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calc/zmath.h
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/*
* zmath - declarations for extended precision integer arithmetic
*
* Copyright (C) 1999-2007,2014,2021,2023 David I. Bell and Landon Curt Noll
*
* Calc is open software; you can redistribute it and/or modify it under
* the terms of the version 2.1 of the GNU Lesser General Public License
* as published by the Free Software Foundation.
*
* Calc is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
* Public License for more details.
*
* A copy of version 2.1 of the GNU Lesser General Public License is
* distributed with calc under the filename COPYING-LGPL. You should have
* received a copy with calc; if not, write to Free Software Foundation, Inc.
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* Under source code control: 1993/07/30 19:42:48
* File existed as early as: 1993
*
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
/*
* Data structure declarations for extended precision integer arithmetic.
* The assumption made is that a long is 32 bits and shorts are 16 bits,
* and longs must be addressable on word boundaries.
*/
#if !defined(INCLUDE_ZMATH_H)
#define INCLUDE_ZMATH_H
#if defined(CALC_SRC) /* if we are building from the calc source tree */
# include "version.h"
# include "bool.h"
# include "decl.h"
# include "alloc.h"
# include "endian_calc.h"
# include "longbits.h"
# include "byteswap.h"
# include "have_stdlib.h"
# include "charbit.h"
#else
# include <calc/version.h>
# include <calc/bool.h>
# include <calc/decl.h>
# include <calc/alloc.h>
# include <calc/endian_calc.h>
# include <calc/longbits.h>
# include <calc/byteswap.h>
# include <calc/have_stdlib.h>
# include <calc/charbit.h>
#endif
#ifdef HAVE_STDLIB_H
# include <stdlib.h>
#endif
#ifndef ALLOCTEST
# define freeh(p) { if (!is_const(p)) { free((void *)(p)); } }
#endif
/*
* NOTE: FULL must be twice the storage size of a HALF
* HALF must be BASEB bits long
*/
#if defined(HAVE_B64)
#define BASEB 32 /* use base 2^32 */
typedef USB32 HALF; /* unit of number storage */
typedef SB32 SHALF; /* signed HALF */
typedef USB64 FULL; /* double unit of number storage */
typedef SB64 SFULL; /* signed FULL */
#define SWAP_HALF_IN_B64(dest, src) SWAP_B32_IN_B64(dest, src)
#define SWAP_HALF_IN_B32(dest, src) (*((HALF *)(dest)) = *((HALF *)(src)))
#define SWAP_HALF_IN_FULL(dest, src) SWAP_B32_IN_B64(dest, src)
#define SWAP_HALF_IN_HASH(dest, src) SWAP_B16_IN_HASH(dest, src)
#define SWAP_HALF_IN_FLAG(dest, src) SWAP_B16_IN_FLAG(dest, src)
#define SWAP_HALF_IN_bool(dest, src) SWAP_B16_IN_bool(dest, src)
#define SWAP_HALF_IN_LEN(dest, src) SWAP_B16_IN_LEN(dest, src)
#define SWAP_B32_IN_FULL(dest, src) SWAP_B32_IN_B64(dest, src)
#define SWAP_B16_IN_FULL(dest, src) SWAP_B16_IN_B64(dest, src)
#define SWAP_B16_IN_HALF(dest, src) SWAP_B16_IN_B32(dest, src)
#define SWAP_B8_IN_FULL(dest, src) SWAP_B8_IN_B64(dest, src)
#define SWAP_B8_IN_HALF(dest, src) SWAP_B8_IN_B32(dest, src)
#else
