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IROperator.h
Go to the documentation of this file.
#ifndef HALIDE_IR_OPERATOR_H
#define HALIDE_IR_OPERATOR_H
/** \file
*
* Defines various operator overloads and utility functions that make
* it more pleasant to work with Halide expressions.
*/
#include <cmath>
#include <map>
#include <optional>
#include "ConstantInterval.h"
#include "Expr.h"
#include "Scope.h"
#include "Target.h"
#include "Tuple.h"
namespace Halide {
namespace Internal {
/** Is the expression either an IntImm, a FloatImm, a StringImm, or a
* Cast of the same, or a Ramp or Broadcast of the same. Doesn't do
* any constant folding. */
bool is_const(const Expr &e);
/** Is the expression an IntImm, FloatImm of a particular value, or a
* Cast, or Broadcast of the same. */
bool is_const(const Expr &e, int64_t v);
/** If an expression is an IntImm or a Broadcast of an IntImm, return
* a its value. Otherwise returns std::nullopt. */
std::optional<int64_t> as_const_int(const Expr &e);
/** If an expression is a UIntImm or a Broadcast of a UIntImm, return
* its value. Otherwise returns std::nullopt. */
std::optional<uint64_t> as_const_uint(const Expr &e);
/** If an expression is a FloatImm or a Broadcast of a FloatImm,
* return its value. Otherwise returns std::nullopt. */
std::optional<double> as_const_float(const Expr &e);
/** Is the expression a constant integer power of two. Returns log base two of
* the expression if it is, or std::nullopt if not. Also returns std::nullopt
* for non-integer types. */
// @{
std::optional<int> is_const_power_of_two_integer(const Expr &e);
std::optional<int> is_const_power_of_two_integer(uint64_t);
std::optional<int> is_const_power_of_two_integer(int64_t);
// @}
/** Is the expression a const (as defined by is_const), and also
* strictly greater than zero (in all lanes, if a vector expression) */
bool is_positive_const(const Expr &e);
/** Is the expression a const (as defined by is_const), and also
* strictly less than zero (in all lanes, if a vector expression) */
bool is_negative_const(const Expr &e);
/** Is the expression an undef */
bool is_undef(const Expr &e);
/** Is the expression a const (as defined by is_const), and also equal
* to zero (in all lanes, if a vector expression) */
bool is_const_zero(const Expr &e);
/** Is the expression a const (as defined by is_const), and also equal
* to one (in all lanes, if a vector expression) */
bool is_const_one(const Expr &e);
/** Is the statement a no-op (which we represent as either an
* undefined Stmt, or as an Evaluate node of a constant) */
bool is_no_op(const Stmt &s);
/** Does the expression
* 1) Take on the same value no matter where it appears in a Stmt, and
* 2) Evaluating it has no side-effects
*/
bool is_pure(const Expr &e);
/** Construct an immediate of the given type from any numeric C++ type. */
// @{
Expr make_const(Type t, int64_t val);
Expr make_const(Type t, uint64_t val);
Expr make_const(Type t, double val);
inline Expr make_const(Type t, int32_t val) {
return make_const(t, (int64_t)val);
}
inline Expr make_const(Type t, uint32_t val) {
return make_const(t, (uint64_t)val);
}
inline Expr make_const(Type t, int16_t val) {
return make_const(t, (int64_t)val);
}
inline Expr make_const(Type t, uint16_t val) {
return make_const(t, (uint64_t)val);
}
inline Expr make_const(Type t, int8_t val) {
return make_const(t, (int64_t)val);
}
inline Expr make_const(Type t, uint8_t val) {
return make_const(t, (uint64_t)val);
}
inline Expr make_const(Type t, bool val) {
return make_const(t, (uint64_t)val);
}
inline Expr make_const(Type t, float val) {
return make_const(t, (double)val);
}
inline Expr make_const(Type t, float16_t val) {
return make_const(t, (double)val);
}
// @}
/** Construct a unique signed_integer_overflow Expr */
Expr make_signed_integer_overflow(Type type);
/** Check if an expression is a signed_integer_overflow */
bool is_signed_integer_overflow(const Expr &expr);
/** Check if a constant value can be correctly represented as the given type. */
void check_representable(Type t, int64_t val);
/** Construct a boolean constant from a C++ boolean value.
* May also be a vector if width is given.
* It is not possible to coerce a C++ boolean to Expr because
* if we provide such a path then char objects can ambiguously
* be converted to Halide Expr or to std::string. The problem
* is that C++ does not have a real bool type - it is in fact
* close enough to char that C++ does not know how to distinguish them.
* make_bool is the explicit coercion. */
Expr make_bool(bool val, int lanes = 1);
/** Construct the representation of zero in the given type */
Expr make_zero(Type t);
/** Construct the representation of one in the given type */
Expr make_one(Type t);
/** Construct the representation of two in the given type */
Expr make_two(Type t);
/** Construct the constant boolean true. May also be a vector of
* trues, if a lanes argument is given. */
Expr const_true(int lanes = 1);
/** Construct the constant boolean false. May also be a vector of
* falses, if a lanes argument is given. */
Expr const_false(int lanes = 1);
/** Attempt to cast an expression to a smaller type while provably not losing
* information. If it can't be done, return an undefined Expr.
*
* Optionally accepts a scope giving the constant bounds of any variables, and a
* map that gives the constant bounds of exprs already analyzed to avoid redoing
* work across many calls to lossless_cast. It is not safe to use this optional
* map in contexts where the same Expr object may take on a different value. For
* example: (let x = 4 in some_expr_object) + (let x = 5 in
* the_same_expr_object)). It is safe to use it after uniquify_variable_names
* has been run. */
Expr lossless_cast(Type t, Expr e,
const Scope<ConstantInterval> &scope = Scope<ConstantInterval>::empty_scope(),
std::map<Expr, ConstantInterval, ExprCompare> *cache = nullptr);
/** Attempt to negate x without introducing new IR and without overflow.
* If it can't be done, return an undefined Expr. */
Expr lossless_negate(const Expr &x);
/** Coerce the two expressions to have the same type, using C-style
* casting rules. For the purposes of casting, a boolean type is
* UInt(1). We use the following procedure:
*
* If the types already match, do nothing.
*
* Then, if one type is a vector and the other is a scalar, the scalar
* is broadcast to match the vector width, and we continue.
*
* Then, if one type is floating-point and the other is not, the
* non-float is cast to the floating-point type, and we're done.
*
* Then, if both types are unsigned ints, the one with fewer bits is
* cast to match the one with more bits and we're done.
*
* Then, if both types are signed ints, the one with fewer bits is
* cast to match the one with more bits and we're done.
*
* Finally, if one type is an unsigned int and the other type is a signed
* int, both are cast to a signed int with the greater of the two
* bit-widths. For example, matching an Int(8) with a UInt(16) results
* in an Int(16).
*
*/
void match_types(Expr &a, Expr &b);
/** Asserts that both expressions are integer types and are either
* both signed or both unsigned. If one argument is scalar and the
* other a vector, the scalar is broadcasted to have the same number
* of lanes as the vector. If one expression is of narrower type than
* the other, it is widened to the bit width of the wider. */
void match_types_bitwise(Expr &a, Expr &b, const char *op_name);
/** Halide's vectorizable transcendentals. */
// @{
Expr halide_log(const Expr &a);
Expr halide_exp(const Expr &a);
Expr halide_erf(const Expr &a);
// @}
/** Raise an expression to an integer power by repeatedly multiplying
* it by itself. */
Expr raise_to_integer_power(Expr a, int64_t b);
/** Split a boolean condition into vector of ANDs. If 'cond' is undefined,
* return an empty vector. */
void split_into_ands(const Expr &cond, std::vector<Expr> &result);
/** A builder to help create Exprs representing halide_buffer_t
* structs (e.g. foo.buffer) via calls to halide_buffer_init. Fill out
* the fields and then call build. The resulting Expr will be a call
* to halide_buffer_init with the struct members as arguments. If the
* buffer_memory field is undefined, it uses a call to alloca to make
* some stack memory for the buffer. If the shape_memory field is
* undefined, it similarly uses stack memory for the shape. If the
* shape_memory field is null, it uses the dim field already in the
* buffer. Other unitialized fields will take on a value of zero in
* the constructed buffer. */
struct BufferBuilder {
Expr buffer_memory, shape_memory;
Expr host, device, device_interface;
Type type;
int dimensions = 0;
std::vector<Expr> mins, extents, strides;
Expr host_dirty, device_dirty;
Expr build() const;
};
/** If e is a ramp expression with stride, default 1, return the base,
* otherwise undefined. */
Expr strided_ramp_base(const Expr &e, int stride = 1);
/** Implementations of division and mod that are specific to Halide.
* Use these implementations; do not use native C division or mod to
* simplify Halide expressions. Halide division and modulo satisify
* the Euclidean definition of division for integers a and b:
*
/code
when b != 0, (a/b)*b + a%b = a
0 <= a%b < |b|
/endcode
*
* Additionally, mod by zero returns zero, and div by zero returns
* zero. This makes mod and div total functions.
*/
// @{
template<typename T>
inline T mod_imp(T a, T b) {
Type t = type_of<T>();
if (!t.is_float() && b == 0) {
return 0;
} else if (t.is_int()) {
int64_t ia = a;
int64_t ib = b;
int64_t a_neg = ia >> 63;
int64_t b_neg = ib >> 63;
int64_t b_zero = (ib == 0) ? -1 : 0;
ia -= a_neg;
int64_t r = ia % (ib | b_zero);
r += (a_neg & ((ib ^ b_neg) + ~b_neg));
r &= ~b_zero;
return r;
} else {
return a % b;
}
}
template<typename T>
inline T div_imp(T a, T b) {
Type t = type_of<T>();
if (!t.is_float() && b == 0) {
return (T)0;
} else if (t.is_int()) {
// Do it as 64-bit
int64_t ia = a;
int64_t ib = b;
int64_t a_neg = ia >> 63;
int64_t b_neg = ib >> 63;
int64_t b_zero = (ib == 0) ? -1 : 0;
ib -= b_zero;
ia -= a_neg;
int64_t q = ia / ib;
q += a_neg & (~b_neg - b_neg);
q &= ~b_zero;
return (T)q;
} else {
return a / b;
}
}
// @}
// Special cases for float, double.
template<>
inline float mod_imp<float>(float a, float b) {
float f = a - b * (floorf(a / b));
// The remainder has the same sign as b.
return f;
}
template<>
inline double mod_imp<double>(double a, double b) {
double f = a - b * (std::floor(a / b));
return f;
}
template<>
inline float div_imp<float>(float a, float b) {
return a / b;
}
template<>
inline double div_imp<double>(double a, double b) {
return a / b;
}
/** Return an Expr that is identical to the input Expr, but with
* all calls to likely() and likely_if_innermost() removed. */
Expr remove_likelies(const Expr &e);
/** Return a Stmt that is identical to the input Stmt, but with
* all calls to likely() and likely_if_innermost() removed. */
Stmt remove_likelies(const Stmt &s);
/** Return an Expr that is identical to the input Expr, but with
* all calls to promise_clamped() and unsafe_promise_clamped() removed. */
Expr remove_promises(const Expr &e);
/** Return a Stmt that is identical to the input Stmt, but with
* all calls to promise_clamped() and unsafe_promise_clamped() removed. */
Stmt remove_promises(const Stmt &s);
/** If the expression is a tag helper call, remove it and return
* the tagged expression. If not, returns the expression. */
Expr unwrap_tags(const Expr &e);
template<typename T>
struct is_printable_arg {
static constexpr bool value = std::is_convertible<T, const char *>::value ||
std::is_convertible<T, Halide::Expr>::value;
};
template<typename... Args>
struct all_are_printable_args : meta_and<is_printable_arg<Args>...> {};
// Secondary args to print can be Exprs or const char *
inline HALIDE_NO_USER_CODE_INLINE void collect_print_args(std::vector<Expr> &args) {
}
template<typename... Args>
inline HALIDE_NO_USER_CODE_INLINE void collect_print_args(std::vector<Expr> &args, const char *arg, Args &&...more_args) {
args.emplace_back(std::string(arg));
collect_print_args(args, std::forward<Args>(more_args)...);
}
template<typename... Args>
inline HALIDE_NO_USER_CODE_INLINE void collect_print_args(std::vector<Expr> &args, Expr arg, Args &&...more_args) {
args.push_back(std::move(arg));
collect_print_args(args, std::forward<Args>(more_args)...);
}
Expr requirement_failed_error(Expr condition, const std::vector<Expr> &args);
Expr memoize_tag_helper(Expr result, const std::vector<Expr> &cache_key_values);
/** Reset the counters used for random-number seeds in random_float/int/uint.
