# $BN\_\>h$,CY$$(B

**URL:** <https://www.ruby-forum.com/t/bn-h-cy-b/92977>\
**Category:** Development\
**Created:** [April 26, 2007, 6:13am UTC](https://www.ruby-forum.com/t/bn-h-cy-b/92977 "2007-04-26T06:13:57Z")\
**Posts on this page:** 6\
**Page:** 1

<div class="post-metadata">

**Author:** ![nobu](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/n/e9c0ed/32.png) [@nobu](https://www.ruby-forum.com/u/nobu)\
**Post date:** [April 26, 2007, 6:13am UTC](https://www.ruby-forum.com/t/bn-h-cy-b/92977/1 "2007-04-26T06:13:57Z")

</div>

e$B$J$+$@$G$9!#e(B

[http://yowaken.dip.jp/tdiary/20070425.html#p02](http://yowaken.dip.jp/tdiary/20070425.html#p02) e$B$K$“$k$h$&$K3N$+e(B  
e$B$KN\_\>h$,CY$$$h$&$G$9!#e(BFixnume$B$G=\<J,$J1i;;$be(BBignume$B$s$G9T$C$F$$$ke(B  
e$B$N$,Bg$-$$$h$&$G$9$,!”$=$l$@$1$G$b$J$$$h$&$G!"$3$l$G$b$^$@e(Bruby  
e$BHG$h$j\>/!9CY$$$h$&$G$9!#e(B

# Index: bignum.c

— bignum.c (revision 12216)  
+++ bignum.c (working copy)  
@@ -1553,5 +1553,5 @@ rb\_big\_pow(VALUE x, VALUE y)  
yy = FIX2LONG(y);  
if (yy \> 0) {

- 

```
 VALUE z = x;

```

- 

```
 VALUE z = (yy & 1) ? x : 0;

 if (RBIGNUM(x)->len * SIZEOF_BDIGITS * yy > 1024*1024) {

```

@@ -1560,13 +1560,11 @@ rb\_big\_pow(VALUE x, VALUE y)  
break;  
}

- 

```
 for (;;) {

```

- yy -= 1;
- if (yy == 0) break;
- while (yy % 2 == 0) {

- 

```
 while (yy &= ~1) {

```

- do {  
yy /= 2;  
x = rb\_big\_mul0(x, x);  
if (!BDIGITS(x)[RBIGNUM(x)-\>len-1]) RBIGNUM(x)-\>len–;

- }
- z = rb\_big\_mul0(z, x);

- } while (yy % 2 == 0);
- z = z ? rb\_big\_mul0(z, x) : x;  
if (!BDIGITS(z)[RBIGNUM(z)-\>len-1]) RBIGNUM(z)-\>len–;  
}  
Index: numeric.c  
===================================================================  
— numeric.c (revision 12216)  
+++ numeric.c (working copy)  
@@ -2260,4 +2260,35 @@ fix\_divmod(VALUE x, VALUE y)  
}

+static VALUE  
+int\_pow(long x, unsigned long y)  
+{

- int sign = x \< 0;
- long z = 1;
- 
- if (sign) x = -x;
- if (y & 1) z = x;
- y &= ~1;
- do {
- while (y % 2 == 0) {
- 

```
 long x2 = x * x;

```

- 

```
 if (x2 < x || !POSFIXABLE(x2)) {

```

- 

```
   bignum:

```

- return rb\_big\_mul(rb\_big\_pow(rb\_int2big(x), LONG2NUM(y)),
- 

```
     rb_int2big(z));

```

- 

```
 }

```

- 

```
 x = x2;

```

- 

```
 y >>= 1;

```

- }
- {
- 

```
 long xz = x * z;

```

- 

```
 if (xz < z || xz < x || !POSFIXABLE(xz)) {

```

- goto bignum;
- 

```
 }

```

- 

```
 z = xz;

```

- }
- } while (–y);
- return LONG2NUM(z);  
+}
- 

/\*

- call-seq:  
@@ -2283,5 +2314,5 @@ fix\_pow(VALUE x, VALUE y)  
a = FIX2LONG(x);  
if (b \> 0) {

- 

```
 return rb_big_pow(rb_int2big(a), y);

