ext/bigdecimal/bigdecimal.c

Go to the documentation of this file.

/*
 *
 * Ruby BigDecimal(Variable decimal precision) extension library.
 *
 * Copyright(C) 2002 by Shigeo Kobayashi(shigeo@tinyforest.gr.jp)
 *
 * You may distribute under the terms of either the GNU General Public
 * License or the Artistic License, as specified in the README file
 * of this BigDecimal distribution.
 *
 *  NOTE: Change log in this source removed to reduce source code size.
 *        See rev. 1.25 if needed.
 *
 */

/* #define BIGDECIMAL_DEBUG 1 */
#ifdef BIGDECIMAL_DEBUG
# define BIGDECIMAL_ENABLE_VPRINT 1
#endif
#include "bigdecimal.h"

#ifndef BIGDECIMAL_DEBUG
# define NDEBUG
#endif
#include <assert.h>

#include <ctype.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <errno.h>
#include <math.h>
#include "math.h"

#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif

/* #define ENABLE_NUMERIC_STRING */

VALUE rb_cBigDecimal;
VALUE rb_mBigMath;

static ID id_BigDecimal_exception_mode;
static ID id_BigDecimal_rounding_mode;
static ID id_BigDecimal_precision_limit;

static ID id_up;
static ID id_down;
static ID id_truncate;
static ID id_half_up;
static ID id_default;
static ID id_half_down;
static ID id_half_even;
static ID id_banker;
static ID id_ceiling;
static ID id_ceil;
static ID id_floor;
static ID id_to_r;
static ID id_eq;

/* MACRO's to guard objects from GC by keeping them in stack */
#define ENTER(n) volatile VALUE vStack[n];int iStack=0
#define PUSH(x)  vStack[iStack++] = (VALUE)(x);
#define SAVE(p)  PUSH(p->obj);
#define GUARD_OBJ(p,y) {p=y;SAVE(p);}

#define BASE_FIG  RMPD_COMPONENT_FIGURES
#define BASE      RMPD_BASE

#define HALF_BASE (BASE/2)
#define BASE1 (BASE/10)

#ifndef DBLE_FIG
#define DBLE_FIG (DBL_DIG+1)    /* figure of double */
#endif

#ifndef RBIGNUM_ZERO_P
# define RBIGNUM_ZERO_P(x) (RBIGNUM_LEN(x) == 0 || \
                            (RBIGNUM_DIGITS(x)[0] == 0 && \
                             (RBIGNUM_LEN(x) == 1 || bigzero_p(x))))
#endif

static inline int
bigzero_p(VALUE x)
{
    long i;
    BDIGIT *ds = RBIGNUM_DIGITS(x);

    for (i = RBIGNUM_LEN(x) - 1; 0 <= i; i--) {
        if (ds[i]) return 0;
    }
    return 1;
}

#ifndef RRATIONAL_ZERO_P
# define RRATIONAL_ZERO_P(x) (FIXNUM_P(RRATIONAL(x)->num) && \
                              FIX2LONG(RRATIONAL(x)->num) == 0)
#endif

#ifndef RRATIONAL_NEGATIVE_P
# define RRATIONAL_NEGATIVE_P(x) RTEST(rb_funcall((x), '<', 1, INT2FIX(0)))
#endif

/*
 * ================== Ruby Interface part ==========================
 */
#define DoSomeOne(x,y,f) rb_num_coerce_bin(x,y,f)

/*
 * Returns the BigDecimal version number.
 *
 * Ruby 1.8.0 returns 1.0.0.
 * Ruby 1.8.1 thru 1.8.3 return 1.0.1.
 */
static VALUE
BigDecimal_version(VALUE self)
{
    /*
     * 1.0.0: Ruby 1.8.0
     * 1.0.1: Ruby 1.8.1
     * 1.1.0: Ruby 1.9.3
    */
    return rb_str_new2("1.1.0");
}

/*
 *   VP routines used in BigDecimal part
 */
static unsigned short VpGetException(void);
static void  VpSetException(unsigned short f);
static void  VpInternalRound(Real *c, size_t ixDigit, BDIGIT vPrev, BDIGIT v);
static int   VpLimitRound(Real *c, size_t ixDigit);
static Real *VpDup(Real const* const x);

/*
 *  **** BigDecimal part ****
 */

static void
BigDecimal_delete(void *pv)
{
    VpFree(pv);
}

static size_t
BigDecimal_memsize(const void *ptr)
{
    const Real *pv = ptr;
    return pv ? (sizeof(*pv) + pv->MaxPrec * sizeof(BDIGIT)) : 0;
}

static const rb_data_type_t BigDecimal_data_type = {
    "BigDecimal",
    {0, BigDecimal_delete, BigDecimal_memsize,},
};

static inline int
is_kind_of_BigDecimal(VALUE const v)
{
    return rb_typeddata_is_kind_of(v, &BigDecimal_data_type);
}

static VALUE
ToValue(Real *p)
{
    if(VpIsNaN(p)) {
        VpException(VP_EXCEPTION_NaN,"Computation results to 'NaN'(Not a Number)",0);
    } else if(VpIsPosInf(p)) {
        VpException(VP_EXCEPTION_INFINITY,"Computation results to 'Infinity'",0);
    } else if(VpIsNegInf(p)) {
        VpException(VP_EXCEPTION_INFINITY,"Computation results to '-Infinity'",0);
    }
    return p->obj;
}

NORETURN(static void cannot_be_coerced_into_BigDecimal(VALUE, VALUE));

static void
cannot_be_coerced_into_BigDecimal(VALUE exc_class, VALUE v)
{
    VALUE str;

    if (rb_special_const_p(v)) {
        str = rb_str_cat2(rb_str_dup(rb_inspect(v)),
                          " can't be coerced into BigDecimal");
    }
    else {
        str = rb_str_cat2(rb_str_dup(rb_class_name(rb_obj_class(v))),
                          " can't be coerced into BigDecimal");
    }

    rb_exc_raise(rb_exc_new3(exc_class, str));
}

static VALUE BigDecimal_div2(int, VALUE*, VALUE);

static Real*
GetVpValueWithPrec(VALUE v, long prec, int must)
{
    Real *pv;
    VALUE num, bg, args[2];
    char szD[128];
    VALUE orig = Qundef;

again:
    switch(TYPE(v))
    {
      case T_FLOAT:
        if (prec < 0) goto unable_to_coerce_without_prec;
        if (prec > DBL_DIG+1)goto SomeOneMayDoIt;
        v = rb_funcall(v, id_to_r, 0);
        goto again;
      case T_RATIONAL:
        if (prec < 0) goto unable_to_coerce_without_prec;

        if (orig == Qundef ? (orig = v, 1) : orig != v) {
            num = RRATIONAL(v)->num;
            pv = GetVpValueWithPrec(num, -1, must);
            if (pv == NULL) goto SomeOneMayDoIt;

            args[0] = RRATIONAL(v)->den;
            args[1] = LONG2NUM(prec);
            v = BigDecimal_div2(2, args, ToValue(pv));
            goto again;
        }

        v = orig;
        goto SomeOneMayDoIt;

      case T_DATA:
        if (is_kind_of_BigDecimal(v)) {
            pv = DATA_PTR(v);
            return pv;
        }
        else {
            goto SomeOneMayDoIt;
        }
        break;

      case T_FIXNUM:
        sprintf(szD, "%ld", FIX2LONG(v));
        return VpCreateRbObject(VpBaseFig() * 2 + 1, szD);

#ifdef ENABLE_NUMERIC_STRING
      case T_STRING:
        SafeStringValue(v);
        return VpCreateRbObject(strlen(RSTRING_PTR(v)) + VpBaseFig() + 1,
                                RSTRING_PTR(v));
#endif /* ENABLE_NUMERIC_STRING */

      case T_BIGNUM:
        bg = rb_big2str(v, 10);
        return VpCreateRbObject(strlen(RSTRING_PTR(bg)) + VpBaseFig() + 1,
                                RSTRING_PTR(bg));
      default:
        goto SomeOneMayDoIt;
    }

SomeOneMayDoIt:
    if (must) {
        cannot_be_coerced_into_BigDecimal(rb_eTypeError, v);
    }
    return NULL; /* NULL means to coerce */

unable_to_coerce_without_prec:
    if (must) {
        rb_raise(rb_eArgError,
                 "%s can't be coerced into BigDecimal without a precision",
                 rb_obj_classname(v));
    }
    return NULL;
}

static Real*
GetVpValue(VALUE v, int must)
{
    return GetVpValueWithPrec(v, -1, must);
}

/* call-seq:
 * BigDecimal.double_fig
 *
 * The BigDecimal.double_fig class method returns the number of digits a
 * Float number is allowed to have. The result depends upon the CPU and OS
 * in use.
 */
static VALUE
BigDecimal_double_fig(VALUE self)
{
    return INT2FIX(VpDblFig());
}

/* call-seq:
 * precs
 *
 * Returns an Array of two Integer values.
 *
 * The first value is the current number of significant digits in the
 * BigDecimal. The second value is the maximum number of significant digits
 * for the BigDecimal.
 */
static VALUE
BigDecimal_prec(VALUE self)
{
    ENTER(1);
    Real *p;
    VALUE obj;

    GUARD_OBJ(p,GetVpValue(self,1));
    obj = rb_assoc_new(INT2NUM(p->Prec*VpBaseFig()),
                       INT2NUM(p->MaxPrec*VpBaseFig()));
    return obj;
}

static VALUE
BigDecimal_hash(VALUE self)
{
    ENTER(1);
    Real *p;
    st_index_t hash;

    GUARD_OBJ(p,GetVpValue(self,1));
    hash = (st_index_t)p->sign;
    /* hash!=2: the case for 0(1),NaN(0) or +-Infinity(3) is sign itself */
    if(hash == 2 || hash == (st_index_t)-2) {
        hash ^= rb_memhash(p->frac, sizeof(BDIGIT)*p->Prec);
        hash += p->exponent;
    }
    return INT2FIX(hash);
}

static VALUE
BigDecimal_dump(int argc, VALUE *argv, VALUE self)
{
    ENTER(5);
    Real *vp;
    char *psz;
    VALUE dummy;
    volatile VALUE dump;

    rb_scan_args(argc, argv, "01", &dummy);
    GUARD_OBJ(vp,GetVpValue(self,1));
    dump = rb_str_new(0,VpNumOfChars(vp,"E")+50);
    psz = RSTRING_PTR(dump);
    sprintf(psz, "%"PRIuSIZE":", VpMaxPrec(vp)*VpBaseFig());
    VpToString(vp, psz+strlen(psz), 0, 0);
    rb_str_resize(dump, strlen(psz));
    return dump;
}

/*
 * Internal method used to provide marshalling support. See the Marshal module.
 */
static VALUE
BigDecimal_load(VALUE self, VALUE str)
{
    ENTER(2);
    Real *pv;
    unsigned char *pch;
    unsigned char ch;
    unsigned long m=0;

    SafeStringValue(str);
    pch = (unsigned char *)RSTRING_PTR(str);
    /* First get max prec */
    while((*pch)!=(unsigned char)'\0' && (ch=*pch++)!=(unsigned char)':') {
        if(!ISDIGIT(ch)) {
            rb_raise(rb_eTypeError, "load failed: invalid character in the marshaled string");
        }
        m = m*10 + (unsigned long)(ch-'0');
    }
    if(m>VpBaseFig()) m -= VpBaseFig();
    GUARD_OBJ(pv,VpNewRbClass(m,(char *)pch,self));
    m /= VpBaseFig();
    if(m && pv->MaxPrec>m) pv->MaxPrec = m+1;
    return ToValue(pv);
}

static unsigned short
check_rounding_mode(VALUE const v)
{
    unsigned short sw;
    ID id;
    switch (TYPE(v)) {
      case T_SYMBOL:
        id = SYM2ID(v);
        if (id == id_up)
            return VP_ROUND_UP;
        if (id == id_down || id == id_truncate)
            return VP_ROUND_DOWN;
        if (id == id_half_up || id == id_default)
            return VP_ROUND_HALF_UP;
        if (id == id_half_down)
            return VP_ROUND_HALF_DOWN;
        if (id == id_half_even || id == id_banker)
            return VP_ROUND_HALF_EVEN;
        if (id == id_ceiling || id == id_ceil)
            return VP_ROUND_CEIL;
        if (id == id_floor)
            return VP_ROUND_FLOOR;
        rb_raise(rb_eArgError, "invalid rounding mode");

      default:
        break;
    }

    Check_Type(v, T_FIXNUM);
    sw = (unsigned short)FIX2UINT(v);
    if (!VpIsRoundMode(sw)) {
        rb_raise(rb_eArgError, "invalid rounding mode");
    }
    return sw;
}

/* call-seq:
 * BigDecimal.mode(mode, value)
 *
 * Controls handling of arithmetic exceptions and rounding. If no value
 * is supplied, the current value is returned.
 *
 * Six values of the mode parameter control the handling of arithmetic
 * exceptions:
 *
 * BigDecimal::EXCEPTION_NaN
 * BigDecimal::EXCEPTION_INFINITY
 * BigDecimal::EXCEPTION_UNDERFLOW
 * BigDecimal::EXCEPTION_OVERFLOW
 * BigDecimal::EXCEPTION_ZERODIVIDE
 * BigDecimal::EXCEPTION_ALL
 *
 * For each mode parameter above, if the value set is false, computation
 * continues after an arithmetic exception of the appropriate type.
 * When computation continues, results are as follows:
 *
 * EXCEPTION_NaN:: NaN
 * EXCEPTION_INFINITY:: +infinity or -infinity
 * EXCEPTION_UNDERFLOW:: 0
 * EXCEPTION_OVERFLOW:: +infinity or -infinity
 * EXCEPTION_ZERODIVIDE:: +infinity or -infinity
 *
 * One value of the mode parameter controls the rounding of numeric values:
 * BigDecimal::ROUND_MODE. The values it can take are:
 *
 * ROUND_UP, :up:: round away from zero
 * ROUND_DOWN, :down, :truncate:: round towards zero (truncate)
 * ROUND_HALF_UP, :half_up, :default:: round towards the nearest neighbor, unless both neighbors are equidistant, in which case round away from zero. (default)
 * ROUND_HALF_DOWN, :half_down:: round towards the nearest neighbor, unless both neighbors are equidistant, in which case round towards zero.
 * ROUND_HALF_EVEN, :half_even, :banker:: round towards the nearest neighbor, unless both neighbors are equidistant, in which case round towards the even neighbor (Banker's rounding)
 * ROUND_CEILING, :ceiling, :ceil:: round towards positive infinity (ceil)
 * ROUND_FLOOR, :floor:: round towards negative infinity (floor)
 *
 */
static VALUE
BigDecimal_mode(int argc, VALUE *argv, VALUE self)
{
    VALUE which;
    VALUE val;
    unsigned long f,fo;

    if(rb_scan_args(argc,argv,"11",&which,&val)==1) val = Qnil;

    Check_Type(which, T_FIXNUM);
    f = (unsigned long)FIX2INT(which);

    if(f&VP_EXCEPTION_ALL) {
        /* Exception mode setting */
        fo = VpGetException();
        if(val==Qnil) return INT2FIX(fo);
        if(val!=Qfalse && val!=Qtrue) {
            rb_raise(rb_eArgError, "second argument must be true or false");
            return Qnil; /* Not reached */
        }
        if(f&VP_EXCEPTION_INFINITY) {
            VpSetException((unsigned short)((val==Qtrue)?(fo|VP_EXCEPTION_INFINITY):
                           (fo&(~VP_EXCEPTION_INFINITY))));
        }
        fo = VpGetException();
        if(f&VP_EXCEPTION_NaN) {
            VpSetException((unsigned short)((val==Qtrue)?(fo|VP_EXCEPTION_NaN):
                           (fo&(~VP_EXCEPTION_NaN))));
        }
        fo = VpGetException();
        if(f&VP_EXCEPTION_UNDERFLOW) {
            VpSetException((unsigned short)((val==Qtrue)?(fo|VP_EXCEPTION_UNDERFLOW):
                           (fo&(~VP_EXCEPTION_UNDERFLOW))));
        }
        fo = VpGetException();
        if(f&VP_EXCEPTION_ZERODIVIDE) {
            VpSetException((unsigned short)((val==Qtrue)?(fo|VP_EXCEPTION_ZERODIVIDE):
                           (fo&(~VP_EXCEPTION_ZERODIVIDE))));
        }
        fo = VpGetException();
        return INT2FIX(fo);
    }
    if (VP_ROUND_MODE == f) {
        /* Rounding mode setting */
        unsigned short sw;
        fo = VpGetRoundMode();
        if (NIL_P(val)) return INT2FIX(fo);
        sw = check_rounding_mode(val);
        fo = VpSetRoundMode(sw);
        return INT2FIX(fo);
    }
    rb_raise(rb_eTypeError, "first argument for BigDecimal#mode invalid");
    return Qnil;
}

static size_t
GetAddSubPrec(Real *a, Real *b)
{
    size_t mxs;
    size_t mx = a->Prec;
    SIGNED_VALUE d;

    if(!VpIsDef(a) || !VpIsDef(b)) return (size_t)-1L;
    if(mx < b->Prec) mx = b->Prec;
    if(a->exponent!=b->exponent) {
        mxs = mx;
        d = a->exponent - b->exponent;
        if (d < 0) d = -d;
        mx = mx + (size_t)d;
        if (mx<mxs) {
            return VpException(VP_EXCEPTION_INFINITY,"Exponent overflow",0);
        }
    }
    return mx;
}

static SIGNED_VALUE
GetPositiveInt(VALUE v)
{
    SIGNED_VALUE n;
    Check_Type(v, T_FIXNUM);
    n = FIX2INT(v);
    if (n < 0) {
        rb_raise(rb_eArgError, "argument must be positive");
    }
    return n;
}

VP_EXPORT Real *
VpNewRbClass(size_t mx, const char *str, VALUE klass)
{
    Real *pv = VpAlloc(mx,str);
    pv->obj = TypedData_Wrap_Struct(klass, &BigDecimal_data_type, pv);
    return pv;
}

VP_EXPORT Real *
VpCreateRbObject(size_t mx, const char *str)
{
    Real *pv = VpAlloc(mx,str);
    pv->obj = TypedData_Wrap_Struct(rb_cBigDecimal, &BigDecimal_data_type, pv);
    return pv;
}

static Real *
VpDup(Real const* const x)
{
    Real *pv;

    assert(x != NULL);

    pv = VpMemAlloc(sizeof(Real) + x->MaxPrec * sizeof(BDIGIT));
    pv->MaxPrec = x->MaxPrec;
    pv->Prec = x->Prec;
    pv->exponent = x->exponent;
    pv->sign = x->sign;
    pv->flag = x->flag;
    MEMCPY(pv->frac, x->frac, BDIGIT, pv->MaxPrec);

    pv->obj = TypedData_Wrap_Struct(
        rb_obj_class(x->obj), &BigDecimal_data_type, pv);

    return pv;
}

/* Returns True if the value is Not a Number */
static VALUE
BigDecimal_IsNaN(VALUE self)
{
    Real *p = GetVpValue(self,1);
    if(VpIsNaN(p))  return Qtrue;
    return Qfalse;
}

/* Returns nil, -1, or +1 depending on whether the value is finite,
 * -infinity, or +infinity.
 */
static VALUE
BigDecimal_IsInfinite(VALUE self)
{
    Real *p = GetVpValue(self,1);
    if(VpIsPosInf(p)) return INT2FIX(1);
    if(VpIsNegInf(p)) return INT2FIX(-1);
    return Qnil;
}

/* Returns True if the value is finite (not NaN or infinite) */
static VALUE
BigDecimal_IsFinite(VALUE self)
{
    Real *p = GetVpValue(self,1);
    if(VpIsNaN(p)) return Qfalse;
    if(VpIsInf(p)) return Qfalse;
    return Qtrue;
}

static void
BigDecimal_check_num(Real *p)
{
    if(VpIsNaN(p)) {
       VpException(VP_EXCEPTION_NaN,"Computation results to 'NaN'(Not a Number)",1);
    } else if(VpIsPosInf(p)) {
       VpException(VP_EXCEPTION_INFINITY,"Computation results to 'Infinity'",1);
    } else if(VpIsNegInf(p)) {
       VpException(VP_EXCEPTION_INFINITY,"Computation results to '-Infinity'",1);
    }
}

static VALUE BigDecimal_split(VALUE self);

/* Returns the value as an integer (Fixnum or Bignum).
 *
 * If the BigNumber is infinity or NaN, raises FloatDomainError.
 */
static VALUE
BigDecimal_to_i(VALUE self)
{
    ENTER(5);
    ssize_t e, nf;
    Real *p;

    GUARD_OBJ(p,GetVpValue(self,1));
    BigDecimal_check_num(p);

    e = VpExponent10(p);
    if(e<=0) return INT2FIX(0);
    nf = VpBaseFig();
    if(e<=nf) {
        return LONG2NUM((long)(VpGetSign(p)*(BDIGIT_DBL_SIGNED)p->frac[0]));
    }
    else {
        VALUE a = BigDecimal_split(self);
        VALUE digits = RARRAY_PTR(a)[1];
        VALUE numerator = rb_funcall(digits, rb_intern("to_i"), 0);
        VALUE ret;
        ssize_t dpower = e - (ssize_t)RSTRING_LEN(digits);

        if (VpGetSign(p) < 0) {
            numerator = rb_funcall(numerator, '*', 1, INT2FIX(-1));
        }
        if (dpower < 0) {
            ret = rb_funcall(numerator, rb_intern("div"), 1,
                              rb_funcall(INT2FIX(10), rb_intern("**"), 1,
                                         INT2FIX(-dpower)));
        }
        else
            ret = rb_funcall(numerator, '*', 1,
                             rb_funcall(INT2FIX(10), rb_intern("**"), 1,
                                        INT2FIX(dpower)));
        if (TYPE(ret) == T_FLOAT)
            rb_raise(rb_eFloatDomainError, "Infinity");
        return ret;
    }
}

/* Returns a new Float object having approximately the same value as the
 * BigDecimal number. Normal accuracy limits and built-in errors of binary
 * Float arithmetic apply.
 */
static VALUE
BigDecimal_to_f(VALUE self)
{
    ENTER(1);
    Real *p;
    double d;
    SIGNED_VALUE e;
    char *buf;
    volatile VALUE str;

    GUARD_OBJ(p, GetVpValue(self, 1));
    if (VpVtoD(&d, &e, p) != 1)
        return rb_float_new(d);
    if (e > (SIGNED_VALUE)(DBL_MAX_10_EXP+BASE_FIG))
        goto overflow;
    if (e < (SIGNED_VALUE)(DBL_MIN_10_EXP-BASE_FIG))
        goto underflow;

    str = rb_str_new(0, VpNumOfChars(p,"E"));
    buf = RSTRING_PTR(str);
    VpToString(p, buf, 0, 0);
    errno = 0;
    d = strtod(buf, 0);
    if (errno == ERANGE)
        goto overflow;
    return rb_float_new(d);

overflow:
    VpException(VP_EXCEPTION_OVERFLOW, "BigDecimal to Float conversion", 0);
    if (d > 0.0)
        return rb_float_new(VpGetDoublePosInf());
    else
        return rb_float_new(VpGetDoubleNegInf());

underflow:
    VpException(VP_EXCEPTION_UNDERFLOW, "BigDecimal to Float conversion", 0);
    if (d > 0.0)
        return rb_float_new(0.0);
    else
        return rb_float_new(-0.0);
}


