support.cpp

// Copyright (c) Microsoft Corporation. All rights reserved.
// Licensed under the MIT License.

//----------------------------------------------------------------------------
//  Package Title  ratpak
//  File           support.c
//  Copyright      (C) 1995-96 Microsoft
//  Date           10-21-96
//
//
//  Description
//
//     Contains support functions for rationals and numbers.
//
//  Special Information
//
//
//
//----------------------------------------------------------------------------

#include <string>
#include <cstring>  // for memmove
#include <iostream> // for wostream
#include "ratpak.h"

using namespace std;

void _readconstants(void);

#if defined(GEN_CONST)
static int cbitsofprecision = 0;
#define READRAWRAT(v)
#define READRAWNUM(v)
#define DUMPRAWRAT(v) _dumprawrat(#v, v, wcout)
#define DUMPRAWNUM(v)                                                                                                                                          \
    fprintf(stderr, "// Autogenerated by _dumprawrat in support.cpp\n");                                                                                       \
    fprintf(stderr, "inline const NUMBER init_" #v "= {\n");                                                                                                   \
    _dumprawnum(v, wcout);                                                                                                                                     \
    fprintf(stderr, "};\n")

#else

#define DUMPRAWRAT(v)
#define DUMPRAWNUM(v)
#define READRAWRAT(v)                                                                                                                                          \
    createrat(v);                                                                                                                                              \
    DUPNUM((v)->pp, (&(init_p_##v)));                                                                                                                          \
    DUPNUM((v)->pq, (&(init_q_##v)));
#define READRAWNUM(v) DUPNUM(v, (&(init_##v)))

#define INIT_AND_DUMP_RAW_NUM_IF_NULL(r, v)                                                                                                                    \
    if (r == nullptr)                                                                                                                                          \
    {                                                                                                                                                          \
        r = i32tonum(v, BASEX);                                                                                                                                \
        DUMPRAWNUM(v);                                                                                                                                         \
    }
#define INIT_AND_DUMP_RAW_RAT_IF_NULL(r, v)                                                                                                                    \
    if (r == nullptr)                                                                                                                                          \
    {                                                                                                                                                          \
        r = i32torat(v);                                                                                                                                       \
        DUMPRAWRAT(v);                                                                                                                                         \
    }

static constexpr int RATIO_FOR_DECIMAL = 9;
static constexpr int DECIMAL = 10;
static constexpr int CALC_DECIMAL_DIGITS_DEFAULT = 32;

static int cbitsofprecision = RATIO_FOR_DECIMAL * DECIMAL * CALC_DECIMAL_DIGITS_DEFAULT;

#include "ratconst.h"

#endif

bool g_ftrueinfinite = false; // Set to true if you don't want
                              // chopping internally
                              // precision used internally

PNUMBER num_one = nullptr;
PNUMBER num_two = nullptr;
PNUMBER num_five = nullptr;
PNUMBER num_six = nullptr;
PNUMBER num_ten = nullptr;

PRAT ln_ten = nullptr;
PRAT ln_two = nullptr;
PRAT rat_zero = nullptr;
PRAT rat_one = nullptr;
PRAT rat_neg_one = nullptr;
PRAT rat_two = nullptr;
PRAT rat_six = nullptr;
PRAT rat_half = nullptr;
PRAT rat_ten = nullptr;
PRAT pt_eight_five = nullptr;
PRAT pi = nullptr;
PRAT pi_over_two = nullptr;
PRAT two_pi = nullptr;
PRAT one_pt_five_pi = nullptr;
PRAT e_to_one_half = nullptr;
PRAT rat_exp = nullptr;
PRAT rad_to_deg = nullptr;
PRAT rad_to_grad = nullptr;
PRAT rat_qword = nullptr;
PRAT rat_dword = nullptr; // unsigned max ui32
PRAT rat_word = nullptr;
PRAT rat_byte = nullptr;
PRAT rat_360 = nullptr;
PRAT rat_400 = nullptr;
PRAT rat_180 = nullptr;
PRAT rat_200 = nullptr;
PRAT rat_nRadix = nullptr;
PRAT rat_smallest = nullptr;
PRAT rat_negsmallest = nullptr;
PRAT rat_max_exp = nullptr;
PRAT rat_min_exp = nullptr;
PRAT rat_max_fact = nullptr;
PRAT rat_min_fact = nullptr;
PRAT rat_min_i32 = nullptr; // min signed i32
PRAT rat_max_i32 = nullptr; // max signed i32

