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1// Copyright 2017, The Go Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style
3// license that can be found in the LICENSE file.
4
5// Package cmp determines equality of values.
6//
7// This package is intended to be a more powerful and safer alternative to
8// [reflect.DeepEqual] for comparing whether two values are semantically equal.
9// It is intended to only be used in tests, as performance is not a goal and
10// it may panic if it cannot compare the values. Its propensity towards
11// panicking means that its unsuitable for production environments where a
12// spurious panic may be fatal.
13//
14// The primary features of cmp are:
15//
16//   - When the default behavior of equality does not suit the test's needs,
17//     custom equality functions can override the equality operation.
18//     For example, an equality function may report floats as equal so long as
19//     they are within some tolerance of each other.
20//
21//   - Types with an Equal method (e.g., [time.Time.Equal]) may use that method
22//     to determine equality. This allows package authors to determine
23//     the equality operation for the types that they define.
24//
25//   - If no custom equality functions are used and no Equal method is defined,
26//     equality is determined by recursively comparing the primitive kinds on
27//     both values, much like [reflect.DeepEqual]. Unlike [reflect.DeepEqual],
28//     unexported fields are not compared by default; they result in panics
29//     unless suppressed by using an [Ignore] option
30//     (see [github.com/google/go-cmp/cmp/cmpopts.IgnoreUnexported])
31//     or explicitly compared using the [Exporter] option.
32package cmp
33
34import (
35	"fmt"
36	"reflect"
37	"strings"
38
39	"github.com/google/go-cmp/cmp/internal/diff"
40	"github.com/google/go-cmp/cmp/internal/function"
41	"github.com/google/go-cmp/cmp/internal/value"
42)
43
44// TODO(≥go1.18): Use any instead of interface{}.
45
46// Equal reports whether x and y are equal by recursively applying the
47// following rules in the given order to x and y and all of their sub-values:
48//
49//   - Let S be the set of all [Ignore], [Transformer], and [Comparer] options that
50//     remain after applying all path filters, value filters, and type filters.
51//     If at least one [Ignore] exists in S, then the comparison is ignored.
52//     If the number of [Transformer] and [Comparer] options in S is non-zero,
53//     then Equal panics because it is ambiguous which option to use.
54//     If S contains a single [Transformer], then use that to transform
55//     the current values and recursively call Equal on the output values.
56//     If S contains a single [Comparer], then use that to compare the current values.
57//     Otherwise, evaluation proceeds to the next rule.
58//
59//   - If the values have an Equal method of the form "(T) Equal(T) bool" or
60//     "(T) Equal(I) bool" where T is assignable to I, then use the result of
61//     x.Equal(y) even if x or y is nil. Otherwise, no such method exists and
62//     evaluation proceeds to the next rule.
63//
64//   - Lastly, try to compare x and y based on their basic kinds.
65//     Simple kinds like booleans, integers, floats, complex numbers, strings,
66//     and channels are compared using the equivalent of the == operator in Go.
67//     Functions are only equal if they are both nil, otherwise they are unequal.
68//
69// Structs are equal if recursively calling Equal on all fields report equal.
70// If a struct contains unexported fields, Equal panics unless an [Ignore] option
71// (e.g., [github.com/google/go-cmp/cmp/cmpopts.IgnoreUnexported]) ignores that field
72// or the [Exporter] option explicitly permits comparing the unexported field.
73//
74// Slices are equal if they are both nil or both non-nil, where recursively
75// calling Equal on all non-ignored slice or array elements report equal.
76// Empty non-nil slices and nil slices are not equal; to equate empty slices,
77// consider using [github.com/google/go-cmp/cmp/cmpopts.EquateEmpty].
78//
79// Maps are equal if they are both nil or both non-nil, where recursively
80// calling Equal on all non-ignored map entries report equal.
81// Map keys are equal according to the == operator.
82// To use custom comparisons for map keys, consider using
83// [github.com/google/go-cmp/cmp/cmpopts.SortMaps].
84// Empty non-nil maps and nil maps are not equal; to equate empty maps,
85// consider using [github.com/google/go-cmp/cmp/cmpopts.EquateEmpty].
86//
87// Pointers and interfaces are equal if they are both nil or both non-nil,
88// where they have the same underlying concrete type and recursively
89// calling Equal on the underlying values reports equal.
90//
91// Before recursing into a pointer, slice element, or map, the current path
92// is checked to detect whether the address has already been visited.