#define BASEB 16 /* use base 2^16 */
typedef USB16 HALF; /* unit of number storage */
typedef SB16 SHALF; /* signed HALF */
typedef USB32 FULL; /* double unit of number storage */
typedef SB32 SFULL; /* signed FULL */
#define SWAP_HALF_IN_B64(dest, src) SWAP_B16_IN_B64(dest, src)
#define SWAP_HALF_IN_B32(dest, src) SWAP_B16_IN_B32(dest, src)
#define SWAP_HALF_IN_FULL(dest, src) SWAP_B16_IN_B32(dest, src)
#define SWAP_HALF_IN_HASH(dest, src) SWAP_B16_IN_HASH(dest, src)
#define SWAP_HALF_IN_FLAG(dest, src) SWAP_B16_IN_FLAG(dest, src)
#define SWAP_HALF_IN_bool(dest, src) SWAP_B16_IN_bool(dest, src)
#define SWAP_HALF_IN_LEN(dest, src) SWAP_B16_IN_LEN(dest, src)
#define SWAP_B32_IN_FULL(dest, src) (*((FULL *)(dest)) = *((FULL *)(src)))
#define SWAP_B16_IN_FULL(dest, src) SWAP_B16_IN_B32(dest, src)
#define SWAP_B16_IN_HALF(dest, src) (*((HALF *)(dest)) = *((HALF *)(src)))
#define SWAP_B8_IN_FULL(dest, src) SWAP_B8_IN_B32(dest, src)
#define SWAP_B8_IN_HALF(dest, src) SWAP_B8_IN_B16(dest, src)
#endif
#define BASE ((FULL)1<<BASEB) /* base for calculations */
#define BASE1 (BASE - (FULL)1) /* one less than base */
#define BASEDIG ((BASEB/16)*5) /* number of digits in base */
#define FULL_BITS (2*BASEB) /* bits in a FULL */
#define HALF_LEN (sizeof(HALF)) /* length of HALF in bites */
#define FULL_LEN (sizeof(FULL)) /* length of FULL in bites */
/*
* ROUNDUP(value, mult) - round up value to the next multiple of mult
*
* NOTE: value and mult musty be of an integer type.
*
* NOTE: mult must != 0
*
* NOTE: If value is a multiple of mult, then ROUNDUP(value, mult)
* will just return value.
*/
#define ROUNDUP(value, mult) ( ( ((value)+(mult)-1) / (mult) ) * (mult) )
#define TOPHALF ((FULL)1 << (BASEB-1)) /* highest bit in a HALF */
#define MAXHALF (TOPHALF - (FULL)1) /* largest SHALF value */
#define TOPFULL ((FULL)1 << (FULL_BITS-1)) /* highest bit in FULL */
#define MAXFULL (TOPFULL - (FULL)1) /* largest SFULL value */
#define MINSFULL ((SFULL)(TOPFULL)) /* most negative SFULL value */
#define MAXUFULL (MAXFULL | TOPFULL) /* largest FULL value */
#define TOPLONG ((unsigned long)1 << (LONG_BITS-1)) /* top long bit */
#define MAXLONG ((long) (TOPLONG - (unsigned long)1)) /* largest long val */
#define MAXULONG (MAXLONG | TOPLONG) /* largest unsigned long val */
/*
* other miscellaneous typedefs
*/
typedef USB32 QCKHASH; /* 32 bit hash value */
#if defined(HAVE_B64) && LONG_BITS == 32
typedef HALF PRINT; /* cast for zio printing functions */
#define SWAP_B16_IN_PRINT(dest, src) SWAP_B16_IN_HALF(dest, src)
#define SWAP_B8_IN_PRINT(dest, src) SWAP_B8_IN_HALF(dest, src)
#else
typedef FULL PRINT; /* cast for zio printing functions */
#define SWAP_B16_IN_PRINT(dest, src) SWAP_B16_IN_FULL(dest, src)
#define SWAP_B8_IN_PRINT(dest, src) SWAP_B8_IN_FULL(dest, src)
#endif
typedef SB32 FLAG; /* small value (e.g. comparison) */
/*
* length of internal integer values in units of HALF
*/
#if MAJOR_VER < 3
typedef SB32 LEN; /* calc v2 compatible unit of length storage */
#else /* MAJOR_VER < 3 */
