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1.1     ! root        1: 
        !             2: 
        !             3: multiple-precision mathematicsOverviewmultiple-precision mathematics
        !             4: 
        !             5: 
        !             6: 
        !             7: 
        !             8: The COHERENT  system includes  the library libmp,  whose routines
        !             9: allow  you  to  perform  multiple  precision  arithmetic.   These
        !            10: functions manipulate  a data structure  called a mint,  or ``mul-
        !            11: tiple-precision integer,'' which  the header file mprec.h defines
        !            12: as follows:
        !            13: 
        !            14: 
        !            15: typedef struct {
        !            16:         unsigned len;
        !            17:         char *val;
        !            18: } mint;
        !            19: 
        !            20: 
        !            21: You should  not depend on the details  of this structure, because
        !            22: on  some machines  a different representation  may be  more effi-
        !            23: cient.  Using the listed functions is always safe.
        !            24: 
        !            25: The following gives the multiple-precision routines:
        !            26: 
        !            27: ggccdd()     Set variable to greatest common divisor
        !            28: iissppooss()   Return if variable is positive or negative
        !            29: iittoomm()    Create a multiple-precision integer
        !            30: mmaadddd()    Add multiple-precision integers
        !            31: mmccmmpp()    Compare multiple-precision integers
        !            32: mmccooppyy()   Copy a multiple-precision integer
        !            33: mmddiivv()    Divide multiple-precision integers
        !            34: mmiinn()     Read multiple-precision integer from stdin
        !            35: mmiinniitt()   Condition global or auto multiple-precision integer
        !            36: mmiinnttffrr()  Free a multiple-precision integer
        !            37: mmiittoomm()   Reinitialize a multiple-precision integer
        !            38: mmnneegg()    Negate multiple-precision integer
        !            39: mmoouutt()    Write multiple-precision integer to stdout
        !            40: mmssqqrrtt()   Compute square root of multiple-precision integer
        !            41: mmssuubb()    Subtract multiple-precision integers
        !            42: mmttooii()    Convert multiple-precision integer to integer
        !            43: mmttooss()    Convert multiple-precision integer to string
        !            44: mmuulltt()    Multiple multiple-precision integers
        !            45: mmvvffrreeee()  Free multiple-precision integer
        !            46: ppooww()     Raise multiple-precision integer to power
        !            47: rrppooww()    Raise multiple-precision integer to power
        !            48: ssddiivv()    Divide multiple-precision integers
        !            49: ssmmuulltt()   Multiply multiple-precision integers
        !            50: ssppooww()    Raise multiple-precision integer to power
        !            51: xxggccdd()    Extended greatest-common-divisor function
        !            52: zzeerroopp()   Indicate if multi-precision integer is zero
        !            53: 
        !            54: itom() creates  a new mint, initializes it  to the signed integer
        !            55: value n,  and returns a  pointer to it.   Storage used by  a mint
        !            56: created with itom may be reclaimed using mintfr().
        !            57: 
        !            58: A mint that already exists may be reinitialized by mitom(), which
        !            59: sets a to  the value n.  If the mint  was declared as a global or
        !            60: automatic variable,  it must be  conditioned before first  use by
        !            61: minit(), which prevents garbage values in the mint structure from
        !            62: 
        !            63: 
        !            64: COHERENT Lexicon                                           Page 1
        !            65: 
        !            66: 
        !            67: 
        !            68: 
        !            69: multiple-precision mathematicsOverviewmultiple-precision mathematics
        !            70: 
        !            71: 
        !            72: 
        !            73: causing  chaos.  A  mint  conditioned by  minit()  has no  value;
        !            74: however, it  may be used  to receive the result  of an operation.
        !            75: For mints automatic to a function, mvfree() should be used before
        !            76: the function is exited to free  the storage used by the val field
        !            77: of  the mint  structure.  Otherwise, this  storage will  never be
        !            78: reclaimed.
        !            79: 
        !            80: madd(),  msub(), and  mult()  set c  to the  sum, difference,  or
        !            81: product of a and b.  mdiv  divides a by b and writes the quotient
        !            82: and remainder  in q and r.   b must not be  zero.  The results of
        !            83: the operation are defined by the following conditions:
        !            84: 
        !            85: 11. _a=_q*_b+_r
        !            86: 
        !            87: 22. The sign of _r equals the sign of q
        !            88: 
        !            89: 33. The absolute value of r < the absolute value of b.
        !            90: 
        !            91: smult() is like mult(),  except the second argument is an integer
        !            92: in the  range 0 <= n  <= 127.  sdiv() is  like mdiv(), except the
        !            93: second argument is an integer in the range 1 <= n <= 128, and the
        !            94: remainder argument points to an int instead of a mint().
        !            95: 
        !            96: pow() sets c to a raised to the b power reduced modulo m.  rpow()
        !            97: sets c to a raised to the b power.  spow() is like rpow(), except
        !            98: the exponent is an integer.  In no case may the exponent be nega-
        !            99: tive.
        !           100: 
        !           101: mcopy() sets b equal to a.  mneg() sets b equal to negative a.
        !           102: 
        !           103: msqrt() sets  b to  the integral  portion of the  positive square
        !           104: root of  a; r is set  to the remainder.  a  must not be negative.
        !           105: The result of the operation is defined by the condition
        !           106: 
        !           107: 
        !           108:      _a = _b * _b + _r
        !           109: 
        !           110: 
        !           111: gcd() sets c  to the greatest common divisor of  a and b.  xgcd()
        !           112: is an  extended gcd  routine that sets  g to the  greatest common
        !           113: divisor of a and b, and sets r and s so the relation
        !           114: 
        !           115: 
        !           116:                _g = _a * _r + _b * _s
        !           117: 
        !           118: 
        !           119: holds.  For xgcd(), r, s and g must all be distinct.
