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Diffstat (limited to 'mysql/libmariadb/ma_dtoa.c')
| -rw-r--r-- | mysql/libmariadb/ma_dtoa.c | 1925 |
1 files changed, 1925 insertions, 0 deletions
diff --git a/mysql/libmariadb/ma_dtoa.c b/mysql/libmariadb/ma_dtoa.c new file mode 100644 index 0000000..e45f792 --- /dev/null +++ b/mysql/libmariadb/ma_dtoa.c @@ -0,0 +1,1925 @@ +/* Copyright (c) 2007, 2012, Oracle and/or its affiliates. All rights reserved. + 2016 MariaDB Corporation AB + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public + License as published by the Free Software Foundation; version 2 + of the License. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program; if not, write to the Free Software + Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA */ + +/**************************************************************** + + This file incorporates work covered by the following copyright and + permission notice: + + 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. + + ***************************************************************/ + +//#include "strings_def.h" +//#include <my_base.h> /* for EOVERFLOW on Windows */ +#include <ma_global.h> +#include <memory.h> +#include "ma_string.h" + +/** + Appears to suffice to not call malloc() in most cases. + @todo + see if it is possible to get rid of malloc(). + this constant is sufficient to avoid malloc() on all inputs I have tried. +*/ +#define DTOA_BUFF_SIZE (460 * sizeof(void *)) + +/* Magic value returned by dtoa() to indicate overflow */ +#define DTOA_OVERFLOW 9999 + +static char *dtoa(double, int, int, int *, int *, char **, char *, size_t); +static void dtoa_free(char *, char *, size_t); + +/** + @brief + Converts a given floating point number to a zero-terminated string + representation using the 'f' format. + + @details + This function is a wrapper around dtoa() to do 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, + in which case we print '0\0' to the output string and indicate an overflow. + + @param x the input floating point number. + @param precision the number of digits after the decimal point. + All properties of sprintf() apply: + - if the number of significant digits after the decimal + point is less than precision, the resulting string is + right-padded with zeros + - if the precision is 0, no decimal point appears + - if a decimal point appears, at least one digit appears + before it + @param to pointer to the output buffer. The longest string which + my_fcvt() can return is FLOATING_POINT_BUFFER bytes + (including the terminating '\0'). + @param error if not NULL, points to a location where the status of + conversion is stored upon return. + FALSE successful conversion + TRUE the input number is [-,+]infinity or nan. + The output string in this case is always '0'. + @return number of written characters (excluding terminating '\0') +*/ + +size_t ma_fcvt(double x, int precision, char *to, my_bool *error) +{ + int decpt, sign, len, i; + char *res, *src, *end, *dst= to; + char buf[DTOA_BUFF_SIZE]; + DBUG_ASSERT(precision >= 0 && precision < NOT_FIXED_DEC && to != NULL); + + res= dtoa(x, 5, precision, &decpt, &sign, &end, buf, sizeof(buf)); + + if (decpt == DTOA_OVERFLOW) + { + dtoa_free(res, buf, sizeof(buf)); + *to++= '0'; + *to= '\0'; + if (error != NULL) + *error= TRUE; + return 1; + } + + src= res; + len= (int)(end - src); + + if (sign) + *dst++= '-'; + + if (decpt <= 0) + { + *dst++= '0'; + *dst++= '.'; + for (i= decpt; i < 0; i++) + *dst++= '0'; + } + + for (i= 1; i <= len; i++) + { + *dst++= *src++; + if (i == decpt && i < len) + *dst++= '.'; + } + while (i++ <= decpt) + *dst++= '0'; + + if (precision > 0) + { + if (len <= decpt) + *dst++= '.'; + + for (i= precision - MAX(0, (len - decpt)); i > 0; i--) + *dst++= '0'; + } + + *dst= '\0'; + if (error != NULL) + *error= FALSE; + + dtoa_free(res, buf, sizeof(buf)); + + return dst - to; +} + +/** + @brief + Converts a given floating point number to a zero-terminated string + representation with a given field width using the 'e' format + (aka scientific notation) or the 'f' one. + + @details + The format is chosen automatically to provide the most number of significant + digits (and thus, precision) with a given field width. In many cases, the + result is similar to that of sprintf(to, "%g", x) with a few notable + differences: + - the conversion is usually more precise than C library