93// If there is a cycle, then the pointed at values are considered equal
94// only if both addresses were previously visited in the same path step.
95func Equal(x, y interface{}, opts ...Option) bool {
96	s := newState(opts)
97	s.compareAny(rootStep(x, y))
98	return s.result.Equal()
99}
100
101// Diff returns a human-readable report of the differences between two values:
102// y - x. It returns an empty string if and only if Equal returns true for the
103// same input values and options.
104//
105// The output is displayed as a literal in pseudo-Go syntax.
106// At the start of each line, a "-" prefix indicates an element removed from x,
107// a "+" prefix to indicates an element added from y, and the lack of a prefix
108// indicates an element common to both x and y. If possible, the output
109// uses fmt.Stringer.String or error.Error methods to produce more humanly
110// readable outputs. In such cases, the string is prefixed with either an
111// 's' or 'e' character, respectively, to indicate that the method was called.
112//
113// Do not depend on this output being stable. If you need the ability to
114// programmatically interpret the difference, consider using a custom Reporter.
115func Diff(x, y interface{}, opts ...Option) string {
116	s := newState(opts)
117
118	// Optimization: If there are no other reporters, we can optimize for the
119	// common case where the result is equal (and thus no reported difference).
120	// This avoids the expensive construction of a difference tree.
121	if len(s.reporters) == 0 {
122		s.compareAny(rootStep(x, y))
123		if s.result.Equal() {
124			return ""
125		}
126		s.result = diff.Result{} // Reset results
127	}
128
129	r := new(defaultReporter)
130	s.reporters = append(s.reporters, reporter{r})
131	s.compareAny(rootStep(x, y))
132	d := r.String()
133	if (d == "") != s.result.Equal() {
134		panic("inconsistent difference and equality results")
135	}
136	return d
137}
138
139// rootStep constructs the first path step. If x and y have differing types,
140// then they are stored within an empty interface type.
141func rootStep(x, y interface{}) PathStep {
142	vx := reflect.ValueOf(x)
143	vy := reflect.ValueOf(y)
144
145	// If the inputs are different types, auto-wrap them in an empty interface
146	// so that they have the same parent type.
147	var t reflect.Type
148	if !vx.IsValid() || !vy.IsValid() || vx.Type() != vy.Type() {
149		t = anyType
150		if vx.IsValid() {
151			vvx := reflect.New(t).Elem()
152			vvx.Set(vx)
153			vx = vvx
154		}
155		if vy.IsValid() {
156			vvy := reflect.New(t).Elem()
157			vvy.Set(vy)
158			vy = vvy
159		}
160	} else {
161		t = vx.Type()
162	}
163
164	return &pathStep{t, vx, vy}
165}
166
167type state struct {
168	// These fields represent the "comparison state".
169	// Calling statelessCompare must not result in observable changes to these.
170	result    diff.Result // The current result of comparison
171	curPath   Path        // The current path in the value tree
172	curPtrs   pointerPath // The current set of visited pointers
173	reporters []reporter  // Optional reporters
174
175	// recChecker checks for infinite cycles applying the same set of
176	// transformers upon the output of itself.
177	recChecker recChecker
178
179	// dynChecker triggers pseudo-random checks for option correctness.
180	// It is safe for statelessCompare to mutate this value.
181	dynChecker dynChecker
182
183	// These fields, once set by processOption, will not change.
184	exporters []exporter // List of exporters for structs with unexported fields
185	opts      Options    // List of all fundamental and filter options
186}
187
188func newState(opts []Option) *state {
189	// Always ensure a validator option exists to validate the inputs.
190	s := &state{opts: Options{validator{}}}
191	s.curPtrs.Init()
192	s.processOption(Options(opts))
193	return s
194}
195
196func (s *state) processOption(opt Option) {
197	switch opt := opt.(type) {
198	case nil:
199	case Options:
200		for _, o := range opt {
201			s.processOption(o)
202		}
203	case coreOption:
204		type filtered interface {
205			isFiltered() bool
206		}
207		if fopt, ok := opt.(filtered); ok && !fopt.isFiltered() {
208			panic(fmt.Sprintf("cannot use an unfiltered option: %v", opt))
209		}
210		s.opts = append(s.opts, opt)
211	case exporter:
212		s.exporters = append(s.exporters, opt)
213	case reporter:
214		s.reporters = append(s.reporters, opt)
215	default:
216		panic(fmt.Sprintf("unknown option %T", opt))
217	}
218}
219
220// statelessCompare compares two values and returns the result.
