Big-int functions were updated to respect the provided abi_size, rather
than inferring a potentially incorrect abi_size implicitly.
In combination with the convention that any required padding bits are
added on the MSB end, this means that exotic integers can potentially
have a well-defined memory layout.
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.
AIR:
* div is renamed to div_trunc.
* Add div_float, div_floor, div_exact.
- Implemented in Sema and LLVM codegen. C backend has a stub.
Improvements to std.math.big.Int:
* Add `eqZero` function to `Mutable`.
* Fix incorrect results for `divFloor`.
Compiler-rt:
* Add muloti4 to the stage2 section.
Before, Sema for comptime `@bitCast` would return the same Value but
change the Type. This gave invalid results because, for example, an
integer Value when the Type is a float would be interpreted numerically,
but `@bitCast` needs it to reinterpret how they would be stored in
memory.
This requires a mechanism to serialize a Value to a byte buffer and
deserialize a Value from a byte buffer.
Not done yet, but needs to happen: comptime dereferencing a pointer
to a Decl needs to perform a comptime bitcast on the loaded value.
Currently the value is silently wrong in the same way that `@bitCast`
was silently wrong before this commit.
The logic in Value for handling readFromMemory for large integers is
only correct for small integers. It needs to be fleshed out for proper
big integers.
As part of this change:
* std.math.big.Int: initial implementations of readTwosComplement and
writeTwosComplement. They only support bit_count <= 128 so far and
panic otherwise.
* compiler-rt: move the compareXf2 exports over to the stage2 section.
Even with the improvements in this commit, I'm still seeing test
failures in the widening behavior tests; more investigation is
needed.
This function can be used to initialize a big integer to either the upper
or lower limit of a 2s-complement integer. Note that the result is still
in sign-magnitude representation, though in order to convert it into twos
complement all one has to do is take the absolute value.
lladd is now implemented in terms of lladdcarry, which returns the carry limb.
Similarly, llsub is implemented using llsubcarry, which returns the borrow limb.
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.
After a right shift, top limbs may be all zero. However, without
normalization, the number of limbs is not going to change.
In order to check if a big number is zero, we used to assume that the
number of limbs is 1. Which may not be the case after right shifts,
even if the actual value is zero.
- Normalize after a right shift
- Add a test for that issue
- Check all the limbs in `eqlZero()`. It may not be necessary if
callers always remember to normalize before calling the function.
But checking all the limbs is very cheap and makes the function less
bug-prone.
