Backported the improvements to the Math class from Godot4.

core/math/math_funcs.cpp

@@ -55,6 +55,10 @@ uint32_t Math::rand() {
 	return default_rand.rand();
 }
 
+double Math::randfn(double mean, double deviation) {
+	return default_rand.randfn(mean, deviation);
+}
+
 int Math::step_decimals(double p_step) {
 	static const int maxn = 10;
 	static const double sd[maxn] = {
@@ -184,3 +188,11 @@ double Math::random(double from, double to) {
 float Math::random(float from, float to) {
 	return default_rand.random(from, to);
 }
+
+real_t Math::randomr(real_t from, real_t to) {
+	return default_rand.randomr(from, to);
+}
+
+int Math::random(int from, int to) {
+	return default_rand.random(from, to);
+}

core/math/math_funcs.h

@@ -104,6 +104,12 @@ public:
 	static _ALWAYS_INLINE_ double log(double p_x) { return ::log(p_x); }
 	static _ALWAYS_INLINE_ float log(float p_x) { return ::logf(p_x); }
 
+	static _ALWAYS_INLINE_ double log1p(double p_x) { return ::log1p(p_x); }
+	static _ALWAYS_INLINE_ float log1p(float p_x) { return ::log1pf(p_x); }
+
+	static _ALWAYS_INLINE_ double log2(double p_x) { return ::log2(p_x); }
+	static _ALWAYS_INLINE_ float log2(float p_x) { return ::log2f(p_x); }
+
 	static _ALWAYS_INLINE_ double exp(double p_x) { return ::exp(p_x); }
 	static _ALWAYS_INLINE_ float exp(float p_x) { return ::expf(p_x); }
 
@@ -211,6 +217,24 @@ public:
 		value += 0.0f;
 		return value;
 	}
+
+	static _ALWAYS_INLINE_ float fposmodp(float p_x, float p_y) {
+		float value = Math::fmod(p_x, p_y);
+		if (value < 0) {
+			value += p_y;
+		}
+		value += 0.0f;
+		return value;
+	}
+	static _ALWAYS_INLINE_ double fposmodp(double p_x, double p_y) {
+		double value = Math::fmod(p_x, p_y);
+		if (value < 0) {
+			value += p_y;
+		}
+		value += 0.0;
+		return value;
+	}
+
 	static _ALWAYS_INLINE_ int64_t posmod(int64_t p_x, int64_t p_y) {
 		int64_t value = p_x % p_y;
 		if (((value < 0) && (p_y > 0)) || ((value > 0) && (p_y < 0))) {
@@ -265,6 +289,42 @@ public:
 		return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value));
 	}
 
+	static _ALWAYS_INLINE_ double cubic_interpolate(double p_from, double p_to, double p_pre, double p_post, double p_weight) {
+		return 0.5 *
+				((p_from * 2.0) +
+						(-p_pre + p_to) * p_weight +
+						(2.0 * p_pre - 5.0 * p_from + 4.0 * p_to - p_post) * (p_weight * p_weight) +
+						(-p_pre + 3.0 * p_from - 3.0 * p_to + p_post) * (p_weight * p_weight * p_weight));
+	}
+	static _ALWAYS_INLINE_ float cubic_interpolate(float p_from, float p_to, float p_pre, float p_post, float p_weight) {
+		return 0.5f *
+				((p_from * 2.0f) +
+						(-p_pre + p_to) * p_weight +
+						(2.0f * p_pre - 5.0f * p_from + 4.0f * p_to - p_post) * (p_weight * p_weight) +
+						(-p_pre + 3.0f * p_from - 3.0f * p_to + p_post) * (p_weight * p_weight * p_weight));
+	}
+
+	static _ALWAYS_INLINE_ double bezier_interpolate(double p_start, double p_control_1, double p_control_2, double p_end, double p_t) {
+		/* Formula from Wikipedia article on Bezier curves. */
+		double omt = (1.0 - p_t);
+		double omt2 = omt * omt;
+		double omt3 = omt2 * omt;
+		double t2 = p_t * p_t;
+		double t3 = t2 * p_t;
+
+		return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3;
+	}
+	static _ALWAYS_INLINE_ float bezier_interpolate(float p_start, float p_control_1, float p_control_2, float p_end, float p_t) {
+		/* Formula from Wikipedia article on Bezier curves. */
+		float omt = (1.0f - p_t);
+		float omt2 = omt * omt;
+		float omt3 = omt2 * omt;
+		float t2 = p_t * p_t;
+		float t3 = t2 * p_t;
+
+		return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0f + p_control_2 * omt * t2 * 3.0f + p_end * t3;
+	}
+
 	static _ALWAYS_INLINE_ double smoothstep(double p_from, double p_to, double p_s) {
 		if (is_equal_approx(p_from, p_to)) {
 			return p_from;
@@ -328,6 +388,19 @@ public:
 		return result;
 	}
 
