diff options
Diffstat (limited to 'ruby_1_8_6/ext/bigdecimal')
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/.cvsignore | 3 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/README | 60 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/bigdecimal.c | 4700 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/bigdecimal.def | 2 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/bigdecimal.h | 216 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/bigdecimal_en.html | 796 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/bigdecimal_ja.html | 799 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/depend | 1 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/extconf.rb | 12 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/jacobian.rb | 85 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/ludcmp.rb | 84 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/math.rb | 235 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/newton.rb | 77 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/util.rb | 65 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/sample/linear.rb | 71 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/sample/nlsolve.rb | 38 | ||||
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/sample/pi.rb | 20 |
17 files changed, 0 insertions, 7264 deletions
diff --git a/ruby_1_8_6/ext/bigdecimal/.cvsignore b/ruby_1_8_6/ext/bigdecimal/.cvsignore deleted file mode 100644 index 4088712231..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/.cvsignore +++ /dev/null @@ -1,3 +0,0 @@ -Makefile -mkmf.log -*.def diff --git a/ruby_1_8_6/ext/bigdecimal/README b/ruby_1_8_6/ext/bigdecimal/README deleted file mode 100644 index a233f47f64..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/README +++ /dev/null @@ -1,60 +0,0 @@ - - Ruby BIGDECIMAL(Variable Precision) extension library. - Copyright (C) 1999 by Shigeo Kobayashi(shigeo@tinyforest.gr.jp) - -BigDecimal is copyrighted free software by Shigeo Kobayashi <shigeo@tinyforest.gr.jp>. -You can redistribute it and/or modify it under either the terms of the GPL -(see COPYING file), or the conditions below: - - 1. You may make and give away verbatim copies of the source form of the - software without restriction, provided that you duplicate all of the - original copyright notices and associated disclaimers. - - 2. You may modify your copy of the software in any way, provided that - you do at least ONE of the following: - - a) place your modifications in the Public Domain or otherwise - make them Freely Available, such as by posting said - modifications to Usenet or an equivalent medium, or by allowing - the author to include your modifications in the software. - - b) use the modified software only within your corporation or - organization. - - c) rename any non-standard executables so the names do not conflict - with standard executables, which must also be provided. - - d) make other distribution arrangements with the author. - - 3. You may distribute the software in object code or executable - form, provided that you do at least ONE of the following: - - a) distribute the executables and library files of the software, - together with instructions (in the manual page or equivalent) - on where to get the original distribution. - - b) accompany the distribution with the machine-readable source of - the software. - - c) give non-standard executables non-standard names, with - instructions on where to get the original software distribution. - - d) make other distribution arrangements with the author. - - 4. You may modify and include the part of the software into any other - software (possibly commercial). - - 5. THIS SOFTWARE IS PROVIDED "AS IS" AND WITHOUT ANY EXPRESS OR - IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED - WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR - PURPOSE. - -* The Author - -Feel free to send comments and bug reports to the author. Here is the -author's latest mail address: - - shigeo@tinyforest.gr.jp - -------------------------------------------------------- -created at: Thu Dec 22 1999 diff --git a/ruby_1_8_6/ext/bigdecimal/bigdecimal.c b/ruby_1_8_6/ext/bigdecimal/bigdecimal.c deleted file mode 100644 index 636c0907d6..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/bigdecimal.c +++ /dev/null @@ -1,4700 +0,0 @@ -/* - * - * Ruby BigDecimal(Variable decimal precision) extension library. - * - * Copyright(C) 2002 by Shigeo Kobayashi(shigeo@tinyforest.gr.jp) - * - * You may distribute under the terms of either the GNU General Public - * License or the Artistic License, as specified in the README file - * of this BigDecimal distribution. - * - * NOTE: Change log in this source removed to reduce source code size. - * See rev. 1.25 if needed. - * - */ - -#include "ruby.h" -#include <ctype.h> -#include <stdio.h> -#include <stdlib.h> -#include <string.h> -#include <errno.h> -#include <float.h> -#include <math.h> -#include "math.h" -#include "version.h" - -/* #define ENABLE_NUMERIC_STRING */ - -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);} - -/* - * ================== Ruby Interface part ========================== - */ -#define DoSomeOne(x,y) rb_num_coerce_bin(x,y) - -#if 0 -/* 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() -{ - /* This is a #if-ed out function to fool Rdoc into documenting the class. */ - /* The real init function is Init_bigdecimal() further down. */ -} -#endif - -/* - * Returns the BigDecimal version number. - * - * Ruby 1.8.0 returns 1.0.0. - * Ruby 1.8.1 thru 1.8.3 return 1.0.1. - */ -static VALUE -BigDecimal_version(VALUE self) -{ - /* - * 1.0.0: Ruby 1.8.0 - * 1.0.1: Ruby 1.8.1 - */ - return rb_str_new2("1.0.1"); -} - -/* - * VP routines used in BigDecimal part - */ -static unsigned short VpGetException(void); -static void VpSetException(unsigned short f); -static void VpInternalRound(Real *c,int ixDigit,U_LONG vPrev,U_LONG v); -static int VpLimitRound(Real *c,U_LONG ixDigit); - -/* - * **** BigDecimal part **** - */ - -static void -BigDecimal_delete(Real *pv) -{ - VpFree(pv); -} - -static VALUE -ToValue(Real *p) -{ - if(VpIsNaN(p)) { - VpException(VP_EXCEPTION_NaN,"Computation results to 'NaN'(Not a Number)",0); - } else if(VpIsPosInf(p)) { - VpException(VP_EXCEPTION_INFINITY,"Computation results to 'Infinity'",0); - } else if(VpIsNegInf(p)) { - VpException(VP_EXCEPTION_INFINITY,"Computation results to '-Infinity'",0); - } - return p->obj; -} - -static Real * -GetVpValue(VALUE v, int must) -{ - Real *pv; - VALUE bg; - char szD[128]; - - switch(TYPE(v)) - { - case T_DATA: - if(RDATA(v)->dfree ==(void *) BigDecimal_delete) { - Data_Get_Struct(v, Real, pv); - return pv; - } else { - goto SomeOneMayDoIt; - } - break; - case T_FIXNUM: - sprintf(szD, "%ld", FIX2LONG(v)); - return VpCreateRbObject(VpBaseFig() * 2 + 1, szD); - -#ifdef ENABLE_NUMERIC_STRING - case T_STRING: - SafeStringValue(v); - return VpCreateRbObject(strlen(RSTRING_PTR(v)) + VpBaseFig() + 1, - RSTRING_PTR(v)); -#endif /* ENABLE_NUMERIC_STRING */ - - case T_BIGNUM: - bg = rb_big2str(v, 10); - return VpCreateRbObject(strlen(RSTRING_PTR(bg)) + VpBaseFig() + 1, - RSTRING_PTR(bg)); - default: - goto SomeOneMayDoIt; - } - -SomeOneMayDoIt: - if(must) { - rb_raise(rb_eTypeError, "%s can't be coerced into BigDecimal", - rb_special_const_p(v)? - RSTRING_PTR(rb_inspect(v)): - rb_obj_classname(v) - ); - } - return NULL; /* NULL means to coerce */ -} - -/* call-seq: - * BigDecimal.double_fig - * - * The BigDecimal.double_fig class method returns the number of digits a - * Float number is allowed to have. The result depends upon the CPU and OS - * in use. - */ -static VALUE -BigDecimal_double_fig(VALUE self) -{ - return INT2FIX(VpDblFig()); -} - -/* call-seq: - * precs - * - * Returns an Array of two Integer values. - * - * The first value is the current number of significant digits in the - * BigDecimal. The second value is the maximum number of significant digits - * for the BigDecimal. - */ -static VALUE -BigDecimal_prec(VALUE self) -{ - ENTER(1); - Real *p; - VALUE obj; - - GUARD_OBJ(p,GetVpValue(self,1)); - obj = rb_assoc_new(INT2NUM(p->Prec*VpBaseFig()), - INT2NUM(p->MaxPrec*VpBaseFig())); - return obj; -} - -static VALUE -BigDecimal_hash(VALUE self) -{ - ENTER(1); - Real *p; - U_LONG hash,i; - - GUARD_OBJ(p,GetVpValue(self,1)); - hash = (U_LONG)p->sign; - /* hash!=2: the case for 0(1),NaN(0) or +-Infinity(3) is sign itself */ - if(hash==2) { - for(i = 0; i < p->Prec;i++) { - hash = 31 * hash + p->frac[i]; - hash ^= p->frac[i]; - } - hash += p->exponent; - } - return INT2FIX(hash); -} - -static VALUE -BigDecimal_dump(int argc, VALUE *argv, VALUE self) -{ - ENTER(5); - char sz[50]; - Real *vp; - char *psz; - VALUE dummy; - rb_scan_args(argc, argv, "01", &dummy); - GUARD_OBJ(vp,GetVpValue(self,1)); - sprintf(sz,"%lu:",VpMaxPrec(vp)*VpBaseFig()); - psz = ALLOCA_N(char,(unsigned int)VpNumOfChars(vp,"E")+strlen(sz)); - sprintf(psz,"%s",sz); - VpToString(vp, psz+strlen(psz), 0, 0); - return rb_str_new2(psz); -} - -/* - * Internal method used to provide marshalling support. See the Marshal module. - */ -static VALUE -BigDecimal_load(VALUE self, VALUE str) -{ - ENTER(2); - Real *pv; - unsigned char *pch; - unsigned char ch; - unsigned long m=0; - - SafeStringValue(str); - pch = (unsigned char *)RSTRING_PTR(str); - /* First get max prec */ - while((*pch)!=(unsigned char)'\0' && (ch=*pch++)!=(unsigned char)':') { - if(!ISDIGIT(ch)) { - rb_raise(rb_eTypeError, "load failed: invalid character in the marshaled string"); - } - m = m*10 + (unsigned long)(ch-'0'); - } - if(m>VpBaseFig()) m -= VpBaseFig(); - GUARD_OBJ(pv,VpNewRbClass(m,(char *)pch,self)); - m /= VpBaseFig(); - if(m && pv->MaxPrec>m) pv->MaxPrec = m+1; - return ToValue(pv); -} - - /* call-seq: - * BigDecimal.mode(mode, value) - * - * Controls handling of arithmetic exceptions and rounding. If no value - * is supplied, the current value is returned. - * - * Six values of the mode parameter control the handling of arithmetic - * exceptions: - * - * BigDecimal::EXCEPTION_NaN - * BigDecimal::EXCEPTION_INFINITY - * BigDecimal::EXCEPTION_UNDERFLOW - * BigDecimal::EXCEPTION_OVERFLOW - * BigDecimal::EXCEPTION_ZERODIVIDE - * BigDecimal::EXCEPTION_ALL - * - * For each mode parameter above, if the value set is false, computation - * continues after an arithmetic exception of the appropriate type. - * When computation continues, results are as follows: - * - * EXCEPTION_NaN:: NaN - * EXCEPTION_INFINITY:: +infinity or -infinity - * EXCEPTION_UNDERFLOW:: 0 - * EXCEPTION_OVERFLOW:: +infinity or -infinity - * EXCEPTION_ZERODIVIDE:: +infinity or -infinity - * - * One value of the mode parameter controls the rounding of numeric values: - * BigDecimal::ROUND_MODE. The values it can take are: - * - * ROUND_UP:: 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)))); - } - if(f&VP_EXCEPTION_NaN) { - VpSetException((unsigned short)((val==Qtrue)?(fo|VP_EXCEPTION_NaN): - (fo&(~VP_EXCEPTION_NaN)))); - } - 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 = (VALUE)Data_Wrap_Struct(klass, 0, BigDecimal_delete, pv); - return pv; -} - -VP_EXPORT Real * -VpCreateRbObject(U_LONG mx, const char *str) -{ - Real *pv = VpAlloc(mx,str); - pv->obj = (VALUE)Data_Wrap_Struct(rb_cBigDecimal, 0, BigDecimal_delete, 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 True if the value is infinite */ -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; -} - -/* Returns the value as an integer (Fixnum or Bignum). - * - * If the BigNumber is infinity or NaN, returns nil. - */ -static VALUE -BigDecimal_to_i(VALUE self) -{ - ENTER(5); - int e,n,i,nf; - U_LONG v,b,j; - char *psz,*pch; - Real *p; - - GUARD_OBJ(p,GetVpValue(self,1)); - - /* Infinity or NaN not converted. */ - if(VpIsNaN(p)) { - VpException(VP_EXCEPTION_NaN,"Computation results to 'NaN'(Not a Number)",0); - return Qnil; - } else if(VpIsPosInf(p)) { - VpException(VP_EXCEPTION_INFINITY,"Computation results to 'Infinity'",0); - return Qnil; - } else if(VpIsNegInf(p)) { - VpException(VP_EXCEPTION_INFINITY,"Computation results to '-Infinity'",0); - return Qnil; - } - - e = VpExponent10(p); - if(e<=0) return INT2FIX(0); - nf = VpBaseFig(); - if(e<=nf) { - e = VpGetSign(p)*p->frac[0]; - return INT2FIX(e); - } - psz = ALLOCA_N(char,(unsigned int)(e+nf+2)); - - n = (e+nf-1)/nf; - pch = psz; - if(VpGetSign(p)<0) *pch++ = '-'; - for(i=0;i<n;++i) { - b = VpBaseVal()/10; - if(i>=(int)p->Prec) { - while(b) { - *pch++ = '0'; - b /= 10; - } - continue; - } - v = p->frac[i]; - while(b) { - j = v/b; - *pch++ = (char)(j + '0'); - v -= j*b; - b /= 10; - } - } - *pch++ = 0; - return rb_cstr2inum(psz,10); -} - -static VALUE -BigDecimal_induced_from(VALUE self, VALUE x) -{ - Real *p = GetVpValue(x,1); - return p->obj; -} - -/* 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; - - GUARD_OBJ(p,GetVpValue(self,1)); - if(VpVtoD(&d, &e, p)!