/**************************************************************************** ** ** Copyright (C) 2013 Digia Plc and/or its subsidiary(-ies). ** Contact: http://www.qt-project.org/legal ** ** This file is part of the QtCore module of the Qt Toolkit. ** ** $QT_BEGIN_LICENSE:LGPL$ ** Commercial License Usage ** Licensees holding valid commercial Qt licenses may use this file in ** accordance with the commercial license agreement provided with the ** Software or, alternatively, in accordance with the terms contained in ** a written agreement between you and Digia. For licensing terms and ** conditions see http://qt.digia.com/licensing. For further information ** use the contact form at http://qt.digia.com/contact-us. ** ** GNU Lesser General Public License Usage ** Alternatively, this file may be used under the terms of the GNU Lesser ** General Public License version 2.1 as published by the Free Software ** Foundation and appearing in the file LICENSE.LGPL included in the ** packaging of this file. Please review the following information to ** ensure the GNU Lesser General Public License version 2.1 requirements ** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html. ** ** In addition, as a special exception, Digia gives you certain additional ** rights. These rights are described in the Digia Qt LGPL Exception ** version 1.1, included in the file LGPL_EXCEPTION.txt in this package. ** ** GNU General Public License Usage ** Alternatively, this file may be used under the terms of the GNU ** General Public License version 3.0 as published by the Free Software ** Foundation and appearing in the file LICENSE.GPL included in the ** packaging of this file. Please review the following information to ** ensure the GNU General Public License version 3.0 requirements will be ** met: http://www.gnu.org/copyleft/gpl.html. ** ** ** $QT_END_LICENSE$ ** ****************************************************************************/ #include "qlocale_tools_p.h" #include "qlocale_p.h" #include "qstring.h" #include #include #include #include #include #include #ifdef Q_OS_WINCE # include "qfunctions_wince.h" // for _control87 #endif #if defined(Q_OS_LINUX) && !defined(__UCLIBC__) # include #endif // Sizes as defined by the ISO C99 standard - fallback #ifndef LLONG_MAX # define LLONG_MAX Q_INT64_C(0x7fffffffffffffff) #endif #ifndef LLONG_MIN # define LLONG_MIN (-LLONG_MAX - Q_INT64_C(1)) #endif #ifndef ULLONG_MAX # define ULLONG_MAX Q_UINT64_C(0xffffffffffffffff) #endif QT_BEGIN_NAMESPACE #ifndef QT_QLOCALE_USES_FCVT static char *_qdtoa( NEEDS_VOLATILE double d, int mode, int ndigits, int *decpt, int *sign, char **rve, char **digits_str); #endif QString qulltoa(qulonglong l, int base, const QChar _zero) { ushort buff[65]; // length of MAX_ULLONG in base 2 ushort *p = buff + 65; if (base != 10 || _zero.unicode() == '0') { while (l != 0) { int c = l % base; --p; if (c < 10) *p = '0' + c; else *p = c - 10 + 'a'; l /= base; } } else { while (l != 0) { int c = l % base; *(--p) = _zero.unicode() + c; l /= base; } } return QString(reinterpret_cast(p), 65 - (p - buff)); } QString qlltoa(qlonglong l, int base, const QChar zero) { return qulltoa(l < 0 ? -l : l, base, zero); } QString &decimalForm(QChar zero, QChar decimal, QChar group, QString &digits, int decpt, uint precision, PrecisionMode pm, bool always_show_decpt, bool thousands_group) { if (decpt < 0) { for (int i = 0; i < -decpt; ++i) digits.prepend(zero); decpt = 0; } else if (decpt > digits.length()) { for (int i = digits.length(); i < decpt; ++i) digits.append(zero); } if (pm == PMDecimalDigits) { uint decimal_digits = digits.length() - decpt; for (uint i = decimal_digits; i < precision; ++i) digits.append(zero); } else if (pm == PMSignificantDigits) { for (uint i = digits.length(); i < precision; ++i) digits.append(zero); } else { // pm == PMChopTrailingZeros } if (always_show_decpt || decpt < digits.length()) digits.insert(decpt, decimal); if (thousands_group) { for (int i = decpt - 3; i > 0; i -= 3) digits.insert(i, group); } if (decpt == 0) digits.prepend(zero); return digits; } QString &exponentForm(QChar zero, QChar decimal, QChar exponential, QChar group, QChar plus, QChar minus, QString &digits, int decpt, uint precision, PrecisionMode pm, bool always_show_decpt) { int exp = decpt - 1; if (pm == PMDecimalDigits) { for (uint i = digits.length(); i < precision + 1; ++i) digits.append(zero); } else if (pm == PMSignificantDigits) { for (uint i = digits.length(); i < precision; ++i) digits.append(zero); } else { // pm == PMChopTrailingZeros } if (always_show_decpt || digits.length() > 1) digits.insert(1, decimal); digits.append(exponential); digits.append(QLocalePrivate::longLongToString(zero, group, plus, minus, exp, 2, 10, -1, QLocalePrivate::AlwaysShowSign)); return digits; } // Removes thousand-group separators in "C" locale. bool removeGroupSeparators(QLocalePrivate::CharBuff *num) { int group_cnt = 0; // counts number of group chars int decpt_idx = -1; char *data = num->data(); int l = qstrlen(data); // Find the decimal point and check if there are any group chars int i = 0; for (; i < l; ++i) { char c = data[i]; if (c == ',') { if (i == 0 || data[i - 1] < '0' || data[i - 1] > '9') return false; if (i == l - 1 || data[i + 1] < '0' || data[i + 1] > '9') return false; ++group_cnt; } else if (c == '.') { // Fail if more than one decimal points if (decpt_idx != -1) return false; decpt_idx = i; } else if (c == 'e' || c == 'E') { // an 'e' or 'E' - if we have not encountered a decimal // point, this is where it "is". if (decpt_idx == -1) decpt_idx = i; } } // If no group chars, we're done if (group_cnt == 0) return true; // No decimal point means that it "is" at the end of the string if (decpt_idx == -1) decpt_idx = l; i = 0; while (i < l && group_cnt > 0) { char c = data[i]; if (c == ',') { // Don't allow group chars after the decimal point if (i > decpt_idx) return false; // Check that it is placed correctly relative to the decpt if ((decpt_idx - i) % 4 != 0) return false; // Remove it memmove(data + i, data + i + 1, l - i - 1); data[--l] = '\0'; --group_cnt; --decpt_idx; } else { // Check that we are not missing a separator if (i < decpt_idx && (decpt_idx - i) % 4 == 0 && !