+	static _ALWAYS_INLINE_ float fract(float value) {
+		return value - floor(value);
+	}
+	static _ALWAYS_INLINE_ double fract(double value) {
+		return value - floor(value);
+	}
+	static _ALWAYS_INLINE_ float pingpong(float value, float length) {
+		return (length != 0.0f) ? abs(fract((value - length) / (length * 2.0f)) * length * 2.0f - length) : 0.0f;
+	}
+	static _ALWAYS_INLINE_ double pingpong(double value, double length) {
+		return (length != 0.0) ? abs(fract((value - length) / (length * 2.0)) * length * 2.0 - length) : 0.0;
+	}
+
 	// double only, as these functions are mainly used by the editor and not performance-critical,
 	static double ease(double p_x, double p_c);
 	static int step_decimals(double p_step);
@@ -347,12 +420,12 @@ public:
 	static _ALWAYS_INLINE_ float randf() {
 		return (float)rand() / (float)Math::RANDOM_32BIT_MAX;
 	}
+	static double randfn(double mean, double deviation);
 
 	static double random(double from, double to);
 	static float random(float from, float to);
-	static real_t random(int from, int to) {
+	static real_t randomr(real_t from, real_t to);
-		return (real_t)random((real_t)from, (real_t)to);
+	static int random(int from, int to);
-	}
 
 	static _ALWAYS_INLINE_ bool is_equal_approx_ratio(real_t a, real_t b, real_t epsilon = CMP_EPSILON, real_t min_epsilon = CMP_EPSILON) {
 		// this is an approximate way to check that numbers are close, as a ratio of their average size

core/math/random_number_generator.h

@@ -43,30 +43,20 @@ protected:
 
 public:
 	_FORCE_INLINE_ void set_seed(uint64_t seed) { randbase.seed(seed); }
-
 	_FORCE_INLINE_ uint64_t get_seed() { return randbase.get_seed(); }
 
 	_FORCE_INLINE_ void set_state(uint64_t p_state) { randbase.set_state(p_state); }
-
 	_FORCE_INLINE_ uint64_t get_state() const { return randbase.get_state(); }
 
 	_FORCE_INLINE_ void randomize() { randbase.randomize(); }
 
 	_FORCE_INLINE_ uint32_t randi() { return randbase.rand(); }
-
 	_FORCE_INLINE_ real_t randf() { return randbase.randf(); }
-
 	_FORCE_INLINE_ real_t randf_range(real_t from, real_t to) { return randbase.random(from, to); }
-
 	_FORCE_INLINE_ real_t randfn(real_t mean = 0.0, real_t deviation = 1.0) { return randbase.randfn(mean, deviation); }
 
 	_FORCE_INLINE_ int randi_range(int from, int to) {
-		unsigned int ret = randbase.rand();
+		return randbase.random(from, to);
-		if (to < from) {
-			return ret % (from - to + 1) + to;
-		} else {
-			return ret % (to - from + 1) + from;
-		}
 	}
 
 	RandomNumberGenerator();

core/math/random_pcg.cpp

@@ -49,3 +49,10 @@ double RandomPCG::random(double p_from, double p_to) {
 float RandomPCG::random(float p_from, float p_to) {
 	return randf() * (p_to - p_from) + p_from;
 }
+
+int RandomPCG::random(int p_from, int p_to) {
+	if (p_from == p_to) {
+		return p_from;
+	}
+	return rand(abs(p_from - p_to) + 1) + MIN(p_from, p_to);
+}

core/math/random_pcg.h

@@ -80,9 +80,11 @@ public:
 
 	void randomize();
 	_FORCE_INLINE_ uint32_t rand() {
-		current_seed = pcg.state;
 		return pcg32_random_r(&pcg);
 	}
+	_FORCE_INLINE_ uint32_t rand(uint32_t bounds) {
+		return pcg32_boundedrand_r(&pcg, bounds);
+	}
 
 	// Obtaining floating point numbers in [0, 1] range with "good enough" uniformity.
 	// These functions sample the output of rand() as the fraction part of an infinite binary number,
@@ -131,7 +133,8 @@ public:
 
 	double random(double p_from, double p_to);
 	float random(float p_from, float p_to);
-	real_t random(int p_from, int p_to) { return (real_t)random((real_t)p_from, (real_t)p_to); }
+	real_t randomr(real_t p_from, real_t p_to) { return random(p_from, p_to); }
+	int random(int p_from, int p_to);
 };
 
 #endif // RANDOM_PCG_H

thirdparty/misc/pcg.cpp

@@ -23,3 +23,36 @@ void pcg32_srandom_r(pcg32_random_t* rng, uint64_t initstate, uint64_t initseq)
     rng->state += initstate;
     pcg32_random_r(rng);
 }
+
+// Source from https://github.com/imneme/pcg-c-basic/blob/master/pcg_basic.c
+// pcg32_boundedrand_r(rng, bound):
+//     Generate a uniformly distributed number, r, where 0 <= r < bound
+uint32_t pcg32_boundedrand_r(pcg32_random_t *rng, 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 % 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 = pcg32_random_r(rng);
+		if (r >= threshold)
+			return r % bound;
+	}
+}

thirdparty/misc/pcg.h

@@ -1,10 +1,8 @@
-#ifndef RANDOM_H
-#define RANDOM_H
 // *Really* minimal PCG32 code / (c) 2014 M.E. O'Neill / pcg-random.org
 // Licensed under Apache License 2.0 (NO WARRANTY, etc. see website)
 
-
+#ifndef RANDOM_H
-
+#define RANDOM_H
 
 #include "core/typedefs.h"
 
@@ -13,5 +11,6 @@
 typedef struct { uint64_t state;  uint64_t inc; } pcg32_random_t;
 uint32_t pcg32_random_r(pcg32_random_t* rng);
 void pcg32_srandom_r(pcg32_random_t* rng, uint64_t initstate, uint64_t initseq);
+uint32_t pcg32_boundedrand_r(pcg32_random_t* rng, uint32_t bound);
 
 #endif // RANDOM_H