//----------------------------------------------------------------------------
//
//  FUNCTION: ChangeConstants
//
//  ARGUMENTS:  base changing to, and precision to use.
//
//  RETURN: None
//
//  SIDE EFFECTS: sets a mess of constants.
//
//
//----------------------------------------------------------------------------

void ChangeConstants(uint32_t radix, int32_t precision)
{
    // ratio is set to the number of digits in the current radix, you can get
    // in the internal BASEX radix, this is important for length calculations
    // in translating from radix to BASEX and back.

    uint64_t limit = static_cast<uint64_t>(BASEX) / static_cast<uint64_t>(radix);
    g_ratio = 0;
    for (uint32_t digit = 1; digit < limit; digit *= radix)
    {
        g_ratio++;
    }
    g_ratio += !g_ratio;

    destroyrat(rat_nRadix);
    rat_nRadix = i32torat(radix);

    // Check to see what we have to recalculate and what we don't
    if (cbitsofprecision < (g_ratio * static_cast<int32_t>(radix) * precision))
    {
        g_ftrueinfinite = false;

        INIT_AND_DUMP_RAW_NUM_IF_NULL(num_one, 1L);
        INIT_AND_DUMP_RAW_NUM_IF_NULL(num_two, 2L);
        INIT_AND_DUMP_RAW_NUM_IF_NULL(num_five, 5L);
        INIT_AND_DUMP_RAW_NUM_IF_NULL(num_six, 6L);
        INIT_AND_DUMP_RAW_NUM_IF_NULL(num_ten, 10L);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_six, 6L);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_two, 2L);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_zero, 0L);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_one, 1L);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_neg_one, -1L);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_ten, 10L);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_word, 0xffff);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_word, 0xff);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_400, 400);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_360, 360);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_200, 200);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_180, 180);
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_max_exp, 100000);

        // 3248, is the max number for which calc is able to compute factorial, after that it is unable to compute due to overflow.
        // Hence restricted factorial range as at most 3248.Beyond that calc will throw overflow error immediately.
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_max_fact, 3249);

        // -1000, is the min number for which calc is able to compute factorial, after that it takes too long to compute.
        INIT_AND_DUMP_RAW_RAT_IF_NULL(rat_min_fact, -1000);

        DUPRAT(rat_smallest, rat_nRadix);
        ratpowi32(&rat_smallest, -precision, precision);
        DUPRAT(rat_negsmallest, rat_smallest);
        rat_negsmallest->pp->sign = -1;
        DUMPRAWRAT(rat_smallest);
        DUMPRAWRAT(rat_negsmallest);

        if (rat_half == nullptr)
        {
            createrat(rat_half);
            DUPNUM(rat_half->pp, num_one);
            DUPNUM(rat_half->pq, num_two);
            DUMPRAWRAT(rat_half);
        }

        if (pt_eight_five == nullptr)
        {
            createrat(pt_eight_five);
            pt_eight_five->pp = i32tonum(85L, BASEX);
            pt_eight_five->pq = i32tonum(100L, BASEX);
            DUMPRAWRAT(pt_eight_five);
        }

        DUPRAT(rat_qword, rat_two);
        numpowi32(&(rat_qword->pp), 64, BASEX, precision);
        subrat(&rat_qword, rat_one, precision);
        DUMPRAWRAT(rat_qword);

        DUPRAT(rat_dword, rat_two);
        numpowi32(&(rat_dword->pp), 32, BASEX, precision);
        subrat(&rat_dword, rat_one, precision);
        DUMPRAWRAT(rat_dword);