* (Note that the counters are incremented for each call, even if a seed is passed in.)
* This is used for multitarget compilation to ensure that each subtarget gets
* the same sequence of random numbers. */
void reset_random_counters();
} // namespace Internal
/** Cast an expression to the halide type corresponding to the C++ type T. */
template<typename T>
inline Expr cast(Expr a) {
return cast(type_of<T>(), std::move(a));
}
/** Cast an expression to a new type. */
Expr cast(Type t, Expr a);
/** Return the sum of two expressions, doing any necessary type
* coercion using \ref Internal::match_types */
Expr operator+(Expr a, Expr b);
/** Add an expression and a constant integer. Coerces the type of the
* integer to match the type of the expression. Errors if the integer
* cannot be represented in the type of the expression. */
// @{
Expr operator+(Expr a, int b);
/** Add a constant integer and an expression. Coerces the type of the
* integer to match the type of the expression. Errors if the integer
* cannot be represented in the type of the expression. */
Expr operator+(int a, Expr b);
/** Modify the first expression to be the sum of two expressions,
* without changing its type. This casts the second argument to match
* the type of the first. */
Expr &operator+=(Expr &a, Expr b);
/** Return the difference of two expressions, doing any necessary type
* coercion using \ref Internal::match_types */
Expr operator-(Expr a, Expr b);
/** Subtracts a constant integer from an expression. Coerces the type of the
* integer to match the type of the expression. Errors if the integer
* cannot be represented in the type of the expression. */
Expr operator-(Expr a, int b);
/** Subtracts an expression from a constant integer. Coerces the type
* of the integer to match the type of the expression. Errors if the
* integer cannot be represented in the type of the expression. */
Expr operator-(int a, Expr b);
/** Return the negative of the argument. Does no type casting, so more
* formally: return that number which when added to the original,
* yields zero of the same type. For unsigned integers the negative is
* still an unsigned integer. E.g. in UInt(8), the negative of 56 is
* 200, because 56 + 200 == 0 */
Expr operator-(Expr a);
/** Modify the first expression to be the difference of two expressions,
* without changing its type. This casts the second argument to match
* the type of the first. */
Expr &operator-=(Expr &a, Expr b);
/** Return the product of two expressions, doing any necessary type
* coercion using \ref Internal::match_types */
Expr operator*(Expr a, Expr b);
/** Multiply an expression and a constant integer. Coerces the type of the
* integer to match the type of the expression. Errors if the integer
* cannot be represented in the type of the expression. */
Expr operator*(Expr a, int b);
/** Multiply a constant integer and an expression. Coerces the type of
* the integer to match the type of the expression. Errors if the
* integer cannot be represented in the type of the expression. */
Expr operator*(int a, Expr b);
/** Modify the first expression to be the product of two expressions,
* without changing its type. This casts the second argument to match
* the type of the first. */
Expr &operator*=(Expr &a, Expr b);
/** Return the ratio of two expressions, doing any necessary type
* coercion using \ref Internal::match_types. Note that integer
* division in Halide is not the same as integer division in C-like
* languages in two ways.
*
* First, signed integer division in Halide rounds according to the
* sign of the denominator. This means towards minus infinity for
* positive denominators, and towards positive infinity for negative
* denominators. This is unlike C, which rounds towards zero. This
* decision ensures that upsampling expressions like f(x/2, y/2) don't
* have funny discontinuities when x and y cross zero.
*
* Second, division by zero returns zero instead of faulting. For
* types where overflow is defined behavior, division of the largest
* negative signed integer by -1 returns the larged negative signed
* integer for the type (i.e. it wraps). This ensures that a division
* operation can never have a side-effect, which is helpful in Halide
* because scheduling directives can expand the domain of computation
* of a Func, potentially introducing new zero-division.
*/
Expr operator/(Expr a, Expr b);
/** Modify the first expression to be the ratio of two expressions,
* without changing its type. This casts the second argument to match
* the type of the first. Note that signed integer division in Halide
* rounds towards minus infinity, unlike C, which rounds towards
* zero. */
Expr &operator/=(Expr &a, Expr b);
/** Divides an expression by a constant integer. Coerces the type
* of the integer to match the type of the expression. Errors if the
* integer cannot be represented in the type of the expression. */
Expr operator/(Expr a, int b);
/** Divides a constant integer by an expression. Coerces the type
* of the integer to match the type of the expression. Errors if the
* integer cannot be represented in the type of the expression. */
Expr operator/(int a, Expr b);
/** Return the first argument reduced modulo the second, doing any
* necessary type coercion using \ref Internal::match_types. There are
* two key differences between C-like languages and Halide for the
* modulo operation, which complement the way division works.
*
* First, the result is never negative, so x % 2 is always zero or
* one, unlike in C-like languages. x % -2 is equivalent, and is also
* always zero or one. Second, mod by zero evaluates to zero (unlike
* in C, where it faults). This makes modulo, like division, a
* side-effect-free operation. */
Expr operator%(Expr a, Expr b);
/** Mods an expression by a constant integer. Coerces the type
* of the integer to match the type of the expression. Errors if the
* integer cannot be represented in the type of the expression. */
Expr operator%(Expr a, int b);
/** Mods a constant integer by an expression. Coerces the type
* of the integer to match the type of the expression. Errors if the
* integer cannot be represented in the type of the expression. */
Expr operator%(int a, Expr b);
/** Return a boolean expression that tests whether the first argument
* is greater than the second, after doing any necessary type coercion
* using \ref Internal::match_types */
Expr operator>(Expr a, Expr b);
/** Return a boolean expression that tests whether an expression is
* greater than a constant integer. Coerces the integer to the type of
* the expression. Errors if the integer is not representable in that
* type. */
Expr operator>(Expr a, int b);
/** Return a boolean expression that tests whether a constant integer is
* greater than an expression. Coerces the integer to the type of
* the expression. Errors if the integer is not representable in that
* type. */
Expr operator>(int a, Expr b);
/** Return a boolean expression that tests whether the first argument
* is less than the second, after doing any necessary type coercion
* using \ref Internal::match_types */
Expr operator<(Expr a, Expr b);
/** Return a boolean expression that tests whether an expression is
* less than a constant integer. Coerces the integer to the type of
* the expression. Errors if the integer is not representable in that
* type. */
Expr operator<(Expr a, int b);
/** Return a boolean expression that tests whether a constant integer is
* less than an expression. Coerces the integer to the type of
* the expression. Errors if the integer is not representable in that
* type. */
Expr operator<(int a, Expr b);
/** Return a boolean expression that tests whether the first argument
* is less than or equal to the second, after doing any necessary type
* coercion using \ref Internal::match_types */
Expr operator<=(Expr a, Expr b);
/** Return a boolean expression that tests whether an expression is
* less than or equal to a constant integer. Coerces the integer to
* the type of the expression. Errors if the integer is not
* representable in that type. */
Expr operator<=(Expr a, int b);
/** Return a boolean expression that tests whether a constant integer
* is less than or equal to an expression. Coerces the integer to the
* type of the expression. Errors if the integer is not representable
* in that type. */
Expr operator<=(int a, Expr b);
/** Return a boolean expression that tests whether the first argument
* is greater than or equal to the second, after doing any necessary
* type coercion using \ref Internal::match_types */
Expr operator>=(Expr a, Expr b);
/** Return a boolean expression that tests whether an expression is
* greater than or equal to a constant integer. Coerces the integer to
* the type of the expression. Errors if the integer is not
* representable in that type. */
Expr operator>=(const Expr &a, int b);
/** Return a boolean expression that tests whether a constant integer
* is greater than or equal to an expression. Coerces the integer to the
* type of the expression. Errors if the integer is not representable
* in that type. */
Expr operator>=(int a, const Expr &b);
/** Return a boolean expression that tests whether the first argument
* is equal to the second, after doing any necessary type coercion
* using \ref Internal::match_types */
Expr operator==(Expr a, Expr b);
/** Return a boolean expression that tests whether an expression is
* equal to a constant integer. Coerces the integer to the type of the
* expression. Errors if the integer is not representable in that
* type. */
Expr operator==(Expr a, int b);
/** Return a boolean expression that tests whether a constant integer
* is equal to an expression. Coerces the integer to the type of the
* expression. Errors if the integer is not representable in that
* type. */
Expr operator==(int a, Expr b);
/** Return a boolean expression that tests whether the first argument
* is not equal to the second, after doing any necessary type coercion
* using \ref Internal::match_types */
Expr operator!=(Expr a, Expr b);
/** Return a boolean expression that tests whether an expression is
* not equal to a constant integer. Coerces the integer to the type of
* the expression. Errors if the integer is not representable in that
* type. */
Expr operator!=(Expr a, int b);
/** Return a boolean expression that tests whether a constant integer
* is not equal to an expression. Coerces the integer to the type of
* the expression. Errors if the integer is not representable in that
* type. */
Expr operator!=(int a, Expr b);
/** Returns the logical and of the two arguments */
Expr operator&&(Expr a, Expr b);
/** Logical and of an Expr and a bool. Either returns the Expr or an
* Expr representing false, depending on the bool. */
// @{
Expr operator&&(Expr a, bool b);
Expr operator&&(bool a, Expr b);
// @}
/** Returns the logical or of the two arguments */
Expr operator||(Expr a, Expr b);
/** Logical or of an Expr and a bool. Either returns the Expr or an
* Expr representing true, depending on the bool. */
// @{
Expr operator||(Expr a, bool b);
Expr operator||(bool a, Expr b);
// @}
/** Returns the logical not the argument */
Expr operator!(Expr a);
/** Returns an expression representing the greater of the two
* arguments, after doing any necessary type coercion using
* \ref Internal::match_types. Vectorizes cleanly on most platforms
* (with the exception of integer types on x86 without SSE4). */
Expr max(Expr a, Expr b);
/** Returns an expression representing the greater of an expression
* and a constant integer. The integer is coerced to the type of the
* expression. Errors if the integer is not representable as that
* type. Vectorizes cleanly on most platforms (with the exception of
* integer types on x86 without SSE4). */
Expr max(Expr a, int b);
/** Returns an expression representing the greater of a constant
* integer and an expression. The integer is coerced to the type of
* the expression. Errors if the integer is not representable as that
* type. Vectorizes cleanly on most platforms (with the exception of
* integer types on x86 without SSE4). */
Expr max(int a, Expr b);
inline Expr max(float a, Expr b) {
return max(Expr(a), std::move(b));
}
inline Expr max(Expr a, float b) {
return max(std::move(a), Expr(b));
}
/** Returns an expression representing the greater of an expressions
* vector, after doing any necessary type coersion using
* \ref Internal::match_types. Vectorizes cleanly on most platforms
* (with the exception of integer types on x86 without SSE4).
