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520053232e
git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@26627 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
4860 lines
124 KiB
C
4860 lines
124 KiB
C
/*
|
||
*
|
||
* 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
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||
* of this BigDecimal distribution.
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*
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* NOTE: Change log in this source removed to reduce source code size.
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* See rev. 1.25 if needed.
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*
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||
*/
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||
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||
#include "ruby/ruby.h"
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#include <ctype.h>
|
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#include <stdio.h>
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||
#include <stdlib.h>
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||
#include <string.h>
|
||
#include <errno.h>
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||
#include <float.h>
|
||
#include <math.h>
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||
#include "math.h"
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||
|
||
#ifdef HAVE_IEEEFP_H
|
||
#include <ieeefp.h>
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#endif
|
||
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||
/* #define ENABLE_NUMERIC_STRING */
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||
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||
VALUE rb_cBigDecimal;
|
||
|
||
#include "bigdecimal.h"
|
||
|
||
/* 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);}
|
||
|
||
#ifndef BASE_FIG
|
||
static U_LONG BASE_FIG = 4; /* =log10(BASE) */
|
||
static U_LONG BASE = 10000L; /* Base value(value must be 10**BASE_FIG) */
|
||
/* The value of BASE**2 + BASE must be represented */
|
||
/* within one U_LONG. */
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||
static U_LONG HALF_BASE = 5000L;/* =BASE/2 */
|
||
static U_LONG BASE1 = 1000L; /* =BASE/10 */
|
||
#else
|
||
#ifndef BASE
|
||
#error BASE_FIG is defined but BASE is not
|
||
#endif
|
||
#define HALF_BASE (BASE/2)
|
||
#define BASE1 (BASE/10)
|
||
#endif
|
||
#ifndef DBLE_FIG
|
||
#define DBLE_FIG (DBL_DIG+1) /* figure of double */
|
||
#endif
|
||
|
||
/*
|
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* ================== Ruby Interface part ==========================
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*/
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#define DoSomeOne(x,y,f) rb_num_coerce_bin(x,y,f)
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||
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/*
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* Returns the BigDecimal version number.
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*
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* Ruby 1.8.0 returns 1.0.0.
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* Ruby 1.8.1 thru 1.8.3 return 1.0.1.
|
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*/
|
||
static VALUE
|
||
BigDecimal_version(VALUE self)
|
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{
|
||
/*
|
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* 1.0.0: Ruby 1.8.0
|
||
* 1.0.1: Ruby 1.8.1
|
||
*/
|
||
return rb_str_new2("1.0.1");
|
||
}
|
||
|
||
/*
|
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* VP routines used in BigDecimal part
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*/
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static unsigned short VpGetException(void);
|
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static void VpSetException(unsigned short f);
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static void VpInternalRound(Real *c,int ixDigit,U_LONG vPrev,U_LONG v);
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||
static int VpLimitRound(Real *c,U_LONG ixDigit);
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||
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/*
|
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* **** BigDecimal part ****
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*/
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||
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static void
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BigDecimal_delete(void *pv)
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{
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VpFree(pv);
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}
|
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static size_t
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BigDecimal_memsize(const void *ptr)
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{
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const Real *pv = ptr;
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return pv ? (sizeof(*pv) + pv->MaxPrec * sizeof(U_LONG)) : 0;
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}
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|
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static const rb_data_type_t BigDecimal_data_type = {
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"BigDecimal",
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0, BigDecimal_delete, BigDecimal_memsize,
|
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};
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static VALUE
|
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ToValue(Real *p)
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{
|
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if(VpIsNaN(p)) {
|
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VpException(VP_EXCEPTION_NaN,"Computation results to 'NaN'(Not a Number)",0);
|
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} else if(VpIsPosInf(p)) {
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VpException(VP_EXCEPTION_INFINITY,"Computation results to 'Infinity'",0);
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} else if(VpIsNegInf(p)) {
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VpException(VP_EXCEPTION_INFINITY,"Computation results to '-Infinity'",0);
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}
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return p->obj;
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}
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static Real *
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GetVpValue(VALUE v, int must)
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{
|
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Real *pv;
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VALUE bg;
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char szD[128];
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VALUE orig = Qundef;
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int util_loaded = 0;
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|
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again:
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switch(TYPE(v))
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{
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case T_RATIONAL:
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if(orig == Qundef ? (orig = v, 1) : orig != v) {
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if(!util_loaded) {
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rb_require("bigdecimal/util");
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util_loaded = 1;
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}
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v = rb_funcall2(v, rb_intern("to_d"), 0, 0);
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goto again;
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}
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v = orig;
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goto SomeOneMayDoIt;
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case T_DATA:
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if(rb_typeddata_is_kind_of(v, &BigDecimal_data_type)) {
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pv = DATA_PTR(v);
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return pv;
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} else {
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goto SomeOneMayDoIt;
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}
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break;
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case T_FIXNUM:
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sprintf(szD, "%ld", FIX2LONG(v));
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return VpCreateRbObject(VpBaseFig() * 2 + 1, szD);
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#ifdef ENABLE_NUMERIC_STRING
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case T_STRING:
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SafeStringValue(v);
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return VpCreateRbObject(strlen(RSTRING_PTR(v)) + VpBaseFig() + 1,
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RSTRING_PTR(v));
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#endif /* ENABLE_NUMERIC_STRING */
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case T_BIGNUM:
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bg = rb_big2str(v, 10);
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return VpCreateRbObject(strlen(RSTRING_PTR(bg)) + VpBaseFig() + 1,
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RSTRING_PTR(bg));
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default:
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goto SomeOneMayDoIt;
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}
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SomeOneMayDoIt:
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if(must) {
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rb_raise(rb_eTypeError, "%s can't be coerced into BigDecimal",
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rb_special_const_p(v)?
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RSTRING_PTR(rb_inspect(v)):
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rb_obj_classname(v)
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);
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}
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return NULL; /* NULL means to coerce */
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}
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/* call-seq:
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* BigDecimal.double_fig
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*
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* The BigDecimal.double_fig class method returns the number of digits a
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* Float number is allowed to have. The result depends upon the CPU and OS
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* in use.
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*/
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static VALUE
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BigDecimal_double_fig(VALUE self)
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{
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return INT2FIX(VpDblFig());
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}
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/* call-seq:
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* precs
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*
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* Returns an Array of two Integer values.
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*
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* The first value is the current number of significant digits in the
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* BigDecimal. The second value is the maximum number of significant digits
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* for the BigDecimal.
