Halide  19.0.0
Halide compiler and libraries
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 
16 namespace Halide {
17 
18 namespace 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. */
22 bool 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. */
26 bool 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. */
30 const 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. */
34 const 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. */
38 const 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. */
43 bool 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) */
47 bool 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) */
51 bool is_negative_const(const Expr &e);
52 
53 /** Is the expression an undef */
54 bool 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) */
58 bool 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) */
62 bool 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) */
66 bool 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  */
72 bool is_pure(const Expr &e);
73 
74 /** Construct an immediate of the given type from any numeric C++ type. */
75 // @{
78 Expr make_const(Type t, double val);
79 inline Expr make_const(Type t, int32_t val) {
80  return make_const(t, (int64_t)val);
81 }
82 inline Expr make_const(Type t, uint32_t val) {
83  return make_const(t, (uint64_t)val);
84 }
85 inline Expr make_const(Type t, int16_t val) {
86  return make_const(t, (int64_t)val);
87 }
88 inline Expr make_const(Type t, uint16_t val) {
89  return make_const(t, (uint64_t)val);
90 }
91 inline Expr make_const(Type t, int8_t val) {
92  return make_const(t, (int64_t)val);
93 }
94 inline Expr make_const(Type t, uint8_t val) {
95  return make_const(t, (uint64_t)val);
96 }
97 inline Expr make_const(Type t, bool val) {
98  return make_const(t, (uint64_t)val);
99 }
100 inline Expr make_const(Type t, float val) {
101  return make_const(t, (double)val);
102 }
103 inline Expr make_const(Type t, float16_t val) {
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. */
125 Expr 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. */
138 Expr 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. */
142 Expr 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. */
153 Expr 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  */
183 void 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. */
190 void match_types_bitwise(Expr &a, Expr &b, const char *op_name);
191 
192 /** Halide's vectorizable transcendentals. */
193 // @{
194 Expr halide_log(const Expr &a);
195 Expr halide_exp(const Expr &a);
196 Expr halide_erf(const Expr &a);
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. */
205 void 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. */
221  int dimensions = 0;
222  std::vector<Expr> mins, extents, strides;
224  Expr build() const;
225 };
226 
227 /** If e is a ramp expression with stride, default 1, return the base,
228  * otherwise undefined. */
229 Expr 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 // @{
245 template<typename T>
246 inline 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 
266 template<typename T>
267 inline 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.
291 template<>
292 inline 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 }
297 template<>
298 inline double mod_imp<double>(double a, double b) {
299  double f = a - b * (std::floor(a / b));
300  return f;
301 }
302 
303 template<>
304 inline float div_imp<float>(float a, float b) {
305  return a / b;
306 }
307 template<>
308 inline 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 
332 template<typename T>
334  static constexpr bool value = std::is_convertible<T, const char *>::value ||
335  std::is_convertible<T, Halide::Expr>::value;
336 };
337 
338 template<typename... Args>
339 struct all_are_printable_args : meta_and<is_printable_arg<Args>...> {};
340 
341 // Secondary args to print can be Exprs or const char *
342 inline HALIDE_NO_USER_CODE_INLINE void collect_print_args(std::vector<Expr> &args) {
343 }
344 
345 template<typename... Args>
346 inline 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 
351 template<typename... Args>
352 inline 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 
357 Expr requirement_failed_error(Expr condition, const std::vector<Expr> &args);
358 
359 Expr 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. */
370 template<typename T>
371 inline 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 // @{
386 Expr operator+(Expr a, int b);
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. */
391 Expr operator+(int a, Expr b);
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. */
405 Expr operator-(Expr a, int b);
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. */
410 Expr operator-(int a, Expr b);
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. */
431 Expr operator*(Expr a, int b);
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. */
436 Expr operator*(int a, Expr b);
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. */
475 Expr operator/(Expr a, int b);
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. */
480 Expr operator/(int a, Expr b);
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. */
497 Expr operator%(Expr a, int b);
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. */
502 Expr operator%(int a, Expr b);
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. */
513 Expr operator>(Expr a, int b);
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. */
519 Expr operator>(int a, Expr b);
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. */
530 Expr operator<(Expr a, int b);
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. */
536 Expr operator<(int a, Expr b);
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. */