221// This function is stateless in that it does not alter the current result,
222// or output to any registered reporters.
223func (s *state) statelessCompare(step PathStep) diff.Result {
224	// We do not save and restore curPath and curPtrs because all of the
225	// compareX methods should properly push and pop from them.
226	// It is an implementation bug if the contents of the paths differ from
227	// when calling this function to when returning from it.
228
229	oldResult, oldReporters := s.result, s.reporters
230	s.result = diff.Result{} // Reset result
231	s.reporters = nil        // Remove reporters to avoid spurious printouts
232	s.compareAny(step)
233	res := s.result
234	s.result, s.reporters = oldResult, oldReporters
235	return res
236}
237
238func (s *state) compareAny(step PathStep) {
239	// Update the path stack.
240	s.curPath.push(step)
241	defer s.curPath.pop()
242	for _, r := range s.reporters {
243		r.PushStep(step)
244		defer r.PopStep()
245	}
246	s.recChecker.Check(s.curPath)
247
248	// Cycle-detection for slice elements (see NOTE in compareSlice).
249	t := step.Type()
250	vx, vy := step.Values()
251	if si, ok := step.(SliceIndex); ok && si.isSlice && vx.IsValid() && vy.IsValid() {
252		px, py := vx.Addr(), vy.Addr()
253		if eq, visited := s.curPtrs.Push(px, py); visited {
254			s.report(eq, reportByCycle)
255			return
256		}
257		defer s.curPtrs.Pop(px, py)
258	}
259
260	// Rule 1: Check whether an option applies on this node in the value tree.
261	if s.tryOptions(t, vx, vy) {
262		return
263	}
264
265	// Rule 2: Check whether the type has a valid Equal method.
266	if s.tryMethod(t, vx, vy) {
267		return
268	}
269
270	// Rule 3: Compare based on the underlying kind.
271	switch t.Kind() {
272	case reflect.Bool:
273		s.report(vx.Bool() == vy.Bool(), 0)
274	case reflect.Int, reflect.Int8, reflect.Int16, reflect.Int32, reflect.Int64:
275		s.report(vx.Int() == vy.Int(), 0)
276	case reflect.Uint, reflect.Uint8, reflect.Uint16, reflect.Uint32, reflect.Uint64, reflect.Uintptr:
277		s.report(vx.Uint() == vy.Uint(), 0)
278	case reflect.Float32, reflect.Float64:
279		s.report(vx.Float() == vy.Float(), 0)
280	case reflect.Complex64, reflect.Complex128:
281		s.report(vx.Complex() == vy.Complex(), 0)
282	case reflect.String:
283		s.report(vx.String() == vy.String(), 0)
284	case reflect.Chan, reflect.UnsafePointer:
285		s.report(vx.Pointer() == vy.Pointer(), 0)
286	case reflect.Func:
287		s.report(vx.IsNil() && vy.IsNil(), 0)
288	case reflect.Struct:
289		s.compareStruct(t, vx, vy)
290	case reflect.Slice, reflect.Array:
291		s.compareSlice(t, vx, vy)
292	case reflect.Map:
293		s.compareMap(t, vx, vy)
294	case reflect.Ptr:
295		s.comparePtr(t, vx, vy)
296	case reflect.Interface:
297		s.compareInterface(t, vx, vy)
298	default:
299		panic(fmt.Sprintf("%v kind not handled", t.Kind()))
300	}
301}
302
303func (s *state) tryOptions(t reflect.Type, vx, vy reflect.Value) bool {
304	// Evaluate all filters and apply the remaining options.
305	if opt := s.opts.filter(s, t, vx, vy); opt != nil {
306		opt.apply(s, vx, vy)
307		return true
308	}
309	return false
310}
311
312func (s *state) tryMethod(t reflect.Type, vx, vy reflect.Value) bool {
313	// Check if this type even has an Equal method.
314	m, ok := t.MethodByName("Equal")
315	if !ok || !function.IsType(m.Type, function.EqualAssignable) {
316		return false
317	}
318
319	eq := s.callTTBFunc(m.Func, vx, vy)
320	s.report(eq, reportByMethod)
321	return true
322}
323
324func (s *state) callTRFunc(f, v reflect.Value, step Transform) reflect.Value {
325	if !s.dynChecker.Next() {
326		return f.Call([]reflect.Value{v})[0]
327	}
328
329	// Run the function twice and ensure that we get the same results back.
