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685f91236c
Fixes GH-343. Patch by @jgarber. git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@41663 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
6187 lines
145 KiB
C
6187 lines
145 KiB
C
/*
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*
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* Ruby BigDecimal(Variable decimal precision) extension library.
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*
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* Copyright(C) 2002 by Shigeo Kobayashi(shigeo@tinyforest.gr.jp)
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*
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* You may distribute under the terms of either the GNU General Public
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* License or the Artistic License, as specified in the README file
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* of this BigDecimal distribution.
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*
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* NOTE: Change log in this source removed to reduce source code size.
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* See rev. 1.25 if needed.
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*
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*/
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/* #define BIGDECIMAL_DEBUG 1 */
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#ifdef BIGDECIMAL_DEBUG
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# define BIGDECIMAL_ENABLE_VPRINT 1
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#endif
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#include "bigdecimal.h"
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#ifndef BIGDECIMAL_DEBUG
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# define NDEBUG
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#endif
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#include <assert.h>
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#include <ctype.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <errno.h>
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#include <math.h>
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#include "math.h"
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#ifdef HAVE_IEEEFP_H
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#include <ieeefp.h>
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#endif
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/* #define ENABLE_NUMERIC_STRING */
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#define MUL_OVERFLOW_SIGNED_INTEGER_P(a, b, min, max) ( \
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(a) == 0 ? 0 : \
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(a) == -1 ? (b) < -(max) : \
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(a) > 0 ? \
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((b) > 0 ? (max) / (a) < (b) : (min) / (a) > (b)) : \
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((b) > 0 ? (min) / (a) < (b) : (max) / (a) > (b)))
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#define SIGNED_VALUE_MAX INTPTR_MAX
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#define SIGNED_VALUE_MIN INTPTR_MIN
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#define MUL_OVERFLOW_SIGNED_VALUE_P(a, b) MUL_OVERFLOW_SIGNED_INTEGER_P(a, b, SIGNED_VALUE_MIN, SIGNED_VALUE_MAX)
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VALUE rb_cBigDecimal;
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VALUE rb_mBigMath;
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static ID id_BigDecimal_exception_mode;
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static ID id_BigDecimal_rounding_mode;
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static ID id_BigDecimal_precision_limit;
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static ID id_up;
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static ID id_down;
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static ID id_truncate;
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static ID id_half_up;
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static ID id_default;
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static ID id_half_down;
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static ID id_half_even;
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static ID id_banker;
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static ID id_ceiling;
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static ID id_ceil;
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static ID id_floor;
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static ID id_to_r;
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static ID id_eq;
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/* MACRO's to guard objects from GC by keeping them in stack */
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#define ENTER(n) volatile VALUE RB_UNUSED_VAR(vStack[n]);int iStack=0
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#define PUSH(x) vStack[iStack++] = (VALUE)(x);
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#define SAVE(p) PUSH(p->obj);
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#define GUARD_OBJ(p,y) {p=y;SAVE(p);}
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#define BASE_FIG RMPD_COMPONENT_FIGURES
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#define BASE RMPD_BASE
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#define HALF_BASE (BASE/2)
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#define BASE1 (BASE/10)
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#ifndef DBLE_FIG
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#define DBLE_FIG (DBL_DIG+1) /* figure of double */
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#endif
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#ifndef RBIGNUM_ZERO_P
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# define RBIGNUM_ZERO_P(x) rb_bigzero_p(x)
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#endif
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#ifndef RRATIONAL_ZERO_P
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# define RRATIONAL_ZERO_P(x) (FIXNUM_P(RRATIONAL(x)->num) && \
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FIX2LONG(RRATIONAL(x)->num) == 0)
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#endif
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#ifndef RRATIONAL_NEGATIVE_P
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# define RRATIONAL_NEGATIVE_P(x) RTEST(rb_funcall((x), '<', 1, INT2FIX(0)))
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#endif
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/*
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* ================== Ruby Interface part ==========================
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*/
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#define DoSomeOne(x,y,f) rb_num_coerce_bin(x,y,f)
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/*
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* Returns the BigDecimal version number.
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*/
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static VALUE
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BigDecimal_version(VALUE self)
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{
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/*
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* 1.0.0: Ruby 1.8.0
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* 1.0.1: Ruby 1.8.1
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* 1.1.0: Ruby 1.9.3
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*/
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return rb_str_new2("1.1.0");
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}
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/*
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* VP routines used in BigDecimal part
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*/
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static unsigned short VpGetException(void);
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static void VpSetException(unsigned short f);
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static void VpInternalRound(Real *c, size_t ixDigit, BDIGIT vPrev, BDIGIT v);
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static int VpLimitRound(Real *c, size_t ixDigit);
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static Real *VpCopy(Real *pv, Real const* const x);
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/*
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* **** BigDecimal part ****
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*/
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static void
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BigDecimal_delete(void *pv)
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{
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VpFree(pv);
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}
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static size_t
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BigDecimal_memsize(const void *ptr)
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{
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const Real *pv = ptr;
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return pv ? (sizeof(*pv) + pv->MaxPrec * sizeof(BDIGIT)) : 0;
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}
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static const rb_data_type_t BigDecimal_data_type = {
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"BigDecimal",
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{ 0, BigDecimal_delete, BigDecimal_memsize, },
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};
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static inline int
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is_kind_of_BigDecimal(VALUE const v)
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{
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return rb_typeddata_is_kind_of(v, &BigDecimal_data_type);
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}
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static VALUE
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ToValue(Real *p)
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{
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if (VpIsNaN(p)) {
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VpException(VP_EXCEPTION_NaN, "Computation results to 'NaN'(Not a Number)", 0);
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}
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else if (VpIsPosInf(p)) {
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VpException(VP_EXCEPTION_INFINITY, "Computation results to 'Infinity'", 0);
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}
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else if (VpIsNegInf(p)) {
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VpException(VP_EXCEPTION_INFINITY, "Computation results to '-Infinity'", 0);
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}
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return p->obj;
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}
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NORETURN(static void cannot_be_coerced_into_BigDecimal(VALUE, VALUE));
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static void
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cannot_be_coerced_into_BigDecimal(VALUE exc_class, VALUE v)
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{
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VALUE str;
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if (rb_special_const_p(v)) {
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str = rb_inspect(v);
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}
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else {
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str = rb_class_name(rb_obj_class(v));
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}
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str = rb_str_cat2(rb_str_dup(str), " can't be coerced into BigDecimal");
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rb_exc_raise(rb_exc_new3(exc_class, str));
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}
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static VALUE BigDecimal_div2(int, VALUE*, VALUE);
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static Real*
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GetVpValueWithPrec(VALUE v, long prec, int must)
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{
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Real *pv;
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VALUE num, bg, args[2];
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char szD[128];
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VALUE orig = Qundef;
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again:
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switch(TYPE(v)) {
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case T_FLOAT:
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if (prec < 0) goto unable_to_coerce_without_prec;
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if (prec > DBL_DIG+1) goto SomeOneMayDoIt;
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v = rb_funcall(v, id_to_r, 0);
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goto again;
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case T_RATIONAL:
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if (prec < 0) goto unable_to_coerce_without_prec;
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if (orig == Qundef ? (orig = v, 1) : orig != v) {
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num = RRATIONAL(v)->num;
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pv = GetVpValueWithPrec(num, -1, must);
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if (pv == NULL) goto SomeOneMayDoIt;
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args[0] = RRATIONAL(v)->den;
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args[1] = LONG2NUM(prec);
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v = BigDecimal_div2(2, args, ToValue(pv));
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goto again;
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}
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v = orig;
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goto SomeOneMayDoIt;
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case T_DATA:
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if (is_kind_of_BigDecimal(v)) {
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pv = DATA_PTR(v);
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return pv;
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}
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else {
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goto SomeOneMayDoIt;
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}
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break;
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case T_FIXNUM:
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sprintf(szD, "%ld", FIX2LONG(v));
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return VpCreateRbObject(VpBaseFig() * 2 + 1, szD);
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#ifdef ENABLE_NUMERIC_STRING
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case T_STRING:
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SafeStringValue(v);
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return VpCreateRbObject(strlen(RSTRING_PTR(v)) + VpBaseFig() + 1,
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RSTRING_PTR(v));
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#endif /* ENABLE_NUMERIC_STRING */
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case T_BIGNUM:
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bg = rb_big2str(v, 10);
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return VpCreateRbObject(strlen(RSTRING_PTR(bg)) + VpBaseFig() + 1,
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RSTRING_PTR(bg));
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default:
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goto SomeOneMayDoIt;
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}
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SomeOneMayDoIt:
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if (must) {
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cannot_be_coerced_into_BigDecimal(rb_eTypeError, v);
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}
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return NULL; /* NULL means to coerce */
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unable_to_coerce_without_prec:
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if (must) {
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rb_raise(rb_eArgError,
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"%s can't be coerced into BigDecimal without a precision",
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rb_obj_classname(v));
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}
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return NULL;
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}
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static Real*
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GetVpValue(VALUE v, int must)
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{
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return GetVpValueWithPrec(v, -1, must);
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}
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/* call-seq:
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* BigDecimal.double_fig
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*
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* The BigDecimal.double_fig class method returns the number of digits a
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* Float number is allowed to have. The result depends upon the CPU and OS
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* in use.
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*/
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static VALUE
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BigDecimal_double_fig(VALUE self)
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{
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return INT2FIX(VpDblFig());
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}
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/* call-seq:
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* precs
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*
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* Returns an Array of two Integer values.
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*
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* The first value is the current number of significant digits in the
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* BigDecimal. The second value is the maximum number of significant digits
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* for the BigDecimal.
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*/
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static VALUE
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BigDecimal_prec(VALUE self)
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{
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ENTER(1);
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Real *p;
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VALUE obj;
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GUARD_OBJ(p, GetVpValue(self, 1));
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obj = rb_assoc_new(INT2NUM(p->Prec*VpBaseFig()),
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INT2NUM(p->MaxPrec*VpBaseFig()));
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return obj;
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}
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/*
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* call-seq: hash
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*
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* Creates a hash for this BigDecimal.
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*
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* Two BigDecimals with equal sign,
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* fractional part and exponent have the same hash.
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*/
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static VALUE
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BigDecimal_hash(VALUE self)
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{
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ENTER(1);
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Real *p;
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st_index_t hash;
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GUARD_OBJ(p, GetVpValue(self, 1));
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hash = (st_index_t)p->sign;
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/* hash!=2: the case for 0(1),NaN(0) or +-Infinity(3) is sign itself */
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if(hash == 2 || hash == (st_index_t)-2) {
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hash ^= rb_memhash(p->frac, sizeof(BDIGIT)*p->Prec);
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hash += p->exponent;
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}
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return INT2FIX(hash);
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}
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/*
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* call-seq: _dump
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*
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* Method used to provide marshalling support.
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*
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* inf = BigDecimal.new('Infinity')
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* => #<BigDecimal:1e16fa8,'Infinity',9(9)>
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* BigDecimal._load(inf._dump)
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* => #<BigDecimal:1df8dc8,'Infinity',9(9)>
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*
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* See the Marshal module.
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*/
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static VALUE
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BigDecimal_dump(int argc, VALUE *argv, VALUE self)
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{
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ENTER(5);
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Real *vp;
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char *psz;
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VALUE dummy;
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volatile VALUE dump;
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rb_scan_args(argc, argv, "01", &dummy);
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GUARD_OBJ(vp,GetVpValue(self, 1));
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dump = rb_str_new(0, VpNumOfChars(vp, "E")+50);
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psz = RSTRING_PTR(dump);
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sprintf(psz, "%"PRIuSIZE":", VpMaxPrec(vp)*VpBaseFig());
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VpToString(vp, psz+strlen(psz), 0, 0);
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rb_str_resize(dump, strlen(psz));
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return dump;
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}
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/*
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* Internal method used to provide marshalling support. See the Marshal module.
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*/
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static VALUE
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BigDecimal_load(VALUE self, VALUE str)
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{
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ENTER(2);
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Real *pv;
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unsigned char *pch;
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unsigned char ch;
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unsigned long m=0;
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SafeStringValue(str);
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pch = (unsigned char *)RSTRING_PTR(str);
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/* First get max prec */
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while((*pch) != (unsigned char)'\0' && (ch = *pch++) != (unsigned char)':') {
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if(!ISDIGIT(ch)) {
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rb_raise(rb_eTypeError, "load failed: invalid character in the marshaled string");
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}
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m = m*10 + (unsigned long)(ch-'0');
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}
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if (m > VpBaseFig()) m -= VpBaseFig();
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GUARD_OBJ(pv, VpNewRbClass(m, (char *)pch, self));
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m /= VpBaseFig();
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if (m && pv->MaxPrec > m) {
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pv->MaxPrec = m+1;
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}
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return ToValue(pv);
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}
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static unsigned short
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check_rounding_mode(VALUE const v)
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{
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unsigned short sw;
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ID id;
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switch (TYPE(v)) {
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case T_SYMBOL:
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id = SYM2ID(v);
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if (id == id_up)
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return VP_ROUND_UP;
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if (id == id_down || id == id_truncate)
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return VP_ROUND_DOWN;
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if (id == id_half_up || id == id_default)
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return VP_ROUND_HALF_UP;
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if (id == id_half_down)
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return VP_ROUND_HALF_DOWN;
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if (id == id_half_even || id == id_banker)
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return VP_ROUND_HALF_EVEN;
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if (id == id_ceiling || id == id_ceil)
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return VP_ROUND_CEIL;
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if (id == id_floor)
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return VP_ROUND_FLOOR;
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rb_raise(rb_eArgError, "invalid rounding mode");
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default:
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break;
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}
|
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Check_Type(v, T_FIXNUM);
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sw = (unsigned short)FIX2UINT(v);
|
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if (!VpIsRoundMode(sw)) {
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rb_raise(rb_eArgError, "invalid rounding mode");
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}
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return sw;
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}
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/* call-seq:
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* BigDecimal.mode(mode, value)
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*
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* Controls handling of arithmetic exceptions and rounding. If no value
|
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* is supplied, the current value is returned.
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*
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* Six values of the mode parameter control the handling of arithmetic
|
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* exceptions:
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*
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* BigDecimal::EXCEPTION_NaN
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* BigDecimal::EXCEPTION_INFINITY
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* BigDecimal::EXCEPTION_UNDERFLOW
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* BigDecimal::EXCEPTION_OVERFLOW
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* BigDecimal::EXCEPTION_ZERODIVIDE
|
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* BigDecimal::EXCEPTION_ALL
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*
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* For each mode parameter above, if the value set is false, computation
|
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* continues after an arithmetic exception of the appropriate type.
|
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* When computation continues, results are as follows:
|
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*
|
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* 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:
|
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* BigDecimal::ROUND_MODE. The values it can take are:
|
|
*
|
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* ROUND_UP, :up:: round away from zero
|
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* ROUND_DOWN, :down, :truncate:: round towards zero (truncate)
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* ROUND_HALF_UP, :half_up, :default:: round towards the nearest neighbor, unless both neighbors are equidistant, in which case round away from zero. (default)
|
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* ROUND_HALF_DOWN, :half_down:: round towards the nearest neighbor, unless both neighbors are equidistant, in which case round towards zero.
|
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* ROUND_HALF_EVEN, :half_even, :banker:: round towards the nearest neighbor, unless both neighbors are equidistant, in which case round towards the even neighbor (Banker's rounding)
|
|
* ROUND_CEILING, :ceiling, :ceil:: round towards positive infinity (ceil)
|
|
* ROUND_FLOOR, :floor:: round towards negative infinity (floor)
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|
*
|
|
*/
|
|
static VALUE
|
|
BigDecimal_mode(int argc, VALUE *argv, VALUE self)
|
|
{
|
|
VALUE which;
|
|
VALUE val;
|
|
unsigned long f,fo;
|
|
|
|
rb_scan_args(argc, argv, "11", &which, &val);
|
|
Check_Type(which, T_FIXNUM);
|
|
f = (unsigned long)FIX2INT(which);
|
|
|
|
if (f & VP_EXCEPTION_ALL) {
|
|
/* Exception mode setting */
|
|
fo = VpGetException();
|
|
if (val == Qnil) return INT2FIX(fo);
|
|
if (val != Qfalse && val!=Qtrue) {
|
|
rb_raise(rb_eArgError, "second argument must be true or false");
|
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return Qnil; /* Not reached */
|
|
}
|
|
if (f & VP_EXCEPTION_INFINITY) {
|
|
VpSetException((unsigned short)((val == Qtrue) ? (fo | VP_EXCEPTION_INFINITY) :
|
|
(fo & (~VP_EXCEPTION_INFINITY))));
|
|
}
|
|
fo = VpGetException();
|
|
if (f & VP_EXCEPTION_NaN) {
|
|
VpSetException((unsigned short)((val == Qtrue) ? (fo | VP_EXCEPTION_NaN) :
|
|
(fo & (~VP_EXCEPTION_NaN))));
|
|
}
|
|
fo = VpGetException();
|
|
if (f & VP_EXCEPTION_UNDERFLOW) {
|
|
VpSetException((unsigned short)((val == Qtrue) ? (fo | VP_EXCEPTION_UNDERFLOW) :
|
|
(fo & (~VP_EXCEPTION_UNDERFLOW))));
|
|
}
|
|
fo = VpGetException();
|
|
if(f & VP_EXCEPTION_ZERODIVIDE) {
|
|
VpSetException((unsigned short)((val == Qtrue) ? (fo | VP_EXCEPTION_ZERODIVIDE) :
|
|
(fo & (~VP_EXCEPTION_ZERODIVIDE))));
|
|
}
|
|
fo = VpGetException();
|
|
return INT2FIX(fo);
|
|
}
|
|
if (VP_ROUND_MODE == f) {
|
|
/* Rounding mode setting */
|
|
unsigned short sw;
|
|
fo = VpGetRoundMode();
|
|
if (NIL_P(val)) return INT2FIX(fo);
|
|
sw = check_rounding_mode(val);
|
|
fo = VpSetRoundMode(sw);
|
|
return INT2FIX(fo);
|
|
}
|
|
rb_raise(rb_eTypeError, "first argument for BigDecimal#mode invalid");
|
|
return Qnil;
|
|
}
|
|
|
|
static size_t
|
|
GetAddSubPrec(Real *a, Real *b)
|
|
{
|
|
size_t mxs;
|
|
size_t mx = a->Prec;
|
|
SIGNED_VALUE d;
|
|
|
|
if (!VpIsDef(a) || !VpIsDef(b)) return (size_t)-1L;
|
|
if (mx < b->Prec) mx = b->Prec;
|
|
if (a->exponent != b->exponent) {
|
|
mxs = mx;
|
|
d = a->exponent - b->exponent;
|
|
if (d < 0) d = -d;
|
|
mx = mx + (size_t)d;
|
|
if (mx < mxs) {
|
|
return VpException(VP_EXCEPTION_INFINITY, "Exponent overflow", 0);
|
|
}
|
|
}
|
|
return mx;
|
|
}
|
|
|
|
static SIGNED_VALUE
|
|
GetPositiveInt(VALUE v)
|
|
{
|
|
SIGNED_VALUE n;
|
|
Check_Type(v, T_FIXNUM);
|
|
n = FIX2INT(v);
|
|
if (n < 0) {
|
|
rb_raise(rb_eArgError, "argument must be positive");
|
|
}
|
|
return n;
|
|
}
|
|
|
|
VP_EXPORT Real *
|
|
VpNewRbClass(size_t mx, const char *str, VALUE klass)
|
|
{
|
|
Real *pv = VpAlloc(mx,str);
|
|
pv->obj = TypedData_Wrap_Struct(klass, &BigDecimal_data_type, pv);
|
|
return pv;
|
|
}
|
|
|
|
VP_EXPORT Real *
|
|
VpCreateRbObject(size_t mx, const char *str)
|
|
{
|
|
Real *pv = VpAlloc(mx,str);
|
|
pv->obj = TypedData_Wrap_Struct(rb_cBigDecimal, &BigDecimal_data_type, pv);
|
|
return pv;
|
|
}
|
|
|
|
#define VpAllocReal(prec) (Real *)VpMemAlloc(offsetof(Real, frac) + (prec) * sizeof(BDIGIT))
|
|
#define VpReallocReal(ptr, prec) (Real *)VpMemRealloc((ptr), offsetof(Real, frac) + (prec) * sizeof(BDIGIT))
|
|
|
|
static Real *
|
|
VpCopy(Real *pv, Real const* const x)
|
|
{
|
|
assert(x != NULL);
|
|
|
|
pv = VpReallocReal(pv, x->MaxPrec);
|
|
pv->MaxPrec = x->MaxPrec;
|
|
pv->Prec = x->Prec;
|
|
pv->exponent = x->exponent;
|
|
pv->sign = x->sign;
|
|
pv->flag = x->flag;
|
|
MEMCPY(pv->frac, x->frac, BDIGIT, pv->MaxPrec);
|
|
|
|
return pv;
|
|
}
|
|
|
|
/* Returns True if the value is Not a Number */
|
|
static VALUE
|
|
BigDecimal_IsNaN(VALUE self)
|
|
{
|
|
Real *p = GetVpValue(self, 1);
|
|
if (VpIsNaN(p)) return Qtrue;
|
|
return Qfalse;
|
|
}
|
|
|
|
/* Returns nil, -1, or +1 depending on whether the value is finite,
|
|
* -infinity, or +infinity.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_IsInfinite(VALUE self)
|
|
{
|
|
Real *p = GetVpValue(self, 1);
|
|
if (VpIsPosInf(p)) return INT2FIX(1);
|
|
if (VpIsNegInf(p)) return INT2FIX(-1);
|
|
return Qnil;
|
|
}
|
|
|
|
/* Returns True if the value is finite (not NaN or infinite) */
|
|
static VALUE
|
|
BigDecimal_IsFinite(VALUE self)
|
|
{
|
|
Real *p = GetVpValue(self, 1);
|
|
if (VpIsNaN(p)) return Qfalse;
|
|
if (VpIsInf(p)) return Qfalse;
|
|
return Qtrue;
|
|
}
|
|
|
|
static void
|
|
BigDecimal_check_num(Real *p)
|
|
{
|
|
if (VpIsNaN(p)) {
|
|
VpException(VP_EXCEPTION_NaN, "Computation results to 'NaN'(Not a Number)", 1);
|
|
}
|
|
else if (VpIsPosInf(p)) {
|
|
VpException(VP_EXCEPTION_INFINITY, "Computation results to 'Infinity'", 1);
|
|
}
|
|
else if (VpIsNegInf(p)) {
|
|
VpException(VP_EXCEPTION_INFINITY, "Computation results to '-Infinity'", 1);
|
|
}
|
|
}
|
|
|
|
static VALUE BigDecimal_split(VALUE self);
|
|
|
|
/* Returns the value as an integer (Fixnum or Bignum).
|
|
*
|
|
* If the BigNumber is infinity or NaN, raises FloatDomainError.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_to_i(VALUE self)
|
|
{
|
|
ENTER(5);
|
|
ssize_t e, nf;
|
|
Real *p;
|
|
|
|
GUARD_OBJ(p, GetVpValue(self, 1));
|
|
BigDecimal_check_num(p);
|
|
|
|
e = VpExponent10(p);
|
|
if (e <= 0) return INT2FIX(0);
|
|
nf = VpBaseFig();
|
|
if (e <= nf) {
|
|
return LONG2NUM((long)(VpGetSign(p) * (BDIGIT_DBL_SIGNED)p->frac[0]));
|
|
}
|
|
else {
|
|
VALUE a = BigDecimal_split(self);
|
|
VALUE digits = RARRAY_PTR(a)[1];
|
|
VALUE numerator = rb_funcall(digits, rb_intern("to_i"), 0);
|
|
VALUE ret;
|
|
ssize_t dpower = e - (ssize_t)RSTRING_LEN(digits);
|
|
|
|
if (VpGetSign(p) < 0) {
|
|
numerator = rb_funcall(numerator, '*', 1, INT2FIX(-1));
|
|
}
|
|
if (dpower < 0) {
|
|
ret = rb_funcall(numerator, rb_intern("div"), 1,
|
|
rb_funcall(INT2FIX(10), rb_intern("**"), 1,
|
|
INT2FIX(-dpower)));
|
|
}
|
|
else {
|
|
ret = rb_funcall(numerator, '*', 1,
|
|
rb_funcall(INT2FIX(10), rb_intern("**"), 1,
|
|
INT2FIX(dpower)));
|
|
}
|
|
if (RB_TYPE_P(ret, T_FLOAT)) {
|
|
rb_raise(rb_eFloatDomainError, "Infinity");
|
|
}
|
|
return ret;
|
|
}
|
|
}
|
|
|
|
/* Returns a new Float object having approximately the same value as the
|
|
* BigDecimal number. Normal accuracy limits and built-in errors of binary
|
|
* Float arithmetic apply.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_to_f(VALUE self)
|
|
{
|
|
ENTER(1);
|
|
Real *p;
|
|
double d;
|
|
SIGNED_VALUE e;
|
|
char *buf;
|
|
volatile VALUE str;
|
|
|
|
GUARD_OBJ(p, GetVpValue(self, 1));
|
|
if (VpVtoD(&d, &e, p) != 1)
|
|
return rb_float_new(d);
|
|
if (e > (SIGNED_VALUE)(DBL_MAX_10_EXP+BASE_FIG))
|
|
goto overflow;
|
|
if (e < (SIGNED_VALUE)(DBL_MIN_10_EXP-BASE_FIG))
|
|
goto underflow;
|
|
|
|
str = rb_str_new(0, VpNumOfChars(p, "E"));
|
|
buf = RSTRING_PTR(str);
|
|
VpToString(p, buf, 0, 0);
|
|
errno = 0;
|
|
d = strtod(buf, 0);
|
|
if (errno == ERANGE) {
|
|
if (d == 0.0) goto underflow;
|
|
if (fabs(d) >= HUGE_VAL) goto overflow;
|
|
}
|
|
return rb_float_new(d);
|
|
|
|
overflow:
|
|
VpException(VP_EXCEPTION_OVERFLOW, "BigDecimal to Float conversion", 0);
|
|
if (p->sign >= 0)
|
|
return rb_float_new(VpGetDoublePosInf());
|
|
else
|
|
return rb_float_new(VpGetDoubleNegInf());
|
|
|
|
underflow:
|
|
VpException(VP_EXCEPTION_UNDERFLOW, "BigDecimal to Float conversion", 0);
|
|
if (p->sign >= 0)
|
|
return rb_float_new(0.0);
|
|
else
|
|
return rb_float_new(-0.0);
|
|
}
|
|
|
|
|
|
/* Converts a BigDecimal to a Rational.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_to_r(VALUE self)
|
|
{
|
|
Real *p;
|
|
ssize_t sign, power, denomi_power;
|
|
VALUE a, digits, numerator;
|
|
|
|
p = GetVpValue(self, 1);
|
|
BigDecimal_check_num(p);
|
|
|
|
sign = VpGetSign(p);
|
|
power = VpExponent10(p);
|
|
a = BigDecimal_split(self);
|
|
digits = RARRAY_PTR(a)[1];
|
|
denomi_power = power - RSTRING_LEN(digits);
|
|
numerator = rb_funcall(digits, rb_intern("to_i"), 0);
|
|
|
|
if (sign < 0) {
|
|
numerator = rb_funcall(numerator, '*', 1, INT2FIX(-1));
|
|
}
|
|
if (denomi_power < 0) {
|
|
return rb_Rational(numerator,
|
|
rb_funcall(INT2FIX(10), rb_intern("**"), 1,
|
|
INT2FIX(-denomi_power)));
|
|
}
|
|
else {
|
|
return rb_Rational1(rb_funcall(numerator, '*', 1,
|
|
rb_funcall(INT2FIX(10), rb_intern("**"), 1,
|
|
INT2FIX(denomi_power))));
|
|
}
|
|
}
|
|
|
|
/* The coerce method provides support for Ruby type coercion. It is not
|
|
* enabled by default.
|
|
*
|
|
* This means that binary operations like + * / or - can often be performed
|
|
* on a BigDecimal and an object of another type, if the other object can
|
|
* be coerced into a BigDecimal value.
|
|
*
|
|
* e.g.
