FORM  4.2.1
Macros | Functions
reken.c File Reference
#include "form3.h"
#include <math.h>

Go to the source code of this file.

Macros

#define GCDMAX   3
 
#define NEWTRICK   1
 
#define COPYLONG(x1, nx1, x2, nx2)   { int i; for(i=0;i<ABS(nx2);i++)x1[i]=x2[i];nx1=nx2; }
 
#define WARMUP   6
 

Functions

VOID Pack (UWORD *a, WORD *na, UWORD *b, WORD nb)
 
VOID UnPack (UWORD *a, WORD na, WORD *denom, WORD *numer)
 
WORD Mully (PHEAD UWORD *a, WORD *na, UWORD *b, WORD nb)
 
WORD Divvy (PHEAD UWORD *a, WORD *na, UWORD *b, WORD nb)
 
WORD AddRat (PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc)
 
WORD MulRat (PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc)
 
WORD DivRat (PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc)
 
WORD Simplify (PHEAD UWORD *a, WORD *na, UWORD *b, WORD *nb)
 
WORD AccumGCD (PHEAD UWORD *a, WORD *na, UWORD *b, WORD nb)
 
int TakeRatRoot (UWORD *a, WORD *n, WORD power)
 
WORD AddLong (UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc)
 
WORD AddPLon (UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc)
 
VOID SubPLon (UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc)
 
WORD MulLong (UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc)
 
WORD BigLong (UWORD *a, WORD na, UWORD *b, WORD nb)
 
WORD DivLong (UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc, UWORD *d, WORD *nd)
 
WORD RaisPow (PHEAD UWORD *a, WORD *na, UWORD b)
 
VOID RaisPowCached (PHEAD WORD x, WORD n, UWORD **c, WORD *nc)
 
WORD RaisPowMod (WORD x, WORD n, WORD m)
 
int NormalModulus (UWORD *a, WORD *na)
 
int MakeInverses ()
 
int GetModInverses (WORD m1, WORD m2, WORD *im1, WORD *im2)
 
int GetLongModInverses (PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *ia, WORD *nia, UWORD *ib, WORD *nib)
 
WORD Product (UWORD *a, WORD *na, WORD b)
 
UWORD Quotient (UWORD *a, WORD *na, WORD b)
 
WORD Remain10 (UWORD *a, WORD *na)
 
WORD Remain4 (UWORD *a, WORD *na)
 
VOID PrtLong (UWORD *a, WORD na, UBYTE *s)
 
WORD GetLong (UBYTE *s, UWORD *a, WORD *na)
 
WORD GcdLong (PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc)
 
WORD GetBinom (UWORD *a, WORD *na, WORD i1, WORD i2)
 
WORD LcmLong (PHEAD UWORD *a, WORD na, UWORD *b, WORD nb, UWORD *c, WORD *nc)
 
int TakeLongRoot (UWORD *a, WORD *n, WORD power)
 
int MakeRational (WORD a, WORD m, WORD *b, WORD *c)
 
int MakeLongRational (PHEAD UWORD *a, WORD na, UWORD *m, WORD nm, UWORD *b, WORD *nb)
 
WORD CompCoef (WORD *term1, WORD *term2)
 
WORD Modulus (WORD *term)
 
WORD TakeModulus (UWORD *a, WORD *na, UWORD *cmodvec, WORD ncmod, WORD par)
 
WORD TakeNormalModulus (UWORD *a, WORD *na, UWORD *c, WORD nc, WORD par)
 
WORD MakeModTable ()
 
int Factorial (PHEAD WORD n, UWORD *a, WORD *na)
 
int Bernoulli (WORD n, UWORD *a, WORD *na)
 
WORD NextPrime (PHEAD WORD num)
 
void iniwranf (PHEAD0)
 
UWORD wranf (PHEAD0)
 
UWORD iranf (PHEAD UWORD imax)
 
UBYTE * PreRandom (UBYTE *s)
 

Detailed Description

This file contains the numerical routines. The arithmetic in FORM is normally over the rational numbers. Hence there are routines for dealing with integers and with rational of 'arbitrary precision' (within limits) There are also routines for that calculus modulus an integer. In addition there are the routines for factorials and bernoulli numbers. The random number function is currently only for internal purposes.

Definition in file reken.c.

Function Documentation

VOID RaisPowCached ( PHEAD WORD  x,
WORD  n,
UWORD **  c,
WORD *  nc 
)

Computes power x^n and caches the value

Description

Calculates the power x^n and stores the results for caching purposes. The pointer c (i.e., the pointer, and not what it points to) is overwritten. What it points to should not be overwritten in the calling function.

Notes

  • Caching is done in AT.small_power[]. This array is extended if necessary.

Definition at line 1286 of file reken.c.

int NormalModulus ( UWORD *  a,
WORD *  na 
)

Brings a modular representation in the range -p/2 to +p/2 The return value tells whether anything was done. Routine made in the general modulus revamp of July 2008 (JV).

Definition at line 1393 of file reken.c.

Referenced by AddCoef(), and MergePatches().

int MakeInverses ( )

Makes a table of inverses in modular calculus The modulus is in AC.cmod and AC.ncmod One should notice that the table of inverses can only be made if the modulus fits inside a single FORM word. Otherwise the table lookup becomes too difficult and the table too long.

Definition at line 1430 of file reken.c.

References GetModInverses().

int GetModInverses ( WORD  m1,
WORD  m2,
WORD *  im1,
WORD *  im2 
)

Input m1 and m2, which are relative prime. determines a*m1+b*m2 = 1 (and 1 is the gcd of m1 and m2) then a*m1 = 1 mod m2 and hence im1 = a. and b*m2 = 1 mod m1 and hence im2 = b. Set m1 = 0*m1+1*m2 = a1*m1+b1*m2 m2 = 1*m1+0*m2 = a2*m1+b2*m2 If everything is OK, the return value is zero

Definition at line 1466 of file reken.c.

Referenced by MakeDollarMod(), MakeInverses(), MakeMod(), TakeContent(), and TakeSymbolContent().

WORD CompCoef ( WORD *  term1,
WORD *  term2 
)
Routine takes a1 mod m1 and a2 mod m2 and returns a mod m1*m2 with
a mod m1 = a1 and a mod m2 = a2

Chinese remainder: a%(m1*m2) = q1*m1+a1 a%(m1*m2) = q2*m2+a2 Compute n1 such that (n1*m1)m2 is one Compute n2 such that (n2*m2)m1 is one Then (a1*n2*m2+a2*n1*m1)%(m1*m2) is a%(m1*m2)

Definition at line 3037 of file reken.c.

Referenced by Compare1().

WORD NextPrime ( PHEAD WORD  num)

Gives the next prime number in the list of prime numbers.

If the list isn't long enough we expand it. For ease in ParForm and because these lists shouldn't be very big we let each worker keep its own list.

The list is cut off at MAXPOWER, because we don't want to get into trouble that the power of a variable gets larger than the prime number.

Definition at line 3654 of file reken.c.