dtoa.c
/****************************************************************
*
* 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).
*/
/*
* This file has been modified to remove dtoa() and all
* non-reentrancy. This makes it slower, but it also makes life a lot
* easier on Windows and other platforms without static lock
* initializers (grumble).
*/
/* Added by dhuggins@cs.cmu.edu to use autoconf results. */
/* We do not care about the VAX. */
#include "config.h"
#ifdef WORDS_BIGENDIAN
#define IEEE_MC68k
#else
#define IEEE_8087
#endif
#ifndef HAVE_LONG_LONG
#define NO_LONG_LONG
#endif
#define Omit_Private_Memory
#include "sphinxbase/ckd_alloc.h"
#undef USE_LOCALE
/* Correct totally bogus typedefs in this code. */
#include "sphinxbase/prim_type.h"
#define Long int32 /* ZOMG */
#define ULong uint32 /* WTF */
/*
* #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.
* #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 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 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.
*/
#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
/* Private memory and other non-reentrant stuff removed. */
#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
#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 YES_ALIAS
#define dval(x) x
#ifdef IEEE_8087
#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
#ifdef IEEE_8087
#define word0(x) ((U*)&x)->L[1]
#define word1(x) ((U*)&x)->L[0]
#else
#define word0(x) ((U*)&x)->L[0]
#define word1(x) ((U*)&x)->L[1]
#endif
#define dval(x) ((U*)&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_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 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)
#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
#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 15
#ifdef __cplusplus
extern "C" double sb_strtod(const char *s00, char **se);
#endif
struct
Bigint {
struct Bigint *next;
int k, maxwds, sign, wds;
ULong x[1];
};
typedef struct Bigint Bigint;
static Bigint *
Balloc
#ifdef KR_headers
(k) int k;
#else
(int k)
#endif
{
int x;
size_t len;
Bigint *rv;
x = 1 << k;
len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
/sizeof(double);
rv = ckd_malloc(len*sizeof(double));
rv->k = k;
rv->maxwds = x;
rv->sign = rv->wds = 0;
return rv;
}
static void
Bfree
#ifdef KR_headers
(v) Bigint *v;
#else
(Bigint *v)
#endif
{
ckd_free(v);
}
#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
y->wds*sizeof(Long) + 2*sizeof(int))
static Bigint *
multadd
#ifdef KR_headers
(b, m, a) Bigint *b; int m, a;
#else
(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++ = 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++] = carry;
b->wds = wds;
}
return b;
}
static Bigint *
s2b
#ifdef KR_headers
(s, nd0, nd, y9) CONST char *s; int nd0, nd; ULong y9;
#else
(CONST char *s, int nd0, int nd, ULong y9)
#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(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
#ifdef KR_headers
(x) register ULong x;
#else
(register ULong x)
#endif
{
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
#ifdef KR_headers
(y) ULong *y;
#else
(ULong *y)
#endif
{
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
#ifdef KR_headers
(i) int i;
#else
(int i)
#endif
{
Bigint *b;
b = Balloc(1);
b->x[0] = i;
b->wds = 1;
return b;
}
static Bigint *
mult
#ifdef KR_headers
(a, b) Bigint *a, *b;
#else
(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(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++)) {
x = xa;
xc = xc0;
carry = 0;
do {
z = *x++ * (ULLong)y + *xc + carry;
carry = z >> 32;
*xc++ = z & FFFFFFFF;
}
while(x < xae);
*xc = 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
(b, k) Bigint *b; int k;
#else
(Bigint *b, int k)
#endif
{
Bigint *b1, *p5, *p51;
int i;
static int CONST p05[3] = { 5, 25, 125 };
if ((i = k & 3))
b = multadd(b, p05[i-1], 0);
if (!(k >>= 2))
return b;
p5 = i2b(625);
for(;;) {
if (k & 1) {
b1 = mult(b, p5);
Bfree(b);
b = b1;
}
if (!(k >>= 1))
break;
p51 = mult(p5,p5);
Bfree(p5);
p5 = p51;
}
Bfree(p5);
return b;
}
static Bigint *
lshift
#ifdef KR_headers
(b, k) Bigint *b; int k;
#else
(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(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(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
(a, b) Bigint *a, *b;
#else
(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(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++ = y & FFFFFFFF;
}
while(xb < xbe);
while(xa < xae) {
y = *xa++ - borrow;
borrow = y >> 32 & (ULong)1;
*xc++ = 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) double x;
#else
(double x)
#endif
{
register Long L;
U a;
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
#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
(d, e, bits) double d; int *e, *bits;
#else
(double _d, int *e, int *bits)
#endif
{
Bigint *b;
int de, k;
ULong *x, y, z;
U d;
#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
dval(d) = _d;
#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)))
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 {
#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
#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-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
#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) double *rvp; CONST char **sp;
#else
(U *rvp, CONST char **sp)
#endif
{
ULong c, x[2];
CONST char *s;
int havedig, udx0, xshift;
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 (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;
}
#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 */
double
sb_strtod
#ifdef KR_headers
(s00, se) CONST char *s00; char **se;
#else
(CONST char *s00, char **se)
#endif
{
#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;
U rv, rv0, aadj1;
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
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') {
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;
#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;
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 */
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 + 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 = -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) {
rv = -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) {
rv = -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))
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))
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 = (uint32)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 = 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 = 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.) {
aadj1 = (double)(int)(aadj + 0.5);
if (!dsign)
aadj1 = -aadj1;
}
adj = 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);
}
#ifdef __cplusplus
}
#endif
ckd_alloc.h
Sphinx&#39;s memory allocation/deallocation routines.
prim_type.h
Basic type definitions used in Sphinx.
ckd_free
SPHINXBASE_EXPORT void ckd_free(void *ptr)
Test and free a 1-D array.
Definition: ckd_alloc.c:241
Bigint
Definition: dtoa.c:500
ckd_malloc
#define ckd_malloc(sz)
Macro for ckd_malloc
Definition: ckd_alloc.h:253
U
Union to extract the bytes of a double.
Definition: dtoa.c:291