Initial commit

src/noise.cpp

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+/*
+ * Minetest
+ * Copyright (C) 2010-2014 celeron55, Perttu Ahola <celeron55@gmail.com>
+ * Copyright (C) 2010-2014 kwolekr, Ryan Kwolek <kwolekr@minetest.net>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification, are
+ * permitted provided that the following conditions are met:
+ *  1. Redistributions of source code must retain the above copyright notice, this list of
+ *     conditions and the following disclaimer.
+ *  2. Redistributions in binary form must reproduce the above copyright notice, this list
+ *     of conditions and the following disclaimer in the documentation and/or other materials
+ *     provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED
+ * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ * FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+ * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+ * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
+ * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+#include <cmath>
+#include "noise.h"
+#include <iostream>
+#include <cstring> // memset
+#include "debug.h"
+#include "util/numeric.h"
+#include "util/string.h"
+#include "exceptions.h"
+
+#define NOISE_MAGIC_X    1619
+#define NOISE_MAGIC_Y    31337
+#define NOISE_MAGIC_Z    52591
+// Unsigned magic seed prevents undefined behavior.
+#define NOISE_MAGIC_SEED 1013U
+
+FlagDesc flagdesc_noiseparams[] = {
+	{"defaults",    NOISE_FLAG_DEFAULTS},
+	{"eased",       NOISE_FLAG_EASED},
+	{"absvalue",    NOISE_FLAG_ABSVALUE},
+	{"pointbuffer", NOISE_FLAG_POINTBUFFER},
+	{"simplex",     NOISE_FLAG_SIMPLEX},
+	{NULL,          0}
+};
+
+///////////////////////////////////////////////////////////////////////////////
+
+PcgRandom::PcgRandom(u64 state, u64 seq)
+{
+	seed(state, seq);
+}
+
+void PcgRandom::seed(u64 state, u64 seq)
+{
+	m_state = 0U;
+	m_inc = (seq << 1u) | 1u;
+	next();
+	m_state += state;
+	next();
+}
+
+
+u32 PcgRandom::next()
+{
+	u64 oldstate = m_state;
+	m_state = oldstate * 6364136223846793005ULL + m_inc;
+
+	u32 xorshifted = ((oldstate >> 18u) ^ oldstate) >> 27u;
+	u32 rot = oldstate >> 59u;
+	return (xorshifted >> rot) | (xorshifted << ((-rot) & 31));
+}
+
+
+u32 PcgRandom::range(u32 bound)
+{
+	// If the bound is 0, we cover the whole RNG's range
+	if (bound == 0)
+		return next();
+
+	/*
+		This is an optimization of the expression:
+		  0x100000000ull % bound
+		since 64-bit modulo operations typically much slower than 32.
+	*/
+	u32 threshold = -bound % bound;
+	u32 r;
+
+	/*
+		If the bound is not a multiple of the RNG's range, it may cause bias,
+		e.g. a RNG has a range from 0 to 3 and we take want a number 0 to 2.
+		Using rand() % 3, the number 0 would be twice as likely to appear.
+		With a very large RNG range, the effect becomes less prevalent but
+		still present.
+
+		This can be solved by modifying the range of the RNG to become a
+		multiple of bound by dropping values above the a threshold.
+
+		In our example, threshold == 4 % 3 == 1, so reject values < 1
+		(that is, 0), thus making the range == 3 with no bias.
+
+		This loop may look dangerous, but will always terminate due to the
+		RNG's property of uniformity.
+	*/
+	while ((r = next()) < threshold)
+		;
+
+	return r % bound;
+}
+
+
+s32 PcgRandom::range(s32 min, s32 max)
+{
+	if (max < min)
+		throw PrngException("Invalid range (max < min)");
+
+	// We have to cast to s64 because otherwise this could overflow,
+	// and signed overflow is undefined behavior.