(i == 0 && (c == '-' || c == '+'))) // check for negative or positive sign at start of string return false; ++i; } } return true; } /*- * Copyright (c) 1992, 1993 * The Regents of the University of California. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. All advertising materials mentioning features or use of this software * must display the following acknowledgment: * This product includes software developed by the University of * California, Berkeley and its contributors. * 4. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ // static char sccsid[] = "@(#)strtouq.c 8.1 (Berkeley) 6/4/93"; // "$FreeBSD: src/lib/libc/stdlib/strtoull.c,v 1.5.2.1 2001/03/02 09:45:20 obrien Exp $"; /* * Convert a string to an unsigned long long integer. * * Ignores `locale' stuff. Assumes that the upper and lower case * alphabets and digits are each contiguous. */ qulonglong qstrtoull(const char *nptr, const char **endptr, int base, bool *ok) { const char *s = nptr; qulonglong acc; unsigned char c; qulonglong qbase, cutoff; int any, cutlim; if (ok != 0) *ok = true; /* * See strtoq for comments as to the logic used. */ s = nptr; do { c = *s++; } while (isspace(c)); if (c == '-') { if (ok != 0) *ok = false; if (endptr != 0) *endptr = s - 1; return 0; } else { if (c == '+') c = *s++; } if ((base == 0 || base == 16) && c == '0' && (*s == 'x' || *s == 'X')) { c = s[1]; s += 2; base = 16; } if (base == 0) base = c == '0' ? 8 : 10; qbase = unsigned(base); cutoff = qulonglong(ULLONG_MAX) / qbase; cutlim = qulonglong(ULLONG_MAX) % qbase; for (acc = 0, any = 0;; c = *s++) { if (!isascii(c)) break; if (isdigit(c)) c -= '0'; else if (isalpha(c)) c -= isupper(c) ? 'A' - 10 : 'a' - 10; else break; if (c >= base) break; if (any < 0 || acc > cutoff || (acc == cutoff && c > cutlim)) any = -1; else { any = 1; acc *= qbase; acc += c; } } if (any == 0) { if (ok != 0) *ok = false; } else if (any < 0) { acc = ULLONG_MAX; if (ok != 0) *ok = false; } if (endptr != 0) *endptr = (any ? s - 1 : nptr); return acc; } // "$FreeBSD: src/lib/libc/stdlib/strtoll.c,v 1.5.2.1 2001/03/02 09:45:20 obrien Exp $"; /* * Convert a string to a long long integer. * * Ignores `locale' stuff. Assumes that the upper and lower case * alphabets and digits are each contiguous. */ qlonglong qstrtoll(const char *nptr, const char **endptr, int base, bool *ok) { const char *s; qulonglong acc; unsigned char c; qulonglong qbase, cutoff; int neg, any, cutlim; /* * Skip white space and pick up leading +/- sign if any. * If base is 0, allow 0x for hex and 0 for octal, else * assume decimal; if base is already 16, allow 0x. */ s = nptr; do { c = *s++; } while (isspace(c)); if (c == '-') { neg = 1; c = *s++; } else { neg = 0; if (c == '+') c = *s++; } if ((base == 0 || base == 16) && c == '0' && (*s == 'x' || *s == 'X')) { c = s[1]; s += 2; base = 16; } if (base == 0) base = c == '0' ? 8 : 10; /* * Compute the cutoff value between legal numbers and illegal * numbers. That is the largest legal value, divided by the * base. An input number that is greater than this value, if * followed by a legal input character, is too big. One that * is equal to this value may be valid or not; the limit * between valid and invalid numbers is then based on the last * digit. For instance, if the range for quads is * [-9223372036854775808..9223372036854775807] and the input base * is 10, cutoff will be set to 922337203685477580 and cutlim to * either 7 (neg==0) or 8 (neg==1), meaning that if we have * accumulated a value > 922337203685477580, or equal but the * next digit is > 7 (or 8), the number is too big, and we will * return a range error. * * Set any if any `digits' consumed; make it negative to indicate * overflow. */ qbase = unsigned(base); cutoff = neg ? qulonglong(0-(LLONG_MIN + LLONG_MAX)) + LLONG_MAX : LLONG_MAX; cutlim = cutoff % qbase; cutoff /= qbase; for (acc = 0, any = 0;; c = *s++) { if (!isascii(c)) break; if (isdigit(c)) c -= '0'; else if (isalpha(c)) c -= isupper(c) ? 'A' - 10 : 'a' - 10; else break; if (c >= base) break; if (any < 0 || acc > cutoff || (acc == cutoff && c > cutlim)) any = -1; else { any = 1; acc *= qbase; acc += c; } } if (any < 0) { acc = neg ? LLONG_MIN : LLONG_MAX; if (ok != 0) *ok = false; } else if (neg) { acc = (~acc) + 1; } if (endptr != 0) *endptr = (any >= 0 ? s - 1 : nptr); if (ok != 0) *ok = any > 0; return acc; } #ifndef QT_QLOCALE_USES_FCVT /* From: NetBSD: strtod.c,v 1.26 1998/02/03 18:44:21 perry Exp */ /* $FreeBSD: src/lib/libc/stdlib/netbsd_strtod.c,v 1.2.2.2 2001/03/02 17:14:15 tegge Exp $ */ /* Please send bug reports to David M. Gay AT&T Bell Laboratories, Room 2C-463 600 Mountain Avenue Murray Hill, NJ 07974-2070 U.S.A. dmg@research.att.com or research!dmg */ /* strtod for IEEE-, VAX-, and IBM-arithmetic machines. * * This strtod returns a nearest machine number to the input decimal * string (or sets errno to ERANGE). With IEEE arithmetic, ties are * broken by the IEEE round-even rule. Otherwise ties are broken by * biased rounding (add half and chop). * * 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, IBM, or VAX double-precision * arithmetic (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). */ /* * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least * significant byte has the lowest address. * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most * significant byte has the lowest address. * #define Long int on machines with 32-bit ints and 64-bit longs. * #define Sudden_Underflow for IEEE-format machines without gradual * underflow (i.e., that flush to zero on underflow). * #define IBM for IBM mainframe-style floating-point arithmetic. * #define VAX for VAX-style floating-point arithmetic. * #define Unsigned_Shifts if >> does treats its left operand as unsigned. * #define No_leftright to omit left-right logic in fast floating-point * computation of