|
|
* a = BigDecimal.new("1.0")
|
|
* b = a / 2.0 -> 0.5
|
|
*
|
|
* Note that coercing a String to a BigDecimal is not supported by default;
|
|
* it requires a special compile-time option when building Ruby.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_coerce(VALUE self, VALUE other)
|
|
{
|
|
ENTER(2);
|
|
VALUE obj;
|
|
Real *b;
|
|
|
|
if (RB_TYPE_P(other, T_FLOAT)) {
|
|
obj = rb_assoc_new(other, BigDecimal_to_f(self));
|
|
}
|
|
else {
|
|
if (RB_TYPE_P(other, T_RATIONAL)) {
|
|
Real* pv = DATA_PTR(self);
|
|
GUARD_OBJ(b, GetVpValueWithPrec(other, pv->Prec*VpBaseFig(), 1));
|
|
}
|
|
else {
|
|
GUARD_OBJ(b, GetVpValue(other, 1));
|
|
}
|
|
obj = rb_assoc_new(b->obj, self);
|
|
}
|
|
|
|
return obj;
|
|
}
|
|
|
|
/*
|
|
* call-seq: +@
|
|
*
|
|
* Return self.
|
|
*
|
|
* e.g.
|
|
* b = +a # b == a
|
|
*/
|
|
static VALUE
|
|
BigDecimal_uplus(VALUE self)
|
|
{
|
|
return self;
|
|
}
|
|
|
|
/*
|
|
* Document-method: BigDecimal#add
|
|
* Document-method: BigDecimal#+
|
|
*
|
|
* call-seq:
|
|
* add(value, digits)
|
|
*
|
|
* Add the specified value.
|
|
*
|
|
* e.g.
|
|
* c = a.add(b,n)
|
|
* c = a + b
|
|
*
|
|
* digits:: If specified and less than the number of significant digits of the
|
|
* result, the result is rounded to that number of digits, according to
|
|
* BigDecimal.mode.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_add(VALUE self, VALUE r)
|
|
{
|
|
ENTER(5);
|
|
Real *c, *a, *b;
|
|
size_t mx;
|
|
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
if (RB_TYPE_P(r, T_FLOAT)) {
|
|
b = GetVpValueWithPrec(r, DBL_DIG+1, 1);
|
|
}
|
|
else if (RB_TYPE_P(r, T_RATIONAL)) {
|
|
b = GetVpValueWithPrec(r, a->Prec*VpBaseFig(), 1);
|
|
}
|
|
else {
|
|
b = GetVpValue(r, 0);
|
|
}
|
|
|
|
if (!b) return DoSomeOne(self,r,'+');
|
|
SAVE(b);
|
|
|
|
if (VpIsNaN(b)) return b->obj;
|
|
if (VpIsNaN(a)) return a->obj;
|
|
|
|
mx = GetAddSubPrec(a, b);
|
|
if (mx == (size_t)-1L) {
|
|
GUARD_OBJ(c,VpCreateRbObject(VpBaseFig() + 1, "0"));
|
|
VpAddSub(c, a, b, 1);
|
|
}
|
|
else {
|
|
GUARD_OBJ(c, VpCreateRbObject(mx * (VpBaseFig() + 1), "0"));
|
|
if(!mx) {
|
|
VpSetInf(c, VpGetSign(a));
|
|
}
|
|
else {
|
|
VpAddSub(c, a, b, 1);
|
|
}
|
|
}
|
|
return ToValue(c);
|
|
}
|
|
|
|
/* call-seq:
|
|
* value - digits -> bigdecimal
|
|
*
|
|
* Subtract the specified value.
|
|
*
|
|
* e.g.
|
|
* c = a - b
|
|
*
|
|
* The precision of the result value depends on the type of +b+.
|
|
*
|
|
* If +b+ is a Float, the precision of the result is Float::DIG+1.
|
|
*
|
|
* If +b+ is a BigDecimal, the precision of the result is +b+'s precision of
|
|
* internal representation from platform. So, it's return value is platform
|
|
* dependent.
|
|
*
|
|
*/
|
|
static VALUE
|
|
BigDecimal_sub(VALUE self, VALUE r)
|
|
{
|
|
ENTER(5);
|
|
Real *c, *a, *b;
|
|
size_t mx;
|
|
|
|
GUARD_OBJ(a, GetVpValue(self,1));
|
|
if (RB_TYPE_P(r, T_FLOAT)) {
|
|
b = GetVpValueWithPrec(r, DBL_DIG+1, 1);
|
|
}
|
|
else if (RB_TYPE_P(r, T_RATIONAL)) {
|
|
b = GetVpValueWithPrec(r, a->Prec*VpBaseFig(), 1);
|
|
}
|
|
else {
|
|
b = GetVpValue(r,0);
|
|
}
|
|
|
|
if (!b) return DoSomeOne(self,r,'-');
|
|
SAVE(b);
|
|
|
|
if (VpIsNaN(b)) return b->obj;
|
|
if (VpIsNaN(a)) return a->obj;
|
|
|
|
mx = GetAddSubPrec(a,b);
|
|
if (mx == (size_t)-1L) {
|
|
GUARD_OBJ(c,VpCreateRbObject(VpBaseFig() + 1, "0"));
|
|
VpAddSub(c, a, b, -1);
|
|
}
|
|
else {
|
|
GUARD_OBJ(c,VpCreateRbObject(mx *(VpBaseFig() + 1), "0"));
|
|
if (!mx) {
|
|
VpSetInf(c,VpGetSign(a));
|
|
}
|
|
else {
|
|
VpAddSub(c, a, b, -1);
|
|
}
|
|
}
|
|
return ToValue(c);
|
|
}
|
|
|
|
static VALUE
|
|
BigDecimalCmp(VALUE self, VALUE r,char op)
|
|
{
|
|
ENTER(5);
|
|
SIGNED_VALUE e;
|
|
Real *a, *b=0;
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
switch (TYPE(r)) {
|
|
case T_DATA:
|
|
if (!is_kind_of_BigDecimal(r)) break;
|
|
/* fall through */
|
|
case T_FIXNUM:
|
|
/* fall through */
|
|
case T_BIGNUM:
|
|
GUARD_OBJ(b, GetVpValue(r, 0));
|
|
break;
|
|
|
|
case T_FLOAT:
|
|
GUARD_OBJ(b, GetVpValueWithPrec(r, DBL_DIG+1, 0));
|
|
break;
|
|
|
|
case T_RATIONAL:
|
|
GUARD_OBJ(b, GetVpValueWithPrec(r, a->Prec*VpBaseFig(), 0));
|
|
break;
|
|
|
|
default:
|
|
break;
|
|
}
|
|
if (b == NULL) {
|
|
ID f = 0;
|
|
|
|
switch (op) {
|
|
case '*':
|
|
return rb_num_coerce_cmp(self, r, rb_intern("<=>"));
|
|
|
|
case '=':
|
|
return RTEST(rb_num_coerce_cmp(self, r, rb_intern("=="))) ? Qtrue : Qfalse;
|
|
|
|
case 'G':
|
|
f = rb_intern(">=");
|
|
break;
|
|
|
|
case 'L':
|
|
f = rb_intern("<=");
|
|
break;
|
|
|
|
case '>':
|
|
/* fall through */
|
|
case '<':
|
|
f = (ID)op;
|
|
break;
|
|
|
|
default:
|
|
break;
|
|
}
|
|
return rb_num_coerce_relop(self, r, f);
|
|
}
|
|
SAVE(b);
|
|
e = VpComp(a, b);
|
|
if (e == 999)
|
|
return (op == '*') ? Qnil : Qfalse;
|
|
switch (op) {
|
|
case '*':
|
|
return INT2FIX(e); /* any op */
|
|
|
|
case '=':
|
|
if (e == 0) return Qtrue;
|
|
return Qfalse;
|
|
|
|
case 'G':
|
|
if (e >= 0) return Qtrue;
|
|
return Qfalse;
|
|
|
|
case '>':
|
|
if (e > 0) return Qtrue;
|
|
return Qfalse;
|
|
|
|
case 'L':
|
|
if (e <= 0) return Qtrue;
|
|
return Qfalse;
|
|
|
|
case '<':
|
|
if (e < 0) return Qtrue;
|
|
return Qfalse;
|
|
|
|
default:
|
|
break;
|
|
}
|
|
|
|
rb_bug("Undefined operation in BigDecimalCmp()");
|
|
|
|
UNREACHABLE;
|
|
}
|
|
|
|
/* Returns True if the value is zero. */
|
|
static VALUE
|
|
BigDecimal_zero(VALUE self)
|
|
{
|
|
Real *a = GetVpValue(self, 1);
|
|
return VpIsZero(a) ? Qtrue : Qfalse;
|
|
}
|
|
|
|
/* Returns self if the value is non-zero, nil otherwise. */
|
|
static VALUE
|
|
BigDecimal_nonzero(VALUE self)
|
|
{
|
|
Real *a = GetVpValue(self, 1);
|
|
return VpIsZero(a) ? Qnil : self;
|
|
}
|
|
|
|
/* The comparison operator.
|
|
* a <=> b is 0 if a == b, 1 if a > b, -1 if a < b.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_comp(VALUE self, VALUE r)
|
|
{
|
|
return BigDecimalCmp(self, r, '*');
|
|
}
|
|
|
|
/*
|
|
* Tests for value equality; returns true if the values are equal.
|
|
*
|
|
* The == and === operators and the eql? method have the same implementation
|
|
* for BigDecimal.
|
|
*
|
|
* Values may be coerced to perform the comparison:
|
|
*
|
|
* BigDecimal.new('1.0') == 1.0 -> true
|
|
*/
|
|
static VALUE
|
|
BigDecimal_eq(VALUE self, VALUE r)
|
|
{
|
|
return BigDecimalCmp(self, r, '=');
|
|
}
|
|
|
|
/* call-seq:
|
|
* a < b
|
|
*
|
|
* Returns true if a is less than b.
|
|
*
|
|
* Values may be coerced to perform the comparison (see ==, BigDecimal#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 ==, BigDecimal#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 ==, BigDecimal#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 ==, BigDecimal#coerce)
|
|
*/
|
|
static VALUE
|
|
BigDecimal_ge(VALUE self, VALUE r)
|
|
{
|
|
return BigDecimalCmp(self, r, 'G');
|
|
}
|
|
|
|
/*
|
|
* call-seq: -@
|
|
*
|
|
* Return the negation of self.
|
|
*
|
|
* e.g.
|
|
* b = -a
|
|
* b == a * -1
|
|
*/
|
|
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);
|
|
}
|
|
|
|
/*
|
|
* Document-method: BigDecimal#mult
|
|
*
|
|
* call-seq: mult(value, digits)
|
|
*
|
|
* Multiply by the specified value.
|
|
*
|
|
* e.g.
|
|
* c = a.mult(b,n)
|
|
* c = a * b
|
|
*
|
|
* digits:: If specified and less than the number of significant digits of the
|
|
* result, the result is rounded to that number of digits, according to
|
|
* BigDecimal.mode.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_mult(VALUE self, VALUE r)
|
|
{
|
|
ENTER(5);
|
|
Real *c, *a, *b;
|
|
size_t mx;
|
|
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
if (RB_TYPE_P(r, T_FLOAT)) {
|
|
b = GetVpValueWithPrec(r, DBL_DIG+1, 1);
|
|
}
|
|
else if (RB_TYPE_P(r, T_RATIONAL)) {
|
|
b = GetVpValueWithPrec(r, a->Prec*VpBaseFig(), 1);
|
|
}
|
|
else {
|
|
b = GetVpValue(r,0);
|
|
}
|
|
|
|
if (!b) return DoSomeOne(self, r, '*');
|
|
SAVE(b);
|
|
|
|
mx = a->Prec + b->Prec;
|
|
GUARD_OBJ(c, VpCreateRbObject(mx *(VpBaseFig() + 1), "0"));
|
|
VpMult(c, a, b);
|
|
return ToValue(c);
|
|
}
|
|
|
|
static VALUE
|
|
BigDecimal_divide(Real **c, Real **res, Real **div, VALUE self, VALUE r)
|
|
/* For c = self.div(r): with round operation */
|
|
{
|
|
ENTER(5);
|
|
Real *a, *b;
|
|
size_t mx;
|
|
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
if (RB_TYPE_P(r, T_FLOAT)) {
|
|
b = GetVpValueWithPrec(r, DBL_DIG+1, 1);
|
|
}
|
|
else if (RB_TYPE_P(r, T_RATIONAL)) {
|
|
b = GetVpValueWithPrec(r, a->Prec*VpBaseFig(), 1);
|
|
}
|
|
else {
|
|
b = GetVpValue(r, 0);
|
|
}
|
|
|
|
if (!b) return DoSomeOne(self, r, '/');
|
|
SAVE(b);
|
|
|
|
*div = b;
|
|
mx = a->Prec + vabs(a->exponent);
|
|
if (mx<b->Prec + vabs(b->exponent)) mx = b->Prec + vabs(b->exponent);
|
|
mx =(mx + 1) * VpBaseFig();
|
|
GUARD_OBJ((*c), VpCreateRbObject(mx, "#0"));
|
|
GUARD_OBJ((*res), VpCreateRbObject((mx+1) * 2 +(VpBaseFig() + 1), "#0"));
|
|
VpDivd(*c, *res, a, b);
|
|
return Qnil;
|
|
}
|
|
|
|
/* 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 <code>div(value, 0)</code> is the same as
|
|
* computing the quotient; see BigDecimal#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 (!NIL_P(r)) return r; /* coerced by other */
|
|
SAVE(c); SAVE(res); SAVE(div);
|
|
/* a/b = c + r/b */
|
|
/* c xxxxx
|
|
r 00000yyyyy ==> (y/b)*BASE >= HALF_BASE
|
|
*/
|
|
/* Round */
|
|
if (VpHasVal(div)) { /* frac[0] must be zero for NaN,INF,Zero */
|
|
VpInternalRound(c, 0, c->frac[c->Prec-1], (BDIGIT)(VpBaseVal() * (BDIGIT_DBL)res->frac[0] / div->frac[0]));
|
|
}
|
|
return ToValue(c);
|
|
}
|
|
|
|
/*
|
|
* %: mod = a%b = a - (a.to_f/b).floor * b
|
|
* div = (a.to_f/b).floor
|
|
*/
|
|
static VALUE
|
|
BigDecimal_DoDivmod(VALUE self, VALUE r, Real **div, Real **mod)
|
|
{
|
|
ENTER(8);
|
|
Real *c=NULL, *d=NULL, *res=NULL;
|
|
Real *a, *b;
|
|
size_t mx;
|
|
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
if (RB_TYPE_P(r, T_FLOAT)) {
|
|
b = GetVpValueWithPrec(r, DBL_DIG+1, 1);
|
|
}
|
|
else if (RB_TYPE_P(r, T_RATIONAL)) {
|
|
b = GetVpValueWithPrec(r, a->Prec*VpBaseFig(), 1);
|
|
}
|
|
else {
|
|
b = GetVpValue(r, 0);
|
|
}
|
|
|
|
if (!b) return Qfalse;
|
|
SAVE(b);
|
|
|
|
if (VpIsNaN(a) || VpIsNaN(b)) goto NaN;
|
|
if (VpIsInf(a) && VpIsInf(b)) goto NaN;
|
|
if (VpIsZero(b)) {
|
|
rb_raise(rb_eZeroDivError, "divided by 0");
|
|
}
|
|
if (VpIsInf(a)) {
|
|
GUARD_OBJ(d, VpCreateRbObject(1, "0"));
|
|
VpSetInf(d, (SIGNED_VALUE)(VpGetSign(a) == VpGetSign(b) ? 1 : -1));
|
|
GUARD_OBJ(c, VpCreateRbObject(1, "NaN"));
|
|
*div = d;
|
|
*mod = c;
|
|
return Qtrue;
|
|
}
|
|
if (VpIsInf(b)) {
|
|
GUARD_OBJ(d, VpCreateRbObject(1, "0"));
|
|
*div = d;
|
|
*mod = a;
|
|
return Qtrue;
|
|
}
|
|
if (VpIsZero(a)) {
|
|
GUARD_OBJ(c, VpCreateRbObject(1, "0"));
|
|
GUARD_OBJ(d, VpCreateRbObject(1, "0"));
|
|
*div = d;
|
|
*mod = c;
|
|
return Qtrue;
|
|
}
|
|
|
|
mx = a->Prec + vabs(a->exponent);
|
|
if (mx<b->Prec + vabs(b->exponent)) mx = b->Prec + vabs(b->exponent);
|
|
mx = (mx + 1) * VpBaseFig();
|
|
GUARD_OBJ(c, VpCreateRbObject(mx, "0"));
|
|
GUARD_OBJ(res, VpCreateRbObject((mx+1) * 2 +(VpBaseFig() + 1), "#0"));
|
|
VpDivd(c, res, a, b);
|
|
mx = c->Prec * (VpBaseFig() + 1);
|
|
GUARD_OBJ(d, VpCreateRbObject(mx, "0"));
|
|
VpActiveRound(d, c, VP_ROUND_DOWN, 0);
|
|
VpMult(res, d, b);
|
|
VpAddSub(c, a, res, -1);
|
|
if (!VpIsZero(c) && (VpGetSign(a) * VpGetSign(b) < 0)) {
|
|
VpAddSub(res, d, VpOne(), -1);
|
|
GUARD_OBJ(d, VpCreateRbObject(GetAddSubPrec(c, b)*(VpBaseFig() + 1), "0"));
|
|
VpAddSub(d, c, b, 1);
|
|
*div = res;
|
|
*mod = d;
|
|
} else {
|
|
*div = d;
|
|
*mod = c;
|
|
}
|
|
return Qtrue;
|
|
|
|
NaN:
|
|
GUARD_OBJ(c, VpCreateRbObject(1, "NaN"));
|
|
GUARD_OBJ(d, VpCreateRbObject(1, "NaN"));
|
|
*div = d;
|
|
*mod = c;
|
|
return Qtrue;
|
|
}
|
|
|
|
/* call-seq:
|
|
* a % b
|
|
* a.modulo(b)
|
|
*
|
|
* Returns the modulus from dividing by b.
|
|
*
|
|
* See BigDecimal#divmod.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_mod(VALUE self, VALUE r) /* %: a%b = a - (a.to_f/b).floor * b */
|
|
{
|
|
ENTER(3);
|
|
Real *div = NULL, *mod = NULL;
|
|
|
|
if (BigDecimal_DoDivmod(self, r, &div, &mod)) {
|
|
SAVE(div); SAVE(mod);
|
|
return ToValue(mod);
|
|
}
|
|
return DoSomeOne(self, r, '%');
|
|
}
|
|
|
|
static VALUE
|
|
BigDecimal_divremain(VALUE self, VALUE r, Real **dv, Real **rv)
|
|
{
|
|
ENTER(10);
|
|
size_t mx;
|
|
Real *a = NULL, *b = NULL, *c = NULL, *res = NULL, *d = NULL, *rr = NULL, *ff = NULL;
|
|
Real *f = NULL;
|
|
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
if (RB_TYPE_P(r, T_FLOAT)) {
|
|
b = GetVpValueWithPrec(r, DBL_DIG+1, 1);
|
|
}
|
|
else if (RB_TYPE_P(r, T_RATIONAL)) {
|
|
b = GetVpValueWithPrec(r, a->Prec*VpBaseFig(), 1);
|
|
}
|
|
else {
|
|
b = GetVpValue(r, 0);
|
|
}
|
|
|
|
if (!b) return DoSomeOne(self, r, rb_intern("remainder"));
|
|
SAVE(b);
|
|
|
|
mx = (a->MaxPrec + b->MaxPrec) *VpBaseFig();
|
|
GUARD_OBJ(c, VpCreateRbObject(mx, "0"));
|
|
GUARD_OBJ(res, VpCreateRbObject((mx+1) * 2 + (VpBaseFig() + 1), "#0"));
|
|
GUARD_OBJ(rr, VpCreateRbObject((mx+1) * 2 + (VpBaseFig() + 1), "#0"));
|
|
GUARD_OBJ(ff, VpCreateRbObject((mx+1) * 2 + (VpBaseFig() + 1), "#0"));
|
|
|
|
VpDivd(c, res, a, b);
|
|
|
|
mx = c->Prec *(VpBaseFig() + 1);
|
|
|
|
GUARD_OBJ(d, VpCreateRbObject(mx, "0"));
|
|
GUARD_OBJ(f, VpCreateRbObject(mx, "0"));
|
|
|
|
VpActiveRound(d, c, VP_ROUND_DOWN, 0); /* 0: round off */
|
|
|
|
VpFrac(f, c);
|
|
VpMult(rr, f, b);
|
|
VpAddSub(ff, res, rr, 1);
|
|
|
|
*dv = d;
|
|
*rv = ff;
|
|
return Qnil;
|
|
}
|
|
|
|
/* Returns the remainder from dividing by the value.
|
|
*
|
|
* x.remainder(y) means x-y*(x/y).truncate
|
|
*/
|
|
static VALUE
|
|
BigDecimal_remainder(VALUE self, VALUE r) /* remainder */
|
|
{
|
|
VALUE f;
|
|
Real *d, *rv = 0;
|
|
f = BigDecimal_divremain(self, r, &d, &rv);
|
|
if (!NIL_P(f)) return f;
|
|
return ToValue(rv);
|
|
}
|
|
|
|
/* Divides by the specified value, and returns the quotient and modulus
|
|
* as BigDecimal numbers. The quotient is rounded towards negative infinity.
|
|
*
|
|
* For example:
|
|
*
|
|
* require 'bigdecimal'
|
|
*
|
|
* a = BigDecimal.new("42")
|
|
* b = BigDecimal.new("9")
|
|
*
|
|
* q,m = a.divmod(b)
|
|
*
|
|
* c = q * b + m
|
|
*
|
|
* a == c -> true
|
|
*
|
|
* The quotient q is (a/b).floor, and the modulus is the amount that must be
|
|
* added to q * b to get a.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_divmod(VALUE self, VALUE r)
|
|
{
|
|
ENTER(5);
|
|
Real *div = NULL, *mod = NULL;
|
|
|
|
if (BigDecimal_DoDivmod(self, r, &div, &mod)) {
|
|
SAVE(div); SAVE(mod);
|
|
return rb_assoc_new(ToValue(div), ToValue(mod));
|
|
}
|
|
return DoSomeOne(self,r,rb_intern("divmod"));
|
|
}
|
|
|
|
/*
|
|
* See BigDecimal#quo
|
|
*/
|
|
static VALUE
|
|
BigDecimal_div2(int argc, VALUE *argv, VALUE self)
|
|
{
|
|
ENTER(5);
|
|
VALUE b,n;
|
|
int na = rb_scan_args(argc, argv, "11", &b, &n);
|
|
if (na == 1) { /* div in Float sense */
|
|
Real *div = NULL;
|
|
Real *mod;
|
|
if (BigDecimal_DoDivmod(self, b, &div, &mod)) {
|
|
return BigDecimal_to_i(ToValue(div));
|
|
}
|
|
return DoSomeOne(self, b, rb_intern("div"));
|
|
} else { /* div in BigDecimal sense */
|
|
SIGNED_VALUE ix = GetPositiveInt(n);
|
|
if (ix == 0) return BigDecimal_div(self, b);
|
|
else {
|
|
Real *res = NULL;
|
|
Real *av = NULL, *bv = NULL, *cv = NULL;
|
|
size_t mx = ix + VpBaseFig()*2;
|
|
size_t pl = VpSetPrecLimit(0);
|
|
|
|
GUARD_OBJ(cv, VpCreateRbObject(mx, "0"));
|
|
GUARD_OBJ(av, GetVpValue(self, 1));
|
|
GUARD_OBJ(bv, GetVpValue(b, 1));
|
|
mx = av->Prec + bv->Prec + 2;
|
|
if (mx <= cv->MaxPrec) mx = cv->MaxPrec + 1;
|
|
GUARD_OBJ(res, VpCreateRbObject((mx * 2 + 2)*VpBaseFig(), "#0"));
|
|
VpDivd(cv, res, av, bv);
|
|
VpSetPrecLimit(pl);
|
|
VpLeftRound(cv, VpGetRoundMode(), ix);
|
|
return ToValue(cv);
|
|
}
|
|
}
|
|
}
|
|
|
|
static VALUE
|
|
BigDecimal_add2(VALUE self, VALUE b, VALUE n)
|
|
{
|
|
ENTER(2);
|
|
Real *cv;
|
|
SIGNED_VALUE mx = GetPositiveInt(n);
|
|
if (mx == 0) return BigDecimal_add(self, b);
|
|
else {
|
|
size_t pl = VpSetPrecLimit(0);
|
|
VALUE c = BigDecimal_add(self, b);
|
|
VpSetPrecLimit(pl);
|
|
GUARD_OBJ(cv, GetVpValue(c, 1));
|
|
VpLeftRound(cv, VpGetRoundMode(), mx);
|
|
return ToValue(cv);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* sub(value, digits) -> bigdecimal
|
|
*
|
|
* Subtract the specified value.
|
|
*
|
|
* e.g.
|
|
* c = a.sub(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.
|
|
*
|
|
*/
|
|
static VALUE
|
|
BigDecimal_sub2(VALUE self, VALUE b, VALUE n)
|
|
{
|
|
ENTER(2);
|
|
Real *cv;
|
|
SIGNED_VALUE mx = GetPositiveInt(n);
|
|
if (mx == 0) return BigDecimal_sub(self, b);
|
|
else {
|
|
size_t pl = VpSetPrecLimit(0);
|
|
VALUE c = BigDecimal_sub(self, b);
|
|
VpSetPrecLimit(pl);
|
|
GUARD_OBJ(cv, GetVpValue(c, 1));
|
|
VpLeftRound(cv, VpGetRoundMode(), mx);
|
|
return ToValue(cv);
|
|
}
|
|
}
|
|
|
|
|
|
static VALUE
|
|
BigDecimal_mult2(VALUE self, VALUE b, VALUE n)
|
|
{
|
|
ENTER(2);
|
|
Real *cv;
|
|
SIGNED_VALUE mx = GetPositiveInt(n);
|
|
if (mx == 0) return BigDecimal_mult(self, b);
|
|
else {
|
|
size_t pl = VpSetPrecLimit(0);
|
|
VALUE c = BigDecimal_mult(self, b);
|
|
VpSetPrecLimit(pl);
|
|
GUARD_OBJ(cv, GetVpValue(c, 1));
|
|
VpLeftRound(cv, VpGetRoundMode(), mx);
|
|
return ToValue(cv);
|
|
}
|
|
}
|
|
|
|
/* Returns the absolute value.
|
|
*
|
|
* BigDecimal('5').abs -> 5
|
|
*
|
|
* BigDecimal('-3').abs -> 3
|
|
*/
|
|
static VALUE
|
|
BigDecimal_abs(VALUE self)
|
|
{
|
|
ENTER(5);
|
|
Real *c, *a;
|
|
size_t mx;
|
|
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
mx = a->Prec *(VpBaseFig() + 1);
|
|
GUARD_OBJ(c, VpCreateRbObject(mx, "0"));
|
|
VpAsgn(c, a, 1);
|
|
VpChangeSign(c, 1);
|
|
return ToValue(c);
|
|
}
|
|
|
|
/* call-seq:
|
|
* sqrt(n)
|
|
*
|
|
* Returns the square root of the value.
|
|
*
|
|
* Result has at least n significant digits.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_sqrt(VALUE self, VALUE nFig)
|
|
{
|
|
ENTER(5);
|
|
Real *c, *a;
|
|
size_t mx, n;
|
|
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
mx = a->Prec *(VpBaseFig() + 1);
|
|
|
|
n = GetPositiveInt(nFig) + VpDblFig() + 1;
|
|
if(mx <= n) mx = n;
|
|
GUARD_OBJ(c, VpCreateRbObject(mx, "0"));
|
|
VpSqrt(c, a);
|
|
return ToValue(c);
|
|
}
|
|
|
|
/* Return the integer part of the number.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_fix(VALUE self)
|
|
{
|
|
ENTER(5);
|
|
Real *c, *a;
|
|
size_t mx;
|
|
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
mx = a->Prec *(VpBaseFig() + 1);
|
|
GUARD_OBJ(c, VpCreateRbObject(mx, "0"));
|
|
VpActiveRound(c, a, VP_ROUND_DOWN, 0); /* 0: round off */
|
|
return ToValue(c);
|
|
}
|
|
|
|
/* call-seq:
|
|
* round(n, mode)
|
|
*
|
|
* Round to the nearest 1 (by default), returning the result as a BigDecimal.
|
|
*
|
|
* BigDecimal('3.14159').round #=> 3
|
|
* BigDecimal('8.7').round #=> 9
|
|
*
|
|
* If n is specified and positive, the fractional part of the result has no
|
|
* more than that many digits.
|
|
*
|
|
* If n is specified and negative, at least that many digits to the left of the
|
|
* decimal point will be 0 in the result.
