Halide 18.0.0
Halide compiler and libraries
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IROperator.h
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1#ifndef HALIDE_IR_OPERATOR_H
2#define HALIDE_IR_OPERATOR_H
3
4/** \file
5 *
6 * Defines various operator overloads and utility functions that make
7 * it more pleasant to work with Halide expressions.
8 */
9
10#include <cmath>
11#include <map>
12
13#include "Expr.h"
14#include "Tuple.h"
15
16namespace Halide {
17
18namespace Internal {
19/** Is the expression either an IntImm, a FloatImm, a StringImm, or a
20 * Cast of the same, or a Ramp or Broadcast of the same. Doesn't do
21 * any constant folding. */
22bool is_const(const Expr &e);
23
24/** Is the expression an IntImm, FloatImm of a particular value, or a
25 * Cast, or Broadcast of the same. */
26bool is_const(const Expr &e, int64_t v);
27
28/** If an expression is an IntImm or a Broadcast of an IntImm, return
29 * a pointer to its value. Otherwise returns nullptr. */
30const int64_t *as_const_int(const Expr &e);
31
32/** If an expression is a UIntImm or a Broadcast of a UIntImm, return
33 * a pointer to its value. Otherwise returns nullptr. */
34const uint64_t *as_const_uint(const Expr &e);
35
36/** If an expression is a FloatImm or a Broadcast of a FloatImm,
37 * return a pointer to its value. Otherwise returns nullptr. */
38const double *as_const_float(const Expr &e);
39
40/** Is the expression a constant integer power of two. Also returns
41 * log base two of the expression if it is. Only returns true for
42 * integer types. */
43bool is_const_power_of_two_integer(const Expr &e, int *bits);
44
45/** Is the expression a const (as defined by is_const), and also
46 * strictly greater than zero (in all lanes, if a vector expression) */
47bool is_positive_const(const Expr &e);
48
49/** Is the expression a const (as defined by is_const), and also
50 * strictly less than zero (in all lanes, if a vector expression) */
51bool is_negative_const(const Expr &e);
52
53/** Is the expression an undef */
54bool is_undef(const Expr &e);
55
56/** Is the expression a const (as defined by is_const), and also equal
57 * to zero (in all lanes, if a vector expression) */
58bool is_const_zero(const Expr &e);
59
60/** Is the expression a const (as defined by is_const), and also equal
61 * to one (in all lanes, if a vector expression) */
62bool is_const_one(const Expr &e);
63
64/** Is the statement a no-op (which we represent as either an
65 * undefined Stmt, or as an Evaluate node of a constant) */
66bool is_no_op(const Stmt &s);
67
68/** Does the expression
69 * 1) Take on the same value no matter where it appears in a Stmt, and
70 * 2) Evaluating it has no side-effects
71 */
72bool is_pure(const Expr &e);
73
74/** Construct an immediate of the given type from any numeric C++ type. */
75// @{
78Expr make_const(Type t, double val);
79inline Expr make_const(Type t, int32_t val) {
80 return make_const(t, (int64_t)val);
81}
82inline Expr make_const(Type t, uint32_t val) {
83 return make_const(t, (uint64_t)val);
84}
85inline Expr make_const(Type t, int16_t val) {
86 return make_const(t, (int64_t)val);
87}
88inline Expr make_const(Type t, uint16_t val) {
89 return make_const(t, (uint64_t)val);
90}
91inline Expr make_const(Type t, int8_t val) {
92 return make_const(t, (int64_t)val);
93}
94inline Expr make_const(Type t, uint8_t val) {
95 return make_const(t, (uint64_t)val);
96}
97inline Expr make_const(Type t, bool val) {
98 return make_const(t, (uint64_t)val);
99}
100inline Expr make_const(Type t, float val) {
101 return make_const(t, (double)val);
102}
104 return make_const(t, (double)val);
105}
106// @}
107
108/** Construct a unique signed_integer_overflow Expr */
110
111/** Check if an expression is a signed_integer_overflow */
113
114/** Check if a constant value can be correctly represented as the given type. */
116
117/** Construct a boolean constant from a C++ boolean value.
118 * May also be a vector if width is given.
119 * It is not possible to coerce a C++ boolean to Expr because
120 * if we provide such a path then char objects can ambiguously
121 * be converted to Halide Expr or to std::string. The problem
122 * is that C++ does not have a real bool type - it is in fact
123 * close enough to char that C++ does not know how to distinguish them.
124 * make_bool is the explicit coercion. */
125Expr make_bool(bool val, int lanes = 1);
126
127/** Construct the representation of zero in the given type */
129
130/** Construct the representation of one in the given type */
132
133/** Construct the representation of two in the given type */
135
136/** Construct the constant boolean true. May also be a vector of
137 * trues, if a lanes argument is given. */
138Expr const_true(int lanes = 1);
139
140/** Construct the constant boolean false. May also be a vector of
141 * falses, if a lanes argument is given. */
142Expr const_false(int lanes = 1);
143
144/** Attempt to cast an expression to a smaller type while provably not losing
145 * information. If it can't be done, return an undefined Expr.
146 *
147 * Optionally accepts a map that gives the constant bounds of exprs already
148 * analyzed to avoid redoing work across many calls to lossless_cast. It is not
149 * safe to use this optional map in contexts where the same Expr object may
150 * take on a different value. For example:
151 * (let x = 4 in some_expr_object) + (let x = 5 in the_same_expr_object)).
152 * It is safe to use it after uniquify_variable_names has been run. */
153Expr lossless_cast(Type t, Expr e, std::map<Expr, ConstantInterval, ExprCompare> *cache = nullptr);
154
155/** Attempt to negate x without introducing new IR and without overflow.
156 * If it can't be done, return an undefined Expr. */
158
159/** Coerce the two expressions to have the same type, using C-style
160 * casting rules. For the purposes of casting, a boolean type is
161 * UInt(1). We use the following procedure:
162 *
163 * If the types already match, do nothing.
164 *
165 * Then, if one type is a vector and the other is a scalar, the scalar
166 * is broadcast to match the vector width, and we continue.
167 *
168 * Then, if one type is floating-point and the other is not, the
169 * non-float is cast to the floating-point type, and we're done.
170 *
171 * Then, if both types are unsigned ints, the one with fewer bits is
172 * cast to match the one with more bits and we're done.
173 *
174 * Then, if both types are signed ints, the one with fewer bits is
175 * cast to match the one with more bits and we're done.
176 *
177 * Finally, if one type is an unsigned int and the other type is a signed
178 * int, both are cast to a signed int with the greater of the two
179 * bit-widths. For example, matching an Int(8) with a UInt(16) results
180 * in an Int(16).
181 *
182 */
183void match_types(Expr &a, Expr &b);
184
185/** Asserts that both expressions are integer types and are either
186 * both signed or both unsigned. If one argument is scalar and the
187 * other a vector, the scalar is broadcasted to have the same number
188 * of lanes as the vector. If one expression is of narrower type than
189 * the other, it is widened to the bit width of the wider. */
190void match_types_bitwise(Expr &a, Expr &b, const char *op_name);
191
192/** Halide's vectorizable transcendentals. */
193// @{
197// @}
198
199/** Raise an expression to an integer power by repeatedly multiplying
200 * it by itself. */
202
203/** Split a boolean condition into vector of ANDs. If 'cond' is undefined,
204 * return an empty vector. */
205void split_into_ands(const Expr &cond, std::vector<Expr> &result);
206
207/** A builder to help create Exprs representing halide_buffer_t
208 * structs (e.g. foo.buffer) via calls to halide_buffer_init. Fill out
209 * the fields and then call build. The resulting Expr will be a call
210 * to halide_buffer_init with the struct members as arguments. If the
211 * buffer_memory field is undefined, it uses a call to alloca to make
212 * some stack memory for the buffer. If the shape_memory field is
213 * undefined, it similarly uses stack memory for the shape. If the
214 * shape_memory field is null, it uses the dim field already in the
215 * buffer. Other unitialized fields will take on a value of zero in
216 * the constructed buffer. */
226
227/** If e is a ramp expression with stride, default 1, return the base,
228 * otherwise undefined. */
229Expr strided_ramp_base(const Expr &e, int stride = 1);
230
231/** Implementations of division and mod that are specific to Halide.
232 * Use these implementations; do not use native C division or mod to
233 * simplify Halide expressions. Halide division and modulo satisify
234 * the Euclidean definition of division for integers a and b:
235 *
236 /code
237 when b != 0, (a/b)*b + a%b = a
238 0 <= a%b < |b|
239 /endcode
240 *
241 * Additionally, mod by zero returns zero, and div by zero returns
242 * zero. This makes mod and div total functions.
243 */
244// @{
245template<typename T>
246inline T mod_imp(T a, T b) {
247 Type t = type_of<T>();
248 if (!t.is_float() && b == 0) {
249 return 0;
250 } else if (t.is_int()) {
251 int64_t ia = a;
252 int64_t ib = b;
253 int64_t a_neg = ia >> 63;
254 int64_t b_neg = ib >> 63;
255 int64_t b_zero = (ib == 0) ? -1 : 0;
256 ia -= a_neg;
257 int64_t r = ia % (ib | b_zero);
258 r += (a_neg & ((ib ^ b_neg) + ~b_neg));
259 r &= ~b_zero;
260 return r;
261 } else {
262 return a % b;
263 }
264}
265
266template<typename T>
267inline T div_imp(T a, T b) {
268 Type t = type_of<T>();
269 if (!t.is_float() && b == 0) {
270 return (T)0;
271 } else if (t.is_int()) {
272 // Do it as 64-bit
273 int64_t ia = a;
274 int64_t ib = b;
275 int64_t a_neg = ia >> 63;
276 int64_t b_neg = ib >> 63;
277 int64_t b_zero = (ib == 0) ? -1 : 0;
278 ib -= b_zero;
279 ia -= a_neg;
280 int64_t q = ia / ib;
281 q += a_neg & (~b_neg - b_neg);
282 q &= ~b_zero;
283 return (T)q;
284 } else {
285 return a / b;
286 }
287}
288// @}
289
290// Special cases for float, double.