        DUPRAT(rat_max_i32, rat_two);
        numpowi32(&(rat_max_i32->pp), 31, BASEX, precision);
        DUPRAT(rat_min_i32, rat_max_i32);
        subrat(&rat_max_i32, rat_one, precision); // rat_max_i32 = 2^31 -1
        DUMPRAWRAT(rat_max_i32);

        rat_min_i32->pp->sign *= -1; // rat_min_i32 = -2^31
        DUMPRAWRAT(rat_min_i32);

        DUPRAT(rat_min_exp, rat_max_exp);
        rat_min_exp->pp->sign *= -1;
        DUMPRAWRAT(rat_min_exp);

        cbitsofprecision = g_ratio * radix * precision;

        // Apparently when dividing 180 by pi, another (internal) digit of
        // precision is needed.
        int32_t extraPrecision = precision + g_ratio;
        DUPRAT(pi, rat_half);
        asinrat(&pi, radix, extraPrecision);
        mulrat(&pi, rat_six, extraPrecision);
        DUMPRAWRAT(pi);

        DUPRAT(two_pi, pi);
        DUPRAT(pi_over_two, pi);
        DUPRAT(one_pt_five_pi, pi);
        addrat(&two_pi, pi, extraPrecision);
        DUMPRAWRAT(two_pi);

        divrat(&pi_over_two, rat_two, extraPrecision);
        DUMPRAWRAT(pi_over_two);

        addrat(&one_pt_five_pi, pi_over_two, extraPrecision);
        DUMPRAWRAT(one_pt_five_pi);

        DUPRAT(e_to_one_half, rat_half);
        _exprat(&e_to_one_half, extraPrecision);
        DUMPRAWRAT(e_to_one_half);

        DUPRAT(rat_exp, rat_one);
        _exprat(&rat_exp, extraPrecision);
        DUMPRAWRAT(rat_exp);

        // WARNING: remember lograt uses exponent constants calculated above...

        DUPRAT(ln_ten, rat_ten);
        lograt(&ln_ten, extraPrecision);
        DUMPRAWRAT(ln_ten);

        DUPRAT(ln_two, rat_two);
        lograt(&ln_two, extraPrecision);
        DUMPRAWRAT(ln_two);

        destroyrat(rad_to_deg);
        rad_to_deg = i32torat(180L);
        divrat(&rad_to_deg, pi, extraPrecision);
        DUMPRAWRAT(rad_to_deg);

        destroyrat(rad_to_grad);
        rad_to_grad = i32torat(200L);
        divrat(&rad_to_grad, pi, extraPrecision);
        DUMPRAWRAT(rad_to_grad);
    }
    else
    {
        _readconstants();

        DUPRAT(rat_smallest, rat_nRadix);
        ratpowi32(&rat_smallest, -precision, precision);
        DUPRAT(rat_negsmallest, rat_smallest);
        rat_negsmallest->pp->sign = -1;
    }
}

//----------------------------------------------------------------------------
//
//  FUNCTION: intrat
//
//  ARGUMENTS:  pointer to x PRAT representation of number
//
//  RETURN: no return value x PRAT is smashed with integral number
//
//
//----------------------------------------------------------------------------

void intrat(_Inout_ PRAT* px, uint32_t radix, int32_t precision)
{
    // Only do the intrat operation if number is nonzero.
    // and only if the bottom part is not one.
    if (!zernum((*px)->pp) && !equnum((*px)->pq, num_one))
    {
        flatrat(*px, radix, precision);

        // Subtract the fractional part of the rational
        PRAT pret = nullptr;
        DUPRAT(pret, *px);
        remrat(&pret, rat_one);

        subrat(px, pret, precision);
        destroyrat(pret);

        // Simplify the value if possible to resolve rounding errors
        flatrat(*px, radix, precision);
    }
}

