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big: Add _private_int_mul_balance.

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This commit is contained in:
Jeroen van Rijn
2021-08-28 18:17:57 +02:00
parent 2cfd6b7024
commit 737b4fde1c
5 changed files with 106 additions and 42 deletions
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4
core/math/big/build.bat
View File

@@ -1,9 +1,9 @@
@echo off
odin run . -vet
:odin run . -vet
set TEST_ARGS=-fast-tests
:odin build . -build-mode:shared -show-timings -o:minimal -no-bounds-check -define:MATH_BIG_EXE=false && python test.py %TEST_ARGS%
:odin build . -build-mode:shared -show-timings -o:size -no-bounds-check -define:MATH_BIG_EXE=false && python test.py %TEST_ARGS%
odin build . -build-mode:shared -show-timings -o:size -no-bounds-check -define:MATH_BIG_EXE=false && python test.py %TEST_ARGS%
:odin build . -build-mode:shared -show-timings -o:size -define:MATH_BIG_EXE=false && python test.py %TEST_ARGS%
:odin build . -build-mode:shared -show-timings -o:speed -no-bounds-check -define:MATH_BIG_EXE=false && python test.py %TEST_ARGS%
:odin build . -build-mode:shared -show-timings -o:speed -define:MATH_BIG_EXE=false && python test.py -fast-tests %TEST_ARGS%

9
core/math/big/example.odin
View File

@@ -205,15 +205,6 @@ int_to_byte_little :: proc(v: ^Int) {
demo :: proc() {
a, b, c, d, e, f := &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{};
defer destroy(a, b, c, d, e, f);
foo := "92232459121502451677697058974826760244863271517919321608054113675118660929276431348516553336313179167211015633639725554914519355444316239500734169769447134357534241879421978647995614218985202290368055757891124109355450669008628757662409138767505519391883751112010824030579849970582074544353971308266211776494228299586414907715854328360867232691292422194412634523666770452490676515117702116926803826546868467146319938818238521874072436856528051486567230096290549225463582766830777324099589751817442141036031904145041055454639783559905920619197290800070679733841430619962318433709503256637256772215111521321630777950145713049902839937043785039344243357384899099910837463164007565230287809026956254332260375327814271845678201";
set(a, foo);
print("a: ", a);
is_sqr, _ := internal_int_is_square(a);
fmt.printf("is_square: %v\n", is_sqr);
}
main :: proc() {

11
core/math/big/internal.odin
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@@ -659,8 +659,7 @@ internal_int_mul :: proc(dest, src, multiplier: ^Int, allocator := context.alloc
Can we use the balance method? Check sizes.
* The smaller one needs to be larger than the Karatsuba cut-off.
* The bigger one needs to be at least about one `_MUL_KARATSUBA_CUTOFF` bigger
* to make some sense, but it depends on architecture, OS, position of the
* stars... so YMMV.
* to make some sense, but it depends on architecture, OS, position of the stars... so YMMV.
* Using it to cut the input into slices small enough for _mul_comba
* was actually slower on the author's machine, but YMMV.
*/
@@ -669,13 +668,11 @@ internal_int_mul :: proc(dest, src, multiplier: ^Int, allocator := context.alloc
max_used := max(src.used, multiplier.used);
digits := src.used + multiplier.used + 1;
if false && min_used >= MUL_KARATSUBA_CUTOFF &&
max_used / 2 >= MUL_KARATSUBA_CUTOFF &&
if min_used >= MUL_KARATSUBA_CUTOFF && (max_used / 2) >= MUL_KARATSUBA_CUTOFF && max_used >= (2 * min_used) {
/*
Not much effect was observed below a ratio of 1:2, but again: YMMV.
*/
max_used >= 2 * min_used {
// err = s_mp_mul_balance(a,b,c);
err = _private_int_mul_balance(dest, src, multiplier);
} else if min_used >= MUL_TOOM_CUTOFF {
/*
Toom path commented out until it no longer fails Factorial 10k or 100k,
@@ -914,7 +911,7 @@ internal_int_factorial :: proc(res: ^Int, n: int, allocator := context.allocator
context.allocator = allocator;
if n >= FACTORIAL_BINARY_SPLIT_CUTOFF {
return #force_inline _private_int_factorial_binary_split(res, n);
return _private_int_factorial_binary_split(res, n);
}
i := len(_factorial_table);

