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big: Add binary split factorial.

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This commit is contained in:
Jeroen van Rijn
2021-08-11 20:59:52 +02:00
parent cd0ce7b76e
commit 491e4ecc74
6 changed files with 103 additions and 54 deletions
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core/math/big/basic.odin
+56 -1
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@@ -751,12 +751,15 @@ sqrmod :: proc { int_sqrmod, };
int_factorial :: proc(res: ^Int, n: DIGIT) -> (err: Error) {
if n < 0 { return .Invalid_Argument; }
if n < 0 || n > _FACTORIAL_MAX_N || res == nil { return .Invalid_Argument; }
i := DIGIT(len(_factorial_table));
if n < i {
return set(res, _factorial_table[n]);
}
if n >= _FACTORIAL_BINARY_SPLIT_CUTOFF {
return int_factorial_binary_split(res, n);
}
a := &Int{};
defer destroy(a);
@@ -771,6 +774,58 @@ int_factorial :: proc(res: ^Int, n: DIGIT) -> (err: Error) {
return .None;
}
_int_recursive_product :: proc(res: ^Int, start, stop: DIGIT, level := int(0)) -> (err: Error) {
t1, t2 := &Int{}, &Int{};
defer destroy(t1, t2);
if level > _FACTORIAL_BINARY_SPLIT_MAX_RECURSIONS { return .Max_Iterations_Reached; }
num_factors := (stop - start) >> 1;
if num_factors == 2 {
if err = set(t1, start); err != .None { return err; }
if err = add(t2, t1, 2); err != .None { return err; }
return mul(res, t1, t2);
}
if num_factors > 1 {
mid := (start + num_factors) | 1;
if err = _int_recursive_product(t1, start, mid, level + 1); err != .None { return err; }
if err = _int_recursive_product(t2, mid, stop, level + 1); err != .None { return err; }
return mul(res, t1, t2);
}
if num_factors == 1 { return set(res, start); }
return one(res);
}
/*
Binary split factorial algo due to: http://www.luschny.de/math/factorial/binarysplitfact.html
*/
int_factorial_binary_split :: proc(res: ^Int, n: DIGIT) -> (err: Error) {
if n < 0 || n > _FACTORIAL_MAX_N || res == nil { return .Invalid_Argument; }
inner, outer, start, stop, temp := &Int{}, &Int{}, &Int{}, &Int{}, &Int{};
defer destroy(inner, outer, start, stop, temp);
if err = one(inner); err != .None { return err; }
if err = one(outer); err != .None { return err; }
bits_used := int(_DIGIT_TYPE_BITS - intrinsics.count_leading_zeros(n));
for i := bits_used; i >= 0; i -= 1 {
start := (n >> (uint(i) + 1)) + 1 | 1;
stop := (n >> uint(i)) + 1 | 1;
if err = _int_recursive_product(temp, start, stop); err != .None { return err; }
if err = mul(inner, inner, temp); err != .None { return err; }
if err = mul(outer, outer, inner); err != .None { return err; }
}
shift := n - intrinsics.count_ones(n);
return shl(res, outer, int(shift));
}
factorial :: proc { int_factorial, };
/*