* The expressions are folded from right ie. max(.., max(.., ..)).
* The arguments can be any mix of types but must all be convertible to Expr. */
template<typename A, typename B, typename C, typename... Rest,
typename std::enable_if<Halide::Internal::all_are_convertible<Expr, Rest...>::value>::type * = nullptr>
inline Expr max(A &&a, B &&b, C &&c, Rest &&...rest) {
return max(std::forward<A>(a), max(std::forward<B>(b), std::forward<C>(c), std::forward<Rest>(rest)...));
}
Expr min(Expr a, Expr b);
/** Returns an expression representing the lesser of an expression
* and a constant integer. The integer is coerced to the type of the
* expression. Errors if the integer is not representable as that
* type. Vectorizes cleanly on most platforms (with the exception of
* integer types on x86 without SSE4). */
Expr min(Expr a, int b);
/** Returns an expression representing the lesser of a constant
* integer and an expression. The integer is coerced to the type of
* the expression. Errors if the integer is not representable as that
* type. Vectorizes cleanly on most platforms (with the exception of
* integer types on x86 without SSE4). */
Expr min(int a, Expr b);
inline Expr min(float a, Expr b) {
return min(Expr(a), std::move(b));
}
inline Expr min(Expr a, float b) {
return min(std::move(a), Expr(b));
}
/** Returns an expression representing the lesser of an expressions
* vector, after doing any necessary type coersion using
* \ref Internal::match_types. Vectorizes cleanly on most platforms
* (with the exception of integer types on x86 without SSE4).
* The expressions are folded from right ie. min(.., min(.., ..)).
* The arguments can be any mix of types but must all be convertible to Expr. */
template<typename A, typename B, typename C, typename... Rest,
typename std::enable_if<Halide::Internal::all_are_convertible<Expr, Rest...>::value>::type * = nullptr>
inline Expr min(A &&a, B &&b, C &&c, Rest &&...rest) {
return min(std::forward<A>(a), min(std::forward<B>(b), std::forward<C>(c), std::forward<Rest>(rest)...));
}
/** Operators on floats treats those floats as Exprs. Making these
* explicit prevents implicit float->int casts that might otherwise
* occur. */
// @{
inline Expr operator+(Expr a, float b) {
return std::move(a) + Expr(b);
}
inline Expr operator+(float a, Expr b) {
return Expr(a) + std::move(b);
}
inline Expr operator-(Expr a, float b) {
return std::move(a) - Expr(b);
}
inline Expr operator-(float a, Expr b) {
return Expr(a) - std::move(b);
}
inline Expr operator*(Expr a, float b) {
return std::move(a) * Expr(b);
}
inline Expr operator*(float a, Expr b) {
return Expr(a) * std::move(b);
}
inline Expr operator/(Expr a, float b) {
return std::move(a) / Expr(b);
}
inline Expr operator/(float a, Expr b) {
return Expr(a) / std::move(b);
}
inline Expr operator%(Expr a, float b) {
return std::move(a) % Expr(b);
}
inline Expr operator%(float a, Expr b) {
return Expr(a) % std::move(b);
}
inline Expr operator>(Expr a, float b) {
return std::move(a) > Expr(b);
}
inline Expr operator>(float a, Expr b) {
return Expr(a) > std::move(b);
}
inline Expr operator<(Expr a, float b) {
return std::move(a) < Expr(b);
}
inline Expr operator<(float a, Expr b) {
return Expr(a) < std::move(b);
}
inline Expr operator>=(Expr a, float b) {
return std::move(a) >= Expr(b);
}
inline Expr operator>=(float a, Expr b) {
return Expr(a) >= std::move(b);
}
inline Expr operator<=(Expr a, float b) {
return std::move(a) <= Expr(b);
}
inline Expr operator<=(float a, Expr b) {
return Expr(a) <= std::move(b);
}
inline Expr operator==(Expr a, float b) {
return std::move(a) == Expr(b);
}
inline Expr operator==(float a, Expr b) {
return Expr(a) == std::move(b);
}
inline Expr operator!=(Expr a, float b) {
return std::move(a) != Expr(b);
}
inline Expr operator!=(float a, Expr b) {
return Expr(a) != std::move(b);
}
// @}
/** Clamps an expression to lie within the given bounds. The bounds
* are type-cast to match the expression. Vectorizes as well as min/max. */
Expr clamp(Expr a, const Expr &min_val, const Expr &max_val);
/** Returns the absolute value of a signed integer or floating-point
* expression. Vectorizes cleanly. Unlike in C, abs of a signed
* integer returns an unsigned integer of the same bit width. This
* means that abs of the most negative integer doesn't overflow. */
Expr abs(Expr a);
/** Return the absolute difference between two values. Vectorizes
* cleanly. Returns an unsigned value of the same bit width. There are
* various ways to write this yourself, but they contain numerous
* gotchas and don't always compile to good code, so use this
* instead. */
Expr absd(Expr a, Expr b);
/** Returns an expression similar to the ternary operator in C, except
* that it always evaluates all arguments. If the first argument is
* true, then return the second, else return the third. Typically
* vectorizes cleanly, but benefits from SSE41 or newer on x86. */
Expr select(Expr condition, Expr true_value, Expr false_value);
/** A multi-way variant of select similar to a switch statement in C,
* which can accept multiple conditions and values in pairs. Evaluates
* to the first value for which the condition is true. Returns the
* final value if all conditions are false. */
template<typename... Args,
typename std::enable_if<Halide::Internal::all_are_convertible<Expr, Args...>::value>::type * = nullptr>
inline Expr select(Expr c0, Expr v0, Expr c1, Expr v1, Args &&...args) {
return select(std::move(c0), std::move(v0), select(std::move(c1), std::move(v1), std::forward<Args>(args)...));
}
/** Equivalent of ternary select(), but taking/returning tuples. If the condition is
* a Tuple, it must match the size of the true and false Tuples. */
// @{
Tuple select(const Tuple &condition, const Tuple &true_value, const Tuple &false_value);
Tuple select(const Expr &condition, const Tuple &true_value, const Tuple &false_value);
// @}
/** Equivalent of multiway select(), but taking/returning tuples. If the condition is
* a Tuple, it must match the size of the true and false Tuples. */
// @{
template<typename... Args>
inline Tuple select(const Tuple &c0, const Tuple &v0, const Tuple &c1, const Tuple &v1, Args &&...args) {
return select(c0, v0, select(c1, v1, std::forward<Args>(args)...));
}
template<typename... Args>
inline Tuple select(const Expr &c0, const Tuple &v0, const Expr &c1, const Tuple &v1, Args &&...args) {
return select(c0, v0, select(c1, v1, std::forward<Args>(args)...));
}
// @}
/** select applied to FuncRefs (e.g. select(x < 100, f(x), g(x))) is assumed to
* return an Expr. A runtime error is produced if this is applied to
* tuple-valued Funcs. In that case you should explicitly cast the second and
* third args to Tuple to remove the ambiguity. */
// @{
Expr select(const Expr &condition, const FuncRef &true_value, const FuncRef &false_value);
template<typename... Args>
inline Expr select(const Expr &c0, const FuncRef &v0, const Expr &c1, const FuncRef &v1, Args &&...args) {
return select(c0, v0, select(c1, v1, std::forward<Args>(args)...));
}
// @}
/** Oftentimes we want to pack a list of expressions with the same type
* into a channel dimension, e.g.,
* img(x, y, c) = select(c == 0, 100, // Red
* c == 1, 50, // Green
* 25); // Blue
* This is tedious when the list is long. The following function
* provide convinent syntax that allow one to write:
* img(x, y, c) = mux(c, {100, 50, 25});
*
* As with the select equivalent, if the first argument (the index) is
* out of range, the expression evaluates to the last value.
*/
// @{
Expr mux(const Expr &id, const std::initializer_list<Expr> &values);
Expr mux(const Expr &id, const std::vector<Expr> &values);
Expr mux(const Expr &id, const Tuple &values);
Expr mux(const Expr &id, const std::initializer_list<FuncRef> &values);
Tuple mux(const Expr &id, const std::initializer_list<Tuple> &values);
Tuple mux(const Expr &id, const std::vector<Tuple> &values);
// @}
/** Return the sine of a floating-point expression. If the argument is
* not floating-point, it is cast to Float(32). Does not vectorize
* well. */
Expr sin(Expr x);
/** Return the arcsine of a floating-point expression. If the argument
* is not floating-point, it is cast to Float(32). Does not vectorize
* well. */
Expr asin(Expr x);
/** Return the cosine of a floating-point expression. If the argument
* is not floating-point, it is cast to Float(32). Does not vectorize
* well. */
Expr cos(Expr x);
/** Return the arccosine of a floating-point expression. If the
* argument is not floating-point, it is cast to Float(32). Does not
* vectorize well. */
Expr acos(Expr x);
/** Return the tangent of a floating-point expression. If the argument
* is not floating-point, it is cast to Float(32). Does not vectorize
* well. */
Expr tan(Expr x);
/** Return the arctangent of a floating-point expression. If the
* argument is not floating-point, it is cast to Float(32). Does not
* vectorize well. */
Expr atan(Expr x);
/** Return the angle of a floating-point gradient. If the argument is
* not floating-point, it is cast to Float(32). Does not vectorize
* well. */
Expr atan2(Expr y, Expr x);
/** Return the hyperbolic sine of a floating-point expression. If the
* argument is not floating-point, it is cast to Float(32). Does not
* vectorize well. */
Expr sinh(Expr x);
/** Return the hyperbolic arcsinhe of a floating-point expression. If
* the argument is not floating-point, it is cast to Float(32). Does
* not vectorize well. */
Expr asinh(Expr x);
/** Return the hyperbolic cosine of a floating-point expression. If
* the argument is not floating-point, it is cast to Float(32). Does
* not vectorize well. */
Expr cosh(Expr x);
/** Return the hyperbolic arccosine of a floating-point expression.
* If the argument is not floating-point, it is cast to
* Float(32). Does not vectorize well. */
Expr acosh(Expr x);
/** Return the hyperbolic tangent of a floating-point expression. If
* the argument is not floating-point, it is cast to Float(32). Does
* not vectorize well. */
Expr tanh(Expr x);
/** Return the hyperbolic arctangent of a floating-point expression.