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*/
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static VALUE
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BigDecimal_prec(VALUE self)
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{
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ENTER(1);
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Real *p;
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VALUE obj;
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GUARD_OBJ(p,GetVpValue(self,1));
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obj = rb_assoc_new(INT2NUM(p->Prec*VpBaseFig()),
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INT2NUM(p->MaxPrec*VpBaseFig()));
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return obj;
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}
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static VALUE
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BigDecimal_hash(VALUE self)
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{
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ENTER(1);
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Real *p;
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U_LONG hash,i;
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GUARD_OBJ(p,GetVpValue(self,1));
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hash = (U_LONG)p->sign;
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/* hash!=2: the case for 0(1),NaN(0) or +-Infinity(3) is sign itself */
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if(hash==2) {
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for(i = 0; i < p->Prec;i++) {
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hash = 31 * hash + p->frac[i];
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hash ^= p->frac[i];
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}
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hash += p->exponent;
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}
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return INT2FIX(hash);
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}
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static VALUE
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BigDecimal_dump(int argc, VALUE *argv, VALUE self)
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{
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ENTER(5);
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Real *vp;
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char *psz;
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VALUE dummy;
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volatile VALUE dump;
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rb_scan_args(argc, argv, "01", &dummy);
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GUARD_OBJ(vp,GetVpValue(self,1));
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dump = rb_str_new(0,VpNumOfChars(vp,"E")+50);
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psz = RSTRING_PTR(dump);
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sprintf(psz,"%lu:",VpMaxPrec(vp)*VpBaseFig());
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VpToString(vp, psz+strlen(psz), 0, 0);
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rb_str_resize(dump, strlen(psz));
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return dump;
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}
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/*
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* Internal method used to provide marshalling support. See the Marshal module.
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*/
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static VALUE
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BigDecimal_load(VALUE self, VALUE str)
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{
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ENTER(2);
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Real *pv;
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unsigned char *pch;
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unsigned char ch;
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unsigned long m=0;
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SafeStringValue(str);
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pch = (unsigned char *)RSTRING_PTR(str);
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/* First get max prec */
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while((*pch)!=(unsigned char)'\0' && (ch=*pch++)!=(unsigned char)':') {
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if(!ISDIGIT(ch)) {
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rb_raise(rb_eTypeError, "load failed: invalid character in the marshaled string");
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}
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m = m*10 + (unsigned long)(ch-'0');
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}
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if(m>VpBaseFig()) m -= VpBaseFig();
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GUARD_OBJ(pv,VpNewRbClass(m,(char *)pch,self));
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m /= VpBaseFig();
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if(m && pv->MaxPrec>m) pv->MaxPrec = m+1;
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return ToValue(pv);
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}
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|
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/* call-seq:
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* BigDecimal.mode(mode, value)
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*
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* Controls handling of arithmetic exceptions and rounding. If no value
|
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* is supplied, the current value is returned.
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*
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* Six values of the mode parameter control the handling of arithmetic
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* exceptions:
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*
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* BigDecimal::EXCEPTION_NaN
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* BigDecimal::EXCEPTION_INFINITY
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* BigDecimal::EXCEPTION_UNDERFLOW
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* BigDecimal::EXCEPTION_OVERFLOW
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* BigDecimal::EXCEPTION_ZERODIVIDE
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* BigDecimal::EXCEPTION_ALL
|
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*
|
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* For each mode parameter above, if the value set is false, computation
|
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* continues after an arithmetic exception of the appropriate type.
|
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* When computation continues, results are as follows:
|
||
*
|
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* EXCEPTION_NaN:: NaN
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* EXCEPTION_INFINITY:: +infinity or -infinity
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||
* EXCEPTION_UNDERFLOW:: 0
|
||
* EXCEPTION_OVERFLOW:: +infinity or -infinity
|
||
* EXCEPTION_ZERODIVIDE:: +infinity or -infinity
|
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*
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* One value of the mode parameter controls the rounding of numeric values:
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* BigDecimal::ROUND_MODE. The values it can take are:
|
||
*
|
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* ROUND_UP:: round away from zero
|
||
* ROUND_DOWN:: round towards zero (truncate)
|
||
* ROUND_HALF_UP:: round up if the appropriate digit >= 5, otherwise truncate (default)
|
||
* ROUND_HALF_DOWN:: round up if the appropriate digit >= 6, otherwise truncate
|
||
* ROUND_HALF_EVEN:: round towards the even neighbor (Banker's rounding)
|
||
* ROUND_CEILING:: round towards positive infinity (ceil)
|
||
* ROUND_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_eTypeError, "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 */
|
||
fo = VpGetRoundMode();
|
||
if(val==Qnil) return INT2FIX(fo);
|
||
Check_Type(val, T_FIXNUM);
|
||
if(!VpIsRoundMode(FIX2INT(val))) {
|
||
rb_raise(rb_eTypeError, "invalid rounding mode");
|
||
return Qnil;
|
||
}
|
||
fo = VpSetRoundMode((unsigned long)FIX2INT(val));
|
||
return INT2FIX(fo);
|
||
}
|
||
rb_raise(rb_eTypeError, "first argument for BigDecimal#mode invalid");
|
||
return Qnil;
|
||
}
|
||
|
||
static U_LONG
|
||
GetAddSubPrec(Real *a, Real *b)
|
||
{
|
||
U_LONG mxs;
|
||
U_LONG mx = a->Prec;
|
||
S_INT d;
|
||
|
||
if(!VpIsDef(a) || !VpIsDef(b)) return (-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+(U_LONG)d;
|
||
if(mx<mxs) {
|
||
return VpException(VP_EXCEPTION_INFINITY,"Exponent overflow",0);
|
||
}
|
||
}
|
||
return mx;
|
||
}
|
||
|
||
static S_INT
|
||
GetPositiveInt(VALUE v)
|
||
{
|
||
S_INT 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(U_LONG 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(U_LONG 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);
|
||
int e,n,i,nf;
|
||
U_LONG v,b,j;
|
||
volatile VALUE str;
|
||
char *psz,*pch;
|
||
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) {
|
||
e = VpGetSign(p)*p->frac[0];
|
||
return INT2FIX(e);
|
||
}
|
||
else {
|
||
VALUE a = BigDecimal_split(self);
|
||
VALUE digits = RARRAY_PTR(a)[1];
|
||
VALUE numerator = rb_funcall(digits, rb_intern("to_i"), 0);
|
||
int dpower = e - 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;
|
||
S_LONG 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 > DBL_MAX_10_EXP+BASE_FIG) goto erange;
|
||
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) {
|
||
erange:
|
||
VpException(VP_EXCEPTION_OVERFLOW,"BigDecimal to Float conversion",0);
|
||
if(d>0.0) d = VpGetDoublePosInf();
|
||
else d = VpGetDoubleNegInf();
|
||
}
|
||
return rb_float_new(d);
|
||
}
|
||
|
||
|
||
/* Converts a BigDecimal to a Rational.