dtoa. * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3. * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines * that use extended-precision instructions to compute rounded * products and quotients) with IBM. * #define ROUND_BIASED for IEEE-format with biased rounding. * #define Inaccurate_Divide for IEEE-format with correctly rounded * products but inaccurate quotients, e.g., for Intel i860. * #define Just_16 to store 16 bits per 32-bit Long when doing high-precision * integer arithmetic. Whether this speeds things up or slows things * down depends on the machine and the number being converted. * #define KR_headers for old-style C function headers. * #define Bad_float_h if your system lacks a float.h or if it does not * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP, * FLT_RADIX, FLT_ROUNDS, and DBL_MAX. * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n) * if memory is available and otherwise does something you deem * appropriate. If MALLOC is undefined, malloc will be invoked * directly -- and assumed always to succeed. */ #if defined(LIBC_SCCS) && !defined(lint) __RCSID("$NetBSD: strtod.c,v 1.26 1998/02/03 18:44:21 perry Exp $"); #endif /* LIBC_SCCS and not lint */ /* #if defined(__m68k__) || defined(__sparc__) || defined(__i386__) || \ defined(__mips__) || defined(__ns32k__) || defined(__alpha__) || \ defined(__powerpc__) || defined(Q_OS_WIN) || defined(Q_OS_DARWIN) || defined(Q_OS_MAC) || \ defined(mips) || defined(Q_OS_AIX) || defined(Q_OS_SOLARIS) # define IEEE_BIG_OR_LITTLE_ENDIAN 1 #endif */ // *All* of our architectures have IEEE arithmetic, don't they? #define IEEE_BIG_OR_LITTLE_ENDIAN 1 #ifdef __arm32__ /* * Although the CPU is little endian the FP has different * byte and word endianness. The byte order is still little endian * but the word order is big endian. */ #define IEEE_BIG_OR_LITTLE_ENDIAN #endif #ifdef vax #define VAX #endif #define Long qint32 #define ULong quint32 #define MALLOC malloc #ifdef BSD_QDTOA_DEBUG QT_BEGIN_INCLUDE_NAMESPACE #include QT_END_INCLUDE_NAMESPACE #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} #endif #ifdef Unsigned_Shifts #define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000; #else #define Sign_Extend(a,b) /*no-op*/ #endif #if (defined(IEEE_BIG_OR_LITTLE_ENDIAN) + defined(VAX) + defined(IBM)) != 1 #error Exactly one of IEEE_BIG_OR_LITTLE_ENDIAN, VAX, or IBM should be defined. #endif static inline ULong getWord0(const NEEDS_VOLATILE double x) { const NEEDS_VOLATILE uchar *ptr = reinterpret_cast(&x); if (QSysInfo::ByteOrder == QSysInfo::BigEndian) { return (ptr[0]<<24) + (ptr[1]<<16) + (ptr[2]<<8) + ptr[3]; } else { return (ptr[7]<<24) + (ptr[6]<<16) + (ptr[5]<<8) + ptr[4]; } } static inline void setWord0(NEEDS_VOLATILE double *x, ULong l) { NEEDS_VOLATILE uchar *ptr = reinterpret_cast(x); if (QSysInfo::ByteOrder == QSysInfo::BigEndian) { ptr[0] = uchar(l>>24); ptr[1] = uchar(l>>16); ptr[2] = uchar(l>>8); ptr[3] = uchar(l); } else { ptr[7] = uchar(l>>24); ptr[6] = uchar(l>>16); ptr[5] = uchar(l>>8); ptr[4] = uchar(l); } } static inline ULong getWord1(const NEEDS_VOLATILE double x) { const NEEDS_VOLATILE uchar *ptr = reinterpret_cast(&x); if (QSysInfo::ByteOrder == QSysInfo::BigEndian) { return (ptr[4]<<24) + (ptr[5]<<16) + (ptr[6]<<8) + ptr[7]; } else { return (ptr[3]<<24) + (ptr[2]<<16) + (ptr[1]<<8) + ptr[0]; } } static inline void setWord1(NEEDS_VOLATILE double *x, ULong l) { NEEDS_VOLATILE uchar *ptr = reinterpret_cast(x); if (QSysInfo::ByteOrder == QSysInfo::BigEndian) { ptr[4] = uchar(l>>24); ptr[5] = uchar(l>>16); ptr[6] = uchar(l>>8); ptr[7] = uchar(l); } else { ptr[3] = uchar(l>>24); ptr[2] = uchar(l>>16); ptr[1] = uchar(l>>8); ptr[0] = uchar(l); } } static inline void Storeinc(ULong *&a, const ULong &b, const ULong &c) { *a = (ushort(b) << 16) | ushort(c); ++a; } /* #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) */ #if defined(IEEE_BIG_OR_LITTLE_ENDIAN) #define Exp_shift 20 #define Exp_shift1 20 #define Exp_msk1 0x100000 #define Exp_msk11 0x100000 #define Exp_mask 0x7ff00000 #define P 53 #define Bias 1023 #define IEEE_Arith #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 #if defined(LSB) && defined(Q_OS_VXWORKS) #undef LSB #endif #define LSB 1 #define Sign_bit 0x80000000 #define Log2P 1 #define Tiny0 0 #define Tiny1 1 #define Quick_max 14 #define Int_max 14 #define Infinite(x) (getWord0(x) == 0x7ff00000) /* sufficient test for here */ #else #undef Sudden_Underflow #define Sudden_Underflow #ifdef IBM #define Exp_shift 24 #define Exp_shift1 24 #define Exp_msk1 0x1000000 #define Exp_msk11 0x1000000 #define Exp_mask 0x7f000000 #define P 14 #define Bias 65 #define Exp_1 0x41000000 #define Exp_11 0x41000000 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ #define Frac_mask 0xffffff #define Frac_mask1 0xffffff #define Bletch 4 #define Ten_pmax 22 #define Bndry_mask 0xefffff #define Bndry_mask1 0xffffff #define LSB 1 #define Sign_bit 0x80000000 #define Log2P 4 #define Tiny0 0x100000 #define Tiny1 0 #define Quick_max 14 #define Int_max 15 #else /* VAX */ #define Exp_shift 23 #define Exp_shift1 7 #define Exp_msk1 0x80 #define Exp_msk11 0x800000 #define Exp_mask 0x7f80 #define P 56 #define Bias 129 #define Exp_1 0x40800000 #define Exp_11 0x4080 #define Ebits 8 #define Frac_mask 0x7fffff #define Frac_mask1 0xffff007f #define Ten_pmax 24 #define Bletch 2 #define Bndry_mask 0xffff007f #define Bndry_mask1 0xffff007f #define LSB 0x10000 #define Sign_bit 0x8000 #define Log2P 1 #define Tiny0 0x80 #define Tiny1 0 #define Quick_max 15 #define Int_max 15 #endif #endif #ifndef IEEE_Arith #define ROUND_BIASED #endif #ifdef RND_PRODQUOT #define rounded_product(a,b) a = rnd_prod(a, b) #define rounded_quotient(a,b) a = rnd_quot(a, b) extern double rnd_prod(double, double), rnd_quot(double, double); #else #define rounded_product(a,b) a *= b #define rounded_quotient(a,b) a /= b #endif #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) #define Big1 0xffffffff #ifndef Just_16 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long. * This