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RAD dtoa
Raw
dtoa.c
// The original author of this software is David M. Gay.
// RAD modifications from here down to the copyright notice
// Actual RAD version of this includes rrCore.h which does
// (among other things) endianness detection - you'll have to
// do that yourself.
#include "dtoa.h"
// Again, we normally use our own assert macros here.
#include <assert.h>
#define rrAssert(x) assert(x)
#if defined(_MSC_VER) && _MSC_VER > 1300
#pragma warning(disable:4127; disable:4204; disable:4244; disable:4221; disable:4700; disable:4706; disable: 4711; disable:4820)
#pragma float_control(precise, on)
#endif
#ifdef __SNC__
// this file needs to have 100% reproducible FP behavior
#pragma control fastmath=0
#pragma control autovecreg=0
#pragma control fusedmadd=0 // if you allow fused madd, you might get crashes!!
#endif
#ifdef __RADWII__
#pragma warn_possunwant off
#endif
#define freedtoa rr_freedtoa
#if defined(__RADLITTLEENDIAN__)
#define IEEE_8087
#elif defined(__RADBIGENDIAN__)
#define IEEE_MC68k
#else
#error "missing endian setting - #define __RADLITTLEENDIAN__ or __RADBIGENDIAN__."
#endif
#define NO_ERRNO
#define NO_HEX_FP
#define Long int
#define ULong unsigned int
#define Llong long long
#define ULLong unsigned long long
#define Local_Private_Memory
#define NO_MALLOC
#define PRIVATE_MEM 2500
#if defined(_MSC_VER)
#if _MSC_VER < 1300
// no fegetround
#define Honor_FLT_ROUNDS
#define Trust_FLT_ROUNDS
#else
// "small" integer? case will fail with 99.0 (rounds up to 100) if we
// don't define this bugger.
#define Check_FLT_ROUNDS
#endif
#endif
/****************************************************************
*
* 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_8087 for IEEE-arithmetic machines where the least
* significant byte has the lowest address.
* #define IEEE_MC68k 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. Unless Trust_FLT_ROUNDS
* is also #defined, fegetround() will be queried for the rounding mode.
* Note that both FLT_ROUNDS and fegetround() are specified by the C99
* standard (and are specified to be consistent, with fesetround()
* affecting the value of FLT_ROUNDS), but that some (Linux) systems
* do not work correctly in this regard, so using fegetround() is more
* portable than using FLT_FOUNDS directly.
* #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. Similarly, if you
* want something other than the system's free() to be called to
* recycle memory acquired from MALLOC, #define FREE to be the
* name of the alternate routine. (FREE or free is only called in
* pathological cases, e.g., in a dtoa call after a dtoa return in
* mode 3 with thousands of digits requested.)
* #define NO_MALLOC to avoid using malloc at all (conversion will
* fail if malloc is needed.) Currently not supported if USE_LOCALE is set.
* #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 Local_Private_Memory to keep private memory on the stack.
* This allows you to avoid the need for locks in multithreaded
* applications. However, it also means the return value can not
* be allocated from the private memory, so it must be passed in.
* #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
* #defined automatically on IEEE systems. On such systems,
* when INFNAN_CHECK is #defined, strtod checks
* 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 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.
* #define NO_HEX_FP to omit recognition of hexadecimal floating-point
* values by strtod.
* #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now)
* to disable logic for "fast" testing of very long input strings
* to strtod. This testing proceeds by initially truncating the
* input string, then if necessary comparing the whole string with
* a decimal expansion to decide close cases. This logic is only
* used for input more than STRTOD_DIGLIM digits long (default 40).
*/
#ifndef Long
#define Long long
#endif
#ifndef ULong
typedef unsigned Long ULong;
#endif
#ifdef DEBUG
#include "stdio.h"
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
#endif
#include "stdlib.h"
#include "string.h"
#ifdef USE_LOCALE
#include "locale.h"
#endif
#ifdef Honor_FLT_ROUNDS
#ifndef Trust_FLT_ROUNDS
#include <fenv.h>
#endif
#endif
#ifdef NO_MALLOC
#define MALLOC x x x
#else
#ifdef MALLOC
#ifdef KR_headers
extern char *MALLOC();
#else
extern void *MALLOC(size_t);
#endif
#else
#define MALLOC malloc
#endif
#endif
#ifndef Omit_Private_Memory
#ifndef PRIVATE_MEM
#define PRIVATE_MEM 2304
#endif
#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
#ifndef Local_Private_Memory
static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
#endif
#endif
#ifdef NO_MALLOC
#undef NO_STRTOD_BIGCOMP
#define NO_STRTOD_BIGCOMPx // don't know how to propogate error out of bigcomp(), so just don't call it
#endif
#undef IEEE_Arith
#undef Avoid_Underflow
#ifdef IEEE_MC68k
#define IEEE_Arith
#endif
#ifdef IEEE_8087
#define IEEE_Arith
#endif
#ifdef IEEE_Arith
#ifndef NO_INFNAN_CHECK
#undef INFNAN_CHECK
#define INFNAN_CHECK
#endif
#else
#undef INFNAN_CHECK
#define NO_STRTOD_BIGCOMP
#endif
#include "errno.h"
#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 */
#ifndef __MATH_H__
#include "math.h"
#endif
#ifdef __cplusplus
extern "C" {
#endif
#ifndef CONST
#ifdef KR_headers
#define CONST /* blank */
#else
#define CONST const
#endif
#endif
#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
#endif
typedef union { double d; ULong L[2]; } U;
#ifdef IEEE_8087
#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
#ifndef STRTOD_DIGLIM
#define STRTOD_DIGLIM 40
#endif
#ifdef DIGLIM_DEBUG
extern int strtod_diglim;
#else
#define strtod_diglim STRTOD_DIGLIM
#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_8087) + defined(VAX)
#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 Nbits 53
#define Bias 1023
#define Emax 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
#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 Nbits 56
#define Bias 65
#define Emax 248
#define Emin (-260)
#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 Nbits 56
#define Bias 129
#define Emax 126
#define Emin (-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)
#ifdef KR_headers
extern double rnd_prod(), rnd_quot();
#else