|
|
*
|
|
* BigDecimal('3.14159').round(3) #=> 3.142
|
|
* BigDecimal('13345.234').round(-2) #=> 13300.0
|
|
*
|
|
* The value of the optional mode argument can be used to determine how
|
|
* rounding is performed; see BigDecimal.mode.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_round(int argc, VALUE *argv, VALUE self)
|
|
{
|
|
ENTER(5);
|
|
Real *c, *a;
|
|
int iLoc = 0;
|
|
VALUE vLoc;
|
|
VALUE vRound;
|
|
size_t mx, pl;
|
|
|
|
unsigned short sw = VpGetRoundMode();
|
|
|
|
switch (rb_scan_args(argc, argv, "02", &vLoc, &vRound)) {
|
|
case 0:
|
|
iLoc = 0;
|
|
break;
|
|
case 1:
|
|
Check_Type(vLoc, T_FIXNUM);
|
|
iLoc = FIX2INT(vLoc);
|
|
break;
|
|
case 2:
|
|
Check_Type(vLoc, T_FIXNUM);
|
|
iLoc = FIX2INT(vLoc);
|
|
sw = check_rounding_mode(vRound);
|
|
break;
|
|
default:
|
|
break;
|
|
}
|
|
|
|
pl = VpSetPrecLimit(0);
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
mx = a->Prec * (VpBaseFig() + 1);
|
|
GUARD_OBJ(c, VpCreateRbObject(mx, "0"));
|
|
VpSetPrecLimit(pl);
|
|
VpActiveRound(c, a, sw, iLoc);
|
|
if (argc == 0) {
|
|
return BigDecimal_to_i(ToValue(c));
|
|
}
|
|
return ToValue(c);
|
|
}
|
|
|
|
/* call-seq:
|
|
* truncate(n)
|
|
*
|
|
* Truncate to the nearest 1, returning the result as a BigDecimal.
|
|
*
|
|
* BigDecimal('3.14159').truncate #=> 3
|
|
* BigDecimal('8.7').truncate #=> 8
|
|
*
|
|
* If n is specified and positive, the fractional part of the result has no
|
|
* more than that many digits.
|
|
*
|
|
* If n is specified and negative, at least that many digits to the left of the
|
|
* decimal point will be 0 in the result.
|
|
*
|
|
* BigDecimal('3.14159').truncate(3) #=> 3.141
|
|
* BigDecimal('13345.234').truncate(-2) #=> 13300.0
|
|
*/
|
|
static VALUE
|
|
BigDecimal_truncate(int argc, VALUE *argv, VALUE self)
|
|
{
|
|
ENTER(5);
|
|
Real *c, *a;
|
|
int iLoc;
|
|
VALUE vLoc;
|
|
size_t mx, pl = VpSetPrecLimit(0);
|
|
|
|
if (rb_scan_args(argc, argv, "01", &vLoc) == 0) {
|
|
iLoc = 0;
|
|
}
|
|
else {
|
|
Check_Type(vLoc, T_FIXNUM);
|
|
iLoc = FIX2INT(vLoc);
|
|
}
|
|
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
mx = a->Prec * (VpBaseFig() + 1);
|
|
GUARD_OBJ(c, VpCreateRbObject(mx, "0"));
|
|
VpSetPrecLimit(pl);
|
|
VpActiveRound(c, a, VP_ROUND_DOWN, iLoc); /* 0: truncate */
|
|
if (argc == 0) {
|
|
return BigDecimal_to_i(ToValue(c));
|
|
}
|
|
return ToValue(c);
|
|
}
|
|
|
|
/* Return the fractional part of the number.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_frac(VALUE self)
|
|
{
|
|
ENTER(5);
|
|
Real *c, *a;
|
|
size_t mx;
|
|
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
mx = a->Prec * (VpBaseFig() + 1);
|
|
GUARD_OBJ(c, VpCreateRbObject(mx, "0"));
|
|
VpFrac(c, a);
|
|
return ToValue(c);
|
|
}
|
|
|
|
/* call-seq:
|
|
* floor(n)
|
|
*
|
|
* Return the largest integer less than or equal to the value, as a BigDecimal.
|
|
*
|
|
* BigDecimal('3.14159').floor #=> 3
|
|
* BigDecimal('-9.1').floor #=> -10
|
|
*
|
|
* If n is specified and positive, the fractional part of the result has no
|
|
* more than that many digits.
|
|
*
|
|
* If n is specified and negative, at least that
|
|
* many digits to the left of the decimal point will be 0 in the result.
|
|
*
|
|
* BigDecimal('3.14159').floor(3) #=> 3.141
|
|
* BigDecimal('13345.234').floor(-2) #=> 13300.0
|
|
*/
|
|
static VALUE
|
|
BigDecimal_floor(int argc, VALUE *argv, VALUE self)
|
|
{
|
|
ENTER(5);
|
|
Real *c, *a;
|
|
int iLoc;
|
|
VALUE vLoc;
|
|
size_t mx, pl = VpSetPrecLimit(0);
|
|
|
|
if (rb_scan_args(argc, argv, "01", &vLoc)==0) {
|
|
iLoc = 0;
|
|
}
|
|
else {
|
|
Check_Type(vLoc, T_FIXNUM);
|
|
iLoc = FIX2INT(vLoc);
|
|
}
|
|
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
mx = a->Prec * (VpBaseFig() + 1);
|
|
GUARD_OBJ(c, VpCreateRbObject(mx, "0"));
|
|
VpSetPrecLimit(pl);
|
|
VpActiveRound(c, a, VP_ROUND_FLOOR, iLoc);
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
VPrint(stderr, "floor: c=%\n", c);
|
|
#endif
|
|
if (argc == 0) {
|
|
return BigDecimal_to_i(ToValue(c));
|
|
}
|
|
return ToValue(c);
|
|
}
|
|
|
|
/* call-seq:
|
|
* ceil(n)
|
|
*
|
|
* Return the smallest integer greater than or equal to the value, as a BigDecimal.
|
|
*
|
|
* BigDecimal('3.14159').ceil #=> 4
|
|
* BigDecimal('-9.1').ceil #=> -9
|
|
*
|
|
* If n is specified and positive, the fractional part of the result has no
|
|
* more than that many digits.
|
|
*
|
|
* If n is specified and negative, at least that
|
|
* many digits to the left of the decimal point will be 0 in the result.
|
|
*
|
|
* BigDecimal('3.14159').ceil(3) #=> 3.142
|
|
* BigDecimal('13345.234').ceil(-2) #=> 13400.0
|
|
*/
|
|
static VALUE
|
|
BigDecimal_ceil(int argc, VALUE *argv, VALUE self)
|
|
{
|
|
ENTER(5);
|
|
Real *c, *a;
|
|
int iLoc;
|
|
VALUE vLoc;
|
|
size_t mx, pl = VpSetPrecLimit(0);
|
|
|
|
if (rb_scan_args(argc, argv, "01", &vLoc) == 0) {
|
|
iLoc = 0;
|
|
} else {
|
|
Check_Type(vLoc, T_FIXNUM);
|
|
iLoc = FIX2INT(vLoc);
|
|
}
|
|
|
|
GUARD_OBJ(a, GetVpValue(self, 1));
|
|
mx = a->Prec * (VpBaseFig() + 1);
|
|
GUARD_OBJ(c, VpCreateRbObject(mx, "0"));
|
|
VpSetPrecLimit(pl);
|
|
VpActiveRound(c, a, VP_ROUND_CEIL, iLoc);
|
|
if (argc == 0) {
|
|
return BigDecimal_to_i(ToValue(c));
|
|
}
|
|
return ToValue(c);
|
|
}
|
|
|
|
/* call-seq:
|
|
* to_s(s)
|
|
*
|
|
* Converts the value to a string.
|
|
*
|
|
* The default format looks like 0.xxxxEnn.
|
|
*
|
|
* The optional parameter s consists of either an integer; or an optional '+'
|
|
* or ' ', followed by an optional number, followed by an optional 'E' or 'F'.
|
|
*
|
|
* If there is a '+' at the start of s, positive values are returned with
|
|
* a leading '+'.
|
|
*
|
|
* A space at the start of s returns positive values with a leading space.
|
|
*
|
|
* If s contains a number, a space is inserted after each group of that many
|
|
* fractional digits.
|
|
*
|
|
* If s ends with an 'E', engineering notation (0.xxxxEnn) is used.
|
|
*
|
|
* If s ends with an 'F', conventional floating point notation is used.
|
|
*
|
|
* Examples:
|
|
*
|
|
* BigDecimal.new('-123.45678901234567890').to_s('5F')
|
|
* #=> '-123.45678 90123 45678 9'
|
|
*
|
|
* BigDecimal.new('123.45678901234567890').to_s('+8F')
|
|
* #=> '+123.45678901 23456789'
|
|
*
|
|
* BigDecimal.new('123.45678901234567890').to_s(' F')
|
|
* #=> ' 123.4567890123456789'
|
|
*/
|
|
static VALUE
|
|
BigDecimal_to_s(int argc, VALUE *argv, VALUE self)
|
|
{
|
|
ENTER(5);
|
|
int fmt = 0; /* 0:E format */
|
|
int fPlus = 0; /* =0:default,=1: set ' ' before digits ,set '+' before digits. */
|
|
Real *vp;
|
|
volatile VALUE str;
|
|
char *psz;
|
|
char ch;
|
|
size_t nc, mc = 0;
|
|
VALUE f;
|
|
|
|
GUARD_OBJ(vp, GetVpValue(self, 1));
|
|
|
|
if (rb_scan_args(argc, argv, "01", &f) == 1) {
|
|
if (RB_TYPE_P(f, T_STRING)) {
|
|
SafeStringValue(f);
|
|
psz = RSTRING_PTR(f);
|
|
if (*psz == ' ') {
|
|
fPlus = 1;
|
|
psz++;
|
|
}
|
|
else if (*psz == '+') {
|
|
fPlus = 2;
|
|
psz++;
|
|
}
|
|
while ((ch = *psz++) != 0) {
|
|
if (ISSPACE(ch)) {
|
|
continue;
|
|
}
|
|
if (!ISDIGIT(ch)) {
|
|
if (ch == 'F' || ch == 'f') {
|
|
fmt = 1; /* F format */
|
|
}
|
|
break;
|
|
}
|
|
mc = mc*10 + ch - '0';
|
|
}
|
|
}
|
|
else {
|
|
mc = (size_t)GetPositiveInt(f);
|
|
}
|
|
}
|
|
if (fmt) {
|
|
nc = VpNumOfChars(vp, "F");
|
|
}
|
|
else {
|
|
nc = VpNumOfChars(vp, "E");
|
|
}
|
|
if (mc > 0) {
|
|
nc += (nc + mc - 1) / mc + 1;
|
|
}
|
|
|
|
str = rb_str_new(0, nc);
|
|
psz = RSTRING_PTR(str);
|
|
|
|
if (fmt) {
|
|
VpToFString(vp, psz, mc, fPlus);
|
|
}
|
|
else {
|
|
VpToString (vp, psz, mc, fPlus);
|
|
}
|
|
rb_str_resize(str, strlen(psz));
|
|
return str;
|
|
}
|
|
|
|
/* Splits a BigDecimal number into four parts, returned as an array of values.
|
|
*
|
|
* The first value represents the sign of the BigDecimal, and is -1 or 1, or 0
|
|
* if the BigDecimal is Not a Number.
|
|
*
|
|
* The second value is a string representing the significant digits of the
|
|
* BigDecimal, with no leading zeros.
|
|
*
|
|
* The third value is the base used for arithmetic (currently always 10) as an
|
|
* Integer.
|
|
*
|
|
* The fourth value is an Integer exponent.
|
|
*
|
|
* If the BigDecimal can be represented as 0.xxxxxx*10**n, then xxxxxx is the
|
|
* string of significant digits with no leading zeros, and n is the exponent.
|
|
*
|
|
* From these values, you can translate a BigDecimal to a float as follows:
|
|
*
|
|
* sign, significant_digits, base, exponent = a.split
|
|
* f = sign * "0.#{significant_digits}".to_f * (base ** exponent)
|
|
*
|
|
* (Note that the to_f method is provided as a more convenient way to translate
|
|
* a BigDecimal to a Float.)
|
|
*/
|
|
static VALUE
|
|
BigDecimal_split(VALUE self)
|
|
{
|
|
ENTER(5);
|
|
Real *vp;
|
|
VALUE obj,str;
|
|
ssize_t e, s;
|
|
char *psz1;
|
|
|
|
GUARD_OBJ(vp, GetVpValue(self, 1));
|
|
str = rb_str_new(0, VpNumOfChars(vp, "E"));
|
|
psz1 = RSTRING_PTR(str);
|
|
VpSzMantissa(vp, psz1);
|
|
s = 1;
|
|
if(psz1[0] == '-') {
|
|
size_t len = strlen(psz1 + 1);
|
|
|
|
memmove(psz1, psz1 + 1, len);
|
|
psz1[len] = '\0';
|
|
s = -1;
|
|
}
|
|
if (psz1[0] == 'N') s = 0; /* NaN */
|
|
e = VpExponent10(vp);
|
|
obj = rb_ary_new2(4);
|
|
rb_ary_push(obj, INT2FIX(s));
|
|
rb_ary_push(obj, str);
|
|
rb_str_resize(str, strlen(psz1));
|
|
rb_ary_push(obj, INT2FIX(10));
|
|
rb_ary_push(obj, INT2NUM(e));
|
|
return obj;
|
|
}
|
|
|
|
/* Returns the exponent of the BigDecimal number, as an Integer.
|
|
*
|
|
* If the number can be represented as 0.xxxxxx*10**n where xxxxxx is a string
|
|
* of digits with no leading zeros, then n is the exponent.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_exponent(VALUE self)
|
|
{
|
|
ssize_t e = VpExponent10(GetVpValue(self, 1));
|
|
return INT2NUM(e);
|
|
}
|
|
|
|
/* Returns debugging information about the value as a string of comma-separated
|
|
* values in angle brackets with a leading #:
|
|
*
|
|
* BigDecimal.new("1234.5678").inspect ->
|
|
* "#<BigDecimal:b7ea1130,'0.12345678E4',8(12)>"
|
|
*
|
|
* The first part is the address, the second is the value as a string, and
|
|
* the final part ss(mm) is the current number of significant digits and the
|
|
* maximum number of significant digits, respectively.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_inspect(VALUE self)
|
|
{
|
|
ENTER(5);
|
|
Real *vp;
|
|
volatile VALUE obj;
|
|
size_t nc;
|
|
char *psz, *tmp;
|
|
|
|
GUARD_OBJ(vp, GetVpValue(self, 1));
|
|
nc = VpNumOfChars(vp, "E");
|
|
nc += (nc + 9) / 10;
|
|
|
|
obj = rb_str_new(0, nc+256);
|
|
psz = RSTRING_PTR(obj);
|
|
sprintf(psz, "#<BigDecimal:%"PRIxVALUE",'", self);
|
|
tmp = psz + strlen(psz);
|
|
VpToString(vp, tmp, 10, 0);
|
|
tmp += strlen(tmp);
|
|
sprintf(tmp, "',%"PRIuSIZE"(%"PRIuSIZE")>", VpPrec(vp)*VpBaseFig(), VpMaxPrec(vp)*VpBaseFig());
|
|
rb_str_resize(obj, strlen(psz));
|
|
return obj;
|
|
}
|
|
|
|
static VALUE BigMath_s_exp(VALUE, VALUE, VALUE);
|
|
static VALUE BigMath_s_log(VALUE, VALUE, VALUE);
|
|
|
|
#define BigMath_exp(x, n) BigMath_s_exp(rb_mBigMath, (x), (n))
|
|
#define BigMath_log(x, n) BigMath_s_log(rb_mBigMath, (x), (n))
|
|
|
|
inline static int
|
|
is_integer(VALUE x)
|
|
{
|
|
return (RB_TYPE_P(x, T_FIXNUM) || RB_TYPE_P(x, T_BIGNUM));
|
|
}
|
|
|
|
inline static int
|
|
is_negative(VALUE x)
|
|
{
|
|
if (FIXNUM_P(x)) {
|
|
return FIX2LONG(x) < 0;
|
|
}
|
|
else if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
return RBIGNUM_NEGATIVE_P(x);
|
|
}
|
|
else if (RB_TYPE_P(x, T_FLOAT)) {
|
|
return RFLOAT_VALUE(x) < 0.0;
|
|
}
|
|
return RTEST(rb_funcall(x, '<', 1, INT2FIX(0)));
|
|
}
|
|
|
|
#define is_positive(x) (!is_negative(x))
|
|
|
|
inline static int
|
|
is_zero(VALUE x)
|
|
{
|
|
VALUE num;
|
|
|
|
switch (TYPE(x)) {
|
|
case T_FIXNUM:
|
|
return FIX2LONG(x) == 0;
|
|
|
|
case T_BIGNUM:
|
|
return Qfalse;
|
|
|
|
case T_RATIONAL:
|
|
num = RRATIONAL(x)->num;
|
|
return FIXNUM_P(num) && FIX2LONG(num) == 0;
|
|
|
|
default:
|
|
break;
|
|
}
|
|
|
|
return RTEST(rb_funcall(x, id_eq, 1, INT2FIX(0)));
|
|
}
|
|
|
|
inline static int
|
|
is_one(VALUE x)
|
|
{
|
|
VALUE num, den;
|
|
|
|
switch (TYPE(x)) {
|
|
case T_FIXNUM:
|
|
return FIX2LONG(x) == 1;
|
|
|
|
case T_BIGNUM:
|
|
return Qfalse;
|
|
|
|
case T_RATIONAL:
|
|
num = RRATIONAL(x)->num;
|
|
den = RRATIONAL(x)->den;
|
|
return FIXNUM_P(den) && FIX2LONG(den) == 1 &&
|
|
FIXNUM_P(num) && FIX2LONG(num) == 1;
|
|
|
|
default:
|
|
break;
|
|
}
|
|
|
|
return RTEST(rb_funcall(x, id_eq, 1, INT2FIX(1)));
|
|
}
|
|
|
|
inline static int
|
|
is_even(VALUE x)
|
|
{
|
|
switch (TYPE(x)) {
|
|
case T_FIXNUM:
|
|
return (FIX2LONG(x) % 2) == 0;
|
|
|
|
case T_BIGNUM:
|
|
{
|
|
unsigned long l;
|
|
rb_big_pack(x, &l, 1);
|
|
return l % 2 == 0;
|
|
}
|
|
|
|
default:
|
|
break;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
static VALUE
|
|
rmpd_power_by_big_decimal(Real const* x, Real const* exp, ssize_t const n)
|
|
{
|
|
VALUE log_x, multiplied, y;
|
|
volatile VALUE obj = exp->obj;
|
|
|
|
if (VpIsZero(exp)) {
|
|
return ToValue(VpCreateRbObject(n, "1"));
|
|
}
|
|
|
|
log_x = BigMath_log(x->obj, SSIZET2NUM(n+1));
|
|
multiplied = BigDecimal_mult2(exp->obj, log_x, SSIZET2NUM(n+1));
|
|
y = BigMath_exp(multiplied, SSIZET2NUM(n));
|
|
RB_GC_GUARD(obj);
|
|
|
|
return y;
|
|
}
|
|
|
|
/* call-seq:
|
|
* power(n)
|
|
* power(n, prec)
|
|
*
|
|
* Returns the value raised to the power of n.
|
|
*
|
|
* Note that n must be an Integer.
|
|
*
|
|
* Also available as the operator **
|
|
*/
|
|
static VALUE
|
|
BigDecimal_power(int argc, VALUE*argv, VALUE self)
|
|
{
|
|
ENTER(5);
|
|
VALUE vexp, prec;
|
|
Real* exp = NULL;
|
|
Real *x, *y;
|
|
ssize_t mp, ma, n;
|
|
SIGNED_VALUE int_exp;
|
|
double d;
|
|
|
|
rb_scan_args(argc, argv, "11", &vexp, &prec);
|
|
|
|
GUARD_OBJ(x, GetVpValue(self, 1));
|
|
n = NIL_P(prec) ? (ssize_t)(x->Prec*VpBaseFig()) : NUM2SSIZET(prec);
|
|
|
|
if (VpIsNaN(x)) {
|
|
y = VpCreateRbObject(n, "0#");
|
|
RB_GC_GUARD(y->obj);
|
|
VpSetNaN(y);
|
|
return ToValue(y);
|
|
}
|
|
|
|
retry:
|
|
switch (TYPE(vexp)) {
|
|
case T_FIXNUM:
|
|
break;
|
|
|
|
case T_BIGNUM:
|
|
break;
|
|
|
|
case T_FLOAT:
|
|
d = RFLOAT_VALUE(vexp);
|
|
if (d == round(d)) {
|
|
if (FIXABLE(d)) {
|
|
vexp = LONG2FIX((long)d);
|
|
}
|
|
else {
|
|
vexp = rb_dbl2big(d);
|
|
}
|
|
goto retry;
|
|
}
|
|
exp = GetVpValueWithPrec(vexp, DBL_DIG+1, 1);
|
|
break;
|
|
|
|
case T_RATIONAL:
|
|
if (is_zero(RRATIONAL(vexp)->num)) {
|
|
if (is_positive(vexp)) {
|
|
vexp = INT2FIX(0);
|
|
goto retry;
|
|
}
|
|
}
|
|
else if (is_one(RRATIONAL(vexp)->den)) {
|
|
vexp = RRATIONAL(vexp)->num;
|
|
goto retry;
|
|
}
|
|
exp = GetVpValueWithPrec(vexp, n, 1);
|
|
break;
|
|
|
|
case T_DATA:
|
|
if (is_kind_of_BigDecimal(vexp)) {
|
|
VALUE zero = INT2FIX(0);
|
|
VALUE rounded = BigDecimal_round(1, &zero, vexp);
|
|
if (RTEST(BigDecimal_eq(vexp, rounded))) {
|
|
vexp = BigDecimal_to_i(vexp);
|
|
goto retry;
|
|
}
|
|
exp = DATA_PTR(vexp);
|
|
break;
|
|
}
|
|
/* fall through */
|
|
default:
|
|
rb_raise(rb_eTypeError,
|
|
"wrong argument type %s (expected scalar Numeric)",
|
|
rb_obj_classname(vexp));
|
|
}
|
|
|
|
if (VpIsZero(x)) {
|
|
if (is_negative(vexp)) {
|
|
y = VpCreateRbObject(n, "#0");
|
|
RB_GC_GUARD(y->obj);
|
|
if (VpGetSign(x) < 0) {
|
|
if (is_integer(vexp)) {
|
|
if (is_even(vexp)) {
|
|
/* (-0) ** (-even_integer) -> Infinity */
|
|
VpSetPosInf(y);
|
|
}
|
|
else {
|
|
/* (-0) ** (-odd_integer) -> -Infinity */
|
|
VpSetNegInf(y);
|
|
}
|
|
}
|
|
else {
|
|
/* (-0) ** (-non_integer) -> Infinity */
|
|
VpSetPosInf(y);
|
|
}
|
|
}
|
|
else {
|
|
/* (+0) ** (-num) -> Infinity */
|
|
VpSetPosInf(y);
|
|
}
|
|
return ToValue(y);
|
|
}
|
|
else if (is_zero(vexp)) {
|
|
return ToValue(VpCreateRbObject(n, "1"));
|
|
}
|
|
else {
|
|
return ToValue(VpCreateRbObject(n, "0"));
|
|
}
|
|
}
|
|
|
|
if (is_zero(vexp)) {
|
|
return ToValue(VpCreateRbObject(n, "1"));
|
|
}
|
|
else if (is_one(vexp)) {
|
|
return self;
|
|
}
|
|
|
|
if (VpIsInf(x)) {
|
|
if (is_negative(vexp)) {
|
|
if (VpGetSign(x) < 0) {
|
|
if (is_integer(vexp)) {
|
|
if (is_even(vexp)) {
|
|
/* (-Infinity) ** (-even_integer) -> +0 */
|
|
return ToValue(VpCreateRbObject(n, "0"));
|
|
}
|
|
else {
|
|
/* (-Infinity) ** (-odd_integer) -> -0 */
|
|
return ToValue(VpCreateRbObject(n, "-0"));
|
|
}
|
|
}
|
|
else {
|
|
/* (-Infinity) ** (-non_integer) -> -0 */
|
|
return ToValue(VpCreateRbObject(n, "-0"));
|
|
}
|
|
}
|
|
else {
|
|
return ToValue(VpCreateRbObject(n, "0"));
|
|
}
|
|
}
|
|
else {
|
|
y = VpCreateRbObject(n, "0#");
|
|
if (VpGetSign(x) < 0) {
|
|
if (is_integer(vexp)) {
|
|
if (is_even(vexp)) {
|
|
VpSetPosInf(y);
|
|
}
|
|
else {
|
|
VpSetNegInf(y);
|
|
}
|
|
}
|
|
else {
|
|
/* TODO: support complex */
|
|
rb_raise(rb_eMathDomainError,
|
|
"a non-integral exponent for a negative base");
|
|
}
|
|
}
|
|
else {
|
|
VpSetPosInf(y);
|
|
}
|
|
return ToValue(y);
|
|
}
|
|
}
|
|
|
|
if (exp != NULL) {
|
|
return rmpd_power_by_big_decimal(x, exp, n);
|
|
}
|
|
else if (RB_TYPE_P(vexp, T_BIGNUM)) {
|
|
VALUE abs_value = BigDecimal_abs(self);
|
|
if (is_one(abs_value)) {
|
|
return ToValue(VpCreateRbObject(n, "1"));
|
|
}
|
|
else if (RTEST(rb_funcall(abs_value, '<', 1, INT2FIX(1)))) {
|
|
if (is_negative(vexp)) {
|
|
y = VpCreateRbObject(n, "0#");
|
|
if (is_even(vexp)) {
|
|
VpSetInf(y, VpGetSign(x));
|
|
}
|
|
else {
|
|
VpSetInf(y, -VpGetSign(x));
|
|
}
|
|
return ToValue(y);
|
|
}
|
|
else if (VpGetSign(x) < 0 && is_even(vexp)) {
|
|
return ToValue(VpCreateRbObject(n, "-0"));
|
|
}
|
|
else {
|
|
return ToValue(VpCreateRbObject(n, "0"));
|
|
}
|
|
}
|
|
else {
|
|
if (is_positive(vexp)) {
|
|
y = VpCreateRbObject(n, "0#");
|
|
if (is_even(vexp)) {
|
|
VpSetInf(y, VpGetSign(x));
|
|
}
|
|
else {
|
|
VpSetInf(y, -VpGetSign(x));
|
|
}
|
|
return ToValue(y);
|
|
}
|
|
else if (VpGetSign(x) < 0 && is_even(vexp)) {
|
|
return ToValue(VpCreateRbObject(n, "-0"));
|
|
}
|
|
else {
|
|
return ToValue(VpCreateRbObject(n, "0"));
|
|
}
|
|
}
|
|
}
|
|
|
|
int_exp = FIX2INT(vexp);
|
|
ma = int_exp;
|
|
if (ma < 0) ma = -ma;
|
|
if (ma == 0) ma = 1;
|
|
|
|
if (VpIsDef(x)) {
|
|
mp = x->Prec * (VpBaseFig() + 1);
|
|
GUARD_OBJ(y, VpCreateRbObject(mp * (ma + 1), "0"));
|
|
}
|
|
else {
|
|
GUARD_OBJ(y, VpCreateRbObject(1, "0"));
|
|
}
|
|
VpPower(y, x, int_exp);
|
|
return ToValue(y);
|
|
}
|
|
|
|
/* call-seq:
|
|
* big_decimal ** exp -> big_decimal
|
|
*
|
|
* It is a synonym of BigDecimal#power(exp).
|
|
*/
|
|
static VALUE
|
|
BigDecimal_power_op(VALUE self, VALUE exp)
|
|
{
|
|
return BigDecimal_power(1, &exp, self);
|
|
}
|
|
|
|
static VALUE
|
|
BigDecimal_s_allocate(VALUE klass)
|
|
{
|
|
return VpNewRbClass(0, NULL, klass)->obj;
|
|
}
|
|
|
|
static Real *BigDecimal_new(int argc, VALUE *argv);
|
|
|
|
/* call-seq:
|
|
* new(initial, digits)
|
|
*
|
|
* Create a new BigDecimal object.
|
|
*
|
|
* initial:: The initial value, as an Integer, a Float, a Rational,
|
|
* a BigDecimal, or a String.
|
|
*
|
|
* If it is a String, spaces are ignored and unrecognized characters
|
|
* terminate the value.