291template<>
292inline float mod_imp<float>(float a, float b) {
293 float f = a - b * (floorf(a / b));
294 // The remainder has the same sign as b.
295 return f;
296}
297template<>
298inline double mod_imp<double>(double a, double b) {
299 double f = a - b * (std::floor(a / b));
300 return f;
301}
302
303template<>
304inline float div_imp<float>(float a, float b) {
305 return a / b;
306}
307template<>
308inline double div_imp<double>(double a, double b) {
309 return a / b;
310}
311
312/** Return an Expr that is identical to the input Expr, but with
313 * all calls to likely() and likely_if_innermost() removed. */
315
316/** Return a Stmt that is identical to the input Stmt, but with
317 * all calls to likely() and likely_if_innermost() removed. */
319
320/** Return an Expr that is identical to the input Expr, but with
321 * all calls to promise_clamped() and unsafe_promise_clamped() removed. */
323
324/** Return a Stmt that is identical to the input Stmt, but with
325 * all calls to promise_clamped() and unsafe_promise_clamped() removed. */
327
328/** If the expression is a tag helper call, remove it and return
329 * the tagged expression. If not, returns the expression. */
331
332template<typename T>
334 static constexpr bool value = std::is_convertible<T, const char *>::value ||
335 std::is_convertible<T, Halide::Expr>::value;
336};
337
338template<typename... Args>
339struct all_are_printable_args : meta_and<is_printable_arg<Args>...> {};
340
341// Secondary args to print can be Exprs or const char *
342inline HALIDE_NO_USER_CODE_INLINE void collect_print_args(std::vector<Expr> &args) {
343}
344
345template<typename... Args>
346inline HALIDE_NO_USER_CODE_INLINE void collect_print_args(std::vector<Expr> &args, const char *arg, Args &&...more_args) {
347 args.emplace_back(std::string(arg));
348 collect_print_args(args, std::forward<Args>(more_args)...);
349}
350
351template<typename... Args>
352inline HALIDE_NO_USER_CODE_INLINE void collect_print_args(std::vector<Expr> &args, Expr arg, Args &&...more_args) {
353 args.push_back(std::move(arg));
354 collect_print_args(args, std::forward<Args>(more_args)...);
355}
356
357Expr requirement_failed_error(Expr condition, const std::vector<Expr> &args);
358
359Expr memoize_tag_helper(Expr result, const std::vector<Expr> &cache_key_values);
360
361/** Reset the counters used for random-number seeds in random_float/int/uint.
362 * (Note that the counters are incremented for each call, even if a seed is passed in.)
363 * This is used for multitarget compilation to ensure that each subtarget gets
364 * the same sequence of random numbers. */
366
367} // namespace Internal
368
369/** Cast an expression to the halide type corresponding to the C++ type T. */
370template<typename T>
371inline Expr cast(Expr a) {
372 return cast(type_of<T>(), std::move(a));
373}
374
375/** Cast an expression to a new type. */
377
378/** Return the sum of two expressions, doing any necessary type
379 * coercion using \ref Internal::match_types */
381
382/** Add an expression and a constant integer. Coerces the type of the
383 * integer to match the type of the expression. Errors if the integer
384 * cannot be represented in the type of the expression. */
385// @{
387
388/** Add a constant integer and an expression. Coerces the type of the
389 * integer to match the type of the expression. Errors if the integer
390 * cannot be represented in the type of the expression. */
392
393/** Modify the first expression to be the sum of two expressions,
394 * without changing its type. This casts the second argument to match
395 * the type of the first. */
397
398/** Return the difference of two expressions, doing any necessary type
399 * coercion using \ref Internal::match_types */
401
402/** Subtracts a constant integer from an expression. Coerces the type of the
403 * integer to match the type of the expression. Errors if the integer
404 * cannot be represented in the type of the expression. */
406
407/** Subtracts an expression from a constant integer. Coerces the type
408 * of the integer to match the type of the expression. Errors if the
409 * integer cannot be represented in the type of the expression. */
411
412/** Return the negative of the argument. Does no type casting, so more
413 * formally: return that number which when added to the original,
414 * yields zero of the same type. For unsigned integers the negative is
415 * still an unsigned integer. E.g. in UInt(8), the negative of 56 is
416 * 200, because 56 + 200 == 0 */
418
419/** Modify the first expression to be the difference of two expressions,
420 * without changing its type. This casts the second argument to match
421 * the type of the first. */
423
424/** Return the product of two expressions, doing any necessary type
425 * coercion using \ref Internal::match_types */
427
428/** Multiply an expression and a constant integer. Coerces the type of the
429 * integer to match the type of the expression. Errors if the integer
430 * cannot be represented in the type of the expression. */
432
433/** Multiply a constant integer and an expression. Coerces the type of
434 * the integer to match the type of the expression. Errors if the
435 * integer cannot be represented in the type of the expression. */
437
438/** Modify the first expression to be the product of two expressions,
439 * without changing its type. This casts the second argument to match
440 * the type of the first. */
442
443/** Return the ratio of two expressions, doing any necessary type
444 * coercion using \ref Internal::match_types. Note that integer
445 * division in Halide is not the same as integer division in C-like
446 * languages in two ways.
447 *
448 * First, signed integer division in Halide rounds according to the
449 * sign of the denominator. This means towards minus infinity for
450 * positive denominators, and towards positive infinity for negative
451 * denominators. This is unlike C, which rounds towards zero. This
452 * decision ensures that upsampling expressions like f(x/2, y/2) don't
453 * have funny discontinuities when x and y cross zero.
454 *
455 * Second, division by zero returns zero instead of faulting. For
456 * types where overflow is defined behavior, division of the largest
457 * negative signed integer by -1 returns the larged negative signed
458 * integer for the type (i.e. it wraps). This ensures that a division
459 * operation can never have a side-effect, which is helpful in Halide
460 * because scheduling directives can expand the domain of computation
461 * of a Func, potentially introducing new zero-division.
462 */
464
465/** Modify the first expression to be the ratio of two expressions,
466 * without changing its type. This casts the second argument to match
467 * the type of the first. Note that signed integer division in Halide
468 * rounds towards minus infinity, unlike C, which rounds towards
469 * zero. */
471
472/** Divides an expression by a constant integer. Coerces the type
473 * of the integer to match the type of the expression. Errors if the
474 * integer cannot be represented in the type of the expression. */
476
477/** Divides a constant integer by an expression. Coerces the type
478 * of the integer to match the type of the expression. Errors if the
479 * integer cannot be represented in the type of the expression. */
481
482/** Return the first argument reduced modulo the second, doing any
483 * necessary type coercion using \ref Internal::match_types. There are
484 * two key differences between C-like languages and Halide for the
485 * modulo operation, which complement the way division works.