extern double rnd_prod(double, double), rnd_quot(double, double);
#endif
#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
typedef struct BCinfo BCinfo;
struct
BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflchk; };
#ifdef KR_headers
#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
#else
#define FFFFFFFF 0xffffffffUL
#endif
#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 */
#ifndef MULTIPLE_THREADS
#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
#define FREE_DTOA_LOCK(n) /*nothing*/
#endif
#define Kmax 7
#ifdef __cplusplus
extern "C" double DTOA_MANGLE(strtod)(const char *s00, char **se);
extern "C" char *DTOA_MANGLE(dtoa)(double d, int mode, int ndigits,
int *decpt, int *sign, char *rv, int rv_length);
#endif
struct
Bigint {
struct Bigint *next;
int k, maxwds, sign, wds;
ULong x[1];
};
typedef struct Bigint Bigint;
#ifdef Local_Private_Memory
typedef struct {
char *return_storage;
int return_storage_size;
int padding;
double *pmem_next, private_mem[PRIVATE_mem];
Bigint *freelist[Kmax+1];
Bigint *p5s;
} MemInfo;
#define mp(v) mem->v
#define KRm1 mem,
#define KRm2 MemInfo *mem;
#define mdec MemInfo *mem,
#define mcall mem,
#else
static Bigint *freelist[Kmax+1];
static Bigint *p5s;
#define mp(v) v
#define KRm1
#define KRm2
#define mdec
#define mcall
#endif
static Bigint *
Balloc
#ifdef KR_headers
(KRm1 k) KRm2 int k;
#else
(mdec int k)
#endif
{
int x;
Bigint *rv;
#ifndef Omit_Private_Memory
unsigned int len;
#endif
ACQUIRE_DTOA_LOCK(0);
/* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
/* but this case seems very unlikely. */
if (k <= Kmax && (rv = mp(freelist)[k]))
mp(freelist)[k] = rv->next;
else {
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);
if (k <= Kmax && mp(pmem_next) - mp(private_mem) + len <= PRIVATE_mem) {
rv = (Bigint*)mp(pmem_next);
mp(pmem_next) += len;
}
else
#ifndef NO_MALLOC
rv = (Bigint*)MALLOC(len*sizeof(double));
#else
rv = 0;
#endif
#endif
if (rv == 0) return rv;
rv->k = k;
rv->maxwds = x;
}
FREE_DTOA_LOCK(0);
rv->sign = rv->wds = 0;
return rv;
}
static void
Bfree
#ifdef KR_headers
(KRm1 v) KRm2 Bigint *v;
#else
(mdec Bigint *v)
#endif
{
if (v) {
if (v->k > Kmax)
#ifdef FREE
FREE((void*)v);
#else
free((void*)v);
#endif
else {
ACQUIRE_DTOA_LOCK(0);
v->next = mp(freelist)[v->k];
mp(freelist)[v->k] = v;
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
#ifdef KR_headers
(KRm1 b, m, a) KRm2 Bigint *b; int m, a;
#else
(mdec Bigint *b, int m, int a) /* multiply by m and add a */
#endif
{
int i, wds;
#ifdef ULLong
ULong *x;
ULLong carry, y;
#else
ULong carry, *x, 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(mcall b->k+1);
if (!b1) return NULL;
Bcopy(b1, b);
Bfree(mcall b);
b = b1;
}
b->x[wds++] = (ULong) carry;
b->wds = wds;
}
return b;
}
static Bigint *
s2b
#ifdef KR_headers
(KRm1 s, nd0, nd, y9, dplen) KRm2 CONST char *s; int nd0, nd, dplen; ULong y9;
#else
(mdec CONST char *s, int nd0, int nd, ULong y9, int dplen)
#endif
{
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(mcall k);
if (b == NULL) return NULL;
b->x[0] = y9;
b->wds = 1;
#else
b = Balloc(mcall k+1);
if (b == NULL) return NULL;
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(mcall b, 10, *s++ - '0');
if (b == NULL) return NULL;
} while(++i < nd0);
s += dplen;
}
else
s += dplen + 9;
for(; i < nd; i++) {
b = multadd(mcall b, 10, *s++ - '0');
if (!b) return NULL;
}
return b;
}
static int
hi0bits
#ifdef KR_headers
(x) ULong x;
#else
(ULong x)
#endif
{
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
#ifdef KR_headers
(y) ULong *y;
#else
(ULong *y)
#endif
{
int k;
ULong x = *y;
if (x & 7) {
if (x & 1)
return 0;
if (x & 2) {
*y = x >> 1;
return 1;
}
*y = x >> 2;
return 2;
}
k = 0;
if (!(x & 0xffff)) {
k = 16;
x >>= 16;
}
if (!(x & 0xff)) {
k += 8;
x >>= 8;
}
if (!(x & 0xf)) {
k += 4;
x >>= 4;
}
if (!(x & 0x3)) {
k += 2;
x >>= 2;
}
if (!(x & 1)) {
k++;
x >>= 1;
if (!x)
return 32;
}
*y = x;
return k;
}
static Bigint *
i2b
#ifdef KR_headers
(KRm1 i) KRm2 int i;
#else
(mdec int i)
#endif
{
Bigint *b;
b = Balloc(mcall 1);
if (b) {
b->x[0] = i;
b->wds = 1;
}
return b;
}
static Bigint *
mult
#ifdef KR_headers
(KRm1 a, b) KRm2 Bigint *a, *b;
#else
(mdec Bigint *a, Bigint *b)
#endif
{
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(mcall k);
if (c == NULL) return NULL;
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++)) {
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) {
x = xa;
xc = xc0;
carry = 0;
do {
z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
carry = z >> 16;
z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
carry = z2 >> 16;
Storeinc(xc, z2, z);
}
while(x < xae);
*xc = carry;
}
if (y = *xb >> 16) {
x = xa;
xc = xc0;
carry = 0;
z2 = *xc;
do {
z = (*x & 0xffff) * y + (*xc >> 16) + carry;
carry = z >> 16;
Storeinc(xc, z, z2);
z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
carry = z2 >> 16;
}
while(x < xae);
*xc = z2;
}
}
#else
for(; xb < xbe; xc0++) {
if (y = *xb++) {
x = xa;
xc = xc0;
carry = 0;
do {
z = *x++ * y + *xc + carry;
carry = z >> 16;
*xc++ = z & 0xffff;
}
while(x < xae);
*xc = carry;
}
}
#endif
#endif
for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
c->wds = wc;
return c;
}
static Bigint *
pow5mult
#ifdef KR_headers
(KRm1 b, k) KRm2 Bigint *b; int k;
#else
(mdec Bigint *b, int k)
#endif
{
Bigint *b1, *p5, *p51;
int i;
static int p05[3] = { 5, 25, 125 };
if ((i = k & 3))
b = multadd(mcall b, p05[i-1], 0);
if (!(k >>= 2))
return b;
if (!(p5 = mp(p5s))) {
/* first time */
#ifdef MULTIPLE_THREADS
ACQUIRE_DTOA_LOCK(1);
if (!(p5 = mp(p5s))) {
p5 = mp(p5s) = i2b(625);
p5->next = 0;
}
FREE_DTOA_LOCK(1);
#else
p5 = mp(p5s) = i2b(mcall 625);
if (p5 == NULL) return NULL;
p5->next = 0;
#endif
}
for(;;) {
if (k & 1) {
b1 = mult(mcall b, p5);
if (b1 == NULL) return NULL;
Bfree(mcall b);
b = b1;
}
if (!(k >>= 1))
break;
if (!(p51 = p5->next)) {
#ifdef MULTIPLE_THREADS
ACQUIRE_DTOA_LOCK(1);
if (!(p51 = p5->next)) {
p51 = p5->next = mult(p5,p5);
p51->next = 0;
}
FREE_DTOA_LOCK(1);
#else
p51 = p5->next = mult(mcall p5,p5);
if (p51 == NULL) return NULL;
p51->next = 0;
#endif
}
p5 = p51;
}
return b;
}
static Bigint *
lshift
#ifdef KR_headers
(KRm1 b, k) KRm2 Bigint *b; int k;
#else
(mdec Bigint *b, int k)
#endif
{