=1) return rb_float_new(d); - buf = ALLOCA_N(char,(unsigned int)VpNumOfChars(p,"E")); - VpToString(p, buf, 0, 0); - errno = 0; - d = strtod(buf, 0); - if(errno == ERANGE) { - VpException(VP_EXCEPTION_OVERFLOW,"BigDecimal to Float conversion",0); - if(d>0.0) return rb_float_new(DBL_MAX); - else return rb_float_new(-DBL_MAX); - } - return rb_float_new(d); -} - -/* The coerce method provides support for Ruby type coercion. It is not - * enabled by default. - * - * This means that binary operations like + * / or - can often be performed - * on a BigDecimal and an object of another type, if the other object can - * be coerced into a BigDecimal value. - * - * e.g. - * a = BigDecimal.new("1.0") - * b = a / 2.0 -> 0.5 - * - * Note that coercing a String to a BigDecimal is not supported by default; - * it requires a special compile-time option when building Ruby. - */ -static VALUE -BigDecimal_coerce(VALUE self, VALUE other) -{ - ENTER(2); - VALUE obj; - Real *b; - if(TYPE(other) == T_FLOAT) { - obj = rb_assoc_new(other, BigDecimal_to_f(self)); - } else { - GUARD_OBJ(b,GetVpValue(other,1)); - obj = rb_assoc_new(b->obj, self); - } - return obj; -} - -static VALUE -BigDecimal_uplus(VALUE self) -{ - return self; -} - - /* call-seq: - * add(value, digits) - * - * Add the specified value. - * - * e.g. - * c = a.add(b,n) - * c = a + b - * - * digits:: If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode. - */ -static VALUE -BigDecimal_add(VALUE self, VALUE r) -{ - ENTER(5); - Real *c, *a, *b; - 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) return rb_num_coerce_cmp(self,r); - SAVE(b); - e = VpComp(a, b); - if(e==999) return Qnil; - switch(op) - { - case '*': return INT2FIX(e); /* any op */ - case '=': if(e==0) return Qtrue ; return Qfalse; - 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 True if the value is non-zero. */ -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->MaxPrec + b->MaxPrec + 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 DoSomeOne(self,r); - SAVE(b); - - if(VpIsNaN(a) || VpIsNaN(b)) goto NaN; - if(VpIsInf(a) || VpIsInf(b)) goto NaN; - if(VpIsZero(b)) goto NaN; - if(VpIsZero(a)) { - GUARD_OBJ(c,VpCreateRbObject(1, "0")); - GUARD_OBJ(d,VpCreateRbObject(1, "0")); - *div = d; - *mod = c; - return (VALUE)0; - } - - mx = a->Prec; - if(mx<b->Prec) mx = b->Prec; - 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); - VpAddSub(d ,c,b, 1); - *div = res; - *mod = d; - } else { - *div = d; - *mod = c; - } - return (VALUE)0; - -NaN: - GUARD_OBJ(c,VpCreateRbObject(1, "NaN")); - GUARD_OBJ(d,VpCreateRbObject(1, "NaN")); - *div = d; - *mod = c; - return (VALUE)0; -} - -/* 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; - - obj = BigDecimal_DoDivmod(self,r,&div,&mod); - if(obj!=(VALUE)0) return obj; - SAVE(div);SAVE(mod); - return ToValue(mod); -} - -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); - 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. - * - * If the values divided are of the same sign, the remainder is the same as - * the modulus (see divmod). - * - * Otherwise, the remainder is the modulus minus the value divided by. - */ -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; - - obj = BigDecimal_DoDivmod(self,r,&div,&mod); - if(obj!=(VALUE)0) return obj; - SAVE(div);SAVE(mod); - obj = rb_assoc_new(ToValue(div), ToValue(mod)); - return obj; -} - -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; - obj = BigDecimal_DoDivmod(self,b,&div,&mod); - if(obj!=(VALUE)0) return obj; - return ToValue(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); - 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 */ - 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); - 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); - 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; - 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; - - psz = ALLOCA_N(char,(unsigned int)nc); - - if(fmt) { - VpToFString(vp, psz, mc, fPlus); - } else { - VpToString (vp, psz, mc, fPlus); - } - return rb_str_new2(psz); -} - -/* 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,obj1; - S_LONG e; - S_LONG s; - char *psz1; - - GUARD_OBJ(vp,GetVpValue(self,1)); - psz1 = ALLOCA_N(char,(unsigned int)VpNumOfChars(vp,"E")); - VpSzMantissa(vp,psz1); - s = 1; - if(psz1[0]=='-') { - s = -1; ++psz1; - } - if(psz1[0]=='N') s=0; /* NaN */ - e = VpExponent10(vp); - obj1 = rb_str_new2(psz1); - obj = rb_ary_new2(4); - rb_ary_push(obj, INT2FIX(s)); - rb_ary_push(obj, obj1); - 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; - VALUE obj; - unsigned int nc; - char *psz1; - char *pszAll; - - GUARD_OBJ(vp,GetVpValue(self,1)); - nc = VpNumOfChars(vp,"E"); - nc +=(nc + 9) / 10; - - psz1 = ALLOCA_N(char,nc); - pszAll = ALLOCA_N(char,nc+256); - VpToString(vp, psz1, 10, 0); - sprintf(pszAll,"#<BigDecimal:%lx,'%s',%lu(%lu)>",self,psz1,VpPrec(vp)*VpBaseFig(),VpMaxPrec(vp)*VpBaseFig()); - obj = rb_str_new2(pszAll); - 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 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); -} - -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, "induced_from",BigDecimal_induced_from, 1); - 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 - * underflow (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, "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 */ -static int gfCheckVal = 1; /* Value checking flag in VpNmlz() */ -#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 */ - -#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. */ -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 - -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; -} - -VP_EXPORT int -VpIsNegDoubleZero(double v) -{ - double z = VpGetDoubleNegZero(); - return MemCmp(&v,&z,sizeof(v))==0; -} - -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_ZERODIVIDE: - case VP_EXCEPTION_OVERFLOW: - */ - case VP_EXCEPTION_INFINITY: - exc = rb_eFloatDomainError; - goto raise; - case VP_EXCEPTION_NaN: - exc = rb_eFloatDomainError; - goto raise; - case VP_EXCEPTION_UNDERFLOW: - exc = rb_eFloatDomainError; - goto raise; - 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 = %lu\n", BASE_FIG); - printf(" DBLE_FIG = %lu\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(); - - 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; - psz = ALLOCA_N(char,strlen(szVal)+1); - 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)) 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, 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 reading 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 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; - } - } - *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; - /* get exponent part */ - e = 0; - ma = a->MaxPrec; - mi = ni; - me = ne; - signe = 1; - 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)) { - return VpException(VP_EXCEPTION_INFINITY,"exponent overflow",0); - } - ++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); - - 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 = %ld\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 - */ -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; -} - -/* - * 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; -} - -/* - * - * f = 0: Round off/Truncate, 1: round up, 2:ceil, 3: floor, 4: Banker's rounding - * 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) { - exptoadd = -nf; - nf = 0; - } - /* ix: x->fraq[ix] contains round position */ - ix = nf/(int)BASE_FIG; - if(((U_LONG)ix)>=y->Prec) return 0; /* Unable to round */ - 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;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(!VpIsDef(x)) { - VpSetNaN(y); /* Not sure !!! */ - 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 */ diff --git a/ruby_1_8_6/ext/bigdecimal/bigdecimal.def b/ruby_1_8_6/ext/bigdecimal/bigdecimal.def deleted file mode 100644 index 8450e164e6..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/bigdecimal.def +++ /dev/null @@ -1,2 +0,0 @@ -EXPORTS -Init_bigdecimal diff --git a/ruby_1_8_6/ext/bigdecimal/bigdecimal.h b/ruby_1_8_6/ext/bigdecimal/bigdecimal.h deleted file mode 100644 index 4f77feab00..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/bigdecimal.h +++ /dev/null @@ -1,216 +0,0 @@ -/* - * - * Ruby BigDecimal(Variable decimal precision) extension library. - * - * Copyright(C) 2002 by Shigeo Kobayashi(shigeo@tinyforest.gr.jp) - * - * You may distribute under the terms of either the GNU General Public - * License or the Artistic License, as specified in the README file - * of this BigDecimal distribution. - * - * NOTES: - * 2003-03-28 V1.0 checked in. - * - */ - -#ifndef ____BIG_DECIMAL__H____ -#define ____BIG_DECIMAL__H____ - -#if defined(__cplusplus) -extern "C" { -#endif - -/* - * NaN & Infinity - */ -#define SZ_NaN "NaN" -#define SZ_INF "Infinity" -#define SZ_PINF "+Infinity" -#define SZ_NINF "-Infinity" - -/* - * #define VP_EXPORT other than static to let VP_ routines - * be called from outside of this module. - */ -#define VP_EXPORT static - -#define U_LONG unsigned long -#define S_LONG long -#define U_INT unsigned int -#define S_INT int - -/* Exception codes */ -#define VP_EXCEPTION_ALL ((unsigned short)0x00FF) -#define VP_EXCEPTION_INFINITY ((unsigned short)0x0001) -#define VP_EXCEPTION_NaN ((unsigned short)0x0002) -#define VP_EXCEPTION_UNDERFLOW ((unsigned short)0x0004) -#define VP_EXCEPTION_OVERFLOW ((unsigned short)0x0001) /* 0x0008) */ -#define VP_EXCEPTION_ZERODIVIDE ((unsigned short)0x0001) /* 0x0010) */ - -/* Following 2 exceptions cann't controlled by user */ -#define VP_EXCEPTION_OP ((unsigned short)0x0020) -#define VP_EXCEPTION_MEMORY ((unsigned short)0x0040) - -/* Computation mode */ -#define VP_ROUND_MODE ((unsigned short)0x0100) -#define VP_ROUND_UP 1 -#define VP_ROUND_DOWN 2 -#define VP_ROUND_HALF_UP 3 -#define VP_ROUND_HALF_DOWN 4 -#define VP_ROUND_CEIL 5 -#define VP_ROUND_FLOOR 6 -#define VP_ROUND_HALF_EVEN 7 - -#define VP_SIGN_NaN 0 /* NaN */ -#define VP_SIGN_POSITIVE_ZERO 1 /* Positive zero */ -#define VP_SIGN_NEGATIVE_ZERO -1 /* Negative zero */ -#define VP_SIGN_POSITIVE_FINITE 2 /* Positive finite number */ -#define VP_SIGN_NEGATIVE_FINITE -2 /* Negative finite number */ -#define VP_SIGN_POSITIVE_INFINITE 3 /* Positive infinite number */ -#define VP_SIGN_NEGATIVE_INFINITE -3 /* Negative infinite number */ - -/* - * VP representation - * r = 0.xxxxxxxxx *BASE**exponent - */ -typedef struct { - VALUE obj; /* Back pointer(VALUE) for Ruby object. */ - U_LONG MaxPrec; /* Maximum precision size */ - /* This is the actual size of pfrac[] */ - /*(frac[0] to frac[MaxPrec] are available). */ - U_LONG Prec; /* Current precision size. */ - /* This indicates how much the. */ - /* the array frac[] is actually used. */ - S_INT exponent;/* Exponent part. */ - short sign; /* Attributes of the value. */ - /* - * ==0 : NaN - * 1 : Positive zero - * -1 : Negative zero - * 2 : Positive number - * -2 : Negative number - * 3 : Positive infinite number - * -3 : Negative infinite number - */ - short flag; /* Not used in vp_routines,space for user. */ - U_LONG frac[1]; /* Pointer to array of fraction part. */ -} Real; - -/* - * ------------------ - * EXPORTables. - * ------------------ - */ - -VP_EXPORT Real * -VpNewRbClass(U_LONG mx,char *str,VALUE klass); - -VP_EXPORT Real *VpCreateRbObject(U_LONG mx,const char *str); - -VP_EXPORT U_LONG VpBaseFig(void); -VP_EXPORT U_LONG VpDblFig(void); -VP_EXPORT U_LONG VpBaseVal(void); - -/* Zero,Inf,NaN (isinf(),isnan() used to check) */ -VP_EXPORT double VpGetDoubleNaN(void); -VP_EXPORT double VpGetDoublePosInf(void); -VP_EXPORT double VpGetDoubleNegInf(void); -VP_EXPORT double VpGetDoubleNegZero(void); - -/* These 2 functions added at v1.1.7 */ -VP_EXPORT U_LONG VpGetPrecLimit(void); -VP_EXPORT U_LONG VpSetPrecLimit(U_LONG n); - -/* Round mode */ -VP_EXPORT int VpIsRoundMode(unsigned long n); -VP_EXPORT unsigned long VpGetRoundMode(void); -VP_EXPORT unsigned long VpSetRoundMode(unsigned long n); - -VP_EXPORT int VpException(unsigned short f,const char *str,int always); -VP_EXPORT int VpIsNegDoubleZero(double v); -VP_EXPORT U_LONG VpNumOfChars(Real *vp,const char *pszFmt); -VP_EXPORT U_LONG VpInit(U_LONG BaseVal); -VP_EXPORT void *VpMemAlloc(U_LONG mb); -VP_EXPORT void VpFree(Real *pv); -VP_EXPORT Real *VpAlloc(U_LONG mx, const char *szVal); -VP_EXPORT int VpAsgn(Real *c,Real *a,int isw); -VP_EXPORT int VpAddSub(Real *c,Real *a,Real *b,int operation); -VP_EXPORT int VpMult(Real *c,Real *a,Real *b); -VP_EXPORT int VpDivd(Real *c,Real *r,Real *a,Real *b); -VP_EXPORT int VpComp(Real *a,Real *b); -VP_EXPORT S_LONG VpExponent10(Real *a); -VP_EXPORT void VpSzMantissa(Real *a,char *psz); -VP_EXPORT int VpToSpecialString(Real *a,char *psz,int fPlus); -VP_EXPORT void VpToString(Real *a,char *psz,int fFmt,int fPlus); -VP_EXPORT void VpToFString(Real *a,char *psz,int fFmt,int fPlus); -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); -VP_EXPORT int VpVtoD(double *d,S_LONG *e,Real *m); -VP_EXPORT void VpDtoV(Real *m,double d); -VP_EXPORT void VpItoV(Real *m,S_INT ival); -VP_EXPORT int VpSqrt(Real *y,Real *x); -VP_EXPORT int VpActiveRound(Real *y,Real *x,int f,int il); -VP_EXPORT int VpMidRound(Real *y, int f, int nf); -VP_EXPORT int VpLeftRound(Real *y, int f, int nf); -VP_EXPORT void VpFrac(Real *y,Real *x); -VP_EXPORT int VpPower(Real *y,Real *x,S_INT n); - -/* VP constants */ -VP_EXPORT Real *VpOne(void); - -/* - * ------------------ - * MACRO definitions. - * ------------------ - */ -#define Abs(a) (((a)>= 0)?