ed/Odin
1
0
Fork 0
mirror of https://github.com/Ed94/Odin.git synced 2026-06-26 15:34:59 -07:00
Code Issues Packages Projects Releases Wiki Activity

big: Add _private_int_mul_toom`.

Browse Source
This commit is contained in:
Jeroen van Rijn
2021-08-16 21:17:21 +02:00
parent 8b49bbb0fc
commit 706e58c1c7
5 changed files with 150 additions and 9 deletions
Download Patch File Download Diff File Expand all files Collapse all files
core/math/big/build.bat
+2 -2
View File
@@ -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
core/math/big/example.odin
+6 -3
View File
@@ -206,11 +206,14 @@ demo :: proc() {
a, b, c, d, e, f := &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{};
defer destroy(a, b, c, d, e, f);
power_of_two(a, 312);
atoi(a, "615037959146039477924633848896619112832171971562900618409305032006863881436080", 10);
print("a: ", a, 10, true, true, true);
power_of_two(b, 314);
atoi(b, "378271691190525325893712245607881659587045836991909505715443874842659307597325888631898626653926188084180707310543535657996185416604973577488563643125766400", 10);
print("b: ", b, 10, true, true, true);
_private_mul_karatsuba(c, a, b);
// _private_mul_karatsuba(c, a, b);
_private_int_mul_toom(c, a, b);
// 232651448952541576870611266174879305550351371288854695862580414333123414997160350830885091499735909790287667499899722495800734048928379224433901855785208987458832826418636718381316545267329375006999278984386253755079362097682611712000
print("c: ", c, 10, true, true, true);
}
core/math/big/internal.odin
+3 -3
View File
@@ -674,10 +674,10 @@ internal_int_mul :: proc(dest, src, multiplier: ^Int, allocator := context.alloc
*/
max_used >= 2 * min_used {
// 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 min_used >= MUL_TOOM_CUTOFF {
err = #force_inline _private_int_mul_toom(dest, src, multiplier);
} else if min_used >= MUL_KARATSUBA_CUTOFF {
err = #force_inline _private_mul_karatsuba(dest, src, multiplier);
err = #force_inline _private_int_mul_karatsuba(dest, src, multiplier);
} else if digits < _WARRAY && min_used <= _MAX_COMBA {
/*
Can we use the fast multiplier?
core/math/big/private.odin
+138 -1
View File
@@ -89,6 +89,143 @@ _private_int_mul :: proc(dest, a, b: ^Int, digits: int, allocator := context.all
return internal_clamp(dest);
}
/*
Multiplication using the Toom-Cook 3-way algorithm.
Much more complicated than Karatsuba but has a lower asymptotic running time of O(N**1.464).
This algorithm is only particularly useful on VERY large inputs.
(We're talking 1000s of digits here...).
This file contains code from J. Arndt's book "Matters Computational"
and the accompanying FXT-library with permission of the author.
Setup from:
Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae."
18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007.
The interpolation from above needed one temporary variable more than the interpolation here:
Bodrato, Marco, and Alberto Zanoni. "What about Toom-Cook matrices optimality."
Centro Vito Volterra Universita di Roma Tor Vergata (2006)
*/
_private_int_mul_toom :: proc(dest, a, b: ^Int, allocator := context.allocator) -> (err: Error) {
context.allocator = allocator;
S1, S2, T1, a0, a1, a2, b0, b1, b2 := &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{};
defer destroy(S1, S2, T1, a0, a1, a2, b0, b1, b2);
/*
Init temps.