//---------------------------------------------------------------------------
//
//  FUNCTION: rat_equ
//
//  ARGUMENTS:  PRAT a and PRAT b
//
//  RETURN: true if equal false otherwise.
//
//
//---------------------------------------------------------------------------

bool rat_equ(_In_ PRAT a, _In_ PRAT b, int32_t precision)

{
    PRAT rattmp = nullptr;
    DUPRAT(rattmp, a);
    rattmp->pp->sign *= -1;
    addrat(&rattmp, b, precision);
    bool bret = zernum(rattmp->pp);
    destroyrat(rattmp);
    return (bret);
}

//---------------------------------------------------------------------------
//
//  FUNCTION: rat_ge
//
//  ARGUMENTS:  PRAT a, PRAT b and int32_t precision
//
//  RETURN: true if a is greater than or equal to b
//
//
//---------------------------------------------------------------------------

bool rat_ge(_In_ PRAT a, _In_ PRAT b, int32_t precision)

{
    PRAT rattmp = nullptr;
    DUPRAT(rattmp, a);
    b->pp->sign *= -1;
    addrat(&rattmp, b, precision);
    b->pp->sign *= -1;
    bool bret = (zernum(rattmp->pp) || SIGN(rattmp) == 1);
    destroyrat(rattmp);
    return (bret);
}

//---------------------------------------------------------------------------
//
//  FUNCTION: rat_gt
//
//  ARGUMENTS:  PRAT a and PRAT b
//
//  RETURN: true if a is greater than b
//
//
//---------------------------------------------------------------------------

bool rat_gt(_In_ PRAT a, _In_ PRAT b, int32_t precision)

{
    PRAT rattmp = nullptr;
    DUPRAT(rattmp, a);
    b->pp->sign *= -1;
    addrat(&rattmp, b, precision);
    b->pp->sign *= -1;
    bool bret = (!zernum(rattmp->pp) && SIGN(rattmp) == 1);
    destroyrat(rattmp);
    return (bret);
}

//---------------------------------------------------------------------------
//
//  FUNCTION: rat_le
//
//  ARGUMENTS:  PRAT a, PRAT b and int32_t precision
//
//  RETURN: true if a is less than or equal to b
//
//
//---------------------------------------------------------------------------

bool rat_le(_In_ PRAT a, _In_ PRAT b, int32_t precision)

{
    PRAT rattmp = nullptr;
    DUPRAT(rattmp, a);
    b->pp->sign *= -1;
    addrat(&rattmp, b, precision);
    b->pp->sign *= -1;
    bool bret = (zernum(rattmp->pp) || SIGN(rattmp) == -1);
    destroyrat(rattmp);
    return (bret);
}

//---------------------------------------------------------------------------
//
//  FUNCTION: rat_lt
//
//  ARGUMENTS:  PRAT a, PRAT b and int32_t precision
//
//  RETURN: true if a is less than b
//
//
//---------------------------------------------------------------------------

bool rat_lt(_In_ PRAT a, _In_ PRAT b, int32_t precision)

{
    PRAT rattmp = nullptr;
    DUPRAT(rattmp, a);
    b->pp->sign *= -1;
    addrat(&rattmp, b, precision);
    b->pp->sign *= -1;
    bool bret = (!zernum(rattmp->pp) && SIGN(rattmp) == -1);
    destroyrat(rattmp);
    return (bret);
}

//---------------------------------------------------------------------------
//
//  FUNCTION: rat_neq
//
//  ARGUMENTS:  PRAT a and PRAT b
//
//  RETURN: true if a is not equal to b
//
//
//---------------------------------------------------------------------------

bool rat_neq(_In_ PRAT a, _In_ PRAT b, int32_t precision)

{
    PRAT rattmp = nullptr;
    DUPRAT(rattmp, a);
    rattmp->pp->sign *= -1;
    addrat(&rattmp, b, precision);
    bool bret = !(zernum(rattmp->pp));
    destroyrat(rattmp);
    return (bret);
}