486 *
487 * First, the result is never negative, so x % 2 is always zero or
488 * one, unlike in C-like languages. x % -2 is equivalent, and is also
489 * always zero or one. Second, mod by zero evaluates to zero (unlike
490 * in C, where it faults). This makes modulo, like division, a
491 * side-effect-free operation. */
493
494/** Mods an expression by a constant integer. Coerces the type
495 * of the integer to match the type of the expression. Errors if the
496 * integer cannot be represented in the type of the expression. */
498
499/** Mods a constant integer by an expression. Coerces the type
500 * of the integer to match the type of the expression. Errors if the
501 * integer cannot be represented in the type of the expression. */
503
504/** Return a boolean expression that tests whether the first argument
505 * is greater than the second, after doing any necessary type coercion
506 * using \ref Internal::match_types */
508
509/** Return a boolean expression that tests whether an expression is
510 * greater than a constant integer. Coerces the integer to the type of
511 * the expression. Errors if the integer is not representable in that
512 * type. */
514
515/** Return a boolean expression that tests whether a constant integer is
516 * greater than an expression. Coerces the integer to the type of
517 * the expression. Errors if the integer is not representable in that
518 * type. */
520
521/** Return a boolean expression that tests whether the first argument
522 * is less than the second, after doing any necessary type coercion
523 * using \ref Internal::match_types */
525
526/** Return a boolean expression that tests whether an expression is
527 * less than a constant integer. Coerces the integer to the type of
528 * the expression. Errors if the integer is not representable in that
529 * type. */
531
532/** Return a boolean expression that tests whether a constant integer is
533 * less than an expression. Coerces the integer to the type of
534 * the expression. Errors if the integer is not representable in that
535 * type. */
537
538/** Return a boolean expression that tests whether the first argument
539 * is less than or equal to the second, after doing any necessary type
540 * coercion using \ref Internal::match_types */
542
543/** Return a boolean expression that tests whether an expression is
544 * less than or equal to a constant integer. Coerces the integer to
545 * the type of the expression. Errors if the integer is not
546 * representable in that type. */
548
549/** Return a boolean expression that tests whether a constant integer
550 * is less than or equal to an expression. Coerces the integer to the
551 * type of the expression. Errors if the integer is not representable
552 * in that type. */
554
555/** Return a boolean expression that tests whether the first argument
556 * is greater than or equal to the second, after doing any necessary
557 * type coercion using \ref Internal::match_types */
559
560/** Return a boolean expression that tests whether an expression is
561 * greater than or equal to a constant integer. Coerces the integer to
562 * the type of the expression. Errors if the integer is not
563 * representable in that type. */
564Expr operator>=(const Expr &a, int b);
565
566/** Return a boolean expression that tests whether a constant integer
567 * is greater than or equal to an expression. Coerces the integer to the
568 * type of the expression. Errors if the integer is not representable
569 * in that type. */
570Expr operator>=(int a, const Expr &b);
571
572/** Return a boolean expression that tests whether the first argument
573 * is equal to the second, after doing any necessary type coercion
574 * using \ref Internal::match_types */
576
577/** Return a boolean expression that tests whether an expression is
578 * equal to a constant integer. Coerces the integer to the type of the
579 * expression. Errors if the integer is not representable in that
580 * type. */
582
583/** Return a boolean expression that tests whether a constant integer
584 * is equal to an expression. Coerces the integer to the type of the
585 * expression. Errors if the integer is not representable in that
586 * type. */
588
589/** Return a boolean expression that tests whether the first argument
590 * is not equal to the second, after doing any necessary type coercion
591 * using \ref Internal::match_types */
593
594/** Return a boolean expression that tests whether an expression is
595 * not equal to a constant integer. Coerces the integer to the type of
596 * the expression. Errors if the integer is not representable in that
597 * type. */
599
600/** Return a boolean expression that tests whether a constant integer
601 * is not equal to an expression. Coerces the integer to the type of
602 * the expression. Errors if the integer is not representable in that
603 * type. */
605
606/** Returns the logical and of the two arguments */
608
609/** Logical and of an Expr and a bool. Either returns the Expr or an
610 * Expr representing false, depending on the bool. */
611// @{
614// @}
615
616/** Returns the logical or of the two arguments */
618
619/** Logical or of an Expr and a bool. Either returns the Expr or an
620 * Expr representing true, depending on the bool. */
621// @{
624// @}
625
626/** Returns the logical not the argument */
628
629/** Returns an expression representing the greater of the two
630 * arguments, after doing any necessary type coercion using
631 * \ref Internal::match_types. Vectorizes cleanly on most platforms
632 * (with the exception of integer types on x86 without SSE4). */
633Expr max(Expr a, Expr b);
634
635/** Returns an expression representing the greater of an expression
636 * and a constant integer. The integer is coerced to the type of the
637 * expression. Errors if the integer is not representable as that
638 * type. Vectorizes cleanly on most platforms (with the exception of
639 * integer types on x86 without SSE4). */
640Expr max(Expr a, int b);
641
642/** Returns an expression representing the greater of a constant
643 * integer and an expression. The integer is coerced to the type of
644 * the expression. Errors if the integer is not representable as that
645 * type. Vectorizes cleanly on most platforms (with the exception of
646 * integer types on x86 without SSE4). */
647Expr max(int a, Expr b);
648
649inline Expr max(float a, Expr b) {
650 return max(Expr(a), std::move(b));
651}
652inline Expr max(Expr a, float b) {
653 return max(std::move(a), Expr(b));
654}
655
656/** Returns an expression representing the greater of an expressions
657 * vector, after doing any necessary type coersion using
658 * \ref Internal::match_types. Vectorizes cleanly on most platforms
659 * (with the exception of integer types on x86 without SSE4).
660 * The expressions are folded from right ie. max(.., max(.., ..)).
661 * The arguments can be any mix of types but must all be convertible to Expr. */
662template<typename A, typename B, typename C, typename... Rest,
663 typename std::enable_if<Halide::Internal::all_are_convertible<Expr, Rest...>::value>::type * = nullptr>
664inline Expr max(A &&a, B &&b, C &&c, Rest &&...rest) {
665 return max(std::forward<A>(a), max(std::forward<B>(b), std::forward<C>(c), std::forward<Rest>(rest)...));
666}
667
668Expr min(Expr a, Expr b);
669
670/** Returns an expression representing the lesser of an expression
671 * and a constant integer. The integer is coerced to the type of the
672 * expression. Errors if the integer is not representable as that
673 * type. Vectorizes cleanly on most platforms (with the exception of
674 * integer types on x86 without SSE4). */
675Expr min(Expr a, int b);
676
677/** Returns an expression representing the lesser of a constant
678 * integer and an expression. The integer is coerced to the type of
679 * the expression. Errors if the integer is not representable as that
680 * type. Vectorizes cleanly on most platforms (with the exception of
681 * integer types on x86 without SSE4). */
682Expr min(int a, Expr b);
683
684inline Expr min(float a, Expr b) {
685 return min(Expr(a), std::move(b));
686}
687inline Expr min(Expr a, float b) {
688 return min(std::move(a), Expr(b));
689}
690
691/** Returns an expression representing the lesser of an expressions
692 * vector, after doing any necessary type coersion using
693 * \ref Internal::match_types. Vectorizes cleanly on most platforms
694 * (with the exception of integer types on x86 without SSE4).
695 * The expressions are folded from right ie. min(.., min(.., ..)).
696 * The arguments can be any mix of types but must all be convertible to Expr. */
697template<typename A, typename B, typename C, typename... Rest,
698 typename std::enable_if<Halide::Internal::all_are_convertible<Expr, Rest...>::value>::type * = nullptr>
699inline Expr min(A &&a, B &&b, C &&c, Rest &&...rest) {
700 return min(std::forward<A>(a), min(std::forward<B>(b), std::forward<C>(c), std::forward<Rest>(rest)...));
701}
702
703/** Operators on floats treats those floats as Exprs. Making these
704 * explicit prevents implicit float->int casts that might otherwise
705 * occur. */
706// @{
707inline Expr operator+(Expr a, float b) {
708 return std::move(a) + Expr(b);
709}
710inline Expr operator+(float a, Expr b) {
711 return Expr(a) + std::move(b);
712}
713inline Expr operator-(Expr a, float b) {
714 return std::move(a) - Expr(b);
715}
716inline Expr operator-(float a, Expr b) {
717 return Expr(a) - std::move(b);
718}
719inline Expr operator*(Expr a, float b) {
720 return std::move(a) * Expr(b);
721}
722inline Expr operator*(float a, Expr b) {
723 return Expr(a) * std::move(b);
724}
725inline Expr operator/(Expr a, float b) {
726 return std::move(a) / Expr(b);
727}
728inline Expr operator/(float a, Expr b) {
729 return Expr(a) / std::move(b);
730}
731inline Expr operator%(Expr a, float b) {
732 return std::move(a) % Expr(b);
733}
734inline Expr operator%(float a, Expr b) {
735 return Expr(a) % std::move(b);
736}
737inline Expr operator>(Expr a, float b) {
738 return std::move(a) > Expr(b);
739}
740inline Expr operator>(float a, Expr b) {
741 return Expr(a) > std::move(b);
742}
743inline Expr operator<(Expr a, float b) {
744 return std::move(a) < Expr(b);
745}
746inline Expr operator<(float a, Expr b) {
747 return Expr(a) < std::move(b);
748}
749inline Expr operator>=(Expr a, float b) {
750 return std::move(a) >= Expr(b);
751}
752inline Expr operator>=(float a, Expr b) {
753 return Expr(a) >= std::move(b);
754}
755inline Expr operator<=(Expr a, float b) {
756 return std::move(a) <= Expr(b);
757}
758inline Expr operator<=(float a, Expr b) {
759 return Expr(a) <= std::move(b);
760}
761inline Expr operator==(Expr a, float b) {
762 return std::move(a) == Expr(b);
763}
764inline Expr operator==(float a, Expr b) {
765 return Expr(a) == std::move(b);
766}
767inline Expr operator!=(Expr a, float b) {
768 return std::move(a) != Expr(b);
769}
770inline Expr operator!=(float a, Expr b) {
771 return Expr(a) != std::move(b);
772}
773// @}
774
775/** Clamps an expression to lie within the given bounds. The bounds
776 * are type-cast to match the expression. Vectorizes as well as min/max. */
777Expr clamp(Expr a, const Expr &min_val, const Expr &max_val);
778
779/** Returns the absolute value of a signed integer or floating-point
780 * expression. Vectorizes cleanly. Unlike in C, abs of a signed
781 * integer returns an unsigned integer of the same bit width. This
782 * means that abs of the most negative integer doesn't overflow. */
784
785/** Return the absolute difference between two values. Vectorizes
786 * cleanly. Returns an unsigned value of the same bit width. There are
787 * various ways to write this yourself, but they contain numerous
788 * gotchas and don't always compile to good code, so use this
789 * instead. */
791
792/** Returns an expression similar to the ternary operator in C, except
793 * that it always evaluates all arguments. If the first argument is
794 * true, then return the second, else return the third. Typically
795 * vectorizes cleanly, but benefits from SSE41 or newer on x86. */
796Expr select(Expr condition, Expr true_value, Expr false_value);
797
798/** A multi-way variant of select similar to a switch statement in C,
799 * which can accept multiple conditions and values in pairs. Evaluates
800 * to the first value for which the condition is true. Returns the
801 * final value if all conditions are false. */
802template<typename... Args,
803 typename std::enable_if<Halide::Internal::all_are_convertible<Expr, Args...>::value>::type * = nullptr>
804inline Expr select(Expr c0, Expr v0, Expr c1, Expr v1, Args &&...args) {
805 return select(std::move(c0), std::move(v0), select(std::move(c1), std::move(v1), std::forward<Args>(args)...));
806}
807
808/** Equivalent of ternary select(), but taking/returning tuples. If the condition is
809 * a Tuple, it must match the size of the true and false Tuples. */
810// @{
811Tuple select(const Tuple &condition, const Tuple &true_value, const Tuple &false_value);
812Tuple select(const Expr &condition, const Tuple &true_value, const Tuple &false_value);
813// @}
814
815/** Equivalent of multiway select(), but taking/returning tuples. If the condition is
816 * a Tuple, it must match the size of the true and false Tuples. */
817// @{
818template<typename... Args>
819inline Tuple select(const Tuple &c0, const Tuple &v0, const Tuple &c1, const Tuple &v1, Args &&...args) {
820 return select(c0, v0, select(c1, v1, std::forward<Args>(args)...));
821}
822template<typename... Args>
823inline Tuple select(const Expr &c0, const Tuple &v0, const Expr &c1, const Tuple &v1, Args &&...args) {
824 return select(c0, v0, select(c1, v1, std::forward<Args>(args)...));
825}
826// @}
827
828/** select applied to FuncRefs (e.g. select(x < 100, f(x), g(x))) is assumed to
829 * return an Expr. A runtime error is produced if this is applied to
830 * tuple-valued Funcs. In that case you should explicitly cast the second and
831 * third args to Tuple to remove the ambiguity. */
832// @{
833Expr select(const Expr &condition, const FuncRef &true_value, const FuncRef &false_value);
834template<typename... Args>
835inline Expr select(const Expr &c0, const FuncRef &v0, const Expr &c1, const FuncRef &v1, Args &&...args) {
836 return select(c0, v0, select(c1, v1, std::forward<Args>(args)...));
837}
838// @}
839
840/** Oftentimes we want to pack a list of expressions with the same type
841 * into a channel dimension, e.g.,
842 * img(x, y, c) = select(c == 0, 100, // Red
843 * c == 1, 50, // Green
844 * 25); // Blue
845 * This is tedious when the list is long. The following function
846 * provide convinent syntax that allow one to write:
847 * img(x, y, c) = mux(c, {100, 50, 25});
848 *
849 * As with the select equivalent, if the first argument (the index) is
850 * out of range, the expression evaluates to the last value.