|
|
*
|
|
* digits:: The number of significant digits, as a Fixnum. If omitted or 0,
|
|
* the number of significant digits is determined from the initial
|
|
* value.
|
|
*
|
|
* The actual number of significant digits used in computation is usually
|
|
* larger than the specified number.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_initialize(int argc, VALUE *argv, VALUE self)
|
|
{
|
|
Real *pv = rb_check_typeddata(self, &BigDecimal_data_type);
|
|
Real *x = BigDecimal_new(argc, argv);
|
|
|
|
if (ToValue(x)) {
|
|
pv = VpCopy(pv, x);
|
|
}
|
|
else {
|
|
VpFree(pv);
|
|
pv = x;
|
|
}
|
|
DATA_PTR(self) = pv;
|
|
pv->obj = self;
|
|
return self;
|
|
}
|
|
|
|
/* :nodoc:
|
|
*
|
|
* private method to dup and clone the provided BigDecimal +other+
|
|
*/
|
|
static VALUE
|
|
BigDecimal_initialize_copy(VALUE self, VALUE other)
|
|
{
|
|
Real *pv = rb_check_typeddata(self, &BigDecimal_data_type);
|
|
Real *x = rb_check_typeddata(other, &BigDecimal_data_type);
|
|
|
|
DATA_PTR(self) = VpCopy(pv, x);
|
|
return self;
|
|
}
|
|
|
|
static Real *
|
|
BigDecimal_new(int argc, VALUE *argv)
|
|
{
|
|
size_t mf;
|
|
VALUE nFig;
|
|
VALUE iniValue;
|
|
|
|
if (rb_scan_args(argc, argv, "11", &iniValue, &nFig) == 1) {
|
|
mf = 0;
|
|
}
|
|
else {
|
|
mf = GetPositiveInt(nFig);
|
|
}
|
|
|
|
switch (TYPE(iniValue)) {
|
|
case T_DATA:
|
|
if (is_kind_of_BigDecimal(iniValue)) {
|
|
return DATA_PTR(iniValue);
|
|
}
|
|
break;
|
|
|
|
case T_FIXNUM:
|
|
/* fall through */
|
|
case T_BIGNUM:
|
|
return GetVpValue(iniValue, 1);
|
|
|
|
case T_FLOAT:
|
|
if (mf > DBL_DIG+1) {
|
|
rb_raise(rb_eArgError, "precision too large.");
|
|
}
|
|
/* fall through */
|
|
case T_RATIONAL:
|
|
if (NIL_P(nFig)) {
|
|
rb_raise(rb_eArgError,
|
|
"can't omit precision for a %s.",
|
|
rb_class2name(CLASS_OF(iniValue)));
|
|
}
|
|
return GetVpValueWithPrec(iniValue, mf, 1);
|
|
|
|
case T_STRING:
|
|
/* fall through */
|
|
default:
|
|
break;
|
|
}
|
|
StringValueCStr(iniValue);
|
|
return VpAlloc(mf, RSTRING_PTR(iniValue));
|
|
}
|
|
|
|
/* See also BigDecimal::new */
|
|
static VALUE
|
|
BigDecimal_global_new(int argc, VALUE *argv, VALUE self)
|
|
{
|
|
Real *pv = BigDecimal_new(argc, argv);
|
|
if (ToValue(pv)) pv = VpCopy(NULL, pv);
|
|
pv->obj = TypedData_Wrap_Struct(rb_cBigDecimal, &BigDecimal_data_type, pv);
|
|
return pv->obj;
|
|
}
|
|
|
|
/* call-seq:
|
|
* BigDecimal.limit(digits)
|
|
*
|
|
* Limit the number of significant digits in newly created BigDecimal
|
|
* numbers to the specified value. Rounding is performed as necessary,
|
|
* as specified by BigDecimal.mode.
|
|
*
|
|
* A limit of 0, the default, means no upper limit.
|
|
*
|
|
* The limit specified by this method takes less priority over any limit
|
|
* specified to instance methods such as ceil, floor, truncate, or round.
|
|
*/
|
|
static VALUE
|
|
BigDecimal_limit(int argc, VALUE *argv, VALUE self)
|
|
{
|
|
VALUE nFig;
|
|
VALUE nCur = INT2NUM(VpGetPrecLimit());
|
|
|
|
if (rb_scan_args(argc, argv, "01", &nFig) == 1) {
|
|
int nf;
|
|
if (NIL_P(nFig)) return nCur;
|
|
Check_Type(nFig, T_FIXNUM);
|
|
nf = FIX2INT(nFig);
|
|
if (nf < 0) {
|
|
rb_raise(rb_eArgError, "argument must be positive");
|
|
}
|
|
VpSetPrecLimit(nf);
|
|
}
|
|
return nCur;
|
|
}
|
|
|
|
/* Returns the sign of the value.
|
|
*
|
|
* Returns a positive value if > 0, a negative value if < 0, and a
|
|
* zero if == 0.
|
|
*
|
|
* The specific value returned indicates the type and sign of the BigDecimal,
|
|
* as follows:
|
|
*
|
|
* BigDecimal::SIGN_NaN:: value is Not a Number
|
|
* BigDecimal::SIGN_POSITIVE_ZERO:: value is +0
|
|
* BigDecimal::SIGN_NEGATIVE_ZERO:: value is -0
|
|
* BigDecimal::SIGN_POSITIVE_INFINITE:: value is +infinity
|
|
* BigDecimal::SIGN_NEGATIVE_INFINITE:: value is -infinity
|
|
* BigDecimal::SIGN_POSITIVE_FINITE:: value is positive
|
|
* BigDecimal::SIGN_NEGATIVE_FINITE:: value is negative
|
|
*/
|
|
static VALUE
|
|
BigDecimal_sign(VALUE self)
|
|
{ /* sign */
|
|
int s = GetVpValue(self, 1)->sign;
|
|
return INT2FIX(s);
|
|
}
|
|
|
|
/*
|
|
* call-seq: BigDecimal.save_exception_mode { ... }
|
|
*
|
|
* Execute the provided block, but preserve the exception mode
|
|
*
|
|
* BigDecimal.save_exception_mode do
|
|
* BigDecimal.mode(BigDecimal::EXCEPTION_OVERFLOW, false)
|
|
* BigDecimal.mode(BigDecimal::EXCEPTION_NaN, false)
|
|
*
|
|
* BigDecimal.new(BigDecimal('Infinity'))
|
|
* BigDecimal.new(BigDecimal('-Infinity'))
|
|
* BigDecimal(BigDecimal.new('NaN'))
|
|
* end
|
|
*
|
|
* For use with the BigDecimal::EXCEPTION_*
|
|
*
|
|
* See BigDecimal.mode
|
|
*/
|
|
static VALUE
|
|
BigDecimal_save_exception_mode(VALUE self)
|
|
{
|
|
unsigned short const exception_mode = VpGetException();
|
|
int state;
|
|
VALUE ret = rb_protect(rb_yield, Qnil, &state);
|
|
VpSetException(exception_mode);
|
|
if (state) rb_jump_tag(state);
|
|
return ret;
|
|
}
|
|
|
|
/*
|
|
* call-seq: BigDecimal.save_rounding_mode { ... }
|
|
*
|
|
* Execute the provided block, but preserve the rounding mode
|
|
*
|
|
* BigDecimal.save_rounding_mode do
|
|
* BigDecimal.mode(BigDecimal::ROUND_MODE, :up)
|
|
* puts BigDecimal.mode(BigDecimal::ROUND_MODE)
|
|
* end
|
|
*
|
|
* For use with the BigDecimal::ROUND_*
|
|
*
|
|
* See BigDecimal.mode
|
|
*/
|
|
static VALUE
|
|
BigDecimal_save_rounding_mode(VALUE self)
|
|
{
|
|
unsigned short const round_mode = VpGetRoundMode();
|
|
int state;
|
|
VALUE ret = rb_protect(rb_yield, Qnil, &state);
|
|
VpSetRoundMode(round_mode);
|
|
if (state) rb_jump_tag(state);
|
|
return ret;
|
|
}
|
|
|
|
/*
|
|
* call-seq: BigDecimal.save_limit { ... }
|
|
*
|
|
* Execute the provided block, but preserve the precision limit
|
|
*
|
|
* BigDecimal.limit(100)
|
|
* puts BigDecimal.limit
|
|
* BigDecimal.save_limit do
|
|
* BigDecimal.limit(200)
|
|
* puts BigDecimal.limit
|
|
* end
|
|
* puts BigDecimal.limit
|
|
*
|
|
*/
|
|
static VALUE
|
|
BigDecimal_save_limit(VALUE self)
|
|
{
|
|
size_t const limit = VpGetPrecLimit();
|
|
int state;
|
|
VALUE ret = rb_protect(rb_yield, Qnil, &state);
|
|
VpSetPrecLimit(limit);
|
|
if (state) rb_jump_tag(state);
|
|
return ret;
|
|
}
|
|
|
|
/* call-seq:
|
|
* BigMath.exp(decimal, numeric) -> BigDecimal
|
|
*
|
|
* Computes the value of e (the base of natural logarithms) raised to the
|
|
* power of +decimal+, to the specified number of digits of precision.
|
|
*
|
|
* If +decimal+ is infinity, returns Infinity.
|
|
*
|
|
* If +decimal+ is NaN, returns NaN.
|
|
*/
|
|
static VALUE
|
|
BigMath_s_exp(VALUE klass, VALUE x, VALUE vprec)
|
|
{
|
|
ssize_t prec, n, i;
|
|
Real* vx = NULL;
|
|
VALUE one, d, x1, y, z;
|
|
int negative = 0;
|
|
int infinite = 0;
|
|
int nan = 0;
|
|
double flo;
|
|
|
|
prec = NUM2SSIZET(vprec);
|
|
if (prec <= 0) {
|
|
rb_raise(rb_eArgError, "Zero or negative precision for exp");
|
|
}
|
|
|
|
/* TODO: the following switch statement is almostly the same as one in the
|
|
* BigDecimalCmp function. */
|
|
switch (TYPE(x)) {
|
|
case T_DATA:
|
|
if (!is_kind_of_BigDecimal(x)) break;
|
|
vx = DATA_PTR(x);
|
|
negative = VpGetSign(vx) < 0;
|
|
infinite = VpIsPosInf(vx) || VpIsNegInf(vx);
|
|
nan = VpIsNaN(vx);
|
|
break;
|
|
|
|
case T_FIXNUM:
|
|
/* fall through */
|
|
case T_BIGNUM:
|
|
vx = GetVpValue(x, 0);
|
|
break;
|
|
|
|
case T_FLOAT:
|
|
flo = RFLOAT_VALUE(x);
|
|
negative = flo < 0;
|
|
infinite = isinf(flo);
|
|
nan = isnan(flo);
|
|
if (!infinite && !nan) {
|
|
vx = GetVpValueWithPrec(x, DBL_DIG+1, 0);
|
|
}
|
|
break;
|
|
|
|
case T_RATIONAL:
|
|
vx = GetVpValueWithPrec(x, prec, 0);
|
|
break;
|
|
|
|
default:
|
|
break;
|
|
}
|
|
if (infinite) {
|
|
if (negative) {
|
|
return ToValue(GetVpValueWithPrec(INT2FIX(0), prec, 1));
|
|
}
|
|
else {
|
|
Real* vy;
|
|
vy = VpCreateRbObject(prec, "#0");
|
|
RB_GC_GUARD(vy->obj);
|
|
VpSetInf(vy, VP_SIGN_POSITIVE_INFINITE);
|
|
return ToValue(vy);
|
|
}
|
|
}
|
|
else if (nan) {
|
|
Real* vy;
|
|
vy = VpCreateRbObject(prec, "#0");
|
|
RB_GC_GUARD(vy->obj);
|
|
VpSetNaN(vy);
|
|
return ToValue(vy);
|
|
}
|
|
else if (vx == NULL) {
|
|
cannot_be_coerced_into_BigDecimal(rb_eArgError, x);
|
|
}
|
|
x = RB_GC_GUARD(vx->obj);
|
|
|
|
n = prec + rmpd_double_figures();
|
|
negative = VpGetSign(vx) < 0;
|
|
if (negative) {
|
|
VpSetSign(vx, 1);
|
|
}
|
|
|
|
RB_GC_GUARD(one) = ToValue(VpCreateRbObject(1, "1"));
|
|
RB_GC_GUARD(x1) = one;
|
|
RB_GC_GUARD(y) = one;
|
|
RB_GC_GUARD(d) = y;
|
|
RB_GC_GUARD(z) = one;
|
|
i = 0;
|
|
|
|
while (!VpIsZero((Real*)DATA_PTR(d))) {
|
|
VALUE argv[2];
|
|
SIGNED_VALUE const ey = VpExponent10(DATA_PTR(y));
|
|
SIGNED_VALUE const ed = VpExponent10(DATA_PTR(d));
|
|
ssize_t m = n - vabs(ey - ed);
|
|
if (m <= 0) {
|
|
break;
|
|
}
|
|
else if ((size_t)m < rmpd_double_figures()) {
|
|
m = rmpd_double_figures();
|
|
}
|
|
|
|
x1 = BigDecimal_mult2(x1, x, SSIZET2NUM(n));
|
|
++i;
|
|
z = BigDecimal_mult(z, SSIZET2NUM(i));
|
|
argv[0] = z;
|
|
argv[1] = SSIZET2NUM(m);
|
|
d = BigDecimal_div2(2, argv, x1);
|
|
y = BigDecimal_add(y, d);
|
|
}
|
|
|
|
if (negative) {
|
|
VALUE argv[2];
|
|
argv[0] = y;
|
|
argv[1] = vprec;
|
|
return BigDecimal_div2(2, argv, one);
|
|
}
|
|
else {
|
|
vprec = SSIZET2NUM(prec - VpExponent10(DATA_PTR(y)));
|
|
return BigDecimal_round(1, &vprec, y);
|
|
}
|
|
}
|
|
|
|
/* call-seq:
|
|
* BigMath.log(decimal, numeric) -> BigDecimal
|
|
*
|
|
* Computes the natural logarithm of +decimal+ to the specified number of
|
|
* digits of precision, +numeric+.
|
|
*
|
|
* If +decimal+ is zero or negative, raises Math::DomainError.
|
|
*
|
|
* If +decimal+ is positive infinity, returns Infinity.
|
|
*
|
|
* If +decimal+ is NaN, returns NaN.
|
|
*/
|
|
static VALUE
|
|
BigMath_s_log(VALUE klass, VALUE x, VALUE vprec)
|
|
{
|
|
ssize_t prec, n, i;
|
|
SIGNED_VALUE expo;
|
|
Real* vx = NULL;
|
|
VALUE argv[2], vn, one, two, w, x2, y, d;
|
|
int zero = 0;
|
|
int negative = 0;
|
|
int infinite = 0;
|
|
int nan = 0;
|
|
double flo;
|
|
long fix;
|
|
|
|
if (!is_integer(vprec)) {
|
|
rb_raise(rb_eArgError, "precision must be an Integer");
|
|
}
|
|
|
|
prec = NUM2SSIZET(vprec);
|
|
if (prec <= 0) {
|
|
rb_raise(rb_eArgError, "Zero or negative precision for exp");
|
|
}
|
|
|
|
/* TODO: the following switch statement is almostly the same as one in the
|
|
* BigDecimalCmp function. */
|
|
switch (TYPE(x)) {
|
|
case T_DATA:
|
|
if (!is_kind_of_BigDecimal(x)) break;
|
|
vx = DATA_PTR(x);
|
|
zero = VpIsZero(vx);
|
|
negative = VpGetSign(vx) < 0;
|
|
infinite = VpIsPosInf(vx) || VpIsNegInf(vx);
|
|
nan = VpIsNaN(vx);
|
|
break;
|
|
|
|
case T_FIXNUM:
|
|
fix = FIX2LONG(x);
|
|
zero = fix == 0;
|
|
negative = fix < 0;
|
|
goto get_vp_value;
|
|
|
|
case T_BIGNUM:
|
|
zero = RBIGNUM_ZERO_P(x);
|
|
negative = RBIGNUM_NEGATIVE_P(x);
|
|
get_vp_value:
|
|
if (zero || negative) break;
|
|
vx = GetVpValue(x, 0);
|
|
break;
|
|
|
|
case T_FLOAT:
|
|
flo = RFLOAT_VALUE(x);
|
|
zero = flo == 0;
|
|
negative = flo < 0;
|
|
infinite = isinf(flo);
|
|
nan = isnan(flo);
|
|
if (!zero && !negative && !infinite && !nan) {
|
|
vx = GetVpValueWithPrec(x, DBL_DIG+1, 1);
|
|
}
|
|
break;
|
|
|
|
case T_RATIONAL:
|
|
zero = RRATIONAL_ZERO_P(x);
|
|
negative = RRATIONAL_NEGATIVE_P(x);
|
|
if (zero || negative) break;
|
|
vx = GetVpValueWithPrec(x, prec, 1);
|
|
break;
|
|
|
|
case T_COMPLEX:
|
|
rb_raise(rb_eMathDomainError,
|
|
"Complex argument for BigMath.log");
|
|
|
|
default:
|
|
break;
|
|
}
|
|
if (infinite && !negative) {
|
|
Real* vy;
|
|
vy = VpCreateRbObject(prec, "#0");
|
|
RB_GC_GUARD(vy->obj);
|
|
VpSetInf(vy, VP_SIGN_POSITIVE_INFINITE);
|
|
return ToValue(vy);
|
|
}
|
|
else if (nan) {
|
|
Real* vy;
|
|
vy = VpCreateRbObject(prec, "#0");
|
|
RB_GC_GUARD(vy->obj);
|
|
VpSetNaN(vy);
|
|
return ToValue(vy);
|
|
}
|
|
else if (zero || negative) {
|
|
rb_raise(rb_eMathDomainError,
|
|
"Zero or negative argument for log");
|
|
}
|
|
else if (vx == NULL) {
|
|
cannot_be_coerced_into_BigDecimal(rb_eArgError, x);
|
|
}
|
|
x = ToValue(vx);
|
|
|
|
RB_GC_GUARD(one) = ToValue(VpCreateRbObject(1, "1"));
|
|
RB_GC_GUARD(two) = ToValue(VpCreateRbObject(1, "2"));
|
|
|
|
n = prec + rmpd_double_figures();
|
|
RB_GC_GUARD(vn) = SSIZET2NUM(n);
|
|
expo = VpExponent10(vx);
|
|
if (expo < 0 || expo >= 3) {
|
|
char buf[16];
|
|
snprintf(buf, 16, "1E%"PRIdVALUE, -expo);
|
|
x = BigDecimal_mult2(x, ToValue(VpCreateRbObject(1, buf)), vn);
|
|
}
|
|
else {
|
|
expo = 0;
|
|
}
|
|
w = BigDecimal_sub(x, one);
|
|
argv[0] = BigDecimal_add(x, one);
|
|
argv[1] = vn;
|
|
x = BigDecimal_div2(2, argv, w);
|
|
RB_GC_GUARD(x2) = BigDecimal_mult2(x, x, vn);
|
|
RB_GC_GUARD(y) = x;
|
|
RB_GC_GUARD(d) = y;
|
|
i = 1;
|
|
while (!VpIsZero((Real*)DATA_PTR(d))) {
|
|
SIGNED_VALUE const ey = VpExponent10(DATA_PTR(y));
|
|
SIGNED_VALUE const ed = VpExponent10(DATA_PTR(d));
|
|
ssize_t m = n - vabs(ey - ed);
|
|
if (m <= 0) {
|
|
break;
|
|
}
|
|
else if ((size_t)m < rmpd_double_figures()) {
|
|
m = rmpd_double_figures();
|
|
}
|
|
|
|
x = BigDecimal_mult2(x2, x, vn);
|
|
i += 2;
|
|
argv[0] = SSIZET2NUM(i);
|
|
argv[1] = SSIZET2NUM(m);
|
|
d = BigDecimal_div2(2, argv, x);
|
|
y = BigDecimal_add(y, d);
|
|
}
|
|
|
|
y = BigDecimal_mult(y, two);
|
|
if (expo != 0) {
|
|
VALUE log10, vexpo, dy;
|
|
log10 = BigMath_s_log(klass, INT2FIX(10), vprec);
|
|
vexpo = ToValue(GetVpValue(SSIZET2NUM(expo), 1));
|
|
dy = BigDecimal_mult(log10, vexpo);
|
|
y = BigDecimal_add(y, dy);
|
|
}
|
|
|
|
return y;
|
|
}
|
|
|
|
/* Document-class: BigDecimal
|
|
* BigDecimal provides arbitrary-precision floating point decimal arithmetic.
|
|
*
|
|
* == 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 #=> 0.9999999999999062
|
|
*
|
|
* 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 #=> 0.1E1
|
|
*
|
|
* 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
|
|
* <code>'Infinity'</code>, <code>'+Infinity'</code> and
|
|
* <code>'-Infinity'</code> (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.
|
|
*
|
|
* BigDecimal.new("1.0") / BigDecimal.new("-Infinity") #=> -0.0
|
|
*
|
|
* If the value is positive, a value of positive zero is returned.
|
|
*
|
|
* 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.
|
|
*
|
|
* == License
|
|
*
|
|
* 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.
|
|
*
|
|
* Maintained by mrkn <mrkn@mrkn.jp> and ruby-core members.
|
|
*
|
|
* Documented by zzak <zachary@zacharyscott.net>, mathew <meta@pobox.com>, and
|
|
* many other contributors.
|
|
*/
|
|
void
|
|
Init_bigdecimal(void)
|
|
{
|
|
VALUE arg;
|
|
|
|
id_BigDecimal_exception_mode = rb_intern_const("BigDecimal.exception_mode");
|
|
id_BigDecimal_rounding_mode = rb_intern_const("BigDecimal.rounding_mode");
|
|
id_BigDecimal_precision_limit = rb_intern_const("BigDecimal.precision_limit");
|
|
|
|
/* Initialize VP routines */
|
|
VpInit(0UL);
|
|
|
|
/* Class and method registration */
|
|
rb_cBigDecimal = rb_define_class("BigDecimal", rb_cNumeric);
|
|
rb_define_alloc_func(rb_cBigDecimal, BigDecimal_s_allocate);
|
|
|
|
/* Global function */
|
|
rb_define_global_function("BigDecimal", BigDecimal_global_new, -1);
|
|
|
|
/* Class methods */
|
|
rb_define_singleton_method(rb_cBigDecimal, "mode", BigDecimal_mode, -1);
|
|
rb_define_singleton_method(rb_cBigDecimal, "limit", BigDecimal_limit, -1);
|
|
rb_define_singleton_method(rb_cBigDecimal, "double_fig", BigDecimal_double_fig, 0);
|
|
rb_define_singleton_method(rb_cBigDecimal, "_load", BigDecimal_load, 1);
|
|
rb_define_singleton_method(rb_cBigDecimal, "ver", BigDecimal_version, 0);
|
|
|
|
rb_define_singleton_method(rb_cBigDecimal, "save_exception_mode", BigDecimal_save_exception_mode, 0);
|
|
rb_define_singleton_method(rb_cBigDecimal, "save_rounding_mode", BigDecimal_save_rounding_mode, 0);
|
|
rb_define_singleton_method(rb_cBigDecimal, "save_limit", BigDecimal_save_limit, 0);
|
|
|
|
/* Constants definition */
|
|
|
|
/*
|
|
* Base value used in internal calculations. On a 32 bit system, BASE
|
|
* is 10000, indicating that calculation is done in groups of 4 digits.
|
|
* (If it were larger, BASE**2 wouldn't fit in 32 bits, so you couldn't
|
|
* guarantee that two groups could always be multiplied together without
|
|
* overflow.)
|
|
*/
|
|
rb_define_const(rb_cBigDecimal, "BASE", INT2FIX((SIGNED_VALUE)VpBaseVal()));
|
|
|
|
/* Exceptions */
|
|
|
|
/*
|
|
* 0xff: Determines whether overflow, underflow or zero divide result in
|
|
* an exception being thrown. See BigDecimal.mode.
|
|
*/
|
|
rb_define_const(rb_cBigDecimal, "EXCEPTION_ALL", INT2FIX(VP_EXCEPTION_ALL));
|
|
|
|
/*
|
|
* 0x02: Determines what happens when the result of a computation is not a
|
|
* number (NaN). See BigDecimal.mode.
|
|
*/
|
|
rb_define_const(rb_cBigDecimal, "EXCEPTION_NaN", INT2FIX(VP_EXCEPTION_NaN));
|
|
|
|
/*
|
|
* 0x01: Determines what happens when the result of a computation is
|
|
* infinity. See BigDecimal.mode.
|
|
*/
|
|
rb_define_const(rb_cBigDecimal, "EXCEPTION_INFINITY", INT2FIX(VP_EXCEPTION_INFINITY));
|
|
|
|
/*
|
|
* 0x04: Determines what happens when the result of a computation is an
|
|
* underflow (a result too small to be represented). See BigDecimal.mode.
|
|
*/
|
|
rb_define_const(rb_cBigDecimal, "EXCEPTION_UNDERFLOW", INT2FIX(VP_EXCEPTION_UNDERFLOW));
|
|
|
|
/*
|
|
* 0x01: Determines what happens when the result of a computation is an
|
|
* overflow (a result too large to be represented). See BigDecimal.mode.
|
|
*/
|
|
rb_define_const(rb_cBigDecimal, "EXCEPTION_OVERFLOW", INT2FIX(VP_EXCEPTION_OVERFLOW));
|
|
|
|
/*
|
|
* 0x01: Determines what happens when a division by zero is performed.
|
|
* See BigDecimal.mode.
|
|
*/
|
|
rb_define_const(rb_cBigDecimal, "EXCEPTION_ZERODIVIDE", INT2FIX(VP_EXCEPTION_ZERODIVIDE));
|
|
|
|
/*
|
|
* 0x100: Determines what happens when a result must be rounded in order to
|
|
* fit in the appropriate number of significant digits. See
|
|
* BigDecimal.mode.
|
|
*/
|
|
rb_define_const(rb_cBigDecimal, "ROUND_MODE", INT2FIX(VP_ROUND_MODE));
|
|
|
|
/* 1: Indicates that values should be rounded away from zero. See
|
|
* BigDecimal.mode.
|
|
*/
|
|
rb_define_const(rb_cBigDecimal, "ROUND_UP", INT2FIX(VP_ROUND_UP));
|
|
|
|
/* 2: Indicates that values should be rounded towards zero. See
|
|
* BigDecimal.mode.
|
|
*/
|
|
rb_define_const(rb_cBigDecimal, "ROUND_DOWN", INT2FIX(VP_ROUND_DOWN));
|
|
|
|
/* 3: Indicates that digits >= 5 should be rounded up, others rounded down.
|
|
* See BigDecimal.mode. */
|
|
rb_define_const(rb_cBigDecimal, "ROUND_HALF_UP", INT2FIX(VP_ROUND_HALF_UP));
|
|
|
|
/* 4: Indicates that digits >= 6 should be rounded up, others rounded down.
|
|
* See BigDecimal.mode.
