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ruby--ruby/missing/dtoa.c

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Split dtoa.c git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@67022 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
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/****************************************************************
*
* 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 "."). */
/* 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.
*/
/* 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 IBM for IBM mainframe-style floating-point arithmetic.
* #define VAX for VAX-style floating-point arithmetic (D_floating).
* #define No_leftright to omit left-right logic in fast floating-point
* computation of dtoa.
* #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
* and strtod 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.
* #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 NO_LONG_LONG on machines that do not have a "long long"
* integer type (of >= 64 bits). On such machines, you can
* #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. If long long is available and the name is
* something other than "long long", #define Llong to be the name,
* and if "unsigned Llong" does not work as an unsigned version of
* Llong, #define #ULLong to be the corresponding unsigned type.
* #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.
* #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
* memory allocations from a private pool of memory when possible.
* When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
* unless #defined to be a different length. This default length
* suffices to get rid of MALLOC calls except for unusual cases,
* such as decimal-to-binary conversion of a very long string of
* digits. The longest string dtoa can return is about 751 bytes
* long. For conversions by strtod of strings of 800 digits and
* all dtoa conversions in single-threaded executions with 8-byte
* pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
* pointers, PRIVATE_MEM >= 7112 appears adequate.
* #define INFNAN_CHECK on IEEE systems to cause strtod to check for
* Infinity and NaN (case insensitively). On some systems (e.g.,
* some HP systems), it may be necessary to #define NAN_WORD0
* appropriately -- to the most significant word of a quiet NaN.
* (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
* When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
* strtod also accepts (case insensitively) strings of the form
* NaN(x), where x is a string of hexadecimal digits and spaces;
* if there is only one string of hexadecimal digits, it is taken
* for the 52 fraction bits of the resulting NaN; if there are two
* or more strings of hex digits, the first is for the high 20 bits,
* the second and subsequent for the low 32 bits, with intervening
* white space ignored; but if this results in none of the 52
* fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
* and NAN_WORD1 are used instead.
* #define MULTIPLE_THREADS if the system offers preemptively scheduled
* multiple threads. In this case, you must provide (or suitably
* #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
* by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
* in pow5mult, ensures lazy evaluation of only one copy of high
* powers of 5; omitting this lock would introduce a small
* probability of wasting memory, but would otherwise be harmless.)
* You must also invoke freedtoa(s) to free the value s returned by
* dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
* #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
* avoids underflows on inputs whose result does not underflow.
* If you #define NO_IEEE_Scale on a machine that uses IEEE-format
* floating-point numbers and flushes underflows to zero rather
* than implementing gradual underflow, then you must also #define
* Sudden_Underflow.
* #define YES_ALIAS to permit aliasing certain double values with
* arrays of ULongs. This leads to slightly better code with
* some compilers and was always used prior to 19990916, but it
* is not strictly legal and can cause trouble with aggressively
* optimizing compilers (e.g., gcc 2.95.1 under -O2).
* #define USE_LOCALE to use the current locale's decimal_point value.
* #define SET_INEXACT if IEEE arithmetic is being used and extra
* computation should be done to set the inexact flag when the
* result is inexact and avoid setting inexact when the result
* is exact. In this case, dtoa.c must be compiled in
* an environment, perhaps provided by #include "dtoa.c" in a
* suitable wrapper, that defines two functions,
* int get_inexact(void);
* void clear_inexact(void);
* such that get_inexact() returns a nonzero value if the
* inexact bit is already set, and clear_inexact() sets the
* inexact bit to 0. When SET_INEXACT is #defined, strtod
* also does extra computations to set the underflow and overflow
* flags when appropriate (i.e., when the result is tiny and
* inexact or when it is a numeric value rounded to +-infinity).
* #define NO_ERRNO if strtod should not assign errno = ERANGE when
* the result overflows to +-Infinity or underflows to 0.
*/
#ifdef WORDS_BIGENDIAN
#define IEEE_BIG_ENDIAN
#else
#define IEEE_LITTLE_ENDIAN
#endif
#ifdef __vax__
#define VAX
#undef IEEE_BIG_ENDIAN
#undef IEEE_LITTLE_ENDIAN
#endif
#if defined(__arm__) && !defined(__VFP_FP__)
#define IEEE_BIG_ENDIAN
#undef IEEE_LITTLE_ENDIAN
#endif
#undef Long
#undef ULong
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#include <limits.h>
#if (INT_MAX >> 30) && !(INT_MAX >> 31)
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#define Long int
#define ULong unsigned int
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#elif (LONG_MAX >> 30) && !(LONG_MAX >> 31)
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#define Long long int
#define ULong unsigned long int
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#else
#error No 32bit integer
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#endif
#if HAVE_LONG_LONG
#define Llong LONG_LONG
#else
#define NO_LONG_LONG
#endif
#ifdef DEBUG
#include <stdio.h>
#define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);}
#endif
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#ifndef ISDIGIT
#include <ctype.h>
#define ISDIGIT(c) isdigit(c)
#endif
#include <errno.h>
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#include <stdlib.h>
#include <string.h>
#ifdef USE_LOCALE
#include <locale.h>
#endif
#ifdef MALLOC
extern void *MALLOC(size_t);
#else
#define MALLOC xmalloc
#endif
#ifdef FREE
extern void FREE(void*);
#else
#define FREE xfree
#endif
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#ifndef NO_SANITIZE
#define NO_SANITIZE(x, y) y
#endif
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#ifndef Omit_Private_Memory
#ifndef PRIVATE_MEM
#define PRIVATE_MEM 2304
#endif
#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
#endif
#undef IEEE_Arith
#undef Avoid_Underflow
#ifdef IEEE_BIG_ENDIAN
#define IEEE_Arith
#endif
#ifdef IEEE_LITTLE_ENDIAN
#define IEEE_Arith
#endif
#ifdef Bad_float_h
#ifdef IEEE_Arith
#define DBL_DIG 15
#define DBL_MAX_10_EXP 308
#define DBL_MAX_EXP 1024
#define FLT_RADIX 2
#endif /*IEEE_Arith*/
#ifdef IBM
#define DBL_DIG 16
#define DBL_MAX_10_EXP 75
#define DBL_MAX_EXP 63
#define FLT_RADIX 16
#define DBL_MAX 7.2370055773322621e+75
#endif
#ifdef VAX
#define DBL_DIG 16
#define DBL_MAX_10_EXP 38
#define DBL_MAX_EXP 127
#define FLT_RADIX 2
#define DBL_MAX 1.7014118346046923e+38
#endif
#ifndef LONG_MAX
#define LONG_MAX 2147483647
#endif
#else /* ifndef Bad_float_h */
#include <float.h>
#endif /* Bad_float_h */
#include <math.h>
#ifdef __cplusplus
extern "C" {
#if 0
} /* satisfy cc-mode */
#endif
#endif
#ifndef hexdigit
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static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF";
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#endif
#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
#endif
typedef union { double d; ULong L[2]; } U;
#ifdef YES_ALIAS
typedef double double_u;
# define dval(x) (x)
# ifdef IEEE_LITTLE_ENDIAN
# define word0(x) (((ULong *)&(x))[1])
# define word1(x) (((ULong *)&(x))[0])
# else
# define word0(x) (((ULong *)&(x))[0])
# define word1(x) (((ULong *)&(x))[1])
# endif
#else
typedef U double_u;
# ifdef IEEE_LITTLE_ENDIAN
# define word0(x) ((x).L[1])
# define word1(x) ((x).L[0])
# else
# define word0(x) ((x).L[0])
# define word1(x) ((x).L[1])
# endif
# define dval(x) ((x).d)
#endif
/* The following definition of Storeinc is appropriate for MIPS processors.