547 Expr operator<=(Expr a, int b);
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. */
553 Expr operator<=(int a, Expr b);
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. */
564 Expr 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. */
570 Expr 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. */
581 Expr operator==(Expr a, int b);
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. */
587 Expr operator==(int a, Expr b);
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. */
598 Expr operator!=(Expr a, int b);
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. */
604 Expr operator!=(int a, Expr b);
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 // @{
612 Expr operator&&(Expr a, bool b);
613 Expr operator&&(bool a, Expr b);
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 // @{
622 Expr operator||(Expr a, bool b);
623 Expr operator||(bool a, Expr b);
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). */
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). */
640 Expr 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). */
647 Expr max(int a, Expr b);
648 
649 inline Expr max(float a, Expr b) {
650  return max(Expr(a), std::move(b));
651 }
652 inline 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. */
662 template<typename A, typename B, typename C, typename... Rest,
663  typename std::enable_if<Halide::Internal::all_are_convertible<Expr, Rest...>::value>::type * = nullptr>
664 inline 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 
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). */
675 Expr 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). */
682 Expr min(int a, Expr b);
683 
684 inline Expr min(float a, Expr b) {
685  return min(Expr(a), std::move(b));
686 }
687 inline 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. */
697 template<typename A, typename B, typename C, typename... Rest,
698  typename std::enable_if<Halide::Internal::all_are_convertible<Expr, Rest...>::value>::type * = nullptr>
699 inline 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 // @{
707 inline Expr operator+(Expr a, float b) {
708  return std::move(a) + Expr(b);
709 }
710 inline Expr operator+(float a, Expr b) {
711  return Expr(a) + std::move(b);
712 }
713 inline Expr operator-(Expr a, float b) {
714  return std::move(a) - Expr(b);
715 }
716 inline Expr operator-(float a, Expr b) {
717  return Expr(a) - std::move(b);
718 }
719 inline Expr operator*(Expr a, float b) {
720  return std::move(a) * Expr(b);
721 }
722 inline Expr operator*(float a, Expr b) {
723  return Expr(a) * std::move(b);
724 }
725 inline Expr operator/(Expr a, float b) {
726  return std::move(a) / Expr(b);
727 }
728 inline Expr operator/(float a, Expr b) {
729  return Expr(a) / std::move(b);
730 }
731 inline Expr operator%(Expr a, float b) {
732  return std::move(a) % Expr(b);
733 }
734 inline Expr operator%(float a, Expr b) {
735  return Expr(a) % std::move(b);
736 }
737 inline Expr operator>(Expr a, float b) {
738  return std::move(a) > Expr(b);
739 }
740 inline Expr operator>(float a, Expr b) {
741  return Expr(a) > std::move(b);
742 }
743 inline Expr operator<(Expr a, float b) {
744  return std::move(a) < Expr(b);
745 }
746 inline Expr operator<(float a, Expr b) {
747  return Expr(a) < std::move(b);
748 }
749 inline Expr operator>=(Expr a, float b) {
750  return std::move(a) >= Expr(b);
751 }
752 inline Expr operator>=(float a, Expr b) {
753  return Expr(a) >= std::move(b);
754 }
755 inline Expr operator<=(Expr a, float b) {
756  return std::move(a) <= Expr(b);
757 }
758 inline Expr operator<=(float a, Expr b) {
759  return Expr(a) <= std::move(b);
760 }
761 inline Expr operator==(Expr a, float b) {
762  return std::move(a) == Expr(b);
763 }
764 inline Expr operator==(float a, Expr b) {
765  return Expr(a) == std::move(b);
766 }
767 inline Expr operator!=(Expr a, float b) {
768  return std::move(a) != Expr(b);
769 }
770 inline 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. */
777 Expr 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. */
796 Expr 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. */
802 template<typename... Args,
803  typename std::enable_if<Halide::Internal::all_are_convertible<Expr, Args...>::value>::type * = nullptr>
804 inline 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 // @{
811 Tuple select(const Tuple &condition, const Tuple &true_value, const Tuple &false_value);
812 Tuple 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 // @{
818 template<typename... Args>
819 inline 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 }
822 template<typename... Args>
823 inline 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 // @{
833 Expr select(const Expr &condition, const FuncRef &true_value, const FuncRef &false_value);
834 template<typename... Args>
835 inline 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 // @{
853 Expr mux(const Expr &id, const std::initializer_list<Expr> &values);
854 Expr mux(const Expr &id, const std::vector<Expr> &values);
855 Expr mux(const Expr &id, const Tuple &values);
856 Expr mux(const Expr &id, const std::initializer_list<FuncRef> &values);
857 Tuple mux(const Expr &id, const std::initializer_list<Tuple> &values);
858 Tuple 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. */
934 Expr 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. */
965 Expr 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 // @{
970 Expr fast_sin(const Expr &x);
971 Expr fast_cos(const Expr &x);
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. */
977 Expr fast_log(const Expr &x);
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. */
983 Expr fast_exp(const Expr &x);
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. */