|
|
*/
|
|
rb_define_const(rb_cBigDecimal, "ROUND_HALF_DOWN", INT2FIX(VP_ROUND_HALF_DOWN));
|
|
/* 5: Round towards +infinity. See BigDecimal.mode. */
|
|
rb_define_const(rb_cBigDecimal, "ROUND_CEILING", INT2FIX(VP_ROUND_CEIL));
|
|
|
|
/* 6: Round towards -infinity. See BigDecimal.mode. */
|
|
rb_define_const(rb_cBigDecimal, "ROUND_FLOOR", INT2FIX(VP_ROUND_FLOOR));
|
|
|
|
/* 7: Round towards the even neighbor. See BigDecimal.mode. */
|
|
rb_define_const(rb_cBigDecimal, "ROUND_HALF_EVEN", INT2FIX(VP_ROUND_HALF_EVEN));
|
|
|
|
/* 0: Indicates that a value is not a number. See BigDecimal.sign. */
|
|
rb_define_const(rb_cBigDecimal, "SIGN_NaN", INT2FIX(VP_SIGN_NaN));
|
|
|
|
/* 1: Indicates that a value is +0. See BigDecimal.sign. */
|
|
rb_define_const(rb_cBigDecimal, "SIGN_POSITIVE_ZERO", INT2FIX(VP_SIGN_POSITIVE_ZERO));
|
|
|
|
/* -1: Indicates that a value is -0. See BigDecimal.sign. */
|
|
rb_define_const(rb_cBigDecimal, "SIGN_NEGATIVE_ZERO", INT2FIX(VP_SIGN_NEGATIVE_ZERO));
|
|
|
|
/* 2: Indicates that a value is positive and finite. See BigDecimal.sign. */
|
|
rb_define_const(rb_cBigDecimal, "SIGN_POSITIVE_FINITE", INT2FIX(VP_SIGN_POSITIVE_FINITE));
|
|
|
|
/* -2: Indicates that a value is negative and finite. See BigDecimal.sign. */
|
|
rb_define_const(rb_cBigDecimal, "SIGN_NEGATIVE_FINITE", INT2FIX(VP_SIGN_NEGATIVE_FINITE));
|
|
|
|
/* 3: Indicates that a value is positive and infinite. See BigDecimal.sign. */
|
|
rb_define_const(rb_cBigDecimal, "SIGN_POSITIVE_INFINITE", INT2FIX(VP_SIGN_POSITIVE_INFINITE));
|
|
|
|
/* -3: Indicates that a value is negative and infinite. See BigDecimal.sign. */
|
|
rb_define_const(rb_cBigDecimal, "SIGN_NEGATIVE_INFINITE", INT2FIX(VP_SIGN_NEGATIVE_INFINITE));
|
|
|
|
arg = rb_str_new2("+Infinity");
|
|
/* Positive infinity value. */
|
|
rb_define_const(rb_cBigDecimal, "INFINITY", BigDecimal_global_new(1, &arg, rb_cBigDecimal));
|
|
arg = rb_str_new2("NaN");
|
|
/* 'Not a Number' value. */
|
|
rb_define_const(rb_cBigDecimal, "NAN", BigDecimal_global_new(1, &arg, rb_cBigDecimal));
|
|
|
|
|
|
/* instance methods */
|
|
rb_define_method(rb_cBigDecimal, "initialize", BigDecimal_initialize, -1);
|
|
rb_define_method(rb_cBigDecimal, "initialize_copy", BigDecimal_initialize_copy, 1);
|
|
rb_define_method(rb_cBigDecimal, "precs", BigDecimal_prec, 0);
|
|
|
|
rb_define_method(rb_cBigDecimal, "add", BigDecimal_add2, 2);
|
|
rb_define_method(rb_cBigDecimal, "sub", BigDecimal_sub2, 2);
|
|
rb_define_method(rb_cBigDecimal, "mult", BigDecimal_mult2, 2);
|
|
rb_define_method(rb_cBigDecimal, "div", BigDecimal_div2, -1);
|
|
rb_define_method(rb_cBigDecimal, "hash", BigDecimal_hash, 0);
|
|
rb_define_method(rb_cBigDecimal, "to_s", BigDecimal_to_s, -1);
|
|
rb_define_method(rb_cBigDecimal, "to_i", BigDecimal_to_i, 0);
|
|
rb_define_method(rb_cBigDecimal, "to_int", BigDecimal_to_i, 0);
|
|
rb_define_method(rb_cBigDecimal, "to_r", BigDecimal_to_r, 0);
|
|
rb_define_method(rb_cBigDecimal, "split", BigDecimal_split, 0);
|
|
rb_define_method(rb_cBigDecimal, "+", BigDecimal_add, 1);
|
|
rb_define_method(rb_cBigDecimal, "-", BigDecimal_sub, 1);
|
|
rb_define_method(rb_cBigDecimal, "+@", BigDecimal_uplus, 0);
|
|
rb_define_method(rb_cBigDecimal, "-@", BigDecimal_neg, 0);
|
|
rb_define_method(rb_cBigDecimal, "*", BigDecimal_mult, 1);
|
|
rb_define_method(rb_cBigDecimal, "/", BigDecimal_div, 1);
|
|
rb_define_method(rb_cBigDecimal, "quo", BigDecimal_div, 1);
|
|
rb_define_method(rb_cBigDecimal, "%", BigDecimal_mod, 1);
|
|
rb_define_method(rb_cBigDecimal, "modulo", BigDecimal_mod, 1);
|
|
rb_define_method(rb_cBigDecimal, "remainder", BigDecimal_remainder, 1);
|
|
rb_define_method(rb_cBigDecimal, "divmod", BigDecimal_divmod, 1);
|
|
/* rb_define_method(rb_cBigDecimal, "dup", BigDecimal_dup, 0); */
|
|
rb_define_method(rb_cBigDecimal, "to_f", BigDecimal_to_f, 0);
|
|
rb_define_method(rb_cBigDecimal, "abs", BigDecimal_abs, 0);
|
|
rb_define_method(rb_cBigDecimal, "sqrt", BigDecimal_sqrt, 1);
|
|
rb_define_method(rb_cBigDecimal, "fix", BigDecimal_fix, 0);
|
|
rb_define_method(rb_cBigDecimal, "round", BigDecimal_round, -1);
|
|
rb_define_method(rb_cBigDecimal, "frac", BigDecimal_frac, 0);
|
|
rb_define_method(rb_cBigDecimal, "floor", BigDecimal_floor, -1);
|
|
rb_define_method(rb_cBigDecimal, "ceil", BigDecimal_ceil, -1);
|
|
rb_define_method(rb_cBigDecimal, "power", BigDecimal_power, -1);
|
|
rb_define_method(rb_cBigDecimal, "**", BigDecimal_power_op, 1);
|
|
rb_define_method(rb_cBigDecimal, "<=>", BigDecimal_comp, 1);
|
|
rb_define_method(rb_cBigDecimal, "==", BigDecimal_eq, 1);
|
|
rb_define_method(rb_cBigDecimal, "===", BigDecimal_eq, 1);
|
|
rb_define_method(rb_cBigDecimal, "eql?", BigDecimal_eq, 1);
|
|
rb_define_method(rb_cBigDecimal, "<", BigDecimal_lt, 1);
|
|
rb_define_method(rb_cBigDecimal, "<=", BigDecimal_le, 1);
|
|
rb_define_method(rb_cBigDecimal, ">", BigDecimal_gt, 1);
|
|
rb_define_method(rb_cBigDecimal, ">=", BigDecimal_ge, 1);
|
|
rb_define_method(rb_cBigDecimal, "zero?", BigDecimal_zero, 0);
|
|
rb_define_method(rb_cBigDecimal, "nonzero?", BigDecimal_nonzero, 0);
|
|
rb_define_method(rb_cBigDecimal, "coerce", BigDecimal_coerce, 1);
|
|
rb_define_method(rb_cBigDecimal, "inspect", BigDecimal_inspect, 0);
|
|
rb_define_method(rb_cBigDecimal, "exponent", BigDecimal_exponent, 0);
|
|
rb_define_method(rb_cBigDecimal, "sign", BigDecimal_sign, 0);
|
|
rb_define_method(rb_cBigDecimal, "nan?", BigDecimal_IsNaN, 0);
|
|
rb_define_method(rb_cBigDecimal, "infinite?", BigDecimal_IsInfinite, 0);
|
|
rb_define_method(rb_cBigDecimal, "finite?", BigDecimal_IsFinite, 0);
|
|
rb_define_method(rb_cBigDecimal, "truncate", BigDecimal_truncate, -1);
|
|
rb_define_method(rb_cBigDecimal, "_dump", BigDecimal_dump, -1);
|
|
|
|
rb_mBigMath = rb_define_module("BigMath");
|
|
rb_define_singleton_method(rb_mBigMath, "exp", BigMath_s_exp, 2);
|
|
rb_define_singleton_method(rb_mBigMath, "log", BigMath_s_log, 2);
|
|
|
|
id_up = rb_intern_const("up");
|
|
id_down = rb_intern_const("down");
|
|
id_truncate = rb_intern_const("truncate");
|
|
id_half_up = rb_intern_const("half_up");
|
|
id_default = rb_intern_const("default");
|
|
id_half_down = rb_intern_const("half_down");
|
|
id_half_even = rb_intern_const("half_even");
|
|
id_banker = rb_intern_const("banker");
|
|
id_ceiling = rb_intern_const("ceiling");
|
|
id_ceil = rb_intern_const("ceil");
|
|
id_floor = rb_intern_const("floor");
|
|
id_to_r = rb_intern_const("to_r");
|
|
id_eq = rb_intern_const("==");
|
|
}
|
|
|
|
/*
|
|
*
|
|
* ============================================================================
|
|
*
|
|
* vp_ routines begin from here.
|
|
*
|
|
* ============================================================================
|
|
*
|
|
*/
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
static int gfDebug = 1; /* Debug switch */
|
|
#if 0
|
|
static int gfCheckVal = 1; /* Value checking flag in VpNmlz() */
|
|
#endif
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
|
|
static Real *VpConstOne; /* constant 1.0 */
|
|
static Real *VpPt5; /* constant 0.5 */
|
|
#define maxnr 100UL /* Maximum iterations for calculating sqrt. */
|
|
/* used in VpSqrt() */
|
|
|
|
/* ETC */
|
|
#define MemCmp(x,y,z) memcmp(x,y,z)
|
|
#define StrCmp(x,y) strcmp(x,y)
|
|
|
|
static int VpIsDefOP(Real *c,Real *a,Real *b,int sw);
|
|
static int AddExponent(Real *a, SIGNED_VALUE n);
|
|
static BDIGIT VpAddAbs(Real *a,Real *b,Real *c);
|
|
static BDIGIT VpSubAbs(Real *a,Real *b,Real *c);
|
|
static size_t VpSetPTR(Real *a, Real *b, Real *c, size_t *a_pos, size_t *b_pos, size_t *c_pos, BDIGIT *av, BDIGIT *bv);
|
|
static int VpNmlz(Real *a);
|
|
static void VpFormatSt(char *psz, size_t fFmt);
|
|
static int VpRdup(Real *m, size_t ind_m);
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
static int gnAlloc = 0; /* Memory allocation counter */
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
|
|
VP_EXPORT void *
|
|
VpMemAlloc(size_t mb)
|
|
{
|
|
void *p = xmalloc(mb);
|
|
if (!p) {
|
|
VpException(VP_EXCEPTION_MEMORY, "failed to allocate memory", 1);
|
|
}
|
|
memset(p, 0, mb);
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
gnAlloc++; /* Count allocation call */
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
return p;
|
|
}
|
|
|
|
VP_EXPORT void *
|
|
VpMemRealloc(void *ptr, size_t mb)
|
|
{
|
|
void *p = xrealloc(ptr, mb);
|
|
if (!p) {
|
|
VpException(VP_EXCEPTION_MEMORY, "failed to allocate memory", 1);
|
|
}
|
|
return p;
|
|
}
|
|
|
|
VP_EXPORT void
|
|
VpFree(Real *pv)
|
|
{
|
|
if (pv != NULL) {
|
|
xfree(pv);
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
gnAlloc--; /* Decrement allocation count */
|
|
if (gnAlloc == 0) {
|
|
printf(" *************** All memories allocated freed ****************");
|
|
getchar();
|
|
}
|
|
if (gnAlloc < 0) {
|
|
printf(" ??????????? Too many memory free calls(%d) ?????????????\n", gnAlloc);
|
|
getchar();
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
}
|
|
}
|
|
|
|
/*
|
|
* EXCEPTION Handling.
|
|
*/
|
|
|
|
#define rmpd_set_thread_local_exception_mode(mode) \
|
|
rb_thread_local_aset( \
|
|
rb_thread_current(), \
|
|
id_BigDecimal_exception_mode, \
|
|
INT2FIX((int)(mode)) \
|
|
)
|
|
|
|
static unsigned short
|
|
VpGetException (void)
|
|
{
|
|
VALUE const vmode = rb_thread_local_aref(
|
|
rb_thread_current(),
|
|
id_BigDecimal_exception_mode
|
|
);
|
|
|
|
if (NIL_P(vmode)) {
|
|
rmpd_set_thread_local_exception_mode(RMPD_EXCEPTION_MODE_DEFAULT);
|
|
return RMPD_EXCEPTION_MODE_DEFAULT;
|
|
}
|
|
|
|
return (unsigned short)FIX2UINT(vmode);
|
|
}
|
|
|
|
static void
|
|
VpSetException(unsigned short f)
|
|
{
|
|
rmpd_set_thread_local_exception_mode(f);
|
|
}
|
|
|
|
/*
|
|
* Precision limit.
|
|
*/
|
|
|
|
#define rmpd_set_thread_local_precision_limit(limit) \
|
|
rb_thread_local_aset( \
|
|
rb_thread_current(), \
|
|
id_BigDecimal_precision_limit, \
|
|
SIZET2NUM(limit) \
|
|
)
|
|
#define RMPD_PRECISION_LIMIT_DEFAULT ((size_t)0)
|
|
|
|
/* These 2 functions added at v1.1.7 */
|
|
VP_EXPORT size_t
|
|
VpGetPrecLimit(void)
|
|
{
|
|
VALUE const vlimit = rb_thread_local_aref(
|
|
rb_thread_current(),
|
|
id_BigDecimal_precision_limit
|
|
);
|
|
|
|
if (NIL_P(vlimit)) {
|
|
rmpd_set_thread_local_precision_limit(RMPD_PRECISION_LIMIT_DEFAULT);
|
|
return RMPD_PRECISION_LIMIT_DEFAULT;
|
|
}
|
|
|
|
return NUM2SIZET(vlimit);
|
|
}
|
|
|
|
VP_EXPORT size_t
|
|
VpSetPrecLimit(size_t n)
|
|
{
|
|
size_t const s = VpGetPrecLimit();
|
|
rmpd_set_thread_local_precision_limit(n);
|
|
return s;
|
|
}
|
|
|
|
/*
|
|
* Rounding mode.
|
|
*/
|
|
|
|
#define rmpd_set_thread_local_rounding_mode(mode) \
|
|
rb_thread_local_aset( \
|
|
rb_thread_current(), \
|
|
id_BigDecimal_rounding_mode, \
|
|
INT2FIX((int)(mode)) \
|
|
)
|
|
|
|
VP_EXPORT unsigned short
|
|
VpGetRoundMode(void)
|
|
{
|
|
VALUE const vmode = rb_thread_local_aref(
|
|
rb_thread_current(),
|
|
id_BigDecimal_rounding_mode
|
|
);
|
|
|
|
if (NIL_P(vmode)) {
|
|
rmpd_set_thread_local_rounding_mode(RMPD_ROUNDING_MODE_DEFAULT);
|
|
return RMPD_ROUNDING_MODE_DEFAULT;
|
|
}
|
|
|
|
return (unsigned short)FIX2INT(vmode);
|
|
}
|
|
|
|
VP_EXPORT int
|
|
VpIsRoundMode(unsigned short n)
|
|
{
|
|
switch (n) {
|
|
case VP_ROUND_UP:
|
|
case VP_ROUND_DOWN:
|
|
case VP_ROUND_HALF_UP:
|
|
case VP_ROUND_HALF_DOWN:
|
|
case VP_ROUND_CEIL:
|
|
case VP_ROUND_FLOOR:
|
|
case VP_ROUND_HALF_EVEN:
|
|
return 1;
|
|
|
|
default:
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
VP_EXPORT unsigned short
|
|
VpSetRoundMode(unsigned short n)
|
|
{
|
|
if (VpIsRoundMode(n)) {
|
|
rmpd_set_thread_local_rounding_mode(n);
|
|
return n;
|
|
}
|
|
|
|
return VpGetRoundMode();
|
|
}
|
|
|
|
/*
|
|
* 0.0 & 1.0 generator
|
|
* These gZero_..... and gOne_..... can be any name
|
|
* referenced from nowhere except Zero() and One().
|
|
* gZero_..... and gOne_..... must have global scope
|
|
* (to let the compiler know they may be changed in outside
|
|
* (... but not actually..)).
|
|
*/
|
|
volatile const double gZero_ABCED9B1_CE73__00400511F31D = 0.0;
|
|
volatile const double gOne_ABCED9B4_CE73__00400511F31D = 1.0;
|
|
static double
|
|
Zero(void)
|
|
{
|
|
return gZero_ABCED9B1_CE73__00400511F31D;
|
|
}
|
|
|
|
static double
|
|
One(void)
|
|
{
|
|
return gOne_ABCED9B4_CE73__00400511F31D;
|
|
}
|
|
|
|
/*
|
|
----------------------------------------------------------------
|
|
Value of sign in Real structure is reserved for future use.
|
|
short sign;
|
|
==0 : NaN
|
|
1 : Positive zero
|
|
-1 : Negative zero
|
|
2 : Positive number
|
|
-2 : Negative number
|
|
3 : Positive infinite number
|
|
-3 : Negative infinite number
|
|
----------------------------------------------------------------
|
|
*/
|
|
|
|
VP_EXPORT double
|
|
VpGetDoubleNaN(void) /* Returns the value of NaN */
|
|
{
|
|
static double fNaN = 0.0;
|
|
if (fNaN == 0.0) fNaN = Zero()/Zero();
|
|
return fNaN;
|
|
}
|
|
|
|
VP_EXPORT double
|
|
VpGetDoublePosInf(void) /* Returns the value of +Infinity */
|
|
{
|
|
static double fInf = 0.0;
|
|
if (fInf == 0.0) fInf = One()/Zero();
|
|
return fInf;
|
|
}
|
|
|
|
VP_EXPORT double
|
|
VpGetDoubleNegInf(void) /* Returns the value of -Infinity */
|
|
{
|
|
static double fInf = 0.0;
|
|
if (fInf == 0.0) fInf = -(One()/Zero());
|
|
return fInf;
|
|
}
|
|
|
|
VP_EXPORT double
|
|
VpGetDoubleNegZero(void) /* Returns the value of -0 */
|
|
{
|
|
static double nzero = 1000.0;
|
|
if (nzero != 0.0) nzero = (One()/VpGetDoubleNegInf());
|
|
return nzero;
|
|
}
|
|
|
|
#if 0 /* unused */
|
|
VP_EXPORT int
|
|
VpIsNegDoubleZero(double v)
|
|
{
|
|
double z = VpGetDoubleNegZero();
|
|
return MemCmp(&v,&z,sizeof(v))==0;
|
|
}
|
|
#endif
|
|
|
|
VP_EXPORT int
|
|
VpException(unsigned short f, const char *str,int always)
|
|
{
|
|
unsigned short const exception_mode = VpGetException();
|
|
|
|
if (f == VP_EXCEPTION_OP || f == VP_EXCEPTION_MEMORY) always = 1;
|
|
|
|
if (always || (exception_mode & f)) {
|
|
switch(f) {
|
|
/* case VP_EXCEPTION_OVERFLOW: */
|
|
case VP_EXCEPTION_ZERODIVIDE:
|
|
case VP_EXCEPTION_INFINITY:
|
|
case VP_EXCEPTION_NaN:
|
|
case VP_EXCEPTION_UNDERFLOW:
|
|
case VP_EXCEPTION_OP:
|
|
rb_raise(rb_eFloatDomainError, "%s", str);
|
|
break;
|
|
case VP_EXCEPTION_MEMORY:
|
|
default:
|
|
rb_fatal("%s", str);
|
|
}
|
|
}
|
|
return 0; /* 0 Means VpException() raised no exception */
|
|
}
|
|
|
|
/* Throw exception or returns 0,when resulting c is Inf or NaN */
|
|
/* sw=1:+ 2:- 3:* 4:/ */
|
|
static int
|
|
VpIsDefOP(Real *c,Real *a,Real *b,int sw)
|
|
{
|
|
if (VpIsNaN(a) || VpIsNaN(b)) {
|
|
/* at least a or b is NaN */
|
|
VpSetNaN(c);
|
|
goto NaN;
|
|
}
|
|
|
|
if (VpIsInf(a)) {
|
|
if (VpIsInf(b)) {
|
|
switch(sw) {
|
|
case 1: /* + */
|
|
if (VpGetSign(a) == VpGetSign(b)) {
|
|
VpSetInf(c, VpGetSign(a));
|
|
goto Inf;
|
|
}
|
|
else {
|
|
VpSetNaN(c);
|
|
goto NaN;
|
|
}
|
|
case 2: /* - */
|
|
if (VpGetSign(a) != VpGetSign(b)) {
|
|
VpSetInf(c, VpGetSign(a));
|
|
goto Inf;
|
|
}
|
|
else {
|
|
VpSetNaN(c);
|
|
goto NaN;
|
|
}
|
|
break;
|
|
case 3: /* * */
|
|
VpSetInf(c, VpGetSign(a)*VpGetSign(b));
|
|
goto Inf;
|
|
break;
|
|
case 4: /* / */
|
|
VpSetNaN(c);
|
|
goto NaN;
|
|
}
|
|
VpSetNaN(c);
|
|
goto NaN;
|
|
}
|
|
/* Inf op Finite */
|
|
switch(sw) {
|
|
case 1: /* + */
|
|
case 2: /* - */
|
|
VpSetInf(c, VpGetSign(a));
|
|
break;
|
|
case 3: /* * */
|
|
if (VpIsZero(b)) {
|
|
VpSetNaN(c);
|
|
goto NaN;
|
|
}
|
|
VpSetInf(c, VpGetSign(a)*VpGetSign(b));
|
|
break;
|
|
case 4: /* / */
|
|
VpSetInf(c, VpGetSign(a)*VpGetSign(b));
|
|
}
|
|
goto Inf;
|
|
}
|
|
|
|
if (VpIsInf(b)) {
|
|
switch(sw) {
|
|
case 1: /* + */
|
|
VpSetInf(c, VpGetSign(b));
|
|
break;
|
|
case 2: /* - */
|
|
VpSetInf(c, -VpGetSign(b));
|
|
break;
|
|
case 3: /* * */
|
|
if (VpIsZero(a)) {
|
|
VpSetNaN(c);
|
|
goto NaN;
|
|
}
|
|
VpSetInf(c, VpGetSign(a)*VpGetSign(b));
|
|
break;
|
|
case 4: /* / */
|
|
VpSetZero(c, VpGetSign(a)*VpGetSign(b));
|
|
}
|
|
goto Inf;
|
|
}
|
|
return 1; /* Results OK */
|
|
|
|
Inf:
|
|
return VpException(VP_EXCEPTION_INFINITY, "Computation results to 'Infinity'", 0);
|
|
NaN:
|
|
return VpException(VP_EXCEPTION_NaN, "Computation results to 'NaN'", 0);
|
|
}
|
|
|
|
/*
|
|
----------------------------------------------------------------
|
|
*/
|
|
|
|
/*
|
|
* returns number of chars needed to represent vp in specified format.
|
|
*/
|
|
VP_EXPORT size_t
|
|
VpNumOfChars(Real *vp,const char *pszFmt)
|
|
{
|
|
SIGNED_VALUE ex;
|
|
size_t nc;
|
|
|
|
if (vp == NULL) return BASE_FIG*2+6;
|
|
if (!VpIsDef(vp)) return 32; /* not sure,may be OK */
|
|
|
|
switch(*pszFmt) {
|
|
case 'F':
|
|
nc = BASE_FIG*(vp->Prec + 1)+2;
|
|
ex = vp->exponent;
|
|
if (ex < 0) {
|
|
nc += BASE_FIG*(size_t)(-ex);
|
|
}
|
|
else {
|
|
if ((size_t)ex > vp->Prec) {
|
|
nc += BASE_FIG*((size_t)ex - vp->Prec);
|
|
}
|
|
}
|
|
break;
|
|
case 'E':
|
|
/* fall through */
|
|
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 calculated so
|
|
* that BASE is as large as possible satisfying the
|
|
* relation MaxVal <= BASE*(BASE+1). Where the value
|
|
* MaxVal is the largest value which can be represented
|
|
* by one BDIGIT word in the computer used.
|
|
*
|
|
* [Returns]
|
|
* 1+DBL_DIG ... OK
|
|
*/
|
|
VP_EXPORT size_t
|
|
VpInit(BDIGIT BaseVal)
|
|
{
|
|
/* Setup +/- Inf NaN -0 */
|
|
VpGetDoubleNaN();
|
|
VpGetDoublePosInf();
|
|
VpGetDoubleNegInf();
|
|
VpGetDoubleNegZero();
|
|
|
|
/* Allocates Vp constants. */
|
|
VpConstOne = VpAlloc(1UL, "1");
|
|
VpPt5 = VpAlloc(1UL, ".5");
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
gnAlloc = 0;
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
printf("VpInit: BaseVal = %lu\n", BaseVal);
|
|
printf(" BASE = %lu\n", BASE);
|
|
printf(" HALF_BASE = %lu\n", HALF_BASE);
|
|
printf(" BASE1 = %lu\n", BASE1);
|
|
printf(" BASE_FIG = %u\n", BASE_FIG);
|
|
printf(" DBLE_FIG = %d\n", DBLE_FIG);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
|
|
return rmpd_double_figures();
|
|
}
|
|
|
|
VP_EXPORT Real *
|
|
VpOne(void)
|
|
{
|
|
return VpConstOne;
|
|
}
|
|
|
|
/* If exponent overflows,then raise exception or returns 0 */
|
|
static int
|
|
AddExponent(Real *a, SIGNED_VALUE n)
|
|
{
|
|
SIGNED_VALUE e = a->exponent;
|
|
SIGNED_VALUE m = e+n;
|
|
SIGNED_VALUE eb, mb;
|
|
if (e > 0) {
|
|
if (n > 0) {
|
|
if (MUL_OVERFLOW_SIGNED_VALUE_P(m, (SIGNED_VALUE)BASE_FIG) ||
|
|
MUL_OVERFLOW_SIGNED_VALUE_P(e, (SIGNED_VALUE)BASE_FIG))
|
|
goto overflow;
|
|
mb = m*(SIGNED_VALUE)BASE_FIG;
|
|
eb = e*(SIGNED_VALUE)BASE_FIG;
|
|
if (mb < eb) goto overflow;
|
|
}
|
|
}
|
|
else if (n < 0) {
|
|
if (MUL_OVERFLOW_SIGNED_VALUE_P(m, (SIGNED_VALUE)BASE_FIG) ||
|
|
MUL_OVERFLOW_SIGNED_VALUE_P(e, (SIGNED_VALUE)BASE_FIG))
|
|
goto underflow;
|
|
mb = m*(SIGNED_VALUE)BASE_FIG;
|
|
eb = e*(SIGNED_VALUE)BASE_FIG;
|
|
if (mb > eb) goto underflow;
|
|
}
|
|
a->exponent = m;
|
|
return 1;
|
|
|
|
/* Overflow/Underflow ==> Raise exception or returns 0 */
|
|
underflow:
|
|
VpSetZero(a, VpGetSign(a));
|
|
return VpException(VP_EXCEPTION_UNDERFLOW, "Exponent underflow", 0);
|
|
|
|
overflow:
|
|
VpSetInf(a, VpGetSign(a));
|
|
return VpException(VP_EXCEPTION_OVERFLOW, "Exponent overflow", 0);
|
|
}
|
|
|
|
/*
|
|
* Allocates variable.
|
|
* [Input]
|
|
* mx ... allocation unit, if zero then mx is determined by szVal.
|
|
* The mx is the number of effective digits can to be stored.
|
|
* szVal ... value assigned(char). If szVal==NULL,then zero is assumed.
|
|
* If szVal[0]=='#' then Max. Prec. will not be considered(1.1.7),
|
|
* full precision specified by szVal is allocated.
|
|
*
|
|
* [Returns]
|
|
* Pointer to the newly allocated variable, or
|
|
* NULL be returned if memory allocation is failed,or any error.