makes some inner loops simpler and sometimes saves work * during multiplications, but it often seems to make things slightly * slower. Hence the default is now to store 32 bits per Long. */ #ifndef Pack_32 #define Pack_32 #endif #endif #define Kmax 15 struct Bigint { struct Bigint *next; int k, maxwds, sign, wds; ULong x[1]; }; typedef struct Bigint Bigint; static Bigint *Balloc(int k) { int x; Bigint *rv; x = 1 << k; rv = static_cast(MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long))); Q_CHECK_PTR(rv); rv->k = k; rv->maxwds = x; rv->sign = rv->wds = 0; return rv; } static void Bfree(Bigint *v) { free(v); } #define Bcopy(x,y) memcpy(reinterpret_cast(&x->sign), reinterpret_cast(&y->sign), \ y->wds*sizeof(Long) + 2*sizeof(int)) /* multiply by m and add a */ static Bigint *multadd(Bigint *b, int m, int a) { int i, wds; ULong *x, y; #ifdef Pack_32 ULong xi, z; #endif Bigint *b1; wds = b->wds; x = b->x; i = 0; do { #ifdef Pack_32 xi = *x; y = (xi & 0xffff) * m + a; z = (xi >> 16) * m + (y >> 16); a = (z >> 16); *x++ = (z << 16) + (y & 0xffff); #else y = *x * m + a; a = (y >> 16); *x++ = y & 0xffff; #endif } while(++i < wds); if (a) { if (wds >= b->maxwds) { b1 = Balloc(b->k+1); Bcopy(b1, b); Bfree(b); b = b1; } b->x[wds++] = a; b->wds = wds; } return b; } static Bigint *s2b(const char *s, int nd0, int nd, ULong y9) { Bigint *b; int i, k; Long x, y; x = (nd + 8) / 9; for(k = 0, y = 1; x > y; y <<= 1, k++) ; #ifdef Pack_32 b = Balloc(k); b->x[0] = y9; b->wds = 1; #else b = Balloc(k+1); b->x[0] = y9 & 0xffff; b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; #endif i = 9; if (9 < nd0) { s += 9; do b = multadd(b, 10, *s++ - '0'); while(++i < nd0); s++; } else s += 10; for(; i < nd; i++) b = multadd(b, 10, *s++ - '0'); 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 & 1) return 32; } *y = x; return k; } static Bigint *i2b(int i) { Bigint *b; b = Balloc(1); b->x[0] = i; b->wds = 1; return b; } static Bigint *mult(Bigint *a, Bigint *b) { Bigint *c; int k, wa, wb, wc; ULong carry, y, z; ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; #ifdef Pack_32 ULong z2; #endif 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); for(x = c->x, xa = x + wc; x < xa; x++) *x = 0; xa = a->x; xae = xa + wa; xb = b->x; xbe = xb + wb; xc0 = c->x; #ifdef Pack_32 for(; xb < xbe; xb++, xc0++) { if ((y = *xb & 0xffff) != 0) { x = xa; xc = xc0; carry = 0; do { z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; carry = z >> 16; z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; carry = z2 >> 16; Storeinc(xc, z2, z); } while(x < xae); *xc = carry; } if ((y = *xb >> 16) != 0) { x = xa; xc = xc0; carry = 0; z2 = *xc; do { z = (*x & 0xffff) * y + (*xc >> 16) + carry; carry = z >> 16; Storeinc(xc, z, z2); z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; carry = z2 >> 16; } while(x < xae); *xc = z2; } } #else for(; xb < xbe; xc0++) { if (y = *xb++) { x = xa; xc = xc0; carry = 0; do { z = *x++ * y + *xc + carry; carry = z >> 16; *xc++ = z & 0xffff; } while(x < xae); *xc = carry; } } #endif for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; c->wds = wc; return c; } static Bigint *p5s; struct p5s_deleter { ~p5s_deleter() { while (p5s) { Bigint *next = p5s->next; Bfree(p5s); p5s = next; } } }; static Bigint *pow5mult(Bigint *b, int k) { Bigint *b1, *p5, *p51; int i; static const int p05[3] = { 5, 25, 125 }; if ((i = k & 3) != 0) b = multadd(b, p05[i-1], 0); if (!(k >>= 2)) return b; if (!(p5 = p5s)) { /* first time */ static p5s_deleter deleter; p5 = p5s = i2b(625); p5->next = 0; } for(;;) { if (k & 1) { b1 = mult(b, p5); Bfree(b); b = b1; } if (!(k >>= 1)) break; if (!(p51 = p5->next)) { p51 = p5->next = mult(p5,p5); p51->next = 0; } p5 = p51; } return b; } static Bigint *lshift(Bigint *b, int k) { int i, k1, n, n1; Bigint *b1; ULong *x, *x1, *xe, z; #ifdef Pack_32 n = k >> 5; #else n = k >> 4; #endif k1 = b->k; n1 = n + b->wds + 1; for(i = b->maxwds; n1 > i; i <<= 1) k1++; b1 = Balloc(k1); x1 = b1->x; for(i = 0; i < n; i++) *x1++ = 0; x = b->x; xe = x + b->wds; #ifdef Pack_32 if (k &= 0x1f) { k1 = 32 - k; z = 0; do { *x1++ = *x << k | z; z = *x++ >> k1; } while(x < xe); if ((*x1 = z) != 0) ++n1; } #else if (k &= 0xf) { k1 = 16 - k; z = 0; do { *x1++ = *x << k & 0xffff | z; z = *x++ >> k1; } while(x < xe); if (*x1 = z) ++n1; } #endif else do *x1++ = *x++; while(x < xe); b1->wds = n1 - 1; Bfree(b); return b1; } static int cmp(Bigint *a, Bigint *b) { ULong *xa, *xa0, *xb, *xb0; int i, j; i = a->wds; j = b->wds; #ifdef BSD_QDTOA_DEBUG if (i > 1 && !a->x[i-1]) Bug("cmp called with a->x[a->wds-1] == 0"); if (j > 1 && !b->x[j-1]) Bug("cmp called with b->x[b->wds-1] == 0"); #endif if (i -= j) return i; xa0 = a->x; xa = xa0 + j; xb0 = b->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) { Bigint *c; int i, wa, wb; Long borrow, y; /* We need signed shifts here. */ ULong *xa, *xae, *xb, *xbe, *xc; #ifdef Pack_32 Long z; #endif i = cmp(a,b); if (!i) { c = Balloc(0); c->wds = 1; c->x[0] = 0; return c; } if (i < 0) { c = a; a = b; b = c; i = 1; } else i = 0; c = Balloc(a->k); c->sign = i; wa = a->wds; xa = a->x; xae = xa + wa; wb = b->wds; xb = b->x; xbe = xb + wb; xc = c->x; borrow = 0; #ifdef Pack_32 do { y = (*xa & 0xffff) - (*xb & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); z = (*xa++ >> 16) - (*xb++ >> 16) + borrow; borrow = z >> 16; Sign_Extend(borrow, z); Storeinc(xc, z, y); } while(xb < xbe); while(xa < xae) { y = (*xa & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); z = (*xa++ >> 16) + borrow; borrow = z >> 16; Sign_Extend(borrow, z); Storeinc(xc, z, y); } #else do { y = *xa++ - *xb++ + borrow; borrow = y >> 16; Sign_Extend(borrow, y); *xc++ = y & 0xffff; } while(xb < xbe); while(xa < xae) { y = *xa++ + borrow; borrow = y >> 16; Sign_Extend(borrow, y); *xc++ = y & 0xffff; } #endif while(!*--xc) wa--; c->wds = wa; return c; } static double ulp(double x) { Long L; double a; L = (getWord0(x) & Exp_mask) - (P-1)*Exp_msk1; #ifndef Sudden_Underflow if (L > 0) { #endif #ifdef IBM L |= Exp_msk1 >> 4; #endif setWord0(&a, L); setWord1(&a, 0); #ifndef Sudden_Underflow } else { L = -L >> Exp_shift; if (L < Exp_shift) { setWord0(&a, 0x80000 >> L); setWord1(&a, 0); } else { setWord0(&a, 0); L -= Exp_shift; setWord1(&a, L >= 31 ? 