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(mcall 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))
++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(mcall b);
return b1;
}
static int
cmp
#ifdef KR_headers
(a, b) Bigint *a, *b;
#else
(Bigint *a, Bigint *b)
#endif
{
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;
}
static Bigint *
diff
#ifdef KR_headers
(KRm1 a, b) KRm2 Bigint *a, *b;
#else
(mdec Bigint *a, Bigint *b)
#endif
{
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(mcall 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(mcall a->k);
if (c == NULL) return NULL;
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
#ifdef KR_headers
(x) U *x;
#else
(U *x)
#endif
{
Long L;
U u;
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(&u) = L;
word1(&u) = 0;
#ifndef Avoid_Underflow
#ifndef Sudden_Underflow
}
else {
L = -L >> Exp_shift;
if (L < Exp_shift) {
word0(&u) = 0x80000 >> L;
word1(&u) = 0;
}
else {
word0(&u) = 0;
L -= Exp_shift;
word1(&u) = L >= 31 ? 1 : 1 << 31 - L;
}
}
#endif
#endif
return dval(&u);
}
static double
b2d
#ifdef KR_headers
(a, e) Bigint *a; int *e;
#else
(Bigint *a, int *e)
#endif
{
ULong *xa, *xa0, w, y, z;
int k;
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
#ifdef KR_headers
(KRm1 d, e, bits) KRm2 U *d; int *e, *bits;
#else
(mdec U *d, int *e, int *bits)
#endif
{
Bigint *b;
int de, k;
ULong *x, y, z;
#ifndef Sudden_Underflow
int i;
#endif
#ifdef VAX
ULong d0, d1;
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(mcall 1);
#else
b = Balloc(mcall 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)))
z |= Exp_msk1;
#endif
#ifdef Pack_32
if ((y = d1)) {
if ((k = lo0bits(&y))) {
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 {
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
#ifdef KR_headers
(a, b) Bigint *a, *b;
#else
(Bigint *a, Bigint *b)
#endif
{
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-256 */
#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
#undef Need_Hexdig
#ifdef INFNAN_CHECK
#ifndef No_Hex_NaN
#define Need_Hexdig
#endif
#endif
#ifndef Need_Hexdig
#ifndef NO_HEX_FP
#define Need_Hexdig
#endif
#endif
#ifdef Need_Hexdig /*{*/
static unsigned char hexdig[256];
static void
#ifdef KR_headers
htinit(h, s, inc) unsigned char *h; unsigned char *s; int inc;
#else
htinit(unsigned char *h, unsigned char *s, int inc)
#endif
{
int i, j;
for(i = 0; (j = s[i]) !=0; i++)
h[j] = i + inc;
}
static void
#ifdef KR_headers
hexdig_init()
#else
hexdig_init(void)
#endif
{
#define USC (unsigned char *)
htinit(hexdig, USC "0123456789", 0x10);
htinit(hexdig, USC "abcdef", 0x10 + 10);
htinit(hexdig, USC "ABCDEF", 0x10 + 10);
}
#endif /* } Need_Hexdig */
#ifdef INFNAN_CHECK
#ifndef NAN_WORD0
#define NAN_WORD0 0x7ff80000
#endif
#ifndef NAN_WORD1
#define NAN_WORD1 0
#endif
static int
match
#ifdef KR_headers
(sp, t) char **sp, *t;
#else
(CONST char **sp, char *t)
#endif
{
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
#ifdef KR_headers
(rvp, sp) U *rvp; CONST char **sp;
#else
(U *rvp, CONST char **sp)
#endif
{
ULong c, x[2];
CONST char *s;
int c1, havedig, udx0, xshift;
if (!hexdig['0'])
hexdig_init();
x[0] = x[1] = 0;
havedig = xshift = 0;
udx0 = 1;
s = *sp;
/* allow optional initial 0x or 0X */
while((c = *(CONST unsigned char*)(s+1)) && c <= ' ')
++s;
if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X'))
s += 2;
while((c = *(CONST unsigned char*)++s)) {
if ((c1 = hexdig[c]))
c = c1 & 0xf;
else if (c <= ' ') {
if (udx0 && havedig) {
udx0 = 0;
xshift = 1;
}
continue;
}
#ifdef GDTOA_NON_PEDANTIC_NANCHECK
else if (/*(*/ c == ')' && havedig) {
*sp = s + 1;
break;
}
else
return; /* invalid form: don't change *sp */
#else
else {
do {
if (/*(*/ c == ')') {
*sp = s + 1;
break;
}
} while((c = *++s));
break;
}
#endif
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 */
#ifdef Pack_32
#define ULbits 32
#define kshift 5
#define kmask 31
#else
#define ULbits 16
#define kshift 4
#define kmask 15
#endif
#ifndef NO_HEX_FP /*{*/
static void
#ifdef KR_headers
rshift(b, k) Bigint *b; int k;
#else
rshift(Bigint *b, int k)
#endif
{
ULong *x, *x1, *xe, y;
int n;
x = x1 = b->x;
n = k >> kshift;
if (n < b->wds) {
xe = x + b->wds;
x += n;
if (k &= kmask) {
n = 32 - k;
y = *x++ >> k;
while(x < xe) {
*x1++ = (y | (*x << n)) & 0xffffffff;
y = *x++ >> k;
}
if ((*x1 = y) !=0)
x1++;
}
else
while(x < xe)
*x1++ = *x++;
}
if ((b->wds = x1 - b->x) == 0)
b->x[0] = 0;
}
static ULong
#ifdef KR_headers
any_on(b, k) Bigint *b; int k;
#else
any_on(Bigint *b, int k)
#endif
{
int n, nwds;
ULong *x, *x0, x1, x2;
x = b->x;
nwds = b->wds;
n = k >> kshift;
if (n > nwds)
n = nwds;
else if (n < nwds && (k &= kmask)) {
x1 = x2 = x[n];
x1 >>= k;
x1 <<= k;
if (x1 != x2)
return 1;
}
x0 = x;
x += n;
while(x > x0)
if (*--x)
return 1;
return 0;
}
enum { /* rounding values: same as FLT_ROUNDS */
Round_zero = 0,
Round_near = 1,
Round_up = 2,
Round_down = 3
};
void
#ifdef KR_headers
gethex(sp, rvp, rounding, sign)
CONST char **sp; U *rvp; int rounding, sign;
#else
gethex( CONST char **sp, U *rvp, int rounding, int sign)
#endif
{
Bigint *b;
CONST unsigned char *decpt, *s0, *s, *s1;
Long e, e1;
ULong L, lostbits, *x;
int big, denorm, esign, havedig, k, n, nbits, up, zret;
#ifdef IBM
int j;
#endif
enum {
#ifdef IEEE_Arith /*{{*/
emax = 0x7fe - Bias - P + 1,
emin = Emin - P + 1
#else /*}{*/
emin = Emin - P,
#ifdef VAX
emax = 0x7ff - Bias - P + 1
#endif
#ifdef IBM
emax = 0x7f - Bias - P
#endif
#endif /*}}*/
};
#ifdef USE_LOCALE
int i;
#ifdef NO_LOCALE_CACHE
const unsigned char *decimalpoint = (unsigned char*)
localeconv()->decimal_point;
#else
const unsigned char *decimalpoint;
static unsigned char *decimalpoint_cache;
if (!(s0 = decimalpoint_cache)) {
s0 = (unsigned char*)localeconv()->decimal_point;
if ((decimalpoint_cache = (unsigned char*)
MALLOC(strlen((CONST char*)s0) + 1))) {
strcpy((char*)decimalpoint_cache, (CONST char*)s0);
s0 = decimalpoint_cache;
}
}
decimalpoint = s0;
#endif
#endif
if (!hexdig['0'])
hexdig_init();
havedig = 0;
s0 = *(CONST unsigned char **)sp + 2;
while(s0[havedig] == '0')
havedig++;
s0 += havedig;
s = s0;
decpt = 0;
zret = 0;
e = 0;
if (hexdig[*s])
havedig++;
else {
zret = 1;
#ifdef USE_LOCALE
for(i = 0; decimalpoint[i]; ++i) {
if (s[i] != decimalpoint[i])
goto pcheck;
}
decpt = s += i;
#else
if (*s != '.')
