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+/*
+ * 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
+ */
+
+#pragma once
+
+#define PCG32_DEFAULT_STATE 0x853c49e6748fea9bULL
+#define PCG32_DEFAULT_STREAM 0xda3e39cb94b95bdbULL
+#define PCG32_MULT 0x5851f42d4c957f2dULL
+
+#include <algorithm>
+#include <cassert>
+#include <cmath>
+#include <cstdint>
+
+/// PCG32 Pseudorandom number generator
+struct Pcg32 {
+    /// Initialize the pseudorandom number generator with default seed
+    Pcg32() : state(PCG32_DEFAULT_STATE), inc(PCG32_DEFAULT_STREAM) {}
+
+    /// Initialize the pseudorandom number generator with the \ref seed() function
+    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)
+     */
+    void seed(uint64_t initstate, uint64_t initseq = 1) {
+        state = 0U;
+        inc = (initseq << 1u) | 1u;
+        next_u32();
+        state += initstate;
+        next_u32();
+    }
+
+    /// Generate a uniformly distributed unsigned 32-bit random number
+    uint32_t next_u32() {
+        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
+    uint32_t next_u32(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_u32();
+            if (r >= threshold)
+                return r % bound;
+        }
+    }
+
+    /// Generate a single precision floating point value on the interval [0, 1)
+    float next_f32() {
+        /* 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_u32() >> 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 nextFloat(), which only uses 23 mantissa bits)
+     */
+    double next_f64() {
+        /* 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_u32() << 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.
+     */
+    void advance(int64_t delta_) {
+        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;
+    }
+
+    /**
+     * \brief Draw uniformly distributed permutation and permute the
+     * given STL container
+     *
+     * From: Knuth, TAoCP Vol. 2 (3rd 3d), Section 3.4.2
+     */
+    template <typename Iterator>
+    void shuffle(Iterator begin, Iterator end) {
+        for (Iterator it = end - 1; it > begin; --it)
+            std::iter_swap(it, begin + next_u32((uint32_t)(it - begin + 1)));
+    }
+
+    /// Compute the distance between two PCG32 pseudorandom number generators
+    int64_t operator-(const Pcg32& other) const {
+        assert(inc == other.inc);
+
+        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;
+            }
+            assert((state & the_bit) == (cur_state & the_bit));
+            the_bit <<= 1;
+            cur_plus = (cur_mult + 1ULL) * cur_plus;
+            cur_mult *= cur_mult;
+        }
+
+        return (int64_t)distance;
+    }
+
+    /// Equality operator
+    bool operator==(const Pcg32& other) const { return state == other.state && inc == other.inc; }
+
+    /// Inequality operator
+    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.
+};