|
||
*/
|
||
static VALUE
|
||
BigDecimal_to_r(VALUE self)
|
||
{
|
||
Real *p;
|
||
S_LONG 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;
|
||
switch (TYPE(other)) {
|
||
case T_FLOAT:
|
||
obj = rb_assoc_new(other, BigDecimal_to_f(self));
|
||
break;
|
||
case T_RATIONAL:
|
||
obj = rb_assoc_new(other, BigDecimal_to_r(self));
|
||
break;
|
||
default:
|
||
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;
|
||
U_LONG 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==(-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;
|
||
U_LONG 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==(-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);
|
||
S_INT 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;
|
||
U_LONG 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;
|
||
U_LONG mx;
|
||
|
||
GUARD_OBJ(a,GetVpValue(self,1));
|
||
b = GetVpValue(r,0);
|
||
if(!b) return DoSomeOne(self,r,'/');
|
||
SAVE(b);
|
||
*div = b;
|
||
mx = a->Prec+abs(a->exponent);
|
||
if(mx<b->Prec+abs(b->exponent)) mx = b->Prec+abs(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],(VpBaseVal()*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;
|
||
U_LONG 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,(S_INT)(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+abs(a->exponent);
|
||
if(mx<b->Prec+abs(b->exponent)) mx = b->Prec+abs(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);
|
||
VALUE obj;
|
||
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);
|
||
U_LONG 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);
|
||
VALUE obj;
|
||
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 */
|
||
VALUE obj;
|
||
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 */
|
||
U_LONG ix = (U_LONG)GetPositiveInt(n);
|
||
if(ix==0) return BigDecimal_div(self,b);
|
||
else {
|
||
Real *res=NULL;
|
||
Real *av=NULL, *bv=NULL, *cv=NULL;
|
||
U_LONG mx = (ix+VpBaseFig()*2);
|
||
U_LONG 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;
|
||
U_LONG mx = (U_LONG)GetPositiveInt(n);
|
||
if(mx==0) return BigDecimal_add(self,b);
|
||
else {
|
||
U_LONG 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;
|
||
U_LONG mx = (U_LONG)GetPositiveInt(n);
|
||
if(mx==0) return BigDecimal_sub(self,b);
|
||
else {
|
||
U_LONG 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;
|
||
U_LONG mx = (U_LONG)GetPositiveInt(n);
|
||
if(mx==0) return BigDecimal_mult(self,b);
|
||
else {
|
||
U_LONG 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;
|
||
U_LONG mx;
|
||
|
||
GUARD_OBJ(a,GetVpValue(self,1));
|
||
mx = a->Prec *(VpBaseFig() + 1);
|
||
GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
|
||
VpAsgn(c, a, 1);
|
||
VpChangeSign(c,(S_INT)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;
|
||
S_INT 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;
|
||
U_LONG 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;
|
||
U_LONG mx;
|
||
VALUE vLoc;
|
||
VALUE vRound;
|
||
U_LONG pl;
|
||
|
||
int sw = VpGetRoundMode();
|
||
|
||
int na = rb_scan_args(argc,argv,"02",&vLoc,&vRound);
|
||
switch(na) {
|
||
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);
|
||
Check_Type(vRound, T_FIXNUM);
|
||
sw = FIX2INT(vRound);
|
||
if(!VpIsRoundMode(sw)) {
|
||
rb_raise(rb_eTypeError, "invalid rounding mode");
|
||
return Qnil;
|
||
}
|
||
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;
|
||
U_LONG mx;
|
||
VALUE vLoc;
|
||
U_LONG 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;
|
||
U_LONG 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;
|
||
U_LONG mx;
|
||
int iLoc;
|
||
VALUE vLoc;
|
||
U_LONG 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);
|
||
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;
|
||
U_LONG mx;
|
||
int iLoc;
|
||
VALUE vLoc;
|
||
U_LONG 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;
|
||
U_LONG nc;
|
||
S_INT 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 = 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;
|
||
S_LONG e;
|
||
S_LONG 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]=='-') {
|
||
int 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)
|
||
{
|
||
S_LONG 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;
|
||
unsigned int 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:%lx,'",self);
|
||
tmp = psz + strlen(psz);
|
||
VpToString(vp, tmp, 10, 0);
|
||
tmp += strlen(tmp);
|
||
sprintf(tmp,"',%lu(%lu)>",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;
|
||
S_LONG mp, ma, 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;
|
||
S_LONG 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;
|
||
S_LONG 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);
|
||
}
|
||
|
||
/* 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)
|
||
{
|
||
/* Initialize VP routines */
|
||
VpInit((U_LONG)0);
|
||
|
||
/* 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);
|
||
|
||
/* 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((S_INT)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));
|
||
|
||
/* 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, 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);
|
||
}
|
||
|
||
/*
|
||
*
|
||
* ============================================================================
|
||
*
|
||
* vp_ routines begin from here.
|
||
*
|
||
* ============================================================================
|
||
*
|
||
*/
|
||
#ifdef _DEBUG
|
||
static int gfDebug = 1; /* Debug switch */
|
||
#if 0
|
||
static int gfCheckVal = 1; /* Value checking flag in VpNmlz() */
|
||
#endif
|
||
#endif /* _DEBUG */
|
||
|
||
static U_LONG gnPrecLimit = 0; /* Global upper limit of the precision newly allocated */
|
||
static U_LONG gfRoundMode = VP_ROUND_HALF_UP; /* Mode for general rounding operation */
|
||
|
||
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,S_INT n);
|
||
static U_LONG VpAddAbs(Real *a,Real *b,Real *c);
|
||
static U_LONG VpSubAbs(Real *a,Real *b,Real *c);
|
||
static U_LONG VpSetPTR(Real *a,Real *b,Real *c,U_LONG *a_pos,U_LONG *b_pos,U_LONG *c_pos,U_LONG *av,U_LONG *bv);
|
||
static int VpNmlz(Real *a);
|
||
static void VpFormatSt(char *psz,S_INT fFmt);
|
||
static int VpRdup(Real *m,U_LONG ind_m);
|
||
|
||
#ifdef _DEBUG
|
||
static int gnAlloc=0; /* Memory allocation counter */
|
||
#endif /* _DEBUG */
|
||
|
||
VP_EXPORT void *
|
||
VpMemAlloc(U_LONG mb)
|
||
{
|
||
void *p = xmalloc((unsigned int)mb);
|
||
if(!p) {
|
||
VpException(VP_EXCEPTION_MEMORY,"failed to allocate memory",1);
|
||
}
|
||
memset(p,0,mb);
|
||
#ifdef _DEBUG
|
||
gnAlloc++; /* Count allocation call */
|
||
#endif /* _DEBUG */
|
||
return p;
|
||
}
|
||
|
||
VP_EXPORT void
|
||
VpFree(Real *pv)
|
||
{
|
||
if(pv != NULL) {
|
||
xfree(pv);
|
||
#ifdef _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 /* _DEBUG */
|
||
}
|
||
}
|
||
|
||
/*
|
||
* EXCEPTION Handling.