typedef uintptr_t LEN; /* unit of length storage */
#endif /* MAJOR_VER < 3 */
#define SWAP_B32_IN_bool(dest, src) (*((bool *)(dest)) = *((bool *)(src)))
#define SWAP_B16_IN_bool(dest, src) SWAP_B16_IN_B32(dest, src)
#define SWAP_B8_IN_bool(dest, src) SWAP_B8_IN_B32(dest, src)
#define SWAP_B32_IN_LEN(dest, src) (*((LEN *)(dest)) = *((LEN *)(src)))
#define SWAP_B16_IN_LEN(dest, src) SWAP_B16_IN_B32(dest, src)
#define SWAP_B8_IN_LEN(dest, src) SWAP_B8_IN_B32(dest, src)
#if LONG_BITS == 64
#define SWAP_HALF_IN_LONG(dest, src) SWAP_HALF_IN_B64(dest, src)
#else /* LONG_BITS == 64 */
#define SWAP_HALF_IN_LONG(dest, src) SWAP_HALF_IN_B32(dest, src)
#endif /* LONG_BITS == 64 */
/*
* Quickhash basis
*
* We start the hash at a non-zero value at the beginning so that
* hashing blocks of data with all 0 bits do not map onto the same
* 0 hash value. The virgin value that we use below is the 32-bit
* FNV-0 hash value that we would get from following 32 ASCII characters:
*
* chongo <Landon Curt Noll> /\../\
*
* Note that the \'s above are not back-slashing escape characters.
* They are literal ASCII backslash 0x5c characters.
*
* The effect of this virgin initial value is the same as starting
* with 0 and pre-pending those 32 characters onto the data being
* hashed.
*
* Yes, even with this non-zero virgin value there is a set of data
* that will result in a zero hash value. Worse, appending any
* about of zero bytes will continue to produce a zero hash value.
* But that would happen with any initial value so long as the
* hash of the initial was the `inverse' of the virgin prefix string.
*
* But then again for any hash function, there exists sets of data
* which that the hash of every member is the same value. That is
* life with many to few mapping functions. All we do here is to
* prevent sets whose members consist of 0 or more bytes of 0's from
* being such an awkward set.
*
* And yes, someone can figure out what the magic 'inverse' of the
* 32 ASCII character are ... but this hash function is NOT intended
* to be a cryptographic hash function, just a fast and reasonably
* good hash function.
*/
#define QUICKHASH_BASIS ((QCKHASH)(0x811c9dc5))
/*
* The largest power of 10 we will compute for our decimal conversion
* internal constants is: 10^(2^TEN_MAX).
*/
#define TEN_MAX 31 /* 10^2^31 requires about 1.66 * 2^29 bytes */
/*
* MAXDATA - largest data object in bytes we will use
*
* We start with MAXDATA as 1/16 of the maximum address space.
* We limit to 1/16 because for a maximum complex value we
* will need 4 huge integers, plus other data, code and stack space.
*/
#if MAJOR_VER < 3
#define MAXDATA (0x80000000>>3) /* calc v2 compatible supported address space */
#else /* MAJOR_VER < 3 */
#define MAXDATA ((LEN) 1<<(UINTPTR_WIDTH-4)) /* 1/16 of address space */
#endif /* MAJOR_VER < 3 */
/*
* MAXLEN - maximum length of internal integer values in units of HALF
*
* We limit MAXLEN based on 1 less than the number of HALFs that
* will fit into MAXDATA bytes.