330	// We run in goroutines so that the race detector (if enabled) can detect
331	// unsafe mutations to the input.
332	c := make(chan reflect.Value)
333	go detectRaces(c, f, v)
334	got := <-c
335	want := f.Call([]reflect.Value{v})[0]
336	if step.vx, step.vy = got, want; !s.statelessCompare(step).Equal() {
337		// To avoid false-positives with non-reflexive equality operations,
338		// we sanity check whether a value is equal to itself.
339		if step.vx, step.vy = want, want; !s.statelessCompare(step).Equal() {
340			return want
341		}
342		panic(fmt.Sprintf("non-deterministic function detected: %s", function.NameOf(f)))
343	}
344	return want
345}
346
347func (s *state) callTTBFunc(f, x, y reflect.Value) bool {
348	if !s.dynChecker.Next() {
349		return f.Call([]reflect.Value{x, y})[0].Bool()
350	}
351
352	// Swapping the input arguments is sufficient to check that
353	// f is symmetric and deterministic.
354	// We run in goroutines so that the race detector (if enabled) can detect
355	// unsafe mutations to the input.
356	c := make(chan reflect.Value)
357	go detectRaces(c, f, y, x)
358	got := <-c
359	want := f.Call([]reflect.Value{x, y})[0].Bool()
360	if !got.IsValid() || got.Bool() != want {
361		panic(fmt.Sprintf("non-deterministic or non-symmetric function detected: %s", function.NameOf(f)))
362	}
363	return want
364}
365
366func detectRaces(c chan<- reflect.Value, f reflect.Value, vs ...reflect.Value) {
367	var ret reflect.Value
368	defer func() {
369		recover() // Ignore panics, let the other call to f panic instead
370		c <- ret
371	}()
372	ret = f.Call(vs)[0]
373}
374
375func (s *state) compareStruct(t reflect.Type, vx, vy reflect.Value) {
376	var addr bool
377	var vax, vay reflect.Value // Addressable versions of vx and vy
378
379	var mayForce, mayForceInit bool
380	step := StructField{&structField{}}
381	for i := 0; i < t.NumField(); i++ {
382		step.typ = t.Field(i).Type
383		step.vx = vx.Field(i)
384		step.vy = vy.Field(i)
385		step.name = t.Field(i).Name
386		step.idx = i
387		step.unexported = !isExported(step.name)
388		if step.unexported {
389			if step.name == "_" {
390				continue
391			}
392			// Defer checking of unexported fields until later to give an
393			// Ignore a chance to ignore the field.
394			if !vax.IsValid() || !vay.IsValid() {
395				// For retrieveUnexportedField to work, the parent struct must
396				// be addressable. Create a new copy of the values if
397				// necessary to make them addressable.
398				addr = vx.CanAddr() || vy.CanAddr()
399				vax = makeAddressable(vx)
400				vay = makeAddressable(vy)
401			}
402			if !mayForceInit {
403				for _, xf := range s.exporters {
404					mayForce = mayForce || xf(t)
405				}
406				mayForceInit = true
407			}
408			step.mayForce = mayForce
409			step.paddr = addr
410			step.pvx = vax
411			step.pvy = vay
412			step.field = t.Field(i)
413		}
414		s.compareAny(step)
415	}
416}
417
418func (s *state) compareSlice(t reflect.Type, vx, vy reflect.Value) {
419	isSlice := t.Kind() == reflect.Slice
420	if isSlice && (vx.IsNil() || vy.IsNil()) {
421		s.report(vx.IsNil() && vy.IsNil(), 0)
422		return
423	}
424
425	// NOTE: It is incorrect to call curPtrs.Push on the slice header pointer
426	// since slices represents a list of pointers, rather than a single pointer.
427	// The pointer checking logic must be handled on a per-element basis
428	// in compareAny.
429	//
430	// A slice header (see reflect.SliceHeader) in Go is a tuple of a starting
431	// pointer P, a length N, and a capacity C. Supposing each slice element has
432	// a memory size of M, then the slice is equivalent to the list of pointers:
433	//	[P+i*M for i in range(N)]
434	//
435	// For example, v[:0] and v[:1] are slices with the same starting pointer,
436	// but they are clearly different values. Using the slice pointer alone
437	// violates the assumption that equal pointers implies equal values.