```

- 

```
 return int_pow(a, b);

```

}  
return rb\_float\_new(pow((double)a, (double)b));

---

<div class="post-metadata">

**Author:** ![nobu](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/n/e9c0ed/32.png) [@nobu](https://www.ruby-forum.com/u/nobu)\
**Post date:** [April 26, 2007, 7:03am UTC](https://www.ruby-forum.com/t/bn-h-cy-b/92977/2 "2007-04-26T07:03:59Z")

</div>

e$B$J$+$@$G$9!#e(B

At Thu, 26 Apr 2007 13:12:48 +0900,  
Nobuyoshi N. wrote in [ruby-dev:30726]:

> +static VALUE  
> +int\_pow(long x, unsigned long y)  
> +{
> 
> - int sign = x \< 0;
> - long z = 1;
> - 
> - if (sign) x = -x;

e$BId9f$rLa$9$N$rK:$l$F$^$7$?!#e(B

> - 
> 
> ```
> if (x2 < x || !POSFIXABLE(x2)) {
> 
> ```
> 
> - 
> 
> ```
> bignum:
> 
> ```
> 
> - return rb\_big\_mul(rb\_big\_pow(rb\_int2big(x), LONG2NUM(y)),

- 

```
     rb_int2big(sign ? -z : z));

```

> - } while (–y);

- if (sign) z = -z;

---

<div class="post-metadata">

**Author:** ![nobu](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/n/e9c0ed/32.png) [@nobu](https://www.ruby-forum.com/u/nobu)\
**Post date:** [April 26, 2007, 8:26am UTC](https://www.ruby-forum.com/t/bn-h-cy-b/92977/3 "2007-04-26T08:26:07Z")

</div>

e$B$^$D$b$He(B e$B$f$-$R$m$G$9e(B

In message “Re: [ruby-dev:30726] e$BN\_\>h$,CY$$e(B”  
on Thu, 26 Apr 2007 13:12:48 +0900, Nobuyoshi N.  
[removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) writes:  
|  
|e$B$J$+$@$G$9!#e(B  
|  
|[http://yowaken.dip.jp/tdiary/20070425.html#p02](http://yowaken.dip.jp/tdiary/20070425.html#p02) e$B$K$“$k$h$&$K3N$+e(B  
|e$B$KN\_\>h$,CY$$$h$&$G$9!#e(BFixnume$B$G=\<J,$J1i;;$be(BBignume$B$s$G9T$C$F$$$ke(B  
|e$B$N$,Bg$-$$$h$&$G$9$,!”$=$l$@$1$G$b$J$$$h$&$G!"$3$l$G$b$^$@e(Bruby  
|e$BHG$h$j\>/!9CY$$$h$&$G$9!#e(B

e$B$H$j$"$($:e(Btrunke$B$K%3%_%C%H$7$F$/$@$5$$!#$,!"$3$l$G$be(BRubye$BHV$he(B  
e$B$jM_$7$$$C$F$N$O?R\>o$8$c$J$$$G$9$M!#$I$&$7$F$J$s$@$m$&!)e(B

---

<div class="post-metadata">

**Author:** ![nobu](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/n/e9c0ed/32.png) [@nobu](https://www.ruby-forum.com/u/nobu)\
**Post date:** [April 26, 2007, 1:34pm UTC](https://www.ruby-forum.com/t/bn-h-cy-b/92977/4 "2007-04-26T13:34:54Z")

</div>

e$BLxED$G$9!#e(B

1.8.5 e$B$G$OFC$KCY$$$H$$$&$3$H$O$J$/e(B 1.8.6 e$B$G$OCY$+$C$?$N$G!"e(B  
ruby\_1\_8 e$B%V%i%s%A$G$I$3$+$iCY$/$J$C$F$k$+D4$Y$F$\_$^$7$?!#e(B

r10880 e$B$N%3%\_%C%He(B

* * *

r10880 | matz | 2006-09-08 01:35:59 +0900 (e$B6be(B, 08 9e$B7ne(B 2006)  
| 9 lines

- numeric.c (fix\_plus): addition in Fixnum will never overflow  
long. a patch from Ondrej B. .  
[ruby-core:08794]

- numeric.c (fix\_minus): ditto.

