gui/dependencies/pcg32/pcg32.h

/*
 * Tiny self-contained version of the PCG Random Number Generation for C++
 * put together from pieces of the much larger C/C++ codebase.
 * Wenzel Jakob, February 2015
 *
 * The PCG random number generator was developed by Melissa O'Neill
 * <[email protected]>
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 * For additional information about the PCG random number generation scheme,
 * including its license and other licensing options, visit
 *
 *     http://www.pcg-random.org
 *
 * Note: This code was modified to work with CUDA by the tiny-cuda-nn authors.
 */

#pragma once

#include <tiny-cuda-nn/common.h>

#define PCG32_DEFAULT_STATE  0x853c49e6748fea9bULL
#define PCG32_DEFAULT_STREAM 0xda3e39cb94b95bdbULL
#define PCG32_MULT           0x5851f42d4c957f2dULL

namespace tcnn {

/// PCG32 Pseudorandom number generator
struct pcg32 {
	/// Initialize the pseudorandom number generator with default seed
	TCNN_HOST_DEVICE pcg32() : state(PCG32_DEFAULT_STATE), inc(PCG32_DEFAULT_STREAM) {}

	/// Initialize the pseudorandom number generator with the \ref seed() function
	TCNN_HOST_DEVICE pcg32(uint64_t initstate, uint64_t initseq = 1u) { seed(initstate, initseq); }

	/**
	 * \brief Seed the pseudorandom number generator
	 *
	 * Specified in two parts: a state initializer and a sequence selection
	 * constant (a.k.a. stream id)
	 */
	TCNN_HOST_DEVICE void seed(uint64_t initstate, uint64_t initseq = 1) {
		state = 0U;
		inc = (initseq << 1u) | 1u;
		next_uint();
		state += initstate;
		next_uint();
	}

	/// Generate a uniformly distributed unsigned 32-bit random number
	TCNN_HOST_DEVICE uint32_t next_uint() {
		uint64_t oldstate = state;
		state = oldstate * PCG32_MULT + inc;
		uint32_t xorshifted = (uint32_t) (((oldstate >> 18u) ^ oldstate) >> 27u);
		uint32_t rot = (uint32_t) (oldstate >> 59u);
		return (xorshifted >> rot) | (xorshifted << ((~rot + 1u) & 31));
	}

	/// Generate a uniformly distributed number, r, where 0 <= r < bound
	TCNN_HOST_DEVICE uint32_t next_uint(uint32_t bound) {
		// To avoid bias, we need to make the range of the RNG a multiple of
		// bound, which we do by dropping output less than a threshold.
		// A naive scheme to calculate the threshold would be to do
		//
		//     uint32_t threshold = 0x100000000ull % bound;
		//
		// but 64-bit div/mod is slower than 32-bit div/mod (especially on
		// 32-bit platforms).  In essence, we do
		//
		//     uint32_t threshold = (0x100000000ull-bound) % bound;
		//
		// because this version will calculate the same modulus, but the LHS
		// value is less than 2^32.

		uint32_t threshold = (~bound+1u) % bound;

		// Uniformity guarantees that this loop will terminate.  In practice, it
		// should usually terminate quickly; on average (assuming all bounds are
		// equally likely), 82.25% of the time, we can expect it to require just
		// one iteration.  In the worst case, someone passes a bound of 2^31 + 1
		// (i.e., 2147483649), which invalidates almost 50% of the range.  In
		// practice, bounds are typically small and only a tiny amount of the range
		// is eliminated.
		for (;;) {
			uint32_t r = next_uint();
			if (r >= threshold)
				return r % bound;
		}
	}

	/// Generate a single precision floating point value on the interval [0, 1)
	TCNN_HOST_DEVICE float next_float() {
		/* Trick from MTGP: generate an uniformly distributed
			single precision number in [1,2) and subtract 1. */
		union {
			uint32_t u;
			float f;
		} x;
		x.u = (next_uint() >> 9) | 0x3f800000u;
		return x.f - 1.0f;
	}

	/**
	 * \brief Generate a double precision floating point value on the interval [0, 1)
	 *
	 * \remark Since the underlying random number generator produces 32 bit output,
	 * only the first 32 mantissa bits will be filled (however, the resolution is still
	 * finer than in \ref next_float(), which only uses 23 mantissa bits)
	 */
	TCNN_HOST_DEVICE double next_double() {
		/* Trick from MTGP: generate an uniformly distributed
			double precision number in [1,2) and subtract 1. */
		union {
			uint64_t u;
			double d;
		} x;
		x.u = ((uint64_t) next_uint() << 20) | 0x3ff0000000000000ULL;
		return x.d - 1.0;
	}

	/**
	 * \brief Multi-step advance function (jump-ahead, jump-back)
	 *
	 * The method used here is based on Brown, "Random Number Generation
	 * with Arbitrary Stride", Transactions of the American Nuclear
	 * Society (Nov. 1994). The algorithm is very similar to fast
	 * exponentiation.
	 *
	 * The default value of 2^32 ensures that the PRNG is advanced
	 * sufficiently far that there is (likely) no overlap with
	 * previously drawn random numbers, even if small advancements.
	 * are made inbetween.
	 */
	TCNN_HOST_DEVICE void advance(int64_t delta_ = (1ll<<32)) {
		uint64_t
			cur_mult = PCG32_MULT,
			cur_plus = inc,
			acc_mult = 1u,
			acc_plus = 0u;

		/* Even though delta is an unsigned integer, we can pass a signed
			integer to go backwards, it just goes "the long way round". */
		uint64_t delta = (uint64_t) delta_;

		while (delta > 0) {
			if (delta & 1) {
				acc_mult *= cur_mult;
				acc_plus = acc_plus * cur_mult + cur_plus;
			}
			cur_plus = (cur_mult + 1) * cur_plus;
			cur_mult *= cur_mult;
			delta /= 2;
		}
		state = acc_mult * state + acc_plus;
	}

	/// Compute the distance between two PCG32 pseudorandom number generators
	TCNN_HOST_DEVICE int64_t operator-(const pcg32 &other) const {
		uint64_t
			cur_mult = PCG32_MULT,
			cur_plus = inc,
			cur_state = other.state,
			the_bit = 1u,
			distance = 0u;

		while (state != cur_state) {
			if ((state & the_bit) != (cur_state & the_bit)) {
				cur_state = cur_state * cur_mult + cur_plus;
				distance |= the_bit;
			}

			the_bit <<= 1;
			cur_plus = (cur_mult + 1ULL) * cur_plus;
			cur_mult *= cur_mult;
		}

		return (int64_t) distance;
	}

	/// Equality operator
	TCNN_HOST_DEVICE bool operator==(const pcg32 &other) const { return state == other.state && inc == other.inc; }

	/// Inequality operator
	TCNN_HOST_DEVICE bool operator!=(const pcg32 &other) const { return state != other.state || inc != other.inc; }

	uint64_t state;  // RNG state.  All values are possible.
	uint64_t inc;    // Controls which RNG sequence (stream) is selected. Must *always* be odd.
};

}