/*  tools.h  by K.Tsuru  */
/******************************
auxiliary tools for SN library
Their .cpp files are in the directory "sn32/src/af"
*******************************/
#ifndef TOOLS_H
#define TOOLS_H

// typedef of uint, ushort, etc.
#ifndef TYPEDEF_H
#include "typedef.h"
#endif  // TYPEDEF_H

#ifndef NC_BLOCK_H
#include "ncblock.h"
#endif  // NC_BLOCK_H

#ifndef SNBLOCK_H
#include "snblock.h"
#endif  // SNBLOCK_H

#ifndef MATH_TEMPLATE_H
#include "mathtp.h"     // to use "sameSign()"
#endif  // MATH_TEMPLATE_H

#include <math.h>
#include <stdio.h>
#include <stdlib.h>

/**************************************************************
Return a value k which satisfies a condition  sz<=k (k = 2^n).
**************************************************************/
uint ceilpow2(uint sz);

/**************************************************************
Return a value n which satisfies a condition  p<= 2^n.
e.g.   p = 5 --> n = 3
***************************************************************/
uint howpow2(uint p);

/*****************************************
It returns how many digits "x" has in radix "r" i.e.
a value x which satisfies a condition  x<= r^n.
e.g.   x = 25, r = 10 --> n = 2
*****************************************/
uint howdigsrdx(long x, long r);

/*****************************************
SNumber sub-function
It converts "long x" to "f[]" in radix R.
and returns "n".
x = f[n-1]*R^(n-1) + ... +f[1]*R + f[0]
*****************************************/
int rdxconv(int *f, long x, long R);

/**************************************************************
 bisection method
 bisectn.cpp
 It solves an equation f(x) = 0 in the region of [a, b].
**************************************************************/
double bisection(double a, double b, double tolerance, double (*f)(double));

/**************************************************************
It returns how many terms are necessary to evaluate exp(x)
in the precision.
parameter log10x : Prease give log10(x).
"expupto.cpp"
***************************************************************/
long upToExpSeries(long precision, double log10x);

/********************************************************
The rough estimate value for the number of prime under N.
pi(x) ~ x/ln(x) (Prime number theorem)
*********************************************************/
ulong PrimeNumberUnder(ulong N);
/****************************************
It makes the prime table between 2 and n
using the sieve of Eratosthenes.
Returns the size of pf[].
*****************************************/
ulong MakePrimeTable(NCBlock <ulong>& table, const ulong upTo);

/*********************************
factorization into prime factor
N! = a^p b^q c^r ...x y z
**********************************/
#ifndef STRUCT_PRIMFACTOR
#define STRUCT_PRIMFACTOR
struct primeFactor {
    ulong prime;
    int   power;
};
#endif  // STRUCT_PRIMFACTOR
int FactorialIntoPrimeFactor(ulong N, SNBlock <primeFactor>& pf);
// Factorial n <= 12 since version 2.30
inline ulong factUL(ulong n) {
    ulong r = n--;
    for( ; n ; n--) r *= n;
    return r;
}
// n! double version n <= 20
inline double factD(ulong n) {
    double r = n--;
    for( ; n ; n--) r *= n;
    return r;
}
// double version of nCk
const long nMax_combD = 48L; // maximum value of n
double combD(ulong n, ulong k);

// It returns the present time in string "hh:mm:ss".
string WhatTimeNow();
// Split large number file
int SplitLargeFile(const char* largeFileName, const long fileLineUnit, const char* outFNameFormat);
/*
When press y | Y key return 1
n | N key return  0
usage : cerr << "Quit ? (Y/N)"; YesOrNo();
*/
int YesOrNo();

#endif  //TOOLS_H