/* Converts a BigDecimal to a Rational.
 */
static VALUE
BigDecimal_to_r(VALUE self)
{
    Real *p;
    ssize_t sign, power, denomi_power;
    VALUE a, digits, numerator;

    p = GetVpValue(self,1);
    BigDecimal_check_num(p);

    sign = VpGetSign(p);
    power = VpExponent10(p);
    a = BigDecimal_split(self);
    digits = RARRAY_PTR(a)[1];
    denomi_power = power - RSTRING_LEN(digits);
    numerator = rb_funcall(digits, rb_intern("to_i"), 0);

    if (sign < 0) {
        numerator = rb_funcall(numerator, '*', 1, INT2FIX(-1));
    }
    if (denomi_power < 0) {
        return rb_Rational(numerator,
                           rb_funcall(INT2FIX(10), rb_intern("**"), 1,
                                      INT2FIX(-denomi_power)));
    }
    else {
        return rb_Rational1(rb_funcall(numerator, '*', 1,
                                       rb_funcall(INT2FIX(10), rb_intern("**"), 1,
                                                  INT2FIX(denomi_power))));
    }
}

/* The coerce method provides support for Ruby type coercion. It is not
 * enabled by default.
 *
 * This means that binary operations like + * / or - can often be performed
 * on a BigDecimal and an object of another type, if the other object can
 * be coerced into a BigDecimal value.
 *
 * e.g.
 * a = BigDecimal.new("1.0")
 * b = a / 2.0  -> 0.5
 *
 * Note that coercing a String to a BigDecimal is not supported by default;
 * it requires a special compile-time option when building Ruby.
 */
static VALUE
BigDecimal_coerce(VALUE self, VALUE other)
{
    ENTER(2);
    VALUE obj;
    Real *b;

    if (TYPE(other) == T_FLOAT) {
        obj = rb_assoc_new(other, BigDecimal_to_f(self));
    }
    else {
        if (TYPE(other) == T_RATIONAL) {
            Real* pv = DATA_PTR(self);
            GUARD_OBJ(b, GetVpValueWithPrec(other, pv->Prec*VpBaseFig(), 1));
        }
        else {
            GUARD_OBJ(b, GetVpValue(other, 1));
        }
        obj = rb_assoc_new(b->obj, self);
    }

    return obj;
}

static VALUE
BigDecimal_uplus(VALUE self)
{
    return self;
}

 /* call-seq:
  * add(value, digits)
  *
  * Add the specified value.
  *
  * e.g.
  *   c = a.add(b,n)
  *   c = a + b
  *
  * digits:: If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.
  */
static VALUE
BigDecimal_add(VALUE self, VALUE r)
{
    ENTER(5);
    Real *c, *a, *b;
    size_t mx;
    GUARD_OBJ(a,GetVpValue(self,1));
    b = GetVpValue(r,0);
    if(!b) return DoSomeOne(self,r,'+');
    SAVE(b);
    if(VpIsNaN(b)) return b->obj;
    if(VpIsNaN(a)) return a->obj;
    mx = GetAddSubPrec(a,b);
    if (mx == (size_t)-1L) {
        GUARD_OBJ(c,VpCreateRbObject(VpBaseFig() + 1, "0"));
        VpAddSub(c, a, b, 1);
    } else {
        GUARD_OBJ(c,VpCreateRbObject(mx *(VpBaseFig() + 1), "0"));
        if(!mx) {
            VpSetInf(c,VpGetSign(a));
        } else {
            VpAddSub(c, a, b, 1);
        }
    }
    return ToValue(c);
}

 /* call-seq:
  * sub(value, digits)
  *
  * Subtract the specified value.
  *
  * e.g.
  *   c = a.sub(b,n)
  *   c = a - b
  *
  * digits:: If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.
  */
static VALUE
BigDecimal_sub(VALUE self, VALUE r)
{
    ENTER(5);
    Real *c, *a, *b;
    size_t mx;

    GUARD_OBJ(a,GetVpValue(self,1));
    b = GetVpValue(r,0);
    if(!b) return DoSomeOne(self,r,'-');
    SAVE(b);

    if(VpIsNaN(b)) return b->obj;
    if(VpIsNaN(a)) return a->obj;

    mx = GetAddSubPrec(a,b);
    if (mx == (size_t)-1L) {
        GUARD_OBJ(c,VpCreateRbObject(VpBaseFig() + 1, "0"));
        VpAddSub(c, a, b, -1);
    } else {
        GUARD_OBJ(c,VpCreateRbObject(mx *(VpBaseFig() + 1), "0"));
        if(!mx) {
            VpSetInf(c,VpGetSign(a));
        } else {
            VpAddSub(c, a, b, -1);
        }
    }
    return ToValue(c);
}

static VALUE
BigDecimalCmp(VALUE self, VALUE r,char op)
{
    ENTER(5);
    SIGNED_VALUE e;
    Real *a, *b=0;
    GUARD_OBJ(a,GetVpValue(self,1));
    switch (TYPE(r)) {
    case T_DATA:
        if (!is_kind_of_BigDecimal(r)) break;
        /* fall through */
    case T_FIXNUM:
        /* fall through */
    case T_BIGNUM:
        GUARD_OBJ(b, GetVpValue(r,0));
        break;

    case T_FLOAT:
        GUARD_OBJ(b, GetVpValueWithPrec(r, DBL_DIG+1, 0));
        break;

    case T_RATIONAL:
        GUARD_OBJ(b, GetVpValueWithPrec(r, a->Prec*VpBaseFig(), 0));
        break;

    default:
        break;
    }
    if (b == NULL) {
        ID f = 0;

        switch (op) {
        case '*':
            return rb_num_coerce_cmp(self, r, rb_intern("<=>"));

        case '=':
            return RTEST(rb_num_coerce_cmp(self, r, rb_intern("=="))) ? Qtrue : Qfalse;

        case 'G':
            f = rb_intern(">=");
            break;

        case 'L':
            f = rb_intern("<=");
            break;

        case '>':
            /* fall through */
        case '<':
            f = (ID)op;
            break;

        default:
            break;
        }
        return rb_num_coerce_relop(self, r, f);
    }
    SAVE(b);
    e = VpComp(a, b);
    if (e == 999)
        return (op == '*') ? Qnil : Qfalse;
    switch (op) {
    case '*':
        return   INT2FIX(e); /* any op */

    case '=':
        if(e==0) return Qtrue;
        return Qfalse;

    case 'G':
        if(e>=0) return Qtrue;
        return Qfalse;

    case '>':
        if(e> 0) return Qtrue;
        return Qfalse;

    case 'L':
        if(e<=0) return Qtrue;
        return Qfalse;

    case '<':
        if(e< 0) return Qtrue;
        return Qfalse;

    default:
        break;
    }

    rb_bug("Undefined operation in BigDecimalCmp()");
}

/* Returns True if the value is zero. */
static VALUE
BigDecimal_zero(VALUE self)
{
    Real *a = GetVpValue(self,1);
    return VpIsZero(a) ? Qtrue : Qfalse;
}

/* Returns self if the value is non-zero, nil otherwise. */
static VALUE
BigDecimal_nonzero(VALUE self)
{
    Real *a = GetVpValue(self,1);
    return VpIsZero(a) ? Qnil : self;
}

/* The comparison operator.
 * a <=> b is 0 if a == b, 1 if a > b, -1 if a < b.
 */
static VALUE
BigDecimal_comp(VALUE self, VALUE r)
{
    return BigDecimalCmp(self, r, '*');
}

/*
 * Tests for value equality; returns true if the values are equal.
 *
 * The == and === operators and the eql? method have the same implementation
 * for BigDecimal.
 *
 * Values may be coerced to perform the comparison:
 *
 * BigDecimal.new('1.0') == 1.0  -> true
 */
static VALUE
BigDecimal_eq(VALUE self, VALUE r)
{
    return BigDecimalCmp(self, r, '=');
}

/* call-seq:
 * a < b
 *
 * Returns true if a is less than b. Values may be coerced to perform the
 * comparison (see ==, coerce).
 */
static VALUE
BigDecimal_lt(VALUE self, VALUE r)
{
    return BigDecimalCmp(self, r, '<');
}

/* call-seq:
 * a <= b
 *
 * Returns true if a is less than or equal to b. Values may be coerced to
 * perform the comparison (see ==, coerce).
 */
static VALUE
BigDecimal_le(VALUE self, VALUE r)
{
    return BigDecimalCmp(self, r, 'L');
}

/* call-seq:
 * a > b
 *
 * Returns true if a is greater than b.  Values may be coerced to
 * perform the comparison (see ==, coerce).
 */
static VALUE
BigDecimal_gt(VALUE self, VALUE r)
{
    return BigDecimalCmp(self, r, '>');
}

/* call-seq:
 * a >= b
 *
 * Returns true if a is greater than or equal to b. Values may be coerced to
 * perform the comparison (see ==, coerce)
 */
static VALUE
BigDecimal_ge(VALUE self, VALUE r)
{
    return BigDecimalCmp(self, r, 'G');
}

static VALUE
BigDecimal_neg(VALUE self)
{
    ENTER(5);
    Real *c, *a;
    GUARD_OBJ(a,GetVpValue(self,1));
    GUARD_OBJ(c,VpCreateRbObject(a->Prec *(VpBaseFig() + 1), "0"));
    VpAsgn(c, a, -1);
    return ToValue(c);
}

 /* call-seq:
  * mult(value, digits)
  *
  * Multiply by the specified value.
  *
  * e.g.
  *   c = a.mult(b,n)
  *   c = a * b
  *
  * digits:: If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.
  */
static VALUE
BigDecimal_mult(VALUE self, VALUE r)
{
    ENTER(5);
    Real *c, *a, *b;
    size_t mx;

    GUARD_OBJ(a,GetVpValue(self,1));
    b = GetVpValue(r,0);
    if(!b) return DoSomeOne(self,r,'*');
    SAVE(b);

    mx = a->Prec + b->Prec;
    GUARD_OBJ(c,VpCreateRbObject(mx *(VpBaseFig() + 1), "0"));
    VpMult(c, a, b);
    return ToValue(c);
}

static VALUE
BigDecimal_divide(Real **c, Real **res, Real **div, VALUE self, VALUE r)
/* For c = self.div(r): with round operation */
{
    ENTER(5);
    Real *a, *b;
    size_t mx;

    GUARD_OBJ(a,GetVpValue(self,1));
    b = GetVpValue(r,0);
    if(!b) return DoSomeOne(self,r,'/');
    SAVE(b);
    *div = b;
    mx = a->Prec + vabs(a->exponent);
    if(mx<b->Prec + vabs(b->exponent)) mx = b->Prec + vabs(b->exponent);
    mx =(mx + 1) * VpBaseFig();
    GUARD_OBJ((*c),VpCreateRbObject(mx, "#0"));
    GUARD_OBJ((*res),VpCreateRbObject((mx+1) * 2 +(VpBaseFig() + 1), "#0"));
    VpDivd(*c, *res, a, b);
    return (VALUE)0;
}

 /* call-seq:
  * div(value, digits)
  * quo(value)
  *
  * Divide by the specified value.
  *
  * e.g.
  *   c = a.div(b,n)
  *
  * digits:: If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.
  *
  * If digits is 0, the result is the same as the / operator. If not, the
  * result is an integer BigDecimal, by analogy with Float#div.
  *
  * The alias quo is provided since div(value, 0) is the same as computing
  * the quotient; see divmod.
  */
static VALUE
BigDecimal_div(VALUE self, VALUE r)
/* For c = self/r: with round operation */
{
    ENTER(5);
    Real *c=NULL, *res=NULL, *div = NULL;
    r = BigDecimal_divide(&c, &res, &div, self, r);
    if(r!=(VALUE)0) return r; /* coerced by other */
    SAVE(c);SAVE(res);SAVE(div);
    /* a/b = c + r/b */
    /* c xxxxx
       r 00000yyyyy  ==> (y/b)*BASE >= HALF_BASE
     */
    /* Round */
    if(VpHasVal(div)) { /* frac[0] must be zero for NaN,INF,Zero */
        VpInternalRound(c, 0, c->frac[c->Prec-1], (BDIGIT)(VpBaseVal()*(BDIGIT_DBL)res->frac[0]/div->frac[0]));
    }
    return ToValue(c);
}

/*
 * %: mod = a%b = a - (a.to_f/b).floor * b
 * div = (a.to_f/b).floor
 */
static VALUE
BigDecimal_DoDivmod(VALUE self, VALUE r, Real **div, Real **mod)
{
    ENTER(8);
    Real *c=NULL, *d=NULL, *res=NULL;
    Real *a, *b;
    size_t mx;

    GUARD_OBJ(a,GetVpValue(self,1));
    b = GetVpValue(r,0);
    if(!b) return Qfalse;
    SAVE(b);

    if(VpIsNaN(a) || VpIsNaN(b)) goto NaN;
    if(VpIsInf(a) && VpIsInf(b)) goto NaN;
    if(VpIsZero(b)) {
        rb_raise(rb_eZeroDivError, "divided by 0");
    }
    if(VpIsInf(a)) {
       GUARD_OBJ(d,VpCreateRbObject(1, "0"));
       VpSetInf(d, (SIGNED_VALUE)(VpGetSign(a) == VpGetSign(b) ? 1 : -1));
       GUARD_OBJ(c,VpCreateRbObject(1, "NaN"));
       *div = d;
       *mod = c;
       return Qtrue;
    }
    if(VpIsInf(b)) {
       GUARD_OBJ(d,VpCreateRbObject(1, "0"));
       *div = d;
       *mod = a;
       return Qtrue;
    }
    if(VpIsZero(a)) {
       GUARD_OBJ(c,VpCreateRbObject(1, "0"));
       GUARD_OBJ(d,VpCreateRbObject(1, "0"));
       *div = d;
       *mod = c;
       return Qtrue;
    }

    mx = a->Prec + vabs(a->exponent);
    if(mx<b->Prec + vabs(b->exponent)) mx = b->Prec + vabs(b->exponent);
    mx =(mx + 1) * VpBaseFig();
    GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
    GUARD_OBJ(res,VpCreateRbObject((mx+1) * 2 +(VpBaseFig() + 1), "#0"));
    VpDivd(c, res, a, b);
    mx = c->Prec *(VpBaseFig() + 1);
    GUARD_OBJ(d,VpCreateRbObject(mx, "0"));
    VpActiveRound(d,c,VP_ROUND_DOWN,0);
    VpMult(res,d,b);
    VpAddSub(c,a,res,-1);
    if(!VpIsZero(c) && (VpGetSign(a)*VpGetSign(b)<0)) {
        VpAddSub(res,d,VpOne(),-1);
        GUARD_OBJ(d,VpCreateRbObject(GetAddSubPrec(c, b)*(VpBaseFig() + 1), "0"));
        VpAddSub(d  ,c,b,       1);
        *div = res;
        *mod = d;
    } else {
        *div = d;
        *mod = c;
    }
    return Qtrue;

NaN:
    GUARD_OBJ(c,VpCreateRbObject(1, "NaN"));
    GUARD_OBJ(d,VpCreateRbObject(1, "NaN"));
    *div = d;
    *mod = c;
    return Qtrue;
}

/* call-seq:
 * a % b
 * a.modulo(b)
 *
 * Returns the modulus from dividing by b. See divmod.
 */
static VALUE
BigDecimal_mod(VALUE self, VALUE r) /* %: a%b = a - (a.to_f/b).floor * b */
{
    ENTER(3);
    Real *div=NULL, *mod=NULL;

    if(BigDecimal_DoDivmod(self,r,&div,&mod)) {
        SAVE(div); SAVE(mod);
        return ToValue(mod);
    }
    return DoSomeOne(self,r,'%');
}

static VALUE
BigDecimal_divremain(VALUE self, VALUE r, Real **dv, Real **rv)
{
    ENTER(10);
    size_t mx;
    Real *a=NULL, *b=NULL, *c=NULL, *res=NULL, *d=NULL, *rr=NULL, *ff=NULL;
    Real *f=NULL;

    GUARD_OBJ(a,GetVpValue(self,1));
    b = GetVpValue(r,0);
    if(!b) return DoSomeOne(self,r,rb_intern("remainder"));
    SAVE(b);

    mx  =(a->MaxPrec + b->MaxPrec) *VpBaseFig();
    GUARD_OBJ(c  ,VpCreateRbObject(mx, "0"));
    GUARD_OBJ(res,VpCreateRbObject((mx+1) * 2 +(VpBaseFig() + 1), "#0"));
    GUARD_OBJ(rr ,VpCreateRbObject((mx+1) * 2 +(VpBaseFig() + 1), "#0"));
    GUARD_OBJ(ff ,VpCreateRbObject((mx+1) * 2 +(VpBaseFig() + 1), "#0"));

    VpDivd(c, res, a, b);

    mx = c->Prec *(VpBaseFig() + 1);

    GUARD_OBJ(d,VpCreateRbObject(mx, "0"));
    GUARD_OBJ(f,VpCreateRbObject(mx, "0"));

    VpActiveRound(d,c,VP_ROUND_DOWN,0); /* 0: round off */

    VpFrac(f, c);
    VpMult(rr,f,b);
    VpAddSub(ff,res,rr,1);

    *dv = d;
    *rv = ff;
    return (VALUE)0;
}

/* Returns the remainder from dividing by the value.
 *
 * x.remainder(y) means x-y*(x/y).truncate
 */
static VALUE
BigDecimal_remainder(VALUE self, VALUE r) /* remainder */
{
    VALUE  f;
    Real  *d,*rv=0;
    f = BigDecimal_divremain(self,r,&d,&rv);
    if(f!=(VALUE)0) return f;
    return ToValue(rv);
}

/* Divides by the specified value, and returns the quotient and modulus
 * as BigDecimal numbers. The quotient is rounded towards negative infinity.
 *
 * For example:
 *
 * require 'bigdecimal'
 *
 * a = BigDecimal.new("42")
 * b = BigDecimal.new("9")
 *
 * q,m = a.divmod(b)
 *
 * c = q * b + m
 *
 * a == c  -> true
 *
 * The quotient q is (a/b).floor, and the modulus is the amount that must be
 * added to q * b to get a.
 */
static VALUE
BigDecimal_divmod(VALUE self, VALUE r)
{
    ENTER(5);
    Real *div=NULL, *mod=NULL;

    if(BigDecimal_DoDivmod(self,r,&div,&mod)) {
        SAVE(div); SAVE(mod);
        return rb_assoc_new(ToValue(div), ToValue(mod));
    }
    return DoSomeOne(self,r,rb_intern("divmod"));
}

static VALUE
BigDecimal_div2(int argc, VALUE *argv, VALUE self)
{
    ENTER(5);
    VALUE b,n;
    int na = rb_scan_args(argc,argv,"11",&b,&n);
    if(na==1) { /* div in Float sense */
       Real *div=NULL;
       Real *mod;
       if(BigDecimal_DoDivmod(self,b,&div,&mod)) {
          return BigDecimal_to_i(ToValue(div));
       }
       return DoSomeOne(self,b,rb_intern("div"));
    } else {    /* div in BigDecimal sense */
       SIGNED_VALUE ix = GetPositiveInt(n);
       if (ix == 0) return BigDecimal_div(self, b);
       else {
          Real *res=NULL;
          Real *av=NULL, *bv=NULL, *cv=NULL;
          size_t mx = (ix+VpBaseFig()*2);
          size_t pl = VpSetPrecLimit(0);

          GUARD_OBJ(cv,VpCreateRbObject(mx,"0"));
          GUARD_OBJ(av,GetVpValue(self,1));
          GUARD_OBJ(bv,GetVpValue(b,1));
          mx = av->Prec + bv->Prec + 2;
          if(mx <= cv->MaxPrec) mx = cv->MaxPrec+1;
          GUARD_OBJ(res,VpCreateRbObject((mx * 2  + 2)*VpBaseFig(), "#0"));
          VpDivd(cv,res,av,bv);
          VpSetPrecLimit(pl);
          VpLeftRound(cv,VpGetRoundMode(),ix);
          return ToValue(cv);
       }
    }
}

static VALUE
BigDecimal_add2(VALUE self, VALUE b, VALUE n)
{
    ENTER(2);
    Real   *cv;
    SIGNED_VALUE mx = GetPositiveInt(n);
    if (mx == 0) return BigDecimal_add(self, b);
    else {
       size_t pl = VpSetPrecLimit(0);
       VALUE   c = BigDecimal_add(self,b);
       VpSetPrecLimit(pl);
       GUARD_OBJ(cv,GetVpValue(c,1));
       VpLeftRound(cv,VpGetRoundMode(),mx);
       return ToValue(cv);
    }
}

static VALUE
BigDecimal_sub2(VALUE self, VALUE b, VALUE n)
{
    ENTER(2);
    Real *cv;
    SIGNED_VALUE mx = GetPositiveInt(n);
    if (mx == 0) return BigDecimal_sub(self, b);
    else {
       size_t pl = VpSetPrecLimit(0);
       VALUE   c = BigDecimal_sub(self,b);
       VpSetPrecLimit(pl);
       GUARD_OBJ(cv,GetVpValue(c,1));
       VpLeftRound(cv,VpGetRoundMode(),mx);
       return ToValue(cv);
    }
}

static VALUE
BigDecimal_mult2(VALUE self, VALUE b, VALUE n)
{
    ENTER(2);
    Real *cv;
    SIGNED_VALUE mx = GetPositiveInt(n);
    if (mx == 0) return BigDecimal_mult(self, b);
    else {
       size_t pl = VpSetPrecLimit(0);
       VALUE   c = BigDecimal_mult(self,b);
       VpSetPrecLimit(pl);
       GUARD_OBJ(cv,GetVpValue(c,1));
       VpLeftRound(cv,VpGetRoundMode(),mx);
       return ToValue(cv);
    }
}

/* Returns the absolute value.
 *
 * BigDecimal('5').abs -> 5
 *
 * BigDecimal('-3').abs -> 3
 */
static VALUE
BigDecimal_abs(VALUE self)
{
    ENTER(5);
    Real *c, *a;
    size_t mx;

    GUARD_OBJ(a,GetVpValue(self,1));
    mx = a->Prec *(VpBaseFig() + 1);
    GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
    VpAsgn(c, a, 1);
    VpChangeSign(c, 1);
    return ToValue(c);
}

/* call-seq:
 * sqrt(n)
 *
 * Returns the square root of the value.
 *
 * If n is specified, returns at least that many significant digits.
 */
static VALUE
BigDecimal_sqrt(VALUE self, VALUE nFig)
{
    ENTER(5);
    Real *c, *a;
    size_t mx, n;

    GUARD_OBJ(a,GetVpValue(self,1));
    mx = a->Prec *(VpBaseFig() + 1);

    n = GetPositiveInt(nFig) + VpDblFig() + 1;
    if(mx <= n) mx = n;
    GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
    VpSqrt(c, a);
    return ToValue(c);
}

/* Return the integer part of the number.
 */
static VALUE
BigDecimal_fix(VALUE self)
{
    ENTER(5);
    Real *c, *a;
    size_t mx;

    GUARD_OBJ(a,GetVpValue(self,1));
    mx = a->Prec *(VpBaseFig() + 1);
    GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
    VpActiveRound(c,a,VP_ROUND_DOWN,0); /* 0: round off */
    return ToValue(c);
}