* An alternative that might be better on some machines is
* #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
*/
#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
#define Storeinc(a,b,c) (((unsigned short *)(a))[1] = (unsigned short)(b), \
((unsigned short *)(a))[0] = (unsigned short)(c), (a)++)
#else
#define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \
((unsigned short *)(a))[1] = (unsigned short)(c), (a)++)
#endif
/* #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) */
#ifdef IEEE_Arith
#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 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 Tiny0 0
#define Tiny1 1
#define Quick_max 14
#define Int_max 14
#ifndef NO_IEEE_Scale
#define Avoid_Underflow
#ifdef Flush_Denorm /* debugging option */
#undef Sudden_Underflow
#endif
#endif
#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
#else /* ifndef IEEE_Arith */
#undef Check_FLT_ROUNDS
#undef Honor_FLT_ROUNDS
#undef SET_INEXACT
#undef Sudden_Underflow
#define Sudden_Underflow
#ifdef IBM
#undef Flt_Rounds
#define Flt_Rounds 0
#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 */
#undef Flt_Rounds
#define Flt_Rounds 1
#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 /* IBM, VAX */
#endif /* IEEE_Arith */
#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 Pack_32
#define Pack_32
#endif
#define FFFFFFFF 0xffffffffUL
#ifdef NO_LONG_LONG
#undef ULLong
#ifdef Just_16
#undef Pack_32
/* 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.
*/
#endif
#else /* long long available */
#ifndef Llong
#define Llong long long
#endif
#ifndef ULLong
#define ULLong unsigned Llong
#endif
#endif /* NO_LONG_LONG */
#define MULTIPLE_THREADS 1
#ifndef MULTIPLE_THREADS
#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
#define FREE_DTOA_LOCK(n) /*nothing*/
#else
#define ACQUIRE_DTOA_LOCK(n) /*unused right now*/
#define FREE_DTOA_LOCK(n) /*unused right now*/
#endif
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#ifndef ATOMIC_PTR_CAS
#define ATOMIC_PTR_CAS(var, old, new) ((var) = (new), (old))
#endif
#ifndef LIKELY
#define LIKELY(x) (x)
#endif
#ifndef UNLIKELY
#define UNLIKELY(x) (x)
#endif
#ifndef ASSUME
#define ASSUME(x) (void)(x)
#endif
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#define Kmax 15
struct Bigint {
struct Bigint *next;
int k, maxwds, sign, wds;
ULong x[1];
};
typedef struct Bigint Bigint;
static Bigint *freelist[Kmax+1];
static Bigint *
Balloc(int k)
{
int x;
Bigint *rv;
#ifndef Omit_Private_Memory
size_t len;
#endif
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rv = 0;
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ACQUIRE_DTOA_LOCK(0);
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if (k <= Kmax) {
rv = freelist[k];
while (rv) {
Bigint *rvn = rv;
rv = ATOMIC_PTR_CAS(freelist[k], rv, rv->next);
if (LIKELY(rvn == rv)) {
ASSUME(rv);
break;
}
}
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}
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if (!rv) {
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x = 1 << k;
#ifdef Omit_Private_Memory
rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
#else
len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
/sizeof(double);
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if (k <= Kmax) {
double *pnext = pmem_next;
while (pnext - private_mem + len <= PRIVATE_mem) {
double *p = pnext;
pnext = ATOMIC_PTR_CAS(pmem_next, pnext, pnext + len);
if (LIKELY(p == pnext)) {
rv = (Bigint*)pnext;
ASSUME(rv);
break;
}
}
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}
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if (!rv)
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rv = (Bigint*)MALLOC(len*sizeof(double));
#endif
rv->k = k;
rv->maxwds = x;
}
FREE_DTOA_LOCK(0);
rv->sign = rv->wds = 0;
return rv;
}
static void
Bfree(Bigint *v)
{
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Bigint *vn;
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if (v) {
if (v->k > Kmax) {
FREE(v);
return;
}
ACQUIRE_DTOA_LOCK(0);
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do {
vn = v->next = freelist[v->k];
} while (UNLIKELY(ATOMIC_PTR_CAS(freelist[v->k], vn, v) != vn));
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FREE_DTOA_LOCK(0);
}
}
#define Bcopy(x,y) memcpy((char *)&(x)->sign, (char *)&(y)->sign, \
(y)->wds*sizeof(Long) + 2*sizeof(int))
static Bigint *
multadd(Bigint *b, int m, int a) /* multiply by m and add a */
{
int i, wds;
ULong *x;
#ifdef ULLong
ULLong carry, y;
#else
ULong carry, y;
#ifdef Pack_32
ULong xi, z;
#endif
#endif
Bigint *b1;
wds = b->wds;
x = b->x;
i = 0;
carry = a;
do {
#ifdef ULLong
y = *x * (ULLong)m + carry;
carry = y >> 32;
*x++ = (ULong)(y & FFFFFFFF);
#else
#ifdef Pack_32
xi = *x;
y = (xi & 0xffff) * m + carry;
z = (xi >> 16) * m + (y >> 16);
carry = z >> 16;
*x++ = (z << 16) + (y & 0xffff);
#else
y = *x * m + carry;
carry = y >> 16;
*x++ = y & 0xffff;
#endif
#endif
} while (++i < wds);
if (carry) {
if (wds >= b->maxwds) {
b1 = Balloc(b->k+1);
Bcopy(b1, b);
Bfree(b);
b = b1;
}
b->x[wds++] = (ULong)carry;
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(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;
}
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 *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
ULong y;
#ifdef ULLong
ULLong carry, z;
#else
ULong carry, z;
#ifdef Pack_32
ULong z2;
#endif
#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 ULLong
for (; xb < xbe; xc0++) {
if ((y = *xb++) != 0) {
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;
}
}
#else
#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 = (ULong)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 = (ULong)carry;
}
}
#endif
#endif
for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
c->wds = wc;
return c;
}
static Bigint *p5s;
static Bigint *
pow5mult(Bigint *b, int k)
{
Bigint *b1, *p5, *p51;
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Bigint *p5tmp;
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int i;
dtoa.c: constified clang seems to locate never modified local data in the const segment implicitly.