+	u32 bound = (s64)max - (s64)min + 1;
+	return range(bound) + min;
+}
+
+
+void PcgRandom::bytes(void *out, size_t len)
+{
+	u8 *outb = (u8 *)out;
+	int bytes_left = 0;
+	u32 r;
+
+	while (len--) {
+		if (bytes_left == 0) {
+			bytes_left = sizeof(u32);
+			r = next();
+		}
+
+		*outb = r & 0xFF;
+		outb++;
+		bytes_left--;
+		r >>= CHAR_BIT;
+	}
+}
+
+
+s32 PcgRandom::randNormalDist(s32 min, s32 max, int num_trials)
+{
+	s32 accum = 0;
+	for (int i = 0; i != num_trials; i++)
+		accum += range(min, max);
+	return myround((float)accum / num_trials);
+}
+
+///////////////////////////////////////////////////////////////////////////////
+
+float noise2d(int x, int y, s32 seed)
+{
+	unsigned int n = (NOISE_MAGIC_X * x + NOISE_MAGIC_Y * y
+			+ NOISE_MAGIC_SEED * seed) & 0x7fffffff;
+	n = (n >> 13) ^ n;
+	n = (n * (n * n * 60493 + 19990303) + 1376312589) & 0x7fffffff;
+	return 1.f - (float)(int)n / 0x40000000;
+}
+
+
+float noise3d(int x, int y, int z, s32 seed)
+{
+	unsigned int n = (NOISE_MAGIC_X * x + NOISE_MAGIC_Y * y + NOISE_MAGIC_Z * z
+			+ NOISE_MAGIC_SEED * seed) & 0x7fffffff;
+	n = (n >> 13) ^ n;
+	n = (n * (n * n * 60493 + 19990303) + 1376312589) & 0x7fffffff;
+	return 1.f - (float)(int)n / 0x40000000;
+}
+
+
+inline float dotProduct(float vx, float vy, float wx, float wy)
+{
+	return vx * wx + vy * wy;
+}
+
+
+inline float linearInterpolation(float v0, float v1, float t)
+{
+	return v0 + (v1 - v0) * t;
+}
+
+
+inline float biLinearInterpolation(
+	float v00, float v10,
+	float v01, float v11,
+	float x, float y,
+	bool eased)
+{
+	// Inlining will optimize this branch out when possible
+	if (eased) {
+		x = easeCurve(x);
+		y = easeCurve(y);
+	}
+	float u = linearInterpolation(v00, v10, x);
+	float v = linearInterpolation(v01, v11, x);
+	return linearInterpolation(u, v, y);
+}
+
+
+inline float triLinearInterpolation(
+	float v000, float v100, float v010, float v110,
+	float v001, float v101, float v011, float v111,
+	float x, float y, float z,
+	bool eased)
+{
+	// Inlining will optimize this branch out when possible
+	if (eased) {
+		x = easeCurve(x);
+		y = easeCurve(y);
+		z = easeCurve(z);
+	}
+	float u = biLinearInterpolation(v000, v100, v010, v110, x, y, false);
+	float v = biLinearInterpolation(v001, v101, v011, v111, x, y, false);
+	return linearInterpolation(u, v, z);
+}
+
+float noise2d_gradient(float x, float y, s32 seed, bool eased)
+{
+	// Calculate the integer coordinates
+	int x0 = myfloor(x);
+	int y0 = myfloor(y);
+	// Calculate the remaining part of the coordinates
+	float xl = x - (float)x0;
+	float yl = y - (float)y0;
+	// Get values for corners of square
+	float v00 = noise2d(x0, y0, seed);
+	float v10 = noise2d(x0+1, y0, seed);
+	float v01 = noise2d(x0, y0+1, seed);
+	float v11 = noise2d(x0+1, y0+1, seed);
+	// Interpolate
+	return biLinearInterpolation(v00, v10, v01, v11, xl, yl, eased);
+}
+
+
+float noise3d_gradient(float x, float y, float z, s32 seed, bool eased)
+{
+	// Calculate the integer coordinates
+	int x0 = myfloor(x);
+	int y0 = myfloor(y);
+	int z0 = myfloor(z);
+	// Calculate the remaining part of the coordinates
+	float xl = x - (float)x0;
+	float yl = y - (float)y0;
+	float zl = z - (float)z0;
+	// Get values for corners of cube
+	float v000 = noise3d(x0,     y0,     z0,     seed);
+	float v100 = noise3d(x0 + 1, y0,     z0,     seed);