851 */
852// @{
853Expr mux(const Expr &id, const std::initializer_list<Expr> &values);
854Expr mux(const Expr &id, const std::vector<Expr> &values);
855Expr mux(const Expr &id, const Tuple &values);
856Expr mux(const Expr &id, const std::initializer_list<FuncRef> &values);
857Tuple mux(const Expr &id, const std::initializer_list<Tuple> &values);
858Tuple mux(const Expr &id, const std::vector<Tuple> &values);
859// @}
860
861/** Return the sine of a floating-point expression. If the argument is
862 * not floating-point, it is cast to Float(32). Does not vectorize
863 * well. */
865
866/** Return the arcsine of a floating-point expression. If the argument
867 * is not floating-point, it is cast to Float(32). Does not vectorize
868 * well. */
870
871/** Return the cosine of a floating-point expression. If the argument
872 * is not floating-point, it is cast to Float(32). Does not vectorize
873 * well. */
875
876/** Return the arccosine of a floating-point expression. If the
877 * argument is not floating-point, it is cast to Float(32). Does not
878 * vectorize well. */
880
881/** Return the tangent of a floating-point expression. If the argument
882 * is not floating-point, it is cast to Float(32). Does not vectorize
883 * well. */
885
886/** Return the arctangent of a floating-point expression. If the
887 * argument is not floating-point, it is cast to Float(32). Does not
888 * vectorize well. */
890
891/** Return the angle of a floating-point gradient. If the argument is
892 * not floating-point, it is cast to Float(32). Does not vectorize
893 * well. */
895
896/** Return the hyperbolic sine of a floating-point expression. If the
897 * argument is not floating-point, it is cast to Float(32). Does not
898 * vectorize well. */
900
901/** Return the hyperbolic arcsinhe of a floating-point expression. If
902 * the argument is not floating-point, it is cast to Float(32). Does
903 * not vectorize well. */
905
906/** Return the hyperbolic cosine of a floating-point expression. If
907 * the argument is not floating-point, it is cast to Float(32). Does
908 * not vectorize well. */
910
911/** Return the hyperbolic arccosine of a floating-point expression.
912 * If the argument is not floating-point, it is cast to
913 * Float(32). Does not vectorize well. */
915
916/** Return the hyperbolic tangent of a floating-point expression. If
917 * the argument is not floating-point, it is cast to Float(32). Does
918 * not vectorize well. */
920
921/** Return the hyperbolic arctangent of a floating-point expression.
922 * If the argument is not floating-point, it is cast to
923 * Float(32). Does not vectorize well. */
925
926/** Return the square root of a floating-point expression. If the
927 * argument is not floating-point, it is cast to Float(32). Typically
928 * vectorizes cleanly. */
930
931/** Return the square root of the sum of the squares of two
932 * floating-point expressions. If the argument is not floating-point,
933 * it is cast to Float(32). Vectorizes cleanly. */
934Expr hypot(const Expr &x, const Expr &y);
935
936/** Return the exponential of a floating-point expression. If the
937 * argument is not floating-point, it is cast to Float(32). For
938 * Float(64) arguments, this calls the system exp function, and does
939 * not vectorize well. For Float(32) arguments, this function is
940 * vectorizable, does the right thing for extremely small or extremely
941 * large inputs, and is accurate up to the last bit of the
942 * mantissa. Vectorizes cleanly. */
944
945/** Return the logarithm of a floating-point expression. If the
946 * argument is not floating-point, it is cast to Float(32). For
947 * Float(64) arguments, this calls the system log function, and does
948 * not vectorize well. For Float(32) arguments, this function is
949 * vectorizable, does the right thing for inputs <= 0 (returns -inf or
950 * nan), and is accurate up to the last bit of the
951 * mantissa. Vectorizes cleanly. */
953
954/** Return one floating point expression raised to the power of
955 * another. The type of the result is given by the type of the first
956 * argument. If the first argument is not a floating-point type, it is
957 * cast to Float(32). For Float(32), cleanly vectorizable, and
958 * accurate up to the last few bits of the mantissa. Gets worse when
959 * approaching overflow. Vectorizes cleanly. */
961
962/** Evaluate the error function erf. Only available for
963 * Float(32). Accurate up to the last three bits of the
964 * mantissa. Vectorizes cleanly. */
965Expr erf(const Expr &x);
966
967/** Fast vectorizable approximation to some trigonometric functions for Float(32).
968 * Absolute approximation error is less than 1e-5. */
969// @{
972// @}
973
974/** Fast approximate cleanly vectorizable log for Float(32). Returns
975 * nonsense for x <= 0.0f. Accurate up to the last 5 bits of the
976 * mantissa. Vectorizes cleanly. */
978
979/** Fast approximate cleanly vectorizable exp for Float(32). Returns
980 * nonsense for inputs that would overflow or underflow. Typically
981 * accurate up to the last 5 bits of the mantissa. Gets worse when
982 * approaching overflow. Vectorizes cleanly. */
984
985/** Fast approximate cleanly vectorizable pow for Float(32). Returns
986 * nonsense for x < 0.0f. Accurate up to the last 5 bits of the
987 * mantissa for typical exponents. Gets worse when approaching
988 * overflow. Vectorizes cleanly. */
990
991/** Fast approximate inverse for Float(32). Corresponds to the rcpps
992 * instruction on x86, and the vrecpe instruction on ARM. Vectorizes
993 * cleanly. Note that this can produce slightly different results
994 * across different implementations of the same architecture (e.g. AMD vs Intel),
995 * even when strict_float is enabled. */
997
998/** Fast approximate inverse square root for Float(32). Corresponds to
999 * the rsqrtps instruction on x86, and the vrsqrte instruction on
1000 * ARM. Vectorizes cleanly. Note that this can produce slightly different results
1001 * across different implementations of the same architecture (e.g. AMD vs Intel),
1002 * even when strict_float is enabled. */
1004
1005/** Return the greatest whole number less than or equal to a
1006 * floating-point expression. If the argument is not floating-point,
1007 * it is cast to Float(32). The return value is still in floating
1008 * point, despite being a whole number. Vectorizes cleanly. */
1010
1011/** Return the least whole number greater than or equal to a
1012 * floating-point expression. If the argument is not floating-point,
1013 * it is cast to Float(32). The return value is still in floating
1014 * point, despite being a whole number. Vectorizes cleanly. */
1016
1017/** Return the whole number closest to a floating-point expression. If the
1018 * argument is not floating-point, it is cast to Float(32). The return value is
1019 * still in floating point, despite being a whole number. On ties, we round
1020 * towards the nearest even integer. Note that this is not the same as
1021 * std::round in C, which rounds away from zero. On platforms without a native
1022 * instruction for this, it is emulated, and may be more expensive than
1023 * cast<int>(x + 0.5f) or similar. */
1025
1026/** Return the integer part of a floating-point expression. If the argument is
1027 * not floating-point, it is cast to Float(32). The return value is still in
1028 * floating point, despite being a whole number. Vectorizes cleanly. */
1030
1031/** Returns true if the argument is a Not a Number (NaN). Requires a
1032 * floating point argument. Vectorizes cleanly.
1033 * Note that the Expr passed in will be evaluated in strict_float mode,
1034 * regardless of whether strict_float mode is enabled in the current Target. */
1036
1037/** Returns true if the argument is Inf or -Inf. Requires a
1038 * floating point argument. Vectorizes cleanly.
1039 * Note that the Expr passed in will be evaluated in strict_float mode,
1040 * regardless of whether strict_float mode is enabled in the current Target. */
1042
1043/** Returns true if the argument is a finite value (ie, neither NaN nor Inf).
1044 * Requires a floating point argument. Vectorizes cleanly.