* If the argument is not floating-point, it is cast to
* Float(32). Does not vectorize well. */
Expr atanh(Expr x);
/** Return the square root of a floating-point expression. If the
* argument is not floating-point, it is cast to Float(32). Typically
* vectorizes cleanly. */
Expr sqrt(Expr x);
/** Return the square root of the sum of the squares of two
* floating-point expressions. If the argument is not floating-point,
* it is cast to Float(32). Vectorizes cleanly. */
Expr hypot(const Expr &x, const Expr &y);
/** Return the exponential of a floating-point expression. If the
* argument is not floating-point, it is cast to Float(32). For
* Float(64) arguments, this calls the system exp function, and does
* not vectorize well. For Float(32) arguments, this function is
* vectorizable, does the right thing for extremely small or extremely
* large inputs, and is accurate up to the last bit of the
* mantissa. Vectorizes cleanly. */
Expr exp(Expr x);
/** Return the logarithm of a floating-point expression. If the
* argument is not floating-point, it is cast to Float(32). For
* Float(64) arguments, this calls the system log function, and does
* not vectorize well. For Float(32) arguments, this function is
* vectorizable, does the right thing for inputs <= 0 (returns -inf or
* nan), and is accurate up to the last bit of the
* mantissa. Vectorizes cleanly. */
Expr log(Expr x);
/** Return one floating point expression raised to the power of
* another. The type of the result is given by the type of the first
* argument. If the first argument is not a floating-point type, it is
* cast to Float(32). For Float(32), cleanly vectorizable, and
* accurate up to the last few bits of the mantissa. Gets worse when
* approaching overflow. Vectorizes cleanly. */
Expr pow(Expr x, Expr y);
/** Evaluate the error function erf. Only available for
* Float(32). Accurate up to the last three bits of the
* mantissa. Vectorizes cleanly. */
Expr erf(const Expr &x);
/** Fast vectorizable approximation to some trigonometric functions for
* Float(32). Absolute approximation error is less than 1e-5. Slow on x86 if
* you don't have at least sse 4.1. */
// @{
Expr fast_sin(const Expr &x);
Expr fast_cos(const Expr &x);
// @}
/** Fast approximate cleanly vectorizable log for Float(32). Returns
* nonsense for x <= 0.0f. Accurate up to the last 5 bits of the
* mantissa. Vectorizes cleanly. Slow on x86 if you don't
* have at least sse 4.1. */
Expr fast_log(const Expr &x);
/** Fast approximate cleanly vectorizable exp for Float(32). Returns
* nonsense for inputs that would overflow or underflow. Typically
* accurate up to the last 5 bits of the mantissa. Gets worse when
* approaching overflow. Vectorizes cleanly. Slow on x86 if you don't
* have at least sse 4.1. */
Expr fast_exp(const Expr &x);
/** Fast approximate cleanly vectorizable pow for Float(32). Returns
* nonsense for x < 0.0f. Accurate up to the last 5 bits of the
* mantissa for typical exponents. Gets worse when approaching
* overflow. Vectorizes cleanly. Slow on x86 if you don't
* have at least sse 4.1. */
Expr fast_pow(Expr x, Expr y);
/** Fast approximate inverse for Float(32). Corresponds to the rcpps
* instruction on x86, and the vrecpe instruction on ARM. Vectorizes
* cleanly. Note that this can produce slightly different results
* across different implementations of the same architecture (e.g. AMD vs Intel),
* even when strict_float is enabled. */
Expr fast_inverse(Expr x);
/** Fast approximate inverse square root for Float(32). Corresponds to
* the rsqrtps instruction on x86, and the vrsqrte instruction on
* ARM. Vectorizes cleanly. Note that this can produce slightly different results
* across different implementations of the same architecture (e.g. AMD vs Intel),
* even when strict_float is enabled. */
Expr fast_inverse_sqrt(Expr x);
/** Return the greatest whole number less than or equal to a
* floating-point expression. If the argument is not floating-point,
* it is cast to Float(32). The return value is still in floating
* point, despite being a whole number. Vectorizes cleanly. */
Expr floor(Expr x);
/** Return the least whole number greater than or equal to a
* floating-point expression. If the argument is not floating-point,
* it is cast to Float(32). The return value is still in floating
* point, despite being a whole number. Vectorizes cleanly. */
Expr ceil(Expr x);
/** Return the whole number closest to a floating-point expression. If the
* argument is not floating-point, it is cast to Float(32). The return value is
* still in floating point, despite being a whole number. On ties, we round
* towards the nearest even integer. Note that this is not the same as
* std::round in C, which rounds away from zero. On platforms without a native
* instruction for this, it is emulated, and may be more expensive than
* cast<int>(x + 0.5f) or similar. */
Expr round(Expr x);
/** Return the integer part of a floating-point expression. If the argument is
* not floating-point, it is cast to Float(32). The return value is still in
* floating point, despite being a whole number. Vectorizes cleanly. */
Expr trunc(Expr x);
/** Returns true if the argument is a Not a Number (NaN). Requires a
* floating point argument. Vectorizes cleanly.
* Note that the Expr passed in will be evaluated in strict_float mode,
* regardless of whether strict_float mode is enabled in the current Target. */
Expr is_nan(Expr x);
/** Returns true if the argument is Inf or -Inf. Requires a
* floating point argument. Vectorizes cleanly.
* Note that the Expr passed in will be evaluated in strict_float mode,
* regardless of whether strict_float mode is enabled in the current Target. */
Expr is_inf(Expr x);
/** Returns true if the argument is a finite value (ie, neither NaN nor Inf).
* Requires a floating point argument. Vectorizes cleanly.
* Note that the Expr passed in will be evaluated in strict_float mode,
* regardless of whether strict_float mode is enabled in the current Target. */
Expr is_finite(Expr x);
/** Return the fractional part of a floating-point expression. If the argument
* is not floating-point, it is cast to Float(32). The return value has the
* same sign as the original expression. Vectorizes cleanly. */
Expr fract(const Expr &x);
/** Reinterpret the bits of one value as another type. */
Expr reinterpret(Type t, Expr e);
template<typename T>
Expr reinterpret(Expr e) {
return reinterpret(type_of<T>(), std::move(e));
}
/** Return the bitwise and of two expressions (which need not have the
* same type). The result type is the wider of the two expressions.
* Only integral types are allowed and both expressions must be signed
* or both must be unsigned. */
Expr operator&(Expr x, Expr y);
/** Return the bitwise and of an expression and an integer. The type
* of the result is the type of the expression argument. */
// @{
Expr operator&(Expr x, int y);
Expr operator&(int x, Expr y);
// @}
/** Return the bitwise or of two expressions (which need not have the
* same type). The result type is the wider of the two expressions.
* Only integral types are allowed and both expressions must be signed
* or both must be unsigned. */
Expr operator|(Expr x, Expr y);
/** Return the bitwise or of an expression and an integer. The type of
* the result is the type of the expression argument. */
// @{
Expr operator|(Expr x, int y);
Expr operator|(int x, Expr y);
// @}
/** Return the bitwise xor of two expressions (which need not have the
* same type). The result type is the wider of the two expressions.
* Only integral types are allowed and both expressions must be signed
* or both must be unsigned. */
Expr operator^(Expr x, Expr y);
/** Return the bitwise xor of an expression and an integer. The type
* of the result is the type of the expression argument. */
// @{
Expr operator^(Expr x, int y);
Expr operator^(int x, Expr y);
// @}
/** Return the bitwise not of an expression. */
Expr operator~(Expr x);
/** Shift the bits of an integer value left. This is actually less
* efficient than multiplying by 2^n, because Halide's optimization
* passes understand multiplication, and will compile it to
* shifting. This operator is only for if you really really need bit
* shifting (e.g. because the exponent is a run-time parameter). The
* type of the result is equal to the type of the first argument. Both
* arguments must have integer type. */
// @{
Expr operator<<(Expr x, Expr y);
Expr operator<<(Expr x, int y);
// @}
/** Shift the bits of an integer value right. Does sign extension for
* signed integers. This is less efficient than dividing by a power of
* two. Halide's definition of division (always round to negative
* infinity) means that all divisions by powers of two get compiled to
* bit-shifting, and Halide's optimization routines understand
* division and can work with it. The type of the result is equal to
* the type of the first argument. Both arguments must have integer
* type. */
// @{
Expr operator>>(Expr x, Expr y);
Expr operator>>(Expr x, int y);
// @}
/** Linear interpolate between the two values according to a weight.
* \param zero_val The result when weight is 0
* \param one_val The result when weight is 1
* \param weight The interpolation amount
*
* Both zero_val and one_val must have the same type. All types are
* supported, including bool.
*
* The weight is treated as its own type and must be float or an
* unsigned integer type. It is scaled to the bit-size of the type of
* x and y if they are integer, or converted to float if they are
* float. Integer weights are converted to float via division by the
* full-range value of the weight's type. Floating-point weights used
* to interpolate between integer values must be between 0.0f and
* 1.0f, and an error may be signaled if it is not provably so. (clamp
* operators can be added to provide proof. Currently an error is only
* signalled for constant weights.)
*
* For integer linear interpolation, out of range values cannot be
* represented. In particular, weights that are conceptually less than
* 0 or greater than 1.0 are not representable. As such the result is
* always between x and y (inclusive of course). For lerp with
* floating-point values and floating-point weight, the full range of
* a float is valid, however underflow and overflow can still occur.
*
* Ordering is not required between zero_val and one_val:
* lerp(42, 69, .5f) == lerp(69, 42, .5f) == 56
*
* Results for integer types are for exactly rounded arithmetic. As
* such, there are cases where 16-bit and float differ because 32-bit
* floating-point (float) does not have enough precision to produce
* the exact result. (Likely true for 32-bit integer
* vs. double-precision floating-point as well.)
*
* At present, double precision and 64-bit integers are not supported.
*
* Generally, lerp will vectorize as if it were an operation on a type
* twice the bit size of the inferred type for x and y.
*
* Some examples:
* \code
*
* // Since Halide does not have direct type delcarations, casts
* // below are used to indicate the types of the parameters.
* // Such casts not required or expected in actual code where types
* // are inferred.
*
* lerp(cast<float>(x), cast<float>(y), cast<float>(w)) ->
* x * (1.0f - w) + y * w
*
* lerp(cast<uint8_t>(x), cast<uint8_t>(y), cast<uint8_t>(w)) ->
* cast<uint8_t>(cast<uint8_t>(x) * (1.0f - cast<uint8_t>(w) / 255.0f) +
* cast<uint8_t>(y) * cast<uint8_t>(w) / 255.0f + .5f)
*
* // Note addition in Halide promoted uint8_t + int8_t to int16_t already,
* // the outer cast is added for clarity.
* lerp(cast<uint8_t>(x), cast<int8_t>(y), cast<uint8_t>(w)) ->
* cast<int16_t>(cast<uint8_t>(x) * (1.0f - cast<uint8_t>(w) / 255.0f) +
* cast<int8_t>(y) * cast<uint8_t>(w) / 255.0f + .5f)
*
* lerp(cast<int8_t>(x), cast<int8_t>(y), cast<float>(w)) ->
* cast<int8_t>(cast<int8_t>(x) * (1.0f - cast<float>(w)) +
* cast<int8_t>(y) * cast<uint8_t>(w))
*
* \endcode
* */
Expr lerp(Expr zero_val, Expr one_val, Expr weight);
/** Count the number of set bits in an expression. */
Expr popcount(Expr x);
/** Count the number of leading zero bits in an expression. If the expression is
* zero, the result is the number of bits in the type. */
Expr count_leading_zeros(Expr x);
/** Count the number of trailing zero bits in an expression. If the expression is
* zero, the result is the number of bits in the type. */
Expr count_trailing_zeros(Expr x);
/** Divide two integers, rounding towards zero. This is the typical
* behavior of most hardware architectures, which differs from
* Halide's division operator, which is Euclidean (rounds towards
* -infinity). Will throw a runtime error if y is zero, or if y is -1
* and x is the minimum signed integer. */
Expr div_round_to_zero(Expr x, Expr y);
/** Compute the remainder of dividing two integers, when division is
* rounding toward zero. This is the typical behavior of most hardware
* architectures, which differs from Halide's mod operator, which is
* Euclidean (produces the remainder when division rounds towards
* -infinity). Will throw a runtime error if y is zero. */
Expr mod_round_to_zero(Expr x, Expr y);
/** Return a random variable representing a uniformly distributed
* float in the half-open interval [0.0f, 1.0f). For random numbers of
* other types, use lerp with a random float as the last parameter.
