This adds a new path which avoids using compiler_rt generated div
udivmod instructions in the case that a divisor is less than half the
max usize value. Two half-limb divisions are performed instead which
ensures that non-emulated division instructions are actually used. This
does not improve the udivmod code which should still be reviewed
independently of this issue.
Notably this improves the performance of the toString implementation of
non-power-of-two bases considerably.
Division performance is improved ~1000% based on some coarse testing.
The following test code is used to provide a rough comparison between
the old vs. new method.
```
const std = @import("std");
const Managed = std.math.big.int.Managed;
const allocator = std.heap.c_allocator;
fn fib(a: *Managed, n: usize) !void {
var b = try Managed.initSet(allocator, 1);
defer b.deinit();
var c = try Managed.init(allocator);
defer c.deinit();
var i: usize = 0;
while (i < n) : (i += 1) {
try c.add(a.toConst(), b.toConst());
a.swap(&b);
b.swap(&c);
}
}
pub fn main() !void {
var a = try Managed.initSet(allocator, 0);
defer a.deinit();
try fib(&a, 1_000_000);
// Note: Next two lines (and printed digit count) omitted on no-print version.
const as = try a.toString(allocator, 10, .lower);
defer allocator.free(as);
std.debug.print("fib: digit count: {}, limb count: {}\n", .{ as.len, a.limbs.len });
}
```
```
==> time.no-print <==
limb count: 10849
________________________________________________________
Executed in 10.60 secs fish external
usr time 10.44 secs 0.00 millis 10.44 secs
sys time 0.02 secs 1.12 millis 0.02 secs
==> time.old <==
fib: digit count: 208988, limb count: 10849
________________________________________________________
Executed in 22.78 secs fish external
usr time 22.43 secs 1.01 millis 22.43 secs
sys time 0.03 secs 0.13 millis 0.03 secs
==> time.optimized <==
fib: digit count: 208988, limb count: 10849
________________________________________________________
Executed in 11.59 secs fish external
usr time 11.56 secs 1.03 millis 11.56 secs
sys time 0.03 secs 0.12 millis 0.03 secs
```
Perf data for non-optimized and optimized, verifying no udivmod is
generated by the new code.
```
$ perf report -i perf.data.old --stdio
- Total Lost Samples: 0
-
- Samples: 90K of event 'cycles:u'
- Event count (approx.): 71603695208
-
- Overhead Command Shared Object Symbol
- ........ ....... ................ ...........................................
-
52.97% t t [.] compiler_rt.udivmod.udivmod
45.97% t t [.] std.math.big.int.Mutable.addCarry
0.83% t t [.] main
0.08% t libc-2.33.so [.] __memmove_avx_unaligned_erms
0.08% t t [.] __udivti3
0.03% t [unknown] [k] 0xffffffff9a0010a7
0.02% t t [.] std.math.big.int.Managed.ensureCapacity
0.01% t libc-2.33.so [.] _int_malloc
0.00% t libc-2.33.so [.] __malloc_usable_size
0.00% t libc-2.33.so [.] _int_free
0.00% t t [.] 0x0000000000004a80
0.00% t t [.] std.heap.CAllocator.resize
0.00% t libc-2.33.so [.] _mid_memalign
0.00% t libc-2.33.so [.] sysmalloc
0.00% t libc-2.33.so [.] __posix_memalign
0.00% t t [.] std.heap.CAllocator.alloc
0.00% t ld-2.33.so [.] do_lookup_x
$ perf report -i perf.data.optimized --stdio
- Total Lost Samples: 0
-
- Samples: 46K of event 'cycles:u'
- Event count (approx.): 36790112336
-
- Overhead Command Shared Object Symbol
- ........ ....... ................ ...........................................
-
79.98% t t [.] std.math.big.int.Mutable.addCarry
15.14% t t [.] main
4.58% t t [.] std.math.big.int.Managed.ensureCapacity
0.21% t libc-2.33.so [.] __memmove_avx_unaligned_erms
0.05% t [unknown] [k] 0xffffffff9a0010a7
0.02% t libc-2.33.so [.] _int_malloc
0.01% t t [.] std.heap.CAllocator.alloc
0.01% t libc-2.33.so [.] __malloc_usable_size
0.00% t libc-2.33.so [.] systrim.constprop.0
0.00% t libc-2.33.so [.] _mid_memalign
0.00% t t [.] 0x0000000000000c7d
0.00% t libc-2.33.so [.] malloc
0.00% t ld-2.33.so [.] check_match
```
Closes#10630.
We already have a LICENSE file that covers the Zig Standard Library. We
no longer need to remind everyone that the license is MIT in every single
file.
Previously this was introduced to clarify the situation for a fork of
Zig that made Zig's LICENSE file harder to find, and replaced it with
their own license that required annual payments to their company.
However that fork now appears to be dead. So there is no need to
reinforce the copyright notice in every single file.
Now there are 3 types:
* std.math.big.int.Const
- the memory is immutable, only stores limbs and is_positive
- all methods operating on constant data go here
* std.math.big.int.Mutable
- the memory is mutable, stores capacity in addition to limbs and
is_positive
- methods here have some Mutable parameters and some Const
parameters. These methods expect callers to pre-calculate the
amount of resources required, and asserts that the resources are
available.
* std.math.big.int.Managed
- the memory is mutable and additionally stores an allocator.
- methods here perform the resource calculations for the programmer.
- this is the high level abstraction from before
Each of these 3 types can be converted to the other ones.
You can see the use case for this in the self-hosted compiler, where we
only store limbs, and construct the big ints as needed.
This gets rid of the hack where the allocator was optional and the
notion of "fixed" versions of the struct. Such things are now modeled
with the `big.int.Const` type.