1045 * Note that the Expr passed in will be evaluated in strict_float mode,
1046 * regardless of whether strict_float mode is enabled in the current Target. */
1048
1049/** Return the fractional part of a floating-point expression. If the argument
1050 * is not floating-point, it is cast to Float(32). The return value has the
1051 * same sign as the original expression. Vectorizes cleanly. */
1052Expr fract(const Expr &x);
1053
1054/** Reinterpret the bits of one value as another type. */
1056
1057template<typename T>
1059 return reinterpret(type_of<T>(), std::move(e));
1060}
1061
1062/** Return the bitwise and of two expressions (which need not have the
1063 * same type). The result type is the wider of the two expressions.
1064 * Only integral types are allowed and both expressions must be signed
1065 * or both must be unsigned. */
1067
1068/** Return the bitwise and of an expression and an integer. The type
1069 * of the result is the type of the expression argument. */
1070// @{
1073// @}
1074
1075/** Return the bitwise or of two expressions (which need not have the
1076 * same type). The result type is the wider of the two expressions.
1077 * Only integral types are allowed and both expressions must be signed
1078 * or both must be unsigned. */
1080
1081/** Return the bitwise or of an expression and an integer. The type of
1082 * the result is the type of the expression argument. */
1083// @{
1086// @}
1087
1088/** Return the bitwise xor of two expressions (which need not have the
1089 * same type). The result type is the wider of the two expressions.
1090 * Only integral types are allowed and both expressions must be signed
1091 * or both must be unsigned. */
1093
1094/** Return the bitwise xor of an expression and an integer. The type
1095 * of the result is the type of the expression argument. */
1096// @{
1099// @}
1100
1101/** Return the bitwise not of an expression. */
1103
1104/** Shift the bits of an integer value left. This is actually less
1105 * efficient than multiplying by 2^n, because Halide's optimization
1106 * passes understand multiplication, and will compile it to
1107 * shifting. This operator is only for if you really really need bit
1108 * shifting (e.g. because the exponent is a run-time parameter). The
1109 * type of the result is equal to the type of the first argument. Both
1110 * arguments must have integer type. */
1111// @{
1114// @}
1115
1116/** Shift the bits of an integer value right. Does sign extension for
1117 * signed integers. This is less efficient than dividing by a power of
1118 * two. Halide's definition of division (always round to negative
1119 * infinity) means that all divisions by powers of two get compiled to
1120 * bit-shifting, and Halide's optimization routines understand
1121 * division and can work with it. The type of the result is equal to
1122 * the type of the first argument. Both arguments must have integer
1123 * type. */
1124// @{
1127// @}
1128
1129/** Linear interpolate between the two values according to a weight.
1130 * \param zero_val The result when weight is 0
1131 * \param one_val The result when weight is 1
1132 * \param weight The interpolation amount
1133 *
1134 * Both zero_val and one_val must have the same type. All types are
1135 * supported, including bool.
1136 *
1137 * The weight is treated as its own type and must be float or an
1138 * unsigned integer type. It is scaled to the bit-size of the type of
1139 * x and y if they are integer, or converted to float if they are
1140 * float. Integer weights are converted to float via division by the
1141 * full-range value of the weight's type. Floating-point weights used
1142 * to interpolate between integer values must be between 0.0f and
1143 * 1.0f, and an error may be signaled if it is not provably so. (clamp
1144 * operators can be added to provide proof. Currently an error is only
1145 * signalled for constant weights.)
1146 *
1147 * For integer linear interpolation, out of range values cannot be
1148 * represented. In particular, weights that are conceptually less than
1149 * 0 or greater than 1.0 are not representable. As such the result is
1150 * always between x and y (inclusive of course). For lerp with
1151 * floating-point values and floating-point weight, the full range of
1152 * a float is valid, however underflow and overflow can still occur.
1153 *
1154 * Ordering is not required between zero_val and one_val:
1155 * lerp(42, 69, .5f) == lerp(69, 42, .5f) == 56
1156 *
1157 * Results for integer types are for exactly rounded arithmetic. As
1158 * such, there are cases where 16-bit and float differ because 32-bit
1159 * floating-point (float) does not have enough precision to produce
1160 * the exact result. (Likely true for 32-bit integer
1161 * vs. double-precision floating-point as well.)
1162 *
1163 * At present, double precision and 64-bit integers are not supported.
1164 *
1165 * Generally, lerp will vectorize as if it were an operation on a type
1166 * twice the bit size of the inferred type for x and y.
1167 *
1168 * Some examples:
1169 * \code
1170 *
1171 * // Since Halide does not have direct type delcarations, casts
1172 * // below are used to indicate the types of the parameters.
1173 * // Such casts not required or expected in actual code where types
1174 * // are inferred.
1175 *
1176 * lerp(cast<float>(x), cast<float>(y), cast<float>(w)) ->
1177 * x * (1.0f - w) + y * w
1178 *
1179 * lerp(cast<uint8_t>(x), cast<uint8_t>(y), cast<uint8_t>(w)) ->
1180 * cast<uint8_t>(cast<uint8_t>(x) * (1.0f - cast<uint8_t>(w) / 255.0f) +
1181 * cast<uint8_t>(y) * cast<uint8_t>(w) / 255.0f + .5f)
1182 *
1183 * // Note addition in Halide promoted uint8_t + int8_t to int16_t already,
1184 * // the outer cast is added for clarity.
1185 * lerp(cast<uint8_t>(x), cast<int8_t>(y), cast<uint8_t>(w)) ->
1186 * cast<int16_t>(cast<uint8_t>(x) * (1.0f - cast<uint8_t>(w) / 255.0f) +
1187 * cast<int8_t>(y) * cast<uint8_t>(w) / 255.0f + .5f)
1188 *
1189 * lerp(cast<int8_t>(x), cast<int8_t>(y), cast<float>(w)) ->
1190 * cast<int8_t>(cast<int8_t>(x) * (1.0f - cast<float>(w)) +
1191 * cast<int8_t>(y) * cast<uint8_t>(w))
1192 *
1193 * \endcode
1194 * */
1196
1197/** Count the number of set bits in an expression. */
1199
1200/** Count the number of leading zero bits in an expression. If the expression is
1201 * zero, the result is the number of bits in the type. */
1203
1204/** Count the number of trailing zero bits in an expression. If the expression is
1205 * zero, the result is the number of bits in the type. */
1207
1208/** Divide two integers, rounding towards zero. This is the typical
1209 * behavior of most hardware architectures, which differs from
1210 * Halide's division operator, which is Euclidean (rounds towards
1211 * -infinity). Will throw a runtime error if y is zero, or if y is -1
1212 * and x is the minimum signed integer. */
1214
1215/** Compute the remainder of dividing two integers, when division is
1216 * rounding toward zero. This is the typical behavior of most hardware
1217 * architectures, which differs from Halide's mod operator, which is
1218 * Euclidean (produces the remainder when division rounds towards
1219 * -infinity). Will throw a runtime error if y is zero. */
1221
1222/** Return a random variable representing a uniformly distributed
1223 * float in the half-open interval [0.0f, 1.0f). For random numbers of
1224 * other types, use lerp with a random float as the last parameter.
1225 *
1226 * Optionally takes a seed.
1227 *
1228 * Note that:
1229 \code
1230 Expr x = random_float();
1231 Expr y = x + x;
1232 \endcode
1233 *
1234 * is very different to
1235 *
1236 \code
1237 Expr y = random_float() + random_float();
1238 \endcode
1239 *
1240 * The first doubles a random variable, and the second adds two
1241 * independent random variables.
1242 *
1243 * A given random variable takes on a unique value that depends
1244 * deterministically on the pure variables of the function they belong
1245 * to, the identity of the function itself, and which definition of
1246 * the function it is used in. They are, however, shared across tuple
1247 * elements.
1248 *
1249 * This function vectorizes cleanly.
1250 */
1252
1253/** Return a random variable representing a uniformly distributed
1254 * unsigned 32-bit integer. See \ref random_float. Vectorizes cleanly. */
1256
1257/** Return a random variable representing a uniformly distributed
1258 * 32-bit integer. See \ref random_float. Vectorizes cleanly. */
1260
1261/** Create an Expr that prints out its value whenever it is
1262 * evaluated. It also prints out everything else in the arguments
1263 * list, separated by spaces. This can include string literals. */
1264//@{
1265Expr print(const std::vector<Expr> &values);
1266
1267template<typename... Args>
1269 std::vector<Expr> collected_args = {std::move(a)};
1270 Internal::collect_print_args(collected_args, std::forward<Args>(args)...);
1271 return print(collected_args);
1272}
1273//@}
1274
1275/** Create an Expr that prints whenever it is evaluated, provided that
1276 * the condition is true. */
1277// @{
1278Expr print_when(Expr condition, const std::vector<Expr> &values);
1279
1280template<typename... Args>
1281inline HALIDE_NO_USER_CODE_INLINE Expr print_when(Expr condition, Expr a, Args &&...args) {
1282 std::vector<Expr> collected_args = {std::move(a)};
1283 Internal::collect_print_args(collected_args, std::forward<Args>(args)...);
1284 return print_when(std::move(condition), collected_args);
1285}
1286
1287// @}
1288
1289/** Create an Expr that that guarantees a precondition.
1290 * If 'condition' is true, the return value is equal to the first Expr.
1291 * If 'condition' is false, halide_error() is called, and the return value
1292 * is arbitrary. Any additional arguments after the first Expr are stringified
1293 * and passed as a user-facing message to halide_error(), similar to print().
1294 *
1295 * Note that this essentially *always* inserts a runtime check into the
1296 * generated code (except when the condition can be proven at compile time);
1297 * as such, it should be avoided inside inner loops, except for debugging
1298 * or testing purposes. Note also that it does not vectorize cleanly (vector
1299 * values will be scalarized for the check).
