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-rw-r--r--core/math/big/build.bat4
-rw-r--r--core/math/big/example.odin12
-rw-r--r--core/math/big/helpers.odin6
-rw-r--r--core/math/big/internal.odin14
-rw-r--r--core/math/big/private.odin106
5 files changed, 116 insertions, 26 deletions
diff --git a/core/math/big/build.bat b/core/math/big/build.bat
index eb6f581aa..540907a3a 100644
--- a/core/math/big/build.bat
+++ b/core/math/big/build.bat
@@ -1,8 +1,8 @@
@echo off
-:odin run . -vet
+odin run . -vet
: -o:size
:odin build . -build-mode:shared -show-timings -o:minimal -no-bounds-check -define:MATH_BIG_EXE=false && python test.py -fast-tests
:odin build . -build-mode:shared -show-timings -o:size -no-bounds-check -define:MATH_BIG_EXE=false && python test.py -fast-tests
:odin build . -build-mode:shared -show-timings -o:size -define:MATH_BIG_EXE=false && python test.py -fast-tests
-odin build . -build-mode:shared -show-timings -o:speed -no-bounds-check -define:MATH_BIG_EXE=false && python test.py -fast-tests
+:odin build . -build-mode:shared -show-timings -o:speed -no-bounds-check -define:MATH_BIG_EXE=false && python test.py -fast-tests
:odin build . -build-mode:shared -show-timings -o:speed -define:MATH_BIG_EXE=false && python test.py -fast-tests \ No newline at end of file
diff --git a/core/math/big/example.odin b/core/math/big/example.odin
index 4fbf44664..2a66251c9 100644
--- a/core/math/big/example.odin
+++ b/core/math/big/example.odin
@@ -206,16 +206,12 @@ demo :: proc() {
a, b, c, d, e, f := &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{};
defer destroy(a, b, c, d, e, f);
- atoi(a, "12980742146337069150589594264770969721", 10);
+ power_of_two(a, 312);
print("a: ", a, 10, true, true, true);
- atoi(b, "4611686018427387904", 10);
+ power_of_two(b, 314);
print("b: ", b, 10, true, true, true);
-
- if err := internal_divmod(c, d, a, b); err != nil {
- fmt.printf("Error: %v\n", err);
- }
- print("c: ", c);
- print("c: ", d);
+ _private_mul_karatsuba(c, a, b);
+ print("c: ", c, 10, true, true, true);
}
main :: proc() {
diff --git a/core/math/big/helpers.odin b/core/math/big/helpers.odin
index ab686b914..e50579ac0 100644
--- a/core/math/big/helpers.odin
+++ b/core/math/big/helpers.odin
@@ -432,18 +432,16 @@ int_init_multi :: proc(integers: ..^Int, allocator := context.allocator) -> (err
init_multi :: proc { int_init_multi, };
-copy_digits :: proc(dest, src: ^Int, digits: int, allocator := context.allocator) -> (err: Error) {
+copy_digits :: proc(dest, src: ^Int, digits: int, offset := int(0), allocator := context.allocator) -> (err: Error) {
context.allocator = allocator;
- digits := digits;
/*
Check that `src` is usable and `dest` isn't immutable.
*/
assert_if_nil(dest, src);
#force_inline internal_clear_if_uninitialized(src) or_return;
- digits = min(digits, len(src.digit), len(dest.digit));
- return #force_inline internal_copy_digits(dest, src, digits);
+ return #force_inline internal_copy_digits(dest, src, digits, offset);
}
/*
diff --git a/core/math/big/internal.odin b/core/math/big/internal.odin
index 2c988f91e..d5cb03cc4 100644
--- a/core/math/big/internal.odin
+++ b/core/math/big/internal.odin
@@ -36,8 +36,6 @@ import "core:mem"
import "core:intrinsics"
import rnd "core:math/rand"
-import "core:fmt"
-
/*
Low-level addition, unsigned. Handbook of Applied Cryptography, algorithm 14.7.
@@ -651,7 +649,6 @@ internal_int_mul :: proc(dest, src, multiplier: ^Int, allocator := context.alloc
Fast comba?
*/
err = #force_inline _private_int_sqr_comba(dest, src);
- //err = #force_inline _private_int_sqr(dest, src);
} else {
err = #force_inline _private_int_sqr(dest, src);
}
@@ -679,8 +676,8 @@ internal_int_mul :: proc(dest, src, multiplier: ^Int, allocator := context.alloc
// err = s_mp_mul_balance(a,b,c);
} else if false && min_used >= MUL_TOOM_CUTOFF {
// err = s_mp_mul_toom(a, b, c);
- } else if false && min_used >= MUL_KARATSUBA_CUTOFF {
- // err = s_mp_mul_karatsuba(a, b, c);
+ } else if min_used >= MUL_KARATSUBA_CUTOFF {
+ err = #force_inline _private_mul_karatsuba(dest, src, multiplier);
} else if digits < _WARRAY && min_used <= _MAX_COMBA {
/*
Can we use the fast multiplier?
@@ -1628,16 +1625,13 @@ internal_int_set_from_integer :: proc(dest: ^Int, src: $T, minimize := false, al
internal_set :: proc { internal_int_set_from_integer, internal_int_copy };
-internal_copy_digits :: #force_inline proc(dest, src: ^Int, digits: int) -> (err: Error) {
+internal_copy_digits :: #force_inline proc(dest, src: ^Int, digits: int, offset := int(0)) -> (err: Error) {
#force_inline internal_error_if_immutable(dest) or_return;
/*
If dest == src, do nothing
*/
- if (dest == src) { return nil; }
-
- #force_inline mem.copy_non_overlapping(&dest.digit[0], &src.digit[0], size_of(DIGIT) * digits);
- return nil;
+ return #force_inline _private_copy_digits(dest, src, digits, offset);
}
/*
diff --git a/core/math/big/private.odin b/core/math/big/private.odin
index a99d6119f..50a6f9c9c 100644
--- a/core/math/big/private.odin
+++ b/core/math/big/private.odin
@@ -90,6 +90,108 @@ _private_int_mul :: proc(dest, a, b: ^Int, digits: int, allocator := context.all
}
/*
+ product = |a| * |b| using Karatsuba Multiplication using three half size multiplications.
