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Diffstat (limited to 'ruby_1_8_6/ext/bigdecimal/bigdecimal.c')
| -rw-r--r-- | ruby_1_8_6/ext/bigdecimal/bigdecimal.c | 4695 |
1 files changed, 4695 insertions, 0 deletions
diff --git a/ruby_1_8_6/ext/bigdecimal/bigdecimal.c b/ruby_1_8_6/ext/bigdecimal/bigdecimal.c new file mode 100644 index 0000000000..a4b769e8cf --- /dev/null +++ b/ruby_1_8_6/ext/bigdecimal/bigdecimal.c @@ -0,0 +1,4695 @@ +/* + * + * 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, d2; + S_LONG e; + + GUARD_OBJ(p,GetVpValue(self,1)); + if(VpVtoD(&d, &e, p)!=1) return rb_float_new(d); + errno = 0; + d2 = pow(10.0,(double)e); + if((errno == ERANGE && e>0) || (d2>1.0 && (fabs(d) > (DBL_MAX / d2)))) { + 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*d2); +} + +/* 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; + 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++) { + 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 */ + +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 S_LONG DBLE_FIG = 8; /* figure of double */ +static U_LONG BASE1 = 1000L; /* =BASE/10 */ + +static Real *VpConstOne; /* constant 1.0 */ +static Real *VpPt5; /* constant 0.5 */ +static U_LONG maxnr = 100; /* 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 double gZero_ABCED9B1_CE73__00400511F31D = 0.0; +volatile 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) +{ + U_LONG w; + double v; + + /* Setup +/- Inf NaN -0 */ + VpGetDoubleNaN(); + VpGetDoublePosInf(); + VpGetDoubleNegInf(); + VpGetDoubleNegZero(); + + if(BaseVal <= 0) { + /* 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; + /* Allocates Vp constants. */ + VpConstOne = VpAlloc((U_LONG)1, "1"); + VpPt5 = VpAlloc((U_LONG)1, ".5"); + +#ifdef _DEBUG + gnAlloc = 0; +#endif /* _DEBUG */ + + /* Determine # of digits available in one 'double'. */ + + v = 1.0; + DBLE_FIG = 0; + while(v + 1.0 > 1.0) { + ++DBLE_FIG; + v /= 10; + } + +#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]) { + 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]) { + 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]) { /* 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]) { + 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=v/10) 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 */ |