
|
|
if (k > 0) {
|
|
ds = tens[k & 0xf];
|
|
j = k >> 4;
|
|
if (j & Bletch) {
|
|
/* prevent overflows */
|
|
j &= Bletch - 1;
|
|
dval(&u) /= bigtens[n_bigtens - 1];
|
|
ieps++;
|
|
}
|
|
for (; j; j >>= 1, i++) {
|
|
if (j & 1) {
|
|
ieps++;
|
|
ds *= bigtens[i];
|
|
}
|
|
}
|
|
dval(&u) /= ds;
|
|
} else if ((j1 = -k)) {
|
|
dval(&u) *= tens[j1 & 0xf];
|
|
for (j = j1 >> 4; j; j >>= 1, i++) {
|
|
if (j & 1) {
|
|
ieps++;
|
|
dval(&u) *= bigtens[i];
|
|
}
|
|
}
|
|
}
|
|
if (k_check && dval(&u) < 1. && ilim > 0) {
|
|
if (ilim1 <= 0) goto fast_failed;
|
|
ilim = ilim1;
|
|
k--;
|
|
dval(&u) *= 10.;
|
|
ieps++;
|
|
}
|
|
dval(&eps) = ieps * dval(&u) + 7.;
|
|
word0(&eps) -= (P - 1) * Exp_msk1;
|
|
if (ilim == 0) {
|
|
S = mhi = 0;
|
|
dval(&u) -= 5.;
|
|
if (dval(&u) > dval(&eps)) goto one_digit;
|
|
if (dval(&u) < -dval(&eps)) goto no_digits;
|
|
goto fast_failed;
|
|
}
|
|
if (leftright) {
|
|
/* Use Steele & White method of only generating digits needed. */
|
|
dval(&eps) = 0.5 / tens[ilim - 1] - dval(&eps);
|
|
for (i = 0;;) {
|
|
L = (Long)dval(&u);
|
|
dval(&u) -= L;
|
|
*s++ = '0' + (int)L;
|
|
if (dval(&u) < dval(&eps)) goto ret1;
|
|
if (1. - dval(&u) < dval(&eps)) goto bump_up;
|
|
if (++i >= ilim) break;
|
|
dval(&eps) *= 10.;
|
|
dval(&u) *= 10.;
|
|
}
|
|
} else {
|
|
/* Generate ilim digits, then fix them up. */
|
|
dval(&eps) *= tens[ilim - 1];
|
|
for (i = 1;; i++, dval(&u) *= 10.) {
|
|
L = (Long)(dval(&u));
|
|
if (!(dval(&u) -= L)) ilim = i;
|
|
*s++ = '0' + (int)L;
|
|
if (i == ilim) {
|
|
if (dval(&u) > 0.5 + dval(&eps))
|
|
goto bump_up;
|
|
else if (dval(&u) < 0.5 - dval(&eps)) {
|
|
while (*--s == '0')
|
|
;
|
|
s++;
|
|
goto ret1;
|
|
}
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
fast_failed:
|
|
s = s0;
|
|
dval(&u) = dval(&d2);
|
|
k = k0;
|
|
ilim = ilim0;
|
|
}
|
|
|
|
/* Do we have a "small" integer? */
|
|
|
|
if (be >= 0 && k <= Int_max) {
|
|
/* Yes. */
|
|
ds = tens[k];
|
|
if (ndigits < 0 && ilim <= 0) {
|
|
S = mhi = 0;
|
|
if (ilim < 0 || dval(&u) <= 5 * ds) goto no_digits;
|
|
goto one_digit;
|
|
}
|
|
for (i = 1;; i++, dval(&u) *= 10.) {
|
|
L = (Long)(dval(&u) / ds);
|
|
dval(&u) -= L * ds;
|
|
#ifdef Check_FLT_ROUNDS
|
|
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
|
|
if (dval(&u) < 0) {
|
|
L--;
|
|
dval(&u) += ds;
|
|
}
|
|
#endif
|
|
*s++ = '0' + (int)L;
|
|
if (!dval(&u)) {
|
|
break;
|
|
}
|
|
if (i == ilim) {
|
|
#ifdef Honor_FLT_ROUNDS
|
|
if (mode > 1) {
|
|
switch (rounding) {
|
|
case 0:
|
|
goto ret1;
|
|
case 2:
|
|
