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math: fix acosh for x < 1 (including negative inputs) #35616

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arshidkv12 wants to merge 6 commits from arshidkv12/zig:acosh-1 into master
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#35315

https://codeberg.org/ziglang/zig/issues/35315
math: fix acosh for x < 1 (including negative inputs)
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I don't think this is the fix we want here.

Specifically, I expect the x < 1.0 case to be handled in the first branch:

return math.log1p(x - 1 + @sqrt((x - 1) * (x - 1) + 2 * (x - 1)));

This handles the cases implicitly by the behaviour of log1p and sqrt. Either the argument to sqrt will be negative (-1 < x < 1), or the argument to log1p will be negative (x < -1) ), as x will grow faster relative to sqrt argument in all other cases. Both of which will propagate a nan through as the acosh return value.

If you run these tests against master, we can see that f32 already produces the correct values according to the tests, suggesting that only acosh64 is an issue.

Based on your debugging, perhaps look at why the second branch is being taken for these negative instead of the first (which should handle the domain issue). Notably the exponent check differs a little.

See also upstream musl which this code was derived from: https://git.musl-libc.org/cgit/musl/tree/src/math/acosh.c

I don't think this is the fix we want here. Specifically, I expect the `x < 1.0` case to be handled in the first branch: ``` return math.log1p(x - 1 + @sqrt((x - 1) * (x - 1) + 2 * (x - 1))); ``` This handles the cases implicitly by the behaviour of log1p and sqrt. Either the argument to sqrt will be negative (`-1 < x < 1`), or the argument to `log1p` will be negative (`x < -1`) ), as x will grow faster relative to `sqrt` argument in all other cases. Both of which will propagate a nan through as the acosh return value. If you run these tests against master, we can see that `f32` already produces the correct values according to the tests, suggesting that only `acosh64` is an issue. Based on your debugging, perhaps look at why the second branch is being taken for these negative instead of the first (which should handle the domain issue). Notably the exponent check differs a little. See also upstream musl which this code was derived from: https://git.musl-libc.org/cgit/musl/tree/src/math/acosh.c
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@tiehuis wrote in #35616 (comment):

I don't think this is the fix we want here.

Specifically, I expect the x < 1.0 case to be handled in the first branch:

return math.log1p(x - 1 + @sqrt((x - 1) * (x - 1) + 2 * (x - 1)));

This handles the cases implicitly by the behaviour of log1p and sqrt. Either the argument to sqrt will be negative (-1 < x < 1), or the argument to log1p will be negative (x < -1) ), as x will grow faster relative to sqrt argument in all other cases. Both of which will propagate a nan through as the acosh return value.

If you run these tests against master, we can see that f32 already produces the correct values according to the tests, suggesting that only acosh64 is an issue.

Based on your debugging, perhaps look at why the second branch is being taken for these negative instead of the first (which should handle the domain issue). Notably the exponent check differs a little.

See also upstream musl which this code was derived from: https://git.musl-libc.org/cgit/musl/tree/src/math/acosh.c

Yes, the acosh32 is working properly. But I think, musl c code also not working.

#include <stdio.h>#include <math.h>#include <stdint.h>
double acosh(double x)
{
	union {double f; uint64_t i;} u = {.f = x};
	unsigned e = u.i >> 52 & 0x7ff;
	/* x < 1 domain error is handled in the called functions */
	if (e < 0x3ff + 1)
		/* |x| < 2, up to 2ulp error in [1,1.125] */
		return log1p(x-1 + sqrt((x-1)*(x-1)+2*(x-1)));
	if (e < 0x3ff + 26)
		/* |x| < 0x1p26 */
		return log(2*x - 1/(x+sqrt(x*x-1)));
	/* |x| >= 0x1p26 or nan */
	return log(x) + 0.693147180559945309417232121458176568;
}
int main(){
 double x = -1.9e4;
 double z = acosh(x);
 printf("out x %f \n", z);
 double y = -2e4;
 double k = acosh(x);
 printf("out x %f \n", k);
}

Out

gcc z.c && ./a.out 
out x -7.288321 
out x -7.288321

Note: x < 1 domain error is handled in the called functions.