//---------------------------------------------------------------------------
//
//  function: scale
//
//  ARGUMENTS:  pointer to x PRAT representation of number, and scaling factor
//
//  RETURN: no return, value x PRAT is smashed with a scaled number in the
//          range of the scalefact.
//
//---------------------------------------------------------------------------

void scale(_Inout_ PRAT* px, _In_ PRAT scalefact, uint32_t radix, int32_t precision)
{
    PRAT pret = nullptr;
    DUPRAT(pret, *px);

    // Logscale is a quick way to tell how much extra precision is needed for
    // scaling by scalefact.
    int32_t logscale = g_ratio * ((pret->pp->cdigit + pret->pp->exp) - (pret->pq->cdigit + pret->pq->exp));
    if (logscale > 0)
    {
        precision += logscale;
    }

    divrat(&pret, scalefact, precision);
    intrat(&pret, radix, precision);
    mulrat(&pret, scalefact, precision);
    pret->pp->sign *= -1;
    addrat(px, pret, precision);

    destroyrat(pret);
}

//---------------------------------------------------------------------------
//
//  function: scale2pi
//
//  ARGUMENTS:  pointer to x PRAT representation of number
//
//  RETURN: no return, value x PRAT is smashed with a scaled number in the
//          range of 0..2pi
//
//---------------------------------------------------------------------------

void scale2pi(_Inout_ PRAT* px, uint32_t radix, int32_t precision)
{
    PRAT pret = nullptr;
    PRAT my_two_pi = nullptr;
    DUPRAT(pret, *px);

    // Logscale is a quick way to tell how much extra precision is needed for
    // scaling by 2 pi.
    int32_t logscale = g_ratio * ((pret->pp->cdigit + pret->pp->exp) - (pret->pq->cdigit + pret->pq->exp));
    if (logscale > 0)
    {
        precision += logscale;
        DUPRAT(my_two_pi, rat_half);
        asinrat(&my_two_pi, radix, precision);
        mulrat(&my_two_pi, rat_six, precision);
        mulrat(&my_two_pi, rat_two, precision);
    }
    else
    {
        DUPRAT(my_two_pi, two_pi);
        logscale = 0;
    }

    divrat(&pret, my_two_pi, precision);
    intrat(&pret, radix, precision);
    mulrat(&pret, my_two_pi, precision);
    pret->pp->sign *= -1;
    addrat(px, pret, precision);

    destroyrat(my_two_pi);
    destroyrat(pret);
}

//---------------------------------------------------------------------------
//
//  FUNCTION: inbetween
//
//  ARGUMENTS:  PRAT *px, and PRAT range.
//
//  RETURN: none, changes *px to -/+range, if px is outside -range..+range
//
//---------------------------------------------------------------------------

void inbetween(_In_ PRAT* px, _In_ PRAT range, int32_t precision)

{
    if (rat_gt(*px, range, precision))
    {
        DUPRAT(*px, range);
    }
    else
    {
        range->pp->sign *= -1;
        if (rat_lt(*px, range, precision))
        {
            DUPRAT(*px, range);
        }
        range->pp->sign *= -1;
    }
}

//---------------------------------------------------------------------------
//
//  FUNCTION: _dumprawrat
//
//  ARGUMENTS:  const wchar *name of variable, PRAT x, output stream out
//
//  RETURN: none, prints the results of a dump of the internal structures
//          of a PRAT, suitable for READRAWRAT to stderr.
//
//---------------------------------------------------------------------------

void _dumprawrat(_In_ const wchar_t* varname, _In_ PRAT rat, wostream& out)

{
    _dumprawnum(varname, rat->pp, out);
    _dumprawnum(varname, rat->pq, out);
}

//---------------------------------------------------------------------------
//
//  FUNCTION: _dumprawnum
//
//  ARGUMENTS:  const wchar *name of variable, PNUMBER num, output stream out
//
//  RETURN: none, prints the results of a dump of the internal structures
//          of a PNUMBER, suitable for READRAWNUM to stderr.
//
//---------------------------------------------------------------------------

void _dumprawnum(_In_ const wchar_t* varname, _In_ PNUMBER num, wostream& out)