|
||
*/
|
||
static unsigned short gfDoException = 0; /* Exception flag */
|
||
|
||
static unsigned short
|
||
VpGetException (void)
|
||
{
|
||
return gfDoException;
|
||
}
|
||
|
||
static void
|
||
VpSetException(unsigned short f)
|
||
{
|
||
gfDoException = f;
|
||
}
|
||
|
||
/* These 2 functions added at v1.1.7 */
|
||
VP_EXPORT U_LONG
|
||
VpGetPrecLimit(void)
|
||
{
|
||
return gnPrecLimit;
|
||
}
|
||
|
||
VP_EXPORT U_LONG
|
||
VpSetPrecLimit(U_LONG n)
|
||
{
|
||
U_LONG s = gnPrecLimit;
|
||
gnPrecLimit = n;
|
||
return s;
|
||
}
|
||
|
||
VP_EXPORT unsigned long
|
||
VpGetRoundMode(void)
|
||
{
|
||
return gfRoundMode;
|
||
}
|
||
|
||
VP_EXPORT int
|
||
VpIsRoundMode(unsigned long n)
|
||
{
|
||
if(n==VP_ROUND_UP || n==VP_ROUND_DOWN ||
|
||
n==VP_ROUND_HALF_UP || n==VP_ROUND_HALF_DOWN ||
|
||
n==VP_ROUND_CEIL || n==VP_ROUND_FLOOR ||
|
||
n==VP_ROUND_HALF_EVEN
|
||
) return 1;
|
||
return 0;
|
||
}
|
||
|
||
VP_EXPORT unsigned long
|
||
VpSetRoundMode(unsigned long n)
|
||
{
|
||
if(VpIsRoundMode(n)) gfRoundMode = n;
|
||
return gfRoundMode;
|
||
}
|
||
|
||
/*
|
||
* 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;
|
||
}
|
||
|
||
VP_EXPORT U_LONG
|
||
VpBaseFig(void)
|
||
{
|
||
return BASE_FIG;
|
||
}
|
||
|
||
VP_EXPORT U_LONG
|
||
VpDblFig(void)
|
||
{
|
||
return DBLE_FIG;
|
||
}
|
||
|
||
VP_EXPORT U_LONG
|
||
VpBaseVal(void)
|
||
{
|
||
return BASE;
|
||
}
|
||
|
||
/*
|
||
----------------------------------------------------------------
|
||
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;
|
||
|
||
if(f==VP_EXCEPTION_OP || f==VP_EXCEPTION_MEMORY) always = 1;
|
||
|
||
if(always||(gfDoException&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 U_LONG
|
||
VpNumOfChars(Real *vp,const char *pszFmt)
|
||
{
|
||
S_INT ex;
|
||
U_LONG 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*(-ex);
|
||
} else {
|
||
if(ex > (S_INT)vp->Prec) {
|
||
nc += BASE_FIG*(ex - (S_INT)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 U_LONG word(LONG) in the computer used.
|
||
*
|
||
* [Returns]
|
||
* DBLE_FIG ... OK
|
||
*/
|
||
VP_EXPORT U_LONG
|
||
VpInit(U_LONG BaseVal)
|
||
{
|
||
/* Setup +/- Inf NaN -0 */
|
||
VpGetDoubleNaN();
|
||
VpGetDoublePosInf();
|
||
VpGetDoubleNegInf();
|
||
VpGetDoubleNegZero();
|
||
|
||
#ifndef BASE_FIG
|
||
if(BaseVal <= 0) {
|
||
U_LONG w;
|
||
/* Base <= 0, then determine Base by calcuration. */
|
||
BASE = 1;
|
||
while(
|
||
(BASE > 0) &&
|
||
((w = BASE *(BASE + 1)) > BASE) &&((w / BASE) ==(BASE + 1))
|
||
) {
|
||
BaseVal = BASE;
|
||
BASE = BaseVal * 10L;
|
||
}
|
||
}
|
||
/* Set Base Values */
|
||
BASE = BaseVal;
|
||
HALF_BASE = BASE / 2;
|
||
BASE1 = BASE / 10;
|
||
BASE_FIG = 0;
|
||
while(BaseVal /= 10) ++BASE_FIG;
|
||
#endif
|
||
|
||
/* Allocates Vp constants. */
|
||
VpConstOne = VpAlloc((U_LONG)1, "1");
|
||
VpPt5 = VpAlloc((U_LONG)1, ".5");
|
||
|
||
#ifdef _DEBUG
|
||
gnAlloc = 0;
|
||
#endif /* _DEBUG */
|
||
|
||
#ifdef _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 = %d\n", BASE_FIG);
|
||
printf(" DBLE_FIG = %d\n", DBLE_FIG);
|
||
}
|
||
#endif /* _DEBUG */
|
||
|
||
return DBLE_FIG;
|
||
}
|
||
|
||
VP_EXPORT Real *
|
||
VpOne(void)
|
||
{
|
||
return VpConstOne;
|
||
}
|
||
|
||
/* If exponent overflows,then raise exception or returns 0 */
|
||
static int
|
||
AddExponent(Real *a,S_INT n)
|
||
{
|
||
S_INT e = a->exponent;
|
||
S_INT m = e+n;
|
||
S_INT eb,mb;
|
||
if(e>0) {
|
||
if(n>0) {
|
||
mb = m*BASE_FIG;
|
||
eb = e*BASE_FIG;
|
||
if(mb<eb) goto overflow;
|
||
}
|
||
} else if(n<0) {
|
||
mb = m*BASE_FIG;
|
||
eb = e*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(U_LONG mx, const char *szVal)
|
||
{
|
||
U_LONG i, ni, ipn, ipf, nf, ipe, ne, nalloc;
|
||
char v,*psz;
|
||
int sign=1;
|
||
Real *vp = NULL;
|
||
U_LONG mf = VpGetPrecLimit();
|
||
volatile 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(U_LONG));
|
||
/* 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_new(0,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(U_LONG));
|
||
vp->MaxPrec = 1; /* set max precision */
|
||
VpSetPosInf(vp);
|
||
return vp;
|
||
}
|
||
if(StrCmp(szVal,SZ_NINF)==0) {
|
||
vp = (Real *) VpMemAlloc(sizeof(Real) + sizeof(U_LONG));
|
||
vp->MaxPrec = 1; /* set max precision */
|
||
VpSetNegInf(vp);
|
||
return vp;
|
||
}
|
||
if(StrCmp(szVal,SZ_NaN)==0) {
|
||
vp = (Real *) VpMemAlloc(sizeof(Real) + sizeof(U_LONG));
|
||
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(U_LONG));