*/
#define MAXLEN ((LEN) ((MAXDATA / HALF_LEN) - 1)) /* longest value allowed */
#define MAXREDC 256 /* number of entries in REDC cache */
#define SQ_ALG2 28 /* size for alternative squaring */
#define MUL_ALG2 28 /* size for alternative multiply */
#define POW_ALG2 20 /* size for using REDC for powers */
/* old REDC_ALG2 was 5/4 of POW_ALG2, so we will keep the same ratio */
#define REDC_ALG2 25 /* size for using alternative REDC */
typedef union {
FULL ivalue;
struct {
HALF Svalue1;
HALF Svalue2;
} sis;
} SIUNION;
#if !defined(LITTLE_ENDIAN)
#define LITTLE_ENDIAN 1234 /* Least Significant Byte first */
#endif
#if !defined(BIG_ENDIAN)
#define BIG_ENDIAN 4321 /* Most Significant Byte first */
#endif
/* PDP_ENDIAN - LSB in word, MSW in long is not supported */
#if CALC_BYTE_ORDER == LITTLE_ENDIAN
# define silow sis.Svalue1 /* low order half of full value */
# define sihigh sis.Svalue2 /* high order half of full value */
#else
# if CALC_BYTE_ORDER == BIG_ENDIAN
# define silow sis.Svalue2 /* low order half of full value */
# define sihigh sis.Svalue1 /* high order half of full value */
# else
/\oo/\ CALC_BYTE_ORDER must be BIG_ENDIAN or LITTLE_ENDIAN /\oo/\ !!!
# endif
#endif
/*
* ZVALUE - multi-prevision integer
*/
#if MAJOR_VER < 3
typedef SB32 SIGN; /* calc v2 compatible sign type */
#else /* MAJOR_VER < 3 */
typedef bool SIGN; /* sign as a C boolean */
#endif /* MAJOR_VER < 3 */
typedef struct {
HALF *v; /* pointer to array of values */
LEN len; /* number of values in array */
SIGN sign; /* sign, nonzero is negative */
} ZVALUE;
/*
* Function prototypes for integer math routines.
*/
E_FUNC HALF * alloc(LEN len);
E_FUNC int is_const(HALF* h);
#ifdef ALLOCTEST
E_FUNC void freeh(HALF *);
#endif
/*
* Input, output, and conversion routines.
*/
E_FUNC void zcopy(ZVALUE z, ZVALUE *res);
E_FUNC void itoz(long i, ZVALUE *res);
E_FUNC void utoz(FULL i, ZVALUE *res);
E_FUNC void stoz(SFULL i, ZVALUE *res);
E_FUNC void str2z(char *s, ZVALUE *res);
E_FUNC long ztoi(ZVALUE z);
E_FUNC FULL ztou(ZVALUE z);
E_FUNC SFULL ztos(ZVALUE z);
E_FUNC void zprintval(ZVALUE z, long decimals, long width);
E_FUNC void zprintx(ZVALUE z, long width);
E_FUNC void zprintb(ZVALUE z, long width);
E_FUNC void zprinto(ZVALUE z, long width);
E_FUNC void fitzprint(ZVALUE, long, long);
/*
* Basic numeric routines.
*/
E_FUNC void zmuli(ZVALUE z, long n, ZVALUE *res);
E_FUNC long zdivi(ZVALUE z, long n, ZVALUE *res);
E_FUNC long zmodi(ZVALUE z, long n);
E_FUNC void zadd(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC void zsub(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC void zmul(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC long zdiv(ZVALUE z1, ZVALUE z2, ZVALUE *res, ZVALUE *rem, long R);
E_FUNC long zquo(ZVALUE z1, ZVALUE z2, ZVALUE *res, long R);
E_FUNC long zmod(ZVALUE z1, ZVALUE z2, ZVALUE *rem, long R);
E_FUNC void zequo(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC bool zdivides(ZVALUE z1, ZVALUE z2);
E_FUNC void zor(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC void zand(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC void zxor(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC void zandnot(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC long zpopcnt(ZVALUE z, int bitval);
E_FUNC void zshift(ZVALUE z, long n, ZVALUE *res);
E_FUNC void zsquare(ZVALUE z, ZVALUE *res);
E_FUNC long zlowbit(ZVALUE z);
E_FUNC LEN zhighbit(ZVALUE z);
E_FUNC void zbitvalue(long n, ZVALUE *res);
E_FUNC bool zisset(ZVALUE z, long n);
E_FUNC bool zisonebit(ZVALUE z);
E_FUNC bool zisallbits(ZVALUE z);
E_FUNC FLAG ztest(ZVALUE z);
E_FUNC FLAG zrel(ZVALUE z1, ZVALUE z2);
E_FUNC FLAG zabsrel(ZVALUE z1, ZVALUE z2);
E_FUNC bool zcmp(ZVALUE z1, ZVALUE z2);
/*
* More complicated numeric functions.