+
+ Let `B` represent the radix [e.g. 2**_DIGIT_BITS] and let `n` represent
+ half of the number of digits in the min(a,b)
+
+ `a` = `a1` * `B`**`n` + `a0`
+ `b` = `b`1 * `B`**`n` + `b0`
+
+ Then, a * b => 1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
+
+ Note that a1b1 and a0b0 are used twice and only need to be computed once.
+ So in total three half size (half # of digit) multiplications are performed,
+ a0b0, a1b1 and (a1+b1)(a0+b0)
+
+ Note that a multiplication of half the digits requires 1/4th the number of
+ single precision multiplications, so in total after one call 25% of the
+ single precision multiplications are saved.
+
+ Note also that the call to `internal_mul` can end up back in this function
+ if the a0, a1, b0, or b1 are above the threshold.
+
+ This is known as divide-and-conquer and leads to the famous O(N**lg(3)) or O(N**1.584)
+ work which is asymptopically lower than the standard O(N**2) that the
+ baseline/comba methods use. Generally though, the overhead of this method doesn't pay off
+ until a certain size is reached, of around 80 used DIGITs.
+*/
+_private_mul_karatsuba :: proc(dest, a, b: ^Int, allocator := context.allocator) -> (err: Error) {
+ context.allocator = allocator;
+
+ x0, x1, y0, y1, t1, x0y0, x1y1 := &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{};
+ defer destroy(x0, x1, y0, y1, t1, x0y0, x1y1);
+
+ /*
+ min # of digits, divided by two.
+ */
+ B := min(a.used, b.used) >> 1;
+
+ /*
+ Init all the temps.
+ */
+ internal_grow(x0, B) or_return;
+ internal_grow(x1, a.used - B) or_return;
+ internal_grow(y0, B) or_return;
+ internal_grow(y1, b.used - B) or_return;
+ internal_grow(t1, B * 2) or_return;
+ internal_grow(x0y0, B * 2) or_return;
+ internal_grow(x1y1, B * 2) or_return;
+
+ /*
+ Now shift the digits.
+ */
+ x0.used, y0.used = B, B;
+ x1.used = a.used - B;
+ y1.used = b.used - B;
+
+ /*
+ We copy the digits directly instead of using higher level functions
+ since we also need to shift the digits.
+ */
+ internal_copy_digits(x0, a, x0.used);
+ internal_copy_digits(y0, b, y0.used);
+ internal_copy_digits(x1, a, x1.used, B);
+ internal_copy_digits(y1, b, y1.used, B);
+
+ /*
+ Only need to clamp the lower words since by definition the
+ upper words x1/y1 must have a known number of digits.
+ */
+ clamp(x0);
+ clamp(y0);
+
+ /*
+ Now calc the products x0y0 and x1y1,
+ after this x0 is no longer required, free temp [x0==t2]!
+ */
+ internal_mul(x0y0, x0, y0) or_return; /* x0y0 = x0*y0 */
+ internal_mul(x1y1, x1, y1) or_return; /* x1y1 = x1*y1 */
+ internal_add(t1, x1, x0) or_return; /* now calc x1+x0 and */
+ internal_add(x0, y1, y0) or_return; /* t2 = y1 + y0 */
+ internal_mul(t1, t1, x0) or_return; /* t1 = (x1 + x0) * (y1 + y0) */
+
+ /*
+ Add x0y0.
+ */
+ internal_add(x0, x0y0, x1y1) or_return; /* t2 = x0y0 + x1y1 */
+ internal_sub(t1, t1, x0) or_return; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
+
+ /*
+ shift by B.
+ */
+ internal_shl_digit(t1, B) or_return; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
+ internal_shl_digit(x1y1, B * 2) or_return; /* x1y1 = x1y1 << 2*B */
+
+ internal_add(t1, x0y0, t1) or_return; /* t1 = x0y0 + t1 */
+ internal_add(dest, t1, x1y1) or_return; /* t1 = x0y0 + t1 + x1y1 */
+
+ return nil;
+}
+
+
+
+/*
Fast (comba) multiplier
This is the fast column-array [comba] multiplier. It is
@@ -1629,7 +1731,7 @@ _private_log_power_of_two :: proc(a: ^Int, base: DIGIT) -> (log: int, err: Error
Copies DIGITs from `src` to `dest`.
Assumes `src` and `dest` to not be `nil` and have been initialized.
*/
-_private_copy_digits :: proc(dest, src: ^Int, digits: int) -> (err: Error) {
+_private_copy_digits :: proc(dest, src: ^Int, digits: int, offset := int(0)) -> (err: Error) {
digits := digits;
/*
If dest == src, do nothing
@@ -1639,7 +1741,7 @@ _private_copy_digits :: proc(dest, src: ^Int, digits: int) -> (err: Error) {
}
digits = min(digits, len(src.digit), len(dest.digit));
- mem.copy_non_overlapping(&dest.digit[0], &src.digit[0], size_of(DIGIT) * digits);
+ mem.copy_non_overlapping(&dest.digit[0], &src.digit[offset], size_of(DIGIT) * digits);
return nil;
}
generated by cgit v1.2.3 (git 2.39.1) at 2026-02-15 11:30:33 +0000