goto bump_up;
|
|
}
|
|
}
|
|
#endif
|
|
dval(&u) += dval(&u);
|
|
if (dval(&u) > ds || (dval(&u) == ds && L & 1)) {
|
|
bump_up:
|
|
while (*--s == '9')
|
|
if (s == s0) {
|
|
k++;
|
|
*s = '0';
|
|
break;
|
|
}
|
|
++*s++;
|
|
}
|
|
break;
|
|
}
|
|
}
|
|
goto ret1;
|
|
}
|
|
|
|
m2 = b2;
|
|
m5 = b5;
|
|
mhi = mlo = 0;
|
|
if (leftright) {
|
|
i = denorm ? be + (Bias + (P - 1) - 1 + 1) : 1 + P - bbits;
|
|
b2 += i;
|
|
s2 += i;
|
|
mhi = i2b(1, &alloc);
|
|
}
|
|
if (m2 > 0 && s2 > 0) {
|
|
i = m2 < s2 ? m2 : s2;
|
|
b2 -= i;
|
|
m2 -= i;
|
|
s2 -= i;
|
|
}
|
|
if (b5 > 0) {
|
|
if (leftright) {
|
|
if (m5 > 0) {
|
|
mhi = pow5mult(mhi, m5, &alloc);
|
|
b1 = mult(mhi, b, &alloc);
|
|
Bfree(b, &alloc);
|
|
b = b1;
|
|
}
|
|
if ((j = b5 - m5)) b = pow5mult(b, j, &alloc);
|
|
} else
|
|
b = pow5mult(b, b5, &alloc);
|
|
}
|
|
S = i2b(1, &alloc);
|
|
if (s5 > 0) S = pow5mult(S, s5, &alloc);
|
|
|
|
/* Check for special case that d is a normalized power of 2. */
|
|
|
|
spec_case = 0;
|
|
if ((mode < 2 || leftright)
|
|
#ifdef Honor_FLT_ROUNDS
|
|
&& rounding == 1
|
|
#endif
|
|
) {
|
|
if (!word1(&u) && !(word0(&u) & Bndry_mask) &&
|
|
word0(&u) & (Exp_mask & ~Exp_msk1)) {
|
|
/* The special case */
|
|
b2 += Log2P;
|
|
s2 += Log2P;
|
|
spec_case = 1;
|
|
}
|
|
}
|
|
|
|
/*
|
|
Arrange for convenient computation of quotients:
|
|
shift left if necessary so divisor has 4 leading 0 bits.
|
|
|
|
Perhaps we should just compute leading 28 bits of S once
|
|
a nd for all and pass them and a shift to quorem, so it
|
|
can do shifts and ors to compute the numerator for q.
|
|
*/
|
|
if ((i = ((s5 ? 32 - hi0bits(S->p.x[S->wds - 1]) : 1) + s2) & 0x1f))
|
|
i = 32 - i;
|
|
if (i > 4) {
|
|
i -= 4;
|
|
b2 += i;
|
|
m2 += i;
|
|
s2 += i;
|
|
} else if (i < 4) {
|
|
i += 28;
|
|
b2 += i;
|
|
m2 += i;
|
|
s2 += i;
|
|
}
|
|
if (b2 > 0) b = lshift(b, b2, &alloc);
|
|
if (s2 > 0) S = lshift(S, s2, &alloc);
|
|
if (k_check) {
|
|
if (cmp(b, S) < 0) {
|
|
k--;
|
|
/* we botched the k estimate */
|
|
b = multadd(b, 10, 0, &alloc);
|
|
if (leftright) mhi = multadd(mhi, 10, 0, &alloc);
|
|
ilim = ilim1;
|
|
}
|
|
}
|
|
if (ilim <= 0 && (mode == 3 || mode == 5)) {
|
|
if (ilim < 0 || cmp(b, S = multadd(S, 5, 0, &alloc)) <= 0) {
|
|
/* no digits, fcvt style */
|
|
no_digits:
|
|
k = -1 - ndigits;
|
|
goto ret;
|
|
}
|
|
one_digit:
|
|
*s++ = '1';
|
|
k++;
|
|
goto ret;
|
|
}
|
|
if (leftright) {
|
|
if (m2 > 0) mhi = lshift(mhi, m2, &alloc);
|
|
|
|
/*
|
|
Compute mlo -- check for special case that d is a normalized power of 2.