1052 Expr fract(const Expr &x);
1053 
1054 /** Reinterpret the bits of one value as another type. */
1056 
1057 template<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 // @{
1071 Expr operator&(Expr x, int y);
1072 Expr operator&(int x, Expr y);
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 // @{
1084 Expr operator|(Expr x, int y);
1085 Expr operator|(int x, Expr y);
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 // @{
1097 Expr operator^(Expr x, int y);
1098 Expr operator^(int x, Expr y);
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  * */
1195 Expr lerp(Expr zero_val, Expr one_val, Expr weight);
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 //@{
1265 Expr print(const std::vector<Expr> &values);
1266 
1267 template<typename... Args>
1268 inline HALIDE_NO_USER_CODE_INLINE Expr print(Expr a, Args &&...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 // @{
1278 Expr print_when(Expr condition, const std::vector<Expr> &values);
1279 
1280 template<typename... Args>
1281 inline 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 // @{
1311 Expr require(Expr condition, const std::vector<Expr> &values);
1312 
1313 template<typename... Args>
1314 inline 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 
1341 template<typename T>
1342 inline Expr undef() {
1343  return undef(type_of<T>());
1344 }
1345 
1346 namespace 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 
1354 template<typename T>
1355 inline Expr unreachable() {
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 // @{
1388 template<typename... Args>
1389 inline HALIDE_NO_USER_CODE_INLINE Expr memoize_tag(Expr result, Args &&...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. */
1417 template<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  */
1451 Expr unsafe_promise_clamped(const Expr &value, const Expr &min, const Expr &max);
1452 
1453 namespace 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  **/
1479 Expr 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
1491 f(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
1503 f(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
1511 f(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
1522 f(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
1540 f(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 //@{
1547 Expr scatter(const std::vector<Expr> &args);
1548 Expr gather(const std::vector<Expr> &args);
1549 
1550 template<typename... Args>
1551 Expr scatter(const Expr &e, Args &&...args) {
1552  return scatter({e, std::forward<Args>(args)...});
1553 }
1554 
1555 template<typename... Args>
1556 Expr 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
1570 f8(x) = extract_bits<uint8_t>(f32(x/4), 8*(x%4));
1571 f8.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
1578 f8.output_buffer().dim(0).set_min(0);
1579 \endcode
1580  *
1581  * See test/correctness/extract_concat_bits.cpp for a complete example. */
1582 // @{
1583 Expr extract_bits(Type t, const Expr &e, const Expr &lsb);
1584 
1585 template<typename T>
1586 Expr 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
1601 f32(x) = concat_bits({f8(4*x), f8(4*x + 1), f8(4*x + 2), f8(4*x + 3)});
1602 f32.vectorize(x, 8);
1603 \endcode
1604  *
1605  * See test/correctness/extract_concat_bits.cpp for a complete example.
1606  */
1607 Expr 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)
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.
Expr unreachable(Type t=Int(32))
Return an expression that should never be evaluated.
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
ConstantInterval min(const ConstantInterval &a, const ConstantInterval &b)
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.
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.
ConstantInterval max(const ConstantInterval &a, const ConstantInterval &b)
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.
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...
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.
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.
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
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 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.
Definition: IROperator.h:1389
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 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)
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).
Expr & operator/=(Expr &a, Expr b)
Modify the first expression to be the ratio of two expressions, without changing its type.
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).
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 min(const FuncRef &a, const FuncRef &b)
Explicit overloads of min and max for FuncRef.
Definition: Func.h:597
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 undef(Type t)
Return an undef value of the given type.
Expr & operator-=(Expr &a, Expr b)
Modify the first expression to be the difference of two expressions, without changing its type.
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
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 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
Expr & operator*=(Expr &a, Expr b)
Modify the first expression to be the product of two expressions, without changing its type.
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 & operator+=(Expr &a, Expr b)
Modify the first expression to be the sum of two expressions, without changing its type.
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 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 max(const FuncRef &a, const FuncRef &b)
Definition: Func.h:600
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
std::vector< Expr > mins
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