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static const int p05[3] = { 5, 25, 125 };
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if ((i = k & 3) != 0)
b = multadd(b, p05[i-1], 0);
if (!(k >>= 2))
return b;
if (!(p5 = p5s)) {
/* first time */
ACQUIRE_DTOA_LOCK(1);
if (!(p5 = p5s)) {
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p5 = i2b(625);
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p5->next = 0;
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p5tmp = ATOMIC_PTR_CAS(p5s, NULL, p5);
if (UNLIKELY(p5tmp)) {
Bfree(p5);
p5 = p5tmp;
}
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}
FREE_DTOA_LOCK(1);
}
for (;;) {
if (k & 1) {
b1 = mult(b, p5);
Bfree(b);
b = b1;
}
if (!(k >>= 1))
break;
if (!(p51 = p5->next)) {
ACQUIRE_DTOA_LOCK(1);
if (!(p51 = p5->next)) {
dtoa.c: make thread-safe by using atomic CAS
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p51 = mult(p5,p5);
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p51->next = 0;
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p5tmp = ATOMIC_PTR_CAS(p5->next, NULL, p51);
if (UNLIKELY(p5tmp)) {
Bfree(p51);
p51 = p5tmp;
}
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}
FREE_DTOA_LOCK(1);
}
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 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;
}
NO_SANITIZE("unsigned-integer-overflow", static Bigint * diff(Bigint *a, Bigint *b));
static Bigint *
diff(Bigint *a, Bigint *b)
{
Bigint *c;
int i, wa, wb;
ULong *xa, *xae, *xb, *xbe, *xc;
#ifdef ULLong
ULLong borrow, y;
#else
ULong borrow, y;
#ifdef Pack_32
ULong z;
#endif
#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 ULLong
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);
}
#else
#ifdef Pack_32
do {
y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(xc, z, y);
} while (xb < xbe);
while (xa < xae) {
y = (*xa & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
z = (*xa++ >> 16) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(xc, z, y);
}
#else
do {
y = *xa++ - *xb++ - borrow;
borrow = (y & 0x10000) >> 16;
*xc++ = y & 0xffff;
} while (xb < xbe);
while (xa < xae) {
y = *xa++ - borrow;
borrow = (y & 0x10000) >> 16;
*xc++ = y & 0xffff;
}
#endif
#endif
while (!*--xc)
wa--;
c->wds = wa;
return c;
}
static double
ulp(double x_)
{
register Long L;
double_u x, a;
dval(x) = x_;
L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
#ifndef Avoid_Underflow
#ifndef Sudden_Underflow
if (L > 0) {
#endif
#endif
#ifdef IBM
L |= Exp_msk1 >> 4;
#endif
word0(a) = L;
word1(a) = 0;
#ifndef Avoid_Underflow
#ifndef Sudden_Underflow
}
else {
L = -L >> Exp_shift;
if (L < Exp_shift) {
word0(a) = 0x80000 >> L;
word1(a) = 0;
}
else {
word0(a) = 0;
L -= Exp_shift;
word1(a) = L >= 31 ? 1 : 1 << 31 - L;
}
}
#endif
#endif
return dval(a);
}
static double
b2d(Bigint *a, int *e)
{
ULong *xa, *xa0, w, y, z;
int k;
double_u d;
#ifdef VAX
ULong d0, d1;
#else
#define d0 word0(d)
#define d1 word1(d)
#endif
xa0 = a->x;
xa = xa0 + a->wds;
y = *--xa;
#ifdef DEBUG
if (!y) Bug("zero y in b2d");
#endif
k = hi0bits(y);
*e = 32 - k;
#ifdef Pack_32
if (k < Ebits) {
d0 = Exp_1 | y >> (Ebits - k);
w = xa > xa0 ? *--xa : 0;
d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
goto ret_d;
}
z = xa > xa0 ? *--xa : 0;
if (k -= Ebits) {
d0 = Exp_1 | y << k | z >> (32 - k);
y = xa > xa0 ? *--xa : 0;
d1 = z << k | y >> (32 - k);
}
else {
d0 = Exp_1 | y;
d1 = z;
}
#else
if (k < Ebits + 16) {
z = xa > xa0 ? *--xa : 0;
d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
w = xa > xa0 ? *--xa : 0;
y = xa > xa0 ? *--xa : 0;
d1 = 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;
d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
y = xa > xa0 ? *--xa : 0;
d1 = w << k + 16 | y << k;
#endif
ret_d:
#ifdef VAX
word0(d) = d0 >> 16 | d0 << 16;
word1(d) = d1 >> 16 | d1 << 16;
#else
#undef d0
#undef d1
#endif
return dval(d);
}
static Bigint *
d2b(double d_, int *e, int *bits)
{
double_u d;
Bigint *b;
int de, k;
ULong *x, y, z;
#ifndef Sudden_Underflow
int i;
#endif
#ifdef VAX
ULong d0, d1;
#endif
dval(d) = d_;
#ifdef VAX
d0 = word0(d) >> 16 | word0(d) << 16;
d1 = word1(d) >> 16 | word1(d) << 16;
#else
#define d0 word0(d)
#define d1 word1(d)
#endif
#ifdef Pack_32
b = Balloc(1);
#else
b = Balloc(2);
#endif
x = b->x;
z = d0 & Frac_mask;
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
#ifdef Sudden_Underflow
de = (int)(d0 >> Exp_shift);
#ifndef IBM
z |= Exp_msk11;
#endif
#else
if ((de = (int)(d0 >> Exp_shift)) != 0)
z |= Exp_msk1;
#endif
#ifdef Pack_32
if ((y = d1) != 0) {
if ((k = lo0bits(&y)) != 0) {
x[0] = y | z << (32 - k);
z >>= k;
}
else
x[0] = y;
#ifndef Sudden_Underflow
i =
#endif
b->wds = (x[1] = z) ? 2 : 1;
}
else {
#ifdef DEBUG
if (!z)
Bug("Zero passed to d2b");
#endif
k = lo0bits(&z);
x[0] = z;
#ifndef Sudden_Underflow
i =
#endif
b->wds = 1;
k += 32;
}
#else
if (y = d1) {
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 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(word0(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;
}
#undef d0
#undef d1
static double
ratio(Bigint *a, Bigint *b)
{
double_u da, db;
int k, ka, kb;
dval(da) = b2d(a, &ka);
dval(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) {
word0(da) += (k >> 2)*Exp_msk1;
if (k &= 3)
dval(da) *= 1 << k;
}
else {
k = -k;
word0(db) += (k >> 2)*Exp_msk1;
if (k &= 3)
dval(db) *= 1 << k;
}
#else
if (k > 0)
word0(da) += k*Exp_msk1;
else {
k = -k;
word0(db) += k*Exp_msk1;
}
#endif
return dval(da) / dval(db);
}
static const double
tens[] = {
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1e20, 1e21, 1e22
#ifdef VAX
, 1e23, 1e24
#endif
};
static const double
#ifdef IEEE_Arith
bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