/* call-seq:
 * round(n, mode)
 *
 * Round to the nearest 1 (by default), returning the result as a BigDecimal.
 *
 * BigDecimal('3.14159').round -> 3
 *
 * BigDecimal('8.7').round -> 9
 *
 * If n is specified and positive, the fractional part of the result has no
 * more than that many digits.
 *
 * If n is specified and negative, at least that many digits to the left of the
 * decimal point will be 0 in the result.
 *
 * BigDecimal('3.14159').round(3) -> 3.142
 *
 * BigDecimal('13345.234').round(-2) -> 13300.0
 *
 * The value of the optional mode argument can be used to determine how
 * rounding is performed; see BigDecimal.mode.
 */
static VALUE
BigDecimal_round(int argc, VALUE *argv, VALUE self)
{
    ENTER(5);
    Real   *c, *a;
    int    iLoc = 0;
    VALUE  vLoc;
    VALUE  vRound;
    size_t mx, pl;

    unsigned short sw = VpGetRoundMode();

    switch (rb_scan_args(argc, argv, "02", &vLoc, &vRound)) {
    case 0:
        iLoc = 0;
        break;
    case 1:
        Check_Type(vLoc, T_FIXNUM);
        iLoc = FIX2INT(vLoc);
        break;
    case 2:
        Check_Type(vLoc, T_FIXNUM);
        iLoc = FIX2INT(vLoc);
        sw = check_rounding_mode(vRound);
        break;
    }

    pl = VpSetPrecLimit(0);
    GUARD_OBJ(a,GetVpValue(self,1));
    mx = a->Prec *(VpBaseFig() + 1);
    GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
    VpSetPrecLimit(pl);
    VpActiveRound(c,a,sw,iLoc);
    if (argc == 0) {
        return BigDecimal_to_i(ToValue(c));
    }
    return ToValue(c);
}

/* call-seq:
 * truncate(n)
 *
 * Truncate to the nearest 1, returning the result as a BigDecimal.
 *
 * BigDecimal('3.14159').truncate -> 3
 *
 * BigDecimal('8.7').truncate -> 8
 *
 * If n is specified and positive, the fractional part of the result has no
 * more than that many digits.
 *
 * If n is specified and negative, at least that many digits to the left of the
 * decimal point will be 0 in the result.
 *
 * BigDecimal('3.14159').truncate(3) -> 3.141
 *
 * BigDecimal('13345.234').truncate(-2) -> 13300.0
 */
static VALUE
BigDecimal_truncate(int argc, VALUE *argv, VALUE self)
{
    ENTER(5);
    Real *c, *a;
    int iLoc;
    VALUE vLoc;
    size_t mx, pl = VpSetPrecLimit(0);

    if(rb_scan_args(argc,argv,"01",&vLoc)==0) {
        iLoc = 0;
    } else {
        Check_Type(vLoc, T_FIXNUM);
        iLoc = FIX2INT(vLoc);
    }

    GUARD_OBJ(a,GetVpValue(self,1));
    mx = a->Prec *(VpBaseFig() + 1);
    GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
    VpSetPrecLimit(pl);
    VpActiveRound(c,a,VP_ROUND_DOWN,iLoc); /* 0: truncate */
    if (argc == 0) {
        return BigDecimal_to_i(ToValue(c));
    }
    return ToValue(c);
}

/* Return the fractional part of the number.
 */
static VALUE
BigDecimal_frac(VALUE self)
{
    ENTER(5);
    Real *c, *a;
    size_t mx;

    GUARD_OBJ(a,GetVpValue(self,1));
    mx = a->Prec *(VpBaseFig() + 1);
    GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
    VpFrac(c, a);
    return ToValue(c);
}

/* call-seq:
 * floor(n)
 *
 * Return the largest integer less than or equal to the value, as a BigDecimal.
 *
 * BigDecimal('3.14159').floor -> 3
 *
 * BigDecimal('-9.1').floor -> -10
 *
 * If n is specified and positive, the fractional part of the result has no
 * more than that many digits.
 *
 * If n is specified and negative, at least that
 * many digits to the left of the decimal point will be 0 in the result.
 *
 * BigDecimal('3.14159').floor(3) -> 3.141
 *
 * BigDecimal('13345.234').floor(-2) -> 13300.0
 */
static VALUE
BigDecimal_floor(int argc, VALUE *argv, VALUE self)
{
    ENTER(5);
    Real *c, *a;
    int iLoc;
    VALUE vLoc;
    size_t mx, pl = VpSetPrecLimit(0);

    if(rb_scan_args(argc,argv,"01",&vLoc)==0) {
        iLoc = 0;
    } else {
        Check_Type(vLoc, T_FIXNUM);
        iLoc = FIX2INT(vLoc);
    }

    GUARD_OBJ(a,GetVpValue(self,1));
    mx = a->Prec *(VpBaseFig() + 1);
    GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
    VpSetPrecLimit(pl);
    VpActiveRound(c,a,VP_ROUND_FLOOR,iLoc);
#ifdef BIGDECIMAL_DEBUG
    VPrint(stderr, "floor: c=%\n", c);
#endif
    if (argc == 0) {
        return BigDecimal_to_i(ToValue(c));
    }
    return ToValue(c);
}

/* call-seq:
 * ceil(n)
 *
 * Return the smallest integer greater than or equal to the value, as a BigDecimal.
 *
 * BigDecimal('3.14159').ceil -> 4
 *
 * BigDecimal('-9.1').ceil -> -9
 *
 * If n is specified and positive, the fractional part of the result has no
 * more than that many digits.
 *
 * If n is specified and negative, at least that
 * many digits to the left of the decimal point will be 0 in the result.
 *
 * BigDecimal('3.14159').ceil(3) -> 3.142
 *
 * BigDecimal('13345.234').ceil(-2) -> 13400.0
 */
static VALUE
BigDecimal_ceil(int argc, VALUE *argv, VALUE self)
{
    ENTER(5);
    Real *c, *a;
    int iLoc;
    VALUE vLoc;
    size_t mx, pl = VpSetPrecLimit(0);

    if(rb_scan_args(argc,argv,"01",&vLoc)==0) {
        iLoc = 0;
    } else {
        Check_Type(vLoc, T_FIXNUM);
        iLoc = FIX2INT(vLoc);
    }

    GUARD_OBJ(a,GetVpValue(self,1));
    mx = a->Prec *(VpBaseFig() + 1);
    GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
    VpSetPrecLimit(pl);
    VpActiveRound(c,a,VP_ROUND_CEIL,iLoc);
    if (argc == 0) {
        return BigDecimal_to_i(ToValue(c));
    }
    return ToValue(c);
}

/* call-seq:
 * to_s(s)
 *
 * Converts the value to a string.
 *
 * The default format looks like  0.xxxxEnn.
 *
 * The optional parameter s consists of either an integer; or an optional '+'
 * or ' ', followed by an optional number, followed by an optional 'E' or 'F'.
 *
 * If there is a '+' at the start of s, positive values are returned with
 * a leading '+'.
 *
 * A space at the start of s returns positive values with a leading space.
 *
 * If s contains a number, a space is inserted after each group of that many
 * fractional digits.
 *
 * If s ends with an 'E', engineering notation (0.xxxxEnn) is used.
 *
 * If s ends with an 'F', conventional floating point notation is used.
 *
 * Examples:
 *
 * BigDecimal.new('-123.45678901234567890').to_s('5F') -> '-123.45678 90123 45678 9'
 *
 * BigDecimal.new('123.45678901234567890').to_s('+8F') -> '+123.45678901 23456789'
 *
 * BigDecimal.new('123.45678901234567890').to_s(' F') -> ' 123.4567890123456789'
 */
static VALUE
BigDecimal_to_s(int argc, VALUE *argv, VALUE self)
{
    ENTER(5);
    int   fmt=0;   /* 0:E format */
    int   fPlus=0; /* =0:default,=1: set ' ' before digits ,set '+' before digits. */
    Real  *vp;
    volatile VALUE str;
    char  *psz;
    char   ch;
    size_t nc, mc = 0;
    VALUE  f;

    GUARD_OBJ(vp,GetVpValue(self,1));

    if(rb_scan_args(argc,argv,"01",&f)==1) {
        if(TYPE(f)==T_STRING) {
            SafeStringValue(f);
            psz = RSTRING_PTR(f);
            if(*psz==' ') {
                fPlus = 1; psz++;
            } else if(*psz=='+') {
                fPlus = 2; psz++;
            }
            while((ch=*psz++)!=0) {
                if(ISSPACE(ch)) continue;
                if(!ISDIGIT(ch)) {
                    if(ch=='F' || ch=='f') fmt = 1; /* F format */
                    break;
                }
                mc = mc * 10 + ch - '0';
            }
        }
        else {
            mc = (size_t)GetPositiveInt(f);
        }
    }
    if(fmt) {
        nc = VpNumOfChars(vp,"F");
    } else {
        nc = VpNumOfChars(vp,"E");
    }
    if(mc>0) nc += (nc + mc - 1) / mc + 1;

    str = rb_str_new(0, nc);
    psz = RSTRING_PTR(str);

    if(fmt) {
        VpToFString(vp, psz, mc, fPlus);
    } else {
        VpToString (vp, psz, mc, fPlus);
    }
    rb_str_resize(str, strlen(psz));
    return str;
}

/* Splits a BigDecimal number into four parts, returned as an array of values.
 *
 * The first value represents the sign of the BigDecimal, and is -1 or 1, or 0
 * if the BigDecimal is Not a Number.
 *
 * The second value is a string representing the significant digits of the
 * BigDecimal, with no leading zeros.
 *
 * The third value is the base used for arithmetic (currently always 10) as an
 * Integer.
 *
 * The fourth value is an Integer exponent.
 *
 * If the BigDecimal can be represented as 0.xxxxxx*10**n, then xxxxxx is the
 * string of significant digits with no leading zeros, and n is the exponent.
 *
 * From these values, you can translate a BigDecimal to a float as follows:
 *
 *   sign, significant_digits, base, exponent = a.split
 *   f = sign * "0.#{significant_digits}".to_f * (base ** exponent)
 *
 * (Note that the to_f method is provided as a more convenient way to translate
 * a BigDecimal to a Float.)
 */
static VALUE
BigDecimal_split(VALUE self)
{
    ENTER(5);
    Real *vp;
    VALUE obj,str;
    ssize_t e, s;
    char *psz1;

    GUARD_OBJ(vp,GetVpValue(self,1));
    str = rb_str_new(0, VpNumOfChars(vp,"E"));
    psz1 = RSTRING_PTR(str);
    VpSzMantissa(vp,psz1);
    s = 1;
    if(psz1[0]=='-') {
        size_t len = strlen(psz1+1);

        memmove(psz1, psz1+1, len);
        psz1[len] = '\0';
        s = -1;
    }
    if(psz1[0]=='N') s=0; /* NaN */
    e = VpExponent10(vp);
    obj  = rb_ary_new2(4);
    rb_ary_push(obj, INT2FIX(s));
    rb_ary_push(obj, str);
    rb_str_resize(str, strlen(psz1));
    rb_ary_push(obj, INT2FIX(10));
    rb_ary_push(obj, INT2NUM(e));
    return obj;
}

/* Returns the exponent of the BigDecimal number, as an Integer.
 *
 * If the number can be represented as 0.xxxxxx*10**n where xxxxxx is a string
 * of digits with no leading zeros, then n is the exponent.
 */
static VALUE
BigDecimal_exponent(VALUE self)
{
    ssize_t e = VpExponent10(GetVpValue(self, 1));
    return INT2NUM(e);
}

/* Returns debugging information about the value as a string of comma-separated
 * values in angle brackets with a leading #:
 *
 * BigDecimal.new("1234.5678").inspect ->
 * "#<BigDecimal:b7ea1130,'0.12345678E4',8(12)>"
 *
 * The first part is the address, the second is the value as a string, and
 * the final part ss(mm) is the current number of significant digits and the
 * maximum number of significant digits, respectively.
 */
static VALUE
BigDecimal_inspect(VALUE self)
{
    ENTER(5);
    Real *vp;
    volatile VALUE obj;
    size_t nc;
    char *psz, *tmp;

    GUARD_OBJ(vp,GetVpValue(self,1));
    nc = VpNumOfChars(vp,"E");
    nc +=(nc + 9) / 10;

    obj = rb_str_new(0, nc+256);
    psz = RSTRING_PTR(obj);
    sprintf(psz,"#<BigDecimal:%"PRIxVALUE",'",self);
    tmp = psz + strlen(psz);
    VpToString(vp, tmp, 10, 0);
    tmp += strlen(tmp);
    sprintf(tmp, "',%"PRIuSIZE"(%"PRIuSIZE")>", VpPrec(vp)*VpBaseFig(), VpMaxPrec(vp)*VpBaseFig());
    rb_str_resize(obj, strlen(psz));
    return obj;
}

static VALUE BigMath_s_exp(VALUE, VALUE, VALUE);
static VALUE BigMath_s_log(VALUE, VALUE, VALUE);

#define BigMath_exp(x, n) BigMath_s_exp(rb_mBigMath, (x), (n))
#define BigMath_log(x, n) BigMath_s_log(rb_mBigMath, (x), (n))

inline static int
is_integer(VALUE x)
{
    return (TYPE(x) == T_FIXNUM || TYPE(x) == T_BIGNUM);
}

inline static int
is_negative(VALUE x)
{
    if (FIXNUM_P(x)) {
        return FIX2LONG(x) < 0;
    }
    else if (TYPE(x) == T_BIGNUM) {
        return RBIGNUM_NEGATIVE_P(x);
    }
    else if (TYPE(x) == T_FLOAT) {
        return RFLOAT_VALUE(x) < 0.0;
    }
    return RTEST(rb_funcall(x, '<', 1, INT2FIX(0)));
}

#define is_positive(x) (!is_negative(x))

inline static int
is_zero(VALUE x)
{
    VALUE num;

    switch (TYPE(x)) {
      case T_FIXNUM:
        return FIX2LONG(x) == 0;

      case T_BIGNUM:
        return Qfalse;

      case T_RATIONAL:
        num = RRATIONAL(x)->num;
        return FIXNUM_P(num) && FIX2LONG(num) == 0;

      default:
        break;
    }

    return RTEST(rb_funcall(x, id_eq, 1, INT2FIX(0)));
}

inline static int
is_one(VALUE x)
{
    VALUE num, den;

    switch (TYPE(x)) {
      case T_FIXNUM:
        return FIX2LONG(x) == 1;

      case T_BIGNUM:
        return Qfalse;

      case T_RATIONAL:
        num = RRATIONAL(x)->num;
        den = RRATIONAL(x)->den;
        return FIXNUM_P(den) && FIX2LONG(den) == 1 &&
               FIXNUM_P(num) && FIX2LONG(num) == 1;

      default:
        break;
    }

    return RTEST(rb_funcall(x, id_eq, 1, INT2FIX(1)));
}

inline static int
is_even(VALUE x)
{
    switch (TYPE(x)) {
      case T_FIXNUM:
        return (FIX2LONG(x) % 2) == 0;

      case T_BIGNUM:
        return (RBIGNUM_DIGITS(x)[0] % 2) == 0;

      default:
        break;
    }

    return 0;
}

static VALUE
rmpd_power_by_big_decimal(Real const* x, Real const* exp, ssize_t const n)
{
    VALUE log_x, multiplied, y;

    if (VpIsZero(exp)) {
        return ToValue(VpCreateRbObject(n, "1"));
    }

    log_x = BigMath_log(x->obj, SSIZET2NUM(n+1));
    multiplied = BigDecimal_mult2(exp->obj, log_x, SSIZET2NUM(n+1));
    y = BigMath_exp(multiplied, SSIZET2NUM(n));

    return y;
}

/* call-seq:
 * power(n)
 * power(n, prec)
 *
 * Returns the value raised to the power of n. Note that n must be an Integer.
 *
 * Also available as the operator **
 */
static VALUE
BigDecimal_power(int argc, VALUE*argv, VALUE self)
{
    ENTER(5);
    VALUE vexp, prec;
    Real* exp = NULL;
    Real *x, *y;
    ssize_t mp, ma, n;
    SIGNED_VALUE int_exp;
    double d;

    rb_scan_args(argc, argv, "11", &vexp, &prec);

    GUARD_OBJ(x, GetVpValue(self, 1));
    n = NIL_P(prec) ? (ssize_t)(x->Prec*VpBaseFig()) : NUM2SSIZET(prec);

    if (VpIsNaN(x)) {
        y = VpCreateRbObject(n, "0#");
        RB_GC_GUARD(y->obj);
        VpSetNaN(y);
        return ToValue(y);
    }

retry:
    switch (TYPE(vexp)) {
      case T_FIXNUM:
        break;

      case T_BIGNUM:
        break;

      case T_FLOAT:
        d = RFLOAT_VALUE(vexp);
        if (d == round(d)) {
            vexp = LL2NUM((LONG_LONG)round(d));
            goto retry;
        }
        exp = GetVpValueWithPrec(vexp, DBL_DIG+1, 1);
        break;

      case T_RATIONAL:
        if (is_zero(RRATIONAL(vexp)->num)) {
            if (is_positive(vexp)) {
                vexp = INT2FIX(0);
                goto retry;
            }
        }
        else if (is_one(RRATIONAL(vexp)->den)) {
            vexp = RRATIONAL(vexp)->num;
            goto retry;
        }
        exp = GetVpValueWithPrec(vexp, n, 1);
        break;

      case T_DATA:
        if (is_kind_of_BigDecimal(vexp)) {
            VALUE zero = INT2FIX(0);
            VALUE rounded = BigDecimal_round(1, &zero, vexp);
            if (RTEST(BigDecimal_eq(vexp, rounded))) {
                vexp = BigDecimal_to_i(vexp);
                goto retry;
            }
            exp = DATA_PTR(vexp);
            break;
        }
        /* fall through */
      default:
        rb_raise(rb_eTypeError,
                 "wrong argument type %s (expected scalar Numeric)",
                 rb_obj_classname(vexp));
    }

    if (VpIsZero(x)) {
        if (is_negative(vexp)) {
            y = VpCreateRbObject(n, "#0");
            RB_GC_GUARD(y->obj);
            if (VpGetSign(x) < 0) {
                if (is_integer(vexp)) {
                    if (is_even(vexp)) {
                        /* (-0) ** (-even_integer)  -> Infinity */
                        VpSetPosInf(y);
                    }
                    else {
                        /* (-0) ** (-odd_integer)  -> -Infinity */
                        VpSetNegInf(y);
                    }
                }
                else {
                    /* (-0) ** (-non_integer)  -> Infinity */
                    VpSetPosInf(y);
                }
            }
            else {
                /* (+0) ** (-num)  -> Infinity */
                VpSetPosInf(y);
            }
            return ToValue(y);
        }
        else if (is_zero(vexp)) {
            return ToValue(VpCreateRbObject(n, "1"));
        }
        else {
            return ToValue(VpCreateRbObject(n, "0"));
        }
    }

    if (is_zero(vexp)) {
        return ToValue(VpCreateRbObject(n, "1"));
    }
    else if (is_one(vexp)) {
        return self;
    }

    if (VpIsInf(x)) {
        if (is_negative(vexp)) {
            if (VpGetSign(x) < 0) {
                if (is_integer(vexp)) {
                    if (is_even(vexp)) {
                        /* (-Infinity) ** (-even_integer) -> +0 */
                        return ToValue(VpCreateRbObject(n, "0"));
                    }
                    else {
                        /* (-Infinity) ** (-odd_integer) -> -0 */
                        return ToValue(VpCreateRbObject(n, "-0"));
                    }
                }
                else {
                    /* (-Infinity) ** (-non_integer) -> -0 */
                    return ToValue(VpCreateRbObject(n, "-0"));
                }
            }
            else {
                return ToValue(VpCreateRbObject(n, "0"));
            }
        }
        else {
            y = VpCreateRbObject(n, "0#");
            if (VpGetSign(x) < 0) {
                if (is_integer(vexp)) {
                    if (is_even(vexp)) {
                        VpSetPosInf(y);
                    }
                    else {
                        VpSetNegInf(y);
                    }
                }
                else {
                    /* TODO: support complex */
                    rb_raise(rb_eMathDomainError,
                             "a non-integral exponent for a negative base");
                }
            }
            else {
                VpSetPosInf(y);
            }
            return ToValue(y);
        }
    }

    if (exp != NULL) {
        return rmpd_power_by_big_decimal(x, exp, n);
    }
    else if (TYPE(vexp) == T_BIGNUM) {
        VALUE abs_value = BigDecimal_abs(self);
        if (is_one(abs_value)) {
            return ToValue(VpCreateRbObject(n, "1"));
        }
        else if (RTEST(rb_funcall(abs_value, '<', 1, INT2FIX(1)))) {
            if (is_negative(vexp)) {
                y = VpCreateRbObject(n, "0#");
                if (is_even(vexp)) {
                    VpSetInf(y, VpGetSign(x));
                }
                else {
                    VpSetInf(y, -VpGetSign(x));
                }
                return ToValue(y);
            }
            else if (VpGetSign(x) < 0 && is_even(vexp)) {
                return ToValue(VpCreateRbObject(n, "-0"));
            }
            else {
                return ToValue(VpCreateRbObject(n, "0"));
            }
        }
        else {
            if (is_positive(vexp)) {
                y = VpCreateRbObject(n, "0#");
                if (is_even(vexp)) {
                    VpSetInf(y, VpGetSign(x));
                }
                else {
                    VpSetInf(y, -VpGetSign(x));
                }
                return ToValue(y);
            }
            else if (VpGetSign(x) < 0 && is_even(vexp)) {
                return ToValue(VpCreateRbObject(n, "-0"));
            }
            else {
                return ToValue(VpCreateRbObject(n, "0"));
            }
        }
    }

    int_exp = FIX2INT(vexp);
    ma = int_exp;
    if (ma < 0)  ma = -ma;
    if (ma == 0) ma = 1;

    if (VpIsDef(x)) {
        mp = x->Prec * (VpBaseFig() + 1);
        GUARD_OBJ(y, VpCreateRbObject(mp * (ma + 1), "0"));
    }
    else {
        GUARD_OBJ(y, VpCreateRbObject(1, "0"));
    }
    VpPower(y, x, int_exp);
    return ToValue(y);
}

/* call-seq:
 *   big_decimal ** exp  -> big_decimal
 *
 * It is a synonym of big_decimal.power(exp).
 */
static VALUE
BigDecimal_power_op(VALUE self, VALUE exp)
{
    return BigDecimal_power(1, &exp, self);
}

/* call-seq:
 *   new(initial, digits)
 *
 * Create a new BigDecimal object.
 *
 * initial:: The initial value, as an Integer, a Float, a Rational,
 *           a BigDecimal, or a String.
 *           If it is a String, spaces are ignored and unrecognized characters
 *           terminate the value.
 *
 * digits:: The number of significant digits, as a Fixnum. If omitted or 0,
 *          the number of significant digits is determined from the initial
 *          value.
 *
 * The actual number of significant digits used in computation is usually
 * larger than the specified number.
 */
static VALUE
BigDecimal_new(int argc, VALUE *argv, VALUE self)
{
    ENTER(5);
    Real *pv;
    size_t mf;
    VALUE  nFig;
    VALUE  iniValue;

    if (rb_scan_args(argc, argv, "11", &iniValue, &nFig) == 1) {
        mf = 0;
    }
    else {
        mf = GetPositiveInt(nFig);
    }

    switch (TYPE(iniValue)) {
      case T_DATA:
        if (is_kind_of_BigDecimal(iniValue)) {
            pv = VpDup(DATA_PTR(iniValue));
            return ToValue(pv);
        }
        break;

      case T_FIXNUM:
        /* fall through */
      case T_BIGNUM:
        return ToValue(GetVpValue(iniValue, 1));

      case T_FLOAT:
        if (mf > DBL_DIG+1) {
            rb_raise(rb_eArgError, "precision too large.");
        }
        /* fall through */
      case T_RATIONAL:
        if (NIL_P(nFig)) {
            rb_raise(rb_eArgError, "can't omit precision for a Rational.");
        }
        return ToValue(GetVpValueWithPrec(iniValue, mf, 1));

      case T_STRING:
        /* fall through */
      default:
        break;
    }
    SafeStringValue(iniValue);
    GUARD_OBJ(pv, VpNewRbClass(mf, RSTRING_PTR(iniValue),self));

    return ToValue(pv);
}

static VALUE
BigDecimal_global_new(int argc, VALUE *argv, VALUE self)
{
    return BigDecimal_new(argc, argv, rb_cBigDecimal);
}