1300 *
1301 * However, using this to make assertions about (say) input values
1302 * can be useful, both in terms of correctness and (potentially) in terms
1303 * of code generation, e.g.
1304 \code
1305 Param<int> p;
1306 Expr y = require(p > 0, p);
1307 \endcode
1308 * will allow the optimizer to assume positive, nonzero values for y.
1309 */
1310// @{
1311Expr require(Expr condition, const std::vector<Expr> &values);
1312
1313template<typename... Args>
1314inline HALIDE_NO_USER_CODE_INLINE Expr require(Expr condition, Expr value, Args &&...args) {
1315 std::vector<Expr> collected_args = {std::move(value)};
1316 Internal::collect_print_args(collected_args, std::forward<Args>(args)...);
1317 return require(std::move(condition), collected_args);
1318}
1319// @}
1320
1321/** Return an undef value of the given type. Halide skips stores that
1322 * depend on undef values, so you can use this to mean "do not modify
1323 * this memory location". This is an escape hatch that can be used for
1324 * several things:
1325 *
1326 * You can define a reduction with no pure step, by setting the pure
1327 * step to undef. Do this only if you're confident that the update
1328 * steps are sufficient to correctly fill in the domain.
1329 *
1330 * For a tuple-valued reduction, you can write an update step that
1331 * only updates some tuple elements.
1332 *
1333 * You can define single-stage pipeline that only has update steps,
1334 * and depends on the values already in the output buffer.
1335 *
1336 * Use this feature with great caution, as you can use it to load from
1337 * uninitialized memory.
1338 */
1340
1341template<typename T>
1342inline Expr undef() {
1343 return undef(type_of<T>());
1344}
1345
1346namespace Internal {
1347
1348/** Return an expression that should never be evaluated. Expressions
1349 * that depend on unreachabale values are also unreachable, and
1350 * statements that execute unreachable expressions are also considered
1351 * unreachable. */
1353
1354template<typename T>
1356 return unreachable(type_of<T>());
1357}
1358
1359} // namespace Internal
1360
1361/** Control the values used in the memoization cache key for memoize.
1362 * Normally parameters and other external dependencies are
1363 * automatically inferred and added to the cache key. The memoize_tag
1364 * operator allows computing one expression and using either the
1365 * computed value, or one or more other expressions in the cache key
1366 * instead of the parameter dependencies of the computation. The
1367 * single argument version is completely safe in that the cache key
1368 * will use the actual computed value -- it is difficult or imposible
1369 * to produce erroneous caching this way. The more-than-one argument
1370 * version allows generating cache keys that do not uniquely identify
1371 * the computation and thus can result in caching errors.
1372 *
1373 * A potential use for the single argument version is to handle a
1374 * floating-point parameter that is quantized to a small
1375 * integer. Mutliple values of the float will produce the same integer
1376 * and moving the caching to using the integer for the key is more
1377 * efficient.
1378 *
1379 * The main use for the more-than-one argument version is to provide
1380 * cache key information for Handles and ImageParams, which otherwise
1381 * are not allowed inside compute_cached operations. E.g. when passing
1382 * a group of parameters to an external array function via a Handle,
1383 * memoize_tag can be used to isolate the actual values used by that
1384 * computation. If an ImageParam is a constant image with a persistent
1385 * digest, memoize_tag can be used to key computations using that image
1386 * on the digest. */
1387// @{
1388template<typename... Args>
1390 std::vector<Expr> collected_args{std::forward<Args>(args)...};
1391 return Internal::memoize_tag_helper(std::move(result), collected_args);
1392}
1393// @}
1394
1395/** Expressions tagged with this intrinsic are considered to be part
1396 * of the steady state of some loop with a nasty beginning and end
1397 * (e.g. a boundary condition). When Halide encounters likely
1398 * intrinsics, it splits the containing loop body into three, and
1399 * tries to simplify down all conditions that lead to the likely. For
1400 * example, given the expression: select(x < 1, bar, x > 10, bar,
1401 * likely(foo)), Halide will split the loop over x into portions where
1402 * x < 1, 1 <= x <= 10, and x > 10.
1403 *
1404 * You're unlikely to want to call this directly. You probably want to
1405 * use the boundary condition helpers in the BoundaryConditions
1406 * namespace instead.
1407 */
1409
1410/** Equivalent to likely, but only triggers a loop partitioning if
1411 * found in an innermost loop. */
1413
1414/** Cast an expression to the halide type corresponding to the C++
1415 * type T. As part of the cast, clamp to the minimum and maximum
1416 * values of the result type. */
1417template<typename T>
1419 return saturating_cast(type_of<T>(), std::move(e));
1420}
1421
1422/** Cast an expression to a new type, clamping to the minimum and
1423 * maximum values of the result type. */
1425
1426/** Makes a best effort attempt to preserve IEEE floating-point
1427 * semantics in evaluating an expression. May not be implemented for
1428 * all backends. (E.g. it is difficult to do this for C++ code
1429 * generation as it depends on the compiler flags used to compile the
1430 * generated code. */
1432
1433/** Create an Expr that that promises another Expr is clamped but do
1434 * not generate code to check the assertion or modify the value. No
1435 * attempt is made to prove the bound at compile time. (If it is
1436 * proved false as a result of something else, an error might be
1437 * generated, but it is also possible the compiler will crash.) The
1438 * promised bound is used in bounds inference so it will allow
1439 * satisfying bounds checks as well as possibly aiding optimization.
1440 *
1441 * unsafe_promise_clamped returns its first argument, the Expr 'value'
1442 *
1443 * This is a very easy way to make Halide generate erroneous code if
1444 * the bound promises is not kept. Use sparingly when there is no
1445 * other way to convey the information to the compiler and it is
1446 * required for a valuable optimization.
1447 *
1448 * Unsafe promises can be checked by turning on
1449 * Target::CheckUnsafePromises. This is intended for debugging only.
1450 */
1451Expr unsafe_promise_clamped(const Expr &value, const Expr &min, const Expr &max);
1452
1453namespace Internal {
1454/**
1455 * FOR INTERNAL USE ONLY.
1456 *
1457 * An entirely unchecked version of unsafe_promise_clamped, used
1458 * inside the compiler as an annotation of the known bounds of an Expr
1459 * when it has proved something is bounded and wants to record that
1460 * fact for later passes (notably bounds inference) to exploit. This
1461 * gets introduced by GuardWithIf tail strategies, because the bounds
1462 * machinery has a hard time exploiting if statement conditions.
1463 *
1464 * Unlike unsafe_promise_clamped, this expression is
1465 * context-dependent, because 'value' might be statically bounded at
1466 * some point in the IR (e.g. due to a containing if statement), but
1467 * not elsewhere.
1468 *
1469 * This intrinsic always evaluates to its first argument. If this value is
1470 * used by a side-effecting operation and it is outside the range specified
1471 * by its second and third arguments, behavior is undefined. The compiler can
1472 * therefore assume that the value is within the range given and optimize
1473 * accordingly. Note that this permits promise_clamped to evaluate to
1474 * something outside of the range, provided that this value is not used.
1475 *
1476 * Note that this produces an intrinsic that is marked as 'pure' and thus is
1477 * allowed to be hoisted, etc.; thus, extra care must be taken with its use.
1478 **/
1479Expr promise_clamped(const Expr &value, const Expr &min, const Expr &max);
1480} // namespace Internal
1481
1482/** Scatter and gather are used for update definition which must store
1483 * multiple values to distinct locations at the same time. The
1484 * multiple expressions on the right-hand-side are bundled together
1485 * into a "gather", which must match a "scatter" the the same number
1486 * of arguments on the left-hand-size. For example, to store the
1487 * values 1 and 2 to the locations (x, y, 3) and (x, y, 4),
1488 * respectively:
1489 *
1490\code
1491f(x, y, scatter(3, 4)) = gather(1, 2);
1492\endcode
1493 *
1494 * The result of gather or scatter can be treated as an
1495 * expression. Any containing operations on it can be assumed to
1496 * distribute over the elements. If two gather expressions are
1497 * combined with an arithmetic operator (e.g. added), they combine
1498 * element-wise. The following example stores the values 2 * x, 2 * y,
1499 * and 2 * c to the locations (x + 1, y, c), (x, y + 3, c), and (x, y,
1500 * c + 2) respectively:
1501 *
1502\code
1503f(x + scatter(1, 0, 0), y + scatter(0, 3, 0), c + scatter(0, 0, 2)) = 2 * gather(x, y, c);
1504\endcode
1505*
1506* Repeated values in the scatter cause multiple stores to the same
1507* location. The stores happen in order from left to right, so the
1508* rightmost value wins. The following code is equivalent to f(x) = 5
1509*
1510\code
1511f(scatter(x, x)) = gather(3, 5);
1512\endcode
1513*
1514* Gathers are most useful for algorithms which require in-place
1515* swapping or permutation of multiple elements, or other kinds of
1516* in-place mutations that require loading multiple inputs, doing some
1517* operations to them jointly, then storing them again. The following
1518* update definition swaps the values of f at locations 3 and 5 if an
1519* input parameter p is true:
1520*
1521\code
1522f(scatter(3, 5)) = f(select(p, gather(5, 3), gather(3, 5)));
1523\endcode
1524*
1525* For more examples of the use of scatter and gather, see
1526* test/correctness/multiple_scatter.cpp
1527*
1528* It is not currently possible to use scatter and gather to write an
1529* update definition in which the *number* of values loaded or stored
1530* varies, as the size of the scatter/gather packet must be fixed a
1531* compile-time. A workaround is to make the unwanted extra operations
1532* a redundant copy of the last operation, which will be
1533* dead-code-eliminated by the compiler. For example, the following
1534* update definition swaps the values at locations 3 and 5 when the
1535* parameter p is true, and rotates the values at locations 1, 2, and 3
1536* when it is false. The load from 3 and store to 5 will be redundantly
1537* repeated:
1538*
1539\code
1540f(select(p, scatter(3, 5, 5), scatter(1, 2, 3))) = f(select(p, gather(5, 3, 3), gather(2, 3, 1)));
1541\endcode
1542*
1543* Note that in the p == true case, we redudantly load from 3 and write
1544* to 5 twice.