+	float v010 = noise3d(x0,     y0 + 1, z0,     seed);
+	float v110 = noise3d(x0 + 1, y0 + 1, z0,     seed);
+	float v001 = noise3d(x0,     y0,     z0 + 1, seed);
+	float v101 = noise3d(x0 + 1, y0,     z0 + 1, seed);
+	float v011 = noise3d(x0,     y0 + 1, z0 + 1, seed);
+	float v111 = noise3d(x0 + 1, y0 + 1, z0 + 1, seed);
+	// Interpolate
+	return triLinearInterpolation(
+		v000, v100, v010, v110,
+		v001, v101, v011, v111,
+		xl, yl, zl,
+		eased);
+}
+
+
+float noise2d_perlin(float x, float y, s32 seed,
+	int octaves, float persistence, bool eased)
+{
+	float a = 0;
+	float f = 1.0;
+	float g = 1.0;
+	for (int i = 0; i < octaves; i++)
+	{
+		a += g * noise2d_gradient(x * f, y * f, seed + i, eased);
+		f *= 2.0;
+		g *= persistence;
+	}
+	return a;
+}
+
+
+float contour(float v)
+{
+	v = std::fabs(v);
+	if (v >= 1.0)
+		return 0.0;
+	return (1.0 - v);
+}
+
+
+///////////////////////// [ New noise ] ////////////////////////////
+
+
+float NoisePerlin2D(const NoiseParams *np, float x, float y, s32 seed)
+{
+	float a = 0;
+	float f = 1.0;
+	float g = 1.0;
+
+	x /= np->spread.X;
+	y /= np->spread.Y;
+	seed += np->seed;
+
+	for (size_t i = 0; i < np->octaves; i++) {
+		float noiseval = noise2d_gradient(x * f, y * f, seed + i,
+			np->flags & (NOISE_FLAG_DEFAULTS | NOISE_FLAG_EASED));
+
+		if (np->flags & NOISE_FLAG_ABSVALUE)
+			noiseval = std::fabs(noiseval);
+
+		a += g * noiseval;
+		f *= np->lacunarity;
+		g *= np->persist;
+	}
+
+	return np->offset + a * np->scale;
+}
+
+
+float NoisePerlin3D(const NoiseParams *np, float x, float y, float z, s32 seed)
+{
+	float a = 0;
+	float f = 1.0;
+	float g = 1.0;
+
+	x /= np->spread.X;
+	y /= np->spread.Y;
+	z /= np->spread.Z;
+	seed += np->seed;
+
+	for (size_t i = 0; i < np->octaves; i++) {
+		float noiseval = noise3d_gradient(x * f, y * f, z * f, seed + i,
+			np->flags & NOISE_FLAG_EASED);
+
+		if (np->flags & NOISE_FLAG_ABSVALUE)
+			noiseval = std::fabs(noiseval);
+
+		a += g * noiseval;
+		f *= np->lacunarity;
+		g *= np->persist;
+	}
+
+	return np->offset + a * np->scale;
+}
+
+
+Noise::Noise(const NoiseParams *np_, s32 seed, u32 sx, u32 sy, u32 sz)
+{
+	np = *np_;
+	this->seed = seed;
+	this->sx   = sx;
+	this->sy   = sy;
+	this->sz   = sz;
+
+	allocBuffers();
+}
+
+
+Noise::~Noise()
+{
+	delete[] gradient_buf;
+	delete[] persist_buf;
+	delete[] noise_buf;
+	delete[] result;
+}
+
+
+void Noise::allocBuffers()
+{
+	if (sx < 1)
+		sx = 1;
+	if (sy < 1)
+		sy = 1;
+	if (sz < 1)
+		sz = 1;
+
+	this->noise_buf = NULL;
+	resizeNoiseBuf(sz > 1);
+
+	delete[] gradient_buf;
+	delete[] persist_buf;
+	delete[] result;
+
+	try {
+		size_t bufsize = sx * sy * sz;
+		this->persist_buf  = NULL;
+		this->gradient_buf = new float[bufsize];
+		this->result       = new float[bufsize];
+	} catch (std::bad_alloc &e) {
+		throw InvalidNoiseParamsException();
+	}
+}
+
+
+void Noise::setSize(u32 sx, u32 sy, u32 sz)
+{
+	this->sx = sx;
+	this->sy = sy;
+	this->sz = sz;
+
+	allocBuffers();
+}
+
+
+void Noise::setSpreadFactor(v3f spread)
+{
+	this->np.spread = spread;
+
+	resizeNoiseBuf(sz > 1);
+}
+
+
+void Noise::setOctaves(int octaves)
+{
+	this->np.octaves = octaves;
+
+	resizeNoiseBuf(sz > 1);
+}
+
+
+void Noise::resizeNoiseBuf(bool is3d)
+{
+	// Maximum possible spread value factor
+	float ofactor = (np.lacunarity > 1.0) ?
