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authormrkn <mrkn@b2dd03c8-39d4-4d8f-98ff-823fe69b080e>2010-09-18 20:19:38 +0000
committermrkn <mrkn@b2dd03c8-39d4-4d8f-98ff-823fe69b080e>2010-09-18 20:19:38 +0000
commit3cbda570c22f0324502a43dc668223b3da5d241b (patch)
tree01a39613da904d9358d63140eef7e17cae8ccbc7 /ext/bigdecimal
parent9dffbcfc09dc54d77bfb99dc91e0c5ea01182925 (diff)
* ext/bigdecimal/bigdecimal.c: fix rounding algorithms for half-down
and half-even. This change is based on the patch created by Matthew Willson, the reporter of this bug. [Bug #3803] [ruby-core:32136] * test/bigdecimal/test_bigdecimal.rb: add tests for above changes. git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@29293 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
Diffstat (limited to 'ext/bigdecimal')
-rw-r--r--ext/bigdecimal/bigdecimal.c165
1 files changed, 111 insertions, 54 deletions
diff --git a/ext/bigdecimal/bigdecimal.c b/ext/bigdecimal/bigdecimal.c
index 776615e..18638e1 100644
--- a/ext/bigdecimal/bigdecimal.c
+++ b/ext/bigdecimal/bigdecimal.c
@@ -308,9 +308,9 @@ BigDecimal_load(VALUE self, VALUE str)
*
* ROUND_UP:: round away from zero
* ROUND_DOWN:: round towards zero (truncate)
- * ROUND_HALF_UP:: round up if the appropriate digit >= 5, otherwise truncate (default)
- * ROUND_HALF_DOWN:: round up if the appropriate digit >= 6, otherwise truncate
- * ROUND_HALF_EVEN:: round towards the even neighbor (Banker's rounding)
+ * ROUND_HALF_UP:: round towards the nearest neighbor, unless both neighbors are equidistant, in which case round away from zero. (default)
+ * ROUND_HALF_DOWN:: round towards the nearest neighbor, unless both neighbors are equidistant, in which case round towards zero.
+ * ROUND_HALF_EVEN:: round towards the nearest neighbor, unless both neighbors are equidistant, in which case round towards the even neighbor (Banker's rounding)
* ROUND_CEILING:: round towards positive infinity (ceil)
* ROUND_FLOOR:: round towards negative infinity (floor)
*
@@ -4559,8 +4559,9 @@ VpMidRound(Real *y, unsigned short f, ssize_t nf)
*/
{
/* 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;
+ int fracf, fracf_1further;
ssize_t n,i,ix,ioffset, exptoadd;
BDIGIT v, shifter;
BDIGIT div;
@@ -4573,62 +4574,111 @@ VpMidRound(Real *y, unsigned short f, ssize_t nf)
VpSetZero(y,VpGetSign(y)); /* truncate everything */
return 0;
}
- exptoadd = -nf;
- nf = 0;
+ exptoadd = -nf;
+ nf = 0;
}
- /* ix: x->fraq[ix] contains round position */
ix = nf / (ssize_t)BASE_FIG;
if ((size_t)ix >= y->Prec) return 0; /* rounding position too right(small). */
- ioffset = nf - ix*(ssize_t)BASE_FIG;
-
v = y->frac[ix];
- /* drop digits after pointed digit */
+ 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;
- if (fracf == 0) {
- for (i=ix+1; (size_t)i < y->Prec; i++) {
- if (y->frac[i] % BASE) {
- fracf = 1;
- break;
- }
- }
+ /* 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 foudn 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: /* Round half up */
+ break;
+ case VP_ROUND_HALF_UP:
if (v>=5) ++div;
break;
- case VP_ROUND_HALF_DOWN: /* Round half down */
- if (v>=6) ++div;
+ case VP_ROUND_HALF_DOWN:
+ if (v > 5 || (v == 5 && fracf_1further)) ++div;
break;
- case VP_ROUND_CEIL: /* ceil */
+ case VP_ROUND_CEIL:
if (fracf && (VpGetSign(y)>0)) ++div;
break;
- case VP_ROUND_FLOOR: /* floor */
+ 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 ((size_t)i == (BASE_FIG-1)) {
- if (ix && (y->frac[ix-1]%2)) ++div;
- }
+ if (v > 5) ++div;
+ else if (v == 5) {
+ if (fracf_1further) {
+ ++div;
+ }
else {
- if (div%2) ++div;
- }
- }
- break;
+ 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) {
@@ -4694,6 +4744,8 @@ VpLimitRound(Real *c, size_t ixDigit)
return VpLeftRound(c, (int)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)
{
@@ -4701,36 +4753,41 @@ VpInternalRound(Real *c, size_t ixDigit, BDIGIT vPrev, BDIGIT v)
unsigned short const rounding_mode = VpGetRoundMode();
- if(VpLimitRound(c,ixDigit)) return;
- if(!v) return;
+ if (VpLimitRound(c, ixDigit)) return;
+ if (!v) return;
v /= BASE1;
switch (rounding_mode) {
case VP_ROUND_DOWN:
- break;
+ break;
case VP_ROUND_UP:
- if(v) f = 1;
- break;
+ if (v) f = 1;
+ break;
case VP_ROUND_HALF_UP:
- if(v >= 5) f = 1;
- break;
+ if (v >= 5) f = 1;
+ break;
case VP_ROUND_HALF_DOWN:
- if(v >= 6) f = 1;
- break;
- case VP_ROUND_CEIL: /* ceil */
- if(v && (VpGetSign(c)>0)) f = 1;
- break;
- case VP_ROUND_FLOOR: /* floor */
- if(v && (VpGetSign(c)<0)) f = 1;
- break;
+ /* 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 */
- if(v>5) f = 1;
- else if(v==5 && vPrev%2) f = 1;
- break;
- }
- if(f) {
- VpRdup(c,ixDigit); /* round up */
- VpNmlz(c);
+ /* 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);
}
}