1545*/
1546//@{
1547Expr scatter(const std::vector<Expr> &args);
1548Expr gather(const std::vector<Expr> &args);
1549
1550template<typename... Args>
1551Expr scatter(const Expr &e, Args &&...args) {
1552 return scatter({e, std::forward<Args>(args)...});
1553}
1554
1555template<typename... Args>
1556Expr gather(const Expr &e, Args &&...args) {
1557 return gather({e, std::forward<Args>(args)...});
1558}
1559// @}
1560
1561/** Extract a contiguous subsequence of the bits of 'e', starting at the bit
1562 * index given by 'lsb', where zero is the least-significant bit, returning a
1563 * value of type 't'. Any out-of-range bits requested are filled with zeros.
1564 *
1565 * extract_bits is especially useful when one wants to load a small vector of a
1566 * wide type, and treat it as a larger vector of a smaller type. For example,
1567 * loading a vector of 32 uint8 values from a uint32 Func can be done as
1568 * follows:
1569\code
1570f8(x) = extract_bits<uint8_t>(f32(x/4), 8*(x%4));
1571f8.align_bounds(x, 4).vectorize(x, 32);
1572\endcode
1573 * Note that the align_bounds call is critical so that the narrow Exprs are
1574 * aligned to the wider Exprs. This makes the x%4 term collapse to a
1575 * constant. If f8 is an output Func, then constraining the min value of x to be
1576 * a known multiple of four would also be sufficient, e.g. via:
1577\code
1578f8.output_buffer().dim(0).set_min(0);
1579\endcode
1580 *
1581 * See test/correctness/extract_concat_bits.cpp for a complete example. */
1582// @{
1583Expr extract_bits(Type t, const Expr &e, const Expr &lsb);
1584
1585template<typename T>
1586Expr extract_bits(const Expr &e, const Expr &lsb) {
1587 return extract_bits(type_of<T>(), e, lsb);
1588}
1589// @}
1590
1591/** Given a number of Exprs of the same type, concatenate their bits producing a
1592 * single Expr of the same type code of the input but with more bits. The
1593 * number of arguments must be a power of two.
1594 *
1595 * concat_bits is especially useful when one wants to treat a Func containing
1596 * values of a narrow type as a Func containing fewer values of a wider
1597 * type. For example, the following code reinterprets vectors of 32 uint8 values
1598 * as a vector of 8 uint32s:
1599 *
1600\code
1601f32(x) = concat_bits({f8(4*x), f8(4*x + 1), f8(4*x + 2), f8(4*x + 3)});
1602f32.vectorize(x, 8);
1603\endcode
1604 *
1605 * See test/correctness/extract_concat_bits.cpp for a complete example.
1606 */
1607Expr concat_bits(const std::vector<Expr> &e);
1608
1609/** Below is a collection of intrinsics for fixed-point programming. Most of
1610 * them can be expressed via other means, but this is more natural for some, as
1611 * it avoids ghost widened intermediates that don't (or shouldn't) actually show
1612 * up in codegen, and doesn't rely on pattern-matching inside the compiler to
1613 * succeed to get good instruction selection.
1614 *
1615 * The semantics of each call are defined in terms of a non-existent 'widen' and
1616 * 'narrow' operators, which stand in for casts that double or halve the
1617 * bit-width of a type respectively.
1618 */
1619
1620/** Compute a + widen(b). */
1622
1623/** Compute a * widen(b). */
1625
1626/** Compute a - widen(b). */
1628
1629/** Compute widen(a) + widen(b). */
1631
1632/** Compute widen(a) * widen(b). a and b may have different signedness, in which
1633 * case the result is signed. */
1635
1636/** Compute widen(a) - widen(b). The result is always signed. */
1638
1639/** Compute widen(a) << b. */
1640//@{
1643//@}
1644
1645/** Compute widen(a) >> b. */
1646//@{
1649//@}
1650
1651/** Compute saturating_narrow(widening_add(a, (1 >> min(b, 0)) / 2) << b).
1652 * When b is positive indicating a left shift, the rounding term is zero. */
1653//@{
1656//@}
1657
1658/** Compute saturating_narrow(widening_add(a, (1 << max(b, 0)) / 2) >> b).
1659 * When b is negative indicating a left shift, the rounding term is zero. */
1660//@{
1663//@}
1664
1665/** Compute saturating_narrow(widen(a) + widen(b)) */
1667
1668/** Compute saturating_narrow(widen(a) - widen(b)) */
1670
1671/** Compute narrow((widen(a) + widen(b)) / 2) */
1673
1674/** Compute narrow((widen(a) + widen(b) + 1) / 2) */
1676
1677/** Compute narrow((widen(a) - widen(b)) / 2) */
1679
1680/** Compute saturating_narrow(shift_right(widening_mul(a, b), q)) */
1681//@{
1684//@}
1685
1686/** Compute saturating_narrow(rounding_shift_right(widening_mul(a, b), q)) */
1687//@{
1690//@}
1691
1692} // namespace Halide
1693
1694#endif
Base classes for Halide expressions (Halide::Expr) and statements (Halide::Internal::Stmt)
Defines Tuple - the front-end handle on small arrays of expressions.
#define HALIDE_NO_USER_CODE_INLINE
Definition Util.h:47
A fragment of front-end syntax of the form f(x, y, z), where x, y, z are Vars or Exprs.
Definition Func.h:491
Create a small array of Exprs for defining and calling functions with multiple outputs.
Definition Tuple.h:18
Expr make_one(Type t)
Construct the representation of one in the given type.
T div_imp(T a, T b)
Definition IROperator.h:267
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,...
Expr memoize_tag_helper(Expr result, const std::vector< Expr > &cache_key_values)
const double * as_const_float(const Expr &e)
If an expression is a FloatImm or a Broadcast of a FloatImm, return a pointer to its value.
Expr make_zero(Type t)
Construct the representation of zero in the given type.
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,...
bool is_undef(const Expr &e)
Is the expression an undef.
Expr requirement_failed_error(Expr condition, const std::vector< Expr > &args)
Expr make_two(Type t)
Construct the representation of two in the given type.
void check_representable(Type t, int64_t val)
Check if a constant value can be correctly represented as the given type.
Expr halide_erf(const Expr &a)
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,...
void match_types(Expr &a, Expr &b)
Coerce the two expressions to have the same type, using C-style casting rules.
double div_imp< double >(double a, double b)
Definition IROperator.h:308
Expr halide_exp(const Expr &a)
Expr make_const(Type t, int64_t val)
Construct an immediate of the given type from any numeric C++ type.
const int64_t * as_const_int(const Expr &e)
If an expression is an IntImm or a Broadcast of an IntImm, return a pointer to its value.
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...
Expr const_true(int lanes=1)
Construct the constant boolean true.
bool is_signed_integer_overflow(const Expr &expr)
Check if an expression is a signed_integer_overflow.
T mod_imp(T a, T b)
Implementations of division and mod that are specific to Halide.
Definition IROperator.h:246
void reset_random_counters()
Reset the counters used for random-number seeds in random_float/int/uint.
Expr halide_log(const Expr &a)
Halide's vectorizable transcendentals.
bool is_pure(const Expr &e)
Does the expression 1) Take on the same value no matter where it appears in a Stmt,...
void split_into_ands(const Expr &cond, std::vector< Expr > &result)
Split a boolean condition into vector of ANDs.
Expr promise_clamped(const Expr &value, const Expr &min, const Expr &max)
FOR INTERNAL USE ONLY.
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...
Expr unwrap_tags(const Expr &e)
If the expression is a tag helper call, remove it and return the tagged expression.
float div_imp< float >(float a, float b)
Definition IROperator.h:304
bool is_const_power_of_two_integer(const Expr &e, int *bits)
Is the expression a constant integer power of two.
Expr lossless_negate(const Expr &x)
Attempt to negate x without introducing new IR and without overflow.
const uint64_t * as_const_uint(const Expr &e)
If an expression is a UIntImm or a Broadcast of a UIntImm, return a pointer to its value.
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.
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...
Expr const_false(int lanes=1)
Construct the constant boolean false.
double mod_imp< double >(double a, double b)
Definition IROperator.h:298
Expr lossless_cast(Type t, Expr e, std::map< Expr, ConstantInterval, ExprCompare > *cache=nullptr)
Attempt to cast an expression to a smaller type while provably not losing information.
Expr make_bool(bool val, int lanes=1)
Construct a boolean constant from a C++ boolean value.
HALIDE_NO_USER_CODE_INLINE void collect_print_args(std::vector< Expr > &args)
Definition IROperator.h:342
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.
float mod_imp< float >(float a, float b)
Definition IROperator.h:292
Expr raise_to_integer_power(Expr a, int64_t b)
Raise an expression to an integer power by repeatedly multiplying it by itself.
Expr make_signed_integer_overflow(Type type)
Construct a unique signed_integer_overflow Expr.
bool is_const(const Expr &e)
Is the expression either an IntImm, a FloatImm, a StringImm, or a Cast of the same,...
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...
This file defines the class FunctionDAG, which is our representation of a Halide pipeline,...
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
Expr log(Expr x)
Return the logarithm of a floating-point expression.