|
||
/* 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);
|
||
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 int
|
||
VpAsgn(Real *c, Real *a, int isw)
|
||
{
|
||
U_LONG 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(U_LONG));
|
||
/* 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 int
|
||
VpAddSub(Real *c, Real *a, Real *b, int operation)
|
||
{
|
||
S_INT sw, isw;
|
||
Real *a_ptr, *b_ptr;
|
||
U_LONG n, na, nb, i;
|
||
U_LONG mrv;
|
||
|
||
#ifdef _DEBUG
|
||
if(gfDebug) {
|
||
VPrint(stdout, "VpAddSub(enter) a=% \n", a);
|
||
VPrint(stdout, " b=% \n", b);
|
||
printf(" operation=%d\n", operation);
|
||
}
|
||
#endif /* _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,(S_INT)1);
|
||
mrv = VpAddAbs(a_ptr, b_ptr, c);
|
||
VpSetSign(c,isw / 2);
|
||
} else { /* subtraction */
|
||
VpSetSign(c,(S_INT)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 _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 /* _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 U_LONG
|
||
VpAddAbs(Real *a, Real *b, Real *c)
|
||
{
|
||
U_LONG word_shift;
|
||
U_LONG carry;
|
||
U_LONG ap;
|
||
U_LONG bp;
|
||
U_LONG cp;
|
||
U_LONG a_pos;
|
||
U_LONG b_pos;
|
||
U_LONG c_pos;
|
||
U_LONG av, bv, mrv;
|
||
|
||
#ifdef _DEBUG
|
||
if(gfDebug) {
|
||
VPrint(stdout, "VpAddAbs called: a = %\n", a);
|
||
VPrint(stdout, " b = %\n", b);
|
||
}
|
||
#endif /* _DEBUG */
|
||
|
||
word_shift = VpSetPTR(a, b, c, &ap, &bp, &cp, &av, &bv);
|
||
a_pos = ap;
|
||
b_pos = bp;
|
||
c_pos = cp;
|
||
if(word_shift==-1L) return 0; /* Overflow */
|
||
if(b_pos == -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. */
|
||
bv = b_pos + word_shift;
|
||
while(a_pos > bv) {
|
||
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 _DEBUG
|
||
if(gfDebug) {
|
||
VPrint(stdout, "VpAddAbs exit: c=% \n", c);
|
||
}
|
||
#endif /* _DEBUG */
|
||
return mrv;
|
||
}
|
||
|
||
/*
|
||
* c = abs(a) - abs(b)
|
||
*/
|
||
static U_LONG
|
||
VpSubAbs(Real *a, Real *b, Real *c)
|
||
{
|
||
U_LONG word_shift;
|
||
U_LONG mrv;
|
||
U_LONG borrow;
|
||
U_LONG ap;
|
||
U_LONG bp;
|
||
U_LONG cp;
|
||
U_LONG a_pos;
|
||
U_LONG b_pos;
|
||
U_LONG c_pos;
|
||
U_LONG av, bv;
|
||
|
||
#ifdef _DEBUG
|
||
if(gfDebug) {
|
||
VPrint(stdout, "VpSubAbs called: a = %\n", a);
|
||
VPrint(stdout, " b = %\n", b);
|
||
}
|
||
#endif /* _DEBUG */
|
||
|
||
word_shift = VpSetPTR(a, b, c, &ap, &bp, &cp, &av, &bv);
|
||
a_pos = ap;
|
||
b_pos = bp;
|
||
c_pos = cp;
|
||
if(word_shift==-1L) return 0; /* Overflow */
|
||
if(b_pos == -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. */
|
||
|
||
bv = b_pos + word_shift;
|
||
while(a_pos > bv) {
|
||
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 _DEBUG
|
||
if(gfDebug) {
|
||
VPrint(stdout, "VpSubAbs exit: c=% \n", c);
|
||
}
|
||
#endif /* _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 U_LONG
|
||
VpSetPTR(Real *a, Real *b, Real *c, U_LONG *a_pos, U_LONG *b_pos, U_LONG *c_pos, U_LONG *av, U_LONG *bv)
|
||
{
|
||
U_LONG 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,(S_LONG)1)) return (-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 int
|
||
VpMult(Real *c, Real *a, Real *b)
|
||
{
|
||
U_LONG MxIndA, MxIndB, MxIndAB, MxIndC;
|
||
U_LONG ind_c, i, ii, nc;
|
||
U_LONG ind_as, ind_ae, ind_bs, ind_be;
|
||
U_LONG Carry, s;
|
||
Real *w;
|
||
|
||
#ifdef _DEBUG
|
||
if(gfDebug) {
|
||
VPrint(stdout, "VpMult(Enter): a=% \n", a);
|
||
VPrint(stdout, " b=% \n", b);
|
||
}
|
||
#endif /* _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((U_LONG)((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(U_LONG)); /* 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 =((a->frac[i]) *(b->frac[ind_bs--]));
|
||
Carry = s / BASE;
|
||
s = s -(Carry * BASE);
|
||
c->frac[ind_c] += s;
|
||
if(c->frac[ind_c] >= BASE) {
|
||
s = c->frac[ind_c] / BASE;
|
||
Carry += s;
|
||
c->frac[ind_c] -= (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 _DEBUG
|
||
if(gfDebug) {
|
||
VPrint(stdout, "VpMult(c=a*b): c=% \n", c);
|
||
VPrint(stdout, " a=% \n", a);
|
||
VPrint(stdout, " b=% \n", b);
|
||
}
|
||
#endif /*_DEBUG */
|
||
return c->Prec*BASE_FIG;
|
||
}
|
||
|
||
/*
|
||
* c = a / b, remainder = r
|
||
*/
|
||
VP_EXPORT int
|
||
VpDivd(Real *c, Real *r, Real *a, Real *b)
|
||
{
|
||
U_LONG word_a, word_b, word_c, word_r;
|
||
U_LONG i, n, ind_a, ind_b, ind_c, ind_r;
|
||
U_LONG nLoop;
|
||