+		pow(np.lacunarity, np.octaves - 1) :
+		np.lacunarity;
+
+	// Noise lattice point count
+	// (int)(sz * spread * ofactor) is # of lattice points crossed due to length
+	float num_noise_points_x = sx * ofactor / np.spread.X;
+	float num_noise_points_y = sy * ofactor / np.spread.Y;
+	float num_noise_points_z = sz * ofactor / np.spread.Z;
+
+	// Protect against obviously invalid parameters
+	if (num_noise_points_x > 1000000000.f ||
+			num_noise_points_y > 1000000000.f ||
+			num_noise_points_z > 1000000000.f)
+		throw InvalidNoiseParamsException();
+
+	// Protect against an octave having a spread < 1, causing broken noise values
+	if (np.spread.X / ofactor < 1.0f ||
+			np.spread.Y / ofactor < 1.0f ||
+			np.spread.Z / ofactor < 1.0f) {
+		errorstream << "A noise parameter has too many octaves: "
+			<< np.octaves << " octaves" << std::endl;
+		throw InvalidNoiseParamsException("A noise parameter has too many octaves");
+	}
+
+	// + 2 for the two initial endpoints
+	// + 1 for potentially crossing a boundary due to offset
+	size_t nlx = (size_t)std::ceil(num_noise_points_x) + 3;
+	size_t nly = (size_t)std::ceil(num_noise_points_y) + 3;
+	size_t nlz = is3d ? (size_t)std::ceil(num_noise_points_z) + 3 : 1;
+
+	delete[] noise_buf;
+	try {
+		noise_buf = new float[nlx * nly * nlz];
+	} catch (std::bad_alloc &e) {
+		throw InvalidNoiseParamsException();
+	}
+}
+
+
+/*
+ * NB:  This algorithm is not optimal in terms of space complexity.  The entire
+ * integer lattice of noise points could be done as 2 lines instead, and for 3D,
+ * 2 lines + 2 planes.
+ * However, this would require the noise calls to be interposed with the
+ * interpolation loops, which may trash the icache, leading to lower overall
+ * performance.
+ * Another optimization that could save half as many noise calls is to carry over
+ * values from the previous noise lattice as midpoints in the new lattice for the
+ * next octave.