438
439	step := SliceIndex{&sliceIndex{pathStep: pathStep{typ: t.Elem()}, isSlice: isSlice}}
440	withIndexes := func(ix, iy int) SliceIndex {
441		if ix >= 0 {
442			step.vx, step.xkey = vx.Index(ix), ix
443		} else {
444			step.vx, step.xkey = reflect.Value{}, -1
445		}
446		if iy >= 0 {
447			step.vy, step.ykey = vy.Index(iy), iy
448		} else {
449			step.vy, step.ykey = reflect.Value{}, -1
450		}
451		return step
452	}
453
454	// Ignore options are able to ignore missing elements in a slice.
455	// However, detecting these reliably requires an optimal differencing
456	// algorithm, for which diff.Difference is not.
457	//
458	// Instead, we first iterate through both slices to detect which elements
459	// would be ignored if standing alone. The index of non-discarded elements
460	// are stored in a separate slice, which diffing is then performed on.
461	var indexesX, indexesY []int
462	var ignoredX, ignoredY []bool
463	for ix := 0; ix < vx.Len(); ix++ {
464		ignored := s.statelessCompare(withIndexes(ix, -1)).NumDiff == 0
465		if !ignored {
466			indexesX = append(indexesX, ix)
467		}
468		ignoredX = append(ignoredX, ignored)
469	}
470	for iy := 0; iy < vy.Len(); iy++ {
471		ignored := s.statelessCompare(withIndexes(-1, iy)).NumDiff == 0
472		if !ignored {
473			indexesY = append(indexesY, iy)
474		}
475		ignoredY = append(ignoredY, ignored)
476	}
477
478	// Compute an edit-script for slices vx and vy (excluding ignored elements).
479	edits := diff.Difference(len(indexesX), len(indexesY), func(ix, iy int) diff.Result {
480		return s.statelessCompare(withIndexes(indexesX[ix], indexesY[iy]))
481	})
482
483	// Replay the ignore-scripts and the edit-script.
484	var ix, iy int
485	for ix < vx.Len() || iy < vy.Len() {
486		var e diff.EditType
487		switch {
488		case ix < len(ignoredX) && ignoredX[ix]:
489			e = diff.UniqueX
490		case iy < len(ignoredY) && ignoredY[iy]:
491			e = diff.UniqueY
492		default:
493			e, edits = edits[0], edits[1:]
494		}
495		switch e {
496		case diff.UniqueX:
497			s.compareAny(withIndexes(ix, -1))
498			ix++
499		case diff.UniqueY:
500			s.compareAny(withIndexes(-1, iy))
501			iy++
502		default:
503			s.compareAny(withIndexes(ix, iy))
504			ix++
505			iy++
506		}
507	}
508}
509
510func (s *state) compareMap(t reflect.Type, vx, vy reflect.Value) {
511	if vx.IsNil() || vy.IsNil() {
512		s.report(vx.IsNil() && vy.IsNil(), 0)
513		return
514	}
515
516	// Cycle-detection for maps.
517	if eq, visited := s.curPtrs.Push(vx, vy); visited {
518		s.report(eq, reportByCycle)
519		return
520	}
521	defer s.curPtrs.Pop(vx, vy)
522
523	// We combine and sort the two map keys so that we can perform the
524	// comparisons in a deterministic order.
525	step := MapIndex{&mapIndex{pathStep: pathStep{typ: t.Elem()}}}
526	for _, k := range value.SortKeys(append(vx.MapKeys(), vy.MapKeys()...)) {
527		step.vx = vx.MapIndex(k)
528		step.vy = vy.MapIndex(k)
529		step.key = k
530		if !step.vx.IsValid() && !step.vy.IsValid() {
531			// It is possible for both vx and vy to be invalid if the
532			// key contained a NaN value in it.
533			//
534			// Even with the ability to retrieve NaN keys in Go 1.12,
535			// there still isn't a sensible way to compare the values since
536			// a NaN key may map to multiple unordered values.
537			// The most reasonable way to compare NaNs would be to compare the
538			// set of values. However, this is impossible to do efficiently
539			// since set equality is provably an O(n^2) operation given only
540			// an Equal function. If we had a Less function or Hash function,
541			// this could be done in O(n*log(n)) or O(n), respectively.
542			//
543			// Rather than adding complex logic to deal with NaNs, make it
544			// the user's responsibility to compare such obscure maps.