#ifdef Avoid_Underflow
9007199254740992.*9007199254740992.e-256
/* = 2^106 * 1e-53 */
#else
1e-256
#endif
};
/* 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
#else
#ifdef IBM
bigtens[] = { 1e16, 1e32, 1e64 };
static const double tinytens[] = { 1e-16, 1e-32, 1e-64 };
#define n_bigtens 3
#else
bigtens[] = { 1e16, 1e32 };
static const double tinytens[] = { 1e-16, 1e-32 };
#define n_bigtens 2
#endif
#endif
#ifndef IEEE_Arith
#undef INFNAN_CHECK
#endif
#ifdef INFNAN_CHECK
#ifndef NAN_WORD0
#define NAN_WORD0 0x7ff80000
#endif
#ifndef NAN_WORD1
#define NAN_WORD1 0
#endif
static int
match(const char **sp, char *t)
{
int c, d;
const char *s = *sp;
while (d = *t++) {
if ((c = *++s) >= 'A' && c <= 'Z')
c += 'a' - 'A';
if (c != d)
return 0;
}
*sp = s + 1;
return 1;
}
#ifndef No_Hex_NaN
static void
hexnan(double *rvp, const char **sp)
{
ULong c, x[2];
const char *s;
int havedig, udx0, xshift;
x[0] = x[1] = 0;
havedig = xshift = 0;
udx0 = 1;
s = *sp;
while (c = *(const unsigned char*)++s) {
if (c >= '0' && c <= '9')
c -= '0';
else if (c >= 'a' && c <= 'f')
c += 10 - 'a';
else if (c >= 'A' && c <= 'F')
c += 10 - 'A';
else if (c <= ' ') {
if (udx0 && havedig) {
udx0 = 0;
xshift = 1;
}
continue;
}
else if (/*(*/ c == ')' && havedig) {
*sp = s + 1;
break;
}
else
return; /* invalid form: don't change *sp */
havedig = 1;
if (xshift) {
xshift = 0;
x[0] = x[1];
x[1] = 0;
}
if (udx0)
x[0] = (x[0] << 4) | (x[1] >> 28);
x[1] = (x[1] << 4) | c;
}
if ((x[0] &= 0xfffff) || x[1]) {
word0(*rvp) = Exp_mask | x[0];
word1(*rvp) = x[1];
}
}
#endif /*No_Hex_NaN*/
#endif /* INFNAN_CHECK */
NO_SANITIZE("unsigned-integer-overflow", double strtod(const char *s00, char **se));
double
strtod(const char *s00, char **se)
{
#ifdef Avoid_Underflow
int scale;
#endif
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, adj;
double_u aadj1, rv, rv0;
Long L;
ULong y, z;
Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
#ifdef SET_INEXACT
int inexact, oldinexact;
#endif
#ifdef Honor_FLT_ROUNDS
int rounding;
#endif
#ifdef USE_LOCALE
const char *s2;
#endif
errno = 0;
sign = nz0 = nz = 0;
dval(rv) = 0.;
for (s = s00;;s++)
switch (*s) {
case '-':
sign = 1;
/* no break */
case '+':
if (*++s)
goto break2;
/* no break */
case 0:
goto ret0;
case '\t':
case '\n':
case '\v':
case '\f':
case '\r':
case ' ':
continue;
default:
goto break2;
}
break2:
if (*s == '0') {
if (s[1] == 'x' || s[1] == 'X') {
s0 = ++s;
adj = 0;
aadj = 1.0;
nd0 = -4;
if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
if (*s == '0') {
while (*++s == '0');
s1 = strchr(hexdigit, *s);
}
if (s1 != NULL) {
do {
adj += aadj * ((s1 - hexdigit) & 15);
nd0 += 4;
aadj /= 16;
} while (*++s && (s1 = strchr(hexdigit, *s)));
}
if (*s == '.') {
dsign = 1;
if (!*++s || !(s1 = strchr(hexdigit, *s))) goto ret0;
if (nd0 < 0) {
while (*s == '0') {
s++;
nd0 -= 4;
}
}
for (; *s && (s1 = strchr(hexdigit, *s)); ++s) {
adj += aadj * ((s1 - hexdigit) & 15);
if ((aadj /= 16) == 0.0) {
while (strchr(hexdigit, *++s));
break;
}
}
}
else {
dsign = 0;
}
if (*s == 'P' || *s == 'p') {
dsign = 0x2C - *++s; /* +: 2B, -: 2D */
if (abs(dsign) == 1) s++;
else dsign = 1;
nd = 0;
c = *s;
if (c < '0' || '9' < c) goto ret0;
do {
nd *= 10;
nd += c;
nd -= '0';
c = *++s;
/* Float("0x0."+("0"*267)+"1fp2095") */
if (nd + dsign * nd0 > 2095) {
while ('0' <= c && c <= '9') c = *++s;
break;
}
} while ('0' <= c && c <= '9');
nd0 += nd * dsign;
}
else {
if (dsign) goto ret0;
}
dval(rv) = ldexp(adj, nd0);
goto ret;
}
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 < DBL_DIG + 2)
z = 10*z + c - '0';
nd0 = nd;
#ifdef USE_LOCALE
s1 = localeconv()->decimal_point;
if (c == *s1) {
c = '.';
if (*++s1) {
s2 = s;
for (;;) {
if (*++s2 != *s1) {
c = 0;
break;
}
if (!*++s1) {
s = s2;
break;
}
}
}
}
#endif
if (c == '.') {
if (!ISDIGIT(s[1]))
goto dig_done;
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 (nd > DBL_DIG * 4) {
continue;
}
if (c -= '0') {
nf += nz;
for (i = 1; i < nz; i++)
if (nd++ < 9)
y *= 10;
else if (nd <= DBL_DIG + 2)
z *= 10;
if (nd++ < 9)
y = 10*y + c;
else if (nd <= DBL_DIG + 2)
z = 10*z + c;
nz = 0;
}
}
}
dig_done:
e = 0;
if (c == 'e' || c == 'E') {
if (!nd && !nz && !nz0) {
goto ret0;
}
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) {
#ifdef INFNAN_CHECK
/* Check for Nan and Infinity */
switch (c) {
case 'i':
case 'I':
if (match(&s,"nf")) {
--s;
if (!match(&s,"inity"))
++s;
word0(rv) = 0x7ff00000;
word1(rv) = 0;
goto ret;
}
break;
case 'n':
case 'N':
if (match(&s, "an")) {
word0(rv) = NAN_WORD0;
word1(rv) = NAN_WORD1;
#ifndef No_Hex_NaN
if (*s == '(') /*)*/
hexnan(&rv, &s);
#endif
goto ret;
}
}
#endif /* INFNAN_CHECK */
ret0:
s = s00;
sign = 0;
}
goto ret;
}
e1 = e -= nf;
/* Now we have nd0 digits, starting at s0, followed by a
* decimal point, followed by nd-nd0 digits. The number we're
* after is the integer represented by those digits times
* 10**e */
if (!nd0)
nd0 = nd;
k = nd < DBL_DIG + 2 ? nd : DBL_DIG + 2;
dval(rv) = y;
if (k > 9) {
#ifdef SET_INEXACT
if (k > DBL_DIG)
oldinexact = get_inexact();
#endif
dval(rv) = tens[k - 9] * dval(rv) + z;
}
bd0 = bb = bd = bs = delta = 0;
if (nd <= DBL_DIG
#ifndef RND_PRODQUOT
#ifndef Honor_FLT_ROUNDS
&& Flt_Rounds == 1
#endif
#endif
) {
if (!e)
goto ret;
if (e > 0) {
if (e <= Ten_pmax) {
#ifdef VAX
goto vax_ovfl_check;
#else
#ifdef Honor_FLT_ROUNDS
/* round correctly FLT_ROUNDS = 2 or 3 */
if (sign) {
dval(rv) = -dval(rv);
sign = 0;
}
#endif
/* rv = */ rounded_product(dval(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.
*/
#ifdef Honor_FLT_ROUNDS
/* round correctly FLT_ROUNDS = 2 or 3 */
if (sign) {
dval(rv) = -dval(rv);
sign = 0;
}
#endif
e -= i;
dval(rv) *= tens[i];
#ifdef VAX
/* VAX exponent range is so narrow we must
* worry about overflow here...