U_LONG q, b1, b1p1, b1b2, b1b2p1, r1r2;
|
||
U_LONG borrow, borrow1, borrow2, qb;
|
||
|
||
#ifdef _DEBUG
|
||
if(gfDebug) {
|
||
VPrint(stdout, " VpDivd(c=a/b) a=% \n", a);
|
||
VPrint(stdout, " b=% \n", b);
|
||
}
|
||
#endif /*_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 = 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;
|
||
c->frac[ind_c] += 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;
|
||
c->frac[ind_c + 1] += 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 = qb / BASE;
|
||
qb = qb - borrow1 * BASE;
|
||
}
|
||
if(r->frac[ind_r] < qb) {
|
||
r->frac[ind_r] +=(BASE - qb);
|
||
borrow2 = borrow2 + borrow1 + 1;
|
||
} else {
|
||
r->frac[ind_r] -= 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,(S_LONG)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,(S_LONG)1)) return 0;
|
||
VpSetSign(r,VpGetSign(a));
|
||
VpNmlz(r); /* normalize r(remainder) */
|
||
goto Exit;
|
||
|
||
space_error:
|
||
#ifdef _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 /* _DEBUG */
|
||
rb_bug("ERROR(VpDivd): space for remainder too small.");
|
||
|
||
Exit:
|
||
#ifdef _DEBUG
|
||
if(gfDebug) {
|
||
VPrint(stdout, " VpDivd(c=a/b), c=% \n", c);
|
||
VPrint(stdout, " r=% \n", r);
|
||
}
|
||
#endif /* _DEBUG */
|
||
return c->Prec*BASE_FIG;
|
||
}
|
||
|
||
/*
|
||
* Input a = 00000xxxxxxxx En(5 preceeding zeros)
|
||
* Output a = xxxxxxxx En-5
|
||
*/
|
||
static int
|
||
VpNmlz(Real *a)
|
||
{
|
||
U_LONG 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,-((S_INT)i))) return 0;
|
||
memmove(&(a->frac[0]),&(a->frac[i]),(a->Prec)*sizeof(U_LONG));
|
||
}
|
||
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;
|
||
U_LONG 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 _DEBUG
|
||
if(gfDebug) {
|
||
VPrint(stdout, " VpComp a=%\n", a);
|
||
VPrint(stdout, " b=%\n", b);
|
||
printf(" ans=%d\n", val);
|
||
}
|
||
#endif /* _DEBUG */
|
||
return (int)val;
|
||
}
|
||
|
||
#ifdef _DEBUG
|
||
/*
|
||
* 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)
|
||
{
|
||
U_LONG i, j, nc, nd, ZeroSup;
|
||
U_LONG n, 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.");
|
||
n = a->Prec;
|
||
for(i=0;i < n;++i) {
|
||
m = BASE1;
|
||
e = a->frac[i];
|
||
while(m) {
|
||
nn = e / m;
|
||
if((!ZeroSup) || nn) {
|
||
nc += fprintf(fp, "%lu", 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%ld", 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 /* _DEBUG */
|
||
|
||
static void
|
||
VpFormatSt(char *psz,S_INT fFmt)
|
||
{
|
||
U_LONG ie;
|
||
U_LONG i;
|
||
S_INT 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 S_LONG
|
||
VpExponent10(Real *a)
|
||
{
|
||
S_LONG ex;
|
||
U_LONG n;
|
||
|
||
if(!VpHasVal(a)) return 0;
|
||
|
||
ex =(a->exponent) * BASE_FIG;
|
||
n = BASE1;
|
||
while((a->frac[0] / n) == 0) {
|
||
--ex;
|
||
n /= 10;
|
||
}
|
||
return ex;
|
||
}
|
||
|
||
VP_EXPORT void
|
||
VpSzMantissa(Real *a,char *psz)
|
||
{
|
||
U_LONG i, ZeroSup;
|
||
U_LONG n, 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", 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,int fFmt,int fPlus)
|
||
/* fPlus =0:default, =1: set ' ' before digits , =2:set '+' before digits. */
|
||
{
|
||
U_LONG i, ZeroSup;
|
||
U_LONG n, m, e, nn;
|
||
char *pszSav = psz;
|
||
S_LONG 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", 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) * BASE_FIG;
|
||
n = BASE1;
|
||
while((a->frac[0] / n) == 0) {
|
||
--ex;
|
||
n /= 10;
|
||
}
|
||
while(psz[-1]=='0') *(--psz) = 0;
|
||
sprintf(psz, "E%ld", ex);
|
||
if(fFmt) VpFormatSt(pszSav, fFmt);
|
||
}
|
||
|
||
VP_EXPORT void
|
||
VpToFString(Real *a,char *psz,int fFmt,int fPlus)
|
||
/* fPlus =0:default,=1: set ' ' before digits ,set '+' before digits. */
|
||
{
|
||
U_LONG i;
|
||
U_LONG n, m, e, nn;
|
||
char *pszSav = psz;
|
||
S_LONG 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", 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, U_LONG ni, const char *frac, U_LONG nf, const char *exp_chr, U_LONG ne)
|
||
{
|
||
U_LONG i, j, ind_a, ma, mi, me;
|
||
U_LONG loc;
|
||
S_INT e,es, eb, ef;
|
||
S_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(U_LONG));
|
||
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*((S_INT)BASE_FIG);
|
||
e = e * 10 + exp_chr[i] - '0';
|
||
if(es>e*((S_INT)BASE_FIG)) {
|
||
exponent_overflow = 1;
|
||
break;
|
||
}
|
||
++i;
|
||
}
|
||
}
|
||
|
||
/* get integer part */
|
||
i = 0;
|
||