 /* call-seq:
  * BigDecimal.limit(digits)
  *
  * Limit the number of significant digits in newly created BigDecimal
  * numbers to the specified value. Rounding is performed as necessary,
  * as specified by BigDecimal.mode.
  *
  * A limit of 0, the default, means no upper limit.
  *
  * The limit specified by this method takes less priority over any limit
  * specified to instance methods such as ceil, floor, truncate, or round.
  */
static VALUE
BigDecimal_limit(int argc, VALUE *argv, VALUE self)
{
    VALUE  nFig;
    VALUE  nCur = INT2NUM(VpGetPrecLimit());

    if(rb_scan_args(argc,argv,"01",&nFig)==1) {
        int nf;
        if(nFig==Qnil) return nCur;
        Check_Type(nFig, T_FIXNUM);
        nf = FIX2INT(nFig);
        if(nf<0) {
            rb_raise(rb_eArgError, "argument must be positive");
        }
        VpSetPrecLimit(nf);
    }
    return nCur;
}

/* Returns the sign of the value.
 *
 * Returns a positive value if > 0, a negative value if < 0, and a
 * zero if == 0.
 *
 * The specific value returned indicates the type and sign of the BigDecimal,
 * as follows:
 *
 * BigDecimal::SIGN_NaN:: value is Not a Number
 * BigDecimal::SIGN_POSITIVE_ZERO:: value is +0
 * BigDecimal::SIGN_NEGATIVE_ZERO:: value is -0
 * BigDecimal::SIGN_POSITIVE_INFINITE:: value is +infinity
 * BigDecimal::SIGN_NEGATIVE_INFINITE:: value is -infinity
 * BigDecimal::SIGN_POSITIVE_FINITE:: value is positive
 * BigDecimal::SIGN_NEGATIVE_FINITE:: value is negative
 */
static VALUE
BigDecimal_sign(VALUE self)
{ /* sign */
    int s = GetVpValue(self,1)->sign;
    return INT2FIX(s);
}

/* call-seq:
 * BigDecimal.save_exception_mode { ... }
 */
static VALUE
BigDecimal_save_exception_mode(VALUE self)
{
    unsigned short const exception_mode = VpGetException();
    int state;
    VALUE ret = rb_protect(rb_yield, Qnil, &state);
    VpSetException(exception_mode);
    if (state) rb_jump_tag(state);
    return ret;
}

/* call-seq:
 * BigDecimal.save_rounding_mode { ... }
 */
static VALUE
BigDecimal_save_rounding_mode(VALUE self)
{
    unsigned short const round_mode = VpGetRoundMode();
    int state;
    VALUE ret = rb_protect(rb_yield, Qnil, &state);
    VpSetRoundMode(round_mode);
    if (state) rb_jump_tag(state);
    return ret;
}

/* call-seq:
 * BigDecimal.save_limit { ... }
 */
static VALUE
BigDecimal_save_limit(VALUE self)
{
    size_t const limit = VpGetPrecLimit();
    int state;
    VALUE ret = rb_protect(rb_yield, Qnil, &state);
    VpSetPrecLimit(limit);
    if (state) rb_jump_tag(state);
    return ret;
}

/* call-seq:
 * BigMath.exp(x, prec)
 *
 * Computes the value of e (the base of natural logarithms) raised to the
 * power of x, to the specified number of digits of precision.
 *
 * If x is infinite, returns Infinity.
 *
 * If x is NaN, returns NaN.
 */
static VALUE
BigMath_s_exp(VALUE klass, VALUE x, VALUE vprec)
{
    ssize_t prec, n, i;
    Real* vx = NULL;
    VALUE one, d, x1, y, z;
    int negative = 0;
    int infinite = 0;
    int nan = 0;
    double flo;

    prec = NUM2SSIZET(vprec);
    if (prec <= 0) {
        rb_raise(rb_eArgError, "Zero or negative precision for exp");
    }

    /* TODO: the following switch statement is almostly the same as one in the
     *       BigDecimalCmp function. */
    switch (TYPE(x)) {
      case T_DATA:
          if (!is_kind_of_BigDecimal(x)) break;
          vx = DATA_PTR(x);
          negative = VpGetSign(vx) < 0;
          infinite = VpIsPosInf(vx) || VpIsNegInf(vx);
          nan = VpIsNaN(vx);
          break;

      case T_FIXNUM:
          /* fall through */
      case T_BIGNUM:
          vx = GetVpValue(x, 0);
          break;

      case T_FLOAT:
        flo = RFLOAT_VALUE(x);
        negative = flo < 0;
        infinite = isinf(flo);
        nan = isnan(flo);
        if (!infinite && !nan) {
            vx = GetVpValueWithPrec(x, DBL_DIG+1, 0);
        }
        break;

      case T_RATIONAL:
        vx = GetVpValueWithPrec(x, prec, 0);
        break;

      default:
        break;
    }
    if (infinite) {
        if (negative) {
            return ToValue(GetVpValueWithPrec(INT2NUM(0), prec, 1));
        }
        else {
            Real* vy;
            vy = VpCreateRbObject(prec, "#0");
            RB_GC_GUARD(vy->obj);
            VpSetInf(vy, VP_SIGN_POSITIVE_INFINITE);
            return ToValue(vy);
        }
    }
    else if (nan) {
        Real* vy;
        vy = VpCreateRbObject(prec, "#0");
        RB_GC_GUARD(vy->obj);
        VpSetNaN(vy);
        return ToValue(vy);
    }
    else if (vx == NULL) {
        cannot_be_coerced_into_BigDecimal(rb_eArgError, x);
    }
    RB_GC_GUARD(vx->obj);

    n = prec + rmpd_double_figures();
    negative = VpGetSign(vx) < 0;
    if (negative) {
        VpSetSign(vx, 1);
    }

    RB_GC_GUARD(one) = ToValue(VpCreateRbObject(1, "1"));
    RB_GC_GUARD(x1) = one;
    RB_GC_GUARD(y)  = one;
    RB_GC_GUARD(d)  = y;
    RB_GC_GUARD(z)  = one;
    i  = 0;

    while (!VpIsZero((Real*)DATA_PTR(d))) {
        VALUE argv[2];
        SIGNED_VALUE const ey = VpExponent10(DATA_PTR(y));
        SIGNED_VALUE const ed = VpExponent10(DATA_PTR(d));
        ssize_t m = n - vabs(ey - ed);
        if (m <= 0) {
            break;
        }
        else if ((size_t)m < rmpd_double_figures()) {
            m = rmpd_double_figures();
        }

        x1 = BigDecimal_mult2(x1, x, SSIZET2NUM(n));
        ++i;
        z = BigDecimal_mult(z, SSIZET2NUM(i));
        argv[0] = z;
        argv[1] = SSIZET2NUM(m);
        d = BigDecimal_div2(2, argv, x1);
        y = BigDecimal_add(y, d);
    }

    if (negative) {
        VALUE argv[2];
        argv[0] = y;
        argv[1] = vprec;
        return BigDecimal_div2(2, argv, one);
    }
    else {
        vprec = SSIZET2NUM(prec - VpExponent10(DATA_PTR(y)));
        return BigDecimal_round(1, &vprec, y);
    }
}

/* call-seq:
 * BigMath.log(x, prec)
 *
 * Computes the natural logarithm of x to the specified number of digits of
 * precision.
 *
 * If x is zero or negative, raises Math::DomainError.
 *
 * If x is positive infinite, returns Infinity.
 *
 * If x is NaN, returns NaN.
 */
static VALUE
BigMath_s_log(VALUE klass, VALUE x, VALUE vprec)
{
    ssize_t prec, n, i;
    SIGNED_VALUE expo;
    Real* vx = NULL;
    VALUE argv[2], vn, one, two, w, x2, y, d;
    int zero = 0;
    int negative = 0;
    int infinite = 0;
    int nan = 0;
    double flo;
    long fix;

    if (TYPE(vprec) != T_FIXNUM && TYPE(vprec) != T_BIGNUM) {
        rb_raise(rb_eArgError, "precision must be an Integer");
    }

    prec = NUM2SSIZET(vprec);
    if (prec <= 0) {
        rb_raise(rb_eArgError, "Zero or negative precision for exp");
    }

    /* TODO: the following switch statement is almostly the same as one in the
     *       BigDecimalCmp function. */
    switch (TYPE(x)) {
      case T_DATA:
          if (!is_kind_of_BigDecimal(x)) break;
          vx = DATA_PTR(x);
          zero = VpIsZero(vx);
          negative = VpGetSign(vx) < 0;
          infinite = VpIsPosInf(vx) || VpIsNegInf(vx);
          nan = VpIsNaN(vx);
          break;

      case T_FIXNUM:
        fix = FIX2LONG(x);
        zero = fix == 0;
        negative = fix < 0;
        goto get_vp_value;

      case T_BIGNUM:
        zero = RBIGNUM_ZERO_P(x);
        negative = RBIGNUM_NEGATIVE_P(x);
get_vp_value:
        if (zero || negative) break;
        vx = GetVpValue(x, 0);
        break;

      case T_FLOAT:
        flo = RFLOAT_VALUE(x);
        zero = flo == 0;
        negative = flo < 0;
        infinite = isinf(flo);
        nan = isnan(flo);
        if (!zero && !negative && !infinite && !nan) {
            vx = GetVpValueWithPrec(x, DBL_DIG+1, 1);
        }
        break;

      case T_RATIONAL:
        zero = RRATIONAL_ZERO_P(x);
        negative = RRATIONAL_NEGATIVE_P(x);
        if (zero || negative) break;
        vx = GetVpValueWithPrec(x, prec, 1);
        break;

      case T_COMPLEX:
        rb_raise(rb_eMathDomainError,
                 "Complex argument for BigMath.log");

      default:
        break;
    }
    if (infinite && !negative) {
        Real* vy;
        vy = VpCreateRbObject(prec, "#0");
        RB_GC_GUARD(vy->obj);
        VpSetInf(vy, VP_SIGN_POSITIVE_INFINITE);
        return ToValue(vy);
    }
    else if (nan) {
        Real* vy;
        vy = VpCreateRbObject(prec, "#0");
        RB_GC_GUARD(vy->obj);
        VpSetNaN(vy);
        return ToValue(vy);
    }
    else if (zero || negative) {
        rb_raise(rb_eMathDomainError,
                 "Zero or negative argument for log");
    }
    else if (vx == NULL) {
        cannot_be_coerced_into_BigDecimal(rb_eArgError, x);
    }
    x = ToValue(vx);

    RB_GC_GUARD(one) = ToValue(VpCreateRbObject(1, "1"));
    RB_GC_GUARD(two) = ToValue(VpCreateRbObject(1, "2"));

    n = prec + rmpd_double_figures();
    RB_GC_GUARD(vn) = SSIZET2NUM(n);
    expo = VpExponent10(vx);
    if (expo < 0 || expo >= 3) {
        char buf[16];
        snprintf(buf, 16, "1E%ld", -expo);
        x = BigDecimal_mult2(x, ToValue(VpCreateRbObject(1, buf)), vn);
    }
    else {
        expo = 0;
    }
    w = BigDecimal_sub(x, one);
    argv[0] = BigDecimal_add(x, one);
    argv[1] = vn;
    x = BigDecimal_div2(2, argv, w);
    RB_GC_GUARD(x2) = BigDecimal_mult2(x, x, vn);
    RB_GC_GUARD(y)  = x;
    RB_GC_GUARD(d)  = y;
    i = 1;
    while (!VpIsZero((Real*)DATA_PTR(d))) {
        SIGNED_VALUE const ey = VpExponent10(DATA_PTR(y));
        SIGNED_VALUE const ed = VpExponent10(DATA_PTR(d));
        ssize_t m = n - vabs(ey - ed);
        if (m <= 0) {
            break;
        }
        else if ((size_t)m < rmpd_double_figures()) {
            m = rmpd_double_figures();
        }

        x = BigDecimal_mult2(x2, x, vn);
        i += 2;
        argv[0] = SSIZET2NUM(i);
        argv[1] = SSIZET2NUM(m);
        d = BigDecimal_div2(2, argv, x);
        y = BigDecimal_add(y, d);
    }

    y = BigDecimal_mult(y, two);
    if (expo != 0) {
        VALUE log10, vexpo, dy;
        log10 = BigMath_s_log(klass, INT2FIX(10), vprec);
        vexpo = ToValue(GetVpValue(SSIZET2NUM(expo), 1));
        dy = BigDecimal_mult(log10, vexpo);
        y = BigDecimal_add(y, dy);
    }

    return y;
}

/* Document-class: BigDecimal
 * BigDecimal provides arbitrary-precision floating point decimal arithmetic.
 *
 * Copyright (C) 2002 by Shigeo Kobayashi <shigeo@tinyforest.gr.jp>.
 * You may distribute under the terms of either the GNU General Public
 * License or the Artistic License, as specified in the README file
 * of the BigDecimal distribution.
 *
 * Documented by mathew <meta@pobox.com>.
 *
 * = Introduction
 *
 * Ruby provides built-in support for arbitrary precision integer arithmetic.
 * For example:
 *
 * 42**13   ->   1265437718438866624512
 *
 * BigDecimal provides similar support for very large or very accurate floating
 * point numbers.
 *
 * Decimal arithmetic is also useful for general calculation, because it
 * provides the correct answers people expect--whereas normal binary floating
 * point arithmetic often introduces subtle errors because of the conversion
 * between base 10 and base 2. For example, try:
 *
 *   sum = 0
 *   for i in (1..10000)
 *     sum = sum + 0.0001
 *   end
 *   print sum
 *
 * and contrast with the output from:
 *
 *   require 'bigdecimal'
 *
 *   sum = BigDecimal.new("0")
 *   for i in (1..10000)
 *     sum = sum + BigDecimal.new("0.0001")
 *   end
 *   print sum
 *
 * Similarly:
 *
 * (BigDecimal.new("1.2") - BigDecimal("1.0")) == BigDecimal("0.2") -> true
 *
 * (1.2 - 1.0) == 0.2 -> false
 *
 * = Special features of accurate decimal arithmetic
 *
 * Because BigDecimal is more accurate than normal binary floating point
 * arithmetic, it requires some special values.
 *
 * == Infinity
 *
 * BigDecimal sometimes needs to return infinity, for example if you divide
 * a value by zero.
 *
 * BigDecimal.new("1.0") / BigDecimal.new("0.0")  -> infinity
 *
 * BigDecimal.new("-1.0") / BigDecimal.new("0.0")  -> -infinity
 *
 * You can represent infinite numbers to BigDecimal using the strings
 * 'Infinity', '+Infinity' and '-Infinity' (case-sensitive)
 *
 * == Not a Number
 *
 * When a computation results in an undefined value, the special value NaN
 * (for 'not a number') is returned.
 *
 * Example:
 *
 * BigDecimal.new("0.0") / BigDecimal.new("0.0") -> NaN
 *
 * You can also create undefined values.  NaN is never considered to be the
 * same as any other value, even NaN itself:
 *
 * n = BigDecimal.new('NaN')
 *
 * n == 0.0 -> nil
 *
 * n == n -> nil
 *
 * == Positive and negative zero
 *
 * If a computation results in a value which is too small to be represented as
 * a BigDecimal within the currently specified limits of precision, zero must
 * be returned.
 *
 * If the value which is too small to be represented is negative, a BigDecimal
 * value of negative zero is returned. If the value is positive, a value of
 * positive zero is returned.
 *
 * BigDecimal.new("1.0") / BigDecimal.new("-Infinity") -> -0.0
 *
 * BigDecimal.new("1.0") / BigDecimal.new("Infinity") -> 0.0
 *
 * (See BigDecimal.mode for how to specify limits of precision.)
 *
 * Note that -0.0 and 0.0 are considered to be the same for the purposes of
 * comparison.
 *
 * Note also that in mathematics, there is no particular concept of negative
 * or positive zero; true mathematical zero has no sign.
 */
void
Init_bigdecimal(void)
{
    VALUE arg;

    id_BigDecimal_exception_mode = rb_intern_const("BigDecimal.exception_mode");
    id_BigDecimal_rounding_mode = rb_intern_const("BigDecimal.rounding_mode");
    id_BigDecimal_precision_limit = rb_intern_const("BigDecimal.precision_limit");

    /* Initialize VP routines */
    VpInit(0UL);

    /* Class and method registration */
    rb_cBigDecimal = rb_define_class("BigDecimal",rb_cNumeric);

    /* Global function */
    rb_define_global_function("BigDecimal", BigDecimal_global_new, -1);

    /* Class methods */
    rb_define_singleton_method(rb_cBigDecimal, "new", BigDecimal_new, -1);
    rb_define_singleton_method(rb_cBigDecimal, "mode", BigDecimal_mode, -1);
    rb_define_singleton_method(rb_cBigDecimal, "limit", BigDecimal_limit, -1);
    rb_define_singleton_method(rb_cBigDecimal, "double_fig", BigDecimal_double_fig, 0);
    rb_define_singleton_method(rb_cBigDecimal, "_load", BigDecimal_load, 1);
    rb_define_singleton_method(rb_cBigDecimal, "ver", BigDecimal_version, 0);

    rb_define_singleton_method(rb_cBigDecimal, "save_exception_mode", BigDecimal_save_exception_mode, 0);
    rb_define_singleton_method(rb_cBigDecimal, "save_rounding_mode", BigDecimal_save_rounding_mode, 0);
    rb_define_singleton_method(rb_cBigDecimal, "save_limit", BigDecimal_save_limit, 0);

    /* Constants definition */

    /*
     * Base value used in internal calculations.  On a 32 bit system, BASE
     * is 10000, indicating that calculation is done in groups of 4 digits.
     * (If it were larger, BASE**2 wouldn't fit in 32 bits, so you couldn't
     * guarantee that two groups could always be multiplied together without
     * overflow.)
     */
    rb_define_const(rb_cBigDecimal, "BASE", INT2FIX((SIGNED_VALUE)VpBaseVal()));

    /* Exceptions */

    /*
     * 0xff: Determines whether overflow, underflow or zero divide result in
     * an exception being thrown. See BigDecimal.mode.
     */
    rb_define_const(rb_cBigDecimal, "EXCEPTION_ALL",INT2FIX(VP_EXCEPTION_ALL));

    /*
     * 0x02: Determines what happens when the result of a computation is not a
     * number (NaN). See BigDecimal.mode.
     */
    rb_define_const(rb_cBigDecimal, "EXCEPTION_NaN",INT2FIX(VP_EXCEPTION_NaN));

    /*
     * 0x01: Determines what happens when the result of a computation is
     * infinity.  See BigDecimal.mode.
     */
    rb_define_const(rb_cBigDecimal, "EXCEPTION_INFINITY",INT2FIX(VP_EXCEPTION_INFINITY));

    /*
     * 0x04: Determines what happens when the result of a computation is an
     * underflow (a result too small to be represented). See BigDecimal.mode.
     */
    rb_define_const(rb_cBigDecimal, "EXCEPTION_UNDERFLOW",INT2FIX(VP_EXCEPTION_UNDERFLOW));

    /*
     * 0x01: Determines what happens when the result of a computation is an
     * overflow (a result too large to be represented). See BigDecimal.mode.
     */
    rb_define_const(rb_cBigDecimal, "EXCEPTION_OVERFLOW",INT2FIX(VP_EXCEPTION_OVERFLOW));

    /*
     * 0x01: Determines what happens when a division by zero is performed.
     * See BigDecimal.mode.
     */
    rb_define_const(rb_cBigDecimal, "EXCEPTION_ZERODIVIDE",INT2FIX(VP_EXCEPTION_ZERODIVIDE));

    /*
     * 0x100: Determines what happens when a result must be rounded in order to
     * fit in the appropriate number of significant digits. See
     * BigDecimal.mode.
     */
    rb_define_const(rb_cBigDecimal, "ROUND_MODE",INT2FIX(VP_ROUND_MODE));

    /* 1: Indicates that values should be rounded away from zero. See
     * BigDecimal.mode.
     */
    rb_define_const(rb_cBigDecimal, "ROUND_UP",INT2FIX(VP_ROUND_UP));

    /* 2: Indicates that values should be rounded towards zero. See
     * BigDecimal.mode.
     */
    rb_define_const(rb_cBigDecimal, "ROUND_DOWN",INT2FIX(VP_ROUND_DOWN));

    /* 3: Indicates that digits >= 5 should be rounded up, others rounded down.
     * See BigDecimal.mode. */
    rb_define_const(rb_cBigDecimal, "ROUND_HALF_UP",INT2FIX(VP_ROUND_HALF_UP));

    /* 4: Indicates that digits >= 6 should be rounded up, others rounded down.
     * See BigDecimal.mode.
     */
    rb_define_const(rb_cBigDecimal, "ROUND_HALF_DOWN",INT2FIX(VP_ROUND_HALF_DOWN));
    /* 5: Round towards +infinity. See BigDecimal.mode. */
    rb_define_const(rb_cBigDecimal, "ROUND_CEILING",INT2FIX(VP_ROUND_CEIL));

    /* 6: Round towards -infinity. See BigDecimal.mode. */
    rb_define_const(rb_cBigDecimal, "ROUND_FLOOR",INT2FIX(VP_ROUND_FLOOR));

    /* 7: Round towards the even neighbor. See BigDecimal.mode. */
    rb_define_const(rb_cBigDecimal, "ROUND_HALF_EVEN",INT2FIX(VP_ROUND_HALF_EVEN));

    /* 0: Indicates that a value is not a number. See BigDecimal.sign. */
    rb_define_const(rb_cBigDecimal, "SIGN_NaN",INT2FIX(VP_SIGN_NaN));

    /* 1: Indicates that a value is +0. See BigDecimal.sign. */
    rb_define_const(rb_cBigDecimal, "SIGN_POSITIVE_ZERO",INT2FIX(VP_SIGN_POSITIVE_ZERO));

    /* -1: Indicates that a value is -0. See BigDecimal.sign. */
    rb_define_const(rb_cBigDecimal, "SIGN_NEGATIVE_ZERO",INT2FIX(VP_SIGN_NEGATIVE_ZERO));

    /* 2: Indicates that a value is positive and finite. See BigDecimal.sign. */
    rb_define_const(rb_cBigDecimal, "SIGN_POSITIVE_FINITE",INT2FIX(VP_SIGN_POSITIVE_FINITE));

    /* -2: Indicates that a value is negative and finite. See BigDecimal.sign. */
    rb_define_const(rb_cBigDecimal, "SIGN_NEGATIVE_FINITE",INT2FIX(VP_SIGN_NEGATIVE_FINITE));

    /* 3: Indicates that a value is positive and infinite. See BigDecimal.sign. */
    rb_define_const(rb_cBigDecimal, "SIGN_POSITIVE_INFINITE",INT2FIX(VP_SIGN_POSITIVE_INFINITE));