*
* Optionally takes a seed.
*
* Note that:
\code
Expr x = random_float();
Expr y = x + x;
\endcode
*
* is very different to
*
\code
Expr y = random_float() + random_float();
\endcode
*
* The first doubles a random variable, and the second adds two
* independent random variables.
*
* A given random variable takes on a unique value that depends
* deterministically on the pure variables of the function they belong
* to, the identity of the function itself, and which definition of
* the function it is used in. They are, however, shared across tuple
* elements.
*
* This function vectorizes cleanly.
*/
Expr random_float(Expr seed = Expr());
/** Return a random variable representing a uniformly distributed
* unsigned 32-bit integer. See \ref random_float. Vectorizes cleanly. */
Expr random_uint(Expr seed = Expr());
/** Return a random variable representing a uniformly distributed
* 32-bit integer. See \ref random_float. Vectorizes cleanly. */
Expr random_int(Expr seed = Expr());
/** Create an Expr that prints out its value whenever it is
* evaluated. It also prints out everything else in the arguments
* list, separated by spaces. This can include string literals. */
//@{
Expr print(const std::vector<Expr> &values);
template<typename... Args>
inline HALIDE_NO_USER_CODE_INLINE Expr print(Expr a, Args &&...args) {
std::vector<Expr> collected_args = {std::move(a)};
Internal::collect_print_args(collected_args, std::forward<Args>(args)...);
return print(collected_args);
}
//@}
/** Create an Expr that prints whenever it is evaluated, provided that
* the condition is true. */
// @{
Expr print_when(Expr condition, const std::vector<Expr> &values);
template<typename... Args>
inline HALIDE_NO_USER_CODE_INLINE Expr print_when(Expr condition, Expr a, Args &&...args) {
std::vector<Expr> collected_args = {std::move(a)};
Internal::collect_print_args(collected_args, std::forward<Args>(args)...);
return print_when(std::move(condition), collected_args);
}
// @}
/** Create an Expr that that guarantees a precondition.
* If 'condition' is true, the return value is equal to the first Expr.
* If 'condition' is false, halide_error() is called, and the return value
* is arbitrary. Any additional arguments after the first Expr are stringified
* and passed as a user-facing message to halide_error(), similar to print().
*
* Note that this essentially *always* inserts a runtime check into the
* generated code (except when the condition can be proven at compile time);
* as such, it should be avoided inside inner loops, except for debugging
* or testing purposes. Note also that it does not vectorize cleanly (vector
* values will be scalarized for the check).
*
* However, using this to make assertions about (say) input values
* can be useful, both in terms of correctness and (potentially) in terms
* of code generation, e.g.
\code
Param<int> p;
Expr y = require(p > 0, p);
\endcode
* will allow the optimizer to assume positive, nonzero values for y.
*/
// @{
Expr require(Expr condition, const std::vector<Expr> &values);
template<typename... Args>
inline HALIDE_NO_USER_CODE_INLINE Expr require(Expr condition, Expr value, Args &&...args) {
std::vector<Expr> collected_args = {std::move(value)};
Internal::collect_print_args(collected_args, std::forward<Args>(args)...);
return require(std::move(condition), collected_args);
}
// @}
/** Return an undef value of the given type. Halide skips stores that
* depend on undef values, so you can use this to mean "do not modify
* this memory location". This is an escape hatch that can be used for
* several things:
*
* You can define a reduction with no pure step, by setting the pure
* step to undef. Do this only if you're confident that the update
* steps are sufficient to correctly fill in the domain.
*
* For a tuple-valued reduction, you can write an update step that
* only updates some tuple elements.
*
* You can define single-stage pipeline that only has update steps,
* and depends on the values already in the output buffer.
*
* Use this feature with great caution, as you can use it to load from
* uninitialized memory.
*/
Expr undef(Type t);
template<typename T>
inline Expr undef() {
return undef(type_of<T>());
}
namespace Internal {
/** Return an expression that should never be evaluated. Expressions
* that depend on unreachabale values are also unreachable, and
* statements that execute unreachable expressions are also considered
* unreachable. */
Expr unreachable(Type t = Int(32));
template<typename T>
inline Expr unreachable() {
return unreachable(type_of<T>());
}
} // namespace Internal
/** Control the values used in the memoization cache key for memoize.
* Normally parameters and other external dependencies are
* automatically inferred and added to the cache key. The memoize_tag
* operator allows computing one expression and using either the
* computed value, or one or more other expressions in the cache key
* instead of the parameter dependencies of the computation. The
* single argument version is completely safe in that the cache key
* will use the actual computed value -- it is difficult or imposible
* to produce erroneous caching this way. The more-than-one argument
* version allows generating cache keys that do not uniquely identify
* the computation and thus can result in caching errors.
*
* A potential use for the single argument version is to handle a
* floating-point parameter that is quantized to a small
* integer. Mutliple values of the float will produce the same integer
* and moving the caching to using the integer for the key is more
* efficient.
*
* The main use for the more-than-one argument version is to provide
* cache key information for Handles and ImageParams, which otherwise
* are not allowed inside compute_cached operations. E.g. when passing
* a group of parameters to an external array function via a Handle,
* memoize_tag can be used to isolate the actual values used by that
* computation. If an ImageParam is a constant image with a persistent
* digest, memoize_tag can be used to key computations using that image
* on the digest. */
// @{
template<typename... Args>
inline HALIDE_NO_USER_CODE_INLINE Expr memoize_tag(Expr result, Args &&...args) {
std::vector<Expr> collected_args{std::forward<Args>(args)...};
return Internal::memoize_tag_helper(std::move(result), collected_args);
}
// @}
/** Expressions tagged with this intrinsic are considered to be part
* of the steady state of some loop with a nasty beginning and end
* (e.g. a boundary condition). When Halide encounters likely
* intrinsics, it splits the containing loop body into three, and
* tries to simplify down all conditions that lead to the likely. For
* example, given the expression: select(x < 1, bar, x > 10, bar,
* likely(foo)), Halide will split the loop over x into portions where
* x < 1, 1 <= x <= 10, and x > 10.
*
* You're unlikely to want to call this directly. You probably want to
* use the boundary condition helpers in the BoundaryConditions
* namespace instead.
*/
Expr likely(Expr e);
/** Equivalent to likely, but only triggers a loop partitioning if
* found in an innermost loop. */
Expr likely_if_innermost(Expr e);
/** Cast an expression to the halide type corresponding to the C++
* type T. As part of the cast, clamp to the minimum and maximum
* values of the result type. */
template<typename T>
Expr saturating_cast(Expr e) {
return saturating_cast(type_of<T>(), std::move(e));
}
/** Cast an expression to a new type, clamping to the minimum and
* maximum values of the result type. */
Expr saturating_cast(Type t, Expr e);
/** Makes a best effort attempt to preserve IEEE floating-point
* semantics in evaluating an expression. May not be implemented for
* all backends. (E.g. it is difficult to do this for C++ code
* generation as it depends on the compiler flags used to compile the
* generated code. */
Expr strict_float(const Expr &e);
/** Create an Expr that that promises another Expr is clamped but do
* not generate code to check the assertion or modify the value. No
* attempt is made to prove the bound at compile time. (If it is
* proved false as a result of something else, an error might be
* generated, but it is also possible the compiler will crash.) The
* promised bound is used in bounds inference so it will allow
* satisfying bounds checks as well as possibly aiding optimization.
*
* unsafe_promise_clamped returns its first argument, the Expr 'value'
*
* This is a very easy way to make Halide generate erroneous code if
* the bound promises is not kept. Use sparingly when there is no
* other way to convey the information to the compiler and it is
* required for a valuable optimization.
*
* Unsafe promises can be checked by turning on
* Target::CheckUnsafePromises. This is intended for debugging only.
*/
Expr unsafe_promise_clamped(const Expr &value, const Expr &min, const Expr &max);
namespace Internal {
/**
* FOR INTERNAL USE ONLY.
*
* An entirely unchecked version of unsafe_promise_clamped, used
* inside the compiler as an annotation of the known bounds of an Expr
* when it has proved something is bounded and wants to record that
* fact for later passes (notably bounds inference) to exploit. This
* gets introduced by GuardWithIf tail strategies, because the bounds
* machinery has a hard time exploiting if statement conditions.
*
* Unlike unsafe_promise_clamped, this expression is
* context-dependent, because 'value' might be statically bounded at
* some point in the IR (e.g. due to a containing if statement), but
* not elsewhere.
*
* This intrinsic always evaluates to its first argument. If this value is
* used by a side-effecting operation and it is outside the range specified
* by its second and third arguments, behavior is undefined. The compiler can
* therefore assume that the value is within the range given and optimize
* accordingly. Note that this permits promise_clamped to evaluate to
* something outside of the range, provided that this value is not used.
*
* Note that this produces an intrinsic that is marked as 'pure' and thus is
* allowed to be hoisted, etc.; thus, extra care must be taken with its use.
**/
Expr promise_clamped(const Expr &value, const Expr &min, const Expr &max);
} // namespace Internal
/** Scatter and gather are used for update definition which must store
* multiple values to distinct locations at the same time. The
* multiple expressions on the right-hand-side are bundled together
* into a "gather", which must match a "scatter" the the same number
* of arguments on the left-hand-size. For example, to store the
* values 1 and 2 to the locations (x, y, 3) and (x, y, 4),
* respectively:
*
\code
f(x, y, scatter(3, 4)) = gather(1, 2);
\endcode
*
* The result of gather or scatter can be treated as an
* expression. Any containing operations on it can be assumed to
* distribute over the elements. If two gather expressions are
* combined with an arithmetic operator (e.g. added), they combine
* element-wise. The following example stores the values 2 * x, 2 * y,
* and 2 * c to the locations (x + 1, y, c), (x, y + 3, c), and (x, y,
* c + 2) respectively:
*
\code
f(x + scatter(1, 0, 0), y + scatter(0, 3, 0), c + scatter(0, 0, 2)) = 2 * gather(x, y, c);
\endcode
*
* Repeated values in the scatter cause multiple stores to the same
* location. The stores happen in order from left to right, so the
* rightmost value wins. The following code is equivalent to f(x) = 5
*
\code
f(scatter(x, x)) = gather(3, 5);
\endcode
*
* Gathers are most useful for algorithms which require in-place
* swapping or permutation of multiple elements, or other kinds of
* in-place mutations that require loading multiple inputs, doing some
* operations to them jointly, then storing them again. The following
* update definition swaps the values of f at locations 3 and 5 if an
* input parameter p is true:
*
\code
f(scatter(3, 5)) = f(select(p, gather(5, 3), gather(3, 5)));
\endcode
*
* For more examples of the use of scatter and gather, see
* test/correctness/multiple_scatter.cpp
*
* It is not currently possible to use scatter and gather to write an
* update definition in which the *number* of values loaded or stored
* varies, as the size of the scatter/gather packet must be fixed a
* compile-time. A workaround is to make the unwanted extra operations
* a redundant copy of the last operation, which will be
* dead-code-eliminated by the compiler. For example, the following
* update definition swaps the values at locations 3 and 5 when the
* parameter p is true, and rotates the values at locations 1, 2, and 3
* when it is false. The load from 3 and store to 5 will be redundantly
* repeated:
*
\code
f(select(p, scatter(3, 5, 5), scatter(1, 2, 3))) = f(select(p, gather(5, 3, 3), gather(2, 3, 1)));
\endcode
*
* Note that in the p == true case, we redundantly load from 3 and write
* to 5 twice.
