diff --git a/core/math/big/build.bat b/core/math/big/build.bat index 540907a3a..eb6f581aa 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 2a66251c9..852adf1e6 100644 --- a/core/math/big/example.odin +++ b/core/math/big/example.odin @@ -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); } diff --git a/core/math/big/internal.odin b/core/math/big/internal.odin index d5cb03cc4..baf102ccb 100644 --- a/core/math/big/internal.odin +++ b/core/math/big/internal.odin @@ -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? diff --git a/core/math/big/private.odin b/core/math/big/private.odin index 50a6f9c9c..a46fab230 100644 --- a/core/math/big/private.odin +++ b/core/math/big/private.odin @@ -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{}; diff --git a/core/math/big/test.py b/core/math/big/test.py index 5b5a86cff..922500e77 100644 --- a/core/math/big/test.py +++ b/core/math/big/test.py @@ -446,6 +446,7 @@ TESTS = { test_mul: [ [ 1234, 5432], [ 0xd3b4e926aaba3040e1c12b5ea553b5, 0x1a821e41257ed9281bee5bc7789ea7 ], + [ 1 << 21_105, 1 << 21_501 ], ], test_sqr: [ [ 5432],