js/src/dtoa.c
author Cristian Tuns <ctuns@mozilla.com>
Thu, 02 Feb 2023 08:48:01 -0500
changeset 651550 ba5f6662ca8058d3e646c042c5bbaa8b0ef027ca
parent 619275 452717550d2c80d18cc900fcdf91c24b4f73694b
permissions -rw-r--r--
Backed out changeset aefea186c9bc (bug 1810790) for causing mochitest failures on performance/browser_preferences_usage.js CLOSED TREE

/* -*- Mode: C; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */
/****************************************************************
 *
 * 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.
 * #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.  (Unless you #define
 *	NO_GLOBAL_STATE and call destroydtoa, 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 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 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_GLOBAL_STATE to avoid defining any non-const global or
 *	static variables. Instead the necessary state is stored in an
 *	opaque struct, DtoaState, a pointer to which must be passed to
 *	every entry point. Two new functions are added to the API:
 *		DtoaState *newdtoa(void);
 *		void destroydtoa(DtoaState *);
 */

#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 MALLOC
#ifdef KR_headers
extern char *MALLOC();
#else
extern void *MALLOC(size_t);
#endif
#else
#define MALLOC malloc
#endif

#ifndef FREE
#define FREE free
#endif

#ifndef Omit_Private_Memory
#ifndef PRIVATE_MEM
#define PRIVATE_MEM 2304
#endif
#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
#endif

#undef IEEE_Arith
#undef Avoid_Underflow
#ifdef IEEE_MC68k
#define IEEE_Arith
#endif
#ifdef IEEE_8087
#define IEEE_Arith
#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

#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
#error "Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined."
#endif

typedef union { double d; ULong L[2]; } U;

#define dval(x) ((x).d)
#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

/* 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 7

 struct
Bigint {
	struct Bigint *next;
	int k, maxwds, sign, wds;
	ULong x[1];
	};

 typedef struct Bigint Bigint;

#ifdef NO_GLOBAL_STATE
#ifdef MULTIPLE_THREADS
#error "cannot have both NO_GLOBAL_STATE and MULTIPLE_THREADS"
#endif
 struct
DtoaState {
#define DECLARE_GLOBAL_STATE  /* nothing */
#else
#define DECLARE_GLOBAL_STATE static
#endif

	DECLARE_GLOBAL_STATE Bigint *freelist[Kmax+1];
	DECLARE_GLOBAL_STATE Bigint *p5s;
#ifndef Omit_Private_Memory
	DECLARE_GLOBAL_STATE double private_mem[PRIVATE_mem];
	DECLARE_GLOBAL_STATE double *pmem_next
#ifndef NO_GLOBAL_STATE
	                                       = private_mem
#endif
	                                                    ;
#endif
#ifdef NO_GLOBAL_STATE
	};
 typedef struct DtoaState DtoaState;
#ifdef KR_headers
#define STATE_PARAM state,
#define STATE_PARAM_DECL DtoaState *state;
#else
#define STATE_PARAM DtoaState *state,
#endif
#define PASS_STATE state,
#define GET_STATE(field) (state->field)

 static DtoaState *
newdtoa(void)
{
	DtoaState *state = (DtoaState *) MALLOC(sizeof(DtoaState));
	if (state) {
		memset(state, 0, sizeof(DtoaState));
#ifndef Omit_Private_Memory
		state->pmem_next = state->private_mem;
#endif
		}
	return state;
}

 static void
destroydtoa
#ifdef KR_headers
	(state) STATE_PARAM_DECL
#else
	(DtoaState *state)
#endif
{
	int i;
	Bigint *v, *next;

	for (i = 0; i <= Kmax; i++) {
		for (v = GET_STATE(freelist)[i]; v; v = next) {
			next = v->next;
#ifndef Omit_Private_Memory
			if ((double*)v < GET_STATE(private_mem) ||
			    (double*)v >= GET_STATE(private_mem) + PRIVATE_mem)
#endif
				FREE((void*)v);
			}
		}
#ifdef Omit_Private_Memory
	Bigint* p5 = GET_STATE(p5s);
	while (p5) {
		Bigint* tmp = p5;
		p5 = p5->next;
		FREE(tmp);
		}
#endif
	FREE((void *)state);
}