1U : 1U << (31 - L)); } } #endif return a; } static double b2d(Bigint *a, int *e) { ULong *xa, *xa0, w, y, z; int k; double d; xa0 = a->x; xa = xa0 + a->wds; y = *--xa; #ifdef BSD_QDTOA_DEBUG if (!y) Bug("zero y in b2d"); #endif k = hi0bits(y); *e = 32 - k; #ifdef Pack_32 if (k < Ebits) { setWord0(&d, Exp_1 | y >> (Ebits - k)); w = xa > xa0 ? *--xa : 0; setWord1(&d, y << ((32-Ebits) + k) | w >> (Ebits - k)); goto ret_d; } z = xa > xa0 ? *--xa : 0; if (k -= Ebits) { setWord0(&d, Exp_1 | y << k | z >> (32 - k)); y = xa > xa0 ? *--xa : 0; setWord1(&d, z << k | y >> (32 - k)); } else { setWord0(&d, Exp_1 | y); setWord1(&d, z); } #else if (k < Ebits + 16) { z = xa > xa0 ? *--xa : 0; setWord0(&d, Exp_1 | y << k - Ebits | z >> Ebits + 16 - k); w = xa > xa0 ? *--xa : 0; y = xa > xa0 ? *--xa : 0; setWord1(&d, z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k); goto ret_d; } z = xa > xa0 ? *--xa : 0; w = xa > xa0 ? *--xa : 0; k -= Ebits + 16; setWord0(&d, Exp_1 | y << k + 16 | z << k | w >> 16 - k); y = xa > xa0 ? *--xa : 0; setWord1(&d, w << k + 16 | y << k); #endif ret_d: return d; } static Bigint *d2b(double d, int *e, int *bits) { Bigint *b; int de, i, k; ULong *x, y, z; #ifdef Pack_32 b = Balloc(1); #else b = Balloc(2); #endif x = b->x; z = getWord0(d) & Frac_mask; setWord0(&d, getWord0(d) & 0x7fffffff); /* clear sign bit, which we ignore */ #ifdef Sudden_Underflow de = (int)(getWord0(d) >> Exp_shift); #ifndef IBM z |= Exp_msk11; #endif #else if ((de = int(getWord0(d) >> Exp_shift)) != 0) z |= Exp_msk1; #endif #ifdef Pack_32 if ((y = getWord1(d)) != 0) { if ((k = lo0bits(&y)) != 0) { x[0] = y | z << (32 - k); z >>= k; } else x[0] = y; i = b->wds = (x[1] = z) ? 2 : 1; } else { #ifdef BSD_QDTOA_DEBUG if (!z) Bug("Zero passed to d2b"); #endif k = lo0bits(&z); x[0] = z; i = b->wds = 1; k += 32; } #else if (y = getWord1(d)) { if (k = lo0bits(&y)) if (k >= 16) { x[0] = y | z << 32 - k & 0xffff; x[1] = z >> k - 16 & 0xffff; x[2] = z >> k; i = 2; } else { x[0] = y & 0xffff; x[1] = y >> 16 | z << 16 - k & 0xffff; x[2] = z >> k & 0xffff; x[3] = z >> k+16; i = 3; } else { x[0] = y & 0xffff; x[1] = y >> 16; x[2] = z & 0xffff; x[3] = z >> 16; i = 3; } } else { #ifdef BSD_QDTOA_DEBUG if (!z) Bug("Zero passed to d2b"); #endif k = lo0bits(&z); if (k >= 16) { x[0] = z; i = 0; } else { x[0] = z & 0xffff; x[1] = z >> 16; i = 1; } k += 32; } while(!x[i]) --i; b->wds = i + 1; #endif #ifndef Sudden_Underflow if (de) { #endif #ifdef IBM *e = (de - Bias - (P-1) << 2) + k; *bits = 4*P + 8 - k - hi0bits(getWord0(d) & Frac_mask); #else *e = de - Bias - (P-1) + k; *bits = P - k; #endif #ifndef Sudden_Underflow } else { *e = de - Bias - (P-1) + 1 + k; #ifdef Pack_32 *bits = 32*i - hi0bits(x[i-1]); #else *bits = (i+2)*16 - hi0bits(x[i]); #endif } #endif return b; } static double ratio(Bigint *a, Bigint *b) { double da, db; int k, ka, kb; da = b2d(a, &ka); db = b2d(b, &kb); #ifdef Pack_32 k = ka - kb + 32*(a->wds - b->wds); #else k = ka - kb + 16*(a->wds - b->wds); #endif #ifdef IBM if (k > 0) { setWord0(&da, getWord0(da) + (k >> 2)*Exp_msk1); if (k &= 3) da *= 1 << k; } else { k = -k; setWord0(&db, getWord0(db) + (k >> 2)*Exp_msk1); if (k &= 3) db *= 1 << k; } #else if (k > 0) setWord0(&da, getWord0(da) + k*Exp_msk1); else { k = -k; setWord0(&db, getWord0(db) + k*Exp_msk1); } #endif return da / 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 #ifdef VAX , 1e23, 1e24 #endif }; #ifdef IEEE_Arith static const double bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 }; #define n_bigtens 5 #else #ifdef IBM static const double bigtens[] = { 1e16, 1e32, 1e64 }; static const double tinytens[] = { 1e-16, 1e-32, 1e-64 }; #define n_bigtens 3 #else static const double bigtens[] = { 1e16, 1e32 }; static const double tinytens[] = { 1e-16, 1e-32 }; #define n_bigtens 2 #endif #endif /* The pre-release gcc3.3 shipped with SuSE 8.2 has a bug which causes the comparison 1e-100 == 0.0 to return true. As a workaround, we compare it to a global variable containing 0.0, which produces correct assembler output. ### consider detecting the broken compilers and using the static ### double for these, and use a #define for all working compilers */ static double g_double_zero = 0.0; Q_CORE_EXPORT double qstrtod(const char *s00, const char **se, bool *ok) { int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; const char *s, *s0, *s1; double aadj, aadj1, adj, rv, rv0; Long L; ULong y, z; Bigint *bb1, *bd0; Bigint *bb = NULL, *bd = NULL, *bs = NULL, *delta = NULL;/* pacify gcc */ /* #ifndef KR_headers const char decimal_point = localeconv()->decimal_point[0]; #else const char decimal_point = '.'; #endif */ if (ok != 0) *ok = true; const char decimal_point = '.'; sign = nz0 = nz = 0; rv = 0.; for(s = s00; isspace(uchar(*s)); s++) ; if (*s == '-') { sign = 1; s++; } else if (*s == '+') { s++; } if (*s == '\0') { s = s00; goto ret; } if (*s == '0') { nz0 = 1; while(*++s == '0') ; if (!