- bignum.c (rb\_big\_pow): eagerly truncate resulting bignum.  
[ruby-core:08794]

* * *

e$B$G!"N\_\>h$,e(B core dump e$B$9$k$h$&$K$J$C$F$$$^$9!#e(B  
e$B$3$ND\>A0$^$G$O!“LdBj$”$j$^$;$s$G$7$?!#e(B

e$B$3$Ne(B core dump e$B$r=$@5$7$?e(B

* * *

r10898 | matz | 2006-09-10 00:27:34 +0900 (e$BF|e(B, 10 9e$B7ne(B 2006)  
| 5 lines

- bignum.c (rb\_big\_mul0): bignum multiplication without  
normalization.

- bignum.c (rb\_big\_pow): use rb\_big\_mul0(). [ruby-dev:29547]

* * *

e$B$3$3$+$iCY$/$J$C$F$$$k$h$&$G$9!#e(B

---

<div class="post-metadata">

**Author:** ![nobu](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/n/e9c0ed/32.png) [@nobu](https://www.ruby-forum.com/u/nobu)\
**Post date:** [April 26, 2007, 4:43pm UTC](https://www.ruby-forum.com/t/bn-h-cy-b/92977/5 "2007-04-26T16:43:47Z")

</div>

e$B$^$D$b$He(B e$B$f$-$R$m$G$9e(B

In message “Re: [ruby-dev:30734] Re: e$BN\_\>h$,CY$$e(B”  
on Thu, 26 Apr 2007 23:11:16 +0900, Nobuyoshi N.  
[removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) writes:

|\> \* bignum.c (rb\_big\_pow): use rb\_big\_mul0(). [ruby-dev:29547]  
|\> -------------------  
|\>  
|\> e$B$3$3$+$iCY$/$J$C$F$$$k$h$&$G$9!#e(B  
|  
|e$B$3$C$A$,LdBj$N$h$&$G$9!#MW$9$k$Ke(B  
|  
|\> \* bignum.c (rb\_big\_pow): eagerly truncate resulting bignum.  
|  
|e$B$O!"0l7e$@$1$G$OB-$j$J$$$H$$$&$3$H$C$]$$$G$9$M!#e(B

e$B$9$$$^$;$s!"$d$C$Q$j;d$N$;$$$G$7$?$M!#e(B

|e$B$3$l$G$h$&$d$/e(Brubye$BHG$H%H%s%H%s$+$d$dB.$$DxEY$K$J$j$^$7$?!#e(B

e$B%3%\_%C%H$7$F$/$@$5$$!#$7$+$7!"$^$@CY$$$N$M!#e(B

---

<div class="post-metadata">

**Author:** ![nobu](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/n/e9c0ed/32.png) [@nobu](https://www.ruby-forum.com/u/nobu)\
**Post date:** [April 26, 2007, 4:11pm UTC](https://www.ruby-forum.com/t/bn-h-cy-b/92977/6 "2007-04-26T16:11:43Z")

</div>

e$B$J$+$@$G$9!#e(B

At Thu, 26 Apr 2007 20:34:23 +0900,  
Kouhei Y. wrote in [ruby-dev:30733]:

> * * *
> 
> r10898 | matz | 2006-09-10 00:27:34 +0900 (e$BF|e(B, 10 9e$B7ne(B 2006) | 5 lines
> 
> - bignum.c (rb\_big\_mul0): bignum multiplication without  
> normalization.
> 
> - bignum.c (rb\_big\_pow): use rb\_big\_mul0(). [ruby-dev:29547]
> 
> * * *
> 
> e$B$3$3$+$iCY$/$J$C$F$$$k$h$&$G$9!#e(B

e$B$3$C$A$,LdBj$N$h$&$G$9!#MW$9$k$Ke(B

> - bignum.c (rb\_big\_pow): eagerly truncate resulting bignum.