*/
E_FUNC FULL uugcd(FULL i1, FULL i2);
E_FUNC long iigcd(long i1, long i2);
E_FUNC void zgcd(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC void zlcm(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC void zreduce(ZVALUE z1, ZVALUE z2, ZVALUE *z1res, ZVALUE *z2res);
E_FUNC void zfact(ZVALUE z, ZVALUE *dest);
E_FUNC void zperm(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC int zcomb(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC FLAG zjacobi(ZVALUE z1, ZVALUE z2);
E_FUNC void zfib(ZVALUE z, ZVALUE *res);
E_FUNC void zpowi(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC void ztenpow(long power, ZVALUE *res);
E_FUNC void zpowermod(ZVALUE z1, ZVALUE z2, ZVALUE z3, ZVALUE *res);
E_FUNC bool zmodinv(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC bool zrelprime(ZVALUE z1, ZVALUE z2);
E_FUNC long zlog(ZVALUE z1, ZVALUE z2);
E_FUNC long zlog10(ZVALUE z, bool *was_10_power);
E_FUNC long zdivcount(ZVALUE z1, ZVALUE z2);
E_FUNC long zfacrem(ZVALUE z1, ZVALUE z2, ZVALUE *rem);
E_FUNC long zgcdrem(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC long zdigits(ZVALUE z1);
E_FUNC long zdigit(ZVALUE z1, long n);
E_FUNC FLAG zsqrt(ZVALUE z1, ZVALUE *dest, long R);
E_FUNC void zroot(ZVALUE z1, ZVALUE z2, ZVALUE *dest);
E_FUNC bool zissquare(ZVALUE z);
E_FUNC void zhnrmod(ZVALUE v, ZVALUE h, ZVALUE zn, ZVALUE zr, ZVALUE *res);
E_FUNC bool zispowerof2(ZVALUE z, FULL *log2);
/*
* Prime related functions.
*/
E_FUNC FLAG zisprime(ZVALUE z);
E_FUNC FULL znprime(ZVALUE z);
E_FUNC FULL next_prime(FULL v);
E_FUNC FULL zpprime(ZVALUE z);
E_FUNC void zpfact(ZVALUE z, ZVALUE *dest);
E_FUNC bool zprimetest(ZVALUE z, long count, ZVALUE skip);
E_FUNC bool zredcprimetest(ZVALUE z, long count, ZVALUE skip);
E_FUNC bool znextcand(ZVALUE z1, long count, ZVALUE skip, ZVALUE res,
ZVALUE mod, ZVALUE *cand);
E_FUNC bool zprevcand(ZVALUE z1, long count, ZVALUE skip, ZVALUE res,
ZVALUE mod, ZVALUE *cand);
E_FUNC FULL zlowfactor(ZVALUE z, long count);
E_FUNC FLAG zfactor(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC long zpix(ZVALUE z1);
E_FUNC void zlcmfact(ZVALUE z, ZVALUE *dest);
/*
* miscellaneous functions. :-)
*/
E_FUNC void zsquaremod(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC void zminmod(ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC bool zcmpmod(ZVALUE z1, ZVALUE z2, ZVALUE z3);
E_FUNC void zio_init(void);
/*
* These functions are for internal use only.
*/
E_FUNC void ztrim(ZVALUE *z);
E_FUNC void zshiftr(ZVALUE z, long n);
E_FUNC void zshiftl(ZVALUE z, long n);
E_FUNC HALF *zalloctemp(LEN len);
/*
* Modulo arithmetic definitions.