        !           120: 
        !           121: mints may be compared with mcmp(), which returns a signed integer
        !           122: less than, equal to, or  greater than zero according to whether a
        !           123: is less than, equal to,  or greater than b.  ispos() returns true
        !           124: (nonzero) if  a is not  negative, false (zero) if  a is negative.
        !           125: zerop returns true if a is zero, false otherwise.
        !           126: 
        !           127: 
        !           128: 
        !           129: 
        !           130: COHERENT Lexicon                                           Page 2
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        !           133: 
        !           134: 
        !           135: multiple-precision mathematicsOverviewmultiple-precision mathematics
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        !           137: 
        !           138: 
        !           139: mtoi() returns an  integer equal to the value of  a.  a should be
        !           140: in the allowable range for a signed integer.
        !           141: 
        !           142: The external  integers ibase and  obase govern the  I/O and ASCII
        !           143: conversion routines.   Allowable bases run from  two to 16.  Per-
        !           144: missible digits are 0 through  9 and A through F (lower-case let-
        !           145: ters are not  allowed).  min reads a mint in  base ibase from the
        !           146: standard input  and sets a to that value.   Leading blanks and an
        !           147: optional leading minus sign are allowed; the number is terminated
        !           148: by the  first non-legal digit.  mout() outputs  a on the standard
        !           149: output  in base  obase.  mtos() performs  the same  conversion as
        !           150: mout(), but the result is placed in a character string instead of
        !           151: being output; a pointer to the string is returned.  The string is
        !           152: actually allocated by malloc(), and may be freed by free().
        !           153: 
        !           154: mzero()  and mone()  point  to mints  with values  zero and  one.
        !           155: mminint() and mmaxint() point to mints containing the minimum and
        !           156: maximum values  that will  fit in  a signed integer.   These con-
        !           157: stants should never be used as the result of an operation.
        !           158: 
        !           159: All the  necessary declarations for  these constants and  for the
        !           160: library functions are contained in the header file mprec.h.  They
        !           161: need not be repeated.
        !           162: 
        !           163: To link  mp modules with  an executable object,  use the argument
        !           164: -lmp with the cc or ld commands.
        !           165: 
        !           166: ***** Example *****
        !           167: 
        !           168: The following  example converts  a string into  a multi-precision
        !           169: integer.
        !           170: 
        !           171: 
        !           172: #include <stdio.h>
        !           173: #include <mprec.h>
        !           174: #include <ctype.h>
        !           175: 
        !           176: 
        !           177: 
        !           178: /*
        !           179:  * "ibase" is an int which contains the input base used by "stom".
        !           180:  * It should be between 2 and 16.
        !           181:  */
        !           182: int ibase = 10;
        !           183: 
        !           184: 
        !           185: 
        !           186: /*
        !           187:  * stom() reads in a number in base ibase from string 'a' and returns
        !           188:  * pointer to multiple-precision integer.
        !           189:  */
        !           190: mint *stom(s)
        !           191: register char *s;
        !           192: {
        !           193:           char cval;
        !           194: 
        !           195: 
        !           196: COHERENT Lexicon                                           Page 3
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        !           198: 
        !           199: 
        !           200: 
        !           201: multiple-precision mathematicsOverviewmultiple-precision mathematics
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        !           203: 
        !           204: 
        !           205:           mint c = {1, &cval};
        !           206:           register int ch;
        !           207:           char mifl = 0;/* leading minus flag */
        !           208:           static mintnumber;
        !           209: 
        !           210: 
        !           211: 
        !           212:           mcopy(mzero, &number);/* set number to zero */
        !           213:           if ((ch = *s) == '-') {/* skip leading '-' */
        !           214:           mifl = 1;
        !           215:           ch = *++s;
        !           216:           }
        !           217: 
        !           218: 
        !           219: 
        !           220:           /* scan thru string 's', building result in "number" */
        !           221:           while (isascii(ch) && isdigit(ch)) {
        !           222:           cval = (isdigit(ch) ? ch - '0': ch - 'A');
        !           223:           smult(&number, ibase, &number);
        !           224:           madd(&number, &c, &number);
        !           225:           ch = *++s;
        !           226:           }
        !           227: 
        !           228: 
        !           229: 
        !           230:           if (mifl)/* adjust sign of a "number" */
        !           231:           mneg(&number, &number);
        !           232:           return(&number);
        !           233: }
        !           234: 
        !           235: 
        !           236: 
        !           237: /* simple test for "stom" */
        !           238: main()
        !           239: {
        !           240:           charbuffer[80];
        !           241: 
        !           242: 
        !           243: 
        !           244:           printf("Input string ? ");
        !           245:           gets(buffer);
        !           246:           mout(stom(buffer)); /* Print in stdout multiple-precision int */
        !           247: }
        !           248: 
        !           249: 
        !           250: ***** Files *****
        !           251: 
        !           252: <mprec.h>
        !           253: /usr/lib/libmp.a
        !           254: 
        !           255: ***** See Also *****
        !           256: 
        !           257: bc, dc, libraries, malloc, mprec.h
        !           258: 
        !           259: 
        !           260: 
        !           261: 
        !           262: COHERENT Lexicon                                           Page 4
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        !           265: 
        !           266: 
        !           267: multiple-precision mathematicsOverviewmultiple-precision mathematics
        !           268: 
        !           269: 
        !           270: 
        !           271: ***** Diagnostics *****
        !           272: 
        !           273: On any error,  such as division by zero, running  out of space or
        !           274: taking the square root  of a negative number, an appropriate mes-
        !           275: sage is printed on the  standard error stream and the program ex-
        !           276: its with a nonzero status.
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        !           328: COHERENT Lexicon                                           Page 5
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