545			const help = "consider providing a Comparer to compare the map"
546			panic(fmt.Sprintf("%#v has map key with NaNs\n%s", s.curPath, help))
547		}
548		s.compareAny(step)
549	}
550}
551
552func (s *state) comparePtr(t reflect.Type, vx, vy reflect.Value) {
553	if vx.IsNil() || vy.IsNil() {
554		s.report(vx.IsNil() && vy.IsNil(), 0)
555		return
556	}
557
558	// Cycle-detection for pointers.
559	if eq, visited := s.curPtrs.Push(vx, vy); visited {
560		s.report(eq, reportByCycle)
561		return
562	}
563	defer s.curPtrs.Pop(vx, vy)
564
565	vx, vy = vx.Elem(), vy.Elem()
566	s.compareAny(Indirect{&indirect{pathStep{t.Elem(), vx, vy}}})
567}
568
569func (s *state) compareInterface(t reflect.Type, vx, vy reflect.Value) {
570	if vx.IsNil() || vy.IsNil() {
571		s.report(vx.IsNil() && vy.IsNil(), 0)
572		return
573	}
574	vx, vy = vx.Elem(), vy.Elem()
575	if vx.Type() != vy.Type() {
576		s.report(false, 0)
577		return
578	}
579	s.compareAny(TypeAssertion{&typeAssertion{pathStep{vx.Type(), vx, vy}}})
580}
581
582func (s *state) report(eq bool, rf resultFlags) {
583	if rf&reportByIgnore == 0 {
584		if eq {
585			s.result.NumSame++
586			rf |= reportEqual
587		} else {
588			s.result.NumDiff++
589			rf |= reportUnequal
590		}
591	}
592	for _, r := range s.reporters {
593		r.Report(Result{flags: rf})
594	}
595}
596
597// recChecker tracks the state needed to periodically perform checks that
598// user provided transformers are not stuck in an infinitely recursive cycle.
599type recChecker struct{ next int }
600
601// Check scans the Path for any recursive transformers and panics when any
602// recursive transformers are detected. Note that the presence of a
603// recursive Transformer does not necessarily imply an infinite cycle.
604// As such, this check only activates after some minimal number of path steps.
605func (rc *recChecker) Check(p Path) {
606	const minLen = 1 << 16
607	if rc.next == 0 {
608		rc.next = minLen
609	}
610	if len(p) < rc.next {
611		return
612	}
613	rc.next <<= 1
614
615	// Check whether the same transformer has appeared at least twice.
616	var ss []string
617	m := map[Option]int{}
618	for _, ps := range p {
619		if t, ok := ps.(Transform); ok {
620			t := t.Option()
621			if m[t] == 1 { // Transformer was used exactly once before
622				tf := t.(*transformer).fnc.Type()
623				ss = append(ss, fmt.Sprintf("%v: %v => %v", t, tf.In(0), tf.Out(0)))
624			}
625			m[t]++
626		}
627	}
628	if len(ss) > 0 {
629		const warning = "recursive set of Transformers detected"
630		const help = "consider using cmpopts.AcyclicTransformer"
631		set := strings.Join(ss, "\n\t")
632		panic(fmt.Sprintf("%s:\n\t%s\n%s", warning, set, help))
633	}
634}
635
636// dynChecker tracks the state needed to periodically perform checks that
637// user provided functions are symmetric and deterministic.
638// The zero value is safe for immediate use.
639type dynChecker struct{ curr, next int }
640
641// Next increments the state and reports whether a check should be performed.
642//
643// Checks occur every Nth function call, where N is a triangular number:
644//
645//	0 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 ...
646//
647// See https://en.wikipedia.org/wiki/Triangular_number
648//
649// This sequence ensures that the cost of checks drops significantly as
650// the number of functions calls grows larger.
651func (dc *dynChecker) Next() bool {
652	ok := dc.curr == dc.next
653	if ok {
654		dc.curr = 0
655		dc.next++
656	}
657	dc.curr++
658	return ok
659}
660
661// makeAddressable returns a value that is always addressable.
662// It returns the input verbatim if it is already addressable,
663// otherwise it creates a new value and returns an addressable copy.
664func makeAddressable(v reflect.Value) reflect.Value {
665	if v.CanAddr() {
666		return v
667	}
668	vc := reflect.New(v.Type()).Elem()
669	vc.Set(v)
670	return vc
671}
672