FTZ checks three separate properties: the specified arithmetic graph, the CPU or shader environment needed by that graph, and the types and definitions visible through an installed package. Packet equality covers the recorded inputs; exact-rational bounds establish only the stated intermediate-value theorems.

Native numerical checks

The default CMake test build exercises both arithmetic policies. Manual m32 runs under gradual and flush controls; hardware h32 runs under admitted flush controls. Hardware policy under gradual controls is a negative admission case. The tests save and restore complete caller FP state, including status bits.

The maintained suites cover:

Scalar, short-vector and native-register arithmetic, typed memory and tails.
Independent FTZ policies, mixed-policy rejection, owning swizzles and masks.
Arrays and wide packs with zero, one and several independent registers.
Classification, sign transport and directed rounding under all four modes.
Exponential, logarithmic and trigonometric operation graphs, including their domain boundaries, exceptional values and signed zeros.
Module type identity, family-typed architecture arguments, scalar mask traits and the provider's default architecture.

ftz.exp.contract checks degrees 1 through 7 against an independent frozen-coefficient graph, including dense windows at output cutoffs and reduction transitions. It exercises scalar, SIMD, array and wide calls under both policies. The same executable can emit input/expected packets for the Metal exponential check. Packets must be generated from the source being tested: changing the range policy changes expected outputs even when the polynomial is unchanged.

The profile check compares 2,208 words against the checked-in finite-range.bin golden. At input 0x42b17217, scalar and wide exp/expm1 expect the finite word 0x7f7fff84. General vector scaling has an independent integer dyadic oracle covering signed flushing, arbitrary exponents, masked results and the minimum-normal boundary.

The tanh, log/log1p, trig and atan2 tests compare packed results with the scalar graph and can write common-width packets for comparisons across architectures. tests/compare_fp32.py permits NaN representation differences; every other word, including signed zero, must match. These checks establish sampled agreement, not exhaustive accuracy against the mathematical function.

Code-generation fixtures expose optimized leaves for inspection separately from runtime tests. Large packs may spill. Multiply and FMA retain boundary repairs; hardware flushing does not promise one instruction per public operation.

Installed consumers

The package fixture builds a third static library that exports an FTZ vector operation through its own named module. PCH and IPO are enabled. The API examples compile scalar policy, FP-environment and vector/array/wide usage.

Hosted CI moves both dependency prefixes to paths containing spaces before building these consumers. Consumers regenerate compatible BMIs from installed sources without using the producer's compiler cache. Header-only shader consumers must not load either host archive. Compilation and package relocation do not by themselves establish CPU instruction admission or GPU execution.

Compiler cache

Compiler-launcher regression tests live in modcache. They check argument and exit-status preservation, unchanged cache hits, raw-source invalidation and changed module inputs using isolated caches. Native and FTZ exercise that launcher in their normal producer builds; installed consumer checks remain uncached.

Independent accuracy checks

Run tests/{tanh,log,atan2}/verify_bounds.py to check live coefficient words and exact-rational intermediate bounds. These scripts do not establish correct rounding of the mathematical function.

The optional MPFR log/log1p suite leaves coefficients, recurrences and rounding points unchanged. It reports exact worst-case input/output words, ULP distance, absolute error near zero, sampled monotonicity and special/domain cases. Its 256/512-bit precision agreement is checked independently. Four retained regression witnesses are:

Function / measure	Input word	Graph output	Rounded FTZ reference
log / ULP distance	17b97dc0	c25c52bc	c25c52bd
log1p / ULP distance	bf7fffee	c15bec2e	c15bec2d
log / near-zero absolute error	3f7ff1f2	b960e62c	b960e62c
log1p / near-zero absolute error	b977e239	b977e9ba	b977e9ba

The assertions permit improved accuracy and preserve the measured per-case ceilings. Zero ULP distance can still have nonzero real error. Sampling does not establish exhaustive accuracy or monotonicity. See the oracle method.

Shader checks and execution scope

The shader fixtures compile HLSL 2021 with DXC, validate SPIR-V and translate to Metal. Separate numerical banks exercise both policies and the 32/64-bit integer implementations. Signed-add admission uses an integer-exact RNE-then-FTZ oracle; directed rounding uses an independent integer-word oracle. Input echoes and output-tail guards remain exact even when NaN output representations differ.

Generated code and successful translation do not establish device behavior. Native device execution must separately admit the compiled arithmetic and check the bank, guards and graphics validation diagnostics. A CPU test, a shader compile or a result from another device does not extend that admission.

Running the checks

Use the build guide and select only profiles admitted on the execution host. The default host build includes the numerical suites. CI results describe the revision, compiler and runner of that run; this page does not certify every architecture or device for the current checkout. Focused installed-consumer projects live beside their tests. Pass an output path to the tanh, log or atan2 executable to retain packets; trig also accepts --common. Keep producer and consumer compiler, standard library, exceptions and FP options compatible. Per-thread environment admission remains required for numerical execution.