    /* -3: Indicates that a value is negative and infinite. See BigDecimal.sign. */
    rb_define_const(rb_cBigDecimal, "SIGN_NEGATIVE_INFINITE",INT2FIX(VP_SIGN_NEGATIVE_INFINITE));

    arg = rb_str_new2("+Infinity");
    rb_define_const(rb_cBigDecimal, "INFINITY", BigDecimal_global_new(1, &arg, rb_cBigDecimal));
    arg = rb_str_new2("NaN");
    rb_define_const(rb_cBigDecimal, "NAN", BigDecimal_global_new(1, &arg, rb_cBigDecimal));


    /* instance methods */
    rb_define_method(rb_cBigDecimal, "precs", BigDecimal_prec, 0);

    rb_define_method(rb_cBigDecimal, "add", BigDecimal_add2, 2);
    rb_define_method(rb_cBigDecimal, "sub", BigDecimal_sub2, 2);
    rb_define_method(rb_cBigDecimal, "mult", BigDecimal_mult2, 2);
    rb_define_method(rb_cBigDecimal, "div", BigDecimal_div2, -1);
    rb_define_method(rb_cBigDecimal, "hash", BigDecimal_hash, 0);
    rb_define_method(rb_cBigDecimal, "to_s", BigDecimal_to_s, -1);
    rb_define_method(rb_cBigDecimal, "to_i", BigDecimal_to_i, 0);
    rb_define_method(rb_cBigDecimal, "to_int", BigDecimal_to_i, 0);
    rb_define_method(rb_cBigDecimal, "to_r", BigDecimal_to_r, 0);
    rb_define_method(rb_cBigDecimal, "split", BigDecimal_split, 0);
    rb_define_method(rb_cBigDecimal, "+", BigDecimal_add, 1);
    rb_define_method(rb_cBigDecimal, "-", BigDecimal_sub, 1);
    rb_define_method(rb_cBigDecimal, "+@", BigDecimal_uplus, 0);
    rb_define_method(rb_cBigDecimal, "-@", BigDecimal_neg, 0);
    rb_define_method(rb_cBigDecimal, "*", BigDecimal_mult, 1);
    rb_define_method(rb_cBigDecimal, "/", BigDecimal_div, 1);
    rb_define_method(rb_cBigDecimal, "quo", BigDecimal_div, 1);
    rb_define_method(rb_cBigDecimal, "%", BigDecimal_mod, 1);
    rb_define_method(rb_cBigDecimal, "modulo", BigDecimal_mod, 1);
    rb_define_method(rb_cBigDecimal, "remainder", BigDecimal_remainder, 1);
    rb_define_method(rb_cBigDecimal, "divmod", BigDecimal_divmod, 1);
    /* rb_define_method(rb_cBigDecimal, "dup", BigDecimal_dup, 0); */
    rb_define_method(rb_cBigDecimal, "to_f", BigDecimal_to_f, 0);
    rb_define_method(rb_cBigDecimal, "abs", BigDecimal_abs, 0);
    rb_define_method(rb_cBigDecimal, "sqrt", BigDecimal_sqrt, 1);
    rb_define_method(rb_cBigDecimal, "fix", BigDecimal_fix, 0);
    rb_define_method(rb_cBigDecimal, "round", BigDecimal_round, -1);
    rb_define_method(rb_cBigDecimal, "frac", BigDecimal_frac, 0);
    rb_define_method(rb_cBigDecimal, "floor", BigDecimal_floor, -1);
    rb_define_method(rb_cBigDecimal, "ceil", BigDecimal_ceil, -1);
    rb_define_method(rb_cBigDecimal, "power", BigDecimal_power, -1);
    rb_define_method(rb_cBigDecimal, "**", BigDecimal_power_op, 1);
    rb_define_method(rb_cBigDecimal, "<=>", BigDecimal_comp, 1);
    rb_define_method(rb_cBigDecimal, "==", BigDecimal_eq, 1);
    rb_define_method(rb_cBigDecimal, "===", BigDecimal_eq, 1);
    rb_define_method(rb_cBigDecimal, "eql?", BigDecimal_eq, 1);
    rb_define_method(rb_cBigDecimal, "<", BigDecimal_lt, 1);
    rb_define_method(rb_cBigDecimal, "<=", BigDecimal_le, 1);
    rb_define_method(rb_cBigDecimal, ">", BigDecimal_gt, 1);
    rb_define_method(rb_cBigDecimal, ">=", BigDecimal_ge, 1);
    rb_define_method(rb_cBigDecimal, "zero?", BigDecimal_zero, 0);
    rb_define_method(rb_cBigDecimal, "nonzero?", BigDecimal_nonzero, 0);
    rb_define_method(rb_cBigDecimal, "coerce", BigDecimal_coerce, 1);
    rb_define_method(rb_cBigDecimal, "inspect", BigDecimal_inspect, 0);
    rb_define_method(rb_cBigDecimal, "exponent", BigDecimal_exponent, 0);
    rb_define_method(rb_cBigDecimal, "sign", BigDecimal_sign, 0);
    rb_define_method(rb_cBigDecimal, "nan?",      BigDecimal_IsNaN, 0);
    rb_define_method(rb_cBigDecimal, "infinite?", BigDecimal_IsInfinite, 0);
    rb_define_method(rb_cBigDecimal, "finite?",   BigDecimal_IsFinite, 0);
    rb_define_method(rb_cBigDecimal, "truncate",  BigDecimal_truncate, -1);
    rb_define_method(rb_cBigDecimal, "_dump", BigDecimal_dump, -1);

    /* mathematical functions */
    rb_mBigMath = rb_define_module("BigMath");
    rb_define_singleton_method(rb_mBigMath, "exp", BigMath_s_exp, 2);
    rb_define_singleton_method(rb_mBigMath, "log", BigMath_s_log, 2);

    id_up = rb_intern_const("up");
    id_down = rb_intern_const("down");
    id_truncate = rb_intern_const("truncate");
    id_half_up = rb_intern_const("half_up");
    id_default = rb_intern_const("default");
    id_half_down = rb_intern_const("half_down");
    id_half_even = rb_intern_const("half_even");
    id_banker = rb_intern_const("banker");
    id_ceiling = rb_intern_const("ceiling");
    id_ceil = rb_intern_const("ceil");
    id_floor = rb_intern_const("floor");
    id_to_r = rb_intern_const("to_r");
    id_eq = rb_intern_const("==");
}

/*
 *
 *  ============================================================================
 *
 *  vp_ routines begin from here.
 *
 *  ============================================================================
 *
 */
#ifdef BIGDECIMAL_DEBUG
static int gfDebug = 1;         /* Debug switch */
#if 0
static int gfCheckVal = 1;      /* Value checking flag in VpNmlz()  */
#endif
#endif /* BIGDECIMAL_DEBUG */

static Real *VpConstOne;    /* constant 1.0 */
static Real *VpPt5;        /* constant 0.5 */
#define maxnr 100UL    /* Maximum iterations for calcurating sqrt. */
                /* used in VpSqrt() */

/* ETC */
#define MemCmp(x,y,z) memcmp(x,y,z)
#define StrCmp(x,y)   strcmp(x,y)

static int VpIsDefOP(Real *c,Real *a,Real *b,int sw);
static int AddExponent(Real *a, SIGNED_VALUE n);
static BDIGIT VpAddAbs(Real *a,Real *b,Real *c);
static BDIGIT VpSubAbs(Real *a,Real *b,Real *c);
static size_t VpSetPTR(Real *a, Real *b, Real *c, size_t *a_pos, size_t *b_pos, size_t *c_pos, BDIGIT *av, BDIGIT *bv);
static int VpNmlz(Real *a);
static void VpFormatSt(char *psz, size_t fFmt);
static int VpRdup(Real *m, size_t ind_m);

#ifdef BIGDECIMAL_DEBUG
static int gnAlloc=0; /* Memory allocation counter */
#endif /* BIGDECIMAL_DEBUG */

VP_EXPORT void *
VpMemAlloc(size_t mb)
{
    void *p = xmalloc(mb);
    if (!p) {
        VpException(VP_EXCEPTION_MEMORY, "failed to allocate memory", 1);
    }
    memset(p, 0, mb);
#ifdef BIGDECIMAL_DEBUG
    gnAlloc++; /* Count allocation call */
#endif /* BIGDECIMAL_DEBUG */
    return p;
}

VP_EXPORT void
VpFree(Real *pv)
{
    if(pv != NULL) {
        xfree(pv);
#ifdef BIGDECIMAL_DEBUG
        gnAlloc--; /* Decrement allocation count */
        if(gnAlloc==0) {
            printf(" *************** All memories allocated freed ****************");
            getchar();
        }
        if(gnAlloc<0) {
            printf(" ??????????? Too many memory free calls(%d) ?????????????\n",gnAlloc);
            getchar();
        }
#endif /* BIGDECIMAL_DEBUG */
    }
}

/*
 * EXCEPTION Handling.
 */

#define rmpd_set_thread_local_exception_mode(mode) \
    rb_thread_local_aset( \
        rb_thread_current(), \
        id_BigDecimal_exception_mode, \
        INT2FIX((int)(mode)) \
    )

static unsigned short
VpGetException (void)
{
    VALUE const vmode = rb_thread_local_aref(
        rb_thread_current(),
        id_BigDecimal_exception_mode
    );

    if (NIL_P(vmode)) {
        rmpd_set_thread_local_exception_mode(RMPD_EXCEPTION_MODE_DEFAULT);
        return RMPD_EXCEPTION_MODE_DEFAULT;
    }

    return (unsigned short)FIX2UINT(vmode);
}

static void
VpSetException(unsigned short f)
{
    rmpd_set_thread_local_exception_mode(f);
}

/*
 * Precision limit.
 */

#define rmpd_set_thread_local_precision_limit(limit) \
    rb_thread_local_aset( \
        rb_thread_current(), \
        id_BigDecimal_precision_limit, \
        SIZET2NUM(limit) \
    )
#define RMPD_PRECISION_LIMIT_DEFAULT ((size_t)0)

/* These 2 functions added at v1.1.7 */
VP_EXPORT size_t
VpGetPrecLimit(void)
{
    VALUE const vlimit = rb_thread_local_aref(
        rb_thread_current(),
        id_BigDecimal_precision_limit
    );

    if (NIL_P(vlimit)) {
        rmpd_set_thread_local_precision_limit(RMPD_PRECISION_LIMIT_DEFAULT);
        return RMPD_PRECISION_LIMIT_DEFAULT;
    }

    return NUM2SIZET(vlimit);
}

VP_EXPORT size_t
VpSetPrecLimit(size_t n)
{
    size_t const s = VpGetPrecLimit();
    rmpd_set_thread_local_precision_limit(n);
    return s;
}

/*
 * Rounding mode.
 */

#define rmpd_set_thread_local_rounding_mode(mode) \
    rb_thread_local_aset( \
        rb_thread_current(), \
        id_BigDecimal_rounding_mode, \
        INT2FIX((int)(mode)) \
    )

VP_EXPORT unsigned short
VpGetRoundMode(void)
{
    VALUE const vmode = rb_thread_local_aref(
        rb_thread_current(),
        id_BigDecimal_rounding_mode
    );

    if (NIL_P(vmode)) {
        rmpd_set_thread_local_rounding_mode(RMPD_ROUNDING_MODE_DEFAULT);
        return RMPD_ROUNDING_MODE_DEFAULT;
    }

    return (unsigned short)FIX2INT(vmode);
}

VP_EXPORT int
VpIsRoundMode(unsigned short n)
{
    switch (n) {
      case VP_ROUND_UP:
      case VP_ROUND_DOWN:
      case VP_ROUND_HALF_UP:
      case VP_ROUND_HALF_DOWN:
      case VP_ROUND_CEIL:
      case VP_ROUND_FLOOR:
      case VP_ROUND_HALF_EVEN:
        return 1;

      default:
        return 0;
    }
}

VP_EXPORT unsigned short
VpSetRoundMode(unsigned short n)
{
    if (VpIsRoundMode(n)) {
        rmpd_set_thread_local_rounding_mode(n);
        return n;
    }

    return VpGetRoundMode();
}

/*
 *  0.0 & 1.0 generator
 *    These gZero_..... and gOne_..... can be any name
 *    referenced from nowhere except Zero() and One().
 *    gZero_..... and gOne_..... must have global scope
 *    (to let the compiler know they may be changed in outside
 *    (... but not actually..)).
 */
volatile const double gZero_ABCED9B1_CE73__00400511F31D = 0.0;
volatile const double gOne_ABCED9B4_CE73__00400511F31D  = 1.0;
static double
Zero(void)
{
    return gZero_ABCED9B1_CE73__00400511F31D;
}

static double
One(void)
{
    return gOne_ABCED9B4_CE73__00400511F31D;
}

/*
  ----------------------------------------------------------------
  Value of sign in Real structure is reserved for future use.
  short sign;
                    ==0 : NaN
                      1 : Positive zero
                     -1 : Negative zero
                      2 : Positive number
                     -2 : Negative number
                      3 : Positive infinite number
                     -3 : Negative infinite number
  ----------------------------------------------------------------
*/

VP_EXPORT double
VpGetDoubleNaN(void) /* Returns the value of NaN */
{
    static double fNaN = 0.0;
    if(fNaN==0.0) fNaN = Zero()/Zero();
    return fNaN;
}

VP_EXPORT double
VpGetDoublePosInf(void) /* Returns the value of +Infinity */
{
    static double fInf = 0.0;
    if(fInf==0.0) fInf = One()/Zero();
    return fInf;
}

VP_EXPORT double
VpGetDoubleNegInf(void) /* Returns the value of -Infinity */
{
    static double fInf = 0.0;
    if(fInf==0.0) fInf = -(One()/Zero());
    return fInf;
}

VP_EXPORT double
VpGetDoubleNegZero(void) /* Returns the value of -0 */
{
    static double nzero = 1000.0;
    if(nzero!=0.0) nzero = (One()/VpGetDoubleNegInf());
    return nzero;
}

#if 0  /* unused */
VP_EXPORT int
VpIsNegDoubleZero(double v)
{
    double z = VpGetDoubleNegZero();
    return MemCmp(&v,&z,sizeof(v))==0;
}
#endif

VP_EXPORT int
VpException(unsigned short f, const char *str,int always)
{
    VALUE exc;
    int   fatal=0;
    unsigned short const exception_mode = VpGetException();

    if(f==VP_EXCEPTION_OP || f==VP_EXCEPTION_MEMORY) always = 1;

    if (always || (exception_mode & f)) {
        switch(f)
        {
        /*
        case VP_EXCEPTION_OVERFLOW:
        */
        case VP_EXCEPTION_ZERODIVIDE:
        case VP_EXCEPTION_INFINITY:
        case VP_EXCEPTION_NaN:
        case VP_EXCEPTION_UNDERFLOW:
        case VP_EXCEPTION_OP:
             exc = rb_eFloatDomainError;
             goto raise;
        case VP_EXCEPTION_MEMORY:
             fatal = 1;
             goto raise;
        default:
             fatal = 1;
             goto raise;
        }
    }
    return 0; /* 0 Means VpException() raised no exception */

raise:
    if(fatal) rb_fatal("%s", str);
    else   rb_raise(exc, "%s", str);
    return 0;
}

/* Throw exception or returns 0,when resulting c is Inf or NaN */
/*  sw=1:+ 2:- 3:* 4:/ */
static int
VpIsDefOP(Real *c,Real *a,Real *b,int sw)
{
    if(VpIsNaN(a) || VpIsNaN(b)) {
        /* at least a or b is NaN */
        VpSetNaN(c);
        goto NaN;
    }

    if(VpIsInf(a)) {
        if(VpIsInf(b)) {
            switch(sw)
            {
            case 1: /* + */
                if(VpGetSign(a)==VpGetSign(b)) {
                    VpSetInf(c,VpGetSign(a));
                    goto Inf;
                } else {
                    VpSetNaN(c);
                    goto NaN;
                }
            case 2: /* - */
                if(VpGetSign(a)!=VpGetSign(b)) {
                    VpSetInf(c,VpGetSign(a));
                    goto Inf;
                } else {
                    VpSetNaN(c);
                    goto NaN;
                }
                break;
            case 3: /* * */
                VpSetInf(c,VpGetSign(a)*VpGetSign(b));
                goto Inf;
                break;
            case 4: /* / */
                VpSetNaN(c);
                goto NaN;
            }
            VpSetNaN(c);
            goto NaN;
        }
        /* Inf op Finite */
        switch(sw)
        {
        case 1: /* + */
        case 2: /* - */
                VpSetInf(c,VpGetSign(a));
                break;
        case 3: /* * */
                if(VpIsZero(b)) {
                    VpSetNaN(c);
                    goto NaN;
                }
                VpSetInf(c,VpGetSign(a)*VpGetSign(b));
                break;
        case 4: /* / */
                VpSetInf(c,VpGetSign(a)*VpGetSign(b));
        }
        goto Inf;
    }

    if(VpIsInf(b)) {
        switch(sw)
        {
        case 1: /* + */
                VpSetInf(c,VpGetSign(b));
                break;
        case 2: /* - */
                VpSetInf(c,-VpGetSign(b));
                break;
        case 3: /* * */
                if(VpIsZero(a)) {
                    VpSetNaN(c);
                    goto NaN;
                }
                VpSetInf(c,VpGetSign(a)*VpGetSign(b));
                break;
        case 4: /* / */
                VpSetZero(c,VpGetSign(a)*VpGetSign(b));
        }
        goto Inf;
    }
    return 1; /* Results OK */

Inf:
    return VpException(VP_EXCEPTION_INFINITY,"Computation results to 'Infinity'",0);
NaN:
    return VpException(VP_EXCEPTION_NaN,"Computation results to 'NaN'",0);
}

/*
  ----------------------------------------------------------------
*/

/*
 *    returns number of chars needed to represent vp in specified format.
 */
VP_EXPORT size_t
VpNumOfChars(Real *vp,const char *pszFmt)
{
    SIGNED_VALUE  ex;
    size_t nc;

    if(vp == NULL)   return BASE_FIG*2+6;
    if(!VpIsDef(vp)) return 32; /* not sure,may be OK */

    switch(*pszFmt)
    {
    case 'F':
         nc = BASE_FIG*(vp->Prec + 1)+2;
         ex = vp->exponent;
         if(ex < 0) {
             nc += BASE_FIG*(size_t)(-ex);
         }
         else {
             if((size_t)ex > vp->Prec) {
                 nc += BASE_FIG*((size_t)ex - vp->Prec);
             }
         }
         break;
    case 'E':
    default:
         nc = BASE_FIG*(vp->Prec + 2)+6; /* 3: sign + exponent chars */
    }
    return nc;
}

/*
 * Initializer for Vp routines and constants used.
 * [Input]
 *   BaseVal: Base value(assigned to BASE) for Vp calculation.
 *   It must be the form BaseVal=10**n.(n=1,2,3,...)
 *   If Base <= 0L,then the BASE will be calcurated so
 *   that BASE is as large as possible satisfying the
 *   relation MaxVal <= BASE*(BASE+1). Where the value
 *   MaxVal is the largest value which can be represented
 *   by one BDIGIT word in the computer used.
 *
 * [Returns]
 * 1+DBL_DIG   ... OK
 */
VP_EXPORT size_t
VpInit(BDIGIT BaseVal)
{
    /* Setup +/- Inf  NaN -0 */
    VpGetDoubleNaN();
    VpGetDoublePosInf();
    VpGetDoubleNegInf();
    VpGetDoubleNegZero();

    /* Allocates Vp constants. */
    VpConstOne = VpAlloc(1UL, "1");
    VpPt5 = VpAlloc(1UL, ".5");

#ifdef BIGDECIMAL_DEBUG
    gnAlloc = 0;
#endif /* BIGDECIMAL_DEBUG */

#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        printf("VpInit: BaseVal   = %lu\n", BaseVal);
        printf("  BASE   = %lu\n", BASE);
        printf("  HALF_BASE = %lu\n", HALF_BASE);
        printf("  BASE1  = %lu\n", BASE1);
        printf("  BASE_FIG  = %u\n", BASE_FIG);
        printf("  DBLE_FIG  = %d\n", DBLE_FIG);
    }
#endif /* BIGDECIMAL_DEBUG */

    return rmpd_double_figures();
}

VP_EXPORT Real *
VpOne(void)
{
    return VpConstOne;
}

/* If exponent overflows,then raise exception or returns 0 */
static int
AddExponent(Real *a, SIGNED_VALUE n)
{
    SIGNED_VALUE e = a->exponent;
    SIGNED_VALUE m = e+n;
    SIGNED_VALUE eb, mb;
    if(e>0) {
        if(n>0) {
            mb = m*(SIGNED_VALUE)BASE_FIG;
            eb = e*(SIGNED_VALUE)BASE_FIG;
            if(mb<eb) goto overflow;
        }
    } else if(n<0) {
        mb = m*(SIGNED_VALUE)BASE_FIG;
        eb = e*(SIGNED_VALUE)BASE_FIG;
        if(mb>eb) goto underflow;
    }
    a->exponent = m;
    return 1;

/* Overflow/Underflow ==> Raise exception or returns 0 */
underflow:
    VpSetZero(a,VpGetSign(a));
    return VpException(VP_EXCEPTION_UNDERFLOW,"Exponent underflow",0);

overflow:
    VpSetInf(a,VpGetSign(a));
    return VpException(VP_EXCEPTION_OVERFLOW,"Exponent overflow",0);
}

/*
 * Allocates variable.
 * [Input]
 *   mx ... allocation unit, if zero then mx is determined by szVal.
 *    The mx is the number of effective digits can to be stored.
 *   szVal ... value assigned(char). If szVal==NULL,then zero is assumed.
 *            If szVal[0]=='#' then Max. Prec. will not be considered(1.1.7),
 *            full precision specified by szVal is allocated.
 *
 * [Returns]
 *   Pointer to the newly allocated variable, or
 *   NULL be returned if memory allocation is failed,or any error.
 */
VP_EXPORT Real *
VpAlloc(size_t mx, const char *szVal)
{
    size_t i, ni, ipn, ipf, nf, ipe, ne, nalloc;
    char v,*psz;
    int  sign=1;
    Real *vp = NULL;
    size_t mf = VpGetPrecLimit();
    VALUE buf;

    mx = (mx + BASE_FIG - 1) / BASE_FIG + 1;    /* Determine allocation unit. */
    if (szVal) {
        while (ISSPACE(*szVal)) szVal++;
        if (*szVal != '#') {
             if (mf) {
                mf = (mf + BASE_FIG - 1) / BASE_FIG + 2; /* Needs 1 more for div */
                if (mx > mf) {
                    mx = mf;
                }
            }
        }
        else {
            ++szVal;
        }
    }
    else {
       /* necessary to be able to store */
       /* at least mx digits. */
       /* szVal==NULL ==> allocate zero value. */
       vp = (Real *) VpMemAlloc(sizeof(Real) + mx * sizeof(BDIGIT));
       /* xmalloc() alway returns(or throw interruption) */
       vp->MaxPrec = mx;    /* set max precision */
       VpSetZero(vp,1);    /* initialize vp to zero. */
       return vp;
    }

