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// Halide tutorial lesson 13: Tuples
// This lesson describes how to write Funcs that evaluate to multiple
// values.
// On linux, you can compile and run it like so:
// g++ lesson_13*.cpp -g -I ../include -L ../bin -lHalide -lpthread -ldl -o lesson_13 -std=c++11
// LD_LIBRARY_PATH=../bin ./lesson_13
// On os x:
// g++ lesson_13*.cpp -g -I ../include -L ../bin -lHalide -o lesson_13 -std=c++11
// DYLD_LIBRARY_PATH=../bin ./lesson_13
// If you have the entire Halide source tree, you can also build it by
// running:
// make tutorial_lesson_13_tuples
// in a shell with the current directory at the top of the halide
// source tree.
#include "Halide.h"
#include <stdio.h>
#include <algorithm>
using namespace Halide;
int main(int argc, char **argv) {
// So far Funcs (such as the one below) have evaluated to a single
// scalar value for each point in their domain.
Func single_valued;
Var x, y;
single_valued(x, y) = x + y;
// One way to write a Func that returns a collection of values is
// to add an additional dimension that indexes that
// collection. This is how we typically deal with color. For
// example, the Func below represents a collection of three values
// for every x, y coordinate indexed by c.
Func color_image;
Var c;
color_image(x, y, c) = select(c == 0, 245, // Red value
c == 1, 42, // Green value
132); // Blue value
// This method is often convenient because it makes it easy to
// operate on this Func in a way that treats each item in the
// collection equally:
Func brighter;
brighter(x, y, c) = color_image(x, y, c) + 10;
// However this method is also inconvenient for three reasons.
// 1) Funcs are defined over an infinite domain, so users of this
// Func can for example access color_image(x, y, -17), which is
// not a meaningful value and is probably indicative of a bug.
// 2) It requires a select, which can impact performance if not
// bounded and unrolled:
// brighter.bound(c, 0, 3).unroll(c);
// 3) With this method, all values in the collection must have the
// same type. While the above two issues are merely inconvenient,
// this one is a hard limitation that makes it impossible to
// express certain things in this way.
// It is also possible to represent a collection of values as a
// collection of Funcs:
Func func_array[3];
func_array[0](x, y) = x + y;
func_array[1](x, y) = sin(x);
func_array[2](x, y) = cos(y);
// This method avoids the three problems above, but introduces a
// new annoyance. Because these are separate Funcs, it is
// difficult to schedule them so that they are all computed
// together inside a single loop over x, y.
// A third alternative is to define a Func as evaluating to a
// Tuple instead of an Expr. A Tuple is a fixed-size collection of
// Exprs. Each Expr in a Tuple may have a different type. The
// following function evaluates to an integer value (x+y), and a
// floating point value (sin(x*y)).
Func multi_valued;
multi_valued(x, y) = Tuple(x + y, sin(x * y));
// Realizing a tuple-valued Func returns a collection of
// Buffers. We call this a Realization. It's equivalent to a
// std::vector of Buffer objects:
Realization r = multi_valued.realize(80, 60);
assert(r.size() == 2);
Buffer<int> im0 = r[0];
Buffer<float> im1 = r[1];
assert(im0(30, 40) == 30 + 40);
assert(im1(30, 40) == sinf(30 * 40));
// All Tuple elements are evaluated together over the same domain
// in the same loop nest, but stored in distinct allocations. The
// equivalent C++ code to the above is:
int multi_valued_0[80*60];
float multi_valued_1[80*60];
for (int y = 0; y < 80; y++) {
for (int x = 0; x < 60; x++) {
multi_valued_0[x + 60*y] = x + y;
multi_valued_1[x + 60*y] = sinf(x*y);
// When compiling ahead-of-time, a Tuple-valued Func evaluates
// into multiple distinct output buffer_t structs. These appear in
// order at the end of the function signature:
// int multi_valued(...input buffers and params...,
// buffer_t *output_1, buffer_t *output_2);
// You can construct a Tuple by passing multiple Exprs to the
// Tuple constructor as we did above. Perhaps more elegantly, you
// can also take advantage of C++11 initializer lists and just
// enclose your Exprs in braces:
Func multi_valued_2;
multi_valued_2(x, y) = {x + y, sin(x*y)};
// Calls to a multi-valued Func cannot be treated as Exprs. The
// following is a syntax error:
// Func consumer;
// consumer(x, y) = multi_valued_2(x, y) + 10;
// Instead you must index a Tuple with square brackets to retrieve
// the individual Exprs:
Expr integer_part = multi_valued_2(x, y)[0];
Expr floating_part = multi_valued_2(x, y)[1];
Func consumer;
consumer(x, y) = {integer_part + 10, floating_part + 10.0f};
// Tuple reductions.
