base_conversion.h

操作系统SunOS 4.1.3版本的源码

/*	@(#)base_conversion.h 1.1 92/07/30 SMI	*/

/*
 * Copyright (c) 1988 by Sun Microsystems, Inc.
 */

#include <errno.h>

#include <floatingpoint.h>

#ifdef DEBUG
#include <stdio.h>
#include <assert.h>
#endif

/* Sun floating-point PRIVATE include file.  */

/* PRIVATE MACROS	 */

#ifdef DEBUG
#define PRIVATE
#else
#define PRIVATE static
#endif

/* PRIVATE CONSTANTS	 */

#define	SINGLE_BIAS	  127
#define DOUBLE_BIAS	 1023
#define EXTENDED_BIAS	16383
#define QUAD_BIAS	16383

#define SINGLE_MAXE	  97	/* Maximum decimal exponent we need to
				 * consider. */
#define DOUBLE_MAXE	 771	/* Maximum decimal exponent we need to
				 * consider. */
#define EXTENDED_MAXE  12330	/* Maximum decimal exponent we need to
				 * consider. */
#define QUAD_MAXE  12330	/* Maximum decimal exponent we need to
				 * consider. */

#define UNPACKED_SIZE	5	/* Size of unpacked significand.  */

/* PRIVATE TYPES 	 */

typedef struct {		/* Unpack floating-point internal format. *//* V
				 * alue is 0.s0s1..sn * 2**(1+exponent) */
	int             sign;
	enum fp_class_type fpclass;
	int             exponent;	/* Unbiased exponent. */
	unsigned        significand[UNPACKED_SIZE];	/* Last word is round
							 * and sticky. */
}
                unpacked;

#ifdef i386
typedef struct {		/* Most significant word formats. */
	unsigned        significand:23;
	unsigned        exponent:8;
	unsigned        sign:1;
}
                single_msw;

typedef struct {
	unsigned        significand:20;
	unsigned        exponent:11;
	unsigned        sign:1;
}
                double_msw;

typedef struct {
	unsigned        exponent:15;
	unsigned        sign:1;
	unsigned        unused:16;
}
                extended_msw;

typedef struct {
	unsigned        significand:16;
	unsigned        exponent:15;
	unsigned        sign:1;
}
                quadruple_msw;

typedef struct {		/* Floating-point formats in detail. */
	single_msw      msw;
}
                single_formatted;

typedef struct {
	unsigned        significand2;
	double_msw      msw;
}
                double_formatted;

typedef struct {
	unsigned        significand2;
	unsigned        significand;
	extended_msw    msw;
}
                extended_formatted;

typedef struct {
	unsigned        significand4;
	unsigned        significand3;
	unsigned        significand2;
	quadruple_msw   msw;
}
                quadruple_formatted;
#else
typedef struct {		/* Most significant word formats. */
	unsigned        sign:1;
	unsigned        exponent:8;
	unsigned        significand:23;
}
                single_msw;

typedef struct {
	unsigned        sign:1;
	unsigned        exponent:11;
	unsigned        significand:20;
}
                double_msw;

typedef struct {
	unsigned        sign:1;
	unsigned        exponent:15;
	unsigned        unused:16;
}
                extended_msw;

typedef struct {
	unsigned        sign:1;
	unsigned        exponent:15;
	unsigned        significand:16;
}
                quadruple_msw;

typedef struct {		/* Floating-point formats in detail. */
	single_msw      msw;
}
                single_formatted;

typedef struct {
	double_msw      msw;
	unsigned        significand2;
}
                double_formatted;

typedef struct {
	extended_msw    msw;
	unsigned        significand;
	unsigned        significand2;
}
                extended_formatted;

typedef struct {
	quadruple_msw   msw;
	unsigned        significand2;
	unsigned        significand3;
	unsigned        significand4;
}
                quadruple_formatted;
#endif

typedef union {			/* Floating-point formats equivalenced. */
	single_formatted f;
	single          x;
}
                single_equivalence;

typedef union {
	double_formatted f;
	double          x;
}
                double_equivalence;

typedef union {
	extended_formatted f;
	extended        x;
}
                extended_equivalence;

typedef union {
	quadruple_formatted f;
	quadruple       x;
}
                quadruple_equivalence;

/* PRIVATE GLOBAL VARIABLES */

fp_exception_field_type _fp_current_exceptions;	/* Current floating-point
						 * exceptions. */

enum fp_direction_type
                _fp_current_direction;	/* Current rounding direction. */

enum fp_precision_type
                _fp_current_precision;	/* Current rounding precision. */

/* PRIVATE FUNCTIONS */

extern void 
_fp_normalize( /* pu */ );
/* unpacked        *pu ;           /* unpacked operand and result */

extern void 
_fp_leftshift( /* pu, n */ );
/*
 * unpacked       *pu; unsigned        n;
 */

extern void 
_fp_set_exception( /* ex */ );
/* enum fp_exception_type ex ;	/* exception to be set in curexcep */