Expr operator>>(Expr x, Expr y)
Shift the bits of an integer value right.
Expr ceil(Expr x)
Return the least whole number greater than or equal to a floating-point expression.
Expr widen_right_add(Expr a, Expr b)
Below is a collection of intrinsics for fixed-point programming.
Expr rounding_shift_right(Expr a, Expr b)
Compute saturating_narrow(widening_add(a, (1 << max(b, 0)) / 2) >> b).
HALIDE_NO_USER_CODE_INLINE Expr memoize_tag(Expr result, Args &&...args)
Control the values used in the memoization cache key for memoize.
Expr fast_log(const Expr &x)
Fast approximate cleanly vectorizable log for Float(32).
Expr count_leading_zeros(Expr x)
Count the number of leading zero bits in an expression.
Expr reinterpret(Type t, Expr e)
Reinterpret the bits of one value as another type.
Expr saturating_add(Expr a, Expr b)
Compute saturating_narrow(widen(a) + widen(b))
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
Expr fast_cos(const Expr &x)
Expr & operator*=(Expr &a, Expr b)
Modify the first expression to be the product of two expressions, without changing its type.
Expr random_uint(Expr seed=Expr())
Return a random variable representing a uniformly distributed unsigned 32-bit integer.
@ Internal
Not visible externally, similar to 'static' linkage in C.
Expr fract(const Expr &x)
Return the fractional part of a floating-point expression.
Expr halving_add(Expr a, Expr b)
Compute narrow((widen(a) + widen(b)) / 2)
Expr & operator-=(Expr &a, Expr b)
Modify the first expression to be the difference of two expressions, without changing its type.
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
Expr widening_shift_right(Expr a, Expr b)
Compute widen(a) >> b.
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
Expr trunc(Expr x)
Return the integer part of a floating-point expression.
Expr halving_sub(Expr a, Expr b)
Compute narrow((widen(a) - widen(b)) / 2)
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
Expr acosh(Expr x)
Return the hyperbolic arccosine of a floating-point expression.
Expr fast_inverse(Expr x)
Fast approximate inverse for Float(32).
Expr asin(Expr x)
Return the arcsine of a floating-point expression.
Expr rounding_shift_left(Expr a, Expr b)
Compute saturating_narrow(widening_add(a, (1 >> min(b, 0)) / 2) << b).
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
Expr clamp(Expr a, const Expr &min_val, const Expr &max_val)
Clamps an expression to lie within the given bounds.
Expr hypot(const Expr &x, const Expr &y)
Return the square root of the sum of the squares of two floating-point expressions.
Expr popcount(Expr x)
Count the number of set bits in an expression.
Expr saturating_sub(Expr a, Expr b)
Compute saturating_narrow(widen(a) - widen(b))
Expr gather(const std::vector< Expr > &args)
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.
Expr widening_shift_left(Expr a, Expr b)
Compute widen(a) << b.
Expr pow(Expr x, Expr y)
Return one floating point expression raised to the power of another.
Expr operator&(Expr x, Expr y)
Return the bitwise and of two expressions (which need not have the same type).
Expr undef()
auto operator!(const GeneratorParam< T > &a) -> decltype(!(T) a)
Not operator for GeneratorParam.
Definition Generator.h:1245
Expr lerp(Expr zero_val, Expr one_val, Expr weight)
Linear interpolate between the two values according to a weight.
Expr atan2(Expr y, Expr x)
Return the angle of a floating-point gradient.
Expr random_float(Expr seed=Expr())
Return a random variable representing a uniformly distributed float in the half-open interval [0....
Expr sin(Expr x)
Return the sine of a floating-point expression.
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...
Expr rounding_halving_add(Expr a, Expr b)
Compute narrow((widen(a) + widen(b) + 1) / 2)
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',...
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 ...
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,...
Expr cosh(Expr x)
Return the hyperbolic cosine of a floating-point expression.
std::ostream & operator<<(std::ostream &stream, const Expr &)
Emit an expression on an output stream (such as std::cout) in human-readable form.
Type Int(int bits, int lanes=1)
Constructing a signed integer type.
Definition Type.h:541
Expr acos(Expr x)
Return the arccosine of a floating-point expression.
Expr fast_exp(const Expr &x)
Fast approximate cleanly vectorizable exp for Float(32).
Expr widening_add(Expr a, Expr b)
Compute widen(a) + widen(b).
Expr cos(Expr x)
Return the cosine of a floating-point expression.
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
Expr exp(Expr x)
Return the exponential of a floating-point expression.
Expr widen_right_mul(Expr a, Expr b)
Compute a * widen(b).
Expr absd(Expr a, Expr b)
Return the absolute difference between two values.
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
Expr fast_sin(const Expr &x)
Fast vectorizable approximation to some trigonometric functions for Float(32).
Expr fast_pow(Expr x, Expr y)
Fast approximate cleanly vectorizable pow for Float(32).
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
@ C
No name mangling.
Expr round(Expr x)
Return the whole number closest to a floating-point expression.
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...
Expr count_trailing_zeros(Expr x)
Count the number of trailing zero bits in an expression.
Expr scatter(const std::vector< Expr > &args)
Scatter and gather are used for update definition which must store multiple values to distinct locati...
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
Expr rounding_mul_shift_right(Expr a, Expr b, Expr q)
Compute saturating_narrow(rounding_shift_right(widening_mul(a, b), q))
Expr random_int(Expr seed=Expr())
Return a random variable representing a uniformly distributed 32-bit integer.
Expr mod_round_to_zero(Expr x, Expr y)
Compute the remainder of dividing two integers, when division is rounding toward zero.
Expr strict_float(Expr e)
Makes a best effort attempt to preserve IEEE floating-point semantics in evaluating an expression.
Expr & operator/=(Expr &a, Expr b)
Modify the first expression to be the ratio of two expressions, without changing its type.
Expr widening_mul(Expr a, Expr b)
Compute widen(a) * widen(b).
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
Expr is_nan(Expr x)
Returns true if the argument is a Not a Number (NaN).
Expr asinh(Expr x)
Return the hyperbolic arcsinhe of a floating-point expression.
Expr sqrt(Expr x)
Return the square root of a floating-point expression.
Expr sinh(Expr x)
Return the hyperbolic sine of a floating-point expression.
Expr atan(Expr x)
Return the arctangent of a floating-point expression.
Expr operator|(Expr x, Expr y)
Return the bitwise or of two expressions (which need not have the same type).
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
Internal::ConstantInterval cast(Type t, const Internal::ConstantInterval &a)
Cast operators for ConstantIntervals.
Expr require(Expr condition, const std::vector< Expr > &values)
Create an Expr that that guarantees a precondition.
Expr is_inf(Expr x)
Returns true if the argument is Inf or -Inf.
Expr is_finite(Expr x)
Returns true if the argument is a finite value (ie, neither NaN nor Inf).
Expr tanh(Expr x)
Return the hyperbolic tangent of a floating-point expression.
Expr likely_if_innermost(Expr e)
Equivalent to likely, but only triggers a loop partitioning if found in an innermost loop.
Expr atanh(Expr x)
Return the hyperbolic arctangent of a floating-point expression.
Expr tan(Expr x)
Return the tangent of a floating-point expression.
Internal::ConstantInterval saturating_cast(Type t, const Internal::ConstantInterval &a)
Expr fast_inverse_sqrt(Expr x)
Fast approximate inverse square root for Float(32).
Expr print(const std::vector< Expr > &values)
Create an Expr that prints out its value whenever it is evaluated.
Expr mul_shift_right(Expr a, Expr b, Expr q)
Compute saturating_narrow(shift_right(widening_mul(a, b), q))
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
Expr & operator+=(Expr &a, Expr b)
Modify the first expression to be the sum of two expressions, without changing its type.
Expr abs(Expr a)
Returns the absolute value of a signed integer or floating-point expression.
Expr widen_right_sub(Expr a, Expr b)
Compute a - widen(b).
Expr floor(Expr x)
Return the greatest whole number less than or equal to a floating-point expression.
Expr div_round_to_zero(Expr x, Expr y)
Divide two integers, rounding towards zero.
Expr widening_sub(Expr a, Expr b)
Compute widen(a) - widen(b).
Expr likely(Expr e)
Expressions tagged with this intrinsic are considered to be part of the steady state of some loop wit...
Expr operator~(Expr x)
Return the bitwise not of an expression.
Expr erf(const Expr &x)
Evaluate the error function erf.
Expr operator^(Expr x, Expr y)
Return the bitwise xor of two expressions (which need not have the same type).
unsigned __INT64_TYPE__ uint64_t
signed __INT64_TYPE__ int64_t
signed __INT32_TYPE__ int32_t
unsigned __INT8_TYPE__ uint8_t
unsigned __INT16_TYPE__ uint16_t
unsigned __INT32_TYPE__ uint32_t
signed __INT16_TYPE__ int16_t
signed __INT8_TYPE__ int8_t
A fragment of Halide syntax.
Definition Expr.h:258
A builder to help create Exprs representing halide_buffer_t structs (e.g.
Definition IROperator.h:217
std::vector< Expr > strides
Definition IROperator.h:222
std::vector< Expr > extents
Definition IROperator.h:222
A reference-counted handle to a statement node.
Definition Expr.h:427
static constexpr bool value
Definition IROperator.h:334
Types in the halide type system.
Definition Type.h:283
HALIDE_ALWAYS_INLINE bool is_int() const
Is this type a signed integer type?
Definition Type.h:435
HALIDE_ALWAYS_INLINE bool is_float() const
Is this type a floating point type (float or double).
Definition Type.h:423
Class that provides a type that implements half precision floating point (IEEE754 2008 binary16) in s...
Definition Float16.h:17