// Tuples are particularly useful in reductions, as they allow
// the reduction to maintain complex state as it walks along
// its domain. The simplest example is an argmax.
// First we create a Buffer to take the argmax over.
Func input_func;
input_func(x) = sin(x);
Buffer<float> input = input_func.realize(100);
// Then we define a 2-valued Tuple which tracks the index of
// the maximum value and the value itself.
Func arg_max;
// Pure definition.
arg_max() = {0, input(0)};
// Update definition.
RDom r(1, 99);
Expr old_index = arg_max()[0];
Expr old_max = arg_max()[1];
Expr new_index = select(old_max < input(r), r, old_index);
Expr new_max = max(input(r), old_max);
arg_max() = {new_index, new_max};
// The equivalent C++ is:
int arg_max_0 = 0;
float arg_max_1 = input(0);
for (int r = 1; r < 100; r++) {
int old_index = arg_max_0;
float old_max = arg_max_1;
int new_index = old_max < input(r) ? r : old_index;
float new_max = std::max(input(r), old_max);
// In a tuple update definition, all loads and computation
// are done before any stores, so that all Tuple elements
// are updated atomically with respect to recursive calls
// to the same Func.
arg_max_0 = new_index;
arg_max_1 = new_max;
// Let's verify that the Halide and C++ found the same maximum
// value and index.
Realization r = arg_max.realize();
Buffer<int> r0 = r[0];
Buffer<float> r1 = r[1];
assert(arg_max_0 == r0(0));
assert(arg_max_1 == r1(0));
// Halide provides argmax and argmin as built-in reductions
// similar to sum, product, maximum, and minimum. They return
// a Tuple consisting of the point in the reduction domain
// corresponding to that value, and the value itself. In the
// case of ties they return the first value found. We'll use
// one of these in the following section.
// Tuples for user-defined types.
// Tuples can also be a convenient way to represent compound
// objects such as complex numbers. Defining an object that
// can be converted to and from a Tuple is one way to extend
// Halide's type system with user-defined types.
struct Complex {
Expr real, imag;
// Construct from a Tuple
Complex(Tuple t) : real(t[0]), imag(t[1]) {}
// Construct from a pair of Exprs
Complex(Expr r, Expr i) : real(r), imag(i) {}
// Construct from a call to a Func by treating it as a Tuple
Complex(FuncRef t) : Complex(Tuple(t)) {}
// Convert to a Tuple
operator Tuple() const {
return {real, imag};
// Complex addition
Complex operator+(const Complex &other) const {
return {real + other.real, imag + other.imag};
// Complex multiplication
Complex operator*(const Complex &other) const {
return {real * other.real - imag * other.imag,
real * other.imag + imag * other.real};
// Complex magnitude
Expr magnitude() const {
return real * real + imag * imag;
// Other complex operators would go here. The above are
// sufficient for this example.
// Let's use the Complex struct to compute a Mandelbrot set.
Func mandelbrot;
// The initial complex value corresponding to an x, y coordinate
// in our Func.
Complex initial(x/15.0f - 2.5f, y/6.0f - 2.0f);
// Pure definition.
Var t;
mandelbrot(x, y, t) = Complex(0.0f, 0.0f);
// We'll use an update definition to take 12 steps.
RDom r(1, 12);
Complex current = mandelbrot(x, y, r-1);
// The following line uses the complex multiplication and
// addition we defined above.
mandelbrot(x, y, r) = current*current + initial;
// We'll use another tuple reduction to compute the iteration
// number where the value first escapes a circle of radius 4.
// This can be expressed as an argmin of a boolean - we want
// the index of the first time the given boolean expression is
// false (we consider false to be less than true). The argmax
// would return the index of the first time the expression is
// true.
Expr escape_condition = Complex(mandelbrot(x, y, r)).magnitude() < 16.0f;
Tuple first_escape = argmin(escape_condition);
// We only want the index, not the value, but argmin returns
// both, so we'll index the argmin Tuple expression using
// square brackets to get the Expr representing the index.
Func escape;
escape(x, y) = first_escape[0];
// Realize the pipeline and print the result as ascii art.
Buffer<int> result = escape.realize(61, 25);
const char *code = " .:-~*={}&%#@";
for (int y = 0; y < result.height(); y++) {
for (int x = 0; x < result.width(); x++) {
printf("%c", code[result(x, y)]);
return 0;