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bignum.c: improve estimate

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* bignum.c (estimate_initial_sqrt, rb_big_isqrt): improve initial
  estimate by sqrt().  [ruby-core:79754] [Feature #13250]

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@57713 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
This commit is contained in:
nobu 2017-02-25 05:44:39 +00:00
parent dab7aa22f7
commit 4dcad25b23
1 changed files with 35 additions and 23 deletions
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56
bignum.c
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@ -6771,26 +6771,37 @@ BDIGIT rb_bdigit_dbl_isqrt(BDIGIT_DBL);
static BDIGIT * static BDIGIT *
estimate_initial_sqrt(VALUE *xp, const size_t xn, const BDIGIT *nds, size_t len) estimate_initial_sqrt(VALUE *xp, const size_t xn, const BDIGIT *nds, size_t len)
{ {
enum {dbl_per_bdig = roomof(DBL_MANT_DIG,BITSPERDIG)};
const int zbits = nlz(nds[len-1]); const int zbits = nlz(nds[len-1]);
const int shift_bits = (len&1 ? BITSPERDIG/2 : BITSPERDIG) - (zbits+1)/2 + 1; VALUE x = *xp = bignew_1(0, xn, 1); /* division may release the GVL */
VALUE x = bignew_1(0, xn, 1); /* division may release the GVL */
BDIGIT *xds = BDIGITS(x); BDIGIT *xds = BDIGITS(x);
BDIGIT_DBL d = bary2bdigitdbl(nds+len-dbl_per_bdig, dbl_per_bdig);
BDIGIT lowbits = 1;
int rshift = (int)((BITSPERDIG*2-zbits+(len&BITSPERDIG&1) - DBL_MANT_DIG + 1) & ~1);
double f;
*xp = x; if (rshift > 0) {
/* x = (n >> (b/2+1)) */ lowbits = (BDIGIT)d & ~(~(BDIGIT)1U << rshift);
if (shift_bits == BITSPERDIG) { d >>= rshift;
MEMCPY(xds, nds+len-xn, BDIGIT, xn);
} }
else if (shift_bits > BITSPERDIG) { else if (rshift < 0) {
bary_small_rshift(xds, nds+len-xn, xn, shift_bits-BITSPERDIG, 0); d <<= -rshift;
d |= nds[len-dbl_per_bdig-1] >> (BITSPERDIG+rshift);
} }
else { f = sqrt((double)d);
bary_small_rshift(xds, nds+len-xn-1, xn, shift_bits, nds[len-1]); d = (BDIGIT_DBL)ceil(f);
if ((double)d == f) {
if (lowbits || (lowbits = !bary_zero_p(nds, len-dbl_per_bdig)))
++d;
} }
/* x |= (1 << (b-1)/2) */ rshift /= 2;
xds[xn-1] |= (BDIGIT)1u << rshift += (2-(len&1))*BITSPERDIG/2;
((len&1 ? 0 : BITSPERDIG/2) + (BITSPERDIG-zbits-1)/2); if (rshift >= 0) {
d <<= rshift;
}
bdigitdbl2bary(&xds[xn-2], 2, d);
if (!lowbits) return NULL; /* special case, exact result */
return xds; return xds;
} }
@ -6799,6 +6810,9 @@ rb_big_isqrt(VALUE n)
{ {
BDIGIT *nds = BDIGITS(n); BDIGIT *nds = BDIGITS(n);
size_t len = BIGNUM_LEN(n); size_t len = BIGNUM_LEN(n);
size_t xn = (len+1) / 2;
VALUE x;
BDIGIT *xds;
if (len <= 2) { if (len <= 2) {
BDIGIT sq = rb_bdigit_dbl_isqrt(bary2bdigitdbl(nds, len)); BDIGIT sq = rb_bdigit_dbl_isqrt(bary2bdigitdbl(nds, len));
@ -6808,30 +6822,28 @@ rb_big_isqrt(VALUE n)
return ULONG2NUM(sq); return ULONG2NUM(sq);
#endif #endif
} }
else { else if ((xds = estimate_initial_sqrt(&x, xn, nds, len)) != 0) {
size_t tn = (len+1) / 2, xn = tn; size_t tn = xn + BIGDIVREM_EXTRA_WORDS;
VALUE t, x; VALUE t = bignew_1(0, tn, 1);
BDIGIT *tds, *xds = estimate_initial_sqrt(&x, xn, nds, len); BDIGIT *tds = BDIGITS(t);
tn = BIGNUM_LEN(t);
/* t = n/x */ /* t = n/x */
tn += BIGDIVREM_EXTRA_WORDS;
t = bignew_1(0, tn, 1);
tds = BDIGITS(t);
tn = BIGNUM_LEN(t);
while (bary_divmod_branch(tds, tn, NULL, 0, nds, len, xds, xn), while (bary_divmod_branch(tds, tn, NULL, 0, nds, len, xds, xn),
bary_cmp(tds, tn, xds, xn) < 0) { bary_cmp(tds, tn, xds, xn) < 0) {
int carry; int carry;
BARY_TRUNC(tds, tn); BARY_TRUNC(tds, tn);
/* x = (x+t)/2 */
carry = bary_add(xds, xn, xds, xn, tds, tn); carry = bary_add(xds, xn, xds, xn, tds, tn);
bary_small_rshift(xds, xds, xn, 1, carry); bary_small_rshift(xds, xds, xn, 1, carry);
tn = BIGNUM_LEN(t); tn = BIGNUM_LEN(t);
} }
rb_big_realloc(t, 0); rb_big_realloc(t, 0);
rb_gc_force_recycle(t); rb_gc_force_recycle(t);
}
RBASIC_SET_CLASS_RAW(x, rb_cInteger); RBASIC_SET_CLASS_RAW(x, rb_cInteger);
return x; return x;
} }
}
/* /*
* Bignum objects hold integers outside the range of * Bignum objects hold integers outside the range of