*/
vax_ovfl_check:
word0(rv) -= P*Exp_msk1;
/* rv = */ rounded_product(dval(rv), tens[e]);
if ((word0(rv) & Exp_mask)
> Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
goto ovfl;
word0(rv) += P*Exp_msk1;
#else
/* rv = */ rounded_product(dval(rv), tens[e]);
#endif
goto ret;
}
}
#ifndef Inaccurate_Divide
else if (e >= -Ten_pmax) {
#ifdef Honor_FLT_ROUNDS
/* round correctly FLT_ROUNDS = 2 or 3 */
if (sign) {
dval(rv) = -dval(rv);
sign = 0;
}
#endif
/* rv = */ rounded_quotient(dval(rv), tens[-e]);
goto ret;
}
#endif
}
e1 += nd - k;
#ifdef IEEE_Arith
#ifdef SET_INEXACT
inexact = 1;
if (k <= DBL_DIG)
oldinexact = get_inexact();
#endif
#ifdef Avoid_Underflow
scale = 0;
#endif
#ifdef Honor_FLT_ROUNDS
if ((rounding = Flt_Rounds) >= 2) {
if (sign)
rounding = rounding == 2 ? 0 : 2;
else
if (rounding != 2)
rounding = 0;
}
#endif
#endif /*IEEE_Arith*/
/* Get starting approximation = rv * 10**e1 */
if (e1 > 0) {
if ((i = e1 & 15) != 0)
dval(rv) *= tens[i];
if (e1 &= ~15) {
if (e1 > DBL_MAX_10_EXP) {
ovfl:
#ifndef NO_ERRNO
errno = ERANGE;
#endif
/* Can't trust HUGE_VAL */
#ifdef IEEE_Arith
#ifdef Honor_FLT_ROUNDS
switch (rounding) {
case 0: /* toward 0 */
case 3: /* toward -infinity */
word0(rv) = Big0;
word1(rv) = Big1;
break;
default:
word0(rv) = Exp_mask;
word1(rv) = 0;
}
#else /*Honor_FLT_ROUNDS*/
word0(rv) = Exp_mask;
word1(rv) = 0;
#endif /*Honor_FLT_ROUNDS*/
#ifdef SET_INEXACT
/* set overflow bit */
dval(rv0) = 1e300;
dval(rv0) *= dval(rv0);
#endif
#else /*IEEE_Arith*/
word0(rv) = Big0;
word1(rv) = Big1;
#endif /*IEEE_Arith*/
if (bd0)
goto retfree;
goto ret;
}
e1 >>= 4;
for (j = 0; e1 > 1; j++, e1 >>= 1)
if (e1 & 1)
dval(rv) *= bigtens[j];
/* The last multiplication could overflow. */
word0(rv) -= P*Exp_msk1;
dval(rv) *= bigtens[j];
if ((z = word0(rv) & Exp_mask)
> Exp_msk1*(DBL_MAX_EXP+Bias-P))
goto ovfl;
if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
/* set to largest number */
/* (Can't trust DBL_MAX) */
word0(rv) = Big0;
word1(rv) = Big1;
}
else
word0(rv) += P*Exp_msk1;
}
}
else if (e1 < 0) {
e1 = -e1;
if ((i = e1 & 15) != 0)
dval(rv) /= tens[i];
if (e1 >>= 4) {
if (e1 >= 1 << n_bigtens)
goto undfl;
#ifdef Avoid_Underflow
if (e1 & Scale_Bit)
scale = 2*P;
for (j = 0; e1 > 0; j++, e1 >>= 1)
if (e1 & 1)
dval(rv) *= tinytens[j];
if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
>> Exp_shift)) > 0) {
/* scaled rv is denormal; zap j low bits */
if (j >= 32) {
word1(rv) = 0;
if (j >= 53)
word0(rv) = (P+2)*Exp_msk1;
else
word0(rv) &= 0xffffffff << (j-32);
}
else
word1(rv) &= 0xffffffff << j;
}
#else
for (j = 0; e1 > 1; j++, e1 >>= 1)
if (e1 & 1)
dval(rv) *= tinytens[j];
/* The last multiplication could underflow. */
dval(rv0) = dval(rv);
dval(rv) *= tinytens[j];
if (!dval(rv)) {
dval(rv) = 2.*dval(rv0);
dval(rv) *= tinytens[j];
#endif
if (!dval(rv)) {
undfl:
dval(rv) = 0.;
#ifndef NO_ERRNO
errno = ERANGE;
#endif
if (bd0)
goto retfree;
goto ret;
}
#ifndef Avoid_Underflow
word0(rv) = Tiny0;
word1(rv) = Tiny1;
/* The refinement below will clean
* this approximation up.
*/
}
#endif
}
}
/* 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(dval(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 Honor_FLT_ROUNDS
if (rounding != 1)
bs2++;
#endif
#ifdef Avoid_Underflow
j = bbe - scale;
i = j + bbbits - 1; /* logb(rv) */
if (i < Emin) /* denormal */
j += P - Emin;
else
j = P + 1 - bbbits;
#else /*Avoid_Underflow*/
#ifdef Sudden_Underflow
#ifdef IBM
j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
#else
j = P + 1 - bbbits;
#endif
#else /*Sudden_Underflow*/
j = bbe;
i = j + bbbits - 1; /* logb(rv) */
if (i < Emin) /* denormal */
j += P - Emin;
else
j = P + 1 - bbbits;
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
bb2 += j;
bd2 += j;
#ifdef Avoid_Underflow
bd2 += scale;
#endif
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);
#ifdef Honor_FLT_ROUNDS
if (rounding != 1) {
if (i < 0) {
/* Error is less than an ulp */
if (!delta->x[0] && delta->wds <= 1) {
/* exact */
#ifdef SET_INEXACT
inexact = 0;
#endif
break;
}
if (rounding) {
if (dsign) {
adj = 1.;
goto apply_adj;
}
}
else if (!dsign) {
adj = -1.;
if (!word1(rv)
&& !(word0(rv) & Frac_mask)) {
y = word0(rv) & Exp_mask;
#ifdef Avoid_Underflow
if (!scale || y > 2*P*Exp_msk1)
#else
if (y)
#endif
{
delta = lshift(delta,Log2P);
if (cmp(delta, bs) <= 0)
adj = -0.5;
}
}
apply_adj:
#ifdef Avoid_Underflow
if (scale && (y = word0(rv) & Exp_mask)
<= 2*P*Exp_msk1)
word0(adj) += (2*P+1)*Exp_msk1 - y;
#else
#ifdef Sudden_Underflow
if ((word0(rv) & Exp_mask) <=
P*Exp_msk1) {
word0(rv) += P*Exp_msk1;
dval(rv) += adj*ulp(dval(rv));
word0(rv) -= P*Exp_msk1;
}
else
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
dval(rv) += adj*ulp(dval(rv));
}
break;
}
adj = ratio(delta, bs);
if (adj < 1.)
adj = 1.;
if (adj <= 0x7ffffffe) {
/* adj = rounding ? ceil(adj) : floor(adj); */
y = adj;
if (y != adj) {
if (!((rounding>>1) ^ dsign))
y++;
adj = y;
}
}
#ifdef Avoid_Underflow
if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
word0(adj) += (2*P+1)*Exp_msk1 - y;
#else
#ifdef Sudden_Underflow
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
word0(rv) += P*Exp_msk1;
adj *= ulp(dval(rv));
if (dsign)
dval(rv) += adj;
else
dval(rv) -= adj;
word0(rv) -= P*Exp_msk1;
goto cont;
}
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
adj *= ulp(dval(rv));
if (dsign)
dval(rv) += adj;
else
dval(rv) -= adj;
goto cont;
}
#endif /*Honor_FLT_ROUNDS*/
if (i < 0) {
/* Error is less than half an ulp -- check for
* special case of mantissa a power of two.
