Add mul_add_relaxed methods for floating-point types

[landsharkiest]

Implements mul_add_relaxed for f16, f32, f64, and f128, which computes (self * a) + b with relaxed precision semantics. Unlike mul_add which guarantees a fused operation, this variant allows the compiler to choose between fused or separate operations based on target performance.

This fills the gap between the precision-guaranteed mul_add and the fully-optimizable algebraic operators, providing target-specific optimization while maintaining reasonable floating-point semantics.

Tracking issue: #151770
#151770

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  • 66f66cc

[tgross35]

f16 and f128 should be covered here too. They just need to be gated behing #[cfg(target_has_reliable_f16_math)] / target_has_reliable_f128_math

[scottmcm]

Can we please include at least one example where they don't give the same result, and the assert has to be "well it's either this or that"?

Here's one I tossed together; there are probably better ones:

let r = 0.1_f32.mul_add_relaxed(0.1_f32, -0.01_f32);
assert!(r == 9.313226e-10 || r == 5.2154064e-10);

[rust-log-analyzer]

The job pr-check-2 failed! Check out the build log: (web) (plain enhanced) (plain)

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ghcr.io/dependabot/dependabot-updater-core   latest    bcec0b4e062b   8 days ago   783MB
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---
---- library/core/src/num/f16.rs - f16::f16::mul_add_relaxed (line 1480) stdout ----
error: unexpected `cfg` condition name: `reliable_f16`
    --> library/core/src/num/f16.rs:1484:7
     |
1484 | #[cfg(reliable_f16)] {
     |       ^^^^^^^^^^^^
     |
     = help: expected names are: `docsrs`, `feature`, `llvm_enzyme`, `no_fp_fmt_parse`, `target_has_reliable_f128`, `target_has_reliable_f128_math`, `target_has_reliable_f16`, `target_has_reliable_f16_math`, and `test` and 31 more
     = help: consider using a Cargo feature instead
     = help: or consider adding in `Cargo.toml` the `check-cfg` lint config for the lint:
              [lints.rust]
              unexpected_cfgs = { level = "warn", check-cfg = ['cfg(reliable_f16)'] }
     = help: or consider adding `println!("cargo::rustc-check-cfg=cfg(reliable_f16)");` to the top of the `build.rs`
     = note: see <https://doc.rust-lang.org/nightly/rustc/check-cfg/cargo-specifics.html> for more information about checking conditional configuration
note: the lint level is defined here
    --> library/core/src/num/f16.rs:1476:9
     |
1476 | #![deny(warnings)]
---

stderr:

thread 'main' (85511) panicked at library/core/src/num/f64.rs:22:1:
assertion failed: r == 9.313225746154785e-10 || r == 2.7755575615628914e-17
stack backtrace:
   0: __rustc::rust_begin_unwind
   1: core::panicking::panic_fmt
   2: core::panicking::panic
   3: rust_out::main::_doctest_main_library_core_src_num_f64_rs_1655_0
   4: rust_out::main
   5: <fn() as core::ops::function::FnOnce<()>>::call_once
note: Some details are omitted, run with `RUST_BACKTRACE=full` for a verbose backtrace.

---- library/core/src/num/f64.rs - f64::f64::mul_add_relaxed (line 1655) stdout end ----

[rust-bors]

☔ The latest upstream changes (presumably #152624) made this pull request unmergeable. Please resolve the merge conflicts.