functions. + - there is no 'precision' argument. instead, we specify the number of + characters available for conversion (i.e. a field width). + - the result never exceeds the specified field width. If the field is too + short to contain even a rounded decimal representation, ma_gcvt() + indicates overflow and truncates the output string to the specified width. + - float-type arguments are handled differently than double ones. For a + float input number (i.e. when the 'type' argument is MY_GCVT_ARG_FLOAT) + we deliberately limit the precision of conversion by FLT_DIG digits to + avoid garbage past the significant digits. + - unlike sprintf(), in cases where the 'e' format is preferred, we don't + zero-pad the exponent to save space for significant digits. The '+' sign + for a positive exponent does not appear for the same reason. + + @param x the input floating point number. + @param type is either MY_GCVT_ARG_FLOAT or MY_GCVT_ARG_DOUBLE. + Specifies the type of the input number (see notes above). + @param width field width in characters. The minimal field width to + hold any number representation (albeit rounded) is 7 + characters ("-Ne-NNN"). + @param to pointer to the output buffer. The result is always + zero-terminated, and the longest returned string is thus + 'width + 1' bytes. + @param error if not NULL, points to a location where the status of + conversion is stored upon return. + FALSE successful conversion + TRUE the input number is [-,+]infinity or nan. + The output string in this case is always '0'. + @return number of written characters (excluding terminating '\0') + + @todo + Check if it is possible and makes sense to do our own rounding on top of + dtoa() instead of calling dtoa() twice in (rare) cases when the resulting + string representation does not fit in the specified field width and we want + to re-round the input number with fewer significant digits. Examples: + + ma_gcvt(-9e-3, ..., 4, ...); + ma_gcvt(-9e-3, ..., 2, ...); + ma_gcvt(1.87e-3, ..., 4, ...); + ma_gcvt(55, ..., 1, ...); + + We do our best to minimize such cases by: + + - passing to dtoa() the field width as the number of significant digits + + - removing the sign of the number early (and decreasing the width before + passing it to dtoa()) + + - choosing the proper format to preserve the most number of significant + digits. +*/ + +size_t ma_gcvt(double x, my_gcvt_arg_type type, int width, char *to, + my_bool *error) +{ + int decpt, sign, len, exp_len; + char *res, *src, *end, *dst= to, *dend= dst + width; + char buf[DTOA_BUFF_SIZE]; + my_bool have_space, force_e_format; + DBUG_ASSERT(width > 0 && to != NULL); + + /* We want to remove '-' from equations early */ + if (x < 0.) + width--; + + res= dtoa(x, 4, type == MY_GCVT_ARG_DOUBLE ? width : MIN(width, FLT_DIG), + &decpt, &sign, &end, buf, sizeof(buf)); + if (decpt == DTOA_OVERFLOW) + { + dtoa_free(res, buf, sizeof(buf)); + *to++= '0'; + *to= '\0'; + if (error != NULL) + *error= TRUE; + return 1; + } + + if (error != NULL) + *error= FALSE; + + src= res; + len= (int)(end - res); + + /* + 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); + + /* + 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= (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. + 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 DBL_DIG. + */ + (!have_space || (decpt >= -DBL_DIG + 1 && + (decpt <= DBL_DIG || 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; +} + +/**************************************************************** + * + * 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 +#else +#define Rounding 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= 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; +} + + +static int hi0bits(register ULong x) +{ + register 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) +{ + register int k; + register 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 }; + my_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 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 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 + + +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, UNINIT_VAR(ilim), ilim0, + UNINIT_VAR(ilim1), 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, *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; + /* 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; + } + 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; +} |