sign = 1;
|
||
if(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 / ((S_INT)BASE_FIG);
|
||
ef = eb - ef * ((S_INT)BASE_FIG);
|
||
if(ef) {
|
||
++j; /* Means to add one more preceeding zero */
|
||
++e;
|
||
}
|
||
}
|
||
|
||
eb = e / ((S_INT)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 < (U_LONG)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 < (U_LONG)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 < (U_LONG)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 ... U_LONG,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, S_LONG *e, Real *m)
|
||
{
|
||
U_LONG 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)((S_INT)BASE);
|
||
*d = *d +((double) ((S_INT)m->frac[ind_m++])) * div;
|
||
}
|
||
*e = m->exponent * ((S_INT)BASE_FIG);
|
||
*d *= VpGetSign(m);
|
||
|
||
Exit:
|
||
#ifdef _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 /*_DEBUG */
|
||
return f;
|
||
}
|
||
|
||
/*
|
||
* m <- d
|
||
*/
|
||
VP_EXPORT void
|
||
VpDtoV(Real *m, double d)
|
||
{
|
||
U_LONG i, ind_m, mm;
|
||
U_LONG ne;
|
||
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)((S_INT)BASE);
|
||
++ne;
|
||
}
|
||
} else {
|
||
val2 = 1.0 /(double)((S_INT)BASE);
|
||
while(val < val2) {
|
||
val *=(double)((S_INT)BASE);
|
||
--ne;
|
||
}
|
||
}
|
||
/* Now val = 0.xxxxx*BASE**ne */
|
||
|
||
mm = m->MaxPrec;
|
||
memset(m->frac, 0, mm * sizeof(U_LONG));
|
||
for(ind_m = 0;val > 0.0 && ind_m < mm;ind_m++) {
|
||
val *=(double)((S_INT)BASE);
|
||
i =(U_LONG) val;
|
||
val -=(double)((S_INT)i);
|
||
m->frac[ind_m] = i;
|
||
}
|
||
if(ind_m >= mm) ind_m = mm - 1;
|
||
if(d > 0.0) {
|
||
VpSetSign(m, (S_INT)1);
|
||
} else {
|
||
VpSetSign(m,-(S_INT)1);
|
||
}
|
||
m->Prec = ind_m + 1;
|
||
m->exponent = ne;
|
||
|
||
VpInternalRound(m,0,(m->Prec>0)?m->frac[m->Prec-1]:0,
|
||
(U_LONG)(val*((double)((S_INT)BASE))));
|
||
|
||
Exit:
|
||
#ifdef _DEBUG
|
||
if(gfDebug) {
|
||
printf("VpDtoV d=%30.30e\n", d);
|
||
VPrint(stdout, " m=%\n", m);
|
||
}
|
||
#endif /* _DEBUG */
|
||
return;
|
||
}
|
||
|
||
/*
|
||
* m <- ival
|
||
*/
|
||
#if 0 /* unused */
|
||
VP_EXPORT void
|
||
VpItoV(Real *m, S_INT ival)
|
||
{
|
||
U_LONG mm, ind_m;
|
||
U_LONG val, v1, v2, v;
|
||
int isign;
|
||
S_INT ne;
|
||
|
||
if(ival == 0) {
|
||
VpSetZero(m,1);
|
||
goto Exit;
|
||
}
|
||
isign = 1;
|
||
val = ival;
|
||
if(ival < 0) {
|
||
isign = -1;
|
||
val =(U_LONG)(-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 _DEBUG
|
||
if(gfDebug) {
|
||
printf(" VpItoV i=%d\n", ival);
|
||
VPrint(stdout, " m=%\n", m);
|
||
}
|
||
#endif /* _DEBUG */
|
||
return;
|
||
}
|
||
#endif
|
||
|
||
/*
|
||
* y = SQRT(x), y*y - x =>0
|
||
*/
|
||
VP_EXPORT int
|
||
VpSqrt(Real *y, Real *x)
|
||
{
|
||
Real *f = NULL;
|
||
Real *r = NULL;
|
||
S_LONG y_prec, f_prec;
|
||
S_LONG n;
|
||
S_LONG e;
|
||
S_LONG prec;
|
||
S_LONG 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 = (S_LONG)y->MaxPrec;
|
||
if((S_LONG)x->MaxPrec > n) n = (S_LONG)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 = (S_LONG)y->MaxPrec;
|
||
f_prec = (S_LONG)f->MaxPrec;
|
||
|
||
prec = x->exponent;
|
||
if(prec > 0) ++prec;
|
||
else --prec;
|
||
prec = prec - (S_LONG)y->MaxPrec;
|
||
VpVtoD(&val, &e, x); /* val <- x */
|
||
e /= ((S_LONG)BASE_FIG);
|
||
n = e / 2;
|
||
if(e - n * 2 != 0) {
|
||
val /=(double)((S_INT)BASE);
|
||
n =(e + 1) / 2;
|
||
}
|
||
VpDtoV(y, sqrt(val)); /* y <- sqrt(val) */
|
||
y->exponent += n;
|
||
n = (DBLE_FIG + BASE_FIG - 1) / BASE_FIG;
|
||
y->MaxPrec = (U_LONG)Min(n , y_prec);
|
||
f->MaxPrec = y->MaxPrec + 1;
|
||
n = y_prec*((S_LONG)BASE_FIG);
|
||
if((U_LONG)n<maxnr) n = (U_LONG)maxnr;
|
||
do {
|
||
y->MaxPrec *= 2;
|
||
if(y->MaxPrec > (U_LONG)y_prec) y->MaxPrec = (U_LONG)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 _DEBUG
|
||
if(gfDebug) {
|
||
printf("ERROR(VpSqrt): did not converge within %ld iterations.\n",
|
||
nr);
|
||
}
|
||
#endif /* _DEBUG */
|
||
y->MaxPrec = y_prec;
|
||
|
||
converge:
|
||
VpChangeSign(y,(S_INT)1);
|
||
#ifdef _DEBUG
|
||
if(gfDebug) {
|
||
VpMult(r, y, y);
|
||
VpAddSub(f, x, r, -1);
|
||
printf("VpSqrt: iterations = %lu\n", nr);
|
||
VPrint(stdout, " y =% \n", y);
|
||
VPrint(stdout, " x =% \n", x);
|
||
VPrint(stdout, " x-y*y = % \n", f);
|
||
}
|
||
#endif /* _DEBUG */
|
||
y->MaxPrec = y_prec;
|
||
|
||
Exit:
|
||
VpFree(f);
|
||
VpFree(r);
|
||
return 1;
|
||
}
|
||
|
||
/*
|
||
*
|
||
* nf: digit position for operation.
