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big: Improve tunables.

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This commit is contained in:
Jeroen van Rijn
2021-08-07 18:44:05 +02:00
parent d4a03acbc3
commit 777e17d80f
7 changed files with 100 additions and 69 deletions
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core/math/big/basic.odin
+2 -4
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@@ -11,8 +11,6 @@ package big
This file contains basic arithmetic operations like `add`, `sub`, `mul`, `div`, ...
*/
import "core:mem"
/*
===========================
User-level routines
@@ -244,7 +242,7 @@ sqrmod :: proc { int_sqrmod, };
int_factorial :: proc(res: ^Int, n: int) -> (err: Error) {
if n < 0 || n > _FACTORIAL_MAX_N { return .Invalid_Argument; }
if n < 0 || n > FACTORIAL_MAX_N { return .Invalid_Argument; }
if res == nil { return .Invalid_Pointer; }
return #force_inline internal_int_factorial(res, n);
@@ -269,7 +267,7 @@ factorial :: proc { int_factorial, };
*/
int_choose_digit :: proc(res: ^Int, n, k: int) -> (err: Error) {
if res == nil { return .Invalid_Pointer; }
if n < 0 || n > _FACTORIAL_MAX_N { return .Invalid_Argument; }
if n < 0 || n > FACTORIAL_MAX_N { return .Invalid_Argument; }
if k > n { return zero(res); }
core/math/big/build.bat
+3 -3
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@@ -1,10 +1,10 @@
@echo off
:odin run . -vet
odin run . -vet
: -o:size
:odin build . -build-mode:shared -show-timings -o:minimal -no-bounds-check
:odin build . -build-mode:shared -show-timings -o:size -no-bounds-check
:odin build . -build-mode:shared -show-timings -o:size
odin build . -build-mode:shared -show-timings -o:speed -no-bounds-check
:odin build . -build-mode:shared -show-timings -o:speed -no-bounds-check
:odin build . -build-mode:shared -show-timings -o:speed
python test.py
:python test.py
core/math/big/common.odin
+55 -34
View File
@@ -13,19 +13,68 @@ import "core:intrinsics"
/*
TODO: Make the tunables runtime adjustable where practical.
This allows to benchmark and/or setting optimized values for a certain CPU without recompiling.
*/
/*
Tunables
========================== TUNABLES ==========================
`initialize_constants` returns `#config(MUL_KARATSUBA_CUTOFF, _DEFAULT_MUL_KARATSUBA_CUTOFF)`
and we initialize this cutoff that way so that the procedure is used and called,
because it handles initializing the constants ONE, ZERO, MINUS_ONE, NAN and INF.
`initialize_constants` also replaces the other `_DEFAULT_*` cutoffs with custom compile-time values if so `#config`ured.
*/
MUL_KARATSUBA_CUTOFF := initialize_constants();
SQR_KARATSUBA_CUTOFF := _DEFAULT_SQR_KARATSUBA_CUTOFF;
MUL_TOOM_CUTOFF := _DEFAULT_MUL_TOOM_CUTOFF;
SQR_TOOM_CUTOFF := _DEFAULT_SQR_TOOM_CUTOFF;
/*
These defaults were tuned on an AMD A8-6600K (64-bit) using libTomMath's `make tune`.
TODO(Jeroen): Port this tuning algorithm and tune them for more modern processors.
It would also be cool if we collected some data across various processor families.
This would let uss set reasonable defaults at runtime as this library initializes
itself by using `cpuid` or the ARM equivalent.
*/
MATH_BIG_FORCE_64_BIT :: false;
MATH_BIG_FORCE_32_BIT :: false;
_DEFAULT_MUL_KARATSUBA_CUTOFF :: #config(MUL_KARATSUBA_CUTOFF, 80);
_DEFAULT_SQR_KARATSUBA_CUTOFF :: #config(SQR_KARATSUBA_CUTOFF, 120);
_DEFAULT_MUL_TOOM_CUTOFF :: #config(MUL_TOOM_CUTOFF, 350);
_DEFAULT_SQR_TOOM_CUTOFF :: #config(SQR_TOOM_CUTOFF, 400);
MAX_ITERATIONS_ROOT_N := 500;
/*
Largest `N` for which we'll compute `N!`
*/
FACTORIAL_MAX_N := 1_000_000;
/*
Cutoff to switch to int_factorial_binary_split, and its max recursion level.
*/
FACTORIAL_BINARY_SPLIT_CUTOFF := 6100;
FACTORIAL_BINARY_SPLIT_MAX_RECURSIONS := 100;
/*
We don't allow these to be switched at runtime for two reasons:
1) 32-bit and 64-bit versions of procedures use different types for their storage,
so we'd have to double the number of procedures, and they couldn't interact.
2) Optimizations thanks to precomputed masks wouldn't work.