/*
 * Default size for _big_float - suitable for single and double precision.
 */

#define _BIG_FLOAT_SIZE	(DECIMAL_STRING_LENGTH/2)
#define _BIG_FLOAT_DIGIT short unsigned	/* big_float significand type */

#define _INTEGER_SIZE	4932	/* Maximum number of integer digits in a
				 * representable extended or quad. */

typedef struct {		/* Variable-precision floating-point type
				 * used for intermediate results.	 */
	unsigned short  bsize;	/* Maximum allowable logical length of
				 * significand. */
	unsigned short  blength;/* Logical length of significand. */
	short int       bexponent;	/* Exponent to be attached to least
					 * significant word of significand.
					 * exponent >= 0 implies all integer,
					 * with decimal point to right of
					 * least significant word of
					 * significand, and is equivalent to
					 * number of omitted trailing zeros
					 * of significand. -length < exponent
					 * < 0  implies decimal point within
					 * significand. exponent = -length
					 * implies decimal point to left of
					 * most significand word. exponent <
					 * -length implies decimal point to
					 * left of most significant word with
					 * -length-exponent leading zeros. */
	/*
	 * NOTE: bexponent represents a power of 2 or 10, even though big
	 * digits are powers of 2**16 or 10**4.
	 */
	_BIG_FLOAT_DIGIT bsignificand[_BIG_FLOAT_SIZE];
	/*
	 * Significand of digits in base 10**4 or 2**16. significand[0] is
	 * least significant, significand[length-1] is most significant.
	 */
}               _big_float;

#define BIG_FLOAT_TIMES_NOMEM	(_big_float *)0
#define BIG_FLOAT_TIMES_TOOBIG	(_big_float *)1

/* Internal functions defined in base conversion support routines. */

extern void     _multiply_base_ten();
extern void     _multiply_base_two_carry();
extern void     _multiply_base_ten_by_two();
extern void     _multiply_base_two();
extern void     _multiply_base_two_by_two();
extern void     _carry_propagate_two();
extern void     _carry_propagate_ten();
extern void     _multiply_base_two_vector();
extern void     _multiply_base_ten_vector();
extern void     _fourdigitsquick();
extern void     _unpacked_to_big_float();
extern void     _big_binary_to_big_decimal();
extern void     _left_shift_base_ten();
extern void     _left_shift_base_two();
extern void     _right_shift_base_two();
extern void     _free_big_float();
extern void	_base_conversion_abort();
extern void	_display_big_float();
extern void	_integerstring_to_big_decimal();
extern void	_fractionstring_to_big_decimal();
extern void	_big_decimal_to_big_binary();
extern void	_fp_rightshift();
extern void	_fp_leftshift();
extern void	_fp_normalize();
extern void	_pack_single();
extern void	_pack_double();
extern void	_pack_extended();
extern void	_pack_quadruple();
extern void	_unpack_single();
extern void	_unpack_double();
extern void	_unpack_extended();
extern void	_unpack_quadruple();
extern void	_unpacked_to_decimal();
extern enum fp_class_type	_class_single();
extern enum fp_class_type	_class_double();
extern enum fp_class_type	_class_extended();
extern enum fp_class_type	_class_quadruple();

/*
   Fundamental utilities that multiply or add two shorts into a unsigned long, 
   sometimes add an unsigned long carry, 
   compute quotient and remainder in underlying base, and return
   quo<<16 | rem as  a unsigned long.
 */

extern unsigned long _umac();		/* p = x * y + c ; return p */
/*
extern unsigned long _prodc_b65536();	/* p = x * y + c ; return p */
#define _prodc_b65536(x,y,c) (_umac((x),(y),(c)))
extern unsigned long _prodc_b10000();	/* p = x * y + c ; return (p/10000 <<
extern unsigned long _prod_b65536();	/* p = x * y ; return p */
extern unsigned long _prod_b10000();	/* p = x * y ; return (p/10000 << 16 | p%10000) */
extern unsigned long _prod_10000_b65536();	/* p = x * 10000 + c ; return
						 * p */
extern unsigned long _prod_65536_b10000();	/* p = x * 65536 + c ; return
						 * (p/10000 << 16 | p%10000) */
/*
extern unsigned long _rshift_b65536();		/* p = x << n + c<<16 ; return p */
#define _rshift_b65536(x,n,c) ((((unsigned long) (x)) << (16-(n))) + ((c)<<16))
/*
extern unsigned long _lshift_b65536();		/* p = x << n + c ; return p */
#define _lshift_b65536(x,n,c) ((((unsigned long) (x)) << (n)) + (c))
extern unsigned long _lshift_b10000();	/* p = x << n + c ; return (p/10000
					 * << 16 | p%10000) */
/*
extern unsigned long _carry_in_b65536();	/* p = x + c ; return p */
#define _carry_in_b65536(x,c) ((x) + (c))
extern unsigned long _carry_in_b10000();	/* p = x + c ; return
						 * (p/10000 << 16 | p%10000) */
/*
extern unsigned long _carry_out_b65536();	/* p = c ; return p */
#define _carry_out_b65536(c) (c)
extern unsigned long _carry_out_b10000();	/* p = c ; return (p/10000 <<
						 * 16 | p%10000) */