*/
if (dsign || word1(rv) || word0(rv) & Bndry_mask
#ifdef IEEE_Arith
#ifdef Avoid_Underflow
|| (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
#else
|| (word0(rv) & Exp_mask) <= Exp_msk1
#endif
#endif
) {
#ifdef SET_INEXACT
if (!delta->x[0] && delta->wds <= 1)
inexact = 0;
#endif
break;
}
if (!delta->x[0] && delta->wds <= 1) {
/* exact result */
#ifdef SET_INEXACT
inexact = 0;
#endif
break;
}
delta = lshift(delta,Log2P);
if (cmp(delta, bs) > 0)
goto drop_down;
break;
}
if (i == 0) {
/* exactly half-way between */
if (dsign) {
if ((word0(rv) & Bndry_mask1) == Bndry_mask1
&& word1(rv) == (
#ifdef Avoid_Underflow
(scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
#endif
0xffffffff)) {
/*boundary case -- increment exponent*/
word0(rv) = (word0(rv) & Exp_mask)
+ Exp_msk1
#ifdef IBM
| Exp_msk1 >> 4
#endif
;
word1(rv) = 0;
#ifdef Avoid_Underflow
dsign = 0;
#endif
break;
}
}
else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
drop_down:
/* boundary case -- decrement exponent */
#ifdef Sudden_Underflow /*{{*/
L = word0(rv) & Exp_mask;
#ifdef IBM
if (L < Exp_msk1)
#else
#ifdef Avoid_Underflow
if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
#else
if (L <= Exp_msk1)
#endif /*Avoid_Underflow*/
#endif /*IBM*/
goto undfl;
L -= Exp_msk1;
#else /*Sudden_Underflow}{*/
#ifdef Avoid_Underflow
if (scale) {
L = word0(rv) & Exp_mask;
if (L <= (2*P+1)*Exp_msk1) {
if (L > (P+2)*Exp_msk1)
/* round even ==> */
/* accept rv */
break;
/* rv = smallest denormal */
goto undfl;
}
}
#endif /*Avoid_Underflow*/
L = (word0(rv) & Exp_mask) - Exp_msk1;
#endif /*Sudden_Underflow}}*/
word0(rv) = L | Bndry_mask1;
word1(rv) = 0xffffffff;
#ifdef IBM
goto cont;
#else
break;
#endif
}
#ifndef ROUND_BIASED
if (!(word1(rv) & LSB))
break;
#endif
if (dsign)
dval(rv) += ulp(dval(rv));
#ifndef ROUND_BIASED
else {
dval(rv) -= ulp(dval(rv));
#ifndef Sudden_Underflow
if (!dval(rv))
goto undfl;
#endif
}
#ifdef Avoid_Underflow
dsign = 1 - dsign;
#endif
#endif
break;
}
if ((aadj = ratio(delta, bs)) <= 2.) {
if (dsign)
aadj = dval(aadj1) = 1.;
else if (word1(rv) || word0(rv) & Bndry_mask) {
#ifndef Sudden_Underflow
if (word1(rv) == Tiny1 && !word0(rv))
goto undfl;
#endif
aadj = 1.;
dval(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;
dval(aadj1) = -aadj;
}
}
else {
aadj *= 0.5;
dval(aadj1) = dsign ? aadj : -aadj;
#ifdef Check_FLT_ROUNDS
switch (Rounding) {
case 2: /* towards +infinity */
dval(aadj1) -= 0.5;
break;
case 0: /* towards 0 */
case 3: /* towards -infinity */
dval(aadj1) += 0.5;
}
#else
if (Flt_Rounds == 0)
dval(aadj1) += 0.5;
#endif /*Check_FLT_ROUNDS*/
}
y = word0(rv) & Exp_mask;
/* Check for overflow */
if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
dval(rv0) = dval(rv);
word0(rv) -= P*Exp_msk1;
adj = dval(aadj1) * ulp(dval(rv));
dval(rv) += adj;
if ((word0(rv) & Exp_mask) >=
Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
if (word0(rv0) == Big0 && word1(rv0) == Big1)
goto ovfl;
word0(rv) = Big0;
word1(rv) = Big1;
goto cont;
}
else
word0(rv) += P*Exp_msk1;
}
else {
#ifdef Avoid_Underflow
if (scale && y <= 2*P*Exp_msk1) {
if (aadj <= 0x7fffffff) {
if ((z = (int)aadj) <= 0)
z = 1;
aadj = z;
dval(aadj1) = dsign ? aadj : -aadj;
}
word0(aadj1) += (2*P+1)*Exp_msk1 - y;
}
adj = dval(aadj1) * ulp(dval(rv));
dval(rv) += adj;
#else
#ifdef Sudden_Underflow
if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
dval(rv0) = dval(rv);
word0(rv) += P*Exp_msk1;
adj = dval(aadj1) * ulp(dval(rv));
dval(rv) += adj;
#ifdef IBM
if ((word0(rv) & Exp_mask) < P*Exp_msk1)
#else
if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
#endif
{
if (word0(rv0) == Tiny0 && word1(rv0) == Tiny1)
goto undfl;
word0(rv) = Tiny0;
word1(rv) = Tiny1;
goto cont;
}
else
word0(rv) -= P*Exp_msk1;
}
else {
adj = dval(aadj1) * ulp(dval(rv));
dval(rv) += adj;
}
#else /*Sudden_Underflow*/
/* 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.) {
dval(aadj1) = (double)(int)(aadj + 0.5);
if (!dsign)
dval(aadj1) = -dval(aadj1);
}
adj = dval(aadj1) * ulp(dval(rv));
dval(rv) += adj;
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
}
z = word0(rv) & Exp_mask;
#ifndef SET_INEXACT
#ifdef Avoid_Underflow
if (!scale)
#endif
if (y == z) {
/* Can we stop now? */
L = (Long)aadj;
aadj -= L;
/* The tolerances below are conservative. */
if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
if (aadj < .4999999 || aadj > .5000001)
break;
}
else if (aadj < .4999999/FLT_RADIX)
break;
}
#endif
cont:
Bfree(bb);
Bfree(bd);
Bfree(bs);
Bfree(delta);
}
#ifdef SET_INEXACT
if (inexact) {
if (!oldinexact) {
word0(rv0) = Exp_1 + (70 << Exp_shift);
word1(rv0) = 0;
dval(rv0) += 1.;
}
}
else if (!oldinexact)
clear_inexact();
#endif
#ifdef Avoid_Underflow
if (scale) {
word0(rv0) = Exp_1 - 2*P*Exp_msk1;
word1(rv0) = 0;
dval(rv) *= dval(rv0);
#ifndef NO_ERRNO
/* try to avoid the bug of testing an 8087 register value */
if (word0(rv) == 0 && word1(rv) == 0)
errno = ERANGE;
#endif
}
#endif /* Avoid_Underflow */
#ifdef SET_INEXACT
if (inexact && !(word0(rv) & Exp_mask)) {
/* set underflow bit */
dval(rv0) = 1e-300;
dval(rv0) *= dval(rv0);
}
#endif
retfree:
Bfree(bb);
Bfree(bd);
Bfree(bs);
Bfree(bd0);
Bfree(delta);
ret:
if (se)
*se = (char *)s;
return sign ? -dval(rv) : dval(rv);
}
NO_SANITIZE("unsigned-integer-overflow", static int quorem(Bigint *b, Bigint *S));
static int
quorem(Bigint *b, Bigint *S)
{
int n;
ULong *bx, *bxe, q, *sx, *sxe;
#ifdef ULLong
ULLong borrow, carry, y, ys;
#else
ULong borrow, carry, y, ys;
#ifdef Pack_32
ULong si, z, zs;
#endif
#endif
n = S->wds;
#ifdef 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 DEBUG
/*debug*/ if (q > 9)
/*debug*/ Bug("oversized quotient in quorem");
#endif
if (q) {
borrow = 0;
carry = 0;
do {
#ifdef ULLong
ys = *sx++ * (ULLong)q + carry;
carry = ys >> 32;
y = *bx - (ys & FFFFFFFF) - borrow;
borrow = y >> 32 & (ULong)1;
*bx++ = (ULong)(y & FFFFFFFF);
#else
#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 & 0x10000) >> 16;
z = (*bx >> 16) - (zs & 0xffff) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(bx, z, y);
#else
ys = *sx++ * q + carry;
carry = ys >> 16;
y = *bx - (ys & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
*bx++ = y & 0xffff;
#endif
#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 ULLong
ys = *sx++ + carry;
carry = ys >> 32;
y = *bx - (ys & FFFFFFFF) - borrow;
borrow = y >> 32 & (ULong)1;
*bx++ = (ULong)(y & FFFFFFFF);
#else
#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 & 0x10000) >> 16;
z = (*bx >> 16) - (zs & 0xffff) - borrow;
borrow = (z & 0x10000) >> 16;
Storeinc(bx, z, y);
#else
ys = *sx++ + carry;
carry = ys >> 16;
y = *bx - (ys & 0xffff) - borrow;
borrow = (y & 0x10000) >> 16;
*bx++ = y & 0xffff;
#endif
#endif
} while (sx <= sxe);
bx = b->x;
bxe = bx + n;
if (!*bxe) {
while (--bxe > bx && !*bxe)
--n;
b->wds = n;
}
}
return q;
}
#ifndef MULTIPLE_THREADS
static char *dtoa_result;
#endif
#ifndef MULTIPLE_THREADS
static char *
rv_alloc(int i)
{
dtoa.c: make compilable independently Except for `-Dxmalloc=malloc -Dxfree=free`.