(a):(-(a))) -#define Max(a, b) (((a)>(b))?(a):(b)) -#define Min(a, b) (((a)>(b))?(b):(a)) - -#define VpMaxPrec(a) ((a)->MaxPrec) -#define VpPrec(a) ((a)->Prec) -#define VpGetFlag(a) ((a)->flag) - -/* Sign */ - -/* VpGetSign(a) returns 1,-1 if a>0,a<0 respectively */ -#define VpGetSign(a) (((a)->sign>0)?1:(-1)) -/* Change sign of a to a>0,a<0 if s = 1,-1 respectively */ -#define VpChangeSign(a,s) {if((s)>0) (a)->sign=(short)Abs((S_LONG)(a)->sign);else (a)->sign=-(short)Abs((S_LONG)(a)->sign);} -/* Sets sign of a to a>0,a<0 if s = 1,-1 respectively */ -#define VpSetSign(a,s) {if((s)>0) (a)->sign=(short)VP_SIGN_POSITIVE_FINITE;else (a)->sign=(short)VP_SIGN_NEGATIVE_FINITE;} - -/* 1 */ -#define VpSetOne(a) {(a)->frac[0]=(a)->exponent=(a)->Prec=1;(a)->sign=VP_SIGN_POSITIVE_FINITE;} - -/* ZEROs */ -#define VpIsPosZero(a) ((a)->sign==VP_SIGN_POSITIVE_ZERO) -#define VpIsNegZero(a) ((a)->sign==VP_SIGN_NEGATIVE_ZERO) -#define VpIsZero(a) (VpIsPosZero(a) || VpIsNegZero(a)) -#define VpSetPosZero(a) ((a)->frac[0]=0,(a)->Prec=1,(a)->sign=VP_SIGN_POSITIVE_ZERO) -#define VpSetNegZero(a) ((a)->frac[0]=0,(a)->Prec=1,(a)->sign=VP_SIGN_NEGATIVE_ZERO) -#define VpSetZero(a,s) ( ((s)>0)?VpSetPosZero(a):VpSetNegZero(a) ) - -/* NaN */ -#define VpIsNaN(a) ((a)->sign==VP_SIGN_NaN) -#define VpSetNaN(a) ((a)->frac[0]=0,(a)->Prec=1,(a)->sign=VP_SIGN_NaN) - -/* Infinity */ -#define VpIsPosInf(a) ((a)->sign==VP_SIGN_POSITIVE_INFINITE) -#define VpIsNegInf(a) ((a)->sign==VP_SIGN_NEGATIVE_INFINITE) -#define VpIsInf(a) (VpIsPosInf(a) || VpIsNegInf(a)) -#define VpIsDef(a) ( !(VpIsNaN(a)||VpIsInf(a)) ) -#define VpSetPosInf(a) ((a)->frac[0]=0,(a)->Prec=1,(a)->sign=VP_SIGN_POSITIVE_INFINITE) -#define VpSetNegInf(a) ((a)->frac[0]=0,(a)->Prec=1,(a)->sign=VP_SIGN_NEGATIVE_INFINITE) -#define VpSetInf(a,s) ( ((s)>0)?VpSetPosInf(a):VpSetNegInf(a) ) -#define VpHasVal(a) (a->frac[0]) -#define VpIsOne(a) ((a->Prec==1)&&(a->frac[0]==1)&&(a->exponent==1)) -#define VpExponent(a) (a->exponent) -#ifdef _DEBUG -int VpVarCheck(Real * v); -VP_EXPORT int VPrint(FILE *fp,char *cntl_chr,Real *a); -#endif /* _DEBUG */ - -#if defined(__cplusplus) -} /* extern "C" { */ -#endif -#endif /* ____BIG_DECIMAL__H____ */ diff --git a/ruby_1_8_6/ext/bigdecimal/bigdecimal_en.html b/ruby_1_8_6/ext/bigdecimal/bigdecimal_en.html deleted file mode 100644 index c2b86faef6..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/bigdecimal_en.html +++ /dev/null @@ -1,796 +0,0 @@ -<!-- saved from url=(0022)http://internet.e-mail --> -<HTML> -<HEAD> -<META HTTP-EQUIV="Content-Type" CONTENT="text/html"> -<style type="text/css"><!-- -body { color: #3f0f0f; background: #fefeff; margin-left: 2em; margin-right: 2em;} -h1 { color: #ffffff; background-color: #3939AD; border-color: #FF00FF; width: 100%; border-style: solid; - border-top-width: 0.1em; border-bottom-width: 0.1em; border-right: none; border-left: none; - padding: 0.1em; font-weight: bold; font-size: 160%; text-align: center;} -h2 { color: #00007f; background-color: #e7e7ff; border-color: #000094; width: 100%; border-style: solid; border-le ft: none; border-right: none; border-top-width: 0.1em; border-bottom-width: 0.1em; padding: 0.1em; - font-weight: bold; font-size: 110%; -} -h3 { color: #00007f; padding: 0.2em; font-size: 110%;} -h4, h5 { color: #000000; padding: 0.2em; font-size: 100%;} -table { margin-top: 0.2em; margin-bottom: 0.2em; margin-left: 2em; margin-right: 2em;} -caption { color: #7f0000; font-weight: bold;} -th { background: #e7e7ff; padding-left: 0.2em; padding-right: 0.2em;} -td { background: #f3f7ff; padding-left: 0.2em; padding-right: 0.2em;} -code { color: #0000df;} -dt { margin-top: 0.2em;} -li { margin-top: 0.2em;} -pre -{ BACKGROUND-COLOR: #d0d0d0; BORDER-BOTTOM: medium none; BORDER-LEFT: medium none; - BORDER-RIGHT: medium none; BORDER-TOP: medium none; LINE-HEIGHT: 100%; MARGIN: 12px 12px 12px 12px; - PADDING-BOTTOM: 12px; PADDING-LEFT: 12px; PADDING-RIGHT: 12px; PADDING-TOP: 12px; - WHITE-SPACE: pre; WIDTH: 100% -} ---></style> - -<TITLE>BigDecimal:An extension library for Ruby</TITLE> -</HEAD> -<BODY BGCOLOR=#FFFFE0> -<H1>BigDecimal(Variable Precision Floating Library for Ruby)</H1> -<DIV align="right"><A HREF="./bigdecimal_ja.html">Japanese</A></DIV><BR> -BigDecimal is an extension library for the Ruby interpreter. -Using BigDecimal class, you can obtain any number of significant digits in computation. -For the details about Ruby see:<BR> -<UL> -<LI><A HREF="http://www.ruby-lang.org/en/">http://www.ruby-lang.org/en/</A>:Official Ruby page(English).</LI> -<LI><A HREF="http://kahori.com/ruby/ring/">http://kahori.com/ruby/ring/</A>:Mutually linked pages relating to Ruby(Japanese). -</LI> -</UL> -NOTE:<BR> - This software is provided "AS IS" and without any express or - implied warranties,including,without limitation,the implied - warranties of merchantibility and fitness for a particular - purpose. For the details,see COPYING and README included in this - distribution. -<BR> -<hr> - -<H2>Contents</H2> -<UL> -<LI><A HREF="#INTRO">Introduction</LI> -<LI><A HREF="#SPEC">Usage and methods</A></LI> -<LI><A HREF="#UNDEF">Infinity,NaN,Zero</A></LI> -<LI><A HREF="#STRUCT">Internal structure</A></LI> -<LI><A HREF="#BASE">Binary or decimal number representation</A></LI> -<LI><A HREF="#PREC">Resulting number of significant digits</A></LI> -</UL> -<HR> - -<A NAME="#INTRO"> -<H2>Introduction</H2> -Ruby already has builtin (variable length integer number) class Bignum. Using Bignum class,you can obtain - any integer value in magnitude. But, variable length decimal number class is not yet built in. -This is why I made variable length floating class BigDecimal. -Feel free to send any comments or bug reports to me. -<A HREF="mailto:shigeo@tinyforest.gr.jp">shigeo@tinyforest.gr.jp</A> -I will try(but can't promise) to fix bugs reported. -<hr> -<H2>Installation</H2> -The Ruby latest version can be downloaded from <A HREF="http://www.ruby-lang.org/en/">Official Ruby page</A>. -Once decompress the downloaded Ruby archive,follow the normal installation procedures according to the -documents included. - -<A NAME="#SPEC"> -<H2>Usage and methods</H2> -Suppose you already know Ruby programming, -to create BigDecimal objects,the program would like:<BR> - -<CODE><PRE> - require 'bigdecimal' - a=BigDecimal::new("0.123456789123456789") - b=BigDecimal("123456.78912345678",40) - c=a+b -</PRE></CODE> - -<H3>List of methods</H3> -In 32 bits integer system,every 4 digits(in decimal) are computed simultaneously. -This means the number of significant digits in BigDecimal is always a multiple of 4. -<P> -Some more methods are available in Ruby code (not C code). -Functions such as sin,cos ...,are in math.rb in bigdecimal directory. -To use them,require math.rb as: -<CODE><PRE> -require "bigdecimal/math.rb" -</PRE></CODE> -For details,see the math.rb code and comments. -Other utility methods are in util.rb. -To use util.rb, require it as: -<CODE><PRE> -require "bigdecimal/util.rb" -</PRE></CODE> -For details,see the util.rb code. - -<H4><U>Class methods</U></H4> -<UL> -<LI><B>new</B></LI><BLOCKQUOTE> -"new" method creates a new BigDecimal object.<BR> -a=BigDecimal::new(s[,n]) or<BR> -a=BigDecimal(s[,n]) or<BR> -where:<BR> -s: Initial value string. Spaces will be ignored. Any unrecognizable character for -representing initial value terminates the string.<BR> -n: Maximum number of significant digits of a. n must be a Fixnum object. -If n is omitted or is equal to 0,then the maximum number of significant digits of a is determined from the length of s. -Actual number of digits handled in computations are usually gretaer than n.<BR> -n is useful when performing divisions like -<CODE><PRE> -BigDecimal("1") / BigDecimal("3") # => 0.3333333333 33E0 -BigDecimal("1",10) / BigDecimal("3",10) # => 0.3333333333 3333333333 33333333E0 -</PRE></CODE> -but the resulting digits obtained may differ in future version. -</BLOCKQUOTE> - -<LI><B>mode</B></LI><BLOCKQUOTE> -f = BigDecimal.mode(s[,v])<BR> -mode method controls BigDecimal computation. If the second argument is not given or is nil,then the value -of current setting is returned. -Following usage are defined.<BR> -<P><B>[EXCEPTION control]</B><P> -Actions when computation results NaN or Infinity can be defined as follows. -<P> -<BLOCKQUOTE> -f = BigDecimal::mode(BigDecimal::EXCEPTION_NaN,flag)<BR> -f = BigDecimal::mode(BigDecimal::EXCEPTION_INFINITY,flag)<BR> -f = BigDecimal::mode(BigDecimal::EXCEPTION_UNDERFLOW,flag)<BR> -f = BigDecimal::mode(BigDecimal::EXCEPTION_OVERFLOW,flag)<BR> -f = BigDecimal::mode(BigDecimal::EXCEPTION_ZERODIVIDE,flag)<BR> -f = BigDecimal::mode(BigDecimal::EXCEPTION_ALL,flag)<BR> -</BLOCKQUOTE> -EXCEPTION_NaN controls the execution when computation results to NaN.<BR> -EXCEPTION_INFINITY controls the execution when computation results to Infinity(±Infinity).<BR> -EXCEPTION_UNDERFLOW controls the execution when computation underflows.<BR> -EXCEPTION_OVERFLOW controls the execution when computation overflows.<BR> -EXCEPTION_ZERODIVIDE controls the execution when zero-division occures.<BR> -EXCEPTION_ALL controls the execution for any exception defined occures.<BR> -If the flag is true,then the relating exception is thrown.<BR> -No exception is thrown when the flag is false(default) and computation -continues with the result:<BR> -<BLOCKQUOTE> -EXCEPTION_NaN results to NaN<BR> -EXCEPTION_INFINITY results to +Infinity or -Infinity<BR> -EXCEPTION_UNDERFLOW results to 0.<BR> -EXCEPTION_OVERFLOW results to +Infinity or -Infinity<BR> -EXCEPTION_ZERODIVIDE results to +Infinity or -Infinity<BR> -</BLOCKQUOTE> -EXCEPTION_INFINITY,EXCEPTION_OVERFLOW, and EXCEPTION_ZERODIVIDE are - currently the same.<BR> -The return value of mode method is the value set.<BR> -If nil is specified for the second argument,then current setting is returned.<BR> -Suppose the return value of the mode method is f,then - f & BigDecimal::EXCEPTION_NaN !=0 means EXCEPTION_NaN is set to on. -<P> -<B>[ROUND error control]</B><P> -Rounding operation can be controlled as: -<BLOCKQUOTE> -f = BigDecimal::mode(BigDecimal::ROUND_MODE,flag) -</BLOCKQUOTE> -where flag must be one of: -<TABLE> - -<TR><TD>ROUND_UP</TD><TD>round away from zero.</TD></TR> -<TR><TD>ROUND_DOWN</TD><TD>round towards zero(truncate).</TD></TR> -<TR><TD>ROUND_HALF_UP</TD><TD>round up if the digit >= 5 otherwise truncated(default).</TD></TR> -<TR><TD>ROUND_HALF_DOWN</TD><TD>round up if the digit >= 6 otherwise truncated.</TD></TR> -<TR><TD>ROUND_HALF_EVEN</TD><TD>round towards the even neighbor(Banker's rounding). -<TR><TD>ROUND_CEILING</TD><TD>round towards positive infinity(ceil).</TD></TR> -<TR><TD>ROUND_FLOOR</TD><TD>round towards negative infinity(floor).</TD></TR> -</TABLE> -New rounding mode is returned. If nil is specified for the second argument,then current setting is returned.<BR> -The digit location for rounding operation can not be specified by this mode method, -use truncate/round/ceil/floor/add/sub/mult/div mthods for each instance instead. -</BLOCKQUOTE> - -<LI><B>limit[(n)]</B></LI><BLOCKQUOTE> -Limits the maximum digits that the newly created BigDecimal objects can hold never exceed n. -This means the rounding operation specified by BigDecimal.mode is -performed if necessary. -limit returns the value before set if n is nil or is not specified. -Zero,the default value,means no upper limit.