{
    out << L"NUMBER " << varname << L" = {\n";
    out << L"\t" << num->sign << L",\n";
    out << L"\t" << num->cdigit << L",\n";
    out << L"\t" << num->exp << L",\n";
    out << L"\t{ ";

    for (int i = 0; i < num->cdigit; i++)
    {
        out << L" " << num->mant[i] << L",";
    }
    out << L"}\n";
    out << L"};\n";
}

void _readconstants(void)

{
    READRAWNUM(num_one);
    READRAWNUM(num_two);
    READRAWNUM(num_five);
    READRAWNUM(num_six);
    READRAWNUM(num_ten);
    READRAWRAT(pt_eight_five);
    READRAWRAT(rat_six);
    READRAWRAT(rat_two);
    READRAWRAT(rat_zero);
    READRAWRAT(rat_one);
    READRAWRAT(rat_neg_one);
    READRAWRAT(rat_half);
    READRAWRAT(rat_ten);
    READRAWRAT(pi);
    READRAWRAT(two_pi);
    READRAWRAT(pi_over_two);
    READRAWRAT(one_pt_five_pi);
    READRAWRAT(e_to_one_half);
    READRAWRAT(rat_exp);
    READRAWRAT(ln_ten);
    READRAWRAT(ln_two);
    READRAWRAT(rad_to_deg);
    READRAWRAT(rad_to_grad);
    READRAWRAT(rat_qword);
    READRAWRAT(rat_dword);
    READRAWRAT(rat_word);
    READRAWRAT(rat_byte);
    READRAWRAT(rat_360);
    READRAWRAT(rat_400);
    READRAWRAT(rat_180);
    READRAWRAT(rat_200);
    READRAWRAT(rat_smallest);
    READRAWRAT(rat_negsmallest);
    READRAWRAT(rat_max_exp);
    READRAWRAT(rat_min_exp);
    READRAWRAT(rat_max_fact);
    READRAWRAT(rat_min_fact);
    READRAWRAT(rat_min_i32);
    READRAWRAT(rat_max_i32);
}

//---------------------------------------------------------------------------
//
//  FUNCTION: trimit
//
//  ARGUMENTS:  PRAT *px, int32_t precision
//
//
//  DESCRIPTION: Chops off digits from rational numbers to avoid time
//  explosions in calculations of functions using series.
//  It can be shown that it is enough to only keep the first n digits
//  of the largest of p or q in the rational p over q form, and of course
//  scale the smaller by the same number of digits.  This will give you
//  n-1 digits of accuracy.  This dramatically speeds up calculations
//  involving hundreds of digits or more.
//  The last part of this trim dealing with exponents never affects accuracy
//
//  RETURN: none, modifies the pointed to PRAT
//
//---------------------------------------------------------------------------

void trimit(_Inout_ PRAT* px, int32_t precision)

{
    if (!g_ftrueinfinite)
    {
        PNUMBER pp = (*px)->pp;
        PNUMBER pq = (*px)->pq;
        int32_t trim = g_ratio * (min((pp->cdigit + pp->exp), (pq->cdigit + pq->exp)) - 1) - precision;
        if (trim > g_ratio)
        {
            trim /= g_ratio;

            if (trim <= pp->exp)
            {
                pp->exp -= trim;
            }
            else
            {
                memmove(pp->mant, &(pp->mant[trim - pp->exp]), sizeof(MANTTYPE) * (pp->cdigit - trim + pp->exp));
                pp->cdigit -= trim - pp->exp;
                pp->exp = 0;
            }

            if (trim <= pq->exp)
            {
                pq->exp -= trim;
            }
            else
            {
                memmove(pq->mant, &(pq->mant[trim - pq->exp]), sizeof(MANTTYPE) * (pq->cdigit - trim + pq->exp));
                pq->cdigit -= trim - pq->exp;
                pq->exp = 0;
            }
        }
        trim = min(pp->exp, pq->exp);
        pp->exp -= trim;
        pq->exp -= trim;
    }
}