|
|
*/
|
|
|
|
mlo = mhi;
|
|
if (spec_case) {
|
|
mhi = Balloc(mhi->k, &alloc);
|
|
Bcopy(mhi, mlo);
|
|
mhi = lshift(mhi, Log2P, &alloc);
|
|
}
|
|
|
|
for (i = 1;; i++) {
|
|
dig = quorem(b, S) + '0';
|
|
/* Do we yet have the shortest decimal string that will round to d? */
|
|
j = cmp(b, mlo);
|
|
delta = diff(S, mhi, &alloc);
|
|
j1 = delta->sign ? 1 : cmp(b, delta);
|
|
Bfree(delta, &alloc);
|
|
if (j1 == 0 && mode != 1 && !(word1(&u) & 1)
|
|
#ifdef Honor_FLT_ROUNDS
|
|
&& rounding >= 1
|
|
#endif
|
|
) {
|
|
if (dig == '9') goto round_9_up;
|
|
if (j > 0) dig++;
|
|
*s++ = dig;
|
|
goto ret;
|
|
}
|
|
if (j < 0 || (j == 0 && mode != 1 && !(word1(&u) & 1))) {
|
|
if (!b->p.x[0] && b->wds <= 1) {
|
|
goto accept_dig;
|
|
}
|
|
#ifdef Honor_FLT_ROUNDS
|
|
if (mode > 1) switch (rounding) {
|
|
case 0:
|
|
goto accept_dig;
|
|
case 2:
|
|
goto keep_dig;
|
|
}
|
|
#endif /*Honor_FLT_ROUNDS*/
|
|
if (j1 > 0) {
|
|
b = lshift(b, 1, &alloc);
|
|
j1 = cmp(b, S);
|
|
if ((j1 > 0 || (j1 == 0 && dig & 1)) && dig++ == '9') goto round_9_up;
|
|
}
|
|
accept_dig:
|
|
*s++ = dig;
|
|
goto ret;
|
|
}
|
|
if (j1 > 0) {
|
|
#ifdef Honor_FLT_ROUNDS
|
|
if (!rounding) goto accept_dig;
|
|
#endif
|
|
if (dig == '9') { /* possible if i == 1 */
|
|
round_9_up:
|
|
*s++ = '9';
|
|
goto roundoff;
|
|
}
|
|
*s++ = dig + 1;
|
|
goto ret;
|
|
}
|
|
#ifdef Honor_FLT_ROUNDS
|
|
keep_dig:
|
|
#endif
|
|
*s++ = dig;
|
|
if (i == ilim) break;
|
|
b = multadd(b, 10, 0, &alloc);
|
|
if (mlo == mhi)
|
|
mlo = mhi = multadd(mhi, 10, 0, &alloc);
|
|
else {
|
|
mlo = multadd(mlo, 10, 0, &alloc);
|
|
mhi = multadd(mhi, 10, 0, &alloc);
|
|
}
|
|
}
|
|
} else
|
|
for (i = 1;; i++) {
|
|
*s++ = dig = quorem(b, S) + '0';
|
|
if (!b->p.x[0] && b->wds <= 1) {
|
|
goto ret;
|
|
}
|
|
if (i >= ilim) break;
|
|
b = multadd(b, 10, 0, &alloc);
|
|
}
|
|
|
|
/* Round off last digit */
|
|
|
|
#ifdef Honor_FLT_ROUNDS
|
|
switch (rounding) {
|
|
case 0:
|
|
goto trimzeros;
|
|
case 2:
|
|
goto roundoff;
|
|
}
|
|
#endif
|
|
b = lshift(b, 1, &alloc);
|
|
j = cmp(b, S);
|
|
if (j > 0 || (j == 0 && dig & 1)) {
|
|
roundoff:
|
|
while (*--s == '9')
|
|
if (s == s0) {
|
|
k++;
|
|
*s++ = '1';
|
|
goto ret;
|
|
}
|
|
++*s++;
|
|
} else {
|
|
#ifdef Honor_FLT_ROUNDS
|
|
trimzeros:
|
|
#endif
|
|
while (*--s == '0')
|
|
;
|
|
s++;
|
|
}
|
|
ret:
|
|
Bfree(S, &alloc);
|
|
if (mhi) {
|
|
if (mlo && mlo != mhi) Bfree(mlo, &alloc);
|
|
Bfree(mhi, &alloc);
|
|
}
|
|
ret1:
|
|
Bfree(b, &alloc);
|
|
*s = 0;
|
|
*decpt = k + 1;
|
|
if (rve) *rve = s;
|
|
return s0;
|
|
}
|
|
|