goto pcheck;
decpt = ++s;
#endif
if (!hexdig[*s])
goto pcheck;
while(*s == '0')
s++;
if (hexdig[*s])
zret = 0;
havedig = 1;
s0 = s;
}
while(hexdig[*s])
s++;
#ifdef USE_LOCALE
if (*s == *decimalpoint && !decpt) {
for(i = 1; decimalpoint[i]; ++i) {
if (s[i] != decimalpoint[i])
goto pcheck;
}
decpt = s += i;
#else
if (*s == '.' && !decpt) {
decpt = ++s;
#endif
while(hexdig[*s])
s++;
}/*}*/
if (decpt)
e = -(((Long)(s-decpt)) << 2);
pcheck:
s1 = s;
big = esign = 0;
switch(*s) {
case 'p':
case 'P':
switch(*++s) {
case '-':
esign = 1;
/* no break */
case '+':
s++;
}
if ((n = hexdig[*s]) == 0 || n > 0x19) {
s = s1;
break;
}
e1 = n - 0x10;
while((n = hexdig[*++s]) !=0 && n <= 0x19) {
if (e1 & 0xf8000000)
big = 1;
e1 = 10*e1 + n - 0x10;
}
if (esign)
e1 = -e1;
e += e1;
}
*sp = (char*)s;
if (!havedig)
*sp = (char*)s0 - 1;
if (zret)
goto retz1;
if (big) {
if (esign) {
#ifdef IEEE_Arith
switch(rounding) {
case Round_up:
if (sign)
break;
goto ret_tiny;
case Round_down:
if (!sign)
break;
goto ret_tiny;
}
#endif
goto retz;
#ifdef IEEE_Arith
ret_tiny:
#ifndef NO_ERRNO
errno = ERANGE;
#endif
word0(rvp) = 0;
word1(rvp) = 1;
return;
#endif /* IEEE_Arith */
}
switch(rounding) {
case Round_near:
goto ovfl1;
case Round_up:
if (!sign)
goto ovfl1;
goto ret_big;
case Round_down:
if (sign)
goto ovfl1;
goto ret_big;
}
ret_big:
word0(rvp) = Big0;
word1(rvp) = Big1;
return;
}
n = s1 - s0 - 1;
for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1)
k++;
b = Balloc(k);
x = b->x;
n = 0;
L = 0;
#ifdef USE_LOCALE
for(i = 0; decimalpoint[i+1]; ++i);
#endif
while(s1 > s0) {
#ifdef USE_LOCALE
if (*--s1 == decimalpoint[i]) {
s1 -= i;
continue;
}
#else
if (*--s1 == '.')
continue;
#endif
if (n == ULbits) {
*x++ = L;
L = 0;
n = 0;
}
L |= (hexdig[*s1] & 0x0f) << n;
n += 4;
}
*x++ = L;
b->wds = n = x - b->x;
n = ULbits*n - hi0bits(L);
nbits = Nbits;
lostbits = 0;
x = b->x;
if (n > nbits) {
n -= nbits;
if (any_on(b,n)) {
lostbits = 1;
k = n - 1;
if (x[k>>kshift] & 1 << (k & kmask)) {
lostbits = 2;
if (k > 0 && any_on(b,k))
lostbits = 3;
}
}
rshift(b, n);
e += n;
}
else if (n < nbits) {
n = nbits - n;
b = lshift(b, n);
e -= n;
x = b->x;
}
if (e > Emax) {
ovfl:
Bfree(b);
ovfl1:
#ifndef NO_ERRNO
errno = ERANGE;
#endif
word0(rvp) = Exp_mask;
word1(rvp) = 0;
return;
}
denorm = 0;
if (e < emin) {
denorm = 1;
n = emin - e;
if (n >= nbits) {
#ifdef IEEE_Arith /*{*/
switch (rounding) {
case Round_near:
if (n == nbits && (n < 2 || any_on(b,n-1)))
goto ret_tiny;
break;
case Round_up:
if (!sign)
goto ret_tiny;
break;
case Round_down:
if (sign)
goto ret_tiny;
}
#endif /* } IEEE_Arith */
Bfree(b);
retz:
#ifndef NO_ERRNO
errno = ERANGE;
#endif
retz1:
rvp->d = 0.;
return;
}
k = n - 1;
if (lostbits)
lostbits = 1;
else if (k > 0)
lostbits = any_on(b,k);
if (x[k>>kshift] & 1 << (k & kmask))
lostbits |= 2;
nbits -= n;
rshift(b,n);
e = emin;
}
if (lostbits) {
up = 0;
switch(rounding) {
case Round_zero:
break;
case Round_near:
if (lostbits & 2
&& (lostbits & 1) | (x[0] & 1))
up = 1;
break;
case Round_up:
up = 1 - sign;
break;
case Round_down:
up = sign;
}
if (up) {
k = b->wds;
b = increment(b);
x = b->x;
if (denorm) {
#if 0
if (nbits == Nbits - 1
&& x[nbits >> kshift] & 1 << (nbits & kmask))
denorm = 0; /* not currently used */
#endif
}
else if (b->wds > k
|| ((n = nbits & kmask) !=0
&& hi0bits(x[k-1]) < 32-n)) {
rshift(b,1);
if (++e > Emax)
goto ovfl;
}
}
}
#ifdef IEEE_Arith
if (denorm)
word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0;
else
word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20);
word1(rvp) = b->x[0];
#endif
#ifdef IBM
if ((j = e & 3)) {
k = b->x[0] & ((1 << j) - 1);
rshift(b,j);
if (k) {
switch(rounding) {
case Round_up:
if (!sign)
increment(b);
break;
case Round_down:
if (sign)
increment(b);
break;
case Round_near:
j = 1 << (j-1);
if (k & j && ((k & (j-1)) | lostbits))
increment(b);
}
}
}
e >>= 2;
word0(rvp) = b->x[1] | ((e + 65 + 13) << 24);
word1(rvp) = b->x[0];
#endif
#ifdef VAX
/* The next two lines ignore swap of low- and high-order 2 bytes. */
/* word0(rvp) = (b->x[1] & ~0x800000) | ((e + 129 + 55) << 23); */
/* word1(rvp) = b->x[0]; */
word0(rvp) = ((b->x[1] & ~0x800000) >> 16) | ((e + 129 + 55) << 7) | (b->x[1] << 16);
word1(rvp) = (b->x[0] >> 16) | (b->x[0] << 16);
#endif
Bfree(b);
}
#endif /*}!NO_HEX_FP*/
static Bigint *
#ifdef KR_headers
increment(KRm1 b) KRm2 Bigint *b;
#else
increment(mdec Bigint *b)
#endif
{
ULong *x, *xe;
Bigint *b1;
x = b->x;
xe = x + b->wds;
do {
if (*x < (ULong)0xffffffffL) {
++*x;
return b;
}
*x++ = 0;
} while(x < xe);
{
if (b->wds >= b->maxwds) {
b1 = Balloc(mcall b->k+1);
Bcopy(b1,b);
Bfree(mcall b);
b = b1;
}
b->x[b->wds++] = 1;
}
return b;
}
static int
#ifdef KR_headers
dshift(b, p2) Bigint *b; int p2;
#else
dshift(Bigint *b, int p2)
#endif
{
int rv = hi0bits(b->x[b->wds-1]) - 4;
if (p2 > 0)
rv -= p2;
return rv & kmask;
}
static int
quorem
#ifdef KR_headers
(b, S) Bigint *b, *S;
#else
(Bigint *b, Bigint *S)
#endif
{
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 NO_STRTOD_BIGCOMP
static void
bigcomp
#ifdef KR_headers
(KRm1 rv, s0, bc)
KRm2 U *rv; CONST char *s0; BCinfo *bc;
#else
(mdec U *rv, CONST char *s0, BCinfo *bc)
#endif
{
Bigint *b, *d;
int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase;
dsign = bc->dsign;
nd = bc->nd;
nd0 = bc->nd0;
p5 = nd + bc->e0 - 1;
speccase = 0;
#ifndef Sudden_Underflow
if (rv->d == 0.) { /* special case: value near underflow-to-zero */
/* threshold was rounded to zero */
b = i2b(mcall 1);
p2 = Emin - P + 1;
bbits = 1;
#ifdef Avoid_Underflow
word0(rv) = (P+2) << Exp_shift;
#else
word1(rv) = 1;
#endif
i = 0;
#ifdef Honor_FLT_ROUNDS
if (bc->rounding == 1)
#endif
{
speccase = 1;
--p2;
dsign = 0;
goto have_i;
}
}
else
#endif
b = d2b(mcall rv, &p2, &bbits);
#ifdef Avoid_Underflow
p2 -= bc->scale;
#endif
/* floor(log2(rv)) == bbits - 1 + p2 */
/* Check for denormal case. */
i = P - bbits;
if (i > (j = P - Emin - 1 + p2)) {
#ifdef Sudden_Underflow
Bfree(b);
b = i2b(1);
p2 = Emin;
i = P - 1;
#ifdef Avoid_Underflow
word0(rv) = (1 + bc->scale) << Exp_shift;
#else
word0(rv) = Exp_msk1;
#endif
word1(rv) = 0;
#else
i = j;
#endif
}
#ifdef Honor_FLT_ROUNDS
if (bc->rounding != 1) {
if (i > 0)
b = lshift(mcall b, i);
if (dsign)
b = increment(mcall b);
}
else
#endif
{
b = lshift(mcall b, ++i);
b->x[0] |= 1;
}
#ifndef Sudden_Underflow
have_i:
#endif
p2 -= p5 + i;
d = i2b(mcall 1);
/* Arrange for convenient computation of quotients:
* shift left if necessary so divisor has 4 leading 0 bits.