/*
 * Header file for revised "fast" base conversion based upon table look-up
 * methods.
 */

extern void
_big_float_times_power(
#ifdef __STDC__
/* function to multiply a big_float times a positive power of two or ten.	 */
		       _big_float * pbf;	/* Operand x, to be replaced
						 * by the product x * mult **
						 * n. */
	int             mult;	/* if mult is two, x is base 10**4; if mult
				 * is ten, x is base 2**16 */
	int             n;
	int             precision;	/* Number of bits of precision
					 * ultimately required (mult=10) or
					 * number of digits of precision
					 * ultimately required (mult=2).
					 * Extra bits are allowed internally
					 * to permit correct rounding. */
	_big_float    **pnewbf;	/* Return result *pnewbf is set to: pbf f
				 * uneventful: *pbf holds the product ;
				 * BIG_FLOAT_TIMES_TOOBIG	if n is
				 * bigger than the tables permit ;
				 * BIG_FLOAT_TIMES_NOMEM	if
				 * pbf->blength was insufficient to hold the
				 * product, and malloc failed to produce a
				 * new block ; &newbf			if
				 * pbf->blength was insufficient to hold the
				 * product, and a new _big_float was
				 * allocated by malloc. newbf holds the
				 * product. It's the caller's responsibility
				 * to free this space when no longer needed. */
#endif
);

/* Variables defined in _small_powers.c and _big_powers.c	 */
/* Used in base conversion. */

/*
 * The run-time structure consists of two large tables of powers - either
 * powers of 10**4 in base 2**16 or vice versa.
 * 
 * Suppose it's powers of T in base B.  Then
 * 
 * _tiny_powers_T       contains TTINY entries, T**0, T**1, ... T**TTINY-1 where
 * T is 2 or 10, TTINY is 16 or 4 _small_powers_T      contains TSMALL
 * entries, T**0, T**1, ... T**TSMALL-1 where T is 2**TTINY or 10**TTINY
 * _big_powers_T        contains TBIG entries, T**0, T**1, ... T**TBIG-1
 * where T is (2**TTINY)**TSMALL or (10**TTINY)**TSMALL
 * 
 * so that any power of T from 0 to T**(TTINY*TSMALL*TBIG-1) can be represented
 * as a product of just two table entries.  Since the powers vary greatly in
 * size, the tables are condensed to exclude leading and trailing zeros.  The
 * following tables
 * 
 * _max_tiny_powers_T			contains one entry, TTINY
 * _start_tiny_powers_T                 contains TTINY entries
 * _leading_zeros_tiny_powers_T         contains TTINY entries
 * _max_small_powers_T			contains one entry, TSMALL
 * _start_small_powers_T                contains TSMALL entries
 * _leading_zeros_small_powers_T        contains TSMALL entries
 * _max_big_powers_T			contains one entry, TBIG
 * _start_big_powers_T                  contains TBIG entries
 * _leading_zeros_big_powers_T          contains TBIG entries
 * 
 * The powers are maintained with x[start] less significant than x[start+1], so
 * 
 * The powers are maintained with x[start] less significant than x[start+1], so
 * that the interpretation of a _small_powers_T entry is that
 * 
T**i = (B**leading_zeros[i]) * (x[start[i]] + x[start[i]+1] * B + ...
 * x[start[i+1]-1] * B**(start[i+1]-start[i]) )
 * 
 * where B = (2 or 10)**TTINY
 * 
 * The powers are listed consecutively in the tables, with start index and
 * leading zero information retained and printed out at the end.
 * 
 */

extern unsigned short _max_tiny_powers_ten;
extern unsigned short _tiny_powers_ten[];
extern unsigned short _start_tiny_powers_ten[];
extern unsigned short _leading_zeros_tiny_powers_ten[];
extern unsigned short _max_tiny_powers_two;
extern unsigned short _tiny_powers_two[];
extern unsigned short _start_tiny_powers_two[];

extern unsigned short _max_small_powers_ten;
extern unsigned short _small_powers_ten[];
extern unsigned short _start_small_powers_ten[];
extern unsigned short _leading_zeros_small_powers_ten[];
extern unsigned short _max_small_powers_two;
extern unsigned short _small_powers_two[];
extern unsigned short _start_small_powers_two[];

extern unsigned short _max_big_powers_ten;
extern unsigned short _big_powers_ten[];
extern unsigned short _start_big_powers_ten[];
extern unsigned short _leading_zeros_big_powers_ten[];
extern unsigned short _max_big_powers_two;
extern unsigned short _big_powers_two[];
extern unsigned short _start_big_powers_two[];