cccl Complex asinh accuracy refinement

Update the complex asinh function to avoid numerical issues.

The current complex asinh function loses accuracy in several places. These mostly relate to over/underflow, and catastrophic cancellation for tough values.

This new version fixes these accuracy issues while retaining it's perf.

Perf

On GH100 we don't have much perf difference. (There used to be a much large perf gap until #5371 got merged, which the current version is availing of). Using the math-teams standard math_bench test we have the following:

Operations/SM/cycle: casinh():

H100	old	new	new/old
fp64	0.2531	0.2549	1.01
fp32	0.6072	0.6334	1.04

Correctness

The current version has several intervals where accuracy gets lost. Apart from the usual over/underflow suspects, there is also some very subtle intervals where accuracy gets badly thrown out, especially by catastrophic cancellation very close to +-i.

This new version fixes these and testing gives the following:

GPU Correctness

For the new version, an intensive bracket and bisect search, along with testing special hard values, gives:

GPU fp64:
Max ulp real error (4.867,1.742) @ (0.007757045272,-0.0002247045536)    (0x3f7fc5d9fc1f5662,0xbf2d73d56affd72d)
        Ours = (0.007756967678,-0.0002246977954)    Ref = (0.007756967678,-0.0002246977954)
        Ours = (0x3f7fc5c527dd1d58,0xbf2d739b5d7a3961)               Ref = (0x3f7fc5c527dd1d53,0xbf2d739b5d7a3963)

Max ulp imag error (0.1719,5.453) @ (7.198570162e+103,-5.623976789e+101)        (0x558011effdb5a3ad,0xd510120190e898df)
        Ours = (239.8333247,-0.007812471425)    Ref = (239.8333247,-0.007812471425)
        Ours = (0x406dfaaa988c99ba,0xbf7ffff854599f01)               Ref = (0x406dfaaa988c99ba,0xbf7ffff854599efc)

GPU fp32:
Max ulp real error (6.619,2.232) @ (0.007812378462,-0.0007928675623)    (0x3bfffefb,0xba4fd871)
        Ours = (0.007812298369,-0.0007928435807)    Ref = (0.007812301628,-0.0007928434643)
        Ours = (0x3bfffe4f,0xba4fd6d5)               Ref = (0x3bfffe56,0xba4fd6d3)

Max ulp imag error (3.732,5.528) @ (0.007806597743,3.029832988e-05)     (0x3bffce7d,0x37fe292b)
        Ours = (0.007806516718,3.029741674e-05)    Ref = (0.007806518581,3.029740583e-05)
        Ours = (0x3bffcdcf,0x37fe2735)               Ref = (0x3bffcdd3,0x37fe272f)

CPU Correctness

CPU fp64:
Max ulp real error (4.125,0) @ (0.01542893159,-0)       (0x3f8f993424afec00,0x8000000000000000)
        Ours = (0.01542831951,-0)    Ref = (0.01542831951,-0)
        Ours = (0x3f8f98e1fdb37251,0x8000000000000000)               Ref = (0x3f8f98e1fdb3724d,0x8000000000000000)

Max ulp imag error (0.5078,3.484) @ (0.8869326854,-1.12001698e-254)     (0x3fec61c0a7b18800,0x8b3505783ad41800)
        Ours = (0.7991224705,-8.379245502e-255)    Ref = (0.7991224705,-8.379245502e-255)
        Ours = (0x3fe99269498d3a37,0x8b2f742347588681)               Ref = (0x3fe99269498d3a36,0x8b2f742347588684)

CPU fp32:
Max ulp real error (4.827,0.5125) @ (0.001131535857,0.9893865585)       (0x3a94500b,0x3f7d4870)
        Ours = (0.007776218932,1.424767017)    Ref = (0.007776216604,1.424766898)
        Ours = (0x3bfecfa7,0x3fb65ec4)               Ref = (0x3bfecfa2,0x3fb65ec3)

Max ulp imag error (0.498,4.695) @ (-5.695841894e+11,3.510264218e+10)   (0xd3049ddd,0x5102c47d)
        Ours = (-27.76321411,0.06155067682)    Ref = (-27.76321411,0.06155069545)
        Ours = (0xc1de1b10,0x3d7c1c90)               Ref = (0xc1de1b10,0x3d7c1c95)

Oct 31 '25 20:10 s-oboyle

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Oct 31 '25 20:10 copy-pr-bot[bot]

😬 CI Workflow Results

🟥 Finished in 2h 13m: Pass: 80%/90 | Total: 1d 06h | Max: 1h 32m | Hits: 94%/152135

See results here.

Nov 03 '25 20:11 github-actions[bot]

😬 CI Workflow Results

🟥 Finished in 3h 18m: Pass: 80%/90 | Total: 23h 44m | Max: 1h 21m | Hits: 95%/154506

See results here.

Nov 06 '25 21:11 github-actions[bot]

😬 CI Workflow Results

🟥 Finished in 1h 25m: Pass: 78%/90 | Total: 1d 01h | Max: 1h 22m | Hits: 96%/154393

See results here.

Nov 07 '25 16:11 github-actions[bot]

/ok to test eb06d29

Nov 07 '25 17:11 miscco

😬 CI Workflow Results

🟥 Finished in 3h 51m: Pass: 86%/90 | Total: 20h 14m | Max: 1h 33m | Hits: 97%/190753

See results here.

Nov 07 '25 21:11 github-actions[bot]

😬 CI Workflow Results

🟥 Finished in 1h 11m: Pass: 98%/90 | Total: 16h 47m | Max: 34m 29s | Hits: 96%/215042

See results here.

Nov 10 '25 17:11 github-actions[bot]

/ok to test fa3bd08

Nov 10 '25 23:11 s-oboyle

😬 CI Workflow Results

🟥 Finished in 56m 56s: Pass: 97%/90 | Total: 19h 03m | Max: 42m 03s | Hits: 97%/210866

See results here.

Nov 11 '25 00:11 github-actions[bot]

🥳 CI Workflow Results

🟩 Finished in 1h 37m: Pass: 100%/88 | Total: 21h 47m | Max: 1h 23m | Hits: 98%/213613

See results here.

Nov 18 '25 13:11 github-actions[bot]

🥳 CI Workflow Results

🟩 Finished in 2h 21m: Pass: 100%/90 | Total: 22h 39m | Max: 2h 20m | Hits: 97%/213937

See results here.

Nov 20 '25 15:11 github-actions[bot]

/ok to test 684c44c

Nov 21 '25 10:11 s-oboyle

🥳 CI Workflow Results

🟩 Finished in 1h 05m: Pass: 100%/90 | Total: 16h 43m | Max: 55m 05s | Hits: 98%/213937

See results here.

Nov 21 '25 11:11 github-actions[bot]

/ok to test eacbe9e

Nov 26 '25 14:11 s-oboyle

🥳 CI Workflow Results

🟩 Finished in 1h 28m: Pass: 100%/90 | Total: 18h 42m | Max: 39m 48s | Hits: 96%/206358

See results here.

Nov 26 '25 15:11 github-actions[bot]

/ok to test 39dbc1c

Dec 02 '25 16:12 s-oboyle

🥳 CI Workflow Results

🟩 Finished in 1h 25m: Pass: 100%/90 | Total: 1d 13h | Max: 1h 22m | Hits: 95%/202196

See results here.

Dec 02 '25 18:12 github-actions[bot]