107
core/math/big/private.odin
View File

@@ -113,7 +113,7 @@ _private_int_mul_toom :: proc(dest, a, b: ^Int, allocator := context.allocator)
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);
defer internal_destroy(S1, S2, T1, a0, a1, a2, b0, b1, b2);
/*
Init temps.
@@ -258,7 +258,7 @@ _private_int_mul_karatsuba :: proc(dest, a, b: ^Int, allocator := context.alloca
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);
defer internal_destroy(x0, x1, y0, y1, t1, x0y0, x1y1);
/*
min # of digits, divided by two.
@@ -546,8 +546,74 @@ _private_int_mul_high_comba :: proc(dest, a, b: ^Int, digits: int, allocator :=
return internal_clamp(dest);
}
/*
Single-digit multiplication with the smaller number as the single-digit.
*/
_private_int_mul_balance :: proc(dest, a, b: ^Int, allocator := context.allocator) -> (err: Error) {
context.allocator = allocator;
a, b := a, b;
a0, tmp, r := &Int{}, &Int{}, &Int{};
defer internal_destroy(a0, tmp, r);
b_size := min(a.used, b.used);
n_blocks := max(a.used, b.used) / b_size;
internal_grow(a0, b_size + 2) or_return;
internal_init_multi(tmp, r) or_return;
/*
Make sure that `a` is the larger one.
*/
if a.used < b.used {
a, b = b, a;
}
assert(a.used >= b.used);
i, j := 0, 0;
for ; i < n_blocks; i += 1 {
/*
Cut a slice off of `a`.
*/
a0.used = b_size;
internal_copy_digits(a0, a, a0.used, j);
j += a0.used;
internal_clamp(a0);
/*
Multiply with `b`.
*/
internal_mul(tmp, a0, b) or_return;
/*
Shift `tmp` to the correct position.
*/
internal_shl_digit(tmp, b_size * i) or_return;
/*
Add to output. No carry needed.
*/
internal_add(r, r, tmp) or_return;
}
/*
The left-overs; there are always left-overs.
*/
if j < a.used {
a0.used = a.used - j;
internal_copy_digits(a0, a, a0.used, j);
j += a0.used;
internal_clamp(a0);
internal_mul(tmp, a0, b) or_return;
internal_shl_digit(tmp, b_size * i) or_return;
internal_add(r, r, tmp) or_return;
}
internal_swap(dest, r);
return;
}
/*
Low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16
@@ -1311,7 +1377,7 @@ _private_int_div_small :: proc(quotient, remainder, numerator, denominator: ^Int
ta, tb, tq, q := &Int{}, &Int{}, &Int{}, &Int{};
c: int;
defer destroy(ta, tb, tq, q);
defer internal_destroy(ta, tb, tq, q);
for {
internal_one(tq) or_return;
@@ -1364,31 +1430,34 @@ _private_int_div_small :: proc(quotient, remainder, numerator, denominator: ^Int
Binary split factorial algo due to: http://www.luschny.de/math/factorial/binarysplitfact.html
*/
_private_int_factorial_binary_split :: proc(res: ^Int, n: int, allocator := context.allocator) -> (err: Error) {
context.allocator = allocator;
inner, outer, start, stop, temp := &Int{}, &Int{}, &Int{}, &Int{}, &Int{};
defer internal_destroy(inner, outer, start, stop, temp);
internal_one(inner, false, allocator) or_return;
internal_one(outer, false, allocator) or_return;
internal_one(inner, false) or_return;
internal_one(outer, false) or_return;
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;
_private_int_recursive_product(temp, start, stop, 0, allocator) or_return;
internal_mul(inner, inner, temp, allocator) or_return;
internal_mul(outer, outer, inner, allocator) or_return;
_private_int_recursive_product(temp, start, stop, 0) or_return;
internal_mul(inner, inner, temp) or_return;
internal_mul(outer, outer, inner) or_return;
}
shift := n - intrinsics.count_ones(n);
return internal_shl(res, outer, int(shift), allocator);
return internal_shl(res, outer, int(shift));
}
/*
Recursive product used by binary split factorial algorithm.
*/
_private_int_recursive_product :: proc(res: ^Int, start, stop: int, level := int(0), allocator := context.allocator) -> (err: Error) {
context.allocator = allocator;
t1, t2 := &Int{}, &Int{};
defer internal_destroy(t1, t2);
@@ -1398,28 +1467,28 @@ _private_int_recursive_product :: proc(res: ^Int, start, stop: int, level := int
num_factors := (stop - start) >> 1;
if num_factors == 2 {
internal_set(t1, start, false, allocator) or_return;
internal_set(t1, start, false) or_return;
when true {
internal_grow(t2, t1.used + 1, false, allocator) or_return;
internal_add(t2, t1, 2, allocator) or_return;
internal_grow(t2, t1.used + 1, false) or_return;
internal_add(t2, t1, 2) or_return;
} else {
add(t2, t1, 2) or_return;
internal_add(t2, t1, 2) or_return;
}
return internal_mul(res, t1, t2, allocator);
return internal_mul(res, t1, t2);
}
if num_factors > 1 {
mid := (start + num_factors) | 1;
_private_int_recursive_product(t1, start, mid, level + 1, allocator) or_return;
_private_int_recursive_product(t2, mid, stop, level + 1, allocator) or_return;
return internal_mul(res, t1, t2, allocator);
_private_int_recursive_product(t1, start, mid, level + 1) or_return;
_private_int_recursive_product(t2, mid, stop, level + 1) or_return;
return internal_mul(res, t1, t2);
}
if num_factors == 1 {
return #force_inline internal_set(res, start, true, allocator);
return #force_inline internal_set(res, start, true);
}
return #force_inline internal_one(res, true, allocator);
return #force_inline internal_one(res, true);
}
/*

17
core/math/big/test.py
View File

@@ -403,14 +403,21 @@ def test_shr_signed(a = 0, bits = 0, expected_error = Error.Okay):
return test("test_shr_signed", res, [a, bits], expected_error, expected_result)
def test_factorial(n = 0, expected_error = Error.Okay):
args = [n]
res = int_factorial(*args)
def test_factorial(number = 0, expected_error = Error.Okay):
print("Factorial:", number)
args = [number]
try:
res = int_factorial(*args)
except OSError as e:
print("{} while trying to factorial {}.".format(e, number))
if EXIT_ON_FAIL: exit(3)
return False
expected_result = None
if expected_error == Error.Okay:
expected_result = math.factorial(n)
expected_result = math.factorial(number)
return test("test_factorial", res, [n], expected_error, expected_result)
return test("test_factorial", res, [number], expected_error, expected_result)
def test_gcd(a = 0, b = 0, expected_error = Error.Okay):
args = [arg_to_odin(a), arg_to_odin(b)]