<BR> -The limit has no more priority than instance methods such as truncate,round,ceil,floor,add,sub,mult,and div. <BR> -mf = BigDecimal::limit(n)<BR> -</BLOCKQUOTE> - -<LI><B>double_fig</B></LI><BLOCKQUOTE> -double_fig is a class method which returns the number of digits -the Float class can have. -<CODE><PRE> - p BigDecimal::double_fig # ==> 20 (depends on the CPU etc.) -</PRE></CODE> -The equivalent C programs which calculates the value of -double_fig is: -<CODE><PRE> - double v = 1.0; - int double_fig = 0; - while(v + 1.0 > 1.0) { - ++double_fig; - v /= 10; - } -</PRE></CODE> -</BLOCKQUOTE> - -<LI><B>BASE</B></LI><BLOCKQUOTE> -Base value used in the BigDecimal calculation. -On 32 bits integer system,the value of BASE is 10000.<BR> -b = BigDecimal::BASE<BR> -</BLOCKQUOTE> -</UL> - -<H4><U>Instance methods</U></H4> -<UL> -<LI><B>+</B></LI><BLOCKQUOTE> -addition(c = a + b)<BR> -For the resulting number of significant digits of c,see <A HREF="#PREC">Resulting number of significant digits</A>. - -</BLOCKQUOTE> -<LI><B>-</B></LI><BLOCKQUOTE> -subtraction (c = a - b) or negation (c = -a)<BR> -For the resulting number of significant digits of c,see <A HREF="#PREC">Resulting number of significant digits</A>. - -</BLOCKQUOTE> -<LI><B>*</B></LI><BLOCKQUOTE> -multiplication(c = a * b)<BR> -For the resulting number of significant digits of c,see <A HREF="#PREC">Resulting number of significant digits</A>. - -</BLOCKQUOTE> -<LI><B>/</B></LI><BLOCKQUOTE> -division(c = a / b)<BR> -For the resulting number of significant digits of c,see <A HREF="#PREC">Resulting number of significant digits</A>. -</BLOCKQUOTE> - -<LI><B>add(b,n)</B></LI><BLOCKQUOTE> -c = a.add(b,n)<BR> -c = a.add(b,n) performs c = a + b.<BR> -If n is less than the actual significant digits of a + b, -then c is rounded properly according to the BigDecimal.limit.<BR> -If n is zero,then the result is the same as +'s. -</BLOCKQUOTE> -<LI><B>sub(b,n)</B></LI><BLOCKQUOTE> -c = a.sub(b,n)<BR> -c = a.sub(b,n) performs c = a - b.<BR> -If n is less than the actual significant digits of a - b, -then c is rounded properly according to the BigDecimal.limit.<BR> -If n is zero,then the result is the same as -'s. - -</BLOCKQUOTE> -<LI><B>mult(b,n)</B></LI><BLOCKQUOTE> -c = a.mult(b,n)<BR> -c = a.mult(b,n) performs c = a * b.<BR> -If n is less than the actual significant digits of a * b, -then c is rounded properly according to the BigDecimal.limit.<BR> -If n is zero,then the result is the same as *'s. - -</BLOCKQUOTE> -<LI><B>div(b[,n])</B></LI><BLOCKQUOTE> -c = a.div(b,n)<BR> -c = a.div(b,n) performs c = a / b.<BR> -If n is less than the actual significant digits of a / b, -then c is rounded properly according to the BigDecimal.limit.<BR> -If n is zero,then the result is the same as /'s. -If n is not given,then the result will be an integer(BigDecimal) like Float#div. -</BLOCKQUOTE> - -<LI><B>fix</B></LI><BLOCKQUOTE> -c = a.fix<BR> -returns integer part of a.<BR> - -</BLOCKQUOTE> -<LI><B>frac</B></LI><BLOCKQUOTE> -c = a.frac<BR> -returns fraction part of a.<BR> - -</BLOCKQUOTE> -<LI><B>floor[(n)]</B></LI><BLOCKQUOTE> -c = a.floor<BR> -returns the maximum integer value (in BigDecimal) which is less than or equal to a. -<CODE><PRE> - c = BigDecimal("1.23456").floor # ==> 1 - c = BigDecimal("-1.23456").floor # ==> -2 -</PRE></CODE> - -As shown in the following example,an optional integer argument (n) specifying the position -of the target digit can be given.<BR> -If n> 0,then the (n+1)th digit counted from the decimal point in fraction part is processed(resulting number of fraction part digits is less than or equal to n).<BR> -If n<0,then the n-th digit counted from the decimal point in integer part is processed(at least n 0's are placed from the decimal point to left). -<CODE><PRE> - c = BigDecimal("1.23456").floor(4) # ==> 1.2345 - c = BigDecimal("15.23456").floor(-1) # ==> 10.0 -</PRE></CODE> - -</BLOCKQUOTE> -<LI><B>ceil[(n)]</B></LI><BLOCKQUOTE> -c = a.ceil<BR> -returns the minimum integer value (in BigDecimal) which is greater than or equal to a. -<CODE><PRE> - c = BigDecimal("1.23456").ceil # ==> 2 - c = BigDecimal("-1.23456").ceil # ==> -1 -</PRE></CODE> - -As shown in the following example,an optional integer argument (n) specifying the position -of the target digit can be given.<BR> -If n>0,then the (n+1)th digit counted from the decimal point in fraction part is processed(resulting number of fraction part digits is less than or equal to n).<BR> -If n<0,then the n-th digit counted from the decimal point in integer part is processed(at least n 0's are placed from the decimal point to left). -<CODE><PRE> - c = BigDecimal("1.23456").ceil(4) # ==> 1.2346 - c = BigDecimal("15.23456").ceil(-1) # ==> 20.0 -</PRE></CODE> - -</BLOCKQUOTE> -<LI><B>round[(n[,b])]</B></LI><BLOCKQUOTE> -c = a.round<BR> -round a to the nearest 1(default)．<BR> -<CODE><PRE> - c = BigDecimal("1.23456").round # ==> 1 - c = BigDecimal("-1.23456").round # ==> -1 -</PRE></CODE> -The rounding operation changes according to BigDecimal::mode(BigDecimal::ROUND_MODE,flag) if specified. - -As shown in the following example,an optional integer argument (n) specifying the position -of the target digit can be given.<BR> -If n>0,then the (n+1)th digit counted from the decimal point in fraction part is processed(resulting number of fraction part digits is less than or equal to n).<BR> -If n<0,then the n-th digit counted from the decimal point in integer part is processed(at least n 0's are placed from the decimal point to left). -<CODE><PRE> -c = BigDecimal::new("1.23456").round(4) # ==> 1.2346 -c = BigDecimal::new("15.23456").round(-1) # ==> 20.0 -</PRE></CODE> - -Rounding operation can be specified by setting the second optional argument b with the valid ROUND_MODE.<BR> -<CODE><PRE> -c = BigDecimal::new("1.23456").round(3,BigDecimal::ROUND_HALF_EVEN) # ==> 1.234 -c = BigDecimal::new("1.23356").round(3,BigDecimal::ROUND_HALF_EVEN) # ==> 1.234 -</PRE></CODE> - -</BLOCKQUOTE> -<LI><B>truncate[(n)]</B></LI><BLOCKQUOTE> -c = a.truncate<BR> -truncate a to the nearest 1．<BR> -As shown in the following example,an optional integer argument (n) specifying the position -of the target digit can be given.<BR> -If n>0,then the (n+1)th digit counted from the decimal point in fraction part is processed(resulting number of fraction part digits is less than or equal to n).<BR> -If n<0,then the n-th digit counted from the decimal point in integer part is processed(at least n 0's are placed from the decimal point to left). - -<CODE><PRE> -c = BigDecimal::new("1.23456").truncate(4) # ==> 1.2345 -c = BigDecimal::new("15.23456").truncate(-1) # ==> 10.0 -</PRE></CODE> -</BLOCKQUOTE> -<LI><B>abs</B></LI><BLOCKQUOTE> -c = a.abs<BR> -returns an absolute value of a.<BR> - -</BLOCKQUOTE> -<LI><B>to_i</B></LI><BLOCKQUOTE> -changes a to an integer.<BR> -i = a.to_i<BR> -i becomes to Fixnum or Bignum. -If a is Infinity or NaN,then i becomes to nil. - -</BLOCKQUOTE> -<LI><B>to_s[(n)]</B></LI><BLOCKQUOTE> -converts to string(default results look like "0.xxxxxEn"). -<CODE><PRE> -BigDecimal("1.23456").to_s # ==> "0.123456E1" -</PRE></CODE> -If n(>0) is given,then a space is inserted to each of two parts divided by the decimal point -after every n digits for readability. -<CODE><PRE> -BigDecimal("0.1234567890123456789").to_s(10) # ==> "0.1234567890 123456789E0" -</PRE></CODE> -n can be a string representing a positive integer number. -<CODE><PRE> -BigDecimal("0.1234567890123456789").to_s("10") # ==> "0.1234567890 123456789E0" -</PRE></CODE> -If the first character is '+'(or ' '),then '+'(or ' ') will be set before value string -when the value is positive. -<CODE><PRE> -BigDecimal("0.1234567890123456789").to_s(" 10") # ==> " 0.1234567890 123456789E0" -BigDecimal("0.1234567890123456789").to_s("+10") # ==> "+0.1234567890 123456789E0" -BigDecimal("-0.1234567890123456789").to_s("10") # ==> "-0.1234567890 123456789E0" -</PRE></CODE> - -At the end of the string,'E'(or 'e') or 'F'(or 'f') can be specified to change -number representation. -<CODE><PRE> -BigDecimal("1234567890.123456789").to_s("E") # ==> "0.1234567890123456789E10" -BigDecimal("1234567890.123456789").to_s("F") # ==> "1234567890.123456789" -BigDecimal("1234567890.123456789").to_s("5E") # ==> "0.12345 67890 12345 6789E10" -BigDecimal("1234567890.123456789").to_s("5F") # ==> "12345 67890.12345 6789" -</PRE></CODE> - -</BLOCKQUOTE> -<LI><B>exponent</B></LI><BLOCKQUOTE> -returns an integer holding exponent value of a.<BR> -n = a.exponent <BR> -means a = 0.xxxxxxx*10**n. -</BLOCKQUOTE> - -<LI><B>precs</B></LI><BLOCKQUOTE> -n,m = a.precs <BR> -prec returns number of significant digits (n) and maximum number of -significant digits (m) of a. -</BLOCKQUOTE> - -<LI><B>to_f</B></LI><BLOCKQUOTE> -Creates a new Float object having (nearly) the same value. -Use split method if you want to convert by yourself. -</BLOCKQUOTE> - -</BLOCKQUOTE> -<LI><B>sign</B></LI><BLOCKQUOTE> -n = a.sign <BR> -returns positive value if a > 0,negative value if a < 0, -otherwise zero if a == 0.<BR> -where the value of n means that a is:<BR> -n = BigDecimal::SIGN_NaN(0) : a is NaN<BR> -n = BigDecimal::SIGN_POSITIVE_ZERO(1) : a is +0<BR> -n = BigDecimal::SIGN_NEGATIVE_ZERO(-1) : a is -0<BR> -n = BigDecimal::SIGN_POSITIVE_FINITE(2) : a is positive<BR> -n = BigDecimal::SIGN_NEGATIVE_FINITE(-2) : a is negative<BR> -n = BigDecimal::SIGN_POSITIVE_INFINITE(3) : a is +Infinity<BR> -n = BigDecimal::SIGN_NEGATIVE_INFINITE(-3) : a is -Infinity<BR> -The value in () is the actual value,see (<A HREF="#STRUCT">Internal structure</A>.<BR> - -</BLOCKQUOTE> -<LI><B>nan?</B></LI><BLOCKQUOTE> -a.nan? returns True when a is NaN. - -</BLOCKQUOTE> -<LI><B>infinite?</B></LI><BLOCKQUOTE> -a.infinite? returns 1 when a is +∞,-1 when a is -∞, nil otherwise. - -</BLOCKQUOTE> -<LI><B>finite?</B></LI><BLOCKQUOTE> -a.finite? returns true when a is neither ∞ nor NaN. -</BLOCKQUOTE> - -<LI><B>zero?</B></LI><BLOCKQUOTE> -c = a.zero?<BR> -returns true if a is equal to 0,otherwise returns false<BR> -</BLOCKQUOTE> -<LI><B>nonzero?</B></LI><BLOCKQUOTE> -c = a.nonzero?<BR> -returns nil if a is 0,otherwise returns a itself.<BR> -</BLOCKQUOTE> - -<LI><B>split</B></LI><BLOCKQUOTE> -decomposes a BigDecimal value to 4 parts. -All 4 parts are returned as an array.<BR> -Parts consist of a sign(0 when the value is NaN,+1 for positive and - -1 for negative value), a string representing fraction part,base value(always 10 currently),and an integer(Fixnum) for exponent respectively. -a=BigDecimal::new("3.14159265")<BR> -f,x,y,z = a.split<BR> -where f=+1,x="314159265",y=10 and z=1<BR> -therefore,you can translate BigDecimal value to Float as:<BR> -s = "0."+x<BR> -b = f*(s.to_f)*(y**z)<BR> - -</BLOCKQUOTE> -<LI><B>inspect</B></LI><BLOCKQUOTE> -is used for debugging output.<BR> -p a=BigDecimal::new("3.14",10)<BR> -should produce output like "#<0x112344:'0.314E1',4(12)%gt;". -where "0x112344" is the address, -'0.314E1' is the value,4 is the number of the significant digits, -and 12 is the maximum number of the significant digits -the object can hold. -</BLOCKQUOTE> - -<LI><B>sqrt</B></LI><BLOCKQUOTE> -c = a.sqrt(n)<BR> -computes square root value of a with significant digit number n at least.<BR> -</BLOCKQUOTE> - -<LI><B>**</B></LI><BLOCKQUOTE> -c = a ** n<BR> -returns the value of a powered by n. -n must be an integer.<BR> - -</BLOCKQUOTE> -<LI><B>power</B></LI><BLOCKQUOTE> -The same as ** method.<BR> -c = a.power(n)<BR> -returns the value of a powered by n(c=a**n). -n must be an integer.<BR> -</BLOCKQUOTE> - -<LI><B>divmod,quo,modulo,%,remainder</B></LI><BLOCKQUOTE> -See,corresponding methods in Float class. -</BLOCKQUOTE> - -</BLOCKQUOTE> -<LI><B><=></B></LI><BLOCKQUOTE> -c = a <=> b <BR> -returns 0 if a==b,1 if a > b,and returns -1 if a < b.<BR> -</BLOCKQUOTE> -</UL> - -Following methods need no explanation.<BR> -<UL> -<LI>==</LI> -<LI>===</LI> -same as ==,used in case statement. -<LI>!=</LI> -<LI><</LI> -<LI><=</LI> -<LI>></LI> -<LI>>=</LI> -</UL> - -<HR> -<H3>About 'coerce'</H3> -<B>For the binary operation like A op B:</B> -<DL> -<DT> 1.Both A and B are BigDecimal objects</DT> -<DD> A op B is normally performed.</DD> -<DT> 2.A is the BigDecimal object but B is other than BigDecimal object</DT> -<DD> Operation is performed,after B is translated to correcponding BigDecimal object(because BigDecimal supports coerce method).