*/
if (p5 > 0)
d = pow5mult(mcall d, p5);
else if (p5 < 0)
b = pow5mult(mcall b, -p5);
if (p2 > 0) {
b2 = p2;
d2 = 0;
}
else {
b2 = 0;
d2 = -p2;
}
i = dshift(d, d2);
if ((b2 += i) > 0)
b = lshift(mcall b, b2);
if ((d2 += i) > 0)
d = lshift(mcall d, d2);
/* Now b/d = exactly half-way between the two floating-point values */
/* on either side of the input string. Compute first digit of b/d. */
if (!(dig = quorem(b,d))) {
b = multadd(mcall b, 10, 0); /* very unlikely */
dig = quorem(b,d);
}
/* Compare b/d with s0 */
dd = 0;
for(i = 0; i < nd0; ) {
if ((dd = s0[i++] - '0' - dig))
goto ret;
if (!b->x[0] && b->wds == 1) {
if (i < nd)
dd = 1;
goto ret;
}
b = multadd(mcall b, 10, 0);
dig = quorem(b,d);
}
for(j = bc->dp1; i++ < nd;) {
if ((dd = s0[j++] - '0' - dig))
goto ret;
if (!b->x[0] && b->wds == 1) {
if (i < nd)
dd = 1;
goto ret;
}
b = multadd(mcall b, 10, 0);
dig = quorem(b,d);
}
if (b->x[0] || b->wds > 1)
dd = -1;
ret:
Bfree(mcall b);
Bfree(mcall d);
#ifdef Honor_FLT_ROUNDS
if (bc->rounding != 1) {
if (dd < 0) {
if (bc->rounding == 0) {
if (!dsign)
goto retlow1;
}
else if (dsign)
goto rethi1;
}
else if (dd > 0) {
if (bc->rounding == 0) {
if (dsign)
goto rethi1;
goto ret1;
}
if (!dsign)
goto rethi1;
dval(rv) += 2.*ulp(rv);
}
else {
bc->inexact = 0;
if (dsign)
goto rethi1;
}
}
else
#endif
if (speccase) {
if (dd <= 0)
rv->d = 0.;
}
else if (dd < 0) {
if (!dsign) /* does not happen for round-near */
retlow1:
dval(rv) -= ulp(rv);
}
else if (dd > 0) {
if (dsign) {
rethi1:
dval(rv) += ulp(rv);
}
}
else {
/* Exact half-way case: apply round-even rule. */
if (word1(rv) & 1) {
if (dsign)
goto rethi1;
goto retlow1;
}
}
#ifdef Honor_FLT_ROUNDS
ret1:
#endif
return;
}
#endif /* NO_STRTOD_BIGCOMP */
double
DTOA_MANGLE(strtod)
#ifdef KR_headers
(s00, se) CONST char *s00; char **se;
#else
(CONST char *s00, char **se)
#endif
{
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1;
int esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
CONST char *s, *s0, *s1;
double aadj, aadj1;
#ifdef Local_Private_Memory
MemInfo meminfo = { 0,0,0 }, *mem = &meminfo;
#endif
Long L;
U aadj2, adj, rv, rv0;
ULong y, z;
BCinfo bc;
Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
#ifdef SET_INEXACT
int oldinexact;
#endif
#ifdef Honor_FLT_ROUNDS /*{*/
#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
bc.rounding = Flt_Rounds;
#else /*}{*/
bc.rounding = 1;
switch(fegetround()) {
case FE_TOWARDZERO: bc.rounding = 0; break;
case FE_UPWARD: bc.rounding = 2; break;
case FE_DOWNWARD: bc.rounding = 3;
}
#endif /*}}*/
#endif /*}*/
#ifdef USE_LOCALE
CONST char *s2;
#endif
#ifdef Local_Private_Memory
meminfo.pmem_next = meminfo.private_mem;
#endif
memset(&meminfo.freelist,0,sizeof(meminfo.freelist)); // this should happen automatically
sign = nz0 = nz = bc.dplen = bc.uflchk = 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') {
#ifndef NO_HEX_FP /*{*/
switch(s[1]) {
case 'x':
case 'X':
#ifdef Honor_FLT_ROUNDS
gethex(&s, &rv, bc.rounding, sign);
#else
gethex(&s, &rv, 1, sign);
#endif
goto ret;
}
#endif /*}*/
nz0 = 1;
while(*++s == '0') ;
if (!*s)
goto ret;
}
s0 = s;
y = z = 0;
for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
if (nd < 9)
y = 10*y + c - '0';
else if (nd < 16)
z = 10*z + c - '0';
nd0 = nd;
bc.dp0 = bc.dp1 = s - s0;
#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 == '.') {
c = *++s;
bc.dp1 = s - s0;
bc.dplen = bc.dp1 - bc.dp0;
if (!nd) {
for(; c == '0'; c = *++s)
nz++;
if (c > '0' && c <= '9') {
s0 = s;
nf += nz;
nz = 0;
goto have_dig;
}
goto dig_done;
}
for(; c >= '0' && c <= '9'; c = *++s) {
have_dig:
nz++;
if (c -= '0') {
nf += nz;
for(i = 1; i < nz; i++)
if (nd++ < 9)
y *= 10;
else if (nd <= DBL_DIG + 1)
z *= 10;
if (nd++ < 9)
y = 10*y + c;
else if (nd <= DBL_DIG + 1)
z = 10*z + c;
nz = 0;
}
}
}
dig_done:
e = 0;
if (c == 'e' || c == 'E') {
if (!nd && !nz && !nz0) {
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 */
if (!bc.dplen)
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;
}
bc.e0 = e1 = e -= nf;
/* Now we have nd0 digits, starting at s0, followed by a
* decimal point, followed by nd-nd0 digits. The number we're
* after is the integer represented by those digits times
* 10**e */
if (!nd0)
nd0 = nd;
k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
dval(&rv) = y;
if (k > 9) {
#ifdef SET_INEXACT
if (k > DBL_DIG)
oldinexact = get_inexact();
#endif
dval(&rv) = tens[k - 9] * dval(&rv) + z;
}
bd0 = 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) {
rv.d = -rv.d;
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) {
rv.d = -rv.d;
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) {
rv.d = -rv.d;
sign = 0;
}
#endif
/* rv = */ rounded_quotient(dval(&rv), tens[-e]);
goto ret;
}
#endif
}
e1 += nd - k;
#ifdef IEEE_Arith
#ifdef SET_INEXACT
bc.inexact = 1;