2021-01-10 01:46:23 -05:00
return dtoa_result = MALLOC(i);
Split dtoa.c git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@67022 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
2019-02-07 03:53:11 -05:00
}
#else
dtoa.c: make compilable independently Except for `-Dxmalloc=malloc -Dxfree=free`.
2021-01-10 01:46:23 -05:00
#define rv_alloc(i) MALLOC(i)
Split dtoa.c git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@67022 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
2019-02-07 03:53:11 -05:00
#endif
static char *
nrv_alloc(const char *s, char **rve, size_t n)
{
char *rv, *t;
t = rv = rv_alloc(n);
while ((*t = *s++) != 0) t++;
if (rve)
*rve = t;
return rv;
}
#define rv_strdup(s, rve) nrv_alloc((s), (rve), strlen(s)+1)
#ifndef MULTIPLE_THREADS
/* freedtoa(s) must be used to free values s returned by dtoa
* when MULTIPLE_THREADS is #defined. It should be used in all cases,
* but for consistency with earlier versions of dtoa, it is optional
* when MULTIPLE_THREADS is not defined.
*/
static void
freedtoa(char *s)
{
dtoa.c: make compilable independently Except for `-Dxmalloc=malloc -Dxfree=free`.
2021-01-10 01:46:23 -05:00
FREE(s);
Split dtoa.c git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@67022 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
2019-02-07 03:53:11 -05:00
}
#endif
static const char INFSTR[] = "Infinity";
static const char NANSTR[] = "NaN";
static const char ZEROSTR[] = "0";
/* 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.
*/
char *
dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve)
{
/* 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.
4,5 ==> similar to 2 and 3, respectively, but (in
round-nearest mode) with the tests of mode 0 to
possibly return a shorter string that rounds to d.
With IEEE arithmetic and compilation with
-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
as modes 2 and 3 when FLT_ROUNDS != 1.
6-9 ==> Debugging modes similar to mode - 4: don't try
fast floating-point estimate (if applicable).
Values of mode other than 0-9 are treated as mode 0.
Sufficient space is allocated to the return value
to hold the suppressed trailing zeros.
*/
int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
spec_case, try_quick, half = 0;
Long L;
#ifndef Sudden_Underflow
int denorm;
ULong x;
#endif
Bigint *b, *b1, *delta, *mlo = 0, *mhi = 0, *S;
double ds;
double_u d, d2, eps;
char *s, *s0;
#ifdef Honor_FLT_ROUNDS
int rounding;
#endif
#ifdef SET_INEXACT
int inexact, oldinexact;
#endif
dval(d) = d_;
#ifndef MULTIPLE_THREADS
if (dtoa_result) {
freedtoa(dtoa_result);
dtoa_result = 0;
}
#endif
if (word0(d) & Sign_bit) {
/* set sign for everything, including 0's and NaNs */
*sign = 1;
word0(d) &= ~Sign_bit; /* clear sign bit */
}
else
*sign = 0;
#if defined(IEEE_Arith) + defined(VAX)
#ifdef IEEE_Arith
if ((word0(d) & Exp_mask) == Exp_mask)
#else
if (word0(d) == 0x8000)
#endif
{
/* Infinity or NaN */
*decpt = 9999;
#ifdef IEEE_Arith
if (!word1(d) && !(word0(d) & 0xfffff))
return rv_strdup(INFSTR, rve);
#endif
return rv_strdup(NANSTR, rve);
}
#endif
#ifdef IBM
dval(d) += 0; /* normalize */
#endif
if (!dval(d)) {
*decpt = 1;
return rv_strdup(ZEROSTR, rve);
}
#ifdef SET_INEXACT
try_quick = oldinexact = get_inexact();
inexact = 1;
#endif
#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(dval(d), &be, &bbits);
#ifdef Sudden_Underflow
i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
#else
if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
#endif
dval(d2) = dval(d);
word0(d2) &= Frac_mask1;
word0(d2) |= Exp_11;
#ifdef IBM
if (j = 11 - hi0bits(word0(d2) & Frac_mask))
dval(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 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
: word1(d) << (32 - i);
dval(d2) = x;
word0(d2) -= 31*Exp_msk1; /* adjust exponent */
i -= (Bias + (P-1) - 1) + 1;
denorm = 1;
}
#endif
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(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;
#ifndef SET_INEXACT
#ifdef Check_FLT_ROUNDS
try_quick = Rounding == 1;
#else
try_quick = 1;
#endif
#endif /*SET_INEXACT*/
if (mode > 5) {
mode -= 4;
try_quick = 0;
}
leftright = 1;
ilim = ilim1 = -1;
switch (mode) {
case 0:
case 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 = rv_alloc(i+1);
#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(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;
dval(d) /= bigtens[n_bigtens-1];
ieps++;
}
for (; j; j >>= 1, i++)
if (j & 1) {
ieps++;
ds *= bigtens[i];
}
dval(d) /= ds;
}
else if ((j1 = -k) != 0) {
dval(d) *= tens[j1 & 0xf];
for (j = j1 >> 4; j; j >>= 1, i++)
if (j & 1) {
ieps++;
dval(d) *= bigtens[i];
}
}
if (k_check && dval(d) < 1. && ilim > 0) {
if (ilim1 <= 0)
goto fast_failed;
ilim = ilim1;
k--;
dval(d) *= 10.;
ieps++;
}
dval(eps) = ieps*dval(d) + 7.;
word0(eps) -= (P-1)*Exp_msk1;
if (ilim == 0) {
S = mhi = 0;
dval(d) -= 5.;
if (dval(d) > dval(eps))
goto one_digit;
if (dval(d) < -dval(eps))
goto no_digits;
goto fast_failed;
}
#ifndef No_leftright
if (leftright) {
/* Use Steele & White method of only
* generating digits needed.