|
||
*
|
||
*/
|
||
VP_EXPORT int
|
||
VpMidRound(Real *y, int f, int 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? */
|
||
/* exptoadd: number of digits needed to compensate negative nf */
|
||
int n,i,ix,ioffset,fracf,exptoadd;
|
||
U_LONG v,shifter;
|
||
U_LONG div;
|
||
|
||
nf += y->exponent*((int)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: x->fraq[ix] contains round position */
|
||
ix = nf/(int)BASE_FIG;
|
||
if(((U_LONG)ix)>=y->Prec) return 0; /* rounding position too right(small). */
|
||
ioffset = nf - ix*((int)BASE_FIG);
|
||
|
||
v = y->frac[ix];
|
||
|
||
/* drop digits after pointed digit */
|
||
n = BASE_FIG - ioffset - 1;
|
||
for(shifter=1,i=0;i<n;++i) shifter *= 10;
|
||
fracf = (v%(shifter*10) > 0);
|
||
v /= shifter;
|
||
div = v/10;
|
||
v = v - div*10;
|
||
if (fracf == 0) {
|
||
for(i=ix+1;(U_LONG)i<y->Prec;i++) {
|
||
if (y->frac[i]%BASE) {
|
||
fracf = 1;
|
||
break;
|
||
}
|
||
}
|
||
}
|
||
memset(y->frac+ix+1, 0, (y->Prec - (ix+1)) * sizeof(U_LONG));
|
||
switch(f) {
|
||
case VP_ROUND_DOWN: /* Truncate */
|
||
break;
|
||
case VP_ROUND_UP: /* Roundup */
|
||
if(fracf) ++div;
|
||
break;
|
||
case VP_ROUND_HALF_UP: /* Round half up */
|
||
if(v>=5) ++div;
|
||
break;
|
||
case VP_ROUND_HALF_DOWN: /* Round half down */
|
||
if(v>=6) ++div;
|
||
break;
|
||
case VP_ROUND_CEIL: /* ceil */
|
||
if(fracf && (VpGetSign(y)>0)) ++div;
|
||
break;
|
||
case VP_ROUND_FLOOR: /* 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((U_LONG)i==(BASE_FIG-1)) {
|
||
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 {
|
||
S_INT s = VpGetSign(y);
|
||
int e = y->exponent;
|
||
VpSetOne(y);
|
||
VpSetSign(y,s);
|
||
y->exponent = e+1;
|
||
}
|
||
} else {
|
||
y->frac[ix] = div;
|
||
VpNmlz(y);
|
||
}
|
||
if (exptoadd > 0) {
|
||
y->exponent += exptoadd/BASE_FIG;
|
||
exptoadd %= 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, int f, int nf)
|
||
/*
|
||
* Round from the left hand side of the digits.
|
||
*/
|
||
{
|
||
U_LONG v;
|
||
if(!VpHasVal(y)) return 0; /* Unable to round */
|
||
v = y->frac[0];
|
||
nf -= VpExponent(y)*BASE_FIG;
|
||
while((v /= 10) != 0) nf--;
|
||
nf += (BASE_FIG-1);
|
||
return VpMidRound(y,f,nf);
|
||
}
|
||
|
||
VP_EXPORT int
|
||
VpActiveRound(Real *y, Real *x, int f, int 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,U_LONG ixDigit)
|
||
{
|
||
U_LONG 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(),ix);
|
||
}
|
||
|
||
static void
|
||
VpInternalRound(Real *c,int ixDigit,U_LONG vPrev,U_LONG v)
|
||
{
|
||
int f = 0;
|
||
|
||
if(VpLimitRound(c,ixDigit)) return;
|
||
if(!v) return;
|
||
|
||
v /= BASE1;
|
||
switch(gfRoundMode) {
|
||
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:
|
||
if(v >= 6) f = 1;
|
||
break;
|
||
case VP_ROUND_CEIL: /* ceil */
|
||
if(v && (VpGetSign(c)>0)) f = 1;
|
||
break;
|
||
case VP_ROUND_FLOOR: /* floor */
|
||
if(v && (VpGetSign(c)<0)) f = 1;
|
||
break;
|
||
case VP_ROUND_HALF_EVEN: /* Banker's rounding */
|
||
if(v>5) f = 1;
|
||
else if(v==5 && vPrev%2) f = 1;
|
||
break;
|
||
}
|
||
if(f) {
|
||
VpRdup(c,ixDigit); /* round up */
|
||
VpNmlz(c);
|
||
}
|
||
}
|
||
|
||
/*
|
||
* Rounds up m(plus one to final digit of m).
|
||
*/
|
||
static int
|
||
VpRdup(Real *m,U_LONG ind_m)
|
||
{
|
||
U_LONG 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,(S_LONG)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)
|
||
{
|
||
U_LONG my, ind_y, ind_x;
|
||
|
||
if(!VpHasVal(x)) {
|
||
VpAsgn(y,x,1);
|
||
goto Exit;
|
||
}
|
||
|
||
if(x->exponent > 0 && (U_LONG)x->exponent >= x->Prec) {
|
||
VpSetZero(y,VpGetSign(x));
|
||
goto Exit;
|
||
} else if(x->exponent <= 0) {
|
||
VpAsgn(y, x, 1);
|
||
goto Exit;
|
||
}
|
||
|
||
y->Prec = x->Prec -(U_LONG) 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 _DEBUG
|
||
if(gfDebug) {
|
||
VPrint(stdout, "VpFrac y=%\n", y);
|
||
VPrint(stdout, " x=%\n", x);
|
||
}
|
||
#endif /* _DEBUG */
|
||
return;
|
||
}
|
||
|
||
/*
|
||
* y = x ** n
|
||
*/
|
||
VP_EXPORT int
|
||
VpPower(Real *y, Real *x, S_INT n)
|
||
{
|
||
U_LONG s, ss;
|
||
S_LONG 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,-(S_INT)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;
|
||
loop1: ss = s;
|
||
s += s;
|
||
if(s >(U_LONG) n) goto out_loop1;
|
||
VpMult(w2, w1, w1);
|
||
VpAsgn(w1, w2, 1);
|
||
goto loop1;
|
||
out_loop1:
|
||
n -= ss;
|
||
VpMult(w2, y, w1);
|
||
VpAsgn(y, w2, 1);
|
||
}
|
||
if(sign < 0) {
|
||
VpDivd(w1, w2, VpConstOne, y);
|
||
VpAsgn(y, w1, 1);
|
||
}
|
||
|
||
Exit:
|
||
#ifdef _DEBUG
|
||
if(gfDebug) {
|
||
VPrint(stdout, "VpPower y=%\n", y);
|
||
VPrint(stdout, "VpPower x=%\n", x);
|
||
printf(" n=%d\n", n);
|
||
}
|
||
#endif /* _DEBUG */
|
||
VpFree(w2);
|
||
VpFree(w1);
|
||
return 1;
|
||
}
|
||
|
||
#ifdef _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
|
||
*/
|
||
{
|
||
U_LONG i;
|
||
|
||
if(v->MaxPrec <= 0) {
|
||
printf("ERROR(VpVarCheck): Illegal Max. Precision(=%lu)\n",
|
||
v->MaxPrec);
|
||
return 1;
|
||
}
|
||
if((v->Prec <= 0) ||((v->Prec) >(v->MaxPrec))) {
|
||
printf("ERROR(VpVarCheck): Illegal Precision(=%lu)\n", v->Prec);
|
||
printf(" Max. Prec.=%lu\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[%ld]=%lu\n", i, v->frac[i]);
|
||
printf(" Prec. =%lu\n", v->Prec);
|
||
printf(" Exp. =%d\n", v->exponent);
|
||
printf(" BASE =%lu\n", BASE);
|
||
return 3;
|
||
}
|
||
}
|
||
return 0;
|
||
}
|
||
#endif /* _DEBUG */
|