if (k <= DBL_DIG)
oldinexact = get_inexact();
#endif
#ifdef Avoid_Underflow
bc.scale = 0;
#endif
#ifdef Honor_FLT_ROUNDS
if (bc.rounding >= 2) {
if (sign)
bc.rounding = bc.rounding == 2 ? 0 : 2;
else
if (bc.rounding != 2)
bc.rounding = 0;
}
#endif
#endif /*IEEE_Arith*/
/* Get starting approximation = rv * 10**e1 */
if (e1 > 0) {
if ((i = e1 & 15))
dval(&rv) *= tens[i];
if (e1 &= ~15) {
if (e1 > DBL_MAX_10_EXP) {
ovfl:
#ifndef NO_ERRNO
errno = ERANGE;
#endif
/* Can't trust HUGE_VAL */
#ifdef IEEE_Arith
#ifdef Honor_FLT_ROUNDS
switch(bc.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*/
goto ret;
}
e1 >>= 4;
for(j = 0; e1 > 1; j++, e1 >>= 1)
if (e1 & 1)
dval(&rv) *= bigtens[j];
/* The last multiplication could overflow. */
word0(&rv) -= P*Exp_msk1;
dval(&rv) *= bigtens[j];
if ((z = word0(&rv) & Exp_mask)
> Exp_msk1*(DBL_MAX_EXP+Bias-P))
goto ovfl;
if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
/* set to largest number */
/* (Can't trust DBL_MAX) */
word0(&rv) = Big0;
word1(&rv) = Big1;
}
else
word0(&rv) += P*Exp_msk1;
}
}
else if (e1 < 0) {
e1 = -e1;
if ((i = e1 & 15))
dval(&rv) /= tens[i];
if (e1 >>= 4) {
if (e1 >= 1 << n_bigtens)
goto undfl;
#ifdef Avoid_Underflow
if (e1 & Scale_Bit)
bc.scale = 2*P;
for(j = 0; e1 > 0; j++, e1 >>= 1)
if (e1 & 1)
dval(&rv) *= tinytens[j];
if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask)
>> Exp_shift)) > 0) {
/* scaled rv is denormal; clear 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
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 */
bc.nd = nd;
#ifndef NO_STRTOD_BIGCOMP
bc.nd0 = nd0; /* Only needed if nd > strtod_diglim, but done here */
/* to silence an erroneous warning about bc.nd0 */
/* possibly not being initialized. */
if (nd > strtod_diglim) {
/* ASSERT(strtod_diglim >= 18); 18 == one more than the */
/* minimum number of decimal digits to distinguish double values */
/* in IEEE arithmetic. */
i = j = 18;
if (i > nd0)
j += bc.dplen;
for(;;) {
if (--j <= bc.dp1 && j >= bc.dp0)
j = bc.dp0 - 1;
if (s0[j] != '0')
break;
--i;
}
e += nd - i;
nd = i;
if (nd0 > nd)
nd0 = nd;
if (nd < 9) { /* must recompute y */
y = 0;
for(i = 0; i < nd0; ++i)
y = 10*y + s0[i] - '0';
for(j = bc.dp1; i < nd; ++i)
y = 10*y + s0[j++] - '0';
}
}
#endif
bd0 = s2b(mcall s0, nd0, nd, y, bc.dplen);
for(;;) {
bd = Balloc(mcall bd0->k);
Bcopy(bd, bd0);
bb = d2b(mcall &rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
bs = i2b(mcall 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 (bc.rounding != 1)
bs2++;
#endif
#ifdef Avoid_Underflow
j = bbe - bc.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 += bc.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(mcall bs, bb5);
bb1 = mult(mcall bs, bb);
Bfree(mcall bb);
bb = bb1;
}
if (bb2 > 0)
bb = lshift(mcall bb, bb2);
if (bd5 > 0)
bd = pow5mult(mcall bd, bd5);
if (bd2 > 0)
bd = lshift(mcall bd, bd2);
if (bs2 > 0)
bs = lshift(mcall bs, bs2);
delta = diff(mcall bb, bd);
bc.dsign = delta->sign;
delta->sign = 0;
i = cmp(delta, bs);
#ifndef NO_STRTOD_BIGCOMP
if (bc.nd > nd && i <= 0) {
if (bc.dsign)
break; /* Must use bigcomp(). */
#ifdef Honor_FLT_ROUNDS
if (bc.rounding != 1) {
if (i < 0)
break;
}
else
#endif
{
bc.nd = nd;
i = -1; /* Discarded digits make delta smaller. */
}
}
#endif
#ifdef Honor_FLT_ROUNDS
if (bc.rounding != 1) {
if (i < 0) {
/* Error is less than an ulp */
if (!delta->x[0] && delta->wds <= 1) {
/* exact */
#ifdef SET_INEXACT
bc.inexact = 0;
#endif
break;
}
if (bc.rounding) {
if (bc.dsign) {
adj.d = 1.;
goto apply_adj;
}
}
else if (!bc.dsign) {
adj.d = -1.;
if (!word1(&rv)
&& !(word0(&rv) & Frac_mask)) {
y = word0(&rv) & Exp_mask;
#ifdef Avoid_Underflow
if (!bc.scale || y > 2*P*Exp_msk1)
#else
if (y)
#endif
{
delta = lshift(mcall delta,Log2P);
if (cmp(delta, bs) <= 0)
adj.d = -0.5;
}
}
apply_adj:
#ifdef Avoid_Underflow
if (bc.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.d*ulp(dval(&rv));
word0(&rv) -= P*Exp_msk1;
}
else
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
dval(&rv) += adj.d*ulp(&rv);
}
break;
}
adj.d = ratio(delta, bs);
if (adj.d < 1.)
adj.d = 1.;
if (adj.d <= 0x7ffffffe) {
/* adj = rounding ? ceil(adj) : floor(adj); */
y = (ULong) adj.d;
if (y != adj.d) {
if (!((bc.rounding>>1) ^ bc.dsign))
y++;
adj.d = y;
}
}
#ifdef Avoid_Underflow
if (bc.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.d *= ulp(dval(&rv));
if (bc.dsign)
dval(&rv) += adj.d;
else
dval(&rv) -= adj.d;
word0(&rv) -= P*Exp_msk1;
goto cont;
}
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
adj.d *= ulp(&rv);
if (bc.dsign) {
if (word0(&rv) == Big0 && word1(&rv) == Big1)
goto ovfl;
dval(&rv) += adj.d;
}
else
dval(&rv) -= adj.d;
goto cont;
}
#endif /*Honor_FLT_ROUNDS*/
if (i < 0) {
/* Error is less than half an ulp -- check for
* special case of mantissa a power of two.