+ */
+#define idx(x, y) ((y) * nlx + (x))
+void Noise::gradientMap2D(
+		float x, float y,
+		float step_x, float step_y,
+		s32 seed)
+{
+	float v00, v01, v10, v11, u, v, orig_u;
+	u32 index, i, j, noisex, noisey;
+	u32 nlx, nly;
+	s32 x0, y0;
+
+	bool eased = np.flags & (NOISE_FLAG_DEFAULTS | NOISE_FLAG_EASED);
+	x0 = std::floor(x);
+	y0 = std::floor(y);
+	u = x - (float)x0;
+	v = y - (float)y0;
+	orig_u = u;
+
+	//calculate noise point lattice
+	nlx = (u32)(u + sx * step_x) + 2;
+	nly = (u32)(v + sy * step_y) + 2;
+	index = 0;
+	for (j = 0; j != nly; j++)
+		for (i = 0; i != nlx; i++)
+			noise_buf[index++] = noise2d(x0 + i, y0 + j, seed);
+
+	//calculate interpolations
+	index  = 0;
+	noisey = 0;
+	for (j = 0; j != sy; j++) {
+		v00 = noise_buf[idx(0, noisey)];
+		v10 = noise_buf[idx(1, noisey)];
+		v01 = noise_buf[idx(0, noisey + 1)];
+		v11 = noise_buf[idx(1, noisey + 1)];
+
+		u = orig_u;
+		noisex = 0;
+		for (i = 0; i != sx; i++) {
+			gradient_buf[index++] =
+				biLinearInterpolation(v00, v10, v01, v11, u, v, eased);
+
+			u += step_x;
+			if (u >= 1.0) {
+				u -= 1.0;
+				noisex++;
+				v00 = v10;
+				v01 = v11;
+				v10 = noise_buf[idx(noisex + 1, noisey)];
+				v11 = noise_buf[idx(noisex + 1, noisey + 1)];
+			}
+		}
+
+		v += step_y;
+		if (v >= 1.0) {
+			v -= 1.0;
+			noisey++;
+		}
+	}
+}
+#undef idx
+
+
+#define idx(x, y, z) ((z) * nly * nlx + (y) * nlx + (x))
+void Noise::gradientMap3D(
+		float x, float y, float z,
+		float step_x, float step_y, float step_z,
+		s32 seed)
+{
+	float v000, v010, v100, v110;
+	float v001, v011, v101, v111;
+	float u, v, w, orig_u, orig_v;
+	u32 index, i, j, k, noisex, noisey, noisez;
+	u32 nlx, nly, nlz;
+	s32 x0, y0, z0;
+
+	bool eased = np.flags & NOISE_FLAG_EASED;
+
+	x0 = std::floor(x);
+	y0 = std::floor(y);
+	z0 = std::floor(z);
+	u = x - (float)x0;
+	v = y - (float)y0;
+	w = z - (float)z0;
+	orig_u = u;
+	orig_v = v;
+
+	//calculate noise point lattice
+	nlx = (u32)(u + sx * step_x) + 2;
+	nly = (u32)(v + sy * step_y) + 2;
+	nlz = (u32)(w + sz * step_z) + 2;
+	index = 0;
+	for (k = 0; k != nlz; k++)
+		for (j = 0; j != nly; j++)
+			for (i = 0; i != nlx; i++)
+				noise_buf[index++] = noise3d(x0 + i, y0 + j, z0 + k, seed);
+
+	//calculate interpolations
+	index  = 0;
+	noisey = 0;
+	noisez = 0;
+	for (k = 0; k != sz; k++) {
+		v = orig_v;
+		noisey = 0;
+		for (j = 0; j != sy; j++) {
+			v000 = noise_buf[idx(0, noisey,     noisez)];
+			v100 = noise_buf[idx(1, noisey,     noisez)];
+			v010 = noise_buf[idx(0, noisey + 1, noisez)];
+			v110 = noise_buf[idx(1, noisey + 1, noisez)];
+			v001 = noise_buf[idx(0, noisey,     noisez + 1)];
+			v101 = noise_buf[idx(1, noisey,     noisez + 1)];
+			v011 = noise_buf[idx(0, noisey + 1, noisez + 1)];
+			v111 = noise_buf[idx(1, noisey + 1, noisez + 1)];
+
+			u = orig_u;
+			noisex = 0;
+			for (i = 0; i != sx; i++) {
+				gradient_buf[index++] = triLinearInterpolation(
+					v000, v100, v010, v110,
+					v001, v101, v011, v111,
+					u, v, w,
+					eased);
+
+				u += step_x;
+				if (u >= 1.0) {
+					u -= 1.0;