e$B$O!"0l7e$@$1$G$OB-$j$J$$$H$$$&$3$H$C$]$$$G$9$M!#e(B

e$B$3$l$G$h$&$d$/e(Brubye$BHG$H%H%s%H%s$+$d$dB.$$DxEY$K$J$j$^$7$?!#e(B

# Index: bignum.c

— bignum.c (revision 12216)  
+++ bignum.c (working copy)  
@@ -91,26 +91,31 @@ rb\_big\_2comp(VALUE x) /\* get 2’s compl

static VALUE  
-bignorm(VALUE x)  
+bigtrunc(VALUE x)  
{

- if (FIXNUM\_P(x)) {
- return x;
- }
- else if (TYPE(x) == T\_BIGNUM) {
- long len = RBIGNUM(x)-\>len;
- BDIGIT \*ds = BDIGITS(x);
- 
- while (len-- && !ds[len]) ;
- RBIGNUM(x)-\>len = ++len;
- 
- if (len\*SIZEOF\_BDIGITS \<= sizeof(VALUE)) {
- 

```
 SIGNED_VALUE num = 0;

```

- 

```
 while (len--) {

```

- num = BIGUP(num) + ds[len];

- long len = RBIGNUM(x)-\>len;
- BDIGIT \*ds = BDIGITS(x);
- 
- while (len-- && !ds[len]);
- RBIGNUM(x)-\>len = ++len;
- return x;  
+}
- 

+static VALUE  
+bigfixize(VALUE x)  
+{

- long len = RBIGNUM(x)-\>len;
- BDIGIT \*ds = BDIGITS(x);
- 
- if (len\*SIZEOF\_BDIGITS \<= sizeof(VALUE)) {
- SIGNED\_VALUE num = 0;
- while (len–) {
- 

```
 num = BIGUP(num) + ds[len];

```

- }
- if (num \>= 0) {
- 

```
 if (RBIGNUM(x)->sign) {

```

- if (POSFIXABLE(num)) return LONG2FIX(num);  
}

- 

```
 if (num >= 0) {

```

- if (RBIGNUM(x)-\>sign) {
- 

```
   if (POSFIXABLE(num)) return LONG2FIX(num);

```

- }
- else if (NEGFIXABLE(-(long)num)) return LONG2FIX(-(long)num);

- 

```
 else {

```

- if (NEGFIXABLE(-(long)num)) return LONG2FIX(-(long)num);  
}  
}  
@@ -119,4 +124,13 @@ bignorm(VALUE x)  
}

+static VALUE  
+bignorm(VALUE x)  
+{

- if (!FIXNUM\_P(x) && TYPE(x) == T\_BIGNUM) {
- x = bigfixize(bigtrunc(x));
- }
- return x;  
+}
- 

VALUE  
rb\_big\_norm(VALUE x)  
@@ -1553,5 +1567,5 @@ rb\_big\_pow(VALUE x, VALUE y)  
yy = FIX2LONG(y);  
if (yy \> 0) {

- 

```
 VALUE z = x;

```

- 

```
 VALUE z = (yy & 1) ? x : 0;

 if (RBIGNUM(x)->len * SIZEOF_BDIGITS * yy > 1024*1024) {

```

@@ -1560,14 +1574,12 @@ rb\_big\_pow(VALUE x, VALUE y)  
break;  
}

- 

```
 for (;;) {

```

- yy -= 1;
- if (yy == 0) break;
- while (yy % 2 == 0) {

- 

```
 while (yy &= ~1) {

```

- do {  
yy /= 2;  
x = rb\_big\_mul0(x, x);

- 

```
   if (!BDIGITS(x)[RBIGNUM(x)->len-1]) RBIGNUM(x)->len--;

```

- }
- z = rb\_big\_mul0(z, x);
- if (!BDIGITS(z)[RBIGNUM(z)-\>len-1]) RBIGNUM(z)-\>len–;

- 

```
   bigtrunc(x);

```

- } while (yy % 2 == 0);
- z = z ? rb\_big\_mul0(z, x) : x;
- bigtrunc(z);  
}  
return bignorm(z);