*/
if (bc.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)
bc.inexact = 0;
#endif
break;
}
if (!delta->x[0] && delta->wds <= 1) {
/* exact result */
#ifdef SET_INEXACT
bc.inexact = 0;
#endif
break;
}
delta = lshift(mcall delta,Log2P);
if (cmp(delta, bs) > 0)
goto drop_down;
break;
}
if (i == 0) {
/* exactly half-way between */
if (bc.dsign) {
if ((word0(&rv) & Bndry_mask1) == Bndry_mask1
&& word1(&rv) == (
#ifdef Avoid_Underflow
(bc.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
bc.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 <= (bc.scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
#else
if (L <= Exp_msk1)
#endif /*Avoid_Underflow*/
#endif /*IBM*/
{
if (bc.nd >nd) {
bc.uflchk = 1;
break;
}
goto undfl;
}
L -= Exp_msk1;
#else /*Sudden_Underflow}{*/
#ifdef Avoid_Underflow
if (bc.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 */
if (bc.nd >nd) {
bc.uflchk = 1;
break;
}
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 (bc.dsign)
dval(&rv) += ulp(&rv);
#ifndef ROUND_BIASED
else {
dval(&rv) -= ulp(&rv);
#ifndef Sudden_Underflow
if (!dval(&rv)) {
if (bc.nd >nd) {
bc.uflchk = 1;
break;
}
goto undfl;
}
#endif
}
#ifdef Avoid_Underflow
bc.dsign = 1 - bc.dsign;
#endif
#endif
break;
}
if ((aadj = ratio(delta, bs)) <= 2.) {
if (bc.dsign)
aadj = aadj1 = 1.;
else if (word1(&rv) || word0(&rv) & Bndry_mask) {
#ifndef Sudden_Underflow
if (word1(&rv) == Tiny1 && !word0(&rv)) {
if (bc.nd >nd) {
bc.uflchk = 1;
break;
}
goto undfl;
}
#endif
aadj = 1.;
aadj1 = -1.;
}
else {
/* special case -- power of FLT_RADIX to be */
/* rounded down... */
if (aadj < 2./FLT_RADIX)
aadj = 1./FLT_RADIX;
else
aadj *= 0.5;
aadj1 = -aadj;
}
}
else {
aadj *= 0.5;
aadj1 = bc.dsign ? aadj : -aadj;
#ifdef Check_FLT_ROUNDS
switch(bc.rounding) {
case 2: /* towards +infinity */
aadj1 -= 0.5;
break;
case 0: /* towards 0 */
case 3: /* towards -infinity */
aadj1 += 0.5;
}
#else
if (Flt_Rounds == 0)
aadj1 += 0.5;
#endif /*Check_FLT_ROUNDS*/
}
y = word0(&rv) & Exp_mask;
/* Check for overflow */
if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
dval(&rv0) = dval(&rv);
word0(&rv) -= P*Exp_msk1;
adj.d = aadj1 * ulp(&rv);
dval(&rv) += adj.d;
if ((word0(&rv) & Exp_mask) >=
Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
if (word0(&rv0) == Big0 && word1(&rv0) == Big1)
goto ovfl;
word0(&rv) = Big0;
word1(&rv) = Big1;
goto cont;
}
else
word0(&rv) += P*Exp_msk1;
}
else {
#ifdef Avoid_Underflow
if (bc.scale && y <= 2*P*Exp_msk1) {
if (aadj <= 0x7fffffff) {
if ((z = (ULong) aadj) <= 0)
z = 1;
aadj = z;
aadj1 = bc.dsign ? aadj : -aadj;
}
dval(&aadj2) = aadj1;
word0(&aadj2) += (2*P+1)*Exp_msk1 - y;
aadj1 = dval(&aadj2);
}
adj.d = aadj1 * ulp(&rv);
dval(&rv) += adj.d;
#else
#ifdef Sudden_Underflow
if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) {
dval(&rv0) = dval(&rv);
word0(&rv) += P*Exp_msk1;
adj.d = aadj1 * ulp(&rv);
dval(&rv) += adj.d;
#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) {
if (bc.nd >nd) {
bc.uflchk = 1;
break;
}
goto undfl;
}
word0(&rv) = Tiny0;
word1(&rv) = Tiny1;
goto cont;
}
else
word0(&rv) -= P*Exp_msk1;
}
else {
adj.d = aadj1 * ulp(&rv);
dval(&rv) += adj.d;
}
#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.) {
aadj1 = (double)(int)(aadj + 0.5);
if (!bc.dsign)
aadj1 = -aadj1;
}
adj.d = aadj1 * ulp(&rv);
dval(&rv) += adj.d;
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
}
z = word0(&rv) & Exp_mask;
#ifndef SET_INEXACT
if (bc.nd == nd) {
#ifdef Avoid_Underflow
if (!bc.scale)
#endif
if (y == z) {
/* Can we stop now? */
L = (Long)aadj;
aadj -= L;
/* The tolerances below are conservative. */
if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
if (aadj < .4999999 || aadj > .5000001)
break;
}
else if (aadj < .4999999/FLT_RADIX)
break;
}
}
#endif
cont:
Bfree(mcall bb);
Bfree(mcall bd);
Bfree(mcall bs);
Bfree(mcall delta);
}
Bfree(mcall bb);
Bfree(mcall bd);
Bfree(mcall bs);
Bfree(mcall bd0);
Bfree(mcall delta);
#ifndef NO_STRTOD_BIGCOMP
if (bc.nd > nd)
bigcomp(mcall &rv, s0, &bc);
#endif
#ifdef SET_INEXACT
if (bc.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 (bc.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 */
#ifdef IEEE_Arith
if (!(word0(&rv) & Exp_mask))
#else
if (word0(&rv) == 0 && word1(&rv) == 0)
#endif
errno = ERANGE;
#endif
}
#endif /* Avoid_Underflow */
#ifdef SET_INEXACT
if (bc.inexact && !(word0(&rv) & Exp_mask)) {
/* set underflow bit */
dval(&rv0) = 1e-300;
dval(&rv0) *= dval(&rv0);
}
#endif
ret:
if (se)
*se = (char *)s;
return sign ? -dval(&rv) : dval(&rv);
}
#if !defined(MULTIPLE_THREADS) && !defined(Local_Private_Memory)
static char *dtoa_result;
#endif
static char *
#ifdef KR_headers
rv_alloc(KRm1 i) KRm2 int i;
#else
rv_alloc(mdec int i)
#endif
{
int j, k, *r;
j = sizeof(ULong);
for(k = 0;
sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned int) i;
j <<= 1)
k++;
#ifdef Local_Private_Memory
if (k > mem->return_storage_size) return NULL;
r = (int *) mem->return_storage;
#else
r = (int*)Balloc(mcall k);
if (r == 0) return NULL;
#endif
*r = k;
return
#if !defined(MULTIPLE_THREADS) && !defined(Local_Private_Memory)
dtoa_result =
#endif
(char *)(r+1);
}
static char *
#ifdef KR_headers
nrv_alloc(KRm1 s, rve, n) KRm2 char *s, **rve; int n;
#else
nrv_alloc(mdec char *s, char **rve, int n)
#endif
{
char *rv, *t;
t = rv = rv_alloc(mcall n);
if (rv == NULL) return NULL;
while((*t = *s++)) t++;
if (rve)
*rve = t;
return rv;
}
/* freedtoa(s) must be used to free values s returned by dtoa
* when MULTIPLE_THREADS is #defined. It should be used in all cases
* except if Local_Private_Memory is defined, but for consistency with
* earlier versions of dtoa, it is optional when MULTIPLE_THREADS is
* not defined.
*/
void
#ifdef KR_headers
freedtoa(s) char *s;
#else
freedtoa(char *s)
#endif
{
#ifndef Local_Private_Memory
Bigint *b = (Bigint *)((int *)s - 1);
b->maxwds = 1 << (b->k = *(int*)b);
Bfree(b);
#ifndef MULTIPLE_THREADS
if (s == dtoa_result)
dtoa_result = 0;
#endif
#endif
s = s; // @@@RAD avoid warning
}
/* 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.