*s) goto ret; } s0 = s; y = z = 0; for(nd = nf = 0; (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 (c == decimal_point) { c = *++s; if (!nd) { for(; c == '0'; c = *++s) nz++; if (c > '0' && c <= '9') { s0 = s; nf += nz; nz = 0; goto have_dig; } goto dig_done; } for(; c >= '0' && c <= '9'; c = *++s) { have_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 (c == 'e' || c == 'E') { if (!nd && !nz && !nz0) { s = s00; goto ret; } s00 = s; esign = 0; switch(c = *++s) { case '-': esign = 1; case '+': c = *++s; } if (c >= '0' && c <= '9') { while(c == '0') c = *++s; if (c > '0' && c <= '9') { L = c - '0'; s1 = s; while((c = *++s) >= '0' && c <= '9') 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) s = s00; 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; rv = y; if (k > 9) rv = tens[k - 9] * rv + z; bd0 = 0; if (nd <= DBL_DIG #ifndef RND_PRODQUOT && FLT_ROUNDS == 1 #endif ) { if (!e) goto ret; if (e > 0) { if (e <= Ten_pmax) { #ifdef VAX goto vax_ovfl_check; #else /* rv = */ rounded_product(rv, tens[e]); goto ret; #endif } i = DBL_DIG - nd; if (e <= Ten_pmax + i) { /* A fancier test would sometimes let us do * this for larger i values. */ e -= i; rv *= tens[i]; #ifdef VAX /* VAX exponent range is so narrow we must * worry about overflow here... */ vax_ovfl_check: setWord0(&rv, getWord0(rv) - P*Exp_msk1); /* rv = */ rounded_product(rv, tens[e]); if ((getWord0(rv) & Exp_mask) > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) goto ovfl; setWord0(&rv, getWord0(rv) + P*Exp_msk1); #else /* rv = */ rounded_product(rv, tens[e]); #endif goto ret; } } #ifndef Inaccurate_Divide else if (e >= -Ten_pmax) { /* rv = */ rounded_quotient(rv, tens[-e]); goto ret; } #endif } e1 += nd - k; /* Get starting approximation = rv * 10**e1 */ if (e1 > 0) { if ((i = e1 & 15) != 0) rv *= tens[i]; if (e1 &= ~15) { if (e1 > DBL_MAX_10_EXP) { ovfl: // errno = ERANGE; if (ok != 0) *ok = false; #ifdef __STDC__ rv = HUGE_VAL; #else /* Can't trust HUGE_VAL */ #ifdef IEEE_Arith setWord0(&rv, Exp_mask); setWord1(&rv, 0); #else setWord0(&rv, Big0); setWord1(&rv, Big1); #endif #endif if (bd0) goto retfree; goto ret; } if (e1 >>= 4) { for(j = 0; e1 > 1; j++, e1 >>= 1) if (e1 & 1) rv *= bigtens[j]; /* The last multiplication could overflow. */ setWord0(&rv, getWord0(rv) - P*Exp_msk1); rv *= bigtens[j]; if ((z = getWord0(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) */ setWord0(&rv, Big0); setWord1(&rv, Big1); } else setWord0(&rv, getWord0(rv) + P*Exp_msk1); } } } else if (e1 < 0) { e1 = -e1; if ((i = e1 & 15) != 0) rv /= tens[i]; if (e1 &= ~15) { e1 >>= 4; if (e1 >= 1 << n_bigtens) goto undfl; for(j = 0; e1 > 1; j++, e1 >>= 1) if (e1 & 1) rv *= tinytens[j]; /* The last multiplication could underflow. */ rv0 = rv; rv *= tinytens[j]; if (rv == g_double_zero) { rv = 2.*rv0; rv *= tinytens[j]; if (rv == g_double_zero) { undfl: rv = 0.; // errno = ERANGE; if (ok != 0) *ok = false; if (bd0) goto retfree; goto ret; } setWord0(&rv, Tiny0); setWord1(&rv, Tiny1); /* The refinement below will clean * this approximation up. */ } } } /* 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); for(;;) { bd = Balloc(bd0->k); Bcopy(bd, bd0); bb = d2b(rv, &bbe, &bbbits); /* rv = bb * 2^bbe */ bs = i2b(1); 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 Sudden_Underflow #ifdef IBM j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); #else j = P + 1 - bbbits; #endif #else i = bbe + bbbits - 1; /* logb(rv) */ if (i < Emin) /* denormal */ j = bbe + (P-Emin); else j = P + 1 - bbbits; #endif bb2 += j; bd2 += j; 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); bb1 = mult(bs, bb); Bfree(bb); bb = bb1; } if (bb2 > 0) bb = lshift(bb, bb2); if (bd5 > 0) bd = pow5mult(bd, bd5); if (bd2 > 0) bd = lshift(bd, bd2); if (bs2 > 0) bs = lshift(bs, bs2); delta = diff(bb, bd); dsign = delta->sign; delta->sign = 0; i = cmp(delta, bs); if (i < 0) { /* Error is less than half an ulp -- check for * special case of mantissa a power of two. */ if (dsign || getWord1(rv) || getWord0(rv) & Bndry_mask) break; delta = lshift(delta,Log2P); if (cmp(delta, bs) > 0) goto drop_down; break; } if (i == 0) { /* exactly half-way between */ if (dsign) { if ((getWord0(rv) & Bndry_mask1) == Bndry_mask1 && getWord1(rv) == 0xffffffff) { /*boundary case -- increment exponent*/ setWord0(&rv, (getWord0(rv) & Exp_mask) + Exp_msk1 #ifdef IBM | Exp_msk1 >> 4 #endif ); setWord1(&rv, 0); break; } } else if (!(getWord0(rv) & Bndry_mask) && !getWord1(rv)) { drop_down: /* boundary case -- decrement exponent */ #ifdef Sudden_Underflow L = getWord0(rv) & Exp_mask; #ifdef IBM if (L < Exp_msk1) #else if (L <= Exp_msk1) #endif goto undfl; L -= Exp_msk1; #else L = (getWord0(rv) & Exp_mask) - Exp_msk1; #endif setWord0(&rv, L | Bndry_mask1); setWord1(&rv, 0xffffffff); #ifdef IBM goto cont; #else break; #endif } #ifndef ROUND_BIASED if (!(getWord1(rv) & LSB)) break; #endif if (dsign) rv += ulp(rv); #ifndef ROUND_BIASED else { rv -= ulp(rv); #ifndef Sudden_Underflow if (rv == g_double_zero) goto undfl; #endif } #endif break; } if ((aadj = ratio(delta, bs)) <= 2.) { if (dsign) aadj = aadj1 = 1.; else if (getWord1(rv) || getWord0(rv) & Bndry_mask) { #ifndef Sudden_Underflow if (getWord1(rv) == Tiny1 && !getWord0(rv)) goto undfl; #endif 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(FLT_ROUNDS) { 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 } y = getWord0(rv) & Exp_mask; /* Check for overflow */ if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { rv0 = rv; setWord0(&rv, getWord0(rv) - P*Exp_msk1); adj = aadj1 * ulp(rv); rv += adj; if ((getWord0(rv) & Exp_mask) >= Exp_msk1*(DBL_MAX_EXP+Bias-P)) { if (getWord0(rv0) == Big0 && getWord1(rv0) == Big1) goto ovfl; setWord0(&rv, Big0); setWord1(&rv, Big1); goto cont; } else setWord0(&rv, getWord0(rv) + P*Exp_msk1); } else { #ifdef Sudden_Underflow if ((getWord0(rv) & Exp_mask) <= P*Exp_msk1) { rv0 = rv; setWord0(&rv, getWord0(rv) + P*Exp_msk1); adj = aadj1 * ulp(rv); rv += adj; #ifdef IBM if ((getWord0(rv) & Exp_mask) < P*Exp_msk1) #else if ((getWord0(rv) & Exp_mask) <= P*Exp_msk1) #endif { if (getWord0(rv0) == Tiny0 && getWord1(rv0) == Tiny1) goto undfl; setWord0(&rv, Tiny0); setWord1(&rv, Tiny1); goto cont; } else setWord0(&rv, getWord0(rv) - P*Exp_msk1); } else { adj = aadj1 * ulp(rv); rv += adj; } #else /* Compute adj so that the IEEE rounding rules will * correctly round rv + adj in some half-way cases. * If rv * ulp(rv) is denormalized (i.e., * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid * trouble from bits lost to denormalization; * example: 1.2e-307 . */ if (y <= (P-1)*Exp_msk1 && aadj >= 1.) { aadj1 = int(aadj + 0.5); if (!dsign) aadj1 = -aadj1; } adj = aadj1 * ulp(rv); rv += adj; #endif } z = getWord0(rv) & Exp_mask; if (y == z) { /* Can we stop now? */ L = Long(aadj); aadj -= L; /* The tolerances below are conservative. */ if (dsign || getWord1(rv) || getWord0(rv) & Bndry_mask) { if (aadj < .4999999 || aadj > .5000001) break; } else if (aadj < .4999999/FLT_RADIX) break; } cont: Bfree(bb); Bfree(bd); Bfree(bs); Bfree(delta); } retfree: Bfree(bb); Bfree(bd); Bfree(bs); Bfree(bd0); Bfree(delta); ret: if (se) *se = s; return sign ? -rv : rv; } static int quorem(Bigint *b, Bigint *S) { int n; Long borrow, y; ULong carry, q, ys; ULong *bx, *bxe, *sx, *sxe; #ifdef Pack_32 Long z; ULong si, zs; #endif n = S->wds; #ifdef BSD_QDTOA_DEBUG /*debug*/ if (b->wds > n) /*debug*/ Bug("oversize b in quorem"); #endif if (b->wds < n) return 0; sx = S->x; sxe = sx + --n; bx = b->x; bxe = bx + n; q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ #ifdef BSD_QDTOA_DEBUG /*debug*/ if (q > 9) /*debug*/ Bug("oversized quotient in quorem"); #endif if (q) { borrow = 0; carry = 0; do { #ifdef Pack_32 si = *sx++; ys = (si & 0xffff) * q + carry; zs = (si >> 16) * q + (ys >> 16); carry = zs >> 16; y = (*bx & 0xffff) - (ys & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); z = (*bx >> 16) - (zs & 0xffff) + borrow; borrow = z >> 16; Sign_Extend(borrow, z); Storeinc(bx, z, y); #else ys = *sx++ * q + carry; carry = ys >> 16; y = *bx - (ys & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); *bx++ = y & 0xffff; #endif } while(sx <= sxe); if (!*bxe) { bx = b->x; while(--bxe > bx && !*bxe) --n; b->wds = n; } } if (cmp(b, S) >= 0) { q++; borrow = 0; carry = 0; bx = b->x; sx = S->x; do { #ifdef Pack_32 si = *sx++; ys = (si & 0xffff) + carry; zs = (si >> 16) + (ys >> 16); carry = zs >> 16; y = (*bx & 0xffff) - (ys & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); z = (*bx >> 16) - (zs & 0xffff) + borrow; borrow = z >> 16; Sign_Extend(borrow, z); Storeinc(bx, z, y); #else ys = *sx++ + carry; carry = ys >> 16; y = *bx - (ys & 0xffff) + borrow; borrow = y >> 16; Sign_Extend(borrow, y); *bx++ = y & 0xffff; #endif } while(sx <= sxe); bx = b->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. 92-101]. * * 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. */ #if defined(Q_OS_WIN) && defined (Q_CC_GNU) && !defined(_clear87) // See QTBUG-7576 extern "C" { __attribute__ ((dllimport)) unsigned int __cdecl __MINGW_NOTHROW _control87 (unsigned int unNew, unsigned int unMask); __attribute__ ((dllimport)) unsigned int __cdecl __MINGW_NOTHROW _clearfp (void); /* Clear the FPU status word */ } # define _clear87 _clearfp #endif /* This actually sometimes returns a pointer to a string literal cast to a char*. Do NOT try to modify the return value. */ Q_CORE_EXPORT char *qdtoa ( double d, int mode, int ndigits, int *decpt, int *sign, char **rve, char **resultp) { // Some values of the floating-point control word can cause _qdtoa to crash with an underflow. // We set a safe value here. #ifdef Q_OS_WIN _clear87(); unsigned int oldbits = _control87(0, 0); #ifndef MCW_EM # ifdef _MCW_EM # define MCW_EM _MCW_EM # else # define MCW_EM 0x0008001F # endif #endif _control87(MCW_EM, MCW_EM); #endif #if defined(Q_OS_LINUX) && !defined(__UCLIBC__) fenv_t envp; feholdexcept(&envp); #endif char *s = _qdtoa(d, mode, ndigits, decpt, sign, rve, resultp); #ifdef Q_OS_WIN _clear87(); #ifndef _M_X64 _control87(oldbits, 0xFFFFF); #else # ifndef _MCW_EM // Potentially missing on MinGW # define _MCW_EM 0x0008001f # endif # ifndef _MCW_RC # define _MCW_RC 0x00000300 # endif # ifndef _MCW_DN # define _MCW_DN 0x03000000 # endif _control87(oldbits, _MCW_EM|_MCW_DN|_MCW_RC); #endif //_M_X64 #endif //Q_OS_WIN #if defined(Q_OS_LINUX) && !defined(__UCLIBC__) fesetenv(&envp); #endif return s; } static char *_qdtoa( NEEDS_VOLATILE double d, int mode, int ndigits, int *decpt, int *sign, char **rve, char **resultp) { /* 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 9999. 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. 4-9 should give the same return values as 2-3, i.e., 4 <= mode <= 9 ==> same return as mode 2 + (mode & 1). These modes are mainly for debugging; often they run slower but sometimes faster than modes 2-3. 4,5,8,9 ==> left-to-right digit generation. 6-9 ==> 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, ilim0, j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, try_quick; int ilim = 0, ilim1 = 0, spec_case = 0; /* pacify gcc */ Long L; #ifndef Sudden_Underflow int denorm; ULong x; #endif Bigint *b, *b1, *delta, *mhi, *S; Bigint *mlo = NULL; /* pacify gcc */ double d2; double ds, eps; char *s, *s0; if (getWord0(d) & Sign_bit) { /* set sign for everything, including 0's and NaNs */ *sign = 1; setWord0(&d, getWord0(d) & ~Sign_bit); /* clear sign bit */ } else *sign = 0; #if defined(IEEE_Arith) + defined(VAX) #ifdef IEEE_Arith if ((getWord0(d) & Exp_mask) == Exp_mask) #else if (getWord0(d) == 0x8000) #endif { /* Infinity or NaN */ *decpt = 9999; s = #ifdef IEEE_Arith !getWord1(d) && !(getWord0(d) & 0xfffff) ? const_cast("Infinity") : #endif const_cast("NaN"); if (rve) *rve = #ifdef IEEE_Arith s[3] ? s + 8 : #endif s + 3; return s; } #endif #ifdef IBM d += 0; /* normalize */ #endif if (d == g_double_zero) { *decpt = 1; s = const_cast("0"); if (rve) *rve = s + 1; return s; } b = d2b(d, &be, &bbits); i = (int)(getWord0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); #ifndef Sudden_Underflow if (i != 0) { #endif d2 = d; setWord0(&d2, getWord0(d2) & Frac_mask1); setWord0(&d2, getWord0(d2) | Exp_11); #ifdef IBM if (j = 11 - hi0bits(getWord0(d2) & Frac_mask)) d2 /= 1 << j; #endif /* 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; #ifdef IBM i <<= 2; i += j; #endif #ifndef Sudden_Underflow denorm = 0; } else { /* d is denormalized */ i = bbits + be + (Bias + (P-1) - 1); x = i > 32 ? getWord0(d) << (64 - i) | getWord1(d) >> (i - 32) : getWord1(d) << (32 - i); d2 = x; setWord0(&d2, getWord0(d2) - 31*Exp_msk1); /* adjust exponent */ i -= (Bias + (P-1) - 1) + 1; denorm = 1; } #endif ds = (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 (d < 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; try_quick = 1; 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; /* no break */ case 4: if (ndigits <= 0) ndigits = 1; ilim = ilim1 = i = ndigits; break; case 3: leftright = 0; /* no break */ case 5: i = ndigits + k + 1; ilim = i; ilim1 = i - 1; if (i <= 0) i = 1; } QT_TRY { *resultp = static_cast(malloc(i + 1)); Q_CHECK_PTR(*resultp); } QT_CATCH(...) { Bfree(b); QT_RETHROW; } s = s0 = *resultp; if (ilim >= 0 && ilim <= Quick_max && try_quick) { /* Try to get by with floating-point arithmetic. */ i = 0; d2 = d; 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; d /= bigtens[n_bigtens-1]; ieps++; } for(; j; j >>= 1, i++) if (j & 1) { ieps++; ds *= bigtens[i]; } d /= ds; } else if ((j1 = -k) != 0) { d *= tens[j1 & 0xf]; for(j = j1 >> 4; j; j >>= 1, i++) if (j & 1) { ieps++; d *= bigtens[i]; } } if (k_check && d < 1. && ilim > 0) { if (ilim1 <= 0) goto fast_failed; ilim = ilim1; k--; d *= 10.; ieps++; } eps = ieps*d + 7.; setWord0(&eps, getWord0(eps) - (P-1)*Exp_msk1); if (ilim == 0) { S = mhi = 0; d -= 5.; if (d > eps) goto one_digit; if (d < -eps) goto no_digits; goto fast_failed; } #ifndef No_leftright if (leftright) { /* Use Steele & White method of only * generating digits needed. */ eps = 0.5/tens[ilim-1] - eps; for(i = 0;;) { L = Long(d); d -= L; *s++ = '0' + int(L); if (d < eps) goto ret1; if (1. - d < eps) goto bump_up; if (++i >= ilim) break; eps *= 10.; d *= 10.; } } else { #endif /* Generate ilim digits, then fix them up. */ eps *= tens[ilim-1]; for(i = 1;; i++, d *= 10.) { L = Long(d); d -= L; *s++ = '0' + int(L); if (i == ilim) { if (d > 0.5 + eps) goto bump_up; else if (d < 0.5 - eps) { while(*--s == '0') {} s++; goto ret1; } break; } } #ifndef No_leftright } #endif fast_failed: s = s0; d = 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 || d <= 5*ds) goto no_digits; goto one_digit; } for(i = 1;; i++) { L = Long(d / ds); d -= L*ds; #ifdef Check_FLT_ROUNDS /* If FLT_ROUNDS == 2, L will usually be high by 1 */ if (d < 0) { L--; d += ds; } #endif *s++ = '0' + int(L); if (i == ilim) { d += d; if (d > ds || (d == ds && L & 1)) { bump_up: while(*--s == '9') if (s == s0) { k++; *s = '0'; break; } ++*s++; } break; } if ((d *= 10.) == g_double_zero) break; } goto ret1; } m2 = b2; m5 = b5; mhi = mlo = 0; if (leftright) { if (mode < 2) { i = #ifndef Sudden_Underflow denorm ? be + (Bias + (P-1) - 1 + 1) : #endif #ifdef IBM 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); #else 1 + P - bbits; #endif } else { j = ilim - 1; if (m5 >= j) m5 -= j; else { s5 += j -= m5; b5 += j; m5 = 0; } if ((i = ilim) < 0) { m2 -= i; i = 0; } } b2 += i; s2 += i; mhi = i2b(1); } 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); b1 = mult(mhi, b); Bfree(b); b = b1; } if ((j = b5 - m5) != 0) b = pow5mult(b, j); } else b = pow5mult(b, b5); } S = i2b(1); if (s5 > 0) S = pow5mult(S, s5); /* Check for special case that d is a normalized power of 2. */ if (mode < 2) { if (!getWord1(d) && !(getWord0(d) & Bndry_mask) #ifndef Sudden_Underflow && getWord0(d) & Exp_mask #endif ) { /* The special case */ b2 += Log2P; s2 += Log2P; spec_case = 1; } else spec_case = 0; } /* 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 * and for all and pass them and a shift to quorem, so it * can do shifts and ors to compute the numerator for q. */ #ifdef Pack_32 if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f) != 0) i = 32 - i; #else if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf) i = 16 - i; #endif 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); if (s2 > 0) S = lshift(S, s2); if (k_check) { if (cmp(b,S) < 0) { k--; b = multadd(b, 10, 0); /* we botched the k estimate */ if (leftright) mhi = multadd(mhi, 10, 0); ilim = ilim1; } } if (ilim <= 0 && mode > 2) { if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 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); /* Compute mlo -- check for special case * that d is a normalized power of 2. */ mlo = mhi; if (spec_case) { mhi = Balloc(mhi->k); Bcopy(mhi, mlo); mhi = lshift(mhi, Log2P); } 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); j1 = delta->sign ? 1 : cmp(b, delta); Bfree(delta); #ifndef ROUND_BIASED if (j1 == 0 && !mode && !(getWord1(d) & 1)) { if (dig == '9') goto round_9_up; if (j > 0) dig++; *s++ = dig; goto ret; } #endif if (j < 0 || (j == 0 && !mode #ifndef ROUND_BIASED && !(getWord1(d) & 1) #endif )) { if (j1 > 0) { b = lshift(b, 1); j1 = cmp(b, S); if ((j1 > 0 || (j1 == 0 && dig & 1)) && dig++ == '9') goto round_9_up; } *s++ = dig; goto ret; } if (j1 > 0) { if (dig == '9') { /* possible if i == 1 */ round_9_up: *s++ = '9'; goto roundoff; } *s++ = dig + 1; goto ret; } *s++ = dig; if (i == ilim) break; b = multadd(b, 10, 0); if (mlo == mhi) mlo = mhi = multadd(mhi, 10, 0); else { mlo = multadd(mlo, 10, 0); mhi = multadd(mhi, 10, 0); } } } else for(i = 1;; i++) { *s++ = dig = quorem(b,S) + '0'; if (i >= ilim) break; b = multadd(b, 10, 0); } /* Round off last digit */ b = lshift(b, 1); 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 { while(*--s == '0') {} s++; } ret: Bfree(S); if (mhi) { if (mlo && mlo != mhi) Bfree(mlo); Bfree(mhi); } ret1: Bfree(b); if (s == s0) { /* don't return empty string */ *s++ = '0'; k = 0; } *s = 0; *decpt = k + 1; if (rve) *rve = s; return s0; } #else // NOT thread safe! #include Q_CORE_EXPORT char *qdtoa( double d, int mode, int ndigits, int *decpt, int *sign, char **rve, char **resultp) { if(rve) *rve = 0; char *res; if (mode == 0) ndigits = 80; if (mode == 3) res = fcvt(d, ndigits, decpt, sign); else res = ecvt(d, ndigits, decpt, sign); int n = qstrlen(res); if (mode == 0) { // remove trailing 0's const int stop = qMax(1, *decpt); int i; for (i = n-1; i >= stop; --i) { if (res[i] != '0') break; } n = i + 1; } *resultp = static_cast(malloc(n + 1)); Q_CHECK_PTR(resultp); qstrncpy(*resultp, res, n + 1); return *resultp; } Q_CORE_EXPORT double qstrtod(const char *s00, const char **se, bool *ok) { double ret = strtod((char*)s00, (char**)se); if (ok) { if((ret == 0.0l && errno == ERANGE) || ret == HUGE_VAL || ret == -HUGE_VAL) *ok = false; else *ok = true; // the result will be that we don't report underflow in this case } return ret; } #endif // QT_QLOCALE_USES_FCVT QT_END_NAMESPACE