[ndgrigorian]

This PR adds integers and the discrete distributions to dpnp.random.Generator, as part of the series splitting #3147. It is stacked on #3158

Adds

• integers, using NumPy's bounded integer algorithm (Lemire's method)
• poisson, binomial (inversion and BTPE), negative_binomial, geometric, logseries, zipf and hypergeometric (HRUA)
• noncentral_chisquare and noncentral_f, which need poisson

The discrete samplers return int64 and compute in double precision, or in single precision on devices without fp64. In single precision, host parameters are clipped so that they stay inside the domain once rounded, and the large log-factorial terms of BTPE and HRUA are gathered into one log1p so that they don't cancel. zipf uses expm1/log1p, deliberately departing from NumPy, whose tail for a close to 1 is too heavy above 2**53 (documented in random.rst)

As in #3158, every rejection sampler returns the smallest int64 for device parameters that would make it loop forever

Also adds umul_hi, which replaces sycl::mul_hi; DPC++ 2026.2 miscompiles sycl::mul_hi on Intel GPUs when one operand is a compile-time constant

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• Have you tested your changes locally for CPU and GPU devices?
• Have you made sure that new changes do not introduce compiler warnings?
• Have you checked performance impact of proposed changes?
• Have you added documentation for your changes, if necessary?
• Have you added your changes to the changelog?

[github-actions]

View rendered docs @ https://intelpython.github.io/dpnp/pull/3159/index.html

[github-actions]

Array API standard conformance tests for dpnp=0.22.0dev0=np2py314h8d9cdd5_29 ran successfully.
Passed: 1491
Failed: 0
Skipped: 6

[coveralls]

Coverage is 81.878% — feature/device-rng-discrete into feature/device-rng-continuous. No base build found for feature/device-rng-continuous.