*/
#ifdef Local_Private_Memory
char *
DTOA_MANGLE(dtoa)
#ifdef KR_headers
(dd, mode, ndigits, decpt, sign, rv, rv_length)
double dd; int mode, ndigits, *decpt, *sign; char *rv; int rv_length;
#else
(double dd, int mode, int ndigits, int *decpt, int *sign, char *rv, int rv_length)
#endif
#else
char *
DTOA_MANGLE(dtoa)
#ifdef KR_headers
(dd, mode, ndigits, decpt, sign, rve)
double dd; int mode, ndigits, *decpt, *sign; char **rve;
#else
(double dd, int mode, int ndigits, int *decpt, int *sign, char **rve)
#endif
#endif
{
/* 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;
Long L;
#ifdef Local_Private_Memory
MemInfo meminfo = { 0,0,0 }, *mem = &meminfo;
char *dummy, **rve = &dummy;
#endif
#ifndef Sudden_Underflow
int denorm;
ULong x;
#endif
Bigint *b, *b1, *delta, *mlo=0, *mhi, *S;
U d2, eps, u;
double ds;
char *s, *s0;
#ifdef SET_INEXACT
int inexact, oldinexact;
#endif
#ifdef Honor_FLT_ROUNDS /*{*/
int Rounding;
#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
Rounding = Flt_Rounds;
#else /*}{*/
Rounding = 1;
switch(fegetround()) {
case FE_TOWARDZERO: Rounding = 0; break;
case FE_UPWARD: Rounding = 2; break;
case FE_DOWNWARD: Rounding = 3;
}
#endif /*}}*/
#endif /*}*/
#ifdef Local_Private_Memory
meminfo.return_storage = rv;
meminfo.return_storage_size = rv_length;
meminfo.pmem_next = meminfo.private_mem;
#endif
#ifndef Local_Private_Memory
#ifndef MULTIPLE_THREADS
if (dtoa_result) {
freedtoa(dtoa_result);
dtoa_result = 0;
}
#endif
#endif
memset(&meminfo.freelist,0,sizeof(meminfo.freelist)); // this should happen automatically
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 defined(IEEE_Arith) + defined(VAX)
#ifdef IEEE_Arith
if ((word0(&u) & Exp_mask) == Exp_mask)
#else
if (word0(&u) == 0x8000)
#endif
{
/* Infinity or NaN */
*decpt = 9999;
#ifdef IEEE_Arith
if (!word1(&u) && !(word0(&u) & 0xfffff))
return nrv_alloc(mcall "Infinity", rve, 8);
#endif
return nrv_alloc(mcall "NaN", rve, 3);
}
#endif
#ifdef IBM
dval(&u) += 0; /* normalize */
#endif
if (!dval(&u)) {
*decpt = 1;
return nrv_alloc(mcall "0", rve, 1);
}
#ifdef SET_INEXACT
try_quick = oldinexact = get_inexact();
inexact = 1;
#endif
#ifdef Honor_FLT_ROUNDS
if (Rounding >= 2) {
if (*sign)
Rounding = Rounding == 2 ? 0 : 2;
else
if (Rounding != 2)
Rounding = 0;
}
#endif
b = d2b(mcall &u, &be, &bbits);
#ifdef Sudden_Underflow
i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
#else
if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
#endif
dval(&d2) = dval(&u);
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(&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;
}
#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(&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;
#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; /* Values for cases 0 and 1; done here to */
/* silence erroneous "gcc -Wall" warning. */
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(mcall i);
#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;
}
#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 = (ULong) dval(&u);
rrAssert(L >= 0 && L <= 9);
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 {
#endif
/* Generate ilim digits, then fix them up. */
dval(&eps) *= tens[ilim-1];
for(i = 1;; i++, dval(&u) *= 10.) {
L = (Long)(dval(&u));
rrAssert(L >= 0 && L <= 9);
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;
}
}
#ifndef No_leftright
}
#endif
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)) {
#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(&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 =
#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(mcall 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(mcall mhi, m5);
b1 = mult(mcall mhi, b);
Bfree(mcall b);
b = b1;
}
if ((j = b5 - m5))
b = pow5mult(mcall b, j);
}
else
b = pow5mult(mcall b, b5);
}
S = i2b(mcall 1);
if (s5 > 0)
S = pow5mult(mcall 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(&u) && !(word0(&u) & Bndry_mask)
#ifndef Sudden_Underflow
&& word0(&u) & (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))
i = 32 - i;
#define iInc 28
#else
if (i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf)
i = 16 - i;
#define iInc 12
#endif
i = dshift(S, s2);
b2 += i;
m2 += i;
s2 += i;
if (b2 > 0)
b = lshift(mcall b, b2);
if (s2 > 0)
S = lshift(mcall S, s2);
if (k_check) {
if (cmp(b,S) < 0) {
k--;
b = multadd(mcall b, 10, 0); /* we botched the k estimate */
if (leftright)
mhi = multadd(mcall mhi, 10, 0);
ilim = ilim1;
}
}
if (ilim <= 0 && (mode == 3 || mode == 5)) {
if (ilim < 0 || cmp(b,S = multadd(mcall 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(mcall mhi, m2);
/* Compute mlo -- check for special case
* that d is a normalized power of 2.
*/
mlo = mhi;
if (spec_case) {
mhi = Balloc(mcall mhi->k);
Bcopy(mhi, mlo);
mhi = lshift(mcall 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(mcall S, mhi);
j1 = delta->sign ? 1 : cmp(b, delta);
Bfree(mcall delta);
#ifndef ROUND_BIASED
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++;
#ifdef SET_INEXACT
else if (!b->x[0] && b->wds <= 1)
inexact = 0;
#endif
*s++ = (char)dig;
goto ret;
}
#endif
if (j < 0 || (j == 0 && mode != 1
#ifndef ROUND_BIASED
&& !(word1(&u) & 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(mcall b, 1);
j1 = cmp(b, S);
if ((j1 > 0 || (j1 == 0 && dig & 1))
&& dig++ == '9')
goto round_9_up;
}
accept_dig:
*s++ = (char)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++ = (char)(dig + 1);
goto ret;
}
#ifdef Honor_FLT_ROUNDS
keep_dig:
#endif
*s++ = (char)dig;
if (i == ilim)
break;
b = multadd(mcall b, 10, 0);
if (mlo == mhi)
mlo = mhi = multadd(mcall mhi, 10, 0);
else {
mlo = multadd(mcall mlo, 10, 0);
mhi = multadd(mcall 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(mcall b, 10, 0);
}
/* Round off last digit */
#ifdef Honor_FLT_ROUNDS
switch(Rounding) {
case 0: goto trimzeros;
case 2: goto roundoff;
}
#endif
b = lshift(mcall b, 1);
j = cmp(b, S);
if (j > 0 || (j == 0 && dig & 1)) {
roundoff:
while(*--s == '9')
if (s == s0) {
k++;
*s++ = '1';
goto ret;
}
++*s++;
}
else {
#ifdef Honor_FLT_ROUNDS
trimzeros:
#endif
while(*--s == '0');
s++;
}
ret:
Bfree(mcall S);
if (mhi) {
if (mlo && mlo != mhi)
Bfree(mcall mlo);
Bfree(mcall mhi);
}
ret1:
#ifdef SET_INEXACT
if (inexact) {
if (!oldinexact) {
word0(&u) = Exp_1 + (70 << Exp_shift);
word1(&u) = 0;
dval(&u) += 1.;
}
}
else if (!oldinexact)
clear_inexact();
#endif
Bfree(mcall b);
*s = 0;
*decpt = k + 1;
if (rve)
*rve = s;
return s0;
}
#ifdef __cplusplus
}
#endif
Raw
dtoa.h
// To avoid name conflicts, add a prefix.
#define DTOA_MANGLE(name) rr_ ## name
#ifdef __cplusplus
extern "C" {
#endif
double DTOA_MANGLE(strtod)(const char *s00, char **se);
char *DTOA_MANGLE(dtoa)(double d, int mode, int ndigits,
int *decpt, int *sign, char *rv, int rv_length);
#ifdef __cplusplus
}
#endif
@gpakosz
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gpakosz commented Jul 8, 2016

https://gist.github.com/rygorous/6628262#file-dtoa-c-L144 <-- FLT_ROUNDS

@gpakosz
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gpakosz commented Nov 21, 2019

When Honor_FLT_ROUNDS and Trust_FLT_ROUNDS are not defined, which is the default for Windows + recent MSVC versions, and other operating systems, then bc.rounding remains undefined: https://gist.github.com/rygorous/6628262#file-dtoa-c-L2566-L2577

#ifdef Honor_FLT_ROUNDS /*{*/
#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
   bc.rounding = Flt_Rounds;
#else /*}{*/
   bc.rounding = 1;
   switch(fegetround()) {
     case FE_TOWARDZERO:   bc.rounding = 0; break;
     case FE_UPWARD:   bc.rounding = 2; break;
     case FE_DOWNWARD:   bc.rounding = 3;
     }
#endif /*}}*/
#endif /*}*/

I made all my double round-trip unit tests pass by initializing bc.rounding to 1:

#ifdef Honor_FLT_ROUNDS /*{*/
#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
   bc.rounding = Flt_Rounds;
#else /*}{*/
   bc.rounding = 1;
   switch(fegetround()) {
     case FE_TOWARDZERO:   bc.rounding = 0; break;
     case FE_UPWARD:   bc.rounding = 2; break;
     case FE_DOWNWARD:   bc.rounding = 3;
     }
#endif /*}}*/
#else
  bc.rounding = 1;
#endif /*}*/

Hope that helps 🤞

@rygorous
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rygorous commented Nov 22, 2019 via email

@gpakosz
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gpakosz commented Nov 23, 2019

No problem. We didn't use strtod() at first as we were only serializing and reading back float values. But since recently we have a need for double values that round-trip

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