* Structure holding state of REDC initialization.
* Multiple instances of this structure can be used allowing
* calculations with more than one modulus at the same time.
* Len of zero means the structure is not initialized.
*/
typedef struct {
LEN len; /* number of words in binary modulus */
ZVALUE mod; /* modulus REDC is computing with */
ZVALUE inv; /* inverse of modulus in binary modulus */
ZVALUE one; /* REDC format for the number 1 */
} REDC;
E_FUNC REDC *zredcalloc(ZVALUE z1);
E_FUNC void zredcfree(REDC *rp);
E_FUNC void zredcencode(REDC *rp, ZVALUE z1, ZVALUE *res);
E_FUNC void zredcdecode(REDC *rp, ZVALUE z1, ZVALUE *res);
E_FUNC void zredcmul(REDC *rp, ZVALUE z1, ZVALUE z2, ZVALUE *res);
E_FUNC void zredcsquare(REDC *rp, ZVALUE z1, ZVALUE *res);
E_FUNC void zredcpower(REDC *rp, ZVALUE z1, ZVALUE z2, ZVALUE *res);
/*
* macro expansions to speed this thing up
*/
#define ziseven(z) (!(*(z).v & 0x1))
#define zisodd(z) (*(z).v & 0x1)
#define ziszero(z) ((*(z).v == 0) && ((z).len == 1))
#define zisneg(z) ((z).sign)
#define zispos(z) (((z).sign == 0) && (*(z).v || ((z).len > 1)))
#define zisunit(z) ((*(z).v == 1) && ((z).len == 1))
#define zisone(z) ((*(z).v == 1) && ((z).len == 1) && !(z).sign)
#define zisnegone(z) ((*(z).v == 1) && ((z).len == 1) && (z).sign)
#define zltnegone(z) (zisneg(z) && (((z).len > 1) || *(z).v > 1))
#define zistwo(z) ((*(z).v == 2) && ((z).len == 1) && !(z).sign)
#define zisabstwo(z) ((*(z).v == 2) && ((z).len == 1))
#define zisabsleone(z) ((*(z).v <= 1) && ((z).len == 1))
#define zislezero(z) (zisneg(z) || ziszero(z))
#define zisleone(z) (zisneg(z) || zisabsleone(z))
#define zistiny(z) ((z).len == 1)
/*
* zgtmaxfull(z) true if abs(z) > MAXFULL
*/
#define zgtmaxfull(z) (((z).len > 2) || (((z).len == 2) && \
(((SHALF)(z).v[1]) < 0)))
/*
* zgtmaxufull(z) true if abs(z) will not fit into a FULL (> MAXUFULL)
*/
#define zgtmaxufull(z) ((z).len > 2)
/*
* zgtmaxulong(z) true if abs(z) > MAXULONG
*/
#if BASEB >= LONG_BITS
#define zgtmaxulong(z) ((z).len > 1)
#else
#define zgtmaxulong(z) zgtmaxufull(z)
#endif
/*
* zgtmaxlong(z) true if abs(z) > MAXLONG
*/
#if BASEB >= LONG_BITS
#define zgtmaxlong(z) (((z).len > 1) || (((z).len == 1) && \
(((SHALF)(z).v[0]) < 0)))
#else
#define zgtmaxlong(z) zgtmaxfull(z)
#endif
/*
* Some algorithms testing for values of a certain length. Macros such as
* zistiny() do this well. In other cases algorithms require tests for values
* in comparison to a given power of 2. In the later case, zistiny() compares
* against a different power of 2 on a 64 bit machine. The macros below
* provide a tests against powers of 2 that are independent of the work size.