*/
MATH_BIG_FORCE_64_BIT :: #config(MATH_BIG_FORCE_64_BIT, false);
MATH_BIG_FORCE_32_BIT :: #config(MATH_BIG_FORCE_32_BIT, false);
when (MATH_BIG_FORCE_32_BIT && MATH_BIG_FORCE_64_BIT) { #panic("Cannot force 32-bit and 64-bit big backend simultaneously."); };
_LOW_MEMORY :: #config(BIGINT_SMALL_MEMORY, false);
_LOW_MEMORY :: #config(BIGINT_SMALL_MEMORY, false);
when _LOW_MEMORY {
_DEFAULT_DIGIT_COUNT :: 8;
} else {
@@ -33,36 +82,8 @@ when _LOW_MEMORY {
}
/*
`initialize_constants` returns `#config(MUL_KARATSUBA_CUTOFF, _DEFAULT_MUL_KARATSUBA_CUTOFF)`
and we initialize this cutoff that way so that the procedure is used and called,
because it handles initializing the constants ONE, ZERO, MINUS_ONE, NAN and INF.
======================= END OF TUNABLES =======================
*/
_MUL_KARATSUBA_CUTOFF := initialize_constants();
_SQR_KARATSUBA_CUTOFF := #config(SQR_KARATSUBA_CUTOFF, _DEFAULT_SQR_KARATSUBA_CUTOFF);
_MUL_TOOM_CUTOFF := #config(MUL_TOOM_CUTOFF, _DEFAULT_MUL_TOOM_CUTOFF);
_SQR_TOOM_CUTOFF := #config(SQR_TOOM_CUTOFF, _DEFAULT_SQR_TOOM_CUTOFF);
/*
These defaults were tuned on an AMD A8-6600K (64-bit) using libTomMath's `make tune`.
TODO(Jeroen): Port this tuning algorithm and tune them for more modern processors.
*/
_DEFAULT_MUL_KARATSUBA_CUTOFF :: 80;
_DEFAULT_SQR_KARATSUBA_CUTOFF :: 120;
_DEFAULT_MUL_TOOM_CUTOFF :: 350;
_DEFAULT_SQR_TOOM_CUTOFF :: 400;
_MAX_ITERATIONS_ROOT_N :: 500;
/*
Largest `N` for which we'll compute `N!`
*/
_FACTORIAL_MAX_N :: 1_000_000;
/*
Cutoff to switch to int_factorial_binary_split, and its max recursion level.
*/
_FACTORIAL_BINARY_SPLIT_CUTOFF :: 6100;
_FACTORIAL_BINARY_SPLIT_MAX_RECURSIONS :: 100;
Sign :: enum u8 {
Zero_or_Positive = 0,
core/math/big/example.odin
+27 -15
View File
@@ -15,17 +15,23 @@ import "core:mem"
print_configation :: proc() {
fmt.printf(
`Configuration:
DIGIT_BITS %v
MIN_DIGIT_COUNT %v
MAX_DIGIT_COUNT %v
DEFAULT_DIGIT_COUNT %v
MAX_COMBA %v
WARRAY %v
MUL_KARATSUBA_CUTOFF %v
SQR_KARATSUBA_CUTOFF %v
MUL_TOOM_CUTOFF %v
SQR_TOOM_CUTOFF %v
`
Configuration:
_DIGIT_BITS %v
_MIN_DIGIT_COUNT %v
_MAX_DIGIT_COUNT %v
_DEFAULT_DIGIT_COUNT %v
_MAX_COMBA %v
_WARRAY %v
Runtime tunable:
MUL_KARATSUBA_CUTOFF %v
SQR_KARATSUBA_CUTOFF %v
MUL_TOOM_CUTOFF %v
SQR_TOOM_CUTOFF %v
MAX_ITERATIONS_ROOT_N %v
FACTORIAL_MAX_N %v
FACTORIAL_BINARY_SPLIT_CUTOFF %v
FACTORIAL_BINARY_SPLIT_MAX_RECURSIONS %v
`, _DIGIT_BITS,
_MIN_DIGIT_COUNT,
@@ -33,10 +39,14 @@ _MAX_DIGIT_COUNT,
_DEFAULT_DIGIT_COUNT,
_MAX_COMBA,
_WARRAY,
_MUL_KARATSUBA_CUTOFF,
_SQR_KARATSUBA_CUTOFF,
_MUL_TOOM_CUTOFF,
_SQR_TOOM_CUTOFF,
MUL_KARATSUBA_CUTOFF,
SQR_KARATSUBA_CUTOFF,
MUL_TOOM_CUTOFF,
SQR_TOOM_CUTOFF,
MAX_ITERATIONS_ROOT_N,
FACTORIAL_MAX_N,
FACTORIAL_BINARY_SPLIT_CUTOFF,
FACTORIAL_BINARY_SPLIT_MAX_RECURSIONS,
);
}
@@ -84,6 +94,8 @@ main :: proc() {
demo();
print_configation();
print_timings();
if len(ta.allocation_map) > 0 {
core/math/big/exp_log.odin
+3 -3
View File
@@ -360,7 +360,7 @@ int_root_n :: proc(dest, src: ^Int, n: int) -> (err: Error) {
}
if c, err = cmp(t1, t2); c == 0 { break; }
iterations += 1;
if iterations == _MAX_ITERATIONS_ROOT_N {