*/
dval(eps) = 0.5/tens[ilim-1] - dval(eps);
for (i = 0;;) {
L = (int)dval(d);
dval(d) -= L;
*s++ = '0' + (int)L;
if (dval(d) < dval(eps))
goto ret1;
if (1. - dval(d) < dval(eps))
goto bump_up;
if (++i >= ilim)
break;
dval(eps) *= 10.;
dval(d) *= 10.;
}
}
else {
#endif
/* Generate ilim digits, then fix them up. */
dval(eps) *= tens[ilim-1];
for (i = 1;; i++, dval(d) *= 10.) {
L = (Long)(dval(d));
if (!(dval(d) -= L))
ilim = i;
*s++ = '0' + (int)L;
if (i == ilim) {
if (dval(d) > 0.5 + dval(eps))
goto bump_up;
else if (dval(d) < 0.5 - dval(eps)) {
while (*--s == '0') ;
s++;
goto ret1;
}
half = 1;
if ((*(s-1) - '0') & 1) {
goto bump_up;
}
break;
}
}
#ifndef No_leftright
}
#endif
fast_failed:
s = s0;
dval(d) = 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(d) <= 5*ds)
goto no_digits;
goto one_digit;
}
for (i = 1;; i++, dval(d) *= 10.) {
L = (Long)(dval(d) / ds);
dval(d) -= L*ds;
#ifdef Check_FLT_ROUNDS
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
if (dval(d) < 0) {
L--;
dval(d) += ds;
}
#endif
*s++ = '0' + (int)L;
if (!dval(d)) {
#ifdef SET_INEXACT
inexact = 0;
#endif
break;
}
if (i == ilim) {
#ifdef Honor_FLT_ROUNDS
if (mode > 1)
switch (rounding) {
case 0: goto ret1;
case 2: goto bump_up;
}
#endif
dval(d) += dval(d);
if (dval(d) > ds || (dval(d) == ds && (L & 1))) {
bump_up:
while (*--s == '9')
if (s == s0) {
k++;
*s = '0';
break;
}
++*s++;
}
break;
}
}
goto ret1;
}
m2 = b2;
m5 = b5;
if (leftright) {
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
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. */
spec_case = 0;
if ((mode < 2 || leftright)
#ifdef Honor_FLT_ROUNDS
&& rounding == 1
#endif
) {
if (!word1(d) && !(word0(d) & Bndry_mask)
#ifndef Sudden_Underflow
&& word0(d) & (Exp_mask & ~Exp_msk1)
#endif
) {
/* 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
* 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) != 0)
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 == 3 || mode == 5)) {
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 != 1 && !(word1(d) & 1)
#ifdef Honor_FLT_ROUNDS
&& rounding >= 1
#endif
) {
if (dig == '9')
goto round_9_up;
if (j > 0)
dig++;
#ifdef SET_INEXACT
else if (!b->x[0] && b->wds <= 1)
inexact = 0;
#endif
*s++ = dig;
goto ret;
}
#endif
if (j < 0 || (j == 0 && mode != 1
#ifndef ROUND_BIASED
&& !(word1(d) & 1)
#endif
)) {
if (!b->x[0] && b->wds <= 1) {
#ifdef SET_INEXACT
inexact = 0;
#endif
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);
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);
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 (!b->x[0] && b->wds <= 1) {
#ifdef SET_INEXACT
inexact = 0;
#endif
goto ret;
}
if (i >= ilim)
break;
b = multadd(b, 10, 0);
}
/* Round off last digit */
#ifdef Honor_FLT_ROUNDS
switch (rounding) {
case 0: goto trimzeros;
case 2: goto roundoff;
}
#endif
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;
}
if (!half || (*s - '0') & 1)
++*s;
}
else {
while (*--s == '0') ;
}
s++;
ret:
Bfree(S);
if (mhi) {
if (mlo && mlo != mhi)
Bfree(mlo);
Bfree(mhi);
}
ret1:
#ifdef SET_INEXACT
if (inexact) {
if (!oldinexact) {
word0(d) = Exp_1 + (70 << Exp_shift);
word1(d) = 0;
dval(d) += 1.;
}
}
else if (!oldinexact)
clear_inexact();
#endif
Bfree(b);
*s = 0;
*decpt = k + 1;
if (rve)
*rve = s;
return s0;
}
/*-
* Copyright (c) 2004-2008 David Schultz <das@FreeBSD.ORG>
* 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.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR 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 AUTHOR 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.
*/
#define DBL_MANH_SIZE 20
#define DBL_MANL_SIZE 32
#define DBL_ADJ (DBL_MAX_EXP - 2)
#define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1)
#define dexp_get(u) ((int)(word0(u) >> Exp_shift) & ~Exp_msk1)
#define dexp_set(u,v) (word0(u) = (((int)(word0(u)) & ~Exp_mask) | ((v) << Exp_shift)))
#define dmanh_get(u) ((uint32_t)(word0(u) & Frac_mask))
#define dmanl_get(u) ((uint32_t)word1(u))
/*
* This procedure converts a double-precision number in IEEE format
* into a string of hexadecimal digits and an exponent of 2. Its
* behavior is bug-for-bug compatible with dtoa() in mode 2, with the
* following exceptions:
*
* - An ndigits < 0 causes it to use as many digits as necessary to
* represent the number exactly.
* - The additional xdigs argument should point to either the string
* "0123456789ABCDEF" or the string "0123456789abcdef", depending on
* which case is desired.
* - This routine does not repeat dtoa's mistake of setting decpt
* to 9999 in the case of an infinity or NaN. INT_MAX is used
* for this purpose instead.
*
* Note that the C99 standard does not specify what the leading digit
* should be for non-zero numbers. For instance, 0x1.3p3 is the same
* as 0x2.6p2 is the same as 0x4.cp3. This implementation always makes
* the leading digit a 1. This ensures that the exponent printed is the
* actual base-2 exponent, i.e., ilogb(d).
*
* Inputs: d, xdigs, ndigits
* Outputs: decpt, sign, rve
*/
char *
hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, char **rve)
{
U u;
char *s, *s0;
int bufsize;
uint32_t manh, manl;
u.d = d;
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 (isinf(d)) { /* FP_INFINITE */
*decpt = INT_MAX;
return rv_strdup(INFSTR, rve);
}
else if (isnan(d)) { /* FP_NAN */
*decpt = INT_MAX;
return rv_strdup(NANSTR, rve);
}
else if (d == 0.0) { /* FP_ZERO */
*decpt = 1;
return rv_strdup(ZEROSTR, rve);
}
else if (dexp_get(u)) { /* FP_NORMAL */
*decpt = dexp_get(u) - DBL_ADJ;
}
else { /* FP_SUBNORMAL */
u.d *= 5.363123171977039e+154 /* 0x1p514 */;
*decpt = dexp_get(u) - (514 + DBL_ADJ);
}
if (ndigits == 0) /* dtoa() compatibility */
ndigits = 1;
/*
* If ndigits < 0, we are expected to auto-size, so we allocate
* enough space for all the digits.
*/
bufsize = (ndigits > 0) ? ndigits : SIGFIGS;
s0 = rv_alloc(bufsize+1);
/* Round to the desired number of digits. */
if (SIGFIGS > ndigits && ndigits > 0) {
float redux = 1.0f;
int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG;
dexp_set(u, offset);
u.d += redux;
u.d -= redux;
*decpt += dexp_get(u) - offset;
}
manh = dmanh_get(u);
manl = dmanl_get(u);
*s0 = '1';
for (s = s0 + 1; s < s0 + bufsize; s++) {
*s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf];
manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4));
manl <<= 4;
}
/* If ndigits < 0, we are expected to auto-size the precision. */
if (ndigits < 0) {
for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--)
;
}
s = s0 + ndigits;
*s = '\0';
if (rve != NULL)
*rve = s;
return (s0);
}
#ifdef __cplusplus
#if 0
{ /* satisfy cc-mode */
#endif
}
#endif
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