*
* zge16b(z) true if abs(z) >= 2^16
* zge24b(z) true if abs(z) >= 2^24
* zge31b(z) true if abs(z) >= 2^31
* zge32b(z) true if abs(z) >= 2^32
* zge64b(z) true if abs(z) >= 2^64
* zge128b(z) true if abs(z) >= 2^128
* zge256b(z) true if abs(z) >= 2^256
* zge512b(z) true if abs(z) >= 2^512
* zge1024b(z) true if abs(z) >= 2^1024
* zge2048b(z) true if abs(z) >= 2^2048
* zge4096b(z) true if abs(z) >= 2^4096
* zge8192b(z) true if abs(z) >= 2^8192
*/
#if BASEB == 32
#define zge16b(z) (!zistiny(z) || ((z).v[0] >= (HALF)0x10000))
#define zge24b(z) (!zistiny(z) || ((z).v[0] >= (HALF)0x1000000))
#define zge31b(z) (!zistiny(z) || (((SHALF)(z).v[0]) < 0))
#define zge32b(z) (!zistiny(z))
#define zge64b(z) ((z).len > 2)
#define zge128b(z) ((z).len > 4)
#define zge256b(z) ((z).len > 8)
#define zge512b(z) ((z).len > 16)
#define zge1024b(z) ((z).len > 32)
#define zge2048b(z) ((z).len > 64)
#define zge4096b(z) ((z).len > 128)
#define zge8192b(z) ((z).len > 256)
#else
#define zge16b(z) (!zistiny(z))
#define zge24b(z) (((z).len > 2) || (((z).len == 2) && \
((z).v[1] >= (HALF)0x100)))
#define zge31b(z) (((z).len > 2) || (((z).len == 2) && \
(((SHALF)(z).v[1]) < 0)))
#define zge32b(z) ((z).len > 2)
#define zge64b(z) ((z).len > 4)
#define zge128b(z) ((z).len > 8)
#define zge256b(z) ((z).len > 16)
#define zge512b(z) ((z).len > 32)
#define zge1024b(z) ((z).len > 64)
#define zge2048b(z) ((z).len > 128)
#define zge4096b(z) ((z).len > 256)
#define zge8192b(z) ((z).len > 512)
#endif
/*
* ztofull - convert an absolute value of a ZVALUE to a FULL if possible
*
* If the value is too large, only the low order bits that are able to
* be converted into a FULL will be used.
*/
#define ztofull(z) (zistiny(z) ? ((FULL)((z).v[0])) : \
((FULL)((z).v[0]) + \
((FULL)((z).v[1]) << BASEB)))
#define z1tol(z) ((long)((z).v[0]))
#define z2tol(z) ((long)(((z).v[0]) + \
(((z).v[1] & MAXHALF) << BASEB)))
/*
* ztoulong - convert an absolute value of a ZVALUE to an unsigned long
*
* If the value is too large, only the low order bits that are able to
* be converted into a long will be used.
*/
#if BASEB >= LONG_BITS
# define ztoulong(z) ((unsigned long)z1tol(z))
#else
# define ztoulong(z) ((unsigned long)ztofull(z))
#endif
/*
* ztolong - convert an absolute value of a ZVALUE to a long
*
* If the value is too large, only the low order bits that are able to
* be converted into a long will be used.
*/
#define ztolong(z) ((long)(ztoulong(z) & MAXLONG))
#define zclearval(z) memset((z).v, 0, (z).len * sizeof(HALF))
#define zcopyval(z1,z2) memcpy((z2).v, (z1).v, (z1).len * sizeof(HALF))
#define zquicktrim(z) {if (((z).len > 1) && ((z).v[(z).len-1] == 0)) \
(z).len--;}
#define zfree(z) {if ((z).len != 0 && (z).v != NULL) { \
freeh((z).v); \
(z).v = NULL; \
(z).len = 0; \
(z).sign = 0; } \
}
/*
* Output modes for numeric displays.