</DD> -<DT> 3.A is not the BigDecimal object but B is BigDecimal object</DT> -<DD>If A has coerce mthod,then B will translate A to corresponding -BigDecimal object and the operation is performed,otherwise an error occures.</DD> -</DL> - -String is not translated to BigDecimal in default. -Uncomment /* #define ENABLE_NUMERIC_STRING */ in bigdecimal.c, compile and install -again if you want to enable string to BigDecimal conversion. -Translation stops without error at the character representing non digit. -For instance,"10XX" is translated to 10,"XXXX" is translated to 0.<BR> -String representing zero or infinity such as "Infinity","+Infinity","-Infinity",and "NaN" can also be translated to BigDecimal unless false is specified by mode method.<BR> - -BigDecimal class supports coerce method(for the details about coerce method,see Ruby documentations). This means the most binary operation can be performed if the BigDecimal object is at the left hand side of the operation.<BR><BR> - - For example: -<CODE><PRE> - a = BigDecimal.E(20) - c = a * "0.123456789123456789123456789" # A String is changed to BigDecimal object. -</PRE></CODE> -is performed normally.<BR> - But,because String does not have coerce method,the following example can not be performed.<BR> - -<CODE><PRE> - a = BigDecimal.E(20) - c = "0.123456789123456789123456789" * a # ERROR -</PRE></CODE> - -If you actually have any inconvenience about the error above. -You can define a new class derived from String class, -and define coerce method within the new class.<BR> - -<hr> -<A NAME="#UNDEF"> -<H2>Infinity,Not a Number(NaN),Zero</H2> -Infinite numbers and NaN can be represented by string writing "+Infinity"(or "Infinity"),"-Infinity",and "NaN" respectively in your program. -Infinite numbers can be obtained by 1.0/0.0(=Infinity) or -1.0/0.0(=-Infinity). -<BR><BR> -NaN(Not a number) can be obtained by undefined computation like 0.0/0.0 -or Infinity-Infinity. -Any computation including NaN results to NaN. -Comparisons with NaN never become true,including comparison with NaN itself. -<BR><BR> -Zero has two different variations as +0.0 and -0.0. -But,still, +0.0==-0.0 is true. -<BR><BR> -Computation results including Infinity,NaN,+0.0 or -0.0 become complicated. -Run following program and comfirm the results. -Send me any incorrect result if you find. - -<CODE><PRE> - require "bigdecimal" - aa = %w(1 -1 +0.0 -0.0 +Infinity -Infinity NaN) - ba = %w(1 -1 +0.0 -0.0 +Infinity -Infinity NaN) - opa = %w(+ - * / <=> > >= < == != <=) - for a in aa - for b in ba - for op in opa - x = BigDecimal::new(a) - y = BigDecimal::new(b) - eval("ans= x #{op} y;print a,' ',op,' ',b,' ==> ',ans.to_s,\"\n\"") - end - end - end -</PRE></CODE> -<hr> - -<A NAME="#STRUCT"> -<H2>Internal structure</H2> -BigDecimal number is defined by the structure Real in BigDecimal.h. -Digits representing a float number are kept in the array frac[] defined in the structure. -In the program,any floating number(BigDecimal number) is represented as:<BR> - <BigDecimal number> = 0.xxxxxxxxx*BASE**n<BR><BR> -where 'x' is any digit representing mantissa(kept in the array frac[]), -BASE is base value(=10000 in 32 bit integer system), -and n is the exponent value.<BR> -Larger BASE value enables smaller size of the array frac[],and increases computation speed. -The value of BASE is defined ind VpInit(). In 32 bit integer system,this value is -10000. In 64 bit integer system,the value becomes larger. -BigDecimal has not yet been compiled and tested on 64 bit integer system. -It will be very nice if anyone try to run BigDecimal on 64 bit system and - inform me the results. -When BASE is 10000,an element of the array frac[] can have vale of from 0 to 9999. -(up to 4 digits).<BR> -The structure Real is defined in bigdecimal.h as:<BR> -<CODE><PRE> - typedef struct { - VALUE obj; /* Back pointer(VALUE) for Ruby object. */ - unsigned long MaxPrec; /* The size of the array frac[] */ - unsigned long Prec; /* Current size of frac[] actually used. */ - short sign; /* Attribute of the value. */ - /* ==0 : NaN */ - /* 1 : +0 */ - /* -1 : -0 */ - /* 2 : Positive number */ - /* -2 : Negative number */ - /* 3 : +Infinity */ - /* -3 : -Infinity */ - unsigned short flag; /* Control flag */ - int exponent; /* Exponent value(0.xxxx*BASE**exponent) */ - unsigned long frac[1]; /* An araay holding mantissa(Variable) */ - } Real; -</CODE></PRE> -The decimal value 1234.56784321 is represented as(BASE=10000):<BR> -<PRE> - 0.1234 5678 4321*(10000)**1 -</PRE> -where frac[0]=1234,frac[1]=5678,frac[2]=4321, -Prec=3,sign=2,exponent=1. MaxPrec can be any value greater than or equal to -Prec. -<hr> - -<A NAME="#BASE"> -<H2>Binary or decimal number representation</H2> -I adopted decimal number representation for BigDecimal implementation. -Of cource,binary number representation is common on the most computers. - -<H3>Advantages using decimal representation</H3> -The reason why I adopted decimal number representation for BigDecimal is:<BR> -<DL> -<DT>Easy for debugging -<DD>The floating number 1234.56784321 can be easily represented as:<BR> - frac[0]=1234,frac[1]=5678,frac[2]=4321,exponent=1,and sign=2. -<DT>Exact representation -<DD>Following program can add all numbers(in decimal) in a file - without any error(no round operation).<BR> - -<CODE><PRE> - file = File::open(....,"r") - s = BigDecimal::new("0") - while line = file.gets - s = s + line - end -</PRE></CODE> - -If the internal representation is binary,translation from decimal to -binary is required and the translation error is inevitable. -For example, 0.1 can not exactly be represented in binary.<BR> -0.1 => b1*2**(-1)+b1*2**(-2)+b3*2**(-3)+b4*2**(-4)....<BR> -where b1=0,b2=0,b3=0,b4=1...<BR> -bn(n=1,2,3,...) is infinite series of digit with value of 0 or 1, -and rounding operation is necessary but where we should round the series ? -Of cource,exact "0.1" is printed if the rouding operation is properly done, -<DT>Significant digit we can have is automatically determined -<DD>In binary representation,0.1 can not be represented in finite series of digit. - -But we only need one element(frac[0]=1) in decimal representation. -This means that we can always determine the size of the array frac[] in Real -structure. -</DL> - -<H3>Disadvantage of decimal representation</H3> -Because most computers have no internal decimal representaion. -Once you use BigDecimal,you need to keep using it without -considering computation cost if exact computation is required. - -<H4>Which is the first input?</H4> -Because most people uses decimal notatin for numeric data representation, -BigDecimal can handle numeric data without loss of translation error. -<hr> - -<A NAME="#PREC"> -<H2>Resulting number of significant digits</H2> -For the fundamental arithmetics such as addition,subtraction, -multiplication,and division,I prepared 2 group of methods<BR> - -<H3>1. +,-,*,/</H3> -For the operation + - * /,you can not specify the resulting -number of significant digits.<BR> -Resulting number of significant digits are defined as:<BR> -1.1 For *,resulting number of significant digits is the sum of the -significant digits of both side of the operator. For / ,resulting number of significant digits is the sum of the -maximum significant digits of both side of the operator.<BR> -1.2 For + and -,resulting number of significant digits is determined so that - no round operation is needed. <br> -For example, c has more than 100 siginificant digits if c is computed as:<BR> -c = 0.1+0.1*10**(-100)<br> -<BR> -As +,-,and * are always exact(no round operation is performed unless BigDecimal.limit is specified), -which means more momories are required to keep computation results. -But,the division such as c=1.0/3.0 will always be rounded.<BR> - -<H3>2. add,sub,mult,div</H3> -The length of the significant digits obtained from +,-,*,/ -is always defined by that of right and left side of the operator. -To specify the length of the significant digits by your self, -use methos add,sub,mult,div. -<CODE><PRE> - BigDecimal("2").div(3,12) # 2.0/3.0 => 0.6666666666 67E0 -</PRE></CODE> -</BLOCKQUOTE> - -<H3>3. truncate,round,ceil,floor</H3> -Using these methods,you can specify rounding location relatively from -decimal point. -<CODE><PRE> - BigDecimal("6.66666666666666").round(12) # => 0.6666666666 667E1 -</PRE></CODE> -</BLOCKQUOTE> - - -<H3>4. Example</H3> -Following example compute the ratio of the circumference of a circle to -its dirmeter(pi=3.14159265358979....) using J.Machin's formula. -<BR><BR> -<CODE><PRE> -#!/usr/local/bin/ruby - -require "bigdecimal" -# -# Calculates 3.1415.... (the number of times that a circle's diameter -# will fit around the circle) using J. Machin's formula. -# -def big_pi(sig) # sig: Number of significant figures - exp = -sig - pi = BigDecimal::new("0") - two = BigDecimal::new("2") - m25 = BigDecimal::new("-0.04") - m57121 = BigDecimal::new("-57121") - - u = BigDecimal::new("1") - k = BigDecimal::new("1") - w = BigDecimal::new("1") - t = BigDecimal::new("-80") - while (u.nonzero? && u.exponent >= exp) - t = t*m25 - u = t.div(k,sig) - pi = pi + u - k = k+two - end - - u = BigDecimal::new("1") - k = BigDecimal::new("1") - w = BigDecimal::new("1") - t = BigDecimal::new("956") - while (u.nonzero? && u.exponent >= exp ) - t = t.div(m57121,sig) - u = t.div(k,sig) - pi = pi + u - k = k+two - end - pi -end - -if $0 == __FILE__ - if ARGV.size == 1 - print "PI("+ARGV[0]+"):\n" - p big_pi(ARGV[0].to_i) - else - print "TRY: ruby pi.rb 1000 \n" - end -end - -</PRE></CODE> -<HR> -<FONT size=2> -<I> -<A HREF="http://www.tinyforest.gr.jp"> -Shigeo Kobayashi -</A> -(E-Mail:<A HREF="mailto:shigeo@tinyforest.gr.jp"><shigeo@tinyforest.gr.jp></U></A>) -</I> -</FONT> -</TD> -</TR> -</TABLE> -</BODY> -</HTML> diff --git a/ruby_1_8_6/ext/bigdecimal/bigdecimal_ja.html b/ruby_1_8_6/ext/bigdecimal/bigdecimal_ja.html deleted file mode 100644 index 37bbcbbb09..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/bigdecimal_ja.html +++ /dev/null @@ -1,799 +0,0 @@ -<!-- saved from url=(0022)http://internet.e-mail --> -<HTML> -<HEAD> -<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=Shift_JIS"> -<style type="text/css"><!-- -body { color: #3f0f0f; background: #fefeff; margin-left: 2em; margin-right: 2em;} -h1 { color: #ffffff; background-color: #3939AD; border-color: #FF00FF; width: 100%; - 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BORDER-RIGHT: medium none; BORDER-TOP: medium none; LINE-HEIGHT: 100%; MARGIN: 12px 12px 12px 12px; - PADDING-BOTTOM: 12px; PADDING-LEFT: 12px; PADDING-RIGHT: 12px; PADDING-TOP: 12px; - WHITE-SPACE: pre; WIDTH: 100% -} ---></style> - -<TITLE>BigDecimal:An extension library for Ruby</TITLE> -</HEAD> -<BODY BGCOLOR=#FFFFE0> -<H1>BigDecimal(可変長浮動少数点演算用拡張ライブラリ)</H1> -<DIV align="right"><A HREF="./bigdecimal_en.html">English</A></DIV><BR> -BigDecimal はオブジェクト指向の強力なスクリプト言語である Ruby に可変長浮動小数点 -計算機能を追加するための拡張ライブラリです。 -Ruby についての詳しい内容は以下のURLを参照してください。 -<UL> -<LI><A HREF="http://www.ruby-lang.org/ja/">http://www.ruby-lang.org/ja/</A>：Ruby公式ページ</LI> -<LI><A HREF="http://kahori.com/ruby/ring/">http://kahori.com/ruby/ring/</A>：Rubyに関するページを辿れます</LI> -</UL> -<hr> -<H2>目次</H2> -<UL> -<LI><A HREF="#INTRO">はじめに</LI> -<LI><A HREF="#SPEC">使用方法とメソッドの一覧</A></LI> -<LI><A HREF="#UNDEF">無限、非数、ゼロの扱い</A></LI> -<LI><A HREF="#STRUCT">内部構造</A></LI> -<LI><A HREF="#BASE">2進と10進</A></LI> -<LI><A HREF="#PREC">計算精度について</A></LI> -</UL> - -<HR> -<A NAME="#INTRO"> -<H2>はじめに</H2> -Ruby には Bignum というクラスがあり、数百桁の整数でも計算することができます。 -ただ、任意桁の浮動少数点演算用クラスが無いようです。そこで、 -任意桁の浮動少数点演算用拡張ライブラリ BigDecimal を作成しました。 -不具合や助言・提案がある場合どしどし、 -<A HREF="mailto:shigeo@tinyforest.gr.jp">shigeo@tinyforest.gr.jp</A> -までお知らせください。不具合を直す気は大いにあります。ただ、時間などの関係で約束 -はできません。また、結果についても保証できるものではありません。 -予め、ご了承ください。 -<BR><BR> -このプログラムは、自由に配布・改変して構いません。ただし、著作権は放棄していません。 -配布・改変等の権利は Ruby のそれに準じます。詳しくは README を読んでください。 - -<hr> -<H2>インストールについて</H2> -BigDecimal を含む Ruby の最新版は<A HREF="http://www.ruby-lang.org/ja/">Ruby公式ページ</A>からダウンロードできます。 -ダウンロードした最新版を解凍したら、通常のインストール手順を実行して下さい。 -Ruby が正しくインストールされれば、同時に BigDecimal も利用できるようになるはずです。 -ソースファイルは -bigdecimal.c,bigdecimal.h -の２個のみです。<BR> - -<hr> -<A NAME="#SPEC"> -<H2>使用方法とメソッドの一覧</H2> -「Rubyは既に書ける」という前提で、 -<CODE><PRE> -require 'bigdecimal' -a=BigDecimal::new("0.123456789123456789") -b=BigDecimal("123456.78912345678",40) -c=a+b -</PRE></CODE> -<br> -というような感じで使用します。 - -<H3>メソッド一覧</H3> -以下のメソッドが利用可能です。 -「有効桁数」とは BigDecimal が精度を保証する桁数です。 -ぴったりではありません、若干の余裕を持って計算されます。 -また、例えば３２ビットのシステムでは１０進で４桁毎に計算します。従って、現状では、 -内部の「有効桁数」は４の倍数となっています。 -<P> -以下のメソッド以外にも、(C ではない) Ruby ソースの形で -提供されているものもあります。例えば、 -<CODE><PRE> -require "bigdecimal/math.rb" -</PRE></CODE> -とすることで、sin や cos といった関数が使用できるようになります。 -使用方法など、詳細は math.rb の内容を参照して下さい。 - -その他、Float との相互変換などのメソッドが util.rb でサポートされています。 -利用するには -<CODE><PRE> -require "bigdecimal/util.rb" -</PRE></CODE> -のようにします。詳細は util.rb の内容を参照して下さい。 - -<H4><U>クラスメソッド</U></H4> -<UL> -<LI><B>new</B></LI><BLOCKQUOTE> -新しい BigDecimal オブジェクトを生成します。<BR> -a=BigDecimal::new(s[,n]) または<BR> -a=BigDecimal(s[,n])<BR> -s は数字を表現する初期値を文字列で指定します。 -スペースは無視されます。また、判断できない文字が出現した時点で -文字列は終了したものとみなされます。 -n は必要な有効桁数（a の最大有効桁数）を整数で指定します。 -n が 0 または省略されたときは、n の値は s の有効桁数とみなされます。 -s の有効桁数より n が小さいときも n=0 のときと同じです。 -a の最大有効桁数は n より若干大い値が採用されます。 -最大有効桁数は以下のような割り算を実行するとき等に意味を持ちます。 -<CODE><PRE> -BigDecimal("1") / BigDecimal("3") # => 0.3333333333 33E0 -BigDecimal("1",10) / BigDecimal("3",10) # => 0.3333333333 3333333333 33333333E0 -</PRE></CODE> -ただし、個々の演算における最大有効桁数 n の取り扱いは将来のバージョンで -若干変更される可能性があります。 -</BLOCKQUOTE> - -<LI><B>mode</B></LI><BLOCKQUOTE> -f = BigDecimal.mode(s[,v])<BR> -BigDecimalの実行結果を制御します。第２引数を省略、または nil を指定すると -現状の設定値が戻ります。<BR> -以下の使用方法が定義されています。 -<P> -<B>[例外処理]</B><P> -計算結果が非数(NaN)やゼロによる除算になったときの処理を定義することができます。 -<BLOCKQUOTE> -f = BigDecimal::mode(BigDecimal::EXCEPTION_NaN,flag)<BR> -f = BigDecimal::mode(BigDecimal::EXCEPTION_INFINITY,flag)<BR> -f = BigDecimal::mode(BigDecimal::EXCEPTION_UNDERFLOW,flag)<BR> -f = BigDecimal::mode(BigDecimal::EXCEPTION_OVERFLOW,flag)<BR> -f = BigDecimal::mode(BigDecimal::EXCEPTION_ZERODIVIDE,flag)<BR> -f = BigDecimal::mode(BigDecimal::EXCEPTION_ALL,flag)<BR> -</BLOCKQUOTE> - -EXCEPTION_NaN は結果が NaN になったときの指定です。<BR> -EXCEPTION_INFINITY は結果が無限大(±Infinity)になったときの指定です。<BR> -EXCEPTION_UNDERFLOW は指数部がアンダーフローするときの指定です。<BR> -EXCEPTION_OVERFLOW は指数部がオーバーフローするときの指定です。<BR> -EXCEPTION_ZERODIVIDE はゼロによる割り算を実行したときの指定です。<BR> -EXCEPTION_ALL は、可能な全てに対して一括して設定するときに使用します。<BR><BR> - -flag が true のときは、指定した状態になったときに例外を発行するようになります。<BR> -flag が false（デフォルト）なら、例外は発行されません。計算結果は以下のようになります。<BR> -<BLOCKQUOTE> -EXCEPTION_NaN のとき、非数(NaN)<BR> -EXCEPTION_INFINITY のとき、無限(+ or -Infinity)<BR> -EXCEPTION_UNDERFLOW のとき、ゼロ<BR> -EXCEPTION_OVERFLOW のとき、+Infinity か -Infinity<BR> -EXCEPTION_ZERODIVIDE のとき、+Infinity か -Infinity<BR> -</BLOCKQUOTE> -EXCEPTION_INFINITY、EXCEPTION_OVERFLOW、EXCEPTION_ZERODIVIDE -は今のところ同じです。<BR> -戻り値は、設定後の値です。「値」の意味は、例えば -BigDecimal::EXCEPTION_NaNと「値」の & が ゼロ以外ならば -EXCEPTION_NaNが設定されているという意味です。 - -<P> -<B>[丸め処理指定]</B><P> -計算途中の丸め操作の指定ができます。 -<BLOCKQUOTE> -f = BigDecimal::mode(BigDecimal::ROUND_MODE,flag) -</BLOCKQUOTE> -の形式で指定します。<BR> -ここで、flag は以下(括弧内は対応するインスタンスメソッド)の一つを指定します。 -<TABLE> -<TR><TD>ROUND_UP</TD><TD>全て切り上げます。</TD></TR> -<TR><TD>ROUND_DOWN</TD><TD>全て切り捨てます(truncate)。</TD></TR> -<TR><TD>ROUND_HALF_UP</TD><TD>四捨五入します(デフォルト)。</TD></TR> -<TR><TD>ROUND_HALF_DOWN</TD><TD>五捨六入します。</TD></TR> -<TR><TD>ROUND_HALF_EVEN</TD><TD>四捨六入します。５の時は上位１桁が奇数の時のみ繰り上げます(Banker's rounding)。</TD></TR> -<TR><TD>ROUND_CEILING</TD><TD>数値の大きい方に繰り上げます(ceil)。</TD></TR> -<TR><TD>ROUND_FLOOR</TD><TD>数値の小さい方に繰り下げます(floor)。</TD></TR> - -</TABLE> -戻り値は指定後の flag の値です。 -第２引数に nil を指定すると、現状の設定値が返ります。 -mode メソッドでは丸め操作の位置をユーザが指定することはできません。 -丸め操作と位置を自分で制御したい場合は BigDecimal::limit や truncate/round/ceil/floor、 -add/sub/mult/div といったインスタンスメソッドを使用して下さい。 -</BLOCKQUOTE> -<LI><B>limit([n])</B></LI><BLOCKQUOTE> -生成されるBigDecimalオブジェクトの最大桁数をn桁に制限します。 -戻り値は設定する前の値です。設定値のデフォルト値は０で、桁数無制限という意味です。 -n を指定しない、または n が nil の場合は、現状の最大桁数が返ります。<BR> -計算を続行する間に、数字の桁数が無制限に増えてしまうような場合 - limit で予め桁数を制限できます。この場合 BigDecimal.mode で指定された -丸め処理が実行されます。 -ただし、インスタンスメソッド (truncate/round/ceil/floor/add/sub/mult/div) の -桁数制限は limit より優先されます。<BR> -mf = BigDecimal::limit(n)<BR> -</BLOCKQUOTE> - -<LI><B>double_fig</B></LI><BLOCKQUOTE> -Ruby の Float クラスが保持できる有効数字の数を返します。 -<CODE><PRE> - p BigDecimal::double_fig # ==> 20 (depends on the CPU etc.) -</PRE></CODE> -double_figは以下の C プログラムの結果と同じです。 -<CODE><PRE> - double v = 1.0; - int double_fig = 0; - while(v + 1.0 > 1.0) { - ++double_fig; - v /= 10; - } -</PRE></CODE> -</BLOCKQUOTE> - -<LI><B>BASE</B></LI><BLOCKQUOTE> -内部で使用される基数の値です。整数が 32 ビットの処理系では10000です。<BR> -b = BigDecimal::BASE<BR> -</BLOCKQUOTE> -</UL> - -<H4><U>インスタンスメソッド</U></H4> -<UL> -<LI><B>+</B></LI><BLOCKQUOTE> -加算（c = a + b）<BR> -c の精度については「<A HREF="#PREC">計算精度について</A>」を参照してください。 -</BLOCKQUOTE> - -<LI><B>-</B></LI><BLOCKQUOTE> -減算（c = a - b）、または符号反転（c = -a）<BR> -c の精度については「<A HREF="#PREC">計算精度について</A>」を参照してください。 - -</BLOCKQUOTE> -<LI><B>*</B></LI><BLOCKQUOTE> -乗算(c = a * b)<BR> -cの精度は(aの精度)+(bの精度)程度です。<br> -詳しくは「<A HREF="#PREC">計算精度について</A>」を参照してください。 - -</BLOCKQUOTE> -<LI><B>/</B></LI><BLOCKQUOTE> -除算(c = a / b)<BR> -c の精度については「<A HREF="#PREC">計算精度について</A>」を参照してください。 - -</BLOCKQUOTE> - -<LI><B>add(b,n)</B></LI><BLOCKQUOTE> -以下のように使用します。<BR> -c = a.add(b,n)<BR> -c = a + b を最大で n 桁まで計算します。<BR> -a + b の精度が n より大きいときは BigDecimal.mode で指定された方法で丸められます。<BR> -n がゼロなら + と同じです。 -</BLOCKQUOTE> -<LI><B>sub(b,n)</B></LI><BLOCKQUOTE> -以下のように使用します。<BR> -c = a.sub(b,n)<BR> -c = a - b を最大で n 桁まで計算します。<BR> -a - b の精度が n より大きいときは BigDecimal.mode で指定された方法で丸められます。<BR> -n がゼロなら - と同じです。 - -</BLOCKQUOTE> -<LI><B>mult(b,n)</B></LI><BLOCKQUOTE> -以下のように使用します。<BR> -c = a.mult(b,n)<BR> -c = a * b を最大で n 桁まで計算します。<BR> -a * b の精度が n より大きいときは BigDecimal.mode で指定された方法で丸められます。<BR> -n がゼロなら * と同じです。 - -</BLOCKQUOTE> -<LI><B>div(b[,n])</B></LI><BLOCKQUOTE> -以下のように使用します。<BR> -c = a.div(b,n)<BR> -c = a / b を最大で n 桁まで計算します。 -a / b の精度が n より大きいときは BigDecimal.mode で指定された方法で丸められます。<BR> -n がゼロなら / と同じです。<BR> -n が省略されたときは Float#div と同様に結果が整数(BigDecimal)になります。 -</BLOCKQUOTE> - -<LI><B>fix</B></LI><BLOCKQUOTE> -a の小数点以下の切り捨て。<BR> -c = a.fix -</BLOCKQUOTE> -<LI><B>frac</B></LI><BLOCKQUOTE> -a の整数部分の切り捨て。<BR> -c = a.frac -</BLOCKQUOTE> - -<LI><B>floor[(n)]</B></LI><BLOCKQUOTE> -c = a.floor<BR> -a 以下の最大整数（BigDecimal 値）を返します。 -<CODE><PRE> -c = BigDecimal("1.23456").floor # ==> 1 -c = BigDecimal("-1.23456").floor # ==> -2 -</PRE></CODE> -以下のように引数 n を与えることもできます。<BR> -n>=0 なら、小数点以下 n+1 位の数字を操作します(少数点以下を、最大 n 桁にします)。<BR> -n が負のときは小数点以上 n 桁目を操作します(小数点位置から左に少なくとも n 個の 0 が並びます)。<BR> -<CODE><PRE> - c = BigDecimal("1.23456").floor(4) # ==> 1.2345 - c = BigDecimal("15.23456").floor(-1) # ==> 10.0 -</PRE></CODE> - -</BLOCKQUOTE> -<LI><B>ceil[(n)]</B></LI><BLOCKQUOTE> -c = a.ceil<BR> -a 以上の整数のうち、最も小さい整数を計算し、その値（BigDecimal 値）を返します。 -<CODE><PRE> -c = BigDecimal("1.23456").ceil # ==> 2 -c = BigDecimal("-1.23456").ceil # ==> -1 -</PRE></CODE> - -以下のように引数を与えて、小数点以下 n+1 位の数字を操作することもできます。<BR> -n>=0 なら、小数点以下 n+1 位の数字を操作します(少数点以下を、最大 n 桁にします)。<BR> - n が負のときは小数点以上 n 桁目をを操作します(小数点位置から左に少なくとも n 個の 0 が並びます)。<BR> -<CODE><PRE> - c = BigDecimal("1.23456").ceil(4) # ==> 1.2346 - c = BigDecimal("15.23456").ceil(-1) # ==> 20.0 -</PRE></CODE> - -</BLOCKQUOTE> -<LI><B>round[(n[,b])]</B></LI><BLOCKQUOTE> -c = a.round<BR> - -クラスメソッド BigDecimal::mode(BigDecimal::ROUND_MODE,flag) で指定した -ROUND_MODE に従って丸め操作を実行します。 -BigDecimal::mode(BigDecimal::ROUND_MODE,flag) で何も指定せず、かつ、引数 -を指定しない場合は「小数点以下第一位の数を四捨五入して整数（BigDecimal 値）」にします。<BR> -<CODE><PRE> - c = BigDecimal("1.23456").round # ==> 1 - c = BigDecimal("-1.23456").round # ==> -1 -</PRE></CODE> - -以下のように引数を与えて、小数点以下 n+1 位の数字を操作することもできます。<BR> -n が正の時は、小数点以下 n+1 位の数字を丸めます(少数点以下を、最大 n 桁にします)。<BR> -n が負のときは小数点以上 n 桁目を丸めます(小数点位置から左に少なくとも n 個の 0 が並びます)。 -<CODE><PRE> -c = BigDecimal("1.23456").round(4) # ==> 1.2346 -c = BigDecimal("15.23456").round(-1) # ==> 20.0 -</PRE></CODE> -２番目の引数を指定すると、BigDecimal#mode の指定を無視して、指定された方法で -丸め操作を実行します。 -<CODE><PRE> -c = BigDecimal("1.23456").round(3,BigDecimal::ROUND_HALF_EVEN) # ==> 1.234 -c = BigDecimal("1.23356").round(3,BigDecimal::ROUND_HALF_EVEN) # ==> 1.234 -</PRE></CODE> - -</BLOCKQUOTE> -<LI><B>truncate</B></LI><BLOCKQUOTE> -c = a.truncate<BR> -小数点以下の数を切り捨てて整数（BigDecimal 値）にします。<BR> -以下のように引数を与えて、小数点以下 n+1 位の数字を操作することもできます。<BR> -n が正の時は、小数点以下 n+1 位の数字を切り捨てます(少数点以下を、最大 n 桁にします)。 -n が負のときは小数点以上 n 桁目をを操作します(小数点位置から左に少なくとも n 個の 0 が並びます)。<BR> -<CODE><PRE> -c = BigDecimal("1.23456").truncate(4) # ==> 1.2345 -c = BigDecimal("15.23456").truncate(-1) # ==> 10.0 -</PRE></CODE> -</BLOCKQUOTE> - -</BLOCKQUOTE> -<LI><B>abs</B></LI><BLOCKQUOTE> -ａの絶対値<BR> -c = a.abs<BR> - -</BLOCKQUOTE> -<LI><B>to_i</B></LI><BLOCKQUOTE> -少数点以下を切り捨てて整数に変換します。<BR> -i = a.to_i<BR> -i は値に応じて Fixnum か Bignum になります。 -a が Infinity や NaN のとき、i は nil になります。 -</BLOCKQUOTE> -<LI><B>to_f</B></LI><BLOCKQUOTE> -Float オブジェクトに変換します。 -よりきめ細かい値が必要ならば split メソッドを利用して -ください。 -</BLOCKQUOTE> -<LI><B>to_s[(n)]</B></LI><BLOCKQUOTE> -文字列に変換します(デフォルトは "0.xxxxxEn" の形になります）。 -<CODE><PRE> -BigDecimal("1.23456").to_s # ==> "0.123456E1" -</PRE></CODE> -引数 n に正の整数が指定されたときは、少数点で分けられる左右部分を、それぞれ n 桁毎 -に空白で区切ります。 -<CODE><PRE> -BigDecimal("0.1234567890123456789").to_s(10) # ==> "0.1234567890 123456789E0" -</PRE></CODE> -引数 n に正の整数を表す文字列を指定することもできます。 -<CODE><PRE> -BigDecimal("0.1234567890123456789").to_s("10") # ==> "0.1234567890 123456789E0" -</PRE></CODE> -文字列の最初に '+'（または ' '）を付けると、値が正の場合、先頭に '+'（または ' '）が付きます -（負の場合は、常に '-' が付きます。）。 -<CODE><PRE> -BigDecimal("0.1234567890123456789").to_s(" 10") # ==> " 0.1234567890 123456789E0" -BigDecimal("0.1234567890123456789").to_s("+10") # ==> "+0.1234567890 123456789E0" -BigDecimal("-0.1234567890123456789").to_s("10") # ==> "-0.1234567890 123456789E0" -</PRE></CODE> - -さらに文字列の最後に E(または e) か F(または f) を指定することで、以下のように -表示形式を変更することができます。 -<CODE><PRE> -BigDecimal("1234567890.123456789").to_s("E") # ==> "0.1234567890123456789E10" -BigDecimal("1234567890.123456789").to_s("F") # ==> "1234567890.123456789" -BigDecimal("1234567890.123456789").to_s("5E") # ==> "0.12345 67890 12345 6789E10" -BigDecimal("1234567890.123456789").to_s("5F") # ==> "12345 67890.12345 6789" -</PRE></CODE> - -</BLOCKQUOTE> -<LI><B>exponent</B></LI><BLOCKQUOTE> -指数部を整数値で返します。 -n = a.exponent <BR> -は a の値が 0.xxxxxxx*10**n を意味します。 -</BLOCKQUOTE> - -<LI><B>precs</B></LI><BLOCKQUOTE> -n,m = a.precs<BR> -a の有効数字 (n) と最大有効数字 (m) の配列を返します。 - -</BLOCKQUOTE> - -<LI><B>sign</B></LI><BLOCKQUOTE> -値が正(sign > 0)、負(sign < 0)、その他(sigh==0)であるかの情報を返します。 -n = a.sign <BR> -としたとき n の値は a が以下のときを意味します。<BR> -() の中の数字は、実際の値です(<A HREF="#STRUCT">「内部構造」</A>を参照)。<BR> -n = BigDecimal::SIGN_NaN(0) : a は NaN<BR> -n = BigDecimal::SIGN_POSITIVE_ZERO(1) : a は +0<BR> -n = BigDecimal::SIGN_NEGATIVE_ZERO(-1) : a は -0<BR> -n = BigDecimal::SIGN_POSITIVE_FINITE(2) : a は正の値<BR> -n = BigDecimal::SIGN_NEGATIVE_FINITE(-2) : a は負の値<BR> -n = BigDecimal::SIGN_POSITIVE_INFINITE(3) : a は+Infinity<BR> -n = BigDecimal::SIGN_NEGATIVE_INFINITE(-3) : a は-Infinity<BR> - -</BLOCKQUOTE> -<LI><B>nan?</B></LI><BLOCKQUOTE> -a.nan? は a がNaNのとき真を返します。 -</BLOCKQUOTE> -<LI><B>infinite?</B></LI><BLOCKQUOTE> -a.infinite? は a が+∞のとき 1 、-∞のときは -1、それ以外のときは nil を返します。 -</BLOCKQUOTE> -<LI><B>finite?</B></LI><BLOCKQUOTE> -a.finite? は a が∞または NaN でないとき真を返します。 -</BLOCKQUOTE> - -<LI><B>zero?</B></LI><BLOCKQUOTE> -a が 0 なら true になります。<BR> -c = a.zero? -</BLOCKQUOTE> -<LI><B>nonzero?</B></LI><BLOCKQUOTE> -a が 0 なら nil、0 以外なら a そのものが返ります。<BR> -c = a.nonzero? - -</BLOCKQUOTE> -<LI><B>split</B></LI><BLOCKQUOTE> -BigDecimal 値を 0.xxxxxxx*10**n と表現したときに、符号（NaNのときは -0、それ以外は+1か-1になります）、 -仮数部分の文字列（"xxxxxxx"）と、基数（10）、更に指数 n を配列で -返します。<BR> -a=BigDecimal::new("3.14159265")<BR> -f,x,y,z = a.split<BR> -とすると、f=+1、x="314159265"、y=10、z=1になります。<BR> -従って、<BR> -s = "0."+x<BR> -b = f*(s.to_f)*(y**z)<BR> -で Float に変換することができます。 -</BLOCKQUOTE> -<LI><B>inspect</B></LI><BLOCKQUOTE> -デバッグ出力に使用されます。<BR> -p a=BigDecimal::new("3.14",10)<BR> -とすると、[0x112344:'0.314E1',4(12)]のように出力されます。 -最初の16進数はオブジェクトのアドレス、次の '0.314E1' は値、 -次の4は現在の有効桁数(表示より若干大きいことがあります)、 -最後はオブジェクトが取り得る最大桁数になります。 -</BLOCKQUOTE> -<LI><B>**</B></LI><BLOCKQUOTE> -a の n 乗を計算します。ｎは整数。<BR> -c = a ** n<BR> -結果として c の有効桁は a の n 倍以上になるので注意。 -</BLOCKQUOTE> -<LI><B>power</B></LI><BLOCKQUOTE> -** と同じで、a の n 乗を計算します。ｎは整数。<BR> -c = a.power(n)<BR> -結果として c の有効桁は a の n 倍以上になるので注意。 -</BLOCKQUOTE> -<LI><B>sqrt</B></LI><BLOCKQUOTE> -aの有効桁 n 桁の平方根（n の平方根ではありません）を -ニュートン法で計算します。<BR> -c = a.sqrt(n)<BR> -</BLOCKQUOTE> - -<LI><B>divmod,quo,modulo,%,remainder</B></LI><BLOCKQUOTE> -詳細は対応する Float の各メソッドを参照して下さい。 -</BLOCKQUOTE> - -<LI><B><=></B></LI><BLOCKQUOTE> -a==b なら 0、a > b なら 1、a < b なら -1 になります。<BR> -c = a <=> b -</BLOCKQUOTE> -</UL> -後は、読んで字の如くです。<BR> -<UL> -<LI><B>==</B></LI> -<LI><B>===</B></LI> -「==」と同じですが case 文で使用されます。 -<LI><B>!=</B></LI> -<LI><B><</B></LI> -<LI><B><=</B></LI> -<LI><B>></B></LI> -<LI><B>>=</B></LI> -</UL> - -<H3>coerceについて</H3> -BigDecimal オブジェクトが算術演算子の左にあるときは、BigDecimal オブジェクトが -右にあるオブジェクトを(必要なら) BigDecimal に変換してから計算します。 -従って、BigDecimal オブジェクト以外でも数値を意味するものなら右に置けば -演算は可能です。<BR> -ただし、文字列は（通常）数値に自動変換することはできません。 -文字列を数値に自動変換したい場合は bigfloat.c の -「/* #define ENABLE_NUMERIC_STRING */」のコメントを外してから、 -再コンパイル、再インストールする必要があります。 -文字列で数値を与える場合は注意が必要です。数値に変換できない文字があると、 -単に変換を止めるだけでエラーにはなりません。"10XX"なら１０、"XXXX"は０ -と扱われます。<BR> -<CODE><PRE> - a = BigDecimal.E(20) - c = a * "0.123456789123456789123456789" # 文字を BigDecimal に変換してから計算 -</PRE></CODE> -無限大や非数を表す文字として、"Infinity"、"+Infinity"、"-Infinity"、"NaN" -も使用できます(大文字・小文字を区別します)。ただし、mode メソッドで false を -指定した場合は例外が発生します。 -<BR> -また、BigDecimalクラスは coerce（Ruby本参照）をサポートしています。 -従って、BigDecimal オブジェクトが右にある場合も大抵は大丈夫です。 -ただ、現在の Ruby インタプリタの仕様上、文字列が左にあると計算できません。<BR> -<CODE><PRE> - a = BigDecimal.E(20) - c = "0.123456789123456789123456789" * a # エラー -</PRE></CODE> -必要性があるとは思いませんが、どうしてもと言う人は - String オブジェクトを継承した新たなクラスを作成してから、 -そのクラスで coerce をサポートしてください。 - -<hr> -<A NAME="#UNDEF"> -<H2>無限、非数、ゼロの扱い</H2> -「無限」とは表現できないくらい大きな数です。特別に扱うために - +Infinity（正の無限大）や -Infinity（負の無限大）という -ように表記されます。 -無限は 1.0/0.0 のようにゼロで割るような計算をしたときに生成されます。 -<BR><BR> -「非数」は 0.0/0.0 や Infinity-Infinity 等の結果が定義できない -計算をしたときに生成されます。非数は NaN（Not a Number）と表記されます。 -NaN を含む計算は全て NaN になります。また NaN は自分も含めて、どんな数 -とも一致しません。 -<BR><BR> -ゼロは +0.0 と -0.0 が存在します。ただし、+0.0==-0.0 は true です。 -<BR><BR> -Infinity、NaN、 +0.0 と -0.0 等を含んだ計算結果は組み合わせに -より複雑です。興味のある人は、以下のプログラムを実行して結果を -確認してください（結果について、疑問や間違いを発見された方は -お知らせ願います）。 - -<PRE> -<CODE> -require "bigdecimal" - -aa = %w(1 -1 +0.0 -0.0 +Infinity -Infinity NaN) -ba = %w(1 -1 +0.0 -0.0 +Infinity -Infinity NaN) -opa = %w(+ - * / <=> > >= < == != <=) - -for a in aa - for b in ba - for op in opa - x = BigDecimal::new(a) - y = BigDecimal::new(b) - eval("ans= x #{op} y;print a,' ',op,' ',b,' ==> ',ans.to_s,\"\n\"") - end - end -end -</CODE> -</PRE> - -<hr> -<A NAME="#STRUCT"> -<H2>内部構造</H2> -BigDecimal内部で浮動小数点は構造体(Real)で表現されます。 -そのうち仮数部は unsigned long の配列(以下の構造体要素frac)で管理されます。 -概念的には、以下のようになります。<BR><BR> - <浮動小数点数> = 0.xxxxxxxxx*BASE**n<BR><BR> -ここで、xは仮数部を表す数字、BASEは基数（１０進なら１０）、nは指数部を表す -整数値です。BASEが大きいほど、大きな数値が表現できます。つまり、配列のサイズを -少なくできます。BASEは大きいほど都合がよいわけですが、デバッグのやりやすさなどを -考慮して、10000になっています（BASEはVpInit()関数で自動的に計算します）。 -これは、32ビット整数の場合です。64ビット整数の場合はもっと大きな値になります。 -残念ながら、64ビット整数でのテストはまだやっていません（もし、やられた方がいれば -結果を教えていただければありがたいです）。 -BASEが10000のときは、以下の仮数部の配列(frac)の各要素には最大で４桁の -数字が格納されます。<BR><BR> -浮動小数点構造体(Real)は以下のようになっています。 -<BR> -<CODE><PRE> - typedef struct { - unsigned long MaxPrec; // 最大精度(frac[]の配列サイズ) - unsigned long Prec; // 精度(frac[]の使用サイズ) - short sign; // 以下のように符号等の状態を定義します。 - // ==0 : NaN - // 1 : +0 - // -1 : -0 - // 2 : 正の値 - // -2 : 負の値 - // 3 : +Infinity - // -3 : -Infinity - unsigned short flag; // 各種の制御フラッグ - int exponent; // 指数部の値(仮数部*BASE**exponent) - unsigned long frac[1]; // 仮数部の配列(可変) - } Real; -</CODE></PRE> -例えば 1234.56784321 という数字は(BASE=10000なら)<BR> -<PRE> - 0.1234 5678 4321*(10000)**1 -</PRE> -ですから frac[0]=1234、frac[1]=5678、frac[2]=4321、 -Prec=3、sign=2、exponent=1 となります。MaxPrecは -Prec より大きければいくつでもかまいません。flag の -使用方法は実装に依存して内部で使用されます。 - -<hr> -<A NAME="#BASE"> -<H2>2進と10進</H2> -BigDecimal は <浮動小数点数> = 0.xxxxxxxxx*10**n という10進形式で数値を保持します。 -しかし、計算機の浮動小数点数の内部表現は、言うまでもなく <浮動小数点数> = 0.bbbbbbbb*2**n という -2進形式が普通です(x は 0 から 9 まで、b は 0 か 1 の数字)。 -BigDecimal がなぜ10進の内部表現形式を採用したのかを以下に説明します。 -<H4>10進のメリット</H4> -<DL> -<DT>デバッグのしやすさ -<DD>まず、プログラム作成が楽です。frac[0]=1234、frac[1]=5678、frac[2]=4321、 -exponent=1、sign=2 なら数値が 1234.56784321 であるのは見れば直ぐに分かります。 - -<DT>10進表記された数値なら確実に内部表現に変換できる -<DD>例えば、以下のようなプログラムは全く誤差無しで -計算することができます。以下の例は、一行に一つの数値 -が書いてあるファイル file の合計数値を求めるものです。 -<CODE><PRE> - file = File::open(....,"r") - s = BigDecimal::new("0") - while line = file.gets - s = s + line - end -</PRE></CODE> -この例を2進数でやると誤差が入り込む可能性があります。 -例えば 0.1 を2進で表現すると 0.1 = b1*2**(-1)+b1*2**(-2)+b3*2**(-3)+b4*2**(-4).... -と無限に続いてしまいます(b1=0,b2=0,b3=0,b4=1...)。ここで bn(n=1,2,3,...) は -2進を表現する 0 か 1 の数字列です。従って、どこかで打ち切る必要があります。 -ここで変換誤差が入ります。もちろん、これを再度10進表記にして印刷するような -場合は適切な丸め操作（四捨五入）によって再び "0.1" と表示されます。しかし、 -内部では正確な 0.1 ではありません。 - -<DT>有効桁数は有限である（つまり自動決定できる） -<DD>0.1 を表現するための領域はたった一つの配列要素（ frac[0]=1 ）で済みます。 -配列要素の数は10進数値から自動的に決定できます。これは、可変長浮動小数点演算では -大事なことです。逆に 0.1 を2進表現したときには2進の有効桁をいくつにするのか 0.1 を -見ただけでは決定できません。 -</DL> - -<H3>10進のデメリット</H3> -実は今までのメリットは、そのままデメリットにもなります。 -そもそも、10進を2進に変換するような操作は変換誤差 -を伴う場合を回避することはできません。 -大概のコンピュータは10進の内部表現を持っていないので、 -BigDecimal を利用して誤差無しの計算をする場合は、計算速度 -を無視しても最後まで BigDecimal を使用続ける必要があります。 - -<H3>最初は何か？</H3> -自分で計算するときにわざわざ2進数を使う人は極めてまれです。 -計算機にデータを入力するときもほとんどの場合、 -10進数で入力します。その結果、double 等の計算機内部 -表現は最初から誤差が入っている場合があります。 -BigDecimal はユーザ入力を誤差無しで取り込むことができます。 -デバッグがしやすいのと、データ読みこみ時に誤差が入らない -というのが実際のメリットです。 - -<hr> -<A NAME="#PREC"> -<H2>計算精度について</H2> -c = a op b という計算(op は + - * /)をしたときの動作は -以下のようになります。<BR><BR> -１．乗算は(a の有効桁数)+(b の有効桁数)、 -除算は(a の最大有効桁数)+(b の最大有効桁数)分の最大桁数（実際は、余裕を持って、 -もう少し大きくなります）を持つ変数 c を新たに生成します。 -加減算の場合は、誤差が出ないだけの精度を持つ c を生成します。例えば - c = 0.1+0.1*10**(-100) のような場合、c の精度は１００桁以上の精度を -持つようになります。 -<BR><BR> -２．次に c = a op b の計算を実行します。<BR><BR> -このように、加減算と乗算での c は必ず「誤差が出ない」だけの精度を -持って生成されます(BigDecimal.limit を指定しない場合)。 -除算は(a の最大有効桁数)+(b の最大有効桁数)分の最大桁数 -を持つ c が生成されますが、c = 1.0/3.0 のような計算で明らかなように、 - c の最大精度を超えるところで計算が打ち切られる場合があります。<BR><BR> -いずれにせよ、c の最大精度は a や b より大きくなりますので c が必要とする -メモリー領域は大きくなることに注意して下さい。 -<BR><BR> -注意：「+,-,*,/」では結果の精度（有効桁数）を自分で指定できません。 -精度をコントロールしたい場合は、以下のインスタンスメソッドを使用します。<BR> -<UL> -<LI>add,sub,mult,div</LI><BLOCKQUOTE> -これらのメソッドは先頭(最左)の数字からの桁数を指定できます。 -<CODE><PRE> - BigDecimal("2").div(3,12) # 2.0/3.0 => 0.6666666666 67E0 -</PRE></CODE> -</BLOCKQUOTE> -<LI>truncate,round,ceil,floor</LI><BLOCKQUOTE> -これらのメソッドは小数点からの相対位置を指定して桁数を決定します。 -<CODE><PRE> - BigDecimal("6.66666666666666").round(12) # => 0.6666666666 667E1 -</PRE></CODE> -</BLOCKQUOTE> -</UL> -<H3>自分で精度をコントロールしたい場合</H3> -自分で精度(有効桁数)をコントロールしたい場合は add、sub、mult、div 等のメソッド -が使用できます。 -以下の円周率を計算するプログラム例のように、 -求める桁数は自分で指定することができます。 -<BR><BR> -<CODE><PRE> -#!/usr/local/bin/ruby - -require "bigdecimal" -# -# Calculates 3.1415.... (the number of times that a circle's diameter -# will fit around the circle) using J. Machin's formula. -# -def big_pi(sig) # sig: Number of significant figures - exp = -sig - pi = BigDecimal::new("0") - two = BigDecimal::new("2") - m25 = BigDecimal::new("-0.04") - m57121 = BigDecimal::new("-57121") - - u = BigDecimal::new("1") - k = BigDecimal::new("1") - w = BigDecimal::new("1") - t = BigDecimal::new("-80") - while (u.nonzero? && u.exponent >= exp) - t = t*m25 - u = t.div(k,sig) - pi = pi + u - k = k+two - end - - u = BigDecimal::new("1") - k = BigDecimal::new("1") - w = BigDecimal::new("1") - t = BigDecimal::new("956") - while (u.nonzero? && u.exponent >= exp ) - t = t.div(m57121,sig) - u = t.div(k,sig) - pi = pi + u - k = k+two - end - pi -end - -if $0 == __FILE__ - if ARGV.size == 1 - print "PI("+ARGV[0]+"):\n" - p big_pi(ARGV[0].to_i) - else - print "TRY: ruby pi.rb 1000 \n" - end -end - -</PRE></CODE> -<HR> -<FONT size=2> -<I> -<A HREF="http://www.tinyforest.gr.jp"> -小林 茂雄 -</A> -(E-Mail:<A HREF="mailto:shigeo@tinyforest.gr.jp"><shigeo@tinyforest.gr.jp></U></A>) -</I> -</FONT> -</TD> -</TR> -</TABLE> -</BODY> -</HTML> diff --git a/ruby_1_8_6/ext/bigdecimal/depend b/ruby_1_8_6/ext/bigdecimal/depend deleted file mode 100644 index 402cae95dd..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/depend +++ /dev/null @@ -1 +0,0 @@ -bigdecimal.o: bigdecimal.c bigdecimal.h $(hdrdir)/ruby.h diff --git a/ruby_1_8_6/ext/bigdecimal/extconf.rb b/ruby_1_8_6/ext/bigdecimal/extconf.rb deleted file mode 100644 index 864aaad862..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/extconf.rb +++ /dev/null @@ -1,12 +0,0 @@ -require 'mkmf' - -base_fig = 0 -src = ("(BASE > 0) && " - "(BASE * (BASE+1)) > BASE && " - "(BASE * (BASE+1)) / BASE == (BASE+1)") -while try_static_assert(src, nil, "-DBASE=10#{'0'*base_fig}UL") - base_fig += 1 -end -$defs << "-DBASE=1#{'0'*base_fig}UL" << "-DBASE_FIG=#{base_fig}" - -create_makefile('bigdecimal') diff --git a/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/jacobian.rb b/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/jacobian.rb deleted file mode 100644 index d80eeab901..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/jacobian.rb +++ /dev/null @@ -1,85 +0,0 @@ -# -# require 'bigdecimal/jacobian' -# -# Provides methods to compute the Jacobian matrix of a set of equations at a -# point x. In the methods below: -# -# f is an Object which is used to compute the Jacobian matrix of the equations. -# It must provide the following methods: -# -# f.values(x):: returns the values of all functions at x -# -# f.zero:: returns 0.0 -# f.one:: returns 1.0 -# f.two:: returns 1.0 -# f.ten:: returns 10.0 -# -# f.eps:: returns the convergence criterion (epsilon value) used to determine whether two values are considered equal. If |a-b| < epsilon, the two values are considered equal. -# -# x is the point at which to compute the Jacobian. -# -# fx is f.values(x). -# -module Jacobian - #-- - def isEqual(a,b,zero=0.0,e=1.0e-8) - aa = a.abs - bb = b.abs - if aa == zero && bb == zero then - true - else - if ((a-b)/(aa+bb)).abs < e then - true - else - false - end - end - end - #++ - - # Computes the derivative of f[i] at x[i]. - # fx is the value of f at x. - def dfdxi(f,fx,x,i) - nRetry = 0 - n = x.size - xSave = x[i] - ok = 0 - ratio = f.ten*f.ten*f.ten - dx = x[i].abs/ratio - dx = fx[i].abs/ratio if isEqual(dx,f.zero,f.zero,f.eps) - dx = f.one/f.ten if isEqual(dx,f.zero,f.zero,f.eps) - until ok>0 do - s = f.zero - deriv = [] - if(nRetry>100) then - raize "Singular Jacobian matrix. No change at x[" + i.to_s + "]" - end - dx = dx*f.two - x[i] += dx - fxNew = f.values(x) - for j in 0...n do - if !isEqual(fxNew[j],fx[j],f.zero,f.eps) then - ok += 1 - deriv <<= (fxNew[j]-fx[j])/dx - else - deriv <<= f.zero - end - end - x[i] = xSave - end - deriv - end - - # Computes the Jacobian of f at x. fx is the value of f at x. - def jacobian(f,fx,x) - n = x.size - dfdx = Array::new(n*n) - for i in 0...n do - df = dfdxi(f,fx,x,i) - for j in 0...n do - dfdx[j*n+i] = df[j] - end - end - dfdx - end -end diff --git a/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/ludcmp.rb b/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/ludcmp.rb deleted file mode 100644 index 8f4888725e..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/ludcmp.rb +++ /dev/null @@ -1,84 +0,0 @@ -# -# Solves a*x = b for x, using LU decomposition. -# -module LUSolve - # Performs LU decomposition of the n by n matrix a. - def ludecomp(a,n,zero=0,one=1) - prec = BigDecimal.limit(nil) - ps = [] - scales = [] - for i in 0...n do # pick up largest(abs. val.) element in each row. - ps <<= i - nrmrow = zero - ixn = i*n - for j in 0...n do - biggst = a[ixn+j].abs - nrmrow = biggst if biggst>nrmrow - end - if nrmrow>zero then - scales <<= one.div(nrmrow,prec) - else - raise "Singular matrix" - end - end - n1 = n - 1 - for k in 0...n1 do # Gaussian elimination with partial pivoting. - biggst = zero; - for i in k...n do - size = a[ps[i]*n+k].abs*scales[ps[i]] - if size>biggst then - biggst = size - pividx = i - end - end - raise "Singular matrix" if biggst<=zero - if pividx!=k then - j = ps[k] - ps[k] = ps[pividx] - ps[pividx] = j - end - pivot = a[ps[k]*n+k] - for i in (k+1)...n do - psin = ps[i]*n - a[psin+k] = mult = a[psin+k].div(pivot,prec) - if mult!=zero then - pskn = ps[k]*n - for j in (k+1)...n do - a[psin+j] -= mult.mult(a[pskn+j],prec) - end - end - end - end - raise "Singular matrix" if a[ps[n1]*n+n1] == zero - ps - end - - # Solves a*x = b for x, using LU decomposition. - # - # a is a matrix, b is a constant vector, x is the solution vector. - # - # ps is the pivot, a vector which indicates the permutation of rows performed - # during LU decomposition. - def lusolve(a,b,ps,zero=0.0) - prec = BigDecimal.limit(nil) - n = ps.size - x = [] - for i in 0...n do - dot = zero - psin = ps[i]*n - for j in 0...i do - dot = a[psin+j].mult(x[j],prec) + dot - end - x <<= b[ps[i]] - dot - end - (n-1).downto(0) do |i| - dot = zero - psin = ps[i]*n - for j in (i+1)...n do - dot = a[psin+j].mult(x[j],prec) + dot - end - x[i] = (x[i]-dot).div(a[psin+i],prec) - end - x - end -end diff --git a/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/math.rb b/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/math.rb deleted file mode 100644 index f3248a3c5c..