    /* Skip all '_' after digit: 2006-6-30 */
    ni = 0;
    buf = rb_str_tmp_new(strlen(szVal)+1);
    psz = RSTRING_PTR(buf);
    i   = 0;
    ipn = 0;
    while ((psz[i]=szVal[ipn]) != 0) {
        if (ISDIGIT(psz[i])) ++ni;
        if (psz[i] == '_') {
            if (ni > 0) { ipn++; continue; }
            psz[i] = 0;
            break;
        }
        ++i;
        ++ipn;
    }
    /* Skip trailing spaces */
    while (--i > 0) {
        if (ISSPACE(psz[i])) psz[i] = 0;
        else break;
    }
    szVal = psz;

    /* Check on Inf & NaN */
    if (StrCmp(szVal, SZ_PINF) == 0 ||
        StrCmp(szVal, SZ_INF)  == 0 ) {
        vp = (Real *) VpMemAlloc(sizeof(Real) + sizeof(BDIGIT));
        vp->MaxPrec = 1;    /* set max precision */
        VpSetPosInf(vp);
        return vp;
    }
    if (StrCmp(szVal, SZ_NINF) == 0) {
        vp = (Real *) VpMemAlloc(sizeof(Real) + sizeof(BDIGIT));
        vp->MaxPrec = 1;    /* set max precision */
        VpSetNegInf(vp);
        return vp;
    }
    if (StrCmp(szVal, SZ_NaN) == 0) {
        vp = (Real *) VpMemAlloc(sizeof(Real) + sizeof(BDIGIT));
        vp->MaxPrec = 1;    /* set max precision */
        VpSetNaN(vp);
        return vp;
    }

    /* check on number szVal[] */
    ipn = i = 0;
    if      (szVal[i] == '-') { sign=-1; ++i; }
    else if (szVal[i] == '+')            ++i;
    /* Skip digits */
    ni = 0;            /* digits in mantissa */
    while ((v = szVal[i]) != 0) {
        if (!ISDIGIT(v)) break;
        ++i;
        ++ni;
    }
    nf  = 0;
    ipf = 0;
    ipe = 0;
    ne  = 0;
    if (v) {
        /* other than digit nor \0 */
        if (szVal[i] == '.') {    /* xxx. */
            ++i;
            ipf = i;
            while ((v = szVal[i]) != 0) {    /* get fraction part. */
                if (!ISDIGIT(v)) break;
                ++i;
                ++nf;
            }
        }
        ipe = 0;        /* Exponent */

        switch (szVal[i]) {
        case '\0':
            break;
        case 'e': case 'E':
        case 'd': case 'D':
            ++i;
            ipe = i;
            v = szVal[i];
            if ((v == '-') || (v == '+')) ++i;
            while ((v=szVal[i]) != 0) {
                if (!ISDIGIT(v)) break;
                ++i;
                ++ne;
            }
            break;
        default:
            break;
        }
    }
    nalloc = (ni + nf + BASE_FIG - 1) / BASE_FIG + 1;    /* set effective allocation  */
    /* units for szVal[]  */
    if (mx <= 0) mx = 1;
    nalloc = Max(nalloc, mx);
    mx = nalloc;
    vp = (Real *) VpMemAlloc(sizeof(Real) + mx * sizeof(BDIGIT));
    /* xmalloc() alway returns(or throw interruption) */
    vp->MaxPrec = mx;        /* set max precision */
    VpSetZero(vp, sign);
    VpCtoV(vp, &szVal[ipn], ni, &szVal[ipf], nf, &szVal[ipe], ne);
    rb_str_resize(buf, 0);
    return vp;
}

/*
 * Assignment(c=a).
 * [Input]
 *   a   ... RHSV
 *   isw ... switch for assignment.
 *    c = a  when isw > 0
 *    c = -a when isw < 0
 *    if c->MaxPrec < a->Prec,then round operation
 *    will be performed.
 * [Output]
 *  c  ... LHSV
 */
VP_EXPORT size_t
VpAsgn(Real *c, Real *a, int isw)
{
    size_t n;
    if(VpIsNaN(a)) {
        VpSetNaN(c);
        return 0;
    }
    if(VpIsInf(a)) {
        VpSetInf(c,isw*VpGetSign(a));
        return 0;
    }

    /* check if the RHS is zero */
    if(!VpIsZero(a)) {
        c->exponent = a->exponent;    /* store  exponent */
        VpSetSign(c,(isw*VpGetSign(a)));    /* set sign */
        n =(a->Prec < c->MaxPrec) ?(a->Prec) :(c->MaxPrec);
        c->Prec = n;
        memcpy(c->frac, a->frac, n * sizeof(BDIGIT));
        /* Needs round ? */
        if(isw!=10) {
            /* Not in ActiveRound */
            if(c->Prec < a->Prec) {
                VpInternalRound(c,n,(n>0)?a->frac[n-1]:0,a->frac[n]);
            } else {
                VpLimitRound(c,0);
            }
        }
    } else {
        /* The value of 'a' is zero.  */
        VpSetZero(c,isw*VpGetSign(a));
        return 1;
    }
    return c->Prec*BASE_FIG;
}

/*
 *   c = a + b  when operation =  1 or 2
 *  = a - b  when operation = -1 or -2.
 *   Returns number of significant digits of c
 */
VP_EXPORT size_t
VpAddSub(Real *c, Real *a, Real *b, int operation)
{
    short sw, isw;
    Real *a_ptr, *b_ptr;
    size_t n, na, nb, i;
    BDIGIT mrv;

#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, "VpAddSub(enter) a=% \n", a);
        VPrint(stdout, "     b=% \n", b);
        printf(" operation=%d\n", operation);
    }
#endif /* BIGDECIMAL_DEBUG */

    if(!VpIsDefOP(c,a,b,(operation>0)?1:2)) return 0; /* No significant digits */

    /* check if a or b is zero  */
    if(VpIsZero(a)) {
        /* a is zero,then assign b to c */
        if(!VpIsZero(b)) {
            VpAsgn(c, b, operation);
        } else {
            /* Both a and b are zero. */
            if(VpGetSign(a)<0 && operation*VpGetSign(b)<0) {
                /* -0 -0 */
                VpSetZero(c,-1);
            } else {
                VpSetZero(c,1);
            }
            return 1; /* 0: 1 significant digits */
        }
        return c->Prec*BASE_FIG;
    }
    if(VpIsZero(b)) {
        /* b is zero,then assign a to c. */
        VpAsgn(c, a, 1);
        return c->Prec*BASE_FIG;
    }

    if(operation < 0) sw = -1;
    else              sw =  1;

    /* compare absolute value. As a result,|a_ptr|>=|b_ptr| */
    if(a->exponent > b->exponent) {
        a_ptr = a;
        b_ptr = b;
    }         /* |a|>|b| */
    else if(a->exponent < b->exponent) {
        a_ptr = b;
        b_ptr = a;
    }                /* |a|<|b| */
    else {
        /* Exponent part of a and b is the same,then compare fraction */
        /* part */
        na = a->Prec;
        nb = b->Prec;
        n = Min(na, nb);
        for(i=0;i < n; ++i) {
            if(a->frac[i] > b->frac[i]) {
                a_ptr = a;
                b_ptr = b;
                goto end_if;
            } else if(a->frac[i] < b->frac[i]) {
                a_ptr = b;
                b_ptr = a;
                goto end_if;
            }
        }
        if(na > nb) {
         a_ptr = a;
            b_ptr = b;
            goto end_if;
        } else if(na < nb) {
            a_ptr = b;
            b_ptr = a;
            goto end_if;
        }
        /* |a| == |b| */
        if(VpGetSign(a) + sw *VpGetSign(b) == 0) {
            VpSetZero(c,1);        /* abs(a)=abs(b) and operation = '-'  */
            return c->Prec*BASE_FIG;
        }
        a_ptr = a;
        b_ptr = b;
    }

end_if:
    isw = VpGetSign(a) + sw *VpGetSign(b);
    /*
     *  isw = 0 ...( 1)+(-1),( 1)-( 1),(-1)+(1),(-1)-(-1)
     *      = 2 ...( 1)+( 1),( 1)-(-1)
     *      =-2 ...(-1)+(-1),(-1)-( 1)
     *   If isw==0, then c =(Sign a_ptr)(|a_ptr|-|b_ptr|)
     *              else c =(Sign ofisw)(|a_ptr|+|b_ptr|)
    */
    if(isw) {            /* addition */
        VpSetSign(c, 1);
        mrv = VpAddAbs(a_ptr, b_ptr, c);
        VpSetSign(c, isw / 2);
    } else {            /* subtraction */
        VpSetSign(c, 1);
        mrv = VpSubAbs(a_ptr, b_ptr, c);
        if(a_ptr == a) {
            VpSetSign(c,VpGetSign(a));
        } else    {
            VpSetSign(c,VpGetSign(a_ptr) * sw);
        }
    }
    VpInternalRound(c,0,(c->Prec>0)?c->frac[c->Prec-1]:0,mrv);

#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, "VpAddSub(result) c=% \n", c);
        VPrint(stdout, "     a=% \n", a);
        VPrint(stdout, "     b=% \n", b);
        printf(" operation=%d\n", operation);
    }
#endif /* BIGDECIMAL_DEBUG */
    return c->Prec*BASE_FIG;
}

/*
 * Addition of two variable precisional variables
 * a and b assuming abs(a)>abs(b).
 *   c = abs(a) + abs(b) ; where |a|>=|b|
 */
static BDIGIT
VpAddAbs(Real *a, Real *b, Real *c)
{
    size_t word_shift;
    size_t ap;
    size_t bp;
    size_t cp;
    size_t a_pos;
    size_t b_pos, b_pos_with_word_shift;
    size_t c_pos;
    BDIGIT av, bv, carry, mrv;

#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, "VpAddAbs called: a = %\n", a);
        VPrint(stdout, "     b = %\n", b);
    }
#endif /* BIGDECIMAL_DEBUG */

    word_shift = VpSetPTR(a, b, c, &ap, &bp, &cp, &av, &bv);
    a_pos = ap;
    b_pos = bp;
    c_pos = cp;
    if(word_shift==(size_t)-1L) return 0; /* Overflow */
    if(b_pos == (size_t)-1L) goto Assign_a;

    mrv = av + bv; /* Most right val. Used for round. */

    /* Just assign the last few digits of b to c because a has no  */
    /* corresponding digits to be added. */
    while(b_pos + word_shift > a_pos) {
        --c_pos;
        if(b_pos > 0) {
            c->frac[c_pos] = b->frac[--b_pos];
        } else {
            --word_shift;
            c->frac[c_pos] = 0;
        }
    }

    /* Just assign the last few digits of a to c because b has no */
    /* corresponding digits to be added. */
    b_pos_with_word_shift = b_pos + word_shift;
    while(a_pos > b_pos_with_word_shift) {
        c->frac[--c_pos] = a->frac[--a_pos];
    }
    carry = 0;    /* set first carry be zero */

    /* Now perform addition until every digits of b will be */
    /* exhausted. */
    while(b_pos > 0) {
        c->frac[--c_pos] = a->frac[--a_pos] + b->frac[--b_pos] + carry;
        if(c->frac[c_pos] >= BASE) {
            c->frac[c_pos] -= BASE;
            carry = 1;
        } else {
            carry = 0;
        }
    }

    /* Just assign the first few digits of a with considering */
    /* the carry obtained so far because b has been exhausted. */
    while(a_pos > 0) {
        c->frac[--c_pos] = a->frac[--a_pos] + carry;
        if(c->frac[c_pos] >= BASE) {
            c->frac[c_pos] -= BASE;
            carry = 1;
        } else {
            carry = 0;
        }
    }
    if(c_pos) c->frac[c_pos - 1] += carry;
    goto Exit;

Assign_a:
    VpAsgn(c, a, 1);
    mrv = 0;

Exit:

#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, "VpAddAbs exit: c=% \n", c);
    }
#endif /* BIGDECIMAL_DEBUG */
    return mrv;
}

/*
 * c = abs(a) - abs(b)
 */
static BDIGIT
VpSubAbs(Real *a, Real *b, Real *c)
{
    size_t word_shift;
    size_t ap;
    size_t bp;
    size_t cp;
    size_t a_pos;
    size_t b_pos, b_pos_with_word_shift;
    size_t c_pos;
    BDIGIT av, bv, borrow, mrv;

#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, "VpSubAbs called: a = %\n", a);
        VPrint(stdout, "     b = %\n", b);
    }
#endif /* BIGDECIMAL_DEBUG */

    word_shift = VpSetPTR(a, b, c, &ap, &bp, &cp, &av, &bv);
    a_pos = ap;
    b_pos = bp;
    c_pos = cp;
    if(word_shift==(size_t)-1L) return 0; /* Overflow */
    if(b_pos == (size_t)-1L) goto Assign_a;

    if(av >= bv) {
        mrv = av - bv;
        borrow = 0;
    } else {
        mrv    = 0;
        borrow = 1;
    }

    /* Just assign the values which are the BASE subtracted by   */
    /* each of the last few digits of the b because the a has no */
    /* corresponding digits to be subtracted. */
    if(b_pos + word_shift > a_pos) {
        while(b_pos + word_shift > a_pos) {
            --c_pos;
            if(b_pos > 0) {
                c->frac[c_pos] = BASE - b->frac[--b_pos] - borrow;
            } else {
                --word_shift;
                c->frac[c_pos] = BASE - borrow;
            }
            borrow = 1;
        }
    }
    /* Just assign the last few digits of a to c because b has no */
    /* corresponding digits to subtract. */

    b_pos_with_word_shift = b_pos + word_shift;
    while(a_pos > b_pos_with_word_shift) {
        c->frac[--c_pos] = a->frac[--a_pos];
    }

    /* Now perform subtraction until every digits of b will be */
    /* exhausted. */
    while(b_pos > 0) {
        --c_pos;
        if(a->frac[--a_pos] < b->frac[--b_pos] + borrow) {
            c->frac[c_pos] = BASE + a->frac[a_pos] - b->frac[b_pos] - borrow;
            borrow = 1;
        } else {
            c->frac[c_pos] = a->frac[a_pos] - b->frac[b_pos] - borrow;
            borrow = 0;
        }
    }

    /* Just assign the first few digits of a with considering */
    /* the borrow obtained so far because b has been exhausted. */
    while(a_pos > 0) {
        --c_pos;
        if(a->frac[--a_pos] < borrow) {
            c->frac[c_pos] = BASE + a->frac[a_pos] - borrow;
            borrow = 1;
        } else {
            c->frac[c_pos] = a->frac[a_pos] - borrow;
            borrow = 0;
        }
    }
    if(c_pos) c->frac[c_pos - 1] -= borrow;
    goto Exit;

Assign_a:
    VpAsgn(c, a, 1);
    mrv = 0;

Exit:
#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, "VpSubAbs exit: c=% \n", c);
    }
#endif /* BIGDECIMAL_DEBUG */
    return mrv;
}

/*
 * Note: If(av+bv)>= HALF_BASE,then 1 will be added to the least significant
 *    digit of c(In case of addition).
 * ------------------------- figure of output -----------------------------------
 *      a =  xxxxxxxxxxx
 *      b =    xxxxxxxxxx
 *      c =xxxxxxxxxxxxxxx
 *      word_shift =  |   |
 *      right_word =  |    | (Total digits in RHSV)
 *      left_word  = |   |   (Total digits in LHSV)
 *      a_pos      =    |
 *      b_pos      =     |
 *      c_pos      =      |
 */
static size_t
VpSetPTR(Real *a, Real *b, Real *c, size_t *a_pos, size_t *b_pos, size_t *c_pos, BDIGIT *av, BDIGIT *bv)
{
    size_t left_word, right_word, word_shift;
    c->frac[0] = 0;
    *av = *bv = 0;
    word_shift =((a->exponent) -(b->exponent));
    left_word = b->Prec + word_shift;
    right_word = Max((a->Prec),left_word);
    left_word =(c->MaxPrec) - 1;    /* -1 ... prepare for round up */
    /*
     * check if 'round' is needed.
     */
    if(right_word > left_word) {    /* round ? */
        /*---------------------------------
         *  Actual size of a = xxxxxxAxx
         *  Actual size of b = xxxBxxxxx
         *  Max. size of   c = xxxxxx
         *  Round off        =   |-----|
         *  c_pos            =   |
         *  right_word       =   |
         *  a_pos            =    |
         */
        *c_pos = right_word = left_word + 1;    /* Set resulting precision */
        /* be equal to that of c */
        if((a->Prec) >=(c->MaxPrec)) {
            /*
             *   a =  xxxxxxAxxx
             *   c =  xxxxxx
             *   a_pos =    |
             */
            *a_pos = left_word;
            *av = a->frac[*a_pos];    /* av is 'A' shown in above. */
        } else {
            /*
             *   a = xxxxxxx
             *   c = xxxxxxxxxx
             *  a_pos =     |
             */
            *a_pos = a->Prec;
        }
        if((b->Prec + word_shift) >= c->MaxPrec) {
            /*
             *   a = xxxxxxxxx
             *   b =  xxxxxxxBxxx
             *   c = xxxxxxxxxxx
             *  b_pos =   |
             */
            if(c->MaxPrec >=(word_shift + 1)) {
                *b_pos = c->MaxPrec - word_shift - 1;
                *bv = b->frac[*b_pos];
            } else {
                *b_pos = -1L;
            }
        } else {
            /*
             *   a = xxxxxxxxxxxxxxxx
             *   b =  xxxxxx
             *   c = xxxxxxxxxxxxx
             *  b_pos =     |
             */
            *b_pos = b->Prec;
        }
    } else {            /* The MaxPrec of c - 1 > The Prec of a + b  */
        /*
         *    a =   xxxxxxx
         *    b =   xxxxxx
         *    c = xxxxxxxxxxx
         *   c_pos =   |
         */
        *b_pos = b->Prec;
        *a_pos = a->Prec;
        *c_pos = right_word + 1;
    }
    c->Prec = *c_pos;
    c->exponent = a->exponent;
    if(!AddExponent(c,1)) return (size_t)-1L;
    return word_shift;
}

/*
 * Return number og significant digits
 *       c = a * b , Where a = a0a1a2 ... an
 *             b = b0b1b2 ... bm
 *             c = c0c1c2 ... cl
 *          a0 a1 ... an   * bm
 *       a0 a1 ... an   * bm-1
 *         .   .    .
 *       .   .   .
 *        a0 a1 .... an    * b0
 *      +_____________________________
 *     c0 c1 c2  ......  cl
 *     nc      <---|
 *     MaxAB |--------------------|
 */
VP_EXPORT size_t
VpMult(Real *c, Real *a, Real *b)
{
    size_t MxIndA, MxIndB, MxIndAB, MxIndC;
    size_t ind_c, i, ii, nc;
    size_t ind_as, ind_ae, ind_bs, ind_be;
    BDIGIT carry;
    BDIGIT_DBL s;
    Real *w;

#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, "VpMult(Enter): a=% \n", a);
        VPrint(stdout, "      b=% \n", b);
    }
#endif /* BIGDECIMAL_DEBUG */

    if(!VpIsDefOP(c,a,b,3)) return 0; /* No significant digit */

    if(VpIsZero(a) || VpIsZero(b)) {
        /* at least a or b is zero */
        VpSetZero(c,VpGetSign(a)*VpGetSign(b));
        return 1; /* 0: 1 significant digit */
    }

    if(VpIsOne(a)) {
        VpAsgn(c, b, VpGetSign(a));
        goto Exit;
    }
    if(VpIsOne(b)) {
        VpAsgn(c, a, VpGetSign(b));
        goto Exit;
    }
    if((b->Prec) >(a->Prec)) {
        /* Adjust so that digits(a)>digits(b) */
        w = a;
        a = b;
        b = w;
    }
    w = NULL;
    MxIndA = a->Prec - 1;
    MxIndB = b->Prec - 1;
    MxIndC = c->MaxPrec - 1;
    MxIndAB = a->Prec + b->Prec - 1;

    if(MxIndC < MxIndAB) {    /* The Max. prec. of c < Prec(a)+Prec(b) */
        w = c;
        c = VpAlloc((size_t)((MxIndAB + 1) * BASE_FIG), "#0");
        MxIndC = MxIndAB;
    }

    /* set LHSV c info */

    c->exponent = a->exponent;    /* set exponent */
    if(!AddExponent(c,b->exponent)) {
        if(w) VpFree(c);
        return 0;
    }
    VpSetSign(c,VpGetSign(a)*VpGetSign(b));    /* set sign  */
    carry = 0;
    nc = ind_c = MxIndAB;
    memset(c->frac, 0, (nc + 1) * sizeof(BDIGIT));        /* Initialize c  */
    c->Prec = nc + 1;        /* set precision */
    for(nc = 0; nc < MxIndAB; ++nc, --ind_c) {
        if(nc < MxIndB) {    /* The left triangle of the Fig. */
            ind_as = MxIndA - nc;
            ind_ae = MxIndA;
            ind_bs = MxIndB;
            ind_be = MxIndB - nc;
        } else if(nc <= MxIndA) {    /* The middle rectangular of the Fig. */
            ind_as = MxIndA - nc;
            ind_ae = MxIndA -(nc - MxIndB);
            ind_bs = MxIndB;
            ind_be = 0;
        } else if(nc > MxIndA) {    /*  The right triangle of the Fig. */
            ind_as = 0;
            ind_ae = MxIndAB - nc - 1;
            ind_bs = MxIndB -(nc - MxIndA);
            ind_be = 0;
        }

        for(i = ind_as; i <= ind_ae; ++i) {
            s = (BDIGIT_DBL)a->frac[i] * b->frac[ind_bs--];
            carry = (BDIGIT)(s / BASE);
            s -= (BDIGIT_DBL)carry * BASE;
            c->frac[ind_c] += (BDIGIT)s;
            if(c->frac[ind_c] >= BASE) {
                s = c->frac[ind_c] / BASE;
                carry += (BDIGIT)s;
                c->frac[ind_c] -= (BDIGIT)(s * BASE);
            }
            if(carry) {
                ii = ind_c;
                while(ii-- > 0) {
                    c->frac[ii] += carry;
                    if(c->frac[ii] >= BASE) {
                        carry = c->frac[ii] / BASE;
                        c->frac[ii] -= (carry * BASE);
                    } else {
                        break;
                    }
                }
            }
        }
    }
    if(w != NULL) {        /* free work variable */
        VpNmlz(c);
        VpAsgn(w, c, 1);
        VpFree(c);
        c = w;
    } else {
        VpLimitRound(c,0);
    }

Exit:
#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, "VpMult(c=a*b): c=% \n", c);
        VPrint(stdout, "      a=% \n", a);
        VPrint(stdout, "      b=% \n", b);
    }
#endif /*BIGDECIMAL_DEBUG */
    return c->Prec*BASE_FIG;
}

/*
 *   c = a / b,  remainder = r
 */
VP_EXPORT size_t
VpDivd(Real *c, Real *r, Real *a, Real *b)
{
    size_t word_a, word_b, word_c, word_r;
    size_t i, n, ind_a, ind_b, ind_c, ind_r;
    size_t nLoop;
    BDIGIT_DBL q, b1, b1p1, b1b2, b1b2p1, r1r2;
    BDIGIT borrow, borrow1, borrow2;
    BDIGIT_DBL qb;

#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, " VpDivd(c=a/b)  a=% \n", a);
        VPrint(stdout, "    b=% \n", b);
    }
#endif /*BIGDECIMAL_DEBUG */