#else
#define STATE_PARAM      /* nothing */
#define STATE_PARAM_DECL /* nothing */
#define PASS_STATE       /* nothing */
#define GET_STATE(name) name
#endif

 static Bigint *
Balloc
#ifdef KR_headers
	(STATE_PARAM k) STATE_PARAM_DECL int k;
#else
	(STATE_PARAM int k)
#endif
{
	int x;
	Bigint *rv;
#ifndef Omit_Private_Memory
	size_t 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 = GET_STATE(freelist)[k]))
		GET_STATE(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 && GET_STATE(pmem_next) - GET_STATE(private_mem) + len <= PRIVATE_mem) {
			rv = (Bigint*)GET_STATE(pmem_next);
			GET_STATE(pmem_next) += len;
			}
		else
			rv = (Bigint*)MALLOC(len*sizeof(double));
#endif
		rv->k = k;
		rv->maxwds = x;
		}
	FREE_DTOA_LOCK(0);
	rv->sign = rv->wds = 0;
	return rv;
	}

 static void
Bfree
#ifdef KR_headers
	(STATE_PARAM v) STATE_PARAM_DECL Bigint *v;
#else
	(STATE_PARAM Bigint *v)
#endif
{
	if (v) {
		if (v->k > Kmax)
			FREE((void*)v);
		else {
			ACQUIRE_DTOA_LOCK(0);
			v->next = GET_STATE(freelist)[v->k];
			GET_STATE(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
	(STATE_PARAM b, m, a) STATE_PARAM_DECL Bigint *b; int m, a;
#else
	(STATE_PARAM 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(PASS_STATE b->k+1);
			Bcopy(b1, b);
			Bfree(PASS_STATE b);
			b = b1;
			}
		b->x[wds++] = (ULong) carry;
		b->wds = wds;
		}
	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
	(STATE_PARAM i) STATE_PARAM_DECL int i;
#else
	(STATE_PARAM int i)
#endif
{
	Bigint *b;

	b = Balloc(PASS_STATE 1);
	b->x[0] = i;
	b->wds = 1;
	return b;
	}

 static Bigint *
lshift
#ifdef KR_headers
	(STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
#else
	(STATE_PARAM 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(PASS_STATE 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(PASS_STATE 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
	(STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
#else
	(STATE_PARAM 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(PASS_STATE 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(PASS_STATE a->k);
	c->sign = i;
	wa = a->wds;
	xa = a->x;
	xae = xa + wa;
	wb = b->wds;
	xb = b->x;
	xbe = xb + wb;
	xc = c->x;
	borrow = 0;
#ifdef ULLong
	do {
		y = (ULLong)*xa++ - *xb++ - borrow;
		borrow = y >> 32 & (ULong)1;
		*xc++ = (ULong) y & FFFFFFFF;
		}
		while(xb < xbe);
	while(xa < xae) {
		y = *xa++ - borrow;
		borrow = y >> 32 & (ULong)1;
		*xc++ = (ULong) y & FFFFFFFF;
		}
#else
#ifdef Pack_32
	do {
		y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
		borrow = (y & 0x10000) >> 16;
		z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
		borrow = (z & 0x10000) >> 16;
		Storeinc(xc, z, y);
		}
		while(xb < xbe);
	while(xa < xae) {
		y = (*xa & 0xffff) - borrow;
		borrow = (y & 0x10000) >> 16;
		z = (*xa++ >> 16) - borrow;
		borrow = (z & 0x10000) >> 16;
		Storeinc(xc, z, y);
		}
#else
	do {
		y = *xa++ - *xb++ - borrow;
		borrow = (y & 0x10000) >> 16;
		*xc++ = y & 0xffff;
		}
		while(xb < xbe);
	while(xa < xae) {
		y = *xa++ - borrow;
		borrow = (y & 0x10000) >> 16;
		*xc++ = y & 0xffff;
		}
#endif
#endif
	while(!*--xc)
		wa--;
	c->wds = wa;
	return c;
	}

 static Bigint *
d2b
#ifdef KR_headers
	(STATE_PARAM d, e, bits) STATE_PARAM_DECL U d; int *e, *bits;
#else
	(STATE_PARAM 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(PASS_STATE 1);
#else
	b = Balloc(PASS_STATE 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

#undef CONST