@tiehuis wrote in https://codeberg.org/ziglang/zig/pulls/35616#issuecomment-16530128: > I don't think this is the fix we want here. > > Specifically, I expect the `x < 1.0` case to be handled in the first branch: > > ```text > return math.log1p(x - 1 + @sqrt((x - 1) * (x - 1) + 2 * (x - 1))); > ``` > > This handles the cases implicitly by the behaviour of log1p and sqrt. Either the argument to sqrt will be negative (`-1 < x < 1`), or the argument to `log1p` will be negative (`x < -1`) ), as x will grow faster relative to `sqrt` argument in all other cases. Both of which will propagate a nan through as the acosh return value. > > If you run these tests against master, we can see that `f32` already produces the correct values according to the tests, suggesting that only `acosh64` is an issue. > > Based on your debugging, perhaps look at why the second branch is being taken for these negative instead of the first (which should handle the domain issue). Notably the exponent check differs a little. > > See also upstream musl which this code was derived from: https://git.musl-libc.org/cgit/musl/tree/src/math/acosh.c Yes, the `acosh32` is working properly. But I think, `musl c` code also not working. ```c #include <stdio.h> #include <math.h> #include <stdint.h> double acosh(double x) { union {double f; uint64_t i;} u = {.f = x}; unsigned e = u.i >> 52 & 0x7ff; /* x < 1 domain error is handled in the called functions */ if (e < 0x3ff + 1) /* |x| < 2, up to 2ulp error in [1,1.125] */ return log1p(x-1 + sqrt((x-1)*(x-1)+2*(x-1))); if (e < 0x3ff + 26) /* |x| < 0x1p26 */ return log(2*x - 1/(x+sqrt(x*x-1))); /* |x| >= 0x1p26 or nan */ return log(x) + 0.693147180559945309417232121458176568; } int main(){ double x = -1.9e4; double z = acosh(x); printf("out x %f \n", z); double y = -2e4; double k = acosh(x); printf("out x %f \n", k); } ``` Out ```bash gcc z.c && ./a.out out x -7.288321 out x -7.288321 ``` Note: x < 1 domain error is handled in the called functions.
math: fix acosh for x < 1 (including negative inputs)
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e90b3bfd4f
math: fix acosh for x < 1 (including negative inputs)
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eb87e0f45a
math: fix acosh for x < 1 (including negative inputs)
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8be54d5dac
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Given we are have some inherent issues with the implementation's accuracy itself, I would be keen to replace the implementation and check that against the libc-test you've got set up. We would feel a bit more confident in the results instead of just handling the 0 case here. This would also help your other pr and we could enable the tests in that PR.

The FreeBSD implementation suggested in the issue is worth a first look.

Given we are have some inherent issues with the implementation's accuracy itself, I would be keen to replace the implementation and check that against the libc-test you've got set up. We would feel a bit more confident in the results instead of just handling the 0 case here. This would also help your other pr and we could enable the tests in that PR. The FreeBSD implementation suggested in the issue is worth a first look.
Fixed acosh -ve value issue
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6fbedd9cd7
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Thank you. I changed it based on FreeBSD.

Thank you. I changed it based on FreeBSD.
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zig cc
Zig as a drop-in C-family compiler.
zig fmt
The Zig source code formatter.
zig reduce
The Zig source code reduction tool.
bounty
https://ziglang.org/news/announcing-donor-bounties
bug
Observed behavior contradicts documented or intended behavior.
contributor-friendly
This issue is limited in scope and/or knowledge of project internals.
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enhancement
Solving this issue will likely involve adding new logic or components to the codebase.
infra
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optimization
A task to improve performance and/or resource usage.
question
No questions on the issue tracker; use a community space instead.
regression
Something that used to work in a previous version stopped working
upstream
An issue with a third-party project that this project uses.
use case
Describes a real use case that is difficult or impossible, but does not propose a solution.
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binutils
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debug info
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linking
miscompilation
os/android
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proposal
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testing
zig cc
zig fmt
zig reduce
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bug
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Reference
ziglang/zig!35616
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ziglang/zig
No description provided.
Delete branch "arshidkv12/zig:acosh-1"

Deleting a branch is permanent. Although the deleted branch may continue to exist for a short time before it actually gets removed, it CANNOT be undone in most cases. Continue?