*/
#define MODE_DEFAULT 0
#define MODE_FRAC 1
#define MODE_INT 2
#define MODE_REAL 3
#define MODE_EXP 4
#define MODE_HEX 5
#define MODE_OCTAL 6
#define MODE_BINARY 7
#define MODE_REAL_AUTO 8
#define MODE_ENG 9
#define MODE_MAX 9
#define MODE2_OFF (MODE_MAX+1)
#define MODE_INITIAL MODE_REAL
#define MODE2_INITIAL MODE2_OFF
/*
* Output routines for either FILE handles or strings.
*/
E_FUNC void math_chr(int ch);
E_FUNC void math_str(char *str);
E_FUNC void math_fill(char *str, long width);
E_FUNC void math_flush(void);
E_FUNC void math_divertio(void);
E_FUNC void math_cleardiversions(void);
E_FUNC char *math_getdivertedio(void);
E_FUNC int math_setmode(int mode);
E_FUNC int math_setmode2(int mode);
E_FUNC LEN math_setdigits(LEN digits);
E_FUNC void math_fmt(char *, ...) __attribute__((format(printf, 1, 2)));
/*
* external swap functions
*/
E_FUNC HALF *swap_b8_in_HALFs(HALF *dest, HALF *src, LEN len);
E_FUNC ZVALUE *swap_b8_in_ZVALUE(ZVALUE *dest, ZVALUE *src, bool all);
E_FUNC HALF *swap_b16_in_HALFs(HALF *dest, HALF *src, LEN len);
E_FUNC HALF *swap_HALFs(HALF *dest, HALF *src, LEN len);
E_FUNC ZVALUE *swap_b16_in_ZVALUE(ZVALUE *dest, ZVALUE *src, bool all);
E_FUNC ZVALUE *swap_HALF_in_ZVALUE(ZVALUE *dest, ZVALUE *src, bool all);
/*
* constants used often by the arithmetic routines
*/
EXTERN HALF _zeroval_[];
EXTERN ZVALUE _zero_;
EXTERN HALF _oneval_[];
EXTERN ZVALUE _one_;
EXTERN ZVALUE _neg_one_;
EXTERN HALF _twoval_[];
EXTERN ZVALUE _two_;
EXTERN HALF _tenval_[];
EXTERN ZVALUE _ten_;
EXTERN HALF _sqbaseval_[];
EXTERN ZVALUE _sqbase_;
EXTERN HALF _pow4baseval_[];
EXTERN ZVALUE _pow4base_;
EXTERN HALF _pow8baseval_[];
EXTERN ZVALUE _pow8base_;
/* _b32_ is _sqbaseval_ or _pow4baseval_ depending on BASEB */
EXTERN ZVALUE _b32_;
/* _b64_ is _pow4baseval_ or _pow8baseval_ depending on BASEB */
EXTERN ZVALUE _b64_;
EXTERN HALF *half_tbl[]; /* preset HALF constants, NULL terminated list */
EXTERN bool _math_abort_; /* nonzero to abort calculations */
EXTERN ZVALUE _tenpowers_[]; /* table of 10^2^n */
/*
* Bit fiddling functions and types
*/
EXTERN HALF bitmask[]; /* bit rotation, norm 0 */
EXTERN HALF lowhalf[]; /* bit masks from low end of HALF */
EXTERN HALF rlowhalf[]; /* reversed bit masks from low end of HALF */
EXTERN HALF highhalf[]; /* bit masks from high end of HALF */
EXTERN HALF rhighhalf[]; /* reversed bit masks from high end of HALF */
#define HAVE_REVERSED_MASKS /* allows old code to know libcalc.a has them */
/*
* BITSTR - string of bits within an array of HALFs
*
* This typedef records a location of a bit in an array of HALFs.
* Bit 0 in a HALF is assumed to be the least significant bit in that HALF.
*
* The most significant bit is found at (loc,bit). Bits of lesser
* significance may be found in previous bits and HALFs.
*/
typedef struct {
HALF *loc; /* half address of most significant bit */
int bit; /* bit position within half of most significant bit */
int len; /* length of string in bits */
} BITSTR;
#endif /* !INCLUDE_ZMATH_H*/
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