+					noisex++;
+					v000 = v100;
+					v010 = v110;
+					v100 = noise_buf[idx(noisex + 1, noisey,     noisez)];
+					v110 = noise_buf[idx(noisex + 1, noisey + 1, noisez)];
+					v001 = v101;
+					v011 = v111;
+					v101 = noise_buf[idx(noisex + 1, noisey,     noisez + 1)];
+					v111 = noise_buf[idx(noisex + 1, noisey + 1, noisez + 1)];
+				}
+			}
+
+			v += step_y;
+			if (v >= 1.0) {
+				v -= 1.0;
+				noisey++;
+			}
+		}
+
+		w += step_z;
+		if (w >= 1.0) {
+			w -= 1.0;
+			noisez++;
+		}
+	}
+}
+#undef idx
+
+
+float *Noise::perlinMap2D(float x, float y, float *persistence_map)
+{
+	float f = 1.0, g = 1.0;
+	size_t bufsize = sx * sy;
+
+	x /= np.spread.X;
+	y /= np.spread.Y;
+
+	memset(result, 0, sizeof(float) * bufsize);
+
+	if (persistence_map) {
+		if (!persist_buf)
+			persist_buf = new float[bufsize];
+		for (size_t i = 0; i != bufsize; i++)
+			persist_buf[i] = 1.0;
+	}
+
+	for (size_t oct = 0; oct < np.octaves; oct++) {
+		gradientMap2D(x * f, y * f,
+			f / np.spread.X, f / np.spread.Y,
+			seed + np.seed + oct);
+
+		updateResults(g, persist_buf, persistence_map, bufsize);
+
+		f *= np.lacunarity;
+		g *= np.persist;
+	}
+
+	if (std::fabs(np.offset - 0.f) > 0.00001 || std::fabs(np.scale - 1.f) > 0.00001) {
+		for (size_t i = 0; i != bufsize; i++)
+			result[i] = result[i] * np.scale + np.offset;
+	}
+
+	return result;
+}
+
+
+float *Noise::perlinMap3D(float x, float y, float z, float *persistence_map)
+{
+	float f = 1.0, g = 1.0;
+	size_t bufsize = sx * sy * sz;
+
+	x /= np.spread.X;
+	y /= np.spread.Y;
+	z /= np.spread.Z;
+
+	memset(result, 0, sizeof(float) * bufsize);
+
+	if (persistence_map) {
+		if (!persist_buf)
+			persist_buf = new float[bufsize];
+		for (size_t i = 0; i != bufsize; i++)
+			persist_buf[i] = 1.0;
+	}
+
+	for (size_t oct = 0; oct < np.octaves; oct++) {
+		gradientMap3D(x * f, y * f, z * f,
+			f / np.spread.X, f / np.spread.Y, f / np.spread.Z,
+			seed + np.seed + oct);
+
+		updateResults(g, persist_buf, persistence_map, bufsize);
+
+		f *= np.lacunarity;
+		g *= np.persist;
+	}
+
+	if (std::fabs(np.offset - 0.f) > 0.00001 || std::fabs(np.scale - 1.f) > 0.00001) {
+		for (size_t i = 0; i != bufsize; i++)
+			result[i] = result[i] * np.scale + np.offset;
+	}
+
+	return result;
+}
+
+
+void Noise::updateResults(float g, float *gmap,
+	const float *persistence_map, size_t bufsize)
+{
+	// This looks very ugly, but it is 50-70% faster than having
+	// conditional statements inside the loop
+	if (np.flags & NOISE_FLAG_ABSVALUE) {
+		if (persistence_map) {
+			for (size_t i = 0; i != bufsize; i++) {
+				result[i] += gmap[i] * std::fabs(gradient_buf[i]);
+				gmap[i] *= persistence_map[i];
+			}
+		} else {
+			for (size_t i = 0; i != bufsize; i++)
+				result[i] += g * std::fabs(gradient_buf[i]);
+		}
+	} else {
+		if (persistence_map) {
+			for (size_t i = 0; i != bufsize; i++) {
+				result[i] += gmap[i] * gradient_buf[i];
+				gmap[i] *= persistence_map[i];
+			}
+		} else {
+			for (size_t i = 0; i != bufsize; i++)
+				result[i] += g * gradient_buf[i];
+		}
+	}
+}