*/
//@{
Expr scatter(const std::vector<Expr> &args);
Expr gather(const std::vector<Expr> &args);
template<typename... Args>
Expr scatter(const Expr &e, Args &&...args) {
return scatter({e, std::forward<Args>(args)...});
}
template<typename... Args>
Expr gather(const Expr &e, Args &&...args) {
return gather({e, std::forward<Args>(args)...});
}
// @}
/** Extract a contiguous subsequence of the bits of 'e', starting at the bit
* index given by 'lsb', where zero is the least-significant bit, returning a
* value of type 't'. Any out-of-range bits requested are filled with zeros.
*
* extract_bits is especially useful when one wants to load a small vector of a
* wide type, and treat it as a larger vector of a smaller type. For example,
* loading a vector of 32 uint8 values from a uint32 Func can be done as
* follows:
\code
f8(x) = extract_bits<uint8_t>(f32(x/4), 8*(x%4));
f8.align_bounds(x, 4).vectorize(x, 32);
\endcode
* Note that the align_bounds call is critical so that the narrow Exprs are
* aligned to the wider Exprs. This makes the x%4 term collapse to a
* constant. If f8 is an output Func, then constraining the min value of x to be
* a known multiple of four would also be sufficient, e.g. via:
\code
f8.output_buffer().dim(0).set_min(0);
\endcode
*
* See test/correctness/extract_concat_bits.cpp for a complete example. */
// @{
Expr extract_bits(Type t, const Expr &e, const Expr &lsb);
template<typename T>
Expr extract_bits(const Expr &e, const Expr &lsb) {
return extract_bits(type_of<T>(), e, lsb);
}
// @}
/** Given a number of Exprs of the same type, concatenate their bits producing a
* single Expr of the same type code of the input but with more bits. The
* number of arguments must be a power of two.
*
* concat_bits is especially useful when one wants to treat a Func containing
* values of a narrow type as a Func containing fewer values of a wider
* type. For example, the following code reinterprets vectors of 32 uint8 values
* as a vector of 8 uint32s:
*
\code
f32(x) = concat_bits({f8(4*x), f8(4*x + 1), f8(4*x + 2), f8(4*x + 3)});
f32.vectorize(x, 8);
\endcode
*
* See test/correctness/extract_concat_bits.cpp for a complete example.
*/
Expr concat_bits(const std::vector<Expr> &e);
/** Below is a collection of intrinsics for fixed-point programming. Most of
* them can be expressed via other means, but this is more natural for some, as
* it avoids ghost widened intermediates that don't (or shouldn't) actually show
* up in codegen, and doesn't rely on pattern-matching inside the compiler to
* succeed to get good instruction selection.
*
* The semantics of each call are defined in terms of a non-existent 'widen' and
* 'narrow' operators, which stand in for casts that double or halve the
* bit-width of a type respectively.
*/
/** Compute a + widen(b). */
Expr widen_right_add(Expr a, Expr b);
/** Compute a * widen(b). */
Expr widen_right_mul(Expr a, Expr b);
/** Compute a - widen(b). */
Expr widen_right_sub(Expr a, Expr b);
/** Compute widen(a) + widen(b). */
Expr widening_add(Expr a, Expr b);
/** Compute widen(a) * widen(b). a and b may have different signedness, in which
* case the result is signed. */
Expr widening_mul(Expr a, Expr b);
/** Compute widen(a) - widen(b). The result is always signed. */
Expr widening_sub(Expr a, Expr b);
/** Compute widen(a) << b. */
//@{
Expr widening_shift_left(Expr a, Expr b);
Expr widening_shift_left(Expr a, int b);
//@}
/** Compute widen(a) >> b. */
//@{
Expr widening_shift_right(Expr a, Expr b);
Expr widening_shift_right(Expr a, int b);
//@}
/** Compute saturating_narrow(widening_add(a, (1 >> min(b, 0)) / 2) << b).
* When b is positive indicating a left shift, the rounding term is zero. */
//@{
Expr rounding_shift_left(Expr a, Expr b);
Expr rounding_shift_left(Expr a, int b);
//@}
/** Compute saturating_narrow(widening_add(a, (1 << max(b, 0)) / 2) >> b).
* When b is negative indicating a left shift, the rounding term is zero. */
//@{
Expr rounding_shift_right(Expr a, Expr b);
Expr rounding_shift_right(Expr a, int b);
//@}
/** Compute saturating_narrow(widen(a) + widen(b)) */
Expr saturating_add(Expr a, Expr b);
/** Compute saturating_narrow(widen(a) - widen(b)) */
Expr saturating_sub(Expr a, Expr b);
/** Compute narrow((widen(a) + widen(b)) / 2) */
Expr halving_add(Expr a, Expr b);
/** Compute narrow((widen(a) + widen(b) + 1) / 2) */
Expr rounding_halving_add(Expr a, Expr b);
/** Compute narrow((widen(a) - widen(b)) / 2) */
Expr halving_sub(Expr a, Expr b);
/** Compute saturating_narrow(shift_right(widening_mul(a, b), q)) */
//@{
Expr mul_shift_right(Expr a, Expr b, Expr q);
Expr mul_shift_right(Expr a, Expr b, int q);
//@}
/** Compute saturating_narrow(rounding_shift_right(widening_mul(a, b), q)) */
//@{
Expr rounding_mul_shift_right(Expr a, Expr b, Expr q);
Expr rounding_mul_shift_right(Expr a, Expr b, int q);
//@}
/** Return a boolean Expr for the corresponding field of the Target
* being used during lowering; they can be useful in writing library
* code without having to plumb a Target through call sites, so that you
* can do things like
\code
Expr e = select(target_arch_is(Target::ARM), something, something_else);
\endcode
* Note that this doesn't do any checking at runtime to verify that the Target
* is valid for the current hardware configuration.
*/
//@{
Expr target_arch_is(Target::Arch arch);
Expr target_os_is(Target::OS os);
Expr target_has_feature(Target::Feature feat);
//@}
/** Return the bit width of the Target used during lowering; this can be useful
* in writing library code without having to plumb a Target through call sites,
* so that you can do things like
\code
Expr e = select(target_bits() == 32, something, something_else);
\endcode
* Note that this doesn't do any checking at runtime to verify that the Target
* is valid for the current hardware configuration.
*/
Expr target_bits();
/** Return the natural vector width for the given Type for the Target
* being used during lowering; this can be useful in writing library
* code without having to plumb a Target through call sites, so that you
* can do things like
\code
f.vectorize(x, target_natural_vector_size(Float(32)));
\endcode
* Note that this doesn't do any checking at runtime to verify that the Target
* is valid for the current hardware configuration.
*/
//@{
Expr target_natural_vector_size(Type t);
template<typename data_t>
Expr target_natural_vector_size() {
return target_natural_vector_size(type_of<data_t>());
}
//@}
} // namespace Halide
#endif
ConstantInterval.h
Defines the ConstantInterval class, and operators on it.
Expr.h
Base classes for Halide expressions (Halide::Expr) and statements (Halide::Internal::Stmt).
Scope.h
Defines the Scope class, which is used for keeping track of names in a scope while traversing IR.
Target.h
Defines the structure that describes a Halide target.
Tuple.h
Defines Tuple - the front-end handle on small arrays of expressions.
HALIDE_NO_USER_CODE_INLINE
#define HALIDE_NO_USER_CODE_INLINE
Definition Util.h:47
Halide::FuncRef
A fragment of front-end syntax of the form f(x, y, z), where x, y, z are Vars or Exprs.
Definition Func.h:494
Halide::Internal::Scope
A common pattern when traversing Halide IR is that you need to keep track of stuff when you find a Le...
Definition Scope.h:94
Halide::Internal::Scope::empty_scope
static const Scope< T > & empty_scope()
A const ref to an empty scope.
Definition Scope.h:120
Halide::Tuple
Create a small array of Exprs for defining and calling functions with multiple outputs.
Definition Tuple.h:18
Halide::Internal
Definition AbstractGenerator.h:24
Halide::Internal::make_one
Expr make_one(Type t)
Construct the representation of one in the given type.
Halide::Internal::div_imp
T div_imp(T a, T b)
Definition IROperator.h:278
Halide::Internal::is_const_zero
bool is_const_zero(const Expr &e)
Is the expression a const (as defined by is_const), and also equal to zero (in all lanes,...
Halide::Internal::as_const_int
std::optional< int64_t > as_const_int(const Expr &e)
If an expression is an IntImm or a Broadcast of an IntImm, return a its value.
Halide::Internal::memoize_tag_helper
Expr memoize_tag_helper(Expr result, const std::vector< Expr > &cache_key_values)
Halide::Internal::make_zero
Expr make_zero(Type t)
Construct the representation of zero in the given type.
Halide::Internal::is_negative_const
bool is_negative_const(const Expr &e)
Is the expression a const (as defined by is_const), and also strictly less than zero (in all lanes,...
Halide::Internal::is_undef
bool is_undef(const Expr &e)
Is the expression an undef.
Halide::Internal::as_const_uint
std::optional< uint64_t > as_const_uint(const Expr &e)
If an expression is a UIntImm or a Broadcast of a UIntImm, return its value.
Halide::Internal::requirement_failed_error
Expr requirement_failed_error(Expr condition, const std::vector< Expr > &args)
Halide::Internal::make_two
Expr make_two(Type t)
Construct the representation of two in the given type.
Halide::Internal::unreachable
Expr unreachable()
Definition IROperator.h:1370
Halide::Internal::check_representable
void check_representable(Type t, int64_t val)
Check if a constant value can be correctly represented as the given type.
Halide::Internal::halide_erf
Expr halide_erf(const Expr &a)
Halide::Internal::is_const_one
bool is_const_one(const Expr &e)
Is the expression a const (as defined by is_const), and also equal to one (in all lanes,...
Halide::Internal::match_types
void match_types(Expr &a, Expr &b)
Coerce the two expressions to have the same type, using C-style casting rules.
Halide::Internal::div_imp< double >
double div_imp< double >(double a, double b)
Definition IROperator.h:319
Halide::Internal::min
ConstantInterval min(const ConstantInterval &a, const ConstantInterval &b)
Halide::Internal::as_const_float
std::optional< double > as_const_float(const Expr &e)
If an expression is a FloatImm or a Broadcast of a FloatImm, return its value.
Halide::Internal::halide_exp
Expr halide_exp(const Expr &a)
Halide::Internal::make_const
Expr make_const(Type t, int64_t val)
Construct an immediate of the given type from any numeric C++ type.
Halide::Internal::is_const_power_of_two_integer
std::optional< int > is_const_power_of_two_integer(const Expr &e)
Is the expression a constant integer power of two.
Halide::Internal::is_positive_const
bool is_positive_const(const Expr &e)
Is the expression a const (as defined by is_const), and also strictly greater than zero (in all lanes...