    VpSetNaN(r);
    if(!VpIsDefOP(c,a,b,4)) goto Exit;
    if(VpIsZero(a)&&VpIsZero(b)) {
        VpSetNaN(c);
        return VpException(VP_EXCEPTION_NaN,"(VpDivd) 0/0 not defined(NaN)",0);
    }
    if(VpIsZero(b)) {
        VpSetInf(c,VpGetSign(a)*VpGetSign(b));
        return VpException(VP_EXCEPTION_ZERODIVIDE,"(VpDivd) Divide by zero",0);
    }
    if(VpIsZero(a)) {
        /* numerator a is zero  */
        VpSetZero(c,VpGetSign(a)*VpGetSign(b));
        VpSetZero(r,VpGetSign(a)*VpGetSign(b));
        goto Exit;
    }
    if(VpIsOne(b)) {
        /* divide by one  */
        VpAsgn(c, a, VpGetSign(b));
        VpSetZero(r,VpGetSign(a));
        goto Exit;
    }

    word_a = a->Prec;
    word_b = b->Prec;
    word_c = c->MaxPrec;
    word_r = r->MaxPrec;

    ind_c = 0;
    ind_r = 1;

    if(word_a >= word_r) goto space_error;

    r->frac[0] = 0;
    while(ind_r <= word_a) {
        r->frac[ind_r] = a->frac[ind_r - 1];
        ++ind_r;
    }

    while(ind_r < word_r) r->frac[ind_r++] = 0;
    while(ind_c < word_c) c->frac[ind_c++] = 0;

    /* initial procedure */
    b1 = b1p1 = b->frac[0];
    if(b->Prec <= 1) {
        b1b2p1 = b1b2 = b1p1 * BASE;
    } else {
        b1p1 = b1 + 1;
        b1b2p1 = b1b2 = b1 * BASE + b->frac[1];
        if(b->Prec > 2) ++b1b2p1;
    }

    /* */
    /* loop start */
    ind_c = word_r - 1;
    nLoop = Min(word_c,ind_c);
    ind_c = 1;
    while(ind_c < nLoop) {
        if(r->frac[ind_c] == 0) {
            ++ind_c;
            continue;
        }
        r1r2 = (BDIGIT_DBL)r->frac[ind_c] * BASE + r->frac[ind_c + 1];
        if(r1r2 == b1b2) {
            /* The first two word digits is the same */
            ind_b = 2;
            ind_a = ind_c + 2;
            while(ind_b < word_b) {
                if(r->frac[ind_a] < b->frac[ind_b]) goto div_b1p1;
                if(r->frac[ind_a] > b->frac[ind_b]) break;
                ++ind_a;
                ++ind_b;
            }
            /* The first few word digits of r and b is the same and */
            /* the first different word digit of w is greater than that */
            /* of b, so quotinet is 1 and just subtract b from r. */
            borrow = 0;        /* quotient=1, then just r-b */
            ind_b = b->Prec - 1;
            ind_r = ind_c + ind_b;
            if(ind_r >= word_r) goto space_error;
            n = ind_b;
            for(i = 0; i <= n; ++i) {
                if(r->frac[ind_r] < b->frac[ind_b] + borrow) {
                    r->frac[ind_r] += (BASE - (b->frac[ind_b] + borrow));
                    borrow = 1;
                } else {
                    r->frac[ind_r] = r->frac[ind_r] - b->frac[ind_b] - borrow;
                    borrow = 0;
                }
                --ind_r;
                --ind_b;
            }
            ++c->frac[ind_c];
            goto carry;
        }
        /* The first two word digits is not the same, */
        /* then compare magnitude, and divide actually. */
        if(r1r2 >= b1b2p1) {
            q = r1r2 / b1b2p1;  /* q == (BDIGIT)q  */
            c->frac[ind_c] += (BDIGIT)q;
            ind_r = b->Prec + ind_c - 1;
            goto sub_mult;
        }

div_b1p1:
        if(ind_c + 1 >= word_c) goto out_side;
        q = r1r2 / b1p1;  /* q == (BDIGIT)q */
        c->frac[ind_c + 1] += (BDIGIT)q;
        ind_r = b->Prec + ind_c;

sub_mult:
        borrow1 = borrow2 = 0;
        ind_b = word_b - 1;
        if(ind_r >= word_r) goto space_error;
        n = ind_b;
        for(i = 0; i <= n; ++i) {
            /* now, perform r = r - q * b */
            qb = q * b->frac[ind_b];
            if (qb < BASE) borrow1 = 0;
            else {
                borrow1 = (BDIGIT)(qb / BASE);
                qb -= (BDIGIT_DBL)borrow1 * BASE;       /* get qb < BASE */
            }
            if(r->frac[ind_r] < qb) {
                r->frac[ind_r] += (BDIGIT)(BASE - qb);
                borrow2 = borrow2 + borrow1 + 1;
            } else {
                r->frac[ind_r] -= (BDIGIT)qb;
                borrow2 += borrow1;
            }
            if(borrow2) {
                if(r->frac[ind_r - 1] < borrow2) {
                    r->frac[ind_r - 1] += (BASE - borrow2);
                    borrow2 = 1;
                } else {
                    r->frac[ind_r - 1] -= borrow2;
                    borrow2 = 0;
                }
            }
            --ind_r;
            --ind_b;
        }

        r->frac[ind_r] -= borrow2;
carry:
        ind_r = ind_c;
        while(c->frac[ind_r] >= BASE) {
            c->frac[ind_r] -= BASE;
            --ind_r;
            ++c->frac[ind_r];
        }
    }
    /* End of operation, now final arrangement */
out_side:
    c->Prec = word_c;
    c->exponent = a->exponent;
    if(!AddExponent(c,2))   return 0;
    if(!AddExponent(c,-(b->exponent))) return 0;

    VpSetSign(c,VpGetSign(a)*VpGetSign(b));
    VpNmlz(c);            /* normalize c */
    r->Prec = word_r;
    r->exponent = a->exponent;
    if(!AddExponent(r,1)) return 0;
    VpSetSign(r,VpGetSign(a));
    VpNmlz(r);            /* normalize r(remainder) */
    goto Exit;

space_error:
#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        printf("   word_a=%lu\n", word_a);
        printf("   word_b=%lu\n", word_b);
        printf("   word_c=%lu\n", word_c);
        printf("   word_r=%lu\n", word_r);
        printf("   ind_r =%lu\n", ind_r);
    }
#endif /* BIGDECIMAL_DEBUG */
    rb_bug("ERROR(VpDivd): space for remainder too small.");

Exit:
#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, " VpDivd(c=a/b), c=% \n", c);
        VPrint(stdout, "    r=% \n", r);
    }
#endif /* BIGDECIMAL_DEBUG */
    return c->Prec*BASE_FIG;
}

/*
 *  Input  a = 00000xxxxxxxx En(5 preceeding zeros)
 *  Output a = xxxxxxxx En-5
 */
static int
VpNmlz(Real *a)
{
    size_t ind_a, i;

    if (!VpIsDef(a)) goto NoVal;
    if (VpIsZero(a)) goto NoVal;

    ind_a = a->Prec;
    while (ind_a--) {
        if (a->frac[ind_a]) {
            a->Prec = ind_a + 1;
            i = 0;
            while (a->frac[i] == 0) ++i;        /* skip the first few zeros */
            if (i) {
                a->Prec -= i;
                if (!AddExponent(a, -(SIGNED_VALUE)i)) return 0;
                memmove(&a->frac[0], &a->frac[i], a->Prec*sizeof(BDIGIT));
            }
            return 1;
        }
    }
    /* a is zero(no non-zero digit) */
    VpSetZero(a, VpGetSign(a));
    return 0;

NoVal:
    a->frac[0] = 0;
    a->Prec = 1;
    return 0;
}

/*
 *  VpComp = 0  ... if a=b,
 *   Pos  ... a>b,
 *   Neg  ... a<b.
 *   999  ... result undefined(NaN)
 */
VP_EXPORT int
VpComp(Real *a, Real *b)
{
    int val;
    size_t mx, ind;
    int e;
    val = 0;
    if(VpIsNaN(a)||VpIsNaN(b)) return 999;
    if(!VpIsDef(a)) {
        if(!VpIsDef(b)) e = a->sign - b->sign;
        else             e = a->sign;
        if(e>0)   return  1;
        else if(e<0) return -1;
        else   return  0;
    }
    if(!VpIsDef(b)) {
        e = -b->sign;
        if(e>0) return  1;
        else return -1;
    }
    /* Zero check */
    if(VpIsZero(a)) {
        if(VpIsZero(b))      return 0; /* both zero */
        val = -VpGetSign(b);
        goto Exit;
    }
    if(VpIsZero(b)) {
        val = VpGetSign(a);
        goto Exit;
    }

    /* compare sign */
    if(VpGetSign(a) > VpGetSign(b)) {
        val = 1;        /* a>b */
        goto Exit;
    }
    if(VpGetSign(a) < VpGetSign(b)) {
        val = -1;        /* a<b */
        goto Exit;
    }

    /* a and b have same sign, && signe!=0,then compare exponent */
    if((a->exponent) >(b->exponent)) {
        val = VpGetSign(a);
        goto Exit;
    }
    if((a->exponent) <(b->exponent)) {
        val = -VpGetSign(b);
        goto Exit;
    }

    /* a and b have same exponent, then compare significand. */
    mx =((a->Prec) <(b->Prec)) ?(a->Prec) :(b->Prec);
    ind = 0;
    while(ind < mx) {
        if((a->frac[ind]) >(b->frac[ind])) {
            val = VpGetSign(a);
         goto Exit;
        }
        if((a->frac[ind]) <(b->frac[ind])) {
            val = -VpGetSign(b);
            goto Exit;
        }
        ++ind;
    }
    if((a->Prec) >(b->Prec)) {
        val = VpGetSign(a);
    } else if((a->Prec) <(b->Prec)) {
        val = -VpGetSign(b);
    }

Exit:
    if  (val> 1) val =  1;
    else if(val<-1) val = -1;

#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, " VpComp a=%\n", a);
        VPrint(stdout, "  b=%\n", b);
        printf("  ans=%d\n", val);
    }
#endif /* BIGDECIMAL_DEBUG */
    return (int)val;
}

#ifdef BIGDECIMAL_ENABLE_VPRINT
/*
 *    cntl_chr ... ASCIIZ Character, print control characters
 *     Available control codes:
 *      %  ... VP variable. To print '%', use '%%'.
 *      \n ... new line
 *      \b ... backspace
 *           ... tab
 *     Note: % must must not appear more than once
 *    a  ... VP variable to be printed
 */
VP_EXPORT int
VPrint(FILE *fp, const char *cntl_chr, Real *a)
{
    size_t i, j, nc, nd, ZeroSup;
    BDIGIT m, e, nn;

    /* Check if NaN & Inf. */
    if(VpIsNaN(a)) {
        fprintf(fp,SZ_NaN);
        return 8;
    }
    if(VpIsPosInf(a)) {
        fprintf(fp,SZ_INF);
        return 8;
    }
    if(VpIsNegInf(a)) {
        fprintf(fp,SZ_NINF);
        return 9;
    }
    if(VpIsZero(a)) {
        fprintf(fp,"0.0");
        return 3;
    }

    j = 0;
    nd = nc = 0;        /*  nd : number of digits in fraction part(every 10 digits, */
    /*    nd<=10). */
    /*  nc : number of caracters printed  */
    ZeroSup = 1;        /* Flag not to print the leading zeros as 0.00xxxxEnn */
    while(*(cntl_chr + j)) {
        if((*(cntl_chr + j) == '%') &&(*(cntl_chr + j + 1) != '%')) {
         nc = 0;
         if(!VpIsZero(a)) {
                if(VpGetSign(a) < 0) {
                    fprintf(fp, "-");
                    ++nc;
                }
                nc += fprintf(fp, "0.");
                for(i=0; i < a->Prec; ++i) {
                    m = BASE1;
                    e = a->frac[i];
                    while(m) {
                        nn = e / m;
                        if((!ZeroSup) || nn) {
                            nc += fprintf(fp, "%lu", (unsigned long)nn);    /* The leading zero(s) */
                            /* as 0.00xx will not */
                            /* be printed. */
                            ++nd;
                            ZeroSup = 0;    /* Set to print succeeding zeros */
                        }
                        if(nd >= 10) {    /* print ' ' after every 10 digits */
                            nd = 0;
                            nc += fprintf(fp, " ");
                        }
                        e = e - nn * m;
                        m /= 10;
                    }
                }
                nc += fprintf(fp, "E%"PRIdSIZE, VpExponent10(a));
            } else {
                nc += fprintf(fp, "0.0");
            }
        } else {
            ++nc;
            if(*(cntl_chr + j) == '\\') {
                switch(*(cntl_chr + j + 1)) {
                case 'n':
                    fprintf(fp, "\n");
                    ++j;
                    break;
                case 't':
                    fprintf(fp, "\t");
                    ++j;
                 break;
                case 'b':
                    fprintf(fp, "\n");
                    ++j;
                    break;
                default:
                    fprintf(fp, "%c", *(cntl_chr + j));
                    break;
                }
            } else {
                fprintf(fp, "%c", *(cntl_chr + j));
                if(*(cntl_chr + j) == '%') ++j;
            }
        }
        j++;
    }
    return (int)nc;
}
#endif /* BIGDECIMAL_ENABLE_VPRINT */

static void
VpFormatSt(char *psz, size_t fFmt)
{
    size_t ie, i, nf = 0;
    char ch;

    if(fFmt<=0) return;

    ie = strlen(psz);
    for(i = 0; i < ie; ++i) {
        ch = psz[i];
        if(!ch) break;
        if(ISSPACE(ch) || ch=='-' || ch=='+') continue;
        if(ch == '.')                { nf = 0;continue;}
        if(ch == 'E') break;
        nf++;
        if(nf > fFmt) {
            memmove(psz + i + 1, psz + i, ie - i + 1);
            ++ie;
            nf = 0;
            psz[i] = ' ';
        }
    }
}

VP_EXPORT ssize_t
VpExponent10(Real *a)
{
    ssize_t ex;
    size_t n;

    if (!VpHasVal(a)) return 0;

    ex = a->exponent * (ssize_t)BASE_FIG;
    n = BASE1;
    while ((a->frac[0] / n) == 0) {
         --ex;
         n /= 10;
    }
    return ex;
}

VP_EXPORT void
VpSzMantissa(Real *a,char *psz)
{
    size_t i, n, ZeroSup;
    BDIGIT_DBL m, e, nn;

    if(VpIsNaN(a)) {
        sprintf(psz,SZ_NaN);
        return;
    }
    if(VpIsPosInf(a)) {
        sprintf(psz,SZ_INF);
        return;
    }
    if(VpIsNegInf(a)) {
        sprintf(psz,SZ_NINF);
        return;
    }

    ZeroSup = 1;        /* Flag not to print the leading zeros as 0.00xxxxEnn */
    if(!VpIsZero(a)) {
        if(VpGetSign(a) < 0) *psz++ = '-';
        n = a->Prec;
        for (i=0; i < n; ++i) {
            m = BASE1;
            e = a->frac[i];
            while (m) {
                nn = e / m;
                if((!ZeroSup) || nn) {
                    sprintf(psz, "%lu", (unsigned long)nn);    /* The leading zero(s) */
                    psz += strlen(psz);
                    /* as 0.00xx will be ignored. */
                    ZeroSup = 0;    /* Set to print succeeding zeros */
                }
                e = e - nn * m;
                m /= 10;
            }
        }
        *psz = 0;
        while(psz[-1]=='0') *(--psz) = 0;
    } else {
        if(VpIsPosZero(a)) sprintf(psz, "0");
        else      sprintf(psz, "-0");
    }
}

VP_EXPORT int
VpToSpecialString(Real *a,char *psz,int fPlus)
/* fPlus =0:default, =1: set ' ' before digits , =2: set '+' before digits. */
{
    if(VpIsNaN(a)) {
        sprintf(psz,SZ_NaN);
        return 1;
    }

    if(VpIsPosInf(a)) {
        if(fPlus==1) {
           *psz++ = ' ';
        } else if(fPlus==2) {
           *psz++ = '+';
        }
        sprintf(psz,SZ_INF);
        return 1;
    }
    if(VpIsNegInf(a)) {
        sprintf(psz,SZ_NINF);
        return 1;
    }
    if(VpIsZero(a)) {
        if(VpIsPosZero(a)) {
            if(fPlus==1)      sprintf(psz, " 0.0");
            else if(fPlus==2) sprintf(psz, "+0.0");
            else              sprintf(psz, "0.0");
        } else    sprintf(psz, "-0.0");
        return 1;
    }
    return 0;
}

VP_EXPORT void
VpToString(Real *a, char *psz, size_t fFmt, int fPlus)
/* fPlus =0:default, =1: set ' ' before digits , =2:set '+' before digits. */
{
    size_t i, n, ZeroSup;
    BDIGIT shift, m, e, nn;
    char *pszSav = psz;
    ssize_t ex;

    if (VpToSpecialString(a, psz, fPlus)) return;

    ZeroSup = 1;    /* Flag not to print the leading zeros as 0.00xxxxEnn */

    if (VpGetSign(a) < 0) *psz++ = '-';
    else if (fPlus == 1)  *psz++ = ' ';
    else if (fPlus == 2)  *psz++ = '+';

    *psz++ = '0';
    *psz++ = '.';
    n = a->Prec;
    for(i=0;i < n;++i) {
        m = BASE1;
        e = a->frac[i];
        while(m) {
            nn = e / m;
            if((!ZeroSup) || nn) {
                sprintf(psz, "%lu", (unsigned long)nn);    /* The reading zero(s) */
                psz += strlen(psz);
                /* as 0.00xx will be ignored. */
                ZeroSup = 0;    /* Set to print succeeding zeros */
            }
            e = e - nn * m;
            m /= 10;
        }
    }
    ex = a->exponent * (ssize_t)BASE_FIG;
    shift = BASE1;
    while(a->frac[0] / shift == 0) {
        --ex;
        shift /= 10;
    }
    while(psz[-1]=='0') *(--psz) = 0;
    sprintf(psz, "E%"PRIdSIZE, ex);
    if(fFmt) VpFormatSt(pszSav, fFmt);
}

VP_EXPORT void
VpToFString(Real *a, char *psz, size_t fFmt, int fPlus)
/* fPlus =0:default,=1: set ' ' before digits ,set '+' before digits. */
{
    size_t i, n;
    BDIGIT m, e, nn;
    char *pszSav = psz;
    ssize_t ex;

    if(VpToSpecialString(a,psz,fPlus)) return;

    if(VpGetSign(a) < 0) *psz++ = '-';
    else if(fPlus==1)    *psz++ = ' ';
    else if(fPlus==2)    *psz++ = '+';

    n  = a->Prec;
    ex = a->exponent;
    if(ex<=0) {
       *psz++ = '0';*psz++ = '.';
       while(ex<0) {
          for(i=0;i<BASE_FIG;++i) *psz++ = '0';
          ++ex;
       }
       ex = -1;
    }

    for(i=0;i < n;++i) {
       --ex;
       if(i==0 && ex >= 0) {
           sprintf(psz, "%lu", (unsigned long)a->frac[i]);
           psz += strlen(psz);
       } else {
           m = BASE1;
           e = a->frac[i];
           while(m) {
               nn = e / m;
               *psz++ = (char)(nn + '0');
               e = e - nn * m;
               m /= 10;
           }
       }
       if(ex == 0) *psz++ = '.';
    }
    while(--ex>=0) {
       m = BASE;
       while(m/=10) *psz++ = '0';
       if(ex == 0) *psz++ = '.';
    }
    *psz = 0;
    while(psz[-1]=='0') *(--psz) = 0;
    if(psz[-1]=='.') sprintf(psz, "0");
    if(fFmt) VpFormatSt(pszSav, fFmt);
}

/*
 *  [Output]
 *   a[]  ... variable to be assigned the value.
 *  [Input]
 *   int_chr[]  ... integer part(may include '+/-').
 *   ni   ... number of characters in int_chr[],not including '+/-'.
 *   frac[]  ... fraction part.
 *   nf   ... number of characters in frac[].
 *   exp_chr[]  ... exponent part(including '+/-').
 *   ne   ... number of characters in exp_chr[],not including '+/-'.
 */
VP_EXPORT int
VpCtoV(Real *a, const char *int_chr, size_t ni, const char *frac, size_t nf, const char *exp_chr, size_t ne)
{
    size_t i, j, ind_a, ma, mi, me;
    size_t loc;
    SIGNED_VALUE e, es, eb, ef;
    int  sign, signe, exponent_overflow;

    /* get exponent part */
    e = 0;
    ma = a->MaxPrec;
    mi = ni;
    me = ne;
    signe = 1;
    exponent_overflow = 0;
    memset(a->frac, 0, ma * sizeof(BDIGIT));
    if (ne > 0) {
        i = 0;
        if (exp_chr[0] == '-') {
            signe = -1;
            ++i;
            ++me;
        }
        else if (exp_chr[0] == '+') {
            ++i;
            ++me;
        }
        while (i < me) {
            es = e * (SIGNED_VALUE)BASE_FIG;
            e = e * 10 + exp_chr[i] - '0';
            if (es > (SIGNED_VALUE)(e*BASE_FIG)) {
                exponent_overflow = 1;
                e = es; /* keep sign */
                break;
            }
            ++i;
        }
    }

    /* get integer part */
    i = 0;
    sign = 1;
    if(1 /*ni >= 0*/) {
        if(int_chr[0] == '-') {
            sign = -1;
            ++i;
            ++mi;
        } else if(int_chr[0] == '+') {
            ++i;
            ++mi;
        }
    }

    e = signe * e;        /* e: The value of exponent part. */
    e = e + ni;        /* set actual exponent size. */

    if (e > 0) signe = 1;
    else       signe = -1;

    /* Adjust the exponent so that it is the multiple of BASE_FIG. */
    j = 0;
    ef = 1;
    while (ef) {
        if (e >= 0) eb =  e;
        else        eb = -e;
        ef = eb / (SIGNED_VALUE)BASE_FIG;
        ef = eb - ef * (SIGNED_VALUE)BASE_FIG;
        if (ef) {
            ++j;        /* Means to add one more preceeding zero */
            ++e;
        }
    }

    eb = e / (SIGNED_VALUE)BASE_FIG;

    if (exponent_overflow) {
        int zero = 1;
        for (     ; i < mi && zero; i++) zero = int_chr[i] == '0';
        for (i = 0; i < nf && zero; i++) zero = frac[i] == '0';
        if (!zero && signe > 0) {
            VpSetInf(a, sign);
            VpException(VP_EXCEPTION_INFINITY, "exponent overflow",0);
        }
        else VpSetZero(a, sign);
        return 1;
    }

    ind_a = 0;
    while (i < mi) {
        a->frac[ind_a] = 0;
        while ((j < BASE_FIG) && (i < mi)) {
            a->frac[ind_a] = a->frac[ind_a] * 10 + int_chr[i] - '0';
            ++j;
            ++i;
        }
        if (i < mi) {
            ++ind_a;
            if (ind_a >= ma) goto over_flow;
            j = 0;
        }
    }
    loc = 1;

    /* get fraction part */

    i = 0;
    while(i < nf) {
        while((j < BASE_FIG) && (i < nf)) {
            a->frac[ind_a] = a->frac[ind_a] * 10 + frac[i] - '0';
            ++j;
            ++i;
        }
        if(i < nf) {
            ++ind_a;
            if(ind_a >= ma) goto over_flow;
            j = 0;
        }
    }
    goto Final;

over_flow:
    rb_warn("Conversion from String to BigDecimal overflow (last few digits discarded).");