|
|
*/
|
|
VP_EXPORT Real *
|
|
VpAlloc(size_t mx, const char *szVal)
|
|
{
|
|
size_t i, ni, ipn, ipf, nf, ipe, ne, nalloc;
|
|
char v, *psz;
|
|
int sign=1;
|
|
Real *vp = NULL;
|
|
size_t mf = VpGetPrecLimit();
|
|
VALUE buf;
|
|
|
|
mx = (mx + BASE_FIG - 1) / BASE_FIG + 1; /* Determine allocation unit. */
|
|
if (szVal) {
|
|
while (ISSPACE(*szVal)) szVal++;
|
|
if (*szVal != '#') {
|
|
if (mf) {
|
|
mf = (mf + BASE_FIG - 1) / BASE_FIG + 2; /* Needs 1 more for div */
|
|
if (mx > mf) {
|
|
mx = mf;
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
++szVal;
|
|
}
|
|
}
|
|
else {
|
|
/* necessary to be able to store */
|
|
/* at least mx digits. */
|
|
/* szVal==NULL ==> allocate zero value. */
|
|
vp = VpAllocReal(mx);
|
|
/* xmalloc() alway returns(or throw interruption) */
|
|
vp->MaxPrec = mx; /* set max precision */
|
|
VpSetZero(vp, 1); /* initialize vp to zero. */
|
|
return vp;
|
|
}
|
|
|
|
/* Skip all '_' after digit: 2006-6-30 */
|
|
ni = 0;
|
|
buf = rb_str_tmp_new(strlen(szVal) + 1);
|
|
psz = RSTRING_PTR(buf);
|
|
i = 0;
|
|
ipn = 0;
|
|
while ((psz[i] = szVal[ipn]) != 0) {
|
|
if (ISDIGIT(psz[i])) ++ni;
|
|
if (psz[i] == '_') {
|
|
if (ni > 0) {
|
|
ipn++;
|
|
continue;
|
|
}
|
|
psz[i] = 0;
|
|
break;
|
|
}
|
|
++i;
|
|
++ipn;
|
|
}
|
|
/* Skip trailing spaces */
|
|
while (--i > 0) {
|
|
if (ISSPACE(psz[i])) psz[i] = 0;
|
|
else break;
|
|
}
|
|
szVal = psz;
|
|
|
|
/* Check on Inf & NaN */
|
|
if (StrCmp(szVal, SZ_PINF) == 0 || StrCmp(szVal, SZ_INF) == 0 ) {
|
|
vp = VpAllocReal(1);
|
|
vp->MaxPrec = 1; /* set max precision */
|
|
VpSetPosInf(vp);
|
|
return vp;
|
|
}
|
|
if (StrCmp(szVal, SZ_NINF) == 0) {
|
|
vp = VpAllocReal(1);
|
|
vp->MaxPrec = 1; /* set max precision */
|
|
VpSetNegInf(vp);
|
|
return vp;
|
|
}
|
|
if (StrCmp(szVal, SZ_NaN) == 0) {
|
|
vp = VpAllocReal(1);
|
|
vp->MaxPrec = 1; /* set max precision */
|
|
VpSetNaN(vp);
|
|
return vp;
|
|
}
|
|
|
|
/* check on number szVal[] */
|
|
ipn = i = 0;
|
|
if (szVal[i] == '-') { sign=-1; ++i; }
|
|
else if (szVal[i] == '+') ++i;
|
|
/* Skip digits */
|
|
ni = 0; /* digits in mantissa */
|
|
while ((v = szVal[i]) != 0) {
|
|
if (!ISDIGIT(v)) break;
|
|
++i;
|
|
++ni;
|
|
}
|
|
nf = 0;
|
|
ipf = 0;
|
|
ipe = 0;
|
|
ne = 0;
|
|
if (v) {
|
|
/* other than digit nor \0 */
|
|
if (szVal[i] == '.') { /* xxx. */
|
|
++i;
|
|
ipf = i;
|
|
while ((v = szVal[i]) != 0) { /* get fraction part. */
|
|
if (!ISDIGIT(v)) break;
|
|
++i;
|
|
++nf;
|
|
}
|
|
}
|
|
ipe = 0; /* Exponent */
|
|
|
|
switch (szVal[i]) {
|
|
case '\0':
|
|
break;
|
|
case 'e': case 'E':
|
|
case 'd': case 'D':
|
|
++i;
|
|
ipe = i;
|
|
v = szVal[i];
|
|
if ((v == '-') || (v == '+')) ++i;
|
|
while ((v=szVal[i]) != 0) {
|
|
if (!ISDIGIT(v)) break;
|
|
++i;
|
|
++ne;
|
|
}
|
|
break;
|
|
default:
|
|
break;
|
|
}
|
|
}
|
|
nalloc = (ni + nf + BASE_FIG - 1) / BASE_FIG + 1; /* set effective allocation */
|
|
/* units for szVal[] */
|
|
if (mx <= 0) mx = 1;
|
|
nalloc = Max(nalloc, mx);
|
|
mx = nalloc;
|
|
vp = VpAllocReal(mx);
|
|
/* xmalloc() alway returns(or throw interruption) */
|
|
vp->MaxPrec = mx; /* set max precision */
|
|
VpSetZero(vp, sign);
|
|
VpCtoV(vp, &szVal[ipn], ni, &szVal[ipf], nf, &szVal[ipe], ne);
|
|
rb_str_resize(buf, 0);
|
|
return vp;
|
|
}
|
|
|
|
/*
|
|
* Assignment(c=a).
|
|
* [Input]
|
|
* a ... RHSV
|
|
* isw ... switch for assignment.
|
|
* c = a when isw > 0
|
|
* c = -a when isw < 0
|
|
* if c->MaxPrec < a->Prec,then round operation
|
|
* will be performed.
|
|
* [Output]
|
|
* c ... LHSV
|
|
*/
|
|
VP_EXPORT size_t
|
|
VpAsgn(Real *c, Real *a, int isw)
|
|
{
|
|
size_t n;
|
|
if (VpIsNaN(a)) {
|
|
VpSetNaN(c);
|
|
return 0;
|
|
}
|
|
if (VpIsInf(a)) {
|
|
VpSetInf(c, isw * VpGetSign(a));
|
|
return 0;
|
|
}
|
|
|
|
/* check if the RHS is zero */
|
|
if (!VpIsZero(a)) {
|
|
c->exponent = a->exponent; /* store exponent */
|
|
VpSetSign(c, isw * VpGetSign(a)); /* set sign */
|
|
n = (a->Prec < c->MaxPrec) ? (a->Prec) : (c->MaxPrec);
|
|
c->Prec = n;
|
|
memcpy(c->frac, a->frac, n * sizeof(BDIGIT));
|
|
/* Needs round ? */
|
|
if (isw != 10) {
|
|
/* Not in ActiveRound */
|
|
if(c->Prec < a->Prec) {
|
|
VpInternalRound(c, n, (n>0) ? a->frac[n-1] : 0, a->frac[n]);
|
|
}
|
|
else {
|
|
VpLimitRound(c,0);
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
/* The value of 'a' is zero. */
|
|
VpSetZero(c, isw * VpGetSign(a));
|
|
return 1;
|
|
}
|
|
return c->Prec * BASE_FIG;
|
|
}
|
|
|
|
/*
|
|
* c = a + b when operation = 1 or 2
|
|
* = a - b when operation = -1 or -2.
|
|
* Returns number of significant digits of c
|
|
*/
|
|
VP_EXPORT size_t
|
|
VpAddSub(Real *c, Real *a, Real *b, int operation)
|
|
{
|
|
short sw, isw;
|
|
Real *a_ptr, *b_ptr;
|
|
size_t n, na, nb, i;
|
|
BDIGIT mrv;
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, "VpAddSub(enter) a=% \n", a);
|
|
VPrint(stdout, " b=% \n", b);
|
|
printf(" operation=%d\n", operation);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
|
|
if (!VpIsDefOP(c, a, b, (operation > 0) ? 1 : 2)) return 0; /* No significant digits */
|
|
|
|
/* check if a or b is zero */
|
|
if (VpIsZero(a)) {
|
|
/* a is zero,then assign b to c */
|
|
if (!VpIsZero(b)) {
|
|
VpAsgn(c, b, operation);
|
|
}
|
|
else {
|
|
/* Both a and b are zero. */
|
|
if (VpGetSign(a) < 0 && operation * VpGetSign(b) < 0) {
|
|
/* -0 -0 */
|
|
VpSetZero(c, -1);
|
|
}
|
|
else {
|
|
VpSetZero(c, 1);
|
|
}
|
|
return 1; /* 0: 1 significant digits */
|
|
}
|
|
return c->Prec * BASE_FIG;
|
|
}
|
|
if (VpIsZero(b)) {
|
|
/* b is zero,then assign a to c. */
|
|
VpAsgn(c, a, 1);
|
|
return c->Prec*BASE_FIG;
|
|
}
|
|
|
|
if (operation < 0) sw = -1;
|
|
else sw = 1;
|
|
|
|
/* compare absolute value. As a result,|a_ptr|>=|b_ptr| */
|
|
if (a->exponent > b->exponent) {
|
|
a_ptr = a;
|
|
b_ptr = b;
|
|
} /* |a|>|b| */
|
|
else if (a->exponent < b->exponent) {
|
|
a_ptr = b;
|
|
b_ptr = a;
|
|
} /* |a|<|b| */
|
|
else {
|
|
/* Exponent part of a and b is the same,then compare fraction */
|
|
/* part */
|
|
na = a->Prec;
|
|
nb = b->Prec;
|
|
n = Min(na, nb);
|
|
for (i=0; i < n; ++i) {
|
|
if (a->frac[i] > b->frac[i]) {
|
|
a_ptr = a;
|
|
b_ptr = b;
|
|
goto end_if;
|
|
}
|
|
else if (a->frac[i] < b->frac[i]) {
|
|
a_ptr = b;
|
|
b_ptr = a;
|
|
goto end_if;
|
|
}
|
|
}
|
|
if (na > nb) {
|
|
a_ptr = a;
|
|
b_ptr = b;
|
|
goto end_if;
|
|
}
|
|
else if (na < nb) {
|
|
a_ptr = b;
|
|
b_ptr = a;
|
|
goto end_if;
|
|
}
|
|
/* |a| == |b| */
|
|
if (VpGetSign(a) + sw *VpGetSign(b) == 0) {
|
|
VpSetZero(c, 1); /* abs(a)=abs(b) and operation = '-' */
|
|
return c->Prec * BASE_FIG;
|
|
}
|
|
a_ptr = a;
|
|
b_ptr = b;
|
|
}
|
|
|
|
end_if:
|
|
isw = VpGetSign(a) + sw *VpGetSign(b);
|
|
/*
|
|
* isw = 0 ...( 1)+(-1),( 1)-( 1),(-1)+(1),(-1)-(-1)
|
|
* = 2 ...( 1)+( 1),( 1)-(-1)
|
|
* =-2 ...(-1)+(-1),(-1)-( 1)
|
|
* If isw==0, then c =(Sign a_ptr)(|a_ptr|-|b_ptr|)
|
|
* else c =(Sign ofisw)(|a_ptr|+|b_ptr|)
|
|
*/
|
|
if (isw) { /* addition */
|
|
VpSetSign(c, 1);
|
|
mrv = VpAddAbs(a_ptr, b_ptr, c);
|
|
VpSetSign(c, isw / 2);
|
|
}
|
|
else { /* subtraction */
|
|
VpSetSign(c, 1);
|
|
mrv = VpSubAbs(a_ptr, b_ptr, c);
|
|
if (a_ptr == a) {
|
|
VpSetSign(c,VpGetSign(a));
|
|
}
|
|
else {
|
|
VpSetSign(c, VpGetSign(a_ptr) * sw);
|
|
}
|
|
}
|
|
VpInternalRound(c, 0, (c->Prec > 0) ? c->frac[c->Prec-1] : 0, mrv);
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, "VpAddSub(result) c=% \n", c);
|
|
VPrint(stdout, " a=% \n", a);
|
|
VPrint(stdout, " b=% \n", b);
|
|
printf(" operation=%d\n", operation);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
return c->Prec * BASE_FIG;
|
|
}
|
|
|
|
/*
|
|
* Addition of two variable precisional variables
|
|
* a and b assuming abs(a)>abs(b).
|
|
* c = abs(a) + abs(b) ; where |a|>=|b|
|
|
*/
|
|
static BDIGIT
|
|
VpAddAbs(Real *a, Real *b, Real *c)
|
|
{
|
|
size_t word_shift;
|
|
size_t ap;
|
|
size_t bp;
|
|
size_t cp;
|
|
size_t a_pos;
|
|
size_t b_pos, b_pos_with_word_shift;
|
|
size_t c_pos;
|
|
BDIGIT av, bv, carry, mrv;
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, "VpAddAbs called: a = %\n", a);
|
|
VPrint(stdout, " b = %\n", b);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
|
|
word_shift = VpSetPTR(a, b, c, &ap, &bp, &cp, &av, &bv);
|
|
a_pos = ap;
|
|
b_pos = bp;
|
|
c_pos = cp;
|
|
if (word_shift == (size_t)-1L) return 0; /* Overflow */
|
|
if (b_pos == (size_t)-1L) goto Assign_a;
|
|
|
|
mrv = av + bv; /* Most right val. Used for round. */
|
|
|
|
/* Just assign the last few digits of b to c because a has no */
|
|
/* corresponding digits to be added. */
|
|
while (b_pos + word_shift > a_pos) {
|
|
--c_pos;
|
|
if (b_pos > 0) {
|
|
c->frac[c_pos] = b->frac[--b_pos];
|
|
}
|
|
else {
|
|
--word_shift;
|
|
c->frac[c_pos] = 0;
|
|
}
|
|
}
|
|
|
|
/* Just assign the last few digits of a to c because b has no */
|
|
/* corresponding digits to be added. */
|
|
b_pos_with_word_shift = b_pos + word_shift;
|
|
while (a_pos > b_pos_with_word_shift) {
|
|
c->frac[--c_pos] = a->frac[--a_pos];
|
|
}
|
|
carry = 0; /* set first carry be zero */
|
|
|
|
/* Now perform addition until every digits of b will be */
|
|
/* exhausted. */
|
|
while (b_pos > 0) {
|
|
c->frac[--c_pos] = a->frac[--a_pos] + b->frac[--b_pos] + carry;
|
|
if (c->frac[c_pos] >= BASE) {
|
|
c->frac[c_pos] -= BASE;
|
|
carry = 1;
|
|
}
|
|
else {
|
|
carry = 0;
|
|
}
|
|
}
|
|
|
|
/* Just assign the first few digits of a with considering */
|
|
/* the carry obtained so far because b has been exhausted. */
|
|
while (a_pos > 0) {
|
|
c->frac[--c_pos] = a->frac[--a_pos] + carry;
|
|
if (c->frac[c_pos] >= BASE) {
|
|
c->frac[c_pos] -= BASE;
|
|
carry = 1;
|
|
}
|
|
else {
|
|
carry = 0;
|
|
}
|
|
}
|
|
if (c_pos) c->frac[c_pos - 1] += carry;
|
|
goto Exit;
|
|
|
|
Assign_a:
|
|
VpAsgn(c, a, 1);
|
|
mrv = 0;
|
|
|
|
Exit:
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, "VpAddAbs exit: c=% \n", c);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
return mrv;
|
|
}
|
|
|
|
/*
|
|
* c = abs(a) - abs(b)
|
|
*/
|
|
static BDIGIT
|
|
VpSubAbs(Real *a, Real *b, Real *c)
|
|
{
|
|
size_t word_shift;
|
|
size_t ap;
|
|
size_t bp;
|
|
size_t cp;
|
|
size_t a_pos;
|
|
size_t b_pos, b_pos_with_word_shift;
|
|
size_t c_pos;
|
|
BDIGIT av, bv, borrow, mrv;
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, "VpSubAbs called: a = %\n", a);
|
|
VPrint(stdout, " b = %\n", b);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
|
|
word_shift = VpSetPTR(a, b, c, &ap, &bp, &cp, &av, &bv);
|
|
a_pos = ap;
|
|
b_pos = bp;
|
|
c_pos = cp;
|
|
if (word_shift == (size_t)-1L) return 0; /* Overflow */
|
|
if (b_pos == (size_t)-1L) goto Assign_a;
|
|
|
|
if (av >= bv) {
|
|
mrv = av - bv;
|
|
borrow = 0;
|
|
}
|
|
else {
|
|
mrv = 0;
|
|
borrow = 1;
|
|
}
|
|
|
|
/* Just assign the values which are the BASE subtracted by */
|
|
/* each of the last few digits of the b because the a has no */
|
|
/* corresponding digits to be subtracted. */
|
|
if (b_pos + word_shift > a_pos) {
|
|
while (b_pos + word_shift > a_pos) {
|
|
--c_pos;
|
|
if (b_pos > 0) {
|
|
c->frac[c_pos] = BASE - b->frac[--b_pos] - borrow;
|
|
}
|
|
else {
|
|
--word_shift;
|
|
c->frac[c_pos] = BASE - borrow;
|
|
}
|
|
borrow = 1;
|
|
}
|
|
}
|
|
/* Just assign the last few digits of a to c because b has no */
|
|
/* corresponding digits to subtract. */
|
|
|
|
b_pos_with_word_shift = b_pos + word_shift;
|
|
while (a_pos > b_pos_with_word_shift) {
|
|
c->frac[--c_pos] = a->frac[--a_pos];
|
|
}
|
|
|
|
/* Now perform subtraction until every digits of b will be */
|
|
/* exhausted. */
|
|
while (b_pos > 0) {
|
|
--c_pos;
|
|
if (a->frac[--a_pos] < b->frac[--b_pos] + borrow) {
|
|
c->frac[c_pos] = BASE + a->frac[a_pos] - b->frac[b_pos] - borrow;
|
|
borrow = 1;
|
|
}
|
|
else {
|
|
c->frac[c_pos] = a->frac[a_pos] - b->frac[b_pos] - borrow;
|
|
borrow = 0;
|
|
}
|
|
}
|
|
|
|
/* Just assign the first few digits of a with considering */
|
|
/* the borrow obtained so far because b has been exhausted. */
|
|
while (a_pos > 0) {
|
|
--c_pos;
|
|
if (a->frac[--a_pos] < borrow) {
|
|
c->frac[c_pos] = BASE + a->frac[a_pos] - borrow;
|
|
borrow = 1;
|
|
}
|
|
else {
|
|
c->frac[c_pos] = a->frac[a_pos] - borrow;
|
|
borrow = 0;
|
|
}
|
|
}
|
|
if (c_pos) c->frac[c_pos - 1] -= borrow;
|
|
goto Exit;
|
|
|
|
Assign_a:
|
|
VpAsgn(c, a, 1);
|
|
mrv = 0;
|
|
|
|
Exit:
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, "VpSubAbs exit: c=% \n", c);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
return mrv;
|
|
}
|
|
|
|
/*
|
|
* Note: If(av+bv)>= HALF_BASE,then 1 will be added to the least significant
|
|
* digit of c(In case of addition).
|
|
* ------------------------- figure of output -----------------------------------
|
|
* a = xxxxxxxxxxx
|
|
* b = xxxxxxxxxx
|
|
* c =xxxxxxxxxxxxxxx
|
|
* word_shift = | |
|
|
* right_word = | | (Total digits in RHSV)
|
|
* left_word = | | (Total digits in LHSV)
|
|
* a_pos = |
|
|
* b_pos = |
|
|
* c_pos = |
|
|
*/
|
|
static size_t
|
|
VpSetPTR(Real *a, Real *b, Real *c, size_t *a_pos, size_t *b_pos, size_t *c_pos, BDIGIT *av, BDIGIT *bv)
|
|
{
|
|
size_t left_word, right_word, word_shift;
|
|
c->frac[0] = 0;
|
|
*av = *bv = 0;
|
|
word_shift = (a->exponent - b->exponent);
|
|
left_word = b->Prec + word_shift;
|
|
right_word = Max(a->Prec, left_word);
|
|
left_word = c->MaxPrec - 1; /* -1 ... prepare for round up */
|
|
/*
|
|
* check if 'round' is needed.
|
|
*/
|
|
if (right_word > left_word) { /* round ? */
|
|
/*---------------------------------
|
|
* Actual size of a = xxxxxxAxx
|
|
* Actual size of b = xxxBxxxxx
|
|
* Max. size of c = xxxxxx
|
|
* Round off = |-----|
|
|
* c_pos = |
|
|
* right_word = |
|
|
* a_pos = |
|
|
*/
|
|
*c_pos = right_word = left_word + 1; /* Set resulting precision */
|
|
/* be equal to that of c */
|
|
if (a->Prec >= c->MaxPrec) {
|
|
/*
|
|
* a = xxxxxxAxxx
|
|
* c = xxxxxx
|
|
* a_pos = |
|
|
*/
|
|
*a_pos = left_word;
|
|
*av = a->frac[*a_pos]; /* av is 'A' shown in above. */
|
|
}
|
|
else {
|
|
/*
|
|
* a = xxxxxxx
|
|
* c = xxxxxxxxxx
|
|
* a_pos = |
|
|
*/
|
|
*a_pos = a->Prec;
|
|
}
|
|
if (b->Prec + word_shift >= c->MaxPrec) {
|
|
/*
|
|
* a = xxxxxxxxx
|
|
* b = xxxxxxxBxxx
|
|
* c = xxxxxxxxxxx
|
|
* b_pos = |
|
|
*/
|
|
if (c->MaxPrec >= word_shift + 1) {
|
|
*b_pos = c->MaxPrec - word_shift - 1;
|
|
*bv = b->frac[*b_pos];
|
|
}
|
|
else {
|
|
*b_pos = -1L;
|
|
}
|
|
}
|
|
else {
|
|
/*
|
|
* a = xxxxxxxxxxxxxxxx
|
|
* b = xxxxxx
|
|
* c = xxxxxxxxxxxxx
|
|
* b_pos = |
|
|
*/
|
|
*b_pos = b->Prec;
|
|
}
|
|
}
|
|
else { /* The MaxPrec of c - 1 > The Prec of a + b */
|
|
/*
|
|
* a = xxxxxxx
|
|
* b = xxxxxx
|
|
* c = xxxxxxxxxxx
|
|
* c_pos = |
|
|
*/
|
|
*b_pos = b->Prec;
|
|
*a_pos = a->Prec;
|
|
*c_pos = right_word + 1;
|
|
}
|
|
c->Prec = *c_pos;
|
|
c->exponent = a->exponent;
|
|
if (!AddExponent(c, 1)) return (size_t)-1L;
|
|
return word_shift;
|
|
}
|
|
|
|
/*
|
|
* Return number of significant digits
|
|
* c = a * b , Where a = a0a1a2 ... an
|
|
* b = b0b1b2 ... bm
|
|
* c = c0c1c2 ... cl
|
|
* a0 a1 ... an * bm
|
|
* a0 a1 ... an * bm-1
|
|
* . . .
|
|
* . . .