Halide::Internal::const_true
Expr const_true(int lanes=1)
Construct the constant boolean true.
Halide::Internal::max
ConstantInterval max(const ConstantInterval &a, const ConstantInterval &b)
Halide::Internal::is_signed_integer_overflow
bool is_signed_integer_overflow(const Expr &expr)
Check if an expression is a signed_integer_overflow.
Halide::Internal::mod_imp
T mod_imp(T a, T b)
Implementations of division and mod that are specific to Halide.
Definition IROperator.h:257
Halide::Internal::reset_random_counters
void reset_random_counters()
Reset the counters used for random-number seeds in random_float/int/uint.
Halide::Internal::halide_log
Expr halide_log(const Expr &a)
Halide's vectorizable transcendentals.
Halide::Internal::is_pure
bool is_pure(const Expr &e)
Does the expression 1) Take on the same value no matter where it appears in a Stmt,...
Halide::Internal::split_into_ands
void split_into_ands(const Expr &cond, std::vector< Expr > &result)
Split a boolean condition into vector of ANDs.
Halide::Internal::promise_clamped
Expr promise_clamped(const Expr &value, const Expr &min, const Expr &max)
FOR INTERNAL USE ONLY.
Halide::Internal::is_no_op
bool is_no_op(const Stmt &s)
Is the statement a no-op (which we represent as either an undefined Stmt, or as an Evaluate node of a...
Halide::Internal::unwrap_tags
Expr unwrap_tags(const Expr &e)
If the expression is a tag helper call, remove it and return the tagged expression.
Halide::Internal::div_imp< float >
float div_imp< float >(float a, float b)
Definition IROperator.h:315
Halide::Internal::lossless_negate
Expr lossless_negate(const Expr &x)
Attempt to negate x without introducing new IR and without overflow.
Halide::Internal::strided_ramp_base
Expr strided_ramp_base(const Expr &e, int stride=1)
If e is a ramp expression with stride, default 1, return the base, otherwise undefined.
Halide::Internal::remove_promises
Expr remove_promises(const Expr &e)
Return an Expr that is identical to the input Expr, but with all calls to promise_clamped() and unsaf...
Halide::Internal::const_false
Expr const_false(int lanes=1)
Construct the constant boolean false.
Halide::Internal::lossless_cast
Expr lossless_cast(Type t, Expr e, const Scope< ConstantInterval > &scope=Scope< ConstantInterval >::empty_scope(), std::map< Expr, ConstantInterval, ExprCompare > *cache=nullptr)
Attempt to cast an expression to a smaller type while provably not losing information.
Halide::Internal::mod_imp< double >
double mod_imp< double >(double a, double b)
Definition IROperator.h:309
Halide::Internal::make_bool
Expr make_bool(bool val, int lanes=1)
Construct a boolean constant from a C++ boolean value.
Halide::Internal::collect_print_args
HALIDE_NO_USER_CODE_INLINE void collect_print_args(std::vector< Expr > &args)
Definition IROperator.h:353
Halide::Internal::match_types_bitwise
void match_types_bitwise(Expr &a, Expr &b, const char *op_name)
Asserts that both expressions are integer types and are either both signed or both unsigned.
Halide::Internal::mod_imp< float >
float mod_imp< float >(float a, float b)
Definition IROperator.h:303
Halide::Internal::raise_to_integer_power
Expr raise_to_integer_power(Expr a, int64_t b)
Raise an expression to an integer power by repeatedly multiplying it by itself.
Halide::Internal::make_signed_integer_overflow
Expr make_signed_integer_overflow(Type type)
Construct a unique signed_integer_overflow Expr.
Halide::Internal::is_const
bool is_const(const Expr &e)
Is the expression either an IntImm, a FloatImm, a StringImm, or a Cast of the same,...
Halide::Internal::remove_likelies
Expr remove_likelies(const Expr &e)
Return an Expr that is identical to the input Expr, but with all calls to likely() and likely_if_inne...
Halide
This file defines the class FunctionDAG, which is our representation of a Halide pipeline,...
Definition AbstractGenerator.h:19
Halide::operator>=
auto operator>=(const Other &a, const GeneratorParam< T > &b) -> decltype(a >=(T) b)
Greater than or equal comparison between GeneratorParam<T> and any type that supports operator>= with...
Definition Generator.h:1104
Halide::log
Expr log(Expr x)
Return the logarithm of a floating-point expression.
Halide::operator>>
Expr operator>>(Expr x, Expr y)
Shift the bits of an integer value right.
Halide::ceil
Expr ceil(Expr x)
Return the least whole number greater than or equal to a floating-point expression.
Halide::widen_right_add
Expr widen_right_add(Expr a, Expr b)
Below is a collection of intrinsics for fixed-point programming.
Halide::rounding_shift_right
Expr rounding_shift_right(Expr a, Expr b)
Compute saturating_narrow(widening_add(a, (1 << max(b, 0)) / 2) >> b).
Halide::target_natural_vector_size
Expr target_natural_vector_size()
Definition IROperator.h:1747
Halide::memoize_tag
HALIDE_NO_USER_CODE_INLINE Expr memoize_tag(Expr result, Args &&...args)
Control the values used in the memoization cache key for memoize.
Definition IROperator.h:1404
Halide::fast_log
Expr fast_log(const Expr &x)
Fast approximate cleanly vectorizable log for Float(32).
Halide::count_leading_zeros
Expr count_leading_zeros(Expr x)
Count the number of leading zero bits in an expression.
Halide::reinterpret
Expr reinterpret(Type t, Expr e)
Reinterpret the bits of one value as another type.
Halide::saturating_add
Expr saturating_add(Expr a, Expr b)
Compute saturating_narrow(widen(a) + widen(b)).
Halide::operator==
auto operator==(const Other &a, const GeneratorParam< T > &b) -> decltype(a==(T) b)
Equality comparison between GeneratorParam<T> and any type that supports operator== with T.
Definition Generator.h:1130
Halide::fast_cos
Expr fast_cos(const Expr &x)
Halide::operator*=
Expr & operator*=(Expr &a, Expr b)
Modify the first expression to be the product of two expressions, without changing its type.
Halide::random_uint
Expr random_uint(Expr seed=Expr())
Return a random variable representing a uniformly distributed unsigned 32-bit integer.
Halide::fract
Expr fract(const Expr &x)
Return the fractional part of a floating-point expression.
Halide::halving_add
Expr halving_add(Expr a, Expr b)
Compute narrow((widen(a) + widen(b)) / 2).
Halide::operator-=
Expr & operator-=(Expr &a, Expr b)
Modify the first expression to be the difference of two expressions, without changing its type.
Halide::operator<
auto operator<(const Other &a, const GeneratorParam< T > &b) -> decltype(a<(T) b)
Less than comparison between GeneratorParam<T> and any type that supports operator< with T.
Definition Generator.h:1091
Halide::widening_shift_right
Expr widening_shift_right(Expr a, Expr b)
Compute widen(a) >> b.
Halide::type_of
Type type_of()
Construct the halide equivalent of a C type.
Definition Type.h:572
Halide::operator*
auto operator*(const Other &a, const GeneratorParam< T > &b) -> decltype(a *(T) b)
Multiplication between GeneratorParam<T> and any type that supports operator* with T.
Definition Generator.h:1039
Halide::strict_float
Expr strict_float(const Expr &e)
Makes a best effort attempt to preserve IEEE floating-point semantics in evaluating an expression.
Halide::trunc
Expr trunc(Expr x)
Return the integer part of a floating-point expression.
Halide::halving_sub
Expr halving_sub(Expr a, Expr b)
Compute narrow((widen(a) - widen(b)) / 2).
Halide::operator||
auto operator||(const Other &a, const GeneratorParam< T > &b) -> decltype(a||(T) b)
Logical or between between GeneratorParam<T> and any type that supports operator|| with T.
Definition Generator.h:1173
Halide::acosh
Expr acosh(Expr x)
Return the hyperbolic arccosine of a floating-point expression.
Halide::fast_inverse
Expr fast_inverse(Expr x)
Fast approximate inverse for Float(32).
Halide::target_arch_is
Expr target_arch_is(Target::Arch arch)
Return a boolean Expr for the corresponding field of the Target being used during lowering; they can ...
Halide::asin
Expr asin(Expr x)
Return the arcsine of a floating-point expression.
Halide::rounding_shift_left
Expr rounding_shift_left(Expr a, Expr b)
Compute saturating_narrow(widening_add(a, (1 >> min(b, 0)) / 2) << b).
Halide::operator-
auto operator-(const Other &a, const GeneratorParam< T > &b) -> decltype(a -(T) b)
Subtraction between GeneratorParam<T> and any type that supports operator- with T.
Definition Generator.h:1026
Halide::clamp
Expr clamp(Expr a, const Expr &min_val, const Expr &max_val)
Clamps an expression to lie within the given bounds.
Halide::hypot
Expr hypot(const Expr &x, const Expr &y)
Return the square root of the sum of the squares of two floating-point expressions.
Halide::popcount
Expr popcount(Expr x)
Count the number of set bits in an expression.
Halide::saturating_sub
Expr saturating_sub(Expr a, Expr b)
Compute saturating_narrow(widen(a) - widen(b)).
Halide::gather
Expr gather(const std::vector< Expr > &args)
Halide::print_when
Expr print_when(Expr condition, const std::vector< Expr > &values)
Create an Expr that prints whenever it is evaluated, provided that the condition is true.
Halide::widening_shift_left
Expr widening_shift_left(Expr a, Expr b)
Compute widen(a) << b.
Halide::pow
Expr pow(Expr x, Expr y)
Return one floating point expression raised to the power of another.
Halide::operator&
Expr operator&(Expr x, Expr y)
Return the bitwise and of two expressions (which need not have the same type).
Halide::undef
Expr undef()
Definition IROperator.h:1357
Halide::operator!
auto operator!(const GeneratorParam< T > &a) -> decltype(!(T) a)
Not operator for GeneratorParam.
Definition Generator.h:1245
Halide::lerp
Expr lerp(Expr zero_val, Expr one_val, Expr weight)
Linear interpolate between the two values according to a weight.
Halide::atan2
Expr atan2(Expr y, Expr x)
Return the angle of a floating-point gradient.
Halide::random_float
Expr random_float(Expr seed=Expr())
Return a random variable representing a uniformly distributed float in the half-open interval [0....
Halide::sin
Expr sin(Expr x)
Return the sine of a floating-point expression.
Halide::unsafe_promise_clamped
Expr unsafe_promise_clamped(const Expr &value, const Expr &min, const Expr &max)
Create an Expr that that promises another Expr is clamped but do not generate code to check the asser...
Halide::rounding_halving_add
Expr rounding_halving_add(Expr a, Expr b)
Compute narrow((widen(a) + widen(b) + 1) / 2).
Halide::extract_bits
Expr extract_bits(Type t, const Expr &e, const Expr &lsb)
Extract a contiguous subsequence of the bits of 'e', starting at the bit index given by 'lsb',...
Halide::concat_bits
Expr concat_bits(const std::vector< Expr > &e)
Given a number of Exprs of the same type, concatenate their bits producing a single Expr of the same ...
Halide::mux
Expr mux(const Expr &id, const std::initializer_list< Expr > &values)
Oftentimes we want to pack a list of expressions with the same type into a channel dimension,...
Halide::cosh
Expr cosh(Expr x)
Return the hyperbolic cosine of a floating-point expression.