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/math.rb +++ /dev/null @@ -1,235 +0,0 @@ -# -#-- -# Contents: -# sqrt(x, prec) -# sin (x, prec) -# cos (x, prec) -# atan(x, prec) Note: |x|<1, x=0.9999 may not converge. -# exp (x, prec) -# log (x, prec) -# PI (prec) -# E (prec) == exp(1.0,prec) -# -# where: -# x ... BigDecimal number to be computed. -# |x| must be small enough to get convergence. -# prec ... Number of digits to be obtained. -#++ -# -# Provides mathematical functions. -# -# Example: -# -# require "bigdecimal" -# require "bigdecimal/math" -# -# include BigMath -# -# a = BigDecimal((PI(100)/2).to_s) -# puts sin(a,100) # -> 0.10000000000000000000......E1 -# -module BigMath - - # Computes the square root of x to the specified number of digits of - # precision. - # - # BigDecimal.new('2').sqrt(16).to_s - # -> "0.14142135623730950488016887242096975E1" - # - def sqrt(x,prec) - x.sqrt(prec) - end - - # Computes the sine of x to the specified number of digits of precision. - # - # If x is infinite or NaN, returns NaN. - def sin(x, prec) - raise ArgumentError, "Zero or negative precision for sin" if prec <= 0 - return BigDecimal("NaN") if x.infinite? || x.nan? - n = prec + BigDecimal.double_fig - one = BigDecimal("1") - two = BigDecimal("2") - x1 = x - x2 = x.mult(x,n) - sign = 1 - y = x - d = y - i = one - z = one - while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) - m = BigDecimal.double_fig if m < BigDecimal.double_fig - sign = -sign - x1 = x2.mult(x1,n) - i += two - z *= (i-one) * i - d = sign * x1.div(z,m) - y += d - end - y - end - - # Computes the cosine of x to the specified number of digits of precision. - # - # If x is infinite or NaN, returns NaN. - def cos(x, prec) - raise ArgumentError, "Zero or negative precision for cos" if prec <= 0 - return BigDecimal("NaN") if x.infinite? || x.nan? - n = prec + BigDecimal.double_fig - one = BigDecimal("1") - two = BigDecimal("2") - x1 = one - x2 = x.mult(x,n) - sign = 1 - y = one - d = y - i = BigDecimal("0") - z = one - while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) - m = BigDecimal.double_fig if m < BigDecimal.double_fig - sign = -sign - x1 = x2.mult(x1,n) - i += two - z *= (i-one) * i - d = sign * x1.div(z,m) - y += d - end - y - end - - # Computes the arctangent of x to the specified number of digits of precision. - # - # If x is infinite or NaN, returns NaN. - # Raises an argument error if x > 1. - def atan(x, prec) - raise ArgumentError, "Zero or negative precision for atan" if prec <= 0 - return BigDecimal("NaN") if x.infinite? || x.nan? - raise ArgumentError, "x.abs must be less than 1.0" if x.abs>=1 - n = prec + BigDecimal.double_fig - y = x - d = y - t = x - r = BigDecimal("3") - x2 = x.mult(x,n) - while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) - m = BigDecimal.double_fig if m < BigDecimal.double_fig - t = -t.mult(x2,n) - d = t.div(r,m) - y += d - r += 2 - end - y - end - - # Computes the value of e (the base of natural logarithms) raised to the - # power of x, to the specified number of digits of precision. - # - # If x is infinite or NaN, returns NaN. - # - # BigMath::exp(BigDecimal.new('1'), 10).to_s - # -> "0.271828182845904523536028752390026306410273E1" - def exp(x, prec) - raise ArgumentError, "Zero or negative precision for exp" if prec <= 0 - return BigDecimal("NaN") if x.infinite? || x.nan? - n = prec + BigDecimal.double_fig - one = BigDecimal("1") - x1 = one - y = one - d = y - z = one - i = 0 - while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) - m = BigDecimal.double_fig if m < BigDecimal.double_fig - x1 = x1.mult(x,n) - i += 1 - z *= i - d = x1.div(z,m) - y += d - end - y - end - - # Computes the natural logarithm of x to the specified number of digits - # of precision. - # - # Returns x if x is infinite or NaN. - # - def log(x, prec) - raise ArgumentError, "Zero or negative argument for log" if x <= 0 || prec <= 0 - return x if x.infinite? || x.nan? - one = BigDecimal("1") - two = BigDecimal("2") - n = prec + BigDecimal.double_fig - x = (x - one).div(x + one,n) - x2 = x.mult(x,n) - y = x - d = y - i = one - while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) - m = BigDecimal.double_fig if m < BigDecimal.double_fig - x = x2.mult(x,n) - i += two - d = x.div(i,m) - y += d - end - y*two - end - - # Computes the value of pi to the specified number of digits of precision. - def PI(prec) - raise ArgumentError, "Zero or negative argument for PI" if prec <= 0 - n = prec + BigDecimal.double_fig - zero = BigDecimal("0") - one = BigDecimal("1") - two = BigDecimal("2") - - m25 = BigDecimal("-0.04") - m57121 = BigDecimal("-57121") - - pi = zero - - d = one - k = one - w = one - t = BigDecimal("-80") - while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0) - m = BigDecimal.double_fig if m < BigDecimal.double_fig - t = t*m25 - d = t.div(k,m) - k = k+two - pi = pi + d - end - - d = one - k = one - w = one - t = BigDecimal("956") - while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0) - m = BigDecimal.double_fig if m < BigDecimal.double_fig - t = t.div(m57121,n) - d = t.div(k,m) - pi = pi + d - k = k+two - end - pi - end - - # Computes e (the base of natural logarithms) to the specified number of - # digits of precision. - def E(prec) - raise ArgumentError, "Zero or negative precision for E" if prec <= 0 - n = prec + BigDecimal.double_fig - one = BigDecimal("1") - y = one - d = y - z = one - i = 0 - while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) - m = BigDecimal.double_fig if m < BigDecimal.double_fig - i += 1 - z *= i - d = one.div(z,m) - y += d - end - y - end -end diff --git a/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/newton.rb b/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/newton.rb deleted file mode 100644 index 59ac0f7f04..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/newton.rb +++ /dev/null @@ -1,77 +0,0 @@ -# -# newton.rb -# -# Solves the nonlinear algebraic equation system f = 0 by Newton's method. -# This program is not dependent on BigDecimal. -# -# To call: -# n = nlsolve(f,x) -# where n is the number of iterations required, -# x is the initial value vector -# f is an Object which is used to compute the values of the equations to be solved. -# It must provide the following methods: -# -# f.values(x):: returns the values of all functions at x -# -# f.zero:: returns 0.0 -# f.one:: returns 1.0 -# f.two:: returns 1.0 -# f.ten:: returns 10.0 -# -# f.eps:: returns the convergence criterion (epsilon value) used to determine whether two values are considered equal. If |a-b| < epsilon, the two values are considered equal. -# -# On exit, x is the solution vector. -# -require "bigdecimal/ludcmp" -require "bigdecimal/jacobian" - -module Newton - include LUSolve - include Jacobian - - def norm(fv,zero=0.0) - s = zero - n = fv.size - for i in 0...n do - s += fv[i]*fv[i] - end - s - end - - def nlsolve(f,x) - nRetry = 0 - n = x.size - - f0 = f.values(x) - zero = f.zero - one = f.one - two = f.two - p5 = one/two - d = norm(f0,zero) - minfact = f.ten*f.ten*f.ten - minfact = one/minfact - e = f.eps - while d >= e do - nRetry += 1 - # Not yet converged. => Compute Jacobian matrix - dfdx = jacobian(f,f0,x) - # Solve dfdx*dx = -f0 to estimate dx - dx = lusolve(dfdx,f0,ludecomp(dfdx,n,zero,one),zero) - fact = two - xs = x.dup - begin - fact *= p5 - if fact < minfact then - raise "Failed to reduce function values." - end - for i in 0...n do - x[i] = xs[i] - dx[i]*fact - end - f0 = f.values(x) - dn = norm(f0,zero) - end while(dn>=d) - d = dn - end - nRetry - end -end diff --git a/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/util.rb b/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/util.rb deleted file mode 100644 index 09e926acd5..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/lib/bigdecimal/util.rb +++ /dev/null @@ -1,65 +0,0 @@ -# -# BigDecimal utility library. -# -# To use these functions, require 'bigdecimal/util' -# -# The following methods are provided to convert other types to BigDecimals: -# -# String#to_d -> BigDecimal -# Float#to_d -> BigDecimal -# Rational#to_d -> BigDecimal -# -# The following method is provided to convert BigDecimals to other types: -# -# BigDecimal#to_r -> Rational -# -# ---------------------------------------------------------------------- -# -class Float < Numeric - def to_d - BigDecimal(self.to_s) - end -end - -class String - def to_d - BigDecimal(self) - end -end - -class BigDecimal < Numeric - # Converts a BigDecimal to a String of the form "nnnnnn.mmm". - # This method is deprecated; use BigDecimal#to_s("F") instead. - def to_digits - if self.nan? || self.infinite? || self.zero? - self.to_s - else - i = self.to_i.to_s - s,f,y,z = self.frac.split - i + "." + ("0"*(-z)) + f - end - end - - # Converts a BigDecimal to a Rational. - def to_r - sign,digits,base,power = self.split - numerator = sign*digits.to_i - denomi_power = power - digits.size # base is always 10 - if denomi_power < 0 - Rational(numerator,base ** (-denomi_power)) - else - Rational(numerator * (base ** denomi_power),1) - end - end -end - -class Rational < Numeric - # Converts a Rational to a BigDecimal - def to_d(nFig=0) - num = self.numerator.to_s - if nFig<=0 - nFig = BigDecimal.double_fig*2+1 - end - BigDecimal.new(num).div(self.denominator,nFig) - end -end diff --git a/ruby_1_8_6/ext/bigdecimal/sample/linear.rb b/ruby_1_8_6/ext/bigdecimal/sample/linear.rb deleted file mode 100644 index 88a62ffa71..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/sample/linear.rb +++ /dev/null @@ -1,71 +0,0 @@ -#!/usr/local/bin/ruby - -# -# linear.rb -# -# Solves linear equation system(A*x = b) by LU decomposition method. -# where A is a coefficient matrix,x is an answer vector,b is a constant vector. -# -# USAGE: -# ruby linear.rb [input file solved] -# - -require "bigdecimal" -require "bigdecimal/ludcmp" - -# -# NOTE: -# Change following BigDecimal::limit() if needed. -BigDecimal::limit(100) -# - -include LUSolve -def rd_order(na) - printf("Number of equations ?") if(na <= 0) - n = ARGF.gets().to_i -end - -na = ARGV.size -zero = BigDecimal::new("0.0") -one = BigDecimal::new("1.0") - -while (n=rd_order(na))>0 - a = [] - as= [] - b = [] - if na <= 0 - # Read data from console. - printf("\nEnter coefficient matrix element A[i,j]\n"); - for i in 0...n do - for j in 0...n do - printf("A[%d,%d]? ",i,j); s = ARGF.gets - a << BigDecimal::new(s); - as << BigDecimal::new(s); - end - printf("Contatant vector element b[%d] ? ",i); b << BigDecimal::new(ARGF.gets); - end - else - # Read data from specified file. - printf("Coefficient matrix and constant vector.\n"); - for i in 0...n do - s = ARGF.gets - printf("%d) %s",i,s) - s = s.split - for j in 0...n do - a << BigDecimal::new(s[j]); - as << BigDecimal::new(s[j]); - end - b << BigDecimal::new(s[n]); - end - end - x = lusolve(a,b,ludecomp(a,n,zero,one),zero) - printf("Answer(x[i] & (A*x-b)[i]) follows\n") - for i in 0...n do - printf("x[%d]=%s ",i,x[i].to_s) - s = zero - for j in 0...n do - s = s + as[i*n+j]*x[j] - end - printf(" & %s\n",(s-b[i]).to_s) - end -end diff --git a/ruby_1_8_6/ext/bigdecimal/sample/nlsolve.rb b/ruby_1_8_6/ext/bigdecimal/sample/nlsolve.rb deleted file mode 100644 index 7f729e6aaa..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/sample/nlsolve.rb +++ /dev/null @@ -1,38 +0,0 @@ -#!/usr/local/bin/ruby - -# -# nlsolve.rb -# An example for solving nonlinear algebraic equation system. -# - -require "bigdecimal" -require "bigdecimal/newton" -include Newton - -class Function - def initialize() - @zero = BigDecimal::new("0.0") - @one = BigDecimal::new("1.0") - @two = BigDecimal::new("2.0") - @ten = BigDecimal::new("10.0") - @eps = BigDecimal::new("1.0e-16") - end - def zero;@zero;end - def one ;@one ;end - def two ;@two ;end - def ten ;@ten ;end - def eps ;@eps ;end - def values(x) # <= defines functions solved - f = [] - f1 = x[0]*x[0] + x[1]*x[1] - @two # f1 = x**2 + y**2 - 2 => 0 - f2 = x[0] - x[1] # f2 = x - y => 0 - f <<= f1 - f <<= f2 - f - end -end - f = BigDecimal::limit(100) - f = Function.new - x = [f.zero,f.zero] # Initial values - n = nlsolve(f,x) - p x diff --git a/ruby_1_8_6/ext/bigdecimal/sample/pi.rb b/ruby_1_8_6/ext/bigdecimal/sample/pi.rb deleted file mode 100644 index 2f7dd27d60..0000000000 --- a/ruby_1_8_6/ext/bigdecimal/sample/pi.rb +++ /dev/null @@ -1,20 +0,0 @@ -#!/usr/local/bin/ruby - -# -# pi.rb -# -# Calculates 3.1415.... (the number of times that a circle's diameter -# will fit around the circle) using J. Machin's formula. -# - -require "bigdecimal" -require "bigdecimal/math.rb" - -include BigMath - -if ARGV.size == 1 - print "PI("+ARGV[0]+"):\n" - p PI(ARGV[0].to_i) -else - print "TRY: ruby pi.rb 1000 \n" -end |