|
|
* a0 a1 .... an * b0
|
|
* +_____________________________
|
|
* c0 c1 c2 ...... cl
|
|
* nc <---|
|
|
* MaxAB |--------------------|
|
|
*/
|
|
VP_EXPORT size_t
|
|
VpMult(Real *c, Real *a, Real *b)
|
|
{
|
|
size_t MxIndA, MxIndB, MxIndAB, MxIndC;
|
|
size_t ind_c, i, ii, nc;
|
|
size_t ind_as, ind_ae, ind_bs;
|
|
BDIGIT carry;
|
|
BDIGIT_DBL s;
|
|
Real *w;
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, "VpMult(Enter): a=% \n", a);
|
|
VPrint(stdout, " b=% \n", b);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
|
|
if (!VpIsDefOP(c, a, b, 3)) return 0; /* No significant digit */
|
|
|
|
if (VpIsZero(a) || VpIsZero(b)) {
|
|
/* at least a or b is zero */
|
|
VpSetZero(c, VpGetSign(a) * VpGetSign(b));
|
|
return 1; /* 0: 1 significant digit */
|
|
}
|
|
|
|
if (VpIsOne(a)) {
|
|
VpAsgn(c, b, VpGetSign(a));
|
|
goto Exit;
|
|
}
|
|
if (VpIsOne(b)) {
|
|
VpAsgn(c, a, VpGetSign(b));
|
|
goto Exit;
|
|
}
|
|
if (b->Prec > a->Prec) {
|
|
/* Adjust so that digits(a)>digits(b) */
|
|
w = a;
|
|
a = b;
|
|
b = w;
|
|
}
|
|
w = NULL;
|
|
MxIndA = a->Prec - 1;
|
|
MxIndB = b->Prec - 1;
|
|
MxIndC = c->MaxPrec - 1;
|
|
MxIndAB = a->Prec + b->Prec - 1;
|
|
|
|
if (MxIndC < MxIndAB) { /* The Max. prec. of c < Prec(a)+Prec(b) */
|
|
w = c;
|
|
c = VpAlloc((size_t)((MxIndAB + 1) * BASE_FIG), "#0");
|
|
MxIndC = MxIndAB;
|
|
}
|
|
|
|
/* set LHSV c info */
|
|
|
|
c->exponent = a->exponent; /* set exponent */
|
|
if (!AddExponent(c, b->exponent)) {
|
|
if (w) VpFree(c);
|
|
return 0;
|
|
}
|
|
VpSetSign(c, VpGetSign(a) * VpGetSign(b)); /* set sign */
|
|
carry = 0;
|
|
nc = ind_c = MxIndAB;
|
|
memset(c->frac, 0, (nc + 1) * sizeof(BDIGIT)); /* Initialize c */
|
|
c->Prec = nc + 1; /* set precision */
|
|
for (nc = 0; nc < MxIndAB; ++nc, --ind_c) {
|
|
if (nc < MxIndB) { /* The left triangle of the Fig. */
|
|
ind_as = MxIndA - nc;
|
|
ind_ae = MxIndA;
|
|
ind_bs = MxIndB;
|
|
}
|
|
else if (nc <= MxIndA) { /* The middle rectangular of the Fig. */
|
|
ind_as = MxIndA - nc;
|
|
ind_ae = MxIndA - (nc - MxIndB);
|
|
ind_bs = MxIndB;
|
|
}
|
|
else /* if (nc > MxIndA) */ { /* The right triangle of the Fig. */
|
|
ind_as = 0;
|
|
ind_ae = MxIndAB - nc - 1;
|
|
ind_bs = MxIndB - (nc - MxIndA);
|
|
}
|
|
|
|
for (i = ind_as; i <= ind_ae; ++i) {
|
|
s = (BDIGIT_DBL)a->frac[i] * b->frac[ind_bs--];
|
|
carry = (BDIGIT)(s / BASE);
|
|
s -= (BDIGIT_DBL)carry * BASE;
|
|
c->frac[ind_c] += (BDIGIT)s;
|
|
if (c->frac[ind_c] >= BASE) {
|
|
s = c->frac[ind_c] / BASE;
|
|
carry += (BDIGIT)s;
|
|
c->frac[ind_c] -= (BDIGIT)(s * BASE);
|
|
}
|
|
if (carry) {
|
|
ii = ind_c;
|
|
while (ii-- > 0) {
|
|
c->frac[ii] += carry;
|
|
if (c->frac[ii] >= BASE) {
|
|
carry = c->frac[ii] / BASE;
|
|
c->frac[ii] -= (carry * BASE);
|
|
}
|
|
else {
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if (w != NULL) { /* free work variable */
|
|
VpNmlz(c);
|
|
VpAsgn(w, c, 1);
|
|
VpFree(c);
|
|
c = w;
|
|
}
|
|
else {
|
|
VpLimitRound(c,0);
|
|
}
|
|
|
|
Exit:
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, "VpMult(c=a*b): c=% \n", c);
|
|
VPrint(stdout, " a=% \n", a);
|
|
VPrint(stdout, " b=% \n", b);
|
|
}
|
|
#endif /*BIGDECIMAL_DEBUG */
|
|
return c->Prec*BASE_FIG;
|
|
}
|
|
|
|
/*
|
|
* c = a / b, remainder = r
|
|
*/
|
|
VP_EXPORT size_t
|
|
VpDivd(Real *c, Real *r, Real *a, Real *b)
|
|
{
|
|
size_t word_a, word_b, word_c, word_r;
|
|
size_t i, n, ind_a, ind_b, ind_c, ind_r;
|
|
size_t nLoop;
|
|
BDIGIT_DBL q, b1, b1p1, b1b2, b1b2p1, r1r2;
|
|
BDIGIT borrow, borrow1, borrow2;
|
|
BDIGIT_DBL qb;
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, " VpDivd(c=a/b) a=% \n", a);
|
|
VPrint(stdout, " b=% \n", b);
|
|
}
|
|
#endif /*BIGDECIMAL_DEBUG */
|
|
|
|
VpSetNaN(r);
|
|
if (!VpIsDefOP(c, a, b, 4)) goto Exit;
|
|
if (VpIsZero(a) && VpIsZero(b)) {
|
|
VpSetNaN(c);
|
|
return VpException(VP_EXCEPTION_NaN, "(VpDivd) 0/0 not defined(NaN)", 0);
|
|
}
|
|
if (VpIsZero(b)) {
|
|
VpSetInf(c, VpGetSign(a) * VpGetSign(b));
|
|
return VpException(VP_EXCEPTION_ZERODIVIDE, "(VpDivd) Divide by zero", 0);
|
|
}
|
|
if (VpIsZero(a)) {
|
|
/* numerator a is zero */
|
|
VpSetZero(c, VpGetSign(a) * VpGetSign(b));
|
|
VpSetZero(r, VpGetSign(a) * VpGetSign(b));
|
|
goto Exit;
|
|
}
|
|
if (VpIsOne(b)) {
|
|
/* divide by one */
|
|
VpAsgn(c, a, VpGetSign(b));
|
|
VpSetZero(r, VpGetSign(a));
|
|
goto Exit;
|
|
}
|
|
|
|
word_a = a->Prec;
|
|
word_b = b->Prec;
|
|
word_c = c->MaxPrec;
|
|
word_r = r->MaxPrec;
|
|
|
|
ind_c = 0;
|
|
ind_r = 1;
|
|
|
|
if (word_a >= word_r) goto space_error;
|
|
|
|
r->frac[0] = 0;
|
|
while (ind_r <= word_a) {
|
|
r->frac[ind_r] = a->frac[ind_r - 1];
|
|
++ind_r;
|
|
}
|
|
|
|
while (ind_r < word_r) r->frac[ind_r++] = 0;
|
|
while (ind_c < word_c) c->frac[ind_c++] = 0;
|
|
|
|
/* initial procedure */
|
|
b1 = b1p1 = b->frac[0];
|
|
if (b->Prec <= 1) {
|
|
b1b2p1 = b1b2 = b1p1 * BASE;
|
|
}
|
|
else {
|
|
b1p1 = b1 + 1;
|
|
b1b2p1 = b1b2 = b1 * BASE + b->frac[1];
|
|
if (b->Prec > 2) ++b1b2p1;
|
|
}
|
|
|
|
/* */
|
|
/* loop start */
|
|
ind_c = word_r - 1;
|
|
nLoop = Min(word_c,ind_c);
|
|
ind_c = 1;
|
|
while (ind_c < nLoop) {
|
|
if (r->frac[ind_c] == 0) {
|
|
++ind_c;
|
|
continue;
|
|
}
|
|
r1r2 = (BDIGIT_DBL)r->frac[ind_c] * BASE + r->frac[ind_c + 1];
|
|
if (r1r2 == b1b2) {
|
|
/* The first two word digits is the same */
|
|
ind_b = 2;
|
|
ind_a = ind_c + 2;
|
|
while (ind_b < word_b) {
|
|
if (r->frac[ind_a] < b->frac[ind_b]) goto div_b1p1;
|
|
if (r->frac[ind_a] > b->frac[ind_b]) break;
|
|
++ind_a;
|
|
++ind_b;
|
|
}
|
|
/* The first few word digits of r and b is the same and */
|
|
/* the first different word digit of w is greater than that */
|
|
/* of b, so quotient is 1 and just subtract b from r. */
|
|
borrow = 0; /* quotient=1, then just r-b */
|
|
ind_b = b->Prec - 1;
|
|
ind_r = ind_c + ind_b;
|
|
if (ind_r >= word_r) goto space_error;
|
|
n = ind_b;
|
|
for (i = 0; i <= n; ++i) {
|
|
if (r->frac[ind_r] < b->frac[ind_b] + borrow) {
|
|
r->frac[ind_r] += (BASE - (b->frac[ind_b] + borrow));
|
|
borrow = 1;
|
|
}
|
|
else {
|
|
r->frac[ind_r] = r->frac[ind_r] - b->frac[ind_b] - borrow;
|
|
borrow = 0;
|
|
}
|
|
--ind_r;
|
|
--ind_b;
|
|
}
|
|
++c->frac[ind_c];
|
|
goto carry;
|
|
}
|
|
/* The first two word digits is not the same, */
|
|
/* then compare magnitude, and divide actually. */
|
|
if (r1r2 >= b1b2p1) {
|
|
q = r1r2 / b1b2p1; /* q == (BDIGIT)q */
|
|
c->frac[ind_c] += (BDIGIT)q;
|
|
ind_r = b->Prec + ind_c - 1;
|
|
goto sub_mult;
|
|
}
|
|
|
|
div_b1p1:
|
|
if (ind_c + 1 >= word_c) goto out_side;
|
|
q = r1r2 / b1p1; /* q == (BDIGIT)q */
|
|
c->frac[ind_c + 1] += (BDIGIT)q;
|
|
ind_r = b->Prec + ind_c;
|
|
|
|
sub_mult:
|
|
borrow1 = borrow2 = 0;
|
|
ind_b = word_b - 1;
|
|
if (ind_r >= word_r) goto space_error;
|
|
n = ind_b;
|
|
for (i = 0; i <= n; ++i) {
|
|
/* now, perform r = r - q * b */
|
|
qb = q * b->frac[ind_b];
|
|
if (qb < BASE) borrow1 = 0;
|
|
else {
|
|
borrow1 = (BDIGIT)(qb / BASE);
|
|
qb -= (BDIGIT_DBL)borrow1 * BASE; /* get qb < BASE */
|
|
}
|
|
if(r->frac[ind_r] < qb) {
|
|
r->frac[ind_r] += (BDIGIT)(BASE - qb);
|
|
borrow2 = borrow2 + borrow1 + 1;
|
|
}
|
|
else {
|
|
r->frac[ind_r] -= (BDIGIT)qb;
|
|
borrow2 += borrow1;
|
|
}
|
|
if (borrow2) {
|
|
if(r->frac[ind_r - 1] < borrow2) {
|
|
r->frac[ind_r - 1] += (BASE - borrow2);
|
|
borrow2 = 1;
|
|
}
|
|
else {
|
|
r->frac[ind_r - 1] -= borrow2;
|
|
borrow2 = 0;
|
|
}
|
|
}
|
|
--ind_r;
|
|
--ind_b;
|
|
}
|
|
|
|
r->frac[ind_r] -= borrow2;
|
|
carry:
|
|
ind_r = ind_c;
|
|
while (c->frac[ind_r] >= BASE) {
|
|
c->frac[ind_r] -= BASE;
|
|
--ind_r;
|
|
++c->frac[ind_r];
|
|
}
|
|
}
|
|
/* End of operation, now final arrangement */
|
|
out_side:
|
|
c->Prec = word_c;
|
|
c->exponent = a->exponent;
|
|
if (!AddExponent(c, 2)) return 0;
|
|
if (!AddExponent(c, -(b->exponent))) return 0;
|
|
|
|
VpSetSign(c, VpGetSign(a) * VpGetSign(b));
|
|
VpNmlz(c); /* normalize c */
|
|
r->Prec = word_r;
|
|
r->exponent = a->exponent;
|
|
if (!AddExponent(r, 1)) return 0;
|
|
VpSetSign(r, VpGetSign(a));
|
|
VpNmlz(r); /* normalize r(remainder) */
|
|
goto Exit;
|
|
|
|
space_error:
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
printf(" word_a=%lu\n", word_a);
|
|
printf(" word_b=%lu\n", word_b);
|
|
printf(" word_c=%lu\n", word_c);
|
|
printf(" word_r=%lu\n", word_r);
|
|
printf(" ind_r =%lu\n", ind_r);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
rb_bug("ERROR(VpDivd): space for remainder too small.");
|
|
|
|
Exit:
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, " VpDivd(c=a/b), c=% \n", c);
|
|
VPrint(stdout, " r=% \n", r);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
return c->Prec * BASE_FIG;
|
|
}
|
|
|
|
/*
|
|
* Input a = 00000xxxxxxxx En(5 preceding zeros)
|
|
* Output a = xxxxxxxx En-5
|
|
*/
|
|
static int
|
|
VpNmlz(Real *a)
|
|
{
|
|
size_t ind_a, i;
|
|
|
|
if (!VpIsDef(a)) goto NoVal;
|
|
if (VpIsZero(a)) goto NoVal;
|
|
|
|
ind_a = a->Prec;
|
|
while (ind_a--) {
|
|
if (a->frac[ind_a]) {
|
|
a->Prec = ind_a + 1;
|
|
i = 0;
|
|
while (a->frac[i] == 0) ++i; /* skip the first few zeros */
|
|
if (i) {
|
|
a->Prec -= i;
|
|
if (!AddExponent(a, -(SIGNED_VALUE)i)) return 0;
|
|
memmove(&a->frac[0], &a->frac[i], a->Prec*sizeof(BDIGIT));
|
|
}
|
|
return 1;
|
|
}
|
|
}
|
|
/* a is zero(no non-zero digit) */
|
|
VpSetZero(a, VpGetSign(a));
|
|
return 0;
|
|
|
|
NoVal:
|
|
a->frac[0] = 0;
|
|
a->Prec = 1;
|
|
return 0;
|
|
}
|
|
|
|
/*
|
|
* VpComp = 0 ... if a=b,
|
|
* Pos ... a>b,
|
|
* Neg ... a<b.
|
|
* 999 ... result undefined(NaN)
|
|
*/
|
|
VP_EXPORT int
|
|
VpComp(Real *a, Real *b)
|
|
{
|
|
int val;
|
|
size_t mx, ind;
|
|
int e;
|
|
val = 0;
|
|
if (VpIsNaN(a) || VpIsNaN(b)) return 999;
|
|
if (!VpIsDef(a)) {
|
|
if (!VpIsDef(b)) e = a->sign - b->sign;
|
|
else e = a->sign;
|
|
|
|
if (e > 0) return 1;
|
|
else if (e < 0) return -1;
|
|
else return 0;
|
|
}
|
|
if (!VpIsDef(b)) {
|
|
e = -b->sign;
|
|
if (e > 0) return 1;
|
|
else return -1;
|
|
}
|
|
/* Zero check */
|
|
if (VpIsZero(a)) {
|
|
if (VpIsZero(b)) return 0; /* both zero */
|
|
val = -VpGetSign(b);
|
|
goto Exit;
|
|
}
|
|
if (VpIsZero(b)) {
|
|
val = VpGetSign(a);
|
|
goto Exit;
|
|
}
|
|
|
|
/* compare sign */
|
|
if (VpGetSign(a) > VpGetSign(b)) {
|
|
val = 1; /* a>b */
|
|
goto Exit;
|
|
}
|
|
if (VpGetSign(a) < VpGetSign(b)) {
|
|
val = -1; /* a<b */
|
|
goto Exit;
|
|
}
|
|
|
|
/* a and b have same sign, && sign!=0,then compare exponent */
|
|
if (a->exponent > b->exponent) {
|
|
val = VpGetSign(a);
|
|
goto Exit;
|
|
}
|
|
if (a->exponent < b->exponent) {
|
|
val = -VpGetSign(b);
|
|
goto Exit;
|
|
}
|
|
|
|
/* a and b have same exponent, then compare significand. */
|
|
mx = (a->Prec < b->Prec) ? a->Prec : b->Prec;
|
|
ind = 0;
|
|
while (ind < mx) {
|
|
if (a->frac[ind] > b->frac[ind]) {
|
|
val = VpGetSign(a);
|
|
goto Exit;
|
|
}
|
|
if (a->frac[ind] < b->frac[ind]) {
|
|
val = -VpGetSign(b);
|
|
goto Exit;
|
|
}
|
|
++ind;
|
|
}
|
|
if (a->Prec > b->Prec) {
|
|
val = VpGetSign(a);
|
|
}
|
|
else if (a->Prec < b->Prec) {
|
|
val = -VpGetSign(b);
|
|
}
|
|
|
|
Exit:
|
|
if (val > 1) val = 1;
|
|
else if (val < -1) val = -1;
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, " VpComp a=%\n", a);
|
|
VPrint(stdout, " b=%\n", b);
|
|
printf(" ans=%d\n", val);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
return (int)val;
|
|
}
|
|
|
|
#ifdef BIGDECIMAL_ENABLE_VPRINT
|
|
/*
|
|
* cntl_chr ... ASCIIZ Character, print control characters
|
|
* Available control codes:
|
|
* % ... VP variable. To print '%', use '%%'.
|
|
* \n ... new line
|
|
* \b ... backspace
|
|
* ... tab
|
|
* Note: % must must not appear more than once
|
|
* a ... VP variable to be printed
|
|
*/
|
|
VP_EXPORT int
|
|
VPrint(FILE *fp, const char *cntl_chr, Real *a)
|
|
{
|
|
size_t i, j, nc, nd, ZeroSup;
|
|
BDIGIT m, e, nn;
|
|
|
|
/* Check if NaN & Inf. */
|
|
if (VpIsNaN(a)) {
|
|
fprintf(fp, SZ_NaN);
|
|
return 8;
|
|
}
|
|
if (VpIsPosInf(a)) {
|
|
fprintf(fp, SZ_INF);
|
|
return 8;
|
|
}
|
|
if (VpIsNegInf(a)) {
|
|
fprintf(fp, SZ_NINF);
|
|
return 9;
|
|
}
|
|
if (VpIsZero(a)) {
|
|
fprintf(fp, "0.0");
|
|
return 3;
|
|
}
|
|
|
|
j = 0;
|
|
nd = nc = 0; /* nd : number of digits in fraction part(every 10 digits, */
|
|
/* nd<=10). */
|
|
/* nc : number of characters printed */
|
|
ZeroSup = 1; /* Flag not to print the leading zeros as 0.00xxxxEnn */
|
|
while (*(cntl_chr + j)) {
|
|
if (*(cntl_chr + j) == '%' && *(cntl_chr + j + 1) != '%') {
|
|
nc = 0;
|
|
if (!VpIsZero(a)) {
|
|
if (VpGetSign(a) < 0) {
|
|
fprintf(fp, "-");
|
|
++nc;
|
|
}
|
|
nc += fprintf(fp, "0.");
|
|
for (i = 0; i < a->Prec; ++i) {
|
|
m = BASE1;
|
|
e = a->frac[i];
|
|
while (m) {
|
|
nn = e / m;
|
|
if (!ZeroSup || nn) {
|
|
nc += fprintf(fp, "%lu", (unsigned long)nn); /* The leading zero(s) */
|
|
/* as 0.00xx will not */
|
|
/* be printed. */
|
|
++nd;
|
|
ZeroSup = 0; /* Set to print succeeding zeros */
|
|
}
|
|
if (nd >= 10) { /* print ' ' after every 10 digits */
|
|
nd = 0;
|
|
nc += fprintf(fp, " ");
|
|
}
|
|
e = e - nn * m;
|
|
m /= 10;
|
|
}
|
|
}
|
|
nc += fprintf(fp, "E%"PRIdSIZE, VpExponent10(a));
|
|
}
|
|
else {
|
|
nc += fprintf(fp, "0.0");
|
|
}
|
|
}
|
|
else {
|
|
++nc;
|
|
if (*(cntl_chr + j) == '\\') {
|
|
switch (*(cntl_chr + j + 1)) {
|
|
case 'n':
|
|
fprintf(fp, "\n");
|
|
++j;
|
|
break;
|
|
case 't':
|
|
fprintf(fp, "\t");
|
|
++j;
|
|
break;
|
|
case 'b':
|
|
fprintf(fp, "\n");
|
|
++j;
|
|
break;
|
|
default:
|
|
fprintf(fp, "%c", *(cntl_chr + j));
|
|
break;
|
|
}
|
|
}
|
|
else {
|
|
fprintf(fp, "%c", *(cntl_chr + j));
|
|
if (*(cntl_chr + j) == '%') ++j;
|
|
}
|
|
}
|
|
j++;
|
|
}
|
|
return (int)nc;
|
|
}
|
|
#endif /* BIGDECIMAL_ENABLE_VPRINT */
|
|
|
|
static void
|
|
VpFormatSt(char *psz, size_t fFmt)
|
|
{
|
|
size_t ie, i, nf = 0;
|
|
char ch;
|
|
|
|
if (fFmt <= 0) return;
|
|
|
|
ie = strlen(psz);
|
|
for (i = 0; i < ie; ++i) {
|
|
ch = psz[i];
|
|
if (!ch) break;
|
|
if (ISSPACE(ch) || ch=='-' || ch=='+') continue;
|
|
if (ch == '.') { nf = 0; continue; }
|
|
if (ch == 'E') break;
|
|
|
|
if (++nf > fFmt) {
|
|
memmove(psz + i + 1, psz + i, ie - i + 1);
|
|
++ie;
|
|
nf = 0;
|
|
psz[i] = ' ';
|
|
}
|
|
}
|
|
}
|
|
|
|
VP_EXPORT ssize_t
|
|
VpExponent10(Real *a)
|
|
{
|
|
ssize_t ex;
|
|
size_t n;
|
|
|
|
if (!VpHasVal(a)) return 0;
|
|
|
|
ex = a->exponent * (ssize_t)BASE_FIG;
|
|
n = BASE1;
|
|
while ((a->frac[0] / n) == 0) {
|
|
--ex;
|
|
n /= 10;
|
|
}
|
|
return ex;
|
|
}
|
|
|
|
VP_EXPORT void
|
|
VpSzMantissa(Real *a,char *psz)
|
|
{
|
|
size_t i, n, ZeroSup;
|
|
BDIGIT_DBL m, e, nn;
|
|
|
|
if (VpIsNaN(a)) {
|
|
sprintf(psz, SZ_NaN);
|
|
return;
|
|
}
|
|
if (VpIsPosInf(a)) {
|
|
sprintf(psz, SZ_INF);
|
|
return;
|
|
}
|
|
if (VpIsNegInf(a)) {
|
|
sprintf(psz, SZ_NINF);
|
|
return;
|
|
}
|
|
|
|
ZeroSup = 1; /* Flag not to print the leading zeros as 0.00xxxxEnn */
|
|
if (!VpIsZero(a)) {
|
|
if (VpGetSign(a) < 0) *psz++ = '-';
|
|
n = a->Prec;
|
|
for (i = 0; i < n; ++i) {
|
|
m = BASE1;
|
|
e = a->frac[i];
|
|
while (m) {
|
|
nn = e / m;
|
|
if (!ZeroSup || nn) {
|
|
sprintf(psz, "%lu", (unsigned long)nn); /* The leading zero(s) */
|
|
psz += strlen(psz);
|
|
/* as 0.00xx will be ignored. */
|
|
ZeroSup = 0; /* Set to print succeeding zeros */
|
|
}
|
|
e = e - nn * m;
|
|
m /= 10;
|
|
}
|
|
}
|
|
*psz = 0;
|
|
while (psz[-1] == '0') *(--psz) = 0;
|
|
}
|
|
else {
|
|
if (VpIsPosZero(a)) sprintf(psz, "0");
|
|
else sprintf(psz, "-0");
|
|
}
|
|
}
|
|
|
|
VP_EXPORT int
|
|
VpToSpecialString(Real *a,char *psz,int fPlus)
|
|
/* fPlus =0:default, =1: set ' ' before digits , =2: set '+' before digits. */
|
|
{
|
|
if (VpIsNaN(a)) {
|
|
sprintf(psz,SZ_NaN);
|
|
return 1;
|
|
}
|
|
|
|
if (VpIsPosInf(a)) {
|
|
if (fPlus == 1) {
|
|
*psz++ = ' ';
|
|
}
|
|
else if (fPlus == 2) {
|
|
*psz++ = '+';
|
|
}
|
|
sprintf(psz, SZ_INF);
|
|
return 1;
|
|
}
|
|
if (VpIsNegInf(a)) {
|
|
sprintf(psz, SZ_NINF);
|
|
return 1;
|
|
}
|
|
if (VpIsZero(a)) {
|
|
if (VpIsPosZero(a)) {
|
|
if (fPlus == 1) sprintf(psz, " 0.0");
|
|
else if (fPlus == 2) sprintf(psz, "+0.0");
|
|
else sprintf(psz, "0.0");
|
|
}
|
|
else sprintf(psz, "-0.0");
|
|
return 1;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
VP_EXPORT void
|
|
VpToString(Real *a, char *psz, size_t fFmt, int fPlus)
|
|
/* fPlus =0:default, =1: set ' ' before digits , =2:set '+' before digits. */
|
|
{
|
|
size_t i, n, ZeroSup;
|
|
BDIGIT shift, m, e, nn;
|
|
char *pszSav = psz;
|
|
ssize_t ex;
|
|
|
|
if (VpToSpecialString(a, psz, fPlus)) return;
|
|
|
|
ZeroSup = 1; /* Flag not to print the leading zeros as 0.00xxxxEnn */
|
|
|
|
if (VpGetSign(a) < 0) *psz++ = '-';
|
|
else if (fPlus == 1) *psz++ = ' ';
|
|
else if (fPlus == 2) *psz++ = '+';
|
|
|
|
*psz++ = '0';
|
|
*psz++ = '.';
|
|
n = a->Prec;
|
|
for (i = 0; i < n; ++i) {
|
|
m = BASE1;
|
|
e = a->frac[i];
|
|
while (m) {
|
|
nn = e / m;
|
|
if (!ZeroSup || nn) {
|
|
sprintf(psz, "%lu", (unsigned long)nn); /* The reading zero(s) */
|
|
psz += strlen(psz);
|
|
/* as 0.00xx will be ignored. */
|
|
ZeroSup = 0; /* Set to print succeeding zeros */
|
|
}
|
|
e = e - nn * m;
|
|
m /= 10;
|
|
}
|
|
}
|
|
ex = a->exponent * (ssize_t)BASE_FIG;
|
|
shift = BASE1;
|
|
while (a->frac[0] / shift == 0) {
|
|
--ex;
|
|
shift /= 10;
|
|
}
|
|
while (psz[-1] == '0') {
|
|
*(--psz) = 0;
|
|
}
|
|
sprintf(psz, "E%"PRIdSIZE, ex);
|
|
if (fFmt) VpFormatSt(pszSav, fFmt);
|
|
}
|
|
|
|
VP_EXPORT void
|
|
VpToFString(Real *a, char *psz, size_t fFmt, int fPlus)
|
|
/* fPlus =0:default,=1: set ' ' before digits ,set '+' before digits. */
|
|
{
|
|
size_t i, n;
|
|
BDIGIT m, e, nn;
|
|
char *pszSav = psz;
|
|
ssize_t ex;
|
|
|
|
if (VpToSpecialString(a, psz, fPlus)) return;
|
|
|
|
if (VpGetSign(a) < 0) *psz++ = '-';
|
|
else if (fPlus == 1) *psz++ = ' ';
|
|
else if (fPlus == 2) *psz++ = '+';
|
|
|
|
n = a->Prec;
|
|
ex = a->exponent;
|
|
if (ex <= 0) {
|
|
*psz++ = '0';*psz++ = '.';
|
|
while (ex < 0) {
|
|
for (i=0; i < BASE_FIG; ++i) *psz++ = '0';
|
|
++ex;
|
|
}
|
|
ex = -1;
|
|
}
|
|
|
|
for (i = 0; i < n; ++i) {
|
|
--ex;
|
|
if (i == 0 && ex >= 0) {
|
|
sprintf(psz, "%lu", (unsigned long)a->frac[i]);
|
|
psz += strlen(psz);
|
|
}
|
|
else {
|
|
m = BASE1;
|
|
e = a->frac[i];
|
|
while (m) {
|
|
nn = e / m;
|
|
*psz++ = (char)(nn + '0');
|
|
e = e - nn * m;
|
|
m /= 10;
|
|
}
|
|
}
|
|
if (ex == 0) *psz++ = '.';
|
|
}
|
|
while (--ex>=0) {
|
|
m = BASE;
|
|
while (m /= 10) *psz++ = '0';
|
|
if (ex == 0) *psz++ = '.';
|
|
}
|
|
*psz = 0;
|
|
while (psz[-1] == '0') *(--psz) = 0;
|
|
if (psz[-1] == '.') sprintf(psz, "0");
|
|
if (fFmt) VpFormatSt(pszSav, fFmt);
|
|
}
|
|
|
|
/*
|
|
* [Output]
|
|
* a[] ... variable to be assigned the value.
|
|
* [Input]
|
|
* int_chr[] ... integer part(may include '+/-').
|
|
* ni ... number of characters in int_chr[],not including '+/-'.
|
|
* frac[] ... fraction part.
|
|
* nf ... number of characters in frac[].
|
|
* exp_chr[] ... exponent part(including '+/-').
|
|
* ne ... number of characters in exp_chr[],not including '+/-'.
|
|
*/
|
|
VP_EXPORT int
|
|
VpCtoV(Real *a, const char *int_chr, size_t ni, const char *frac, size_t nf, const char *exp_chr, size_t ne)
|
|
{
|
|
size_t i, j, ind_a, ma, mi, me;
|
|
SIGNED_VALUE e, es, eb, ef;
|
|
int sign, signe, exponent_overflow;
|
|
|
|
/* get exponent part */
|
|
e = 0;
|
|
ma = a->MaxPrec;
|
|
mi = ni;
|
|
me = ne;
|
|
signe = 1;
|
|
exponent_overflow = 0;
|
|
memset(a->frac, 0, ma * sizeof(BDIGIT));
|
|
if (ne > 0) {
|
|
i = 0;
|
|
if (exp_chr[0] == '-') {
|
|
signe = -1;
|
|
++i;
|
|
++me;
|
|
}
|
|
else if (exp_chr[0] == '+') {
|
|
++i;
|
|
++me;
|
|
}
|
|
while (i < me) {
|
|
if (MUL_OVERFLOW_SIGNED_VALUE_P(e, (SIGNED_VALUE)BASE_FIG)) {
|
|
es = e;
|
|
goto exp_overflow;
|
|
}
|
|
es = e * (SIGNED_VALUE)BASE_FIG;
|
|
if (MUL_OVERFLOW_SIGNED_VALUE_P(e, 10) ||
|
|
SIGNED_VALUE_MAX - (exp_chr[i] - '0') < e * 10)
|
|
goto exp_overflow;
|
|
e = e * 10 + exp_chr[i] - '0';
|
|
if (MUL_OVERFLOW_SIGNED_VALUE_P(e, (SIGNED_VALUE)BASE_FIG))
|
|
goto exp_overflow;
|
|
if (es > (SIGNED_VALUE)(e * BASE_FIG)) {
|
|
exp_overflow:
|
|
exponent_overflow = 1;
|
|
e = es; /* keep sign */
|
|
break;
|
|
}
|
|
++i;
|
|
}
|
|
}
|
|
|
|
/* get integer part */
|
|
i = 0;
|
|
sign = 1;
|
|
if (1 /*ni >= 0*/) {
|
|
if (int_chr[0] == '-') {
|
|
sign = -1;
|
|
++i;
|
|
++mi;
|
|
}
|
|
else if (int_chr[0] == '+') {
|
|
++i;
|
|
++mi;
|
|
}
|
|
}
|
|
|
|
e = signe * e; /* e: The value of exponent part. */
|
|
e = e + ni; /* set actual exponent size. */
|
|
|
|
if (e > 0) signe = 1;
|
|
else signe = -1;
|
|
|
|
/* Adjust the exponent so that it is the multiple of BASE_FIG. */
|
|
j = 0;
|
|
ef = 1;
|
|
while (ef) {
|
|
if (e >= 0) eb = e;
|
|
else eb = -e;
|
|
ef = eb / (SIGNED_VALUE)BASE_FIG;
|
|
ef = eb - ef * (SIGNED_VALUE)BASE_FIG;
|
|
if (ef) {
|
|
++j; /* Means to add one more preceding zero */
|
|
++e;
|
|
}
|
|
}
|
|
|
|
eb = e / (SIGNED_VALUE)BASE_FIG;
|
|
|
|
if (exponent_overflow) {
|
|
int zero = 1;
|
|
for ( ; i < mi && zero; i++) zero = int_chr[i] == '0';
|
|
for (i = 0; i < nf && zero; i++) zero = frac[i] == '0';
|
|
if (!zero && signe > 0) {
|
|
VpSetInf(a, sign);
|
|
VpException(VP_EXCEPTION_INFINITY, "exponent overflow",0);
|
|
}
|
|
else VpSetZero(a, sign);
|
|
return 1;
|
|
}
|
|
|
|
ind_a = 0;
|
|
while (i < mi) {
|
|
a->frac[ind_a] = 0;
|
|
while (j < BASE_FIG && i < mi) {
|
|
a->frac[ind_a] = a->frac[ind_a] * 10 + int_chr[i] - '0';
|
|
++j;
|
|
++i;
|
|
}
|
|
if (i < mi) {
|
|
++ind_a;
|
|
if (ind_a >= ma) goto over_flow;
|
|
j = 0;
|
|
}
|
|
}
|
|
|
|
/* get fraction part */
|
|
|
|
i = 0;
|
|
while (i < nf) {
|
|
while (j < BASE_FIG && i < nf) {
|
|
a->frac[ind_a] = a->frac[ind_a] * 10 + frac[i] - '0';
|
|
++j;
|
|
++i;
|
|
}
|
|
if (i < nf) {
|
|
++ind_a;
|
|
if (ind_a >= ma) goto over_flow;
|
|
j = 0;
|
|
}
|
|
}
|
|
goto Final;
|
|
|
|
over_flow:
|
|
rb_warn("Conversion from String to BigDecimal overflow (last few digits discarded).");
|
|
|
|
Final:
|
|
if (ind_a >= ma) ind_a = ma - 1;
|
|
while (j < BASE_FIG) {
|
|
a->frac[ind_a] = a->frac[ind_a] * 10;
|
|
++j;
|
|
}
|
|
a->Prec = ind_a + 1;
|
|
a->exponent = eb;
|
|
VpSetSign(a, sign);
|
|
VpNmlz(a);
|
|
return 1;
|
|
}
|
|
|
|
/*
|
|
* [Input]
|
|
* *m ... Real
|
|
* [Output]
|
|
* *d ... fraction part of m(d = 0.xxxxxxx). where # of 'x's is fig.