Halide::operator<<
std::ostream & operator<<(std::ostream &stream, const Expr &)
Emit an expression on an output stream (such as std::cout) in human-readable form.
Halide::Int
Type Int(int bits, int lanes=1)
Constructing a signed integer type.
Definition Type.h:541
Halide::acos
Expr acos(Expr x)
Return the arccosine of a floating-point expression.
Halide::fast_exp
Expr fast_exp(const Expr &x)
Fast approximate cleanly vectorizable exp for Float(32).
Halide::widening_add
Expr widening_add(Expr a, Expr b)
Compute widen(a) + widen(b).
Halide::target_os_is
Expr target_os_is(Target::OS os)
Halide::cos
Expr cos(Expr x)
Return the cosine of a floating-point expression.
Halide::operator+
auto operator+(const Other &a, const GeneratorParam< T > &b) -> decltype(a+(T) b)
Addition between GeneratorParam<T> and any type that supports operator+ with T.
Definition Generator.h:1013
Halide::min
Expr min(const FuncRef &a, const FuncRef &b)
Explicit overloads of min and max for FuncRef.
Definition Func.h:603
Halide::exp
Expr exp(Expr x)
Return the exponential of a floating-point expression.
Halide::widen_right_mul
Expr widen_right_mul(Expr a, Expr b)
Compute a * widen(b).
Halide::absd
Expr absd(Expr a, Expr b)
Return the absolute difference between two values.
Halide::operator&&
auto operator&&(const Other &a, const GeneratorParam< T > &b) -> decltype(a &&(T) b)
Logical and between between GeneratorParam<T> and any type that supports operator&& with T.
Definition Generator.h:1156
Halide::fast_sin
Expr fast_sin(const Expr &x)
Fast vectorizable approximation to some trigonometric functions for Float(32).
Halide::fast_pow
Expr fast_pow(Expr x, Expr y)
Fast approximate cleanly vectorizable pow for Float(32).
Halide::operator%
auto operator%(const Other &a, const GeneratorParam< T > &b) -> decltype(a %(T) b)
Modulo between GeneratorParam<T> and any type that supports operator% with T.
Definition Generator.h:1065
Halide::NameMangling::C
@ C
No name mangling.
Definition Function.h:28
Halide::round
Expr round(Expr x)
Return the whole number closest to a floating-point expression.
Halide::select
Expr select(Expr condition, Expr true_value, Expr false_value)
Returns an expression similar to the ternary operator in C, except that it always evaluates all argum...
Halide::count_trailing_zeros
Expr count_trailing_zeros(Expr x)
Count the number of trailing zero bits in an expression.
Halide::scatter
Expr scatter(const std::vector< Expr > &args)
Scatter and gather are used for update definition which must store multiple values to distinct locati...
Halide::operator<=
auto operator<=(const Other &a, const GeneratorParam< T > &b) -> decltype(a<=(T) b)
Less than or equal comparison between GeneratorParam<T> and any type that supports operator<= with T.
Definition Generator.h:1117
Halide::rounding_mul_shift_right
Expr rounding_mul_shift_right(Expr a, Expr b, Expr q)
Compute saturating_narrow(rounding_shift_right(widening_mul(a, b), q)).
Halide::random_int
Expr random_int(Expr seed=Expr())
Return a random variable representing a uniformly distributed 32-bit integer.
Halide::mod_round_to_zero
Expr mod_round_to_zero(Expr x, Expr y)
Compute the remainder of dividing two integers, when division is rounding toward zero.
Halide::operator/=
Expr & operator/=(Expr &a, Expr b)
Modify the first expression to be the ratio of two expressions, without changing its type.
Halide::widening_mul
Expr widening_mul(Expr a, Expr b)
Compute widen(a) * widen(b).
Halide::operator>
auto operator>(const Other &a, const GeneratorParam< T > &b) -> decltype(a >(T) b)
Greater than comparison between GeneratorParam<T> and any type that supports operator> with T.
Definition Generator.h:1078
Halide::is_nan
Expr is_nan(Expr x)
Returns true if the argument is a Not a Number (NaN).
Halide::asinh
Expr asinh(Expr x)
Return the hyperbolic arcsinhe of a floating-point expression.
Halide::sqrt
Expr sqrt(Expr x)
Return the square root of a floating-point expression.
Halide::sinh
Expr sinh(Expr x)
Return the hyperbolic sine of a floating-point expression.
Halide::atan
Expr atan(Expr x)
Return the arctangent of a floating-point expression.
Halide::operator|
Expr operator|(Expr x, Expr y)
Return the bitwise or of two expressions (which need not have the same type).
Halide::operator!=
auto operator!=(const Other &a, const GeneratorParam< T > &b) -> decltype(a !=(T) b)
Inequality comparison between between GeneratorParam<T> and any type that supports operator!...
Definition Generator.h:1143
Halide::target_bits
Expr target_bits()
Return the bit width of the Target used during lowering; this can be useful in writing library code w...
Halide::cast
Internal::ConstantInterval cast(Type t, const Internal::ConstantInterval &a)
Cast operators for ConstantIntervals.
Halide::require
Expr require(Expr condition, const std::vector< Expr > &values)
Create an Expr that that guarantees a precondition.
Halide::is_inf
Expr is_inf(Expr x)
Returns true if the argument is Inf or -Inf.
Halide::is_finite
Expr is_finite(Expr x)
Returns true if the argument is a finite value (ie, neither NaN nor Inf).
Halide::tanh
Expr tanh(Expr x)
Return the hyperbolic tangent of a floating-point expression.
Halide::likely_if_innermost
Expr likely_if_innermost(Expr e)
Equivalent to likely, but only triggers a loop partitioning if found in an innermost loop.
Halide::atanh
Expr atanh(Expr x)
Return the hyperbolic arctangent of a floating-point expression.
Halide::tan
Expr tan(Expr x)
Return the tangent of a floating-point expression.
Halide::saturating_cast
Internal::ConstantInterval saturating_cast(Type t, const Internal::ConstantInterval &a)
Halide::fast_inverse_sqrt
Expr fast_inverse_sqrt(Expr x)
Fast approximate inverse square root for Float(32).
Halide::print
Expr print(const std::vector< Expr > &values)
Create an Expr that prints out its value whenever it is evaluated.
Halide::mul_shift_right
Expr mul_shift_right(Expr a, Expr b, Expr q)
Compute saturating_narrow(shift_right(widening_mul(a, b), q)).
Halide::operator/
auto operator/(const Other &a, const GeneratorParam< T > &b) -> decltype(a/(T) b)
Division between GeneratorParam<T> and any type that supports operator/ with T.
Definition Generator.h:1052
Halide::operator+=
Expr & operator+=(Expr &a, Expr b)
Modify the first expression to be the sum of two expressions, without changing its type.
Halide::abs
Expr abs(Expr a)
Returns the absolute value of a signed integer or floating-point expression.
Halide::widen_right_sub
Expr widen_right_sub(Expr a, Expr b)
Compute a - widen(b).
Halide::max
Expr max(const FuncRef &a, const FuncRef &b)
Definition Func.h:606
Halide::floor
Expr floor(Expr x)
Return the greatest whole number less than or equal to a floating-point expression.
Halide::div_round_to_zero
Expr div_round_to_zero(Expr x, Expr y)
Divide two integers, rounding towards zero.
Halide::widening_sub
Expr widening_sub(Expr a, Expr b)
Compute widen(a) - widen(b).
Halide::likely
Expr likely(Expr e)
Expressions tagged with this intrinsic are considered to be part of the steady state of some loop wit...
Halide::operator~
Expr operator~(Expr x)
Return the bitwise not of an expression.
Halide::erf
Expr erf(const Expr &x)
Evaluate the error function erf.
Halide::target_has_feature
Expr target_has_feature(Target::Feature feat)
Halide::operator^
Expr operator^(Expr x, Expr y)
Return the bitwise xor of two expressions (which need not have the same type).
uint64_t
unsigned __INT64_TYPE__ uint64_t
Definition runtime_internal.h:23
int64_t
signed __INT64_TYPE__ int64_t
Definition runtime_internal.h:22
int32_t
signed __INT32_TYPE__ int32_t
Definition runtime_internal.h:24
uint8_t
unsigned __INT8_TYPE__ uint8_t
Definition runtime_internal.h:29
uint16_t
unsigned __INT16_TYPE__ uint16_t
Definition runtime_internal.h:27
uint32_t
unsigned __INT32_TYPE__ uint32_t
Definition runtime_internal.h:25
int16_t
signed __INT16_TYPE__ int16_t
Definition runtime_internal.h:26
int8_t
signed __INT8_TYPE__ int8_t
Definition runtime_internal.h:28
Halide::Expr
A fragment of Halide syntax.
Definition Expr.h:258
Halide::Internal::BufferBuilder
A builder to help create Exprs representing halide_buffer_t structs (e.g.
Definition IROperator.h:228
Halide::Internal::BufferBuilder::device
Expr device
Definition IROperator.h:230
Halide::Internal::BufferBuilder::host_dirty
Expr host_dirty
Definition IROperator.h:234
Halide::Internal::BufferBuilder::dimensions
int dimensions
Definition IROperator.h:232
Halide::Internal::BufferBuilder::type
Type type
Definition IROperator.h:231
Halide::Internal::BufferBuilder::host
Expr host
Definition IROperator.h:230
Halide::Internal::BufferBuilder::strides
std::vector< Expr > strides
Definition IROperator.h:233
Halide::Internal::BufferBuilder::shape_memory
Expr shape_memory
Definition IROperator.h:229
Halide::Internal::BufferBuilder::build
Expr build() const
Halide::Internal::BufferBuilder::device_interface
Expr device_interface
Definition IROperator.h:230
Halide::Internal::BufferBuilder::device_dirty
Expr device_dirty
Definition IROperator.h:234
Halide::Internal::BufferBuilder::extents
std::vector< Expr > extents
Definition IROperator.h:233
Halide::Internal::BufferBuilder::mins
std::vector< Expr > mins
Definition IROperator.h:233
Halide::Internal::BufferBuilder::buffer_memory
Expr buffer_memory
Definition IROperator.h:229
Halide::Internal::Stmt
A reference-counted handle to a statement node.
Definition Expr.h:427
Halide::Internal::all_are_convertible
Definition Util.h:256
Halide::Internal::all_are_printable_args
Definition IROperator.h:350
Halide::Internal::cond
Definition Generator.h:380
Halide::Internal::is_printable_arg
Definition IROperator.h:344
Halide::Internal::is_printable_arg::value
static constexpr bool value
Definition IROperator.h:345
Halide::Internal::meta_and
Definition Util.h:244
Halide::Target::Feature
Feature
Optional features a target can have.
Definition Target.h:84
Halide::Target::Arch
Arch
The architecture used by the target.
Definition Target.h:39
Halide::Target::OS
OS
The operating system used by the target.
Definition Target.h:23
Halide::Type
Types in the halide type system.
Definition Type.h:283
Halide::Type::is_int
HALIDE_ALWAYS_INLINE bool is_int() const
Is this type a signed integer type?
Definition Type.h:435
Halide::Type::is_float
HALIDE_ALWAYS_INLINE bool is_float() const
Is this type a floating point type (float or double).
Definition Type.h:423
Halide::float16_t
Class that provides a type that implements half precision floating point (IEEE754 2008 binary16) in s...
Definition Float16.h:17