/ext/bigdecimal/bigdecimal.c

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/*
 *
 * 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 */
#include "bigdecimal.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;

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;

/* 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++] = (unsigned long)(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

/*
 * ================== 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
    */
    return rb_str_new2("1.0.1");
}

/*
 *   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);

/*
 *  **** 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 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;
}

static Real *
GetVpValue(VALUE v, int must)
{
    Real *pv;
    VALUE bg;
    char szD[128];
    VALUE orig = Qundef;
    int util_loaded = 0;

again:
    switch(TYPE(v))
    {
    case T_RATIONAL:
        if(orig == Qundef ? (orig = v, 1) : orig != v) {
            if(!util_loaded) {
                rb_require("bigdecimal/util");
                util_loaded = 1;
            }
            v = rb_funcall2(v, rb_intern("to_d"), 0, 0);
            goto again;
        }
        v = orig;
        goto SomeOneMayDoIt;

    case T_DATA:
        if(rb_typeddata_is_kind_of(v, &BigDecimal_data_type)) {
            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) {
        rb_raise(rb_eTypeError, "%s can't be coerced into BigDecimal",
                    rb_special_const_p(v)?
                    RSTRING_PTR(rb_inspect(v)):
                    rb_obj_classname(v)
                );
    }
    return NULL; /* NULL means to coerce */
}

/* 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, 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;
}

/* 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);
	ssize_t dpower = e - (ssize_t)RSTRING_LEN(digits);

	if (VpGetSign(p) < 0) {
	    numerator = rb_funcall(numerator, '*', 1, INT2FIX(-1));
	}
	if (dpower < 0) {
	    return rb_funcall(numerator, rb_intern("div"), 1,
			      rb_funcall(INT2FIX(10), rb_intern("**"), 1,
					 INT2FIX(-dpower)));
	}
        return rb_funcall(numerator, '*', 1,
			  rb_funcall(INT2FIX(10), rb_intern("**"), 1,
				     INT2FIX(dpower)));
    }
}

/* 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 {
	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;
    GUARD_OBJ(a,GetVpValue(self,1));
    b = GetVpValue(r,0);
    if(!b) {
	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 '>': case '<': f = (ID)op; 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;
    }
    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,(int)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,(int)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,(int)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,(int)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;
}

/* call-seq:
 * power(n)
 *
 * 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(VALUE self, VALUE p)
{
    ENTER(5);
    Real *x, *y;
    ssize_t mp, ma;
    SIGNED_VALUE n;

    Check_Type(p, T_FIXNUM);
    n = FIX2INT(p);
    ma = n;
    if (ma < 0)  ma = -ma;
    if (ma == 0) ma = 1;

    GUARD_OBJ(x, GetVpValue(self, 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, n);
    return ToValue(y);
}

static VALUE
BigDecimal_global_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);
    }
    SafeStringValue(iniValue);
    GUARD_OBJ(pv,VpCreateRbObject(mf, RSTRING_PTR(iniValue)));
    return ToValue(pv);
}

 /* call-seq:
  * new(initial, digits)
  *
  * Create a new BigDecimal object.
  *
  * initial:: The initial value, as a String. Spaces are ignored, 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);
    }
    SafeStringValue(iniValue);
    GUARD_OBJ(pv,VpNewRbClass(mf, RSTRING_PTR(iniValue),self));
    return ToValue(pv);
}

 /* 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 Qnil;
}

/* 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 Qnil;
}

/* 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") / …