*/
internal_init_multi(S1, S2, T1) or_return;
/*
B
*/
B := min(a.used, b.used) / 3;
/*
a = a2 * x^2 + a1 * x + a0;
*/
internal_grow(a0, B) or_return;
internal_grow(a1, B) or_return;
internal_grow(a2, a.used - 2 * B) or_return;
a0.used, a1.used = B, B;
a2.used = a.used - 2 * B;
internal_copy_digits(a0, a, a0.used) or_return;
internal_copy_digits(a1, a, a1.used, B) or_return;
internal_copy_digits(a2, a, a2.used, 2 * B) or_return;
internal_clamp(a0);
internal_clamp(a1);
internal_clamp(a2);
/*
b = b2 * x^2 + b1 * x + b0;
*/
internal_grow(b0, B) or_return;
internal_grow(b1, B) or_return;
internal_grow(b2, b.used - 2 * B) or_return;
b0.used, b1.used = B, B;
b2.used = b.used - 2 * B;
internal_copy_digits(b0, b, b0.used) or_return;
internal_copy_digits(b1, b, b1.used, B) or_return;
internal_copy_digits(b2, b, b2.used, 2 * B) or_return;
internal_clamp(b0);
internal_clamp(b1);
internal_clamp(b2);
/*
\\ S1 = (a2+a1+a0) * (b2+b1+b0);
*/
internal_add(T1, a2, a1) or_return; /* T1 = a2 + a1; */
internal_add(S2, T1, a0) or_return; /* S2 = T1 + a0; */
internal_add(dest, b2, b1) or_return; /* dest = b2 + b1; */
internal_add(S1, dest, b0) or_return; /* S1 = c + b0; */
internal_mul(S1, S1, S2) or_return; /* S1 = S1 * S2; */
/*
\\S2 = (4*a2+2*a1+a0) * (4*b2+2*b1+b0);
*/
internal_add(T1, T1, a2) or_return; /* T1 = T1 + a2; */
internal_int_shl1(T1, T1) or_return; /* T1 = T1 << 1; */
internal_add(T1, T1, a0) or_return; /* T1 = T1 + a0; */
internal_add(dest, dest, b2) or_return; /* c = c + b2; */
internal_int_shl1(dest, dest) or_return; /* c = c << 1; */
internal_add(dest, dest, b0) or_return; /* c = c + b0; */
internal_mul(S2, T1, dest) or_return; /* S2 = T1 * c; */
/*
\\S3 = (a2-a1+a0) * (b2-b1+b0);
*/
internal_sub(a1, a2, a1) or_return; /* a1 = a2 - a1; */
internal_add(a1, a1, a0) or_return; /* a1 = a1 + a0; */
internal_sub(b1, b2, b1) or_return; /* b1 = b2 - b1; */
internal_add(b1, b1, b0) or_return; /* b1 = b1 + b0; */
internal_mul(a1, a1, b1) or_return; /* a1 = a1 * b1; */
internal_mul(b1, a2, b2) or_return; /* b1 = a2 * b2; */
/*
\\S2 = (S2 - S3) / 3;
*/
internal_sub(S2, S2, a1) or_return; /* S2 = S2 - a1; */
_private_int_div_3(S2, S2) or_return; /* S2 = S2 / 3; \\ this is an exact division */
internal_sub(a1, S1, a1) or_return; /* a1 = S1 - a1; */
internal_int_shr1(a1, a1) or_return; /* a1 = a1 >> 1; */
internal_mul(a0, a0, b0) or_return; /* a0 = a0 * b0; */
internal_sub(S1, S1, a0) or_return; /* S1 = S1 - a0; */
internal_sub(S2, S2, S1) or_return; /* S2 = S2 - S1; */
internal_int_shr1(S2, S2) or_return; /* S2 = S2 >> 1; */
internal_sub(S1, S1, a1) or_return; /* S1 = S1 - a1; */
internal_sub(S1, S1, b1) or_return; /* S1 = S1 - b1; */
internal_int_shl1(T1, b1) or_return; /* T1 = b1 << 1; */
internal_sub(S2, S2, T1) or_return; /* S2 = S2 - T1; */
internal_sub(a1, a1, S2) or_return; /* a1 = a1 - S2; */
/*
P = b1*x^4+ S2*x^3+ S1*x^2+ a1*x + a0;
*/
internal_shl_digit(b1, 4 * B) or_return;
internal_shl_digit(S2, 3 * B) or_return;
internal_add(b1, b1, S2) or_return;
internal_shl_digit(S1, 2 * B) or_return;
internal_add(b1, b1, S1) or_return;
internal_shl_digit(a1, 1 * B) or_return;
internal_add(b1, b1, a1) or_return;
internal_add(dest, b1, a0) or_return;
/*
a * b - P
*/
return nil;
}
/*
product = |a| * |b| using Karatsuba Multiplication using three half size multiplications.
@@ -116,7 +253,7 @@ _private_int_mul :: proc(dest, a, b: ^Int, digits: int, allocator := context.all
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) {
_private_int_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{};
core/math/big/test.py
+1
View File
@@ -446,6 +446,7 @@ TESTS = {
test_mul: [
[ 1234, 5432],
[ 0xd3b4e926aaba3040e1c12b5ea553b5, 0x1a821e41257ed9281bee5bc7789ea7 ],
[ 1 << 21_105, 1 << 21_501 ],
],
test_sqr: [
[ 5432],