|
|
* *e ... exponent of m.
|
|
* DBLE_FIG ... Number of digits in a double variable.
|
|
*
|
|
* m -> d*10**e, 0<d<BASE
|
|
* [Returns]
|
|
* 0 ... Zero
|
|
* 1 ... Normal
|
|
* 2 ... Infinity
|
|
* -1 ... NaN
|
|
*/
|
|
VP_EXPORT int
|
|
VpVtoD(double *d, SIGNED_VALUE *e, Real *m)
|
|
{
|
|
size_t ind_m, mm, fig;
|
|
double div;
|
|
int f = 1;
|
|
|
|
if (VpIsNaN(m)) {
|
|
*d = VpGetDoubleNaN();
|
|
*e = 0;
|
|
f = -1; /* NaN */
|
|
goto Exit;
|
|
}
|
|
else if (VpIsPosZero(m)) {
|
|
*d = 0.0;
|
|
*e = 0;
|
|
f = 0;
|
|
goto Exit;
|
|
}
|
|
else if (VpIsNegZero(m)) {
|
|
*d = VpGetDoubleNegZero();
|
|
*e = 0;
|
|
f = 0;
|
|
goto Exit;
|
|
}
|
|
else if (VpIsPosInf(m)) {
|
|
*d = VpGetDoublePosInf();
|
|
*e = 0;
|
|
f = 2;
|
|
goto Exit;
|
|
}
|
|
else if (VpIsNegInf(m)) {
|
|
*d = VpGetDoubleNegInf();
|
|
*e = 0;
|
|
f = 2;
|
|
goto Exit;
|
|
}
|
|
/* Normal number */
|
|
fig = (DBLE_FIG + BASE_FIG - 1) / BASE_FIG;
|
|
ind_m = 0;
|
|
mm = Min(fig, m->Prec);
|
|
*d = 0.0;
|
|
div = 1.;
|
|
while (ind_m < mm) {
|
|
div /= (double)BASE;
|
|
*d = *d + (double)m->frac[ind_m++] * div;
|
|
}
|
|
*e = m->exponent * (SIGNED_VALUE)BASE_FIG;
|
|
*d *= VpGetSign(m);
|
|
|
|
Exit:
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, " VpVtoD: m=%\n", m);
|
|
printf(" d=%e * 10 **%ld\n", *d, *e);
|
|
printf(" DBLE_FIG = %d\n", DBLE_FIG);
|
|
}
|
|
#endif /*BIGDECIMAL_DEBUG */
|
|
return f;
|
|
}
|
|
|
|
/*
|
|
* m <- d
|
|
*/
|
|
VP_EXPORT void
|
|
VpDtoV(Real *m, double d)
|
|
{
|
|
size_t ind_m, mm;
|
|
SIGNED_VALUE ne;
|
|
BDIGIT i;
|
|
double val, val2;
|
|
|
|
if (isnan(d)) {
|
|
VpSetNaN(m);
|
|
goto Exit;
|
|
}
|
|
if (isinf(d)) {
|
|
if (d > 0.0) VpSetPosInf(m);
|
|
else VpSetNegInf(m);
|
|
goto Exit;
|
|
}
|
|
|
|
if (d == 0.0) {
|
|
VpSetZero(m, 1);
|
|
goto Exit;
|
|
}
|
|
val = (d > 0.) ? d : -d;
|
|
ne = 0;
|
|
if (val >= 1.0) {
|
|
while (val >= 1.0) {
|
|
val /= (double)BASE;
|
|
++ne;
|
|
}
|
|
}
|
|
else {
|
|
val2 = 1.0 / (double)BASE;
|
|
while (val < val2) {
|
|
val *= (double)BASE;
|
|
--ne;
|
|
}
|
|
}
|
|
/* Now val = 0.xxxxx*BASE**ne */
|
|
|
|
mm = m->MaxPrec;
|
|
memset(m->frac, 0, mm * sizeof(BDIGIT));
|
|
for (ind_m = 0; val > 0.0 && ind_m < mm; ind_m++) {
|
|
val *= (double)BASE;
|
|
i = (BDIGIT)val;
|
|
val -= (double)i;
|
|
m->frac[ind_m] = i;
|
|
}
|
|
if (ind_m >= mm) ind_m = mm - 1;
|
|
VpSetSign(m, (d > 0.0) ? 1 : -1);
|
|
m->Prec = ind_m + 1;
|
|
m->exponent = ne;
|
|
|
|
VpInternalRound(m, 0, (m->Prec > 0) ? m->frac[m->Prec-1] : 0,
|
|
(BDIGIT)(val*(double)BASE));
|
|
|
|
Exit:
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
printf("VpDtoV d=%30.30e\n", d);
|
|
VPrint(stdout, " m=%\n", m);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
return;
|
|
}
|
|
|
|
/*
|
|
* m <- ival
|
|
*/
|
|
#if 0 /* unused */
|
|
VP_EXPORT void
|
|
VpItoV(Real *m, SIGNED_VALUE ival)
|
|
{
|
|
size_t mm, ind_m;
|
|
size_t val, v1, v2, v;
|
|
int isign;
|
|
SIGNED_VALUE ne;
|
|
|
|
if (ival == 0) {
|
|
VpSetZero(m, 1);
|
|
goto Exit;
|
|
}
|
|
isign = 1;
|
|
val = ival;
|
|
if (ival < 0) {
|
|
isign = -1;
|
|
val =(size_t)(-ival);
|
|
}
|
|
ne = 0;
|
|
ind_m = 0;
|
|
mm = m->MaxPrec;
|
|
while (ind_m < mm) {
|
|
m->frac[ind_m] = 0;
|
|
++ind_m;
|
|
}
|
|
ind_m = 0;
|
|
while (val > 0) {
|
|
if (val) {
|
|
v1 = val;
|
|
v2 = 1;
|
|
while (v1 >= BASE) {
|
|
v1 /= BASE;
|
|
v2 *= BASE;
|
|
}
|
|
val = val - v2 * v1;
|
|
v = v1;
|
|
}
|
|
else {
|
|
v = 0;
|
|
}
|
|
m->frac[ind_m] = v;
|
|
++ind_m;
|
|
++ne;
|
|
}
|
|
m->Prec = ind_m - 1;
|
|
m->exponent = ne;
|
|
VpSetSign(m, isign);
|
|
VpNmlz(m);
|
|
|
|
Exit:
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
printf(" VpItoV i=%d\n", ival);
|
|
VPrint(stdout, " m=%\n", m);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
return;
|
|
}
|
|
#endif
|
|
|
|
/*
|
|
* y = SQRT(x), y*y - x =>0
|
|
*/
|
|
VP_EXPORT int
|
|
VpSqrt(Real *y, Real *x)
|
|
{
|
|
Real *f = NULL;
|
|
Real *r = NULL;
|
|
size_t y_prec;
|
|
SIGNED_VALUE n, e;
|
|
SIGNED_VALUE prec;
|
|
ssize_t nr;
|
|
double val;
|
|
|
|
/* Zero, NaN or Infinity ? */
|
|
if (!VpHasVal(x)) {
|
|
if (VpIsZero(x) || VpGetSign(x) > 0) {
|
|
VpAsgn(y,x,1);
|
|
goto Exit;
|
|
}
|
|
VpSetNaN(y);
|
|
return VpException(VP_EXCEPTION_OP, "(VpSqrt) SQRT(NaN or negative value)", 0);
|
|
goto Exit;
|
|
}
|
|
|
|
/* Negative ? */
|
|
if (VpGetSign(x) < 0) {
|
|
VpSetNaN(y);
|
|
return VpException(VP_EXCEPTION_OP, "(VpSqrt) SQRT(negative value)", 0);
|
|
}
|
|
|
|
/* One ? */
|
|
if (VpIsOne(x)) {
|
|
VpSetOne(y);
|
|
goto Exit;
|
|
}
|
|
|
|
n = (SIGNED_VALUE)y->MaxPrec;
|
|
if (x->MaxPrec > (size_t)n) n = (ssize_t)x->MaxPrec;
|
|
/* allocate temporally variables */
|
|
f = VpAlloc(y->MaxPrec * (BASE_FIG + 2), "#1");
|
|
r = VpAlloc((n + n) * (BASE_FIG + 2), "#1");
|
|
|
|
nr = 0;
|
|
y_prec = y->MaxPrec;
|
|
|
|
prec = x->exponent - (ssize_t)y_prec;
|
|
if (x->exponent > 0)
|
|
++prec;
|
|
else
|
|
--prec;
|
|
|
|
VpVtoD(&val, &e, x); /* val <- x */
|
|
e /= (SIGNED_VALUE)BASE_FIG;
|
|
n = e / 2;
|
|
if (e - n * 2 != 0) {
|
|
val /= BASE;
|
|
n = (e + 1) / 2;
|
|
}
|
|
VpDtoV(y, sqrt(val)); /* y <- sqrt(val) */
|
|
y->exponent += n;
|
|
n = (SIGNED_VALUE)((DBLE_FIG + BASE_FIG - 1) / BASE_FIG);
|
|
y->MaxPrec = Min((size_t)n , y_prec);
|
|
f->MaxPrec = y->MaxPrec + 1;
|
|
n = (SIGNED_VALUE)(y_prec * BASE_FIG);
|
|
if (n < (SIGNED_VALUE)maxnr) n = (SIGNED_VALUE)maxnr;
|
|
do {
|
|
y->MaxPrec *= 2;
|
|
if (y->MaxPrec > y_prec) y->MaxPrec = y_prec;
|
|
f->MaxPrec = y->MaxPrec;
|
|
VpDivd(f, r, x, y); /* f = x/y */
|
|
VpAddSub(r, f, y, -1); /* r = f - y */
|
|
VpMult(f, VpPt5, r); /* f = 0.5*r */
|
|
if (VpIsZero(f)) goto converge;
|
|
VpAddSub(r, f, y, 1); /* r = y + f */
|
|
VpAsgn(y, r, 1); /* y = r */
|
|
if (f->exponent <= prec) goto converge;
|
|
} while(++nr < n);
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
printf("ERROR(VpSqrt): did not converge within %ld iterations.\n", nr);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
y->MaxPrec = y_prec;
|
|
|
|
converge:
|
|
VpChangeSign(y, 1);
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VpMult(r, y, y);
|
|
VpAddSub(f, x, r, -1);
|
|
printf("VpSqrt: iterations = %"PRIdSIZE"\n", nr);
|
|
VPrint(stdout, " y =% \n", y);
|
|
VPrint(stdout, " x =% \n", x);
|
|
VPrint(stdout, " x-y*y = % \n", f);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
y->MaxPrec = y_prec;
|
|
|
|
Exit:
|
|
VpFree(f);
|
|
VpFree(r);
|
|
return 1;
|
|
}
|
|
|
|
/*
|
|
*
|
|
* nf: digit position for operation.
|
|
*
|
|
*/
|
|
VP_EXPORT int
|
|
VpMidRound(Real *y, unsigned short f, ssize_t nf)
|
|
/*
|
|
* Round relatively from the decimal point.
|
|
* f: rounding mode
|
|
* nf: digit location to round from the decimal point.
|
|
*/
|
|
{
|
|
/* fracf: any positive digit under rounding position? */
|
|
/* fracf_1further: any positive digits under one further than the rounding position? */
|
|
/* exptoadd: number of digits needed to compensate negative nf */
|
|
int fracf, fracf_1further;
|
|
ssize_t n,i,ix,ioffset, exptoadd;
|
|
BDIGIT v, shifter;
|
|
BDIGIT div;
|
|
|
|
nf += y->exponent * (ssize_t)BASE_FIG;
|
|
exptoadd=0;
|
|
if (nf < 0) {
|
|
/* rounding position too left(large). */
|
|
if (f != VP_ROUND_CEIL && f != VP_ROUND_FLOOR) {
|
|
VpSetZero(y, VpGetSign(y)); /* truncate everything */
|
|
return 0;
|
|
}
|
|
exptoadd = -nf;
|
|
nf = 0;
|
|
}
|
|
|
|
ix = nf / (ssize_t)BASE_FIG;
|
|
if ((size_t)ix >= y->Prec) return 0; /* rounding position too right(small). */
|
|
v = y->frac[ix];
|
|
|
|
ioffset = nf - ix*(ssize_t)BASE_FIG;
|
|
n = (ssize_t)BASE_FIG - ioffset - 1;
|
|
for (shifter = 1, i = 0; i < n; ++i) shifter *= 10;
|
|
|
|
/* so the representation used (in y->frac) is an array of BDIGIT, where
|
|
each BDIGIT contains a value between 0 and BASE-1, consisting of BASE_FIG
|
|
decimal places.
|
|
|
|
(that numbers of decimal places are typed as ssize_t is somewhat confusing)
|
|
|
|
nf is now position (in decimal places) of the digit from the start of
|
|
the array.
|
|
|
|
ix is the position (in BDIGITS) of the BDIGIT containing the decimal digit,
|
|
from the start of the array.
|
|
|
|
v is the value of this BDIGIT
|
|
|
|
ioffset is the number of extra decimal places along of this decimal digit
|
|
within v.
|
|
|
|
n is the number of decimal digits remaining within v after this decimal digit
|
|
shifter is 10**n,
|
|
|
|
v % shifter are the remaining digits within v
|
|
v % (shifter * 10) are the digit together with the remaining digits within v
|
|
v / shifter are the digit's predecessors together with the digit
|
|
div = v / shifter / 10 is just the digit's precessors
|
|
(v / shifter) - div*10 is just the digit, which is what v ends up being reassigned to.
|
|
*/
|
|
|
|
fracf = (v % (shifter * 10) > 0);
|
|
fracf_1further = ((v % shifter) > 0);
|
|
|
|
v /= shifter;
|
|
div = v / 10;
|
|
v = v - div*10;
|
|
/* now v is just the digit required.
|
|
now fracf is whether the digit or any of the remaining digits within v are non-zero
|
|
now fracf_1further is whether any of the remaining digits within v are non-zero
|
|
*/
|
|
|
|
/* now check all the remaining BDIGITS for zero-ness a whole BDIGIT at a time.
|
|
if we spot any non-zeroness, that means that we found a positive digit under
|
|
rounding position, and we also found a positive digit under one further than
|
|
the rounding position, so both searches (to see if any such non-zero digit exists)
|
|
can stop */
|
|
|
|
for (i = ix + 1; (size_t)i < y->Prec; i++) {
|
|
if (y->frac[i] % BASE) {
|
|
fracf = fracf_1further = 1;
|
|
break;
|
|
}
|
|
}
|
|
|
|
/* now fracf = does any positive digit exist under the rounding position?
|
|
now fracf_1further = does any positive digit exist under one further than the
|
|
rounding position?
|
|
now v = the first digit under the rounding position */
|
|
|
|
/* drop digits after pointed digit */
|
|
memset(y->frac + ix + 1, 0, (y->Prec - (ix + 1)) * sizeof(BDIGIT));
|
|
|
|
switch (f) {
|
|
case VP_ROUND_DOWN: /* Truncate */
|
|
break;
|
|
case VP_ROUND_UP: /* Roundup */
|
|
if (fracf) ++div;
|
|
break;
|
|
case VP_ROUND_HALF_UP:
|
|
if (v>=5) ++div;
|
|
break;
|
|
case VP_ROUND_HALF_DOWN:
|
|
if (v > 5 || (v == 5 && fracf_1further)) ++div;
|
|
break;
|
|
case VP_ROUND_CEIL:
|
|
if (fracf && (VpGetSign(y) > 0)) ++div;
|
|
break;
|
|
case VP_ROUND_FLOOR:
|
|
if (fracf && (VpGetSign(y) < 0)) ++div;
|
|
break;
|
|
case VP_ROUND_HALF_EVEN: /* Banker's rounding */
|
|
if (v > 5) ++div;
|
|
else if (v == 5) {
|
|
if (fracf_1further) {
|
|
++div;
|
|
}
|
|
else {
|
|
if (ioffset == 0) {
|
|
/* v is the first decimal digit of its BDIGIT;
|
|
need to grab the previous BDIGIT if present
|
|
to check for evenness of the previous decimal
|
|
digit (which is same as that of the BDIGIT since
|
|
base 10 has a factor of 2) */
|
|
if (ix && (y->frac[ix-1] % 2)) ++div;
|
|
}
|
|
else {
|
|
if (div % 2) ++div;
|
|
}
|
|
}
|
|
}
|
|
break;
|
|
}
|
|
for (i = 0; i <= n; ++i) div *= 10;
|
|
if (div >= BASE) {
|
|
if (ix) {
|
|
y->frac[ix] = 0;
|
|
VpRdup(y, ix);
|
|
}
|
|
else {
|
|
short s = VpGetSign(y);
|
|
SIGNED_VALUE e = y->exponent;
|
|
VpSetOne(y);
|
|
VpSetSign(y, s);
|
|
y->exponent = e + 1;
|
|
}
|
|
}
|
|
else {
|
|
y->frac[ix] = div;
|
|
VpNmlz(y);
|
|
}
|
|
if (exptoadd > 0) {
|
|
y->exponent += (SIGNED_VALUE)(exptoadd / BASE_FIG);
|
|
exptoadd %= (ssize_t)BASE_FIG;
|
|
for (i = 0; i < exptoadd; i++) {
|
|
y->frac[0] *= 10;
|
|
if (y->frac[0] >= BASE) {
|
|
y->frac[0] /= BASE;
|
|
y->exponent++;
|
|
}
|
|
}
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
VP_EXPORT int
|
|
VpLeftRound(Real *y, unsigned short f, ssize_t nf)
|
|
/*
|
|
* Round from the left hand side of the digits.
|
|
*/
|
|
{
|
|
BDIGIT v;
|
|
if (!VpHasVal(y)) return 0; /* Unable to round */
|
|
v = y->frac[0];
|
|
nf -= VpExponent(y) * (ssize_t)BASE_FIG;
|
|
while ((v /= 10) != 0) nf--;
|
|
nf += (ssize_t)BASE_FIG-1;
|
|
return VpMidRound(y, f, nf);
|
|
}
|
|
|
|
VP_EXPORT int
|
|
VpActiveRound(Real *y, Real *x, unsigned short f, ssize_t nf)
|
|
{
|
|
/* First,assign whole value in truncation mode */
|
|
if (VpAsgn(y, x, 10) <= 1) return 0; /* Zero,NaN,or Infinity */
|
|
return VpMidRound(y, f, nf);
|
|
}
|
|
|
|
static int
|
|
VpLimitRound(Real *c, size_t ixDigit)
|
|
{
|
|
size_t ix = VpGetPrecLimit();
|
|
if (!VpNmlz(c)) return -1;
|
|
if (!ix) return 0;
|
|
if (!ixDigit) ixDigit = c->Prec-1;
|
|
if ((ix + BASE_FIG - 1) / BASE_FIG > ixDigit + 1) return 0;
|
|
return VpLeftRound(c, VpGetRoundMode(), (ssize_t)ix);
|
|
}
|
|
|
|
/* If I understand correctly, this is only ever used to round off the final decimal
|
|
digit of precision */
|
|
static void
|
|
VpInternalRound(Real *c, size_t ixDigit, BDIGIT vPrev, BDIGIT v)
|
|
{
|
|
int f = 0;
|
|
|
|
unsigned short const rounding_mode = VpGetRoundMode();
|
|
|
|
if (VpLimitRound(c, ixDigit)) return;
|
|
if (!v) return;
|
|
|
|
v /= BASE1;
|
|
switch (rounding_mode) {
|
|
case VP_ROUND_DOWN:
|
|
break;
|
|
case VP_ROUND_UP:
|
|
if (v) f = 1;
|
|
break;
|
|
case VP_ROUND_HALF_UP:
|
|
if (v >= 5) f = 1;
|
|
break;
|
|
case VP_ROUND_HALF_DOWN:
|
|
/* this is ok - because this is the last digit of precision,
|
|
the case where v == 5 and some further digits are nonzero
|
|
will never occur */
|
|
if (v >= 6) f = 1;
|
|
break;
|
|
case VP_ROUND_CEIL:
|
|
if (v && (VpGetSign(c) > 0)) f = 1;
|
|
break;
|
|
case VP_ROUND_FLOOR:
|
|
if (v && (VpGetSign(c) < 0)) f = 1;
|
|
break;
|
|
case VP_ROUND_HALF_EVEN: /* Banker's rounding */
|
|
/* as per VP_ROUND_HALF_DOWN, because this is the last digit of precision,
|
|
there is no case to worry about where v == 5 and some further digits are nonzero */
|
|
if (v > 5) f = 1;
|
|
else if (v == 5 && vPrev % 2) f = 1;
|
|
break;
|
|
}
|
|
if (f) {
|
|
VpRdup(c, ixDigit);
|
|
VpNmlz(c);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* Rounds up m(plus one to final digit of m).
|
|
*/
|
|
static int
|
|
VpRdup(Real *m, size_t ind_m)
|
|
{
|
|
BDIGIT carry;
|
|
|
|
if (!ind_m) ind_m = m->Prec;
|
|
|
|
carry = 1;
|
|
while (carry > 0 && ind_m--) {
|
|
m->frac[ind_m] += carry;
|
|
if (m->frac[ind_m] >= BASE) m->frac[ind_m] -= BASE;
|
|
else carry = 0;
|
|
}
|
|
if (carry > 0) { /* Overflow,count exponent and set fraction part be 1 */
|
|
if (!AddExponent(m, 1)) return 0;
|
|
m->Prec = m->frac[0] = 1;
|
|
}
|
|
else {
|
|
VpNmlz(m);
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
/*
|
|
* y = x - fix(x)
|
|
*/
|
|
VP_EXPORT void
|
|
VpFrac(Real *y, Real *x)
|
|
{
|
|
size_t my, ind_y, ind_x;
|
|
|
|
if (!VpHasVal(x)) {
|
|
VpAsgn(y, x, 1);
|
|
goto Exit;
|
|
}
|
|
|
|
if (x->exponent > 0 && (size_t)x->exponent >= x->Prec) {
|
|
VpSetZero(y, VpGetSign(x));
|
|
goto Exit;
|
|
}
|
|
else if (x->exponent <= 0) {
|
|
VpAsgn(y, x, 1);
|
|
goto Exit;
|
|
}
|
|
|
|
/* satisfy: x->exponent > 0 */
|
|
|
|
y->Prec = x->Prec - (size_t)x->exponent;
|
|
y->Prec = Min(y->Prec, y->MaxPrec);
|
|
y->exponent = 0;
|
|
VpSetSign(y, VpGetSign(x));
|
|
ind_y = 0;
|
|
my = y->Prec;
|
|
ind_x = x->exponent;
|
|
while (ind_y < my) {
|
|
y->frac[ind_y] = x->frac[ind_x];
|
|
++ind_y;
|
|
++ind_x;
|
|
}
|
|
VpNmlz(y);
|
|
|
|
Exit:
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, "VpFrac y=%\n", y);
|
|
VPrint(stdout, " x=%\n", x);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
return;
|
|
}
|
|
|
|
/*
|
|
* y = x ** n
|
|
*/
|
|
VP_EXPORT int
|
|
VpPower(Real *y, Real *x, SIGNED_VALUE n)
|
|
{
|
|
size_t s, ss;
|
|
ssize_t sign;
|
|
Real *w1 = NULL;
|
|
Real *w2 = NULL;
|
|
|
|
if (VpIsZero(x)) {
|
|
if (n == 0) {
|
|
VpSetOne(y);
|
|
goto Exit;
|
|
}
|
|
sign = VpGetSign(x);
|
|
if (n < 0) {
|
|
n = -n;
|
|
if (sign < 0) sign = (n % 2) ? -1 : 1;
|
|
VpSetInf(y, sign);
|
|
}
|
|
else {
|
|
if (sign < 0) sign = (n % 2) ? -1 : 1;
|
|
VpSetZero(y,sign);
|
|
}
|
|
goto Exit;
|
|
}
|
|
if (VpIsNaN(x)) {
|
|
VpSetNaN(y);
|
|
goto Exit;
|
|
}
|
|
if (VpIsInf(x)) {
|
|
if (n == 0) {
|
|
VpSetOne(y);
|
|
goto Exit;
|
|
}
|
|
if (n > 0) {
|
|
VpSetInf(y, (n % 2 == 0 || VpIsPosInf(x)) ? 1 : -1);
|
|
goto Exit;
|
|
}
|
|
VpSetZero(y, (n % 2 == 0 || VpIsPosInf(x)) ? 1 : -1);
|
|
goto Exit;
|
|
}
|
|
|
|
if (x->exponent == 1 && x->Prec == 1 && x->frac[0] == 1) {
|
|
/* abs(x) = 1 */
|
|
VpSetOne(y);
|
|
if (VpGetSign(x) > 0) goto Exit;
|
|
if ((n % 2) == 0) goto Exit;
|
|
VpSetSign(y, -1);
|
|
goto Exit;
|
|
}
|
|
|
|
if (n > 0) sign = 1;
|
|
else if (n < 0) {
|
|
sign = -1;
|
|
n = -n;
|
|
}
|
|
else {
|
|
VpSetOne(y);
|
|
goto Exit;
|
|
}
|
|
|
|
/* Allocate working variables */
|
|
|
|
w1 = VpAlloc((y->MaxPrec + 2) * BASE_FIG, "#0");
|
|
w2 = VpAlloc((w1->MaxPrec * 2 + 1) * BASE_FIG, "#0");
|
|
/* calculation start */
|
|
|
|
VpAsgn(y, x, 1);
|
|
--n;
|
|
while (n > 0) {
|
|
VpAsgn(w1, x, 1);
|
|
s = 1;
|
|
while (ss = s, (s += s) <= (size_t)n) {
|
|
VpMult(w2, w1, w1);
|
|
VpAsgn(w1, w2, 1);
|
|
}
|
|
n -= (SIGNED_VALUE)ss;
|
|
VpMult(w2, y, w1);
|
|
VpAsgn(y, w2, 1);
|
|
}
|
|
if (sign < 0) {
|
|
VpDivd(w1, w2, VpConstOne, y);
|
|
VpAsgn(y, w1, 1);
|
|
}
|
|
|
|
Exit:
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
if (gfDebug) {
|
|
VPrint(stdout, "VpPower y=%\n", y);
|
|
VPrint(stdout, "VpPower x=%\n", x);
|
|
printf(" n=%d\n", n);
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|
|
VpFree(w2);
|
|
VpFree(w1);
|
|
return 1;
|
|
}
|
|
|
|
#ifdef BIGDECIMAL_DEBUG
|
|
int
|
|
VpVarCheck(Real * v)
|
|
/*
|
|
* Checks the validity of the Real variable v.
|
|
* [Input]
|
|
* v ... Real *, variable to be checked.
|
|
* [Returns]
|
|
* 0 ... correct v.
|
|
* other ... error
|
|
*/
|
|
{
|
|
size_t i;
|
|
|
|
if (v->MaxPrec <= 0) {
|
|
printf("ERROR(VpVarCheck): Illegal Max. Precision(=%"PRIuSIZE")\n",
|
|
v->MaxPrec);
|
|
return 1;
|
|
}
|
|
if (v->Prec <= 0 || v->Prec > v->MaxPrec) {
|
|
printf("ERROR(VpVarCheck): Illegal Precision(=%"PRIuSIZE")\n", v->Prec);
|
|
printf(" Max. Prec.=%"PRIuSIZE"\n", v->MaxPrec);
|
|
return 2;
|
|
}
|
|
for (i = 0; i < v->Prec; ++i) {
|
|
if (v->frac[i] >= BASE) {
|
|
printf("ERROR(VpVarCheck): Illegal fraction\n");
|
|
printf(" Frac[%"PRIuSIZE"]=%lu\n", i, v->frac[i]);
|
|
printf(" Prec. =%"PRIuSIZE"\n", v->Prec);
|
|
printf(" Exp. =%"PRIdVALUE"\n", v->exponent);
|
|
printf(" BASE =%lu\n", BASE);
|
|
return 3;
|
|
}
|
|
}
|
|
return 0;
|
|
}
|
|
#endif /* BIGDECIMAL_DEBUG */
|