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53e6c719ef
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.
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