if iterations == MAX_ITERATIONS_ROOT_N {
return .Max_Iterations_Reached;
}
}
@@ -383,7 +383,7 @@ int_root_n :: proc(dest, src: ^Int, n: int) -> (err: Error) {
}
iterations += 1;
if iterations == _MAX_ITERATIONS_ROOT_N {
if iterations == MAX_ITERATIONS_ROOT_N {
return .Max_Iterations_Reached;
}
}
@@ -401,7 +401,7 @@ int_root_n :: proc(dest, src: ^Int, n: int) -> (err: Error) {
}
iterations += 1;
if iterations == _MAX_ITERATIONS_ROOT_N {
if iterations == MAX_ITERATIONS_ROOT_N {
return .Max_Iterations_Reached;
}
}
core/math/big/helpers.odin
+1 -1
View File
@@ -691,7 +691,7 @@ initialize_constants :: proc() -> (res: int) {
set( INF, 1); INF.flags = {.Immutable, .Inf};
set( INF, -1); MINUS_INF.flags = {.Immutable, .Inf};
return #config(MUL_KARATSUBA_CUTOFF, _DEFAULT_MUL_KARATSUBA_CUTOFF);
return _DEFAULT_MUL_KARATSUBA_CUTOFF;
}
destroy_constants :: proc() {
core/math/big/internal.odin
+9 -9
View File
@@ -597,10 +597,10 @@ internal_int_mul :: proc(dest, src, multiplier: ^Int, allocator := context.alloc
/*
Do we need to square?
*/
if false && src.used >= _SQR_TOOM_CUTOFF {
if false && src.used >= SQR_TOOM_CUTOFF {
/* Use Toom-Cook? */
// err = s_mp_sqr_toom(a, c);
} else if false && src.used >= _SQR_KARATSUBA_CUTOFF {
} else if false && src.used >= SQR_KARATSUBA_CUTOFF {
/* Karatsuba? */
// err = s_mp_sqr_karatsuba(a, c);
} else if false && ((src.used * 2) + 1) < _WARRAY &&
@@ -625,16 +625,16 @@ 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 false && min_used >= MUL_KARATSUBA_CUTOFF &&
max_used / 2 >= MUL_KARATSUBA_CUTOFF &&
/*
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);
} else if false && min_used >= _MUL_TOOM_CUTOFF {
} else if false && min_used >= MUL_TOOM_CUTOFF {
// err = s_mp_mul_toom(a, b, c);
} else if false && min_used >= _MUL_KARATSUBA_CUTOFF {
} else if false && min_used >= MUL_KARATSUBA_CUTOFF {
// err = s_mp_mul_karatsuba(a, b, c);
} else if digits < _WARRAY && min_used <= _MAX_COMBA {
/*
@@ -676,7 +676,7 @@ internal_int_divmod :: proc(quotient, remainder, numerator, denominator: ^Int, a
return nil;
}
if false && (denominator.used > 2 * _MUL_KARATSUBA_CUTOFF) && (denominator.used <= (numerator.used/3) * 2) {
if false && (denominator.used > 2 * MUL_KARATSUBA_CUTOFF) && (denominator.used <= (numerator.used/3) * 2) {
// err = _int_div_recursive(quotient, remainder, numerator, denominator);
} else {
when true {
@@ -846,7 +846,7 @@ internal_sqrmod :: proc { internal_int_sqrmod, };
This way we'll have to reallocate less, possibly not at all.
*/
internal_int_factorial :: proc(res: ^Int, n: int) -> (err: Error) {
if n >= _FACTORIAL_BINARY_SPLIT_CUTOFF {
if n >= FACTORIAL_BINARY_SPLIT_CUTOFF {
return #force_inline _private_int_factorial_binary_split(res, n);
}
@@ -1490,7 +1490,7 @@ _private_int_recursive_product :: proc(res: ^Int, start, stop: int, level := int
t1, t2 := &Int{}, &Int{};
defer destroy(t1, t2);
if level > _FACTORIAL_BINARY_SPLIT_MAX_RECURSIONS { return .Max_Iterations_Reached; }
if level > FACTORIAL_BINARY_SPLIT_MAX_RECURSIONS { return .Max_Iterations_Reached; }
num_factors := (stop - start) >> 1;
if num_factors == 2 {