Final:
    if (ind_a >= ma) ind_a = ma - 1;
    while (j < BASE_FIG) {
        a->frac[ind_a] = a->frac[ind_a] * 10;
        ++j;
    }
    a->Prec = ind_a + 1;
    a->exponent = eb;
    VpSetSign(a,sign);
    VpNmlz(a);
    return 1;
}

/*
 * [Input]
 *   *m  ... Real
 * [Output]
 *   *d  ... fraction part of m(d = 0.xxxxxxx). where # of 'x's is fig.
 *   *e  ... exponent of m.
 * DBLE_FIG ... Number of digits in a double variable.
 *
 *  m -> d*10**e, 0<d<BASE
 * [Returns]
 *   0 ... Zero
 *   1 ... Normal
 *   2 ... Infinity
 *  -1 ... NaN
 */
VP_EXPORT int
VpVtoD(double *d, SIGNED_VALUE *e, Real *m)
{
    size_t ind_m, mm, fig;
    double div;
    int    f = 1;

    if(VpIsNaN(m)) {
        *d = VpGetDoubleNaN();
        *e = 0;
        f = -1; /* NaN */
        goto Exit;
    } else
    if(VpIsPosZero(m)) {
        *d = 0.0;
        *e = 0;
        f  = 0;
        goto Exit;
    } else
    if(VpIsNegZero(m)) {
        *d = VpGetDoubleNegZero();
        *e = 0;
        f  = 0;
        goto Exit;
    } else
    if(VpIsPosInf(m)) {
        *d = VpGetDoublePosInf();
        *e = 0;
        f  = 2;
        goto Exit;
    } else
    if(VpIsNegInf(m)) {
        *d = VpGetDoubleNegInf();
        *e = 0;
        f  = 2;
        goto Exit;
    }
    /* Normal number */
    fig =(DBLE_FIG + BASE_FIG - 1) / BASE_FIG;
    ind_m = 0;
    mm = Min(fig,(m->Prec));
    *d = 0.0;
    div = 1.;
    while(ind_m < mm) {
        div /= (double)BASE;
        *d = *d + (double)m->frac[ind_m++] * div;
    }
    *e = m->exponent * (SIGNED_VALUE)BASE_FIG;
    *d *= VpGetSign(m);

Exit:
#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, " VpVtoD: m=%\n", m);
        printf("   d=%e * 10 **%ld\n", *d, *e);
        printf("   DBLE_FIG = %d\n", DBLE_FIG);
    }
#endif /*BIGDECIMAL_DEBUG */
    return f;
}

/*
 * m <- d
 */
VP_EXPORT void
VpDtoV(Real *m, double d)
{
    size_t ind_m, mm;
    SIGNED_VALUE ne;
    BDIGIT i;
    double  val, val2;

    if(isnan(d)) {
        VpSetNaN(m);
        goto Exit;
    }
    if(isinf(d)) {
        if(d>0.0) VpSetPosInf(m);
        else   VpSetNegInf(m);
        goto Exit;
    }

    if(d == 0.0) {
        VpSetZero(m,1);
        goto Exit;
    }
    val =(d > 0.) ? d :(-d);
    ne = 0;
    if(val >= 1.0) {
        while(val >= 1.0) {
            val /= (double)BASE;
            ++ne;
        }
    } else {
        val2 = 1.0 /(double)BASE;
        while(val < val2) {
            val *= (double)BASE;
            --ne;
        }
    }
    /* Now val = 0.xxxxx*BASE**ne */

    mm = m->MaxPrec;
    memset(m->frac, 0, mm * sizeof(BDIGIT));
    for(ind_m = 0;val > 0.0 && ind_m < mm;ind_m++) {
        val *= (double)BASE;
        i = (BDIGIT)val;
        val -= (double)i;
        m->frac[ind_m] = i;
    }
    if(ind_m >= mm) ind_m = mm - 1;
    VpSetSign(m, (d > 0.0) ? 1 : -1);
    m->Prec = ind_m + 1;
    m->exponent = ne;

    VpInternalRound(m, 0, (m->Prec > 0) ? m->frac[m->Prec-1] : 0,
                      (BDIGIT)(val*(double)BASE));

Exit:
#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        printf("VpDtoV d=%30.30e\n", d);
        VPrint(stdout, "  m=%\n", m);
    }
#endif /* BIGDECIMAL_DEBUG */
    return;
}

/*
 *  m <- ival
 */
#if 0  /* unused */
VP_EXPORT void
VpItoV(Real *m, SIGNED_VALUE ival)
{
    size_t mm, ind_m;
    size_t val, v1, v2, v;
    int isign;
    SIGNED_VALUE ne;

    if(ival == 0) {
        VpSetZero(m,1);
        goto Exit;
    }
    isign = 1;
    val = ival;
    if(ival < 0) {
        isign = -1;
        val =(size_t)(-ival);
    }
    ne = 0;
    ind_m = 0;
    mm = m->MaxPrec;
    while(ind_m < mm) {
        m->frac[ind_m] = 0;
        ++ind_m;
    }
    ind_m = 0;
    while(val > 0) {
        if(val) {
         v1 = val;
         v2 = 1;
            while(v1 >= BASE) {
                v1 /= BASE;
                v2 *= BASE;
            }
            val = val - v2 * v1;
            v = v1;
        } else {
            v = 0;
        }
        m->frac[ind_m] = v;
        ++ind_m;
        ++ne;
    }
    m->Prec = ind_m - 1;
    m->exponent = ne;
    VpSetSign(m,isign);
    VpNmlz(m);

Exit:
#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        printf(" VpItoV i=%d\n", ival);
        VPrint(stdout, "  m=%\n", m);
    }
#endif /* BIGDECIMAL_DEBUG */
    return;
}
#endif

/*
 * y = SQRT(x),  y*y - x =>0
 */
VP_EXPORT int
VpSqrt(Real *y, Real *x)
{
    Real *f = NULL;
    Real *r = NULL;
    size_t y_prec, f_prec;
    SIGNED_VALUE n, e;
    SIGNED_VALUE prec;
    ssize_t nr;
    double val;

    /* Zero, NaN or Infinity ? */
    if(!VpHasVal(x)) {
        if(VpIsZero(x)||VpGetSign(x)>0) {
            VpAsgn(y,x,1);
            goto Exit;
        }
        VpSetNaN(y);
        return VpException(VP_EXCEPTION_OP,"(VpSqrt) SQRT(NaN or negative value)",0);
        goto Exit;
    }

     /* Negative ? */
    if(VpGetSign(x) < 0) {
        VpSetNaN(y);
        return VpException(VP_EXCEPTION_OP,"(VpSqrt) SQRT(negative value)",0);
    }

    /* One ? */
    if(VpIsOne(x)) {
        VpSetOne(y);
        goto Exit;
    }

    n = (SIGNED_VALUE)y->MaxPrec;
    if (x->MaxPrec > (size_t)n) n = (ssize_t)x->MaxPrec;
    /* allocate temporally variables  */
    f = VpAlloc(y->MaxPrec * (BASE_FIG + 2), "#1");
    r = VpAlloc((n + n) * (BASE_FIG + 2), "#1");

    nr = 0;
    y_prec = y->MaxPrec;
    f_prec = f->MaxPrec;

    prec = x->exponent - (ssize_t)y_prec;
    if (x->exponent > 0)
        ++prec;
    else
        --prec;

    VpVtoD(&val, &e, x);    /* val <- x  */
    e /= (SIGNED_VALUE)BASE_FIG;
    n = e / 2;
    if (e - n * 2 != 0) {
        val /= BASE;
        n = (e + 1) / 2;
    }
    VpDtoV(y, sqrt(val));    /* y <- sqrt(val) */
    y->exponent += n;
    n = (SIGNED_VALUE)((DBLE_FIG + BASE_FIG - 1) / BASE_FIG);
    y->MaxPrec = Min((size_t)n , y_prec);
    f->MaxPrec = y->MaxPrec + 1;
    n = (SIGNED_VALUE)(y_prec * BASE_FIG);
    if (n < (SIGNED_VALUE)maxnr) n = (SIGNED_VALUE)maxnr;
    do {
        y->MaxPrec *= 2;
        if (y->MaxPrec > y_prec) y->MaxPrec = y_prec;
        f->MaxPrec = y->MaxPrec;
        VpDivd(f, r, x, y);     /* f = x/y    */
        VpAddSub(r, f, y, -1);  /* r = f - y  */
        VpMult(f, VpPt5, r);    /* f = 0.5*r  */
        if(VpIsZero(f))         goto converge;
        VpAddSub(r, f, y, 1);   /* r = y + f  */
        VpAsgn(y, r, 1);        /* y = r      */
        if(f->exponent <= prec) goto converge;
    } while(++nr < n);
    /* */
#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        printf("ERROR(VpSqrt): did not converge within %ld iterations.\n",
            nr);
    }
#endif /* BIGDECIMAL_DEBUG */
    y->MaxPrec = y_prec;

converge:
    VpChangeSign(y, 1);
#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VpMult(r, y, y);
        VpAddSub(f, x, r, -1);
        printf("VpSqrt: iterations = %"PRIdSIZE"\n", nr);
        VPrint(stdout, "  y =% \n", y);
        VPrint(stdout, "  x =% \n", x);
        VPrint(stdout, "  x-y*y = % \n", f);
    }
#endif /* BIGDECIMAL_DEBUG */
    y->MaxPrec = y_prec;

Exit:
    VpFree(f);
    VpFree(r);
    return 1;
}

/*
 *
 * nf: digit position for operation.
 *
 */
VP_EXPORT int
VpMidRound(Real *y, unsigned short f, ssize_t nf)
/*
 * Round reletively from the decimal point.
 *    f: rounding mode
 *   nf: digit location to round from the the decimal point.
 */
{
    /* fracf: any positive digit under rounding position? */
    /* fracf_1further: any positive digits under one further than the rounding position? */
    /* exptoadd: number of digits needed to compensate negative nf */
    int fracf, fracf_1further;
    ssize_t n,i,ix,ioffset, exptoadd;
    BDIGIT v, shifter;
    BDIGIT div;

    nf += y->exponent * (ssize_t)BASE_FIG;
    exptoadd=0;
    if (nf < 0) {
        /* rounding position too left(large). */
        if((f!=VP_ROUND_CEIL) && (f!=VP_ROUND_FLOOR)) {
            VpSetZero(y,VpGetSign(y)); /* truncate everything */
            return 0;
        }
        exptoadd = -nf;
        nf = 0;
    }

    ix = nf / (ssize_t)BASE_FIG;
    if ((size_t)ix >= y->Prec) return 0;  /* rounding position too right(small). */
    v = y->frac[ix];

    ioffset = nf - ix*(ssize_t)BASE_FIG;
    n = (ssize_t)BASE_FIG - ioffset - 1;
    for (shifter=1,i=0; i<n; ++i) shifter *= 10;

    /* so the representation used (in y->frac) is an array of BDIGIT, where
       each BDIGIT contains a value between 0 and BASE-1, consisting of BASE_FIG
       decimal places.

       (that numbers of decimal places are typed as ssize_t is somewhat confusing)

       nf is now position (in decimal places) of the digit from the start of
          the array.
       ix is the position (in BDIGITS) of the BDIGIT containing the decimal digit,
          from the start of the array.
       v is the value of this BDIGIT
       ioffset is the number of extra decimal places along of this decimal digit
          within v.
       n is the number of decimal digits remaining within v after this decimal digit
       shifter is 10**n,
       v % shifter are the remaining digits within v
       v % (shifter * 10) are the digit together with the remaining digits within v
       v / shifter are the digit's predecessors together with the digit
       div = v / shifter / 10 is just the digit's precessors
       (v / shifter) - div*10 is just the digit, which is what v ends up being reassigned to.
    */

    fracf = (v % (shifter * 10) > 0);
    fracf_1further = ((v % shifter) > 0);

    v /= shifter;
    div = v / 10;
    v = v - div*10;
    /* now v is just the digit required.
       now fracf is whether the digit or any of the remaining digits within v are non-zero
       now fracf_1further is whether any of the remaining digits within v are non-zero
    */

    /* now check all the remaining BDIGITS for zero-ness a whole BDIGIT at a time.
       if we spot any non-zeroness, that means that we foudn a positive digit under
       rounding position, and we also found a positive digit under one further than
       the rounding position, so both searches (to see if any such non-zero digit exists)
       can stop */

    for (i=ix+1; (size_t)i < y->Prec; i++) {
        if (y->frac[i] % BASE) {
            fracf = fracf_1further = 1;
            break;
        }
    }

    /* now fracf = does any positive digit exist under the rounding position?
       now fracf_1further = does any positive digit exist under one further than the
       rounding position?
       now v = the first digit under the rounding position */

    /* drop digits after pointed digit */
    memset(y->frac+ix+1, 0, (y->Prec - (ix+1)) * sizeof(BDIGIT));

    switch(f) {
    case VP_ROUND_DOWN: /* Truncate */
         break;
    case VP_ROUND_UP:   /* Roundup */
        if (fracf) ++div;
        break;
    case VP_ROUND_HALF_UP:
        if (v>=5) ++div;
        break;
    case VP_ROUND_HALF_DOWN:
        if (v > 5 || (v == 5 && fracf_1further)) ++div;
        break;
    case VP_ROUND_CEIL:
        if (fracf && (VpGetSign(y)>0)) ++div;
        break;
    case VP_ROUND_FLOOR:
        if (fracf && (VpGetSign(y)<0)) ++div;
        break;
    case VP_ROUND_HALF_EVEN: /* Banker's rounding */
        if (v > 5) ++div;
        else if (v == 5) {
            if (fracf_1further) {
              ++div;
            }
            else {
                if (ioffset == 0) {
                    /* v is the first decimal digit of its BDIGIT;
                       need to grab the previous BDIGIT if present
                       to check for evenness of the previous decimal
                       digit (which is same as that of the BDIGIT since
                       base 10 has a factor of 2) */
                    if (ix && (y->frac[ix-1] % 2)) ++div;
                }
                else {
                    if (div % 2) ++div;
                }
            }
        }
        break;
    }
    for (i=0; i<=n; ++i) div *= 10;
    if (div>=BASE) {
        if(ix) {
            y->frac[ix] = 0;
            VpRdup(y,ix);
        } else {
            short s = VpGetSign(y);
            SIGNED_VALUE e = y->exponent;
            VpSetOne(y);
            VpSetSign(y, s);
            y->exponent = e+1;
        }
    } else {
        y->frac[ix] = div;
        VpNmlz(y);
    }
    if (exptoadd > 0) {
        y->exponent += (SIGNED_VALUE)(exptoadd/BASE_FIG);
        exptoadd %= (ssize_t)BASE_FIG;
        for(i=0;i<exptoadd;i++) {
            y->frac[0] *= 10;
            if (y->frac[0] >= BASE) {
                y->frac[0] /= BASE;
                y->exponent++;
            }
        }
    }
    return 1;
}

VP_EXPORT int
VpLeftRound(Real *y, unsigned short f, ssize_t nf)
/*
 * Round from the left hand side of the digits.
 */
{
    BDIGIT v;
    if (!VpHasVal(y)) return 0; /* Unable to round */
    v = y->frac[0];
    nf -= VpExponent(y)*(ssize_t)BASE_FIG;
    while ((v /= 10) != 0) nf--;
    nf += (ssize_t)BASE_FIG-1;
    return VpMidRound(y,f,nf);
}

VP_EXPORT int
VpActiveRound(Real *y, Real *x, unsigned short f, ssize_t nf)
{
    /* First,assign whole value in truncation mode */
    if (VpAsgn(y, x, 10) <= 1) return 0; /* Zero,NaN,or Infinity */
    return VpMidRound(y,f,nf);
}

static int
VpLimitRound(Real *c, size_t ixDigit)
{
    size_t ix = VpGetPrecLimit();
    if(!VpNmlz(c))    return -1;
    if(!ix)           return 0;
    if(!ixDigit) ixDigit = c->Prec-1;
    if((ix+BASE_FIG-1)/BASE_FIG > ixDigit+1) return 0;
    return VpLeftRound(c, VpGetRoundMode(), (ssize_t)ix);
}

/* If I understand correctly, this is only ever used to round off the final decimal
   digit of precision */
static void
VpInternalRound(Real *c, size_t ixDigit, BDIGIT vPrev, BDIGIT v)
{
    int f = 0;

    unsigned short const rounding_mode = VpGetRoundMode();

    if (VpLimitRound(c, ixDigit)) return;
    if (!v) return;

    v /= BASE1;
    switch (rounding_mode) {
    case VP_ROUND_DOWN:
        break;
    case VP_ROUND_UP:
        if (v) f = 1;
        break;
    case VP_ROUND_HALF_UP:
        if (v >= 5) f = 1;
        break;
    case VP_ROUND_HALF_DOWN:
        /* this is ok - because this is the last digit of precision,
           the case where v == 5 and some further digits are nonzero
           will never occur */
        if (v >= 6) f = 1;
        break;
    case VP_ROUND_CEIL:
        if (v && (VpGetSign(c) > 0)) f = 1;
        break;
    case VP_ROUND_FLOOR:
        if (v && (VpGetSign(c) < 0)) f = 1;
        break;
    case VP_ROUND_HALF_EVEN:  /* Banker's rounding */
        /* as per VP_ROUND_HALF_DOWN, because this is the last digit of precision,
           there is no case to worry about where v == 5 and some further digits are nonzero */
        if (v > 5) f = 1;
        else if (v == 5 && vPrev % 2) f = 1;
        break;
    }
    if (f) {
        VpRdup(c, ixDigit);
        VpNmlz(c);
    }
}

/*
 *  Rounds up m(plus one to final digit of m).
 */
static int
VpRdup(Real *m, size_t ind_m)
{
    BDIGIT carry;

    if (!ind_m) ind_m = m->Prec;

    carry = 1;
    while (carry > 0 && (ind_m--)) {
        m->frac[ind_m] += carry;
        if (m->frac[ind_m] >= BASE) m->frac[ind_m] -= BASE;
        else                        carry = 0;
    }
    if(carry > 0) {        /* Overflow,count exponent and set fraction part be 1  */
        if (!AddExponent(m, 1)) return 0;
        m->Prec = m->frac[0] = 1;
    } else {
        VpNmlz(m);
    }
    return 1;
}

/*
 *  y = x - fix(x)
 */
VP_EXPORT void
VpFrac(Real *y, Real *x)
{
    size_t my, ind_y, ind_x;

    if(!VpHasVal(x)) {
        VpAsgn(y,x,1);
        goto Exit;
    }

    if (x->exponent > 0 && (size_t)x->exponent >= x->Prec) {
        VpSetZero(y,VpGetSign(x));
        goto Exit;
    }
    else if(x->exponent <= 0) {
        VpAsgn(y, x, 1);
        goto Exit;
    }

    /* satisfy: x->exponent > 0 */

    y->Prec = x->Prec - (size_t)x->exponent;
    y->Prec = Min(y->Prec, y->MaxPrec);
    y->exponent = 0;
    VpSetSign(y,VpGetSign(x));
    ind_y = 0;
    my = y->Prec;
    ind_x = x->exponent;
    while(ind_y < my) {
        y->frac[ind_y] = x->frac[ind_x];
        ++ind_y;
        ++ind_x;
    }
    VpNmlz(y);

Exit:
#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, "VpFrac y=%\n", y);
        VPrint(stdout, "    x=%\n", x);
    }
#endif /* BIGDECIMAL_DEBUG */
    return;
}

/*
 *   y = x ** n
 */
VP_EXPORT int
VpPower(Real *y, Real *x, SIGNED_VALUE n)
{
    size_t s, ss;
    ssize_t sign;
    Real *w1 = NULL;
    Real *w2 = NULL;

    if(VpIsZero(x)) {
        if(n==0) {
           VpSetOne(y);
           goto Exit;
        }
        sign = VpGetSign(x);
        if(n<0) {
           n = -n;
           if(sign<0) sign = (n%2)?(-1):(1);
           VpSetInf (y,sign);
        } else {
           if(sign<0) sign = (n%2)?(-1):(1);
           VpSetZero(y,sign);
        }
        goto Exit;
    }
    if(VpIsNaN(x)) {
        VpSetNaN(y);
        goto Exit;
    }
    if(VpIsInf(x)) {
        if(n==0) {
            VpSetOne(y);
            goto Exit;
        }
        if(n>0) {
            VpSetInf(y, (n%2==0 || VpIsPosInf(x)) ? 1 : -1);
            goto Exit;
        }
        VpSetZero(y, (n%2==0 || VpIsPosInf(x)) ? 1 : -1);
        goto Exit;
    }

    if((x->exponent == 1) &&(x->Prec == 1) &&(x->frac[0] == 1)) {
        /* abs(x) = 1 */
        VpSetOne(y);
        if(VpGetSign(x) > 0) goto Exit;
        if((n % 2) == 0) goto Exit;
        VpSetSign(y, -1);
        goto Exit;
    }

    if(n > 0) sign = 1;
    else if(n < 0) {
        sign = -1;
        n = -n;
    } else {
        VpSetOne(y);
        goto Exit;
    }

    /* Allocate working variables  */

    w1 = VpAlloc((y->MaxPrec + 2) * BASE_FIG, "#0");
    w2 = VpAlloc((w1->MaxPrec * 2 + 1) * BASE_FIG, "#0");
    /* calculation start */

    VpAsgn(y, x, 1);
    --n;
    while(n > 0) {
        VpAsgn(w1, x, 1);
        s = 1;
        while (ss = s, (s += s) <= (size_t)n) {
            VpMult(w2, w1, w1);
            VpAsgn(w1, w2, 1);
        }
        n -= (SIGNED_VALUE)ss;
        VpMult(w2, y, w1);
        VpAsgn(y, w2, 1);
    }
    if(sign < 0) {
        VpDivd(w1, w2, VpConstOne, y);
        VpAsgn(y, w1, 1);
    }

Exit:
#ifdef BIGDECIMAL_DEBUG
    if(gfDebug) {
        VPrint(stdout, "VpPower y=%\n", y);
        VPrint(stdout, "VpPower x=%\n", x);
        printf("  n=%d\n", n);
    }
#endif /* BIGDECIMAL_DEBUG */
    VpFree(w2);
    VpFree(w1);
    return 1;
}

#ifdef BIGDECIMAL_DEBUG
int
VpVarCheck(Real * v)
/*
 * Checks the validity of the Real variable v.
 * [Input]
 *   v ... Real *, variable to be checked.
 * [Returns]
 *   0  ... correct v.
 *   other ... error
 */
{
    size_t i;

    if(v->MaxPrec <= 0) {
        printf("ERROR(VpVarCheck): Illegal Max. Precision(=%"PRIuSIZE")\n",
            v->MaxPrec);
        return 1;
    }
    if((v->Prec <= 0) ||((v->Prec) >(v->MaxPrec))) {
        printf("ERROR(VpVarCheck): Illegal Precision(=%"PRIuSIZE")\n", v->Prec);
        printf("       Max. Prec.=%"PRIuSIZE"\n", v->MaxPrec);
        return 2;
    }
    for(i = 0; i < v->Prec; ++i) {
        if((v->frac[i] >= BASE)) {
            printf("ERROR(VpVarCheck): Illegal fraction\n");
            printf("       Frac[%"PRIuSIZE"]=%lu\n", i, v->frac[i]);
            printf("       Prec.   =%"PRIuSIZE"\n", v->Prec);
            printf("       Exp. =%"PRIdVALUE"\n", v->exponent);
            printf("       BASE =%lu\n", BASE);
            return 3;
        }
    }
    return 0;
}
#endif /* BIGDECIMAL_DEBUG */