Derive FFT twiddle phase type from scalar lanes

[PhysicistJohn]

Context

This fork draft targets draft/generic-metal-fft, the source branch reviewed in ml-explore/mlx#3969. That work templates the Metal C2C FFT over its scalar lane type, but get_twiddle<T> still names float directly for phase evaluation.

This is the next narrow step toward generalizing FFT precision across all Metal planning paths.

Current MLX executes FFTs at one scalar precision: public transforms cast inputs to float32 or complex64, the Metal planner table instantiates only float/float2, and Bluestein's chirp and convolution constants are complex64. The restriction applies to Stockham, Rader, Bluestein, and four-step rather than Bluestein alone.

• Public FFT promotion to float32 / complex64
• Metal planner instantiations
• Bluestein complex64 constants

Change

Derive the twiddle phase type from the templated scalar lane and Metal's pi constant:

using phase_T = decltype(M_PI_F * T(0));

The phase expression then remains in phase_T until fast::sin and fast::cos; the resulting twiddle is converted to the FFT lane type at the existing boundary.

Deriving from the phase arithmetic is intentional. decltype(fast::sin(T(0))) is include-context dependent because MLX's BF16 math wrapper declares a BF16 result while evaluating through FP32. In a JIT kernel that form prematurely quantized the phase, reduced accuracy, and slowed every measured planner. The arithmetic-promotion form is stable across static and JIT compilation.

Scope

• One file and one commit.
• No public dtype, API, host dispatch, or kernel-instantiation changes.
• No claim of reduced-precision FFT support in this patch.
• Shared by Stockham, Rader, Bluestein, and four-step through get_twiddle<T>.

Validation

• Native xcrun metal compilation of the production FFT planner table.
• Compile-only half2 and bfloat2 C2C instantiations across all four planners.
• Baseline and patched AIR are byte-identical for both production and reduced-precision compile sets.
• Exported symbols unchanged: 75 production; 85 with the compile-only reduced planners.
• Float, FP16, and BF16 correctness summaries exactly match baseline across Stockham, Rader, Bluestein, and four-step.
• Sixteen paired timing rounds show no measurable performance change:

Planner	Patched / baseline throughput
Stockham	1.003x
Rader	1.004x
Bluestein	1.001x
Four-step	0.995x

• clang-format --dry-run --Werror and git diff --check pass.

[PhysicistJohn]

Folded into ml-explore#3969 as part of its amended single commit (611e080). This fork PR remains the isolated review record.