fix_2_053119869 = 16819
	fix_2_562915447 = 20995
	fix_3_072711026 = 25172
)

const (
	constBits     = 13
	pass1Bits     = 2
	centerJSample = 128
)

// fdct performs a forward DCT on an 8x8 block of coefficients, including a
// level shift.
func fdct(b *block) {
	// Pass 1: process rows.
	for y := 0; y < 8; y++ {
		y8 := y * 8
		s := b[y8 : y8+8 : y8+8] // Small cap improves performance, see https://golang.org/issue/27857

			got[j] = got[j]/8 + 128
		}
		if differ(&got, &want) {
			t.Errorf("i=%d: IDCT(FDCT)\nsrc\n%s\ngot\n%s\nwant\n%s\n", i, &b, &got, &want)
		}
	}

	// Check that the optimized and slow FDCT implementations agree.
	// The fdct function already does a scale and level shift.
	for i, b := range blocks {
		got, want := b, b
		fdct(&got)
		for j := range want {
			want[j] = (want[j] - 128) * 8
		}
		slowFDCT(&want)

	}
}

// writeBlock writes a block of pixel data using the given quantization table,
// returning the post-quantized DC value of the DCT-transformed block. b is in
// natural (not zig-zag) order.
func (e *encoder) writeBlock(b *block, q quantIndex, prevDC int32) int32 {
	fdct(b)
	// Emit the DC delta.
	dc := div(b[0], 8*int32(e.quant[q][0]))
	e.emitHuffRLE(huffIndex(2*q+0), 0, dc-prevDC)
	// Emit the AC components.

package main

import "fmt"

func fact[T interface{ ~int | ~int64 | ~float64 }](n T) T {
	if n == 1 {
		return 1
	}
	return n * fact(n-1)
}

func main() {
	const want = 120

	if got := fact(5); got != want {
		panic(fmt.Sprintf("got %d, want %d", got, want))
	}

	if got := fact[int64](5); got != want {
		panic(fmt.Sprintf("got %d, want %d", got, want))
	}

		s[5] = (x0 - x4) >> 8
		s[6] = (x3 - x2) >> 8
		s[7] = (x7 - x1) >> 8
	}

	// Vertical 1-D IDCT.
	for x := 0; x < 8; x++ {
		// Similar to the horizontal 1-D IDCT case, if all the AC components are zero, then the IDCT is trivial.
		// However, after performing the horizontal 1-D IDCT, there are typically non-zero AC components, so
		// we do not bother to check for the all-zero case.

					// TODO(adonovan): audit for other possibilities.
					logf("no object for path: %v; discarding %s", err, f.Fact)
					continue
				}
				key.obj = obj
				logf("read %T fact %s for %v", f.Fact, f.Fact, key.obj)
			} else {
				// package fact
				logf("read %T fact %s for %v", f.Fact, f.Fact, factPkg)
			}
			m[key] = f.Fact
		}
	}

	return &Set{pkg: d.pkg, m: m}, nil
}

	ImportPackageFact func(pkg *types.Package, fact Fact) bool

	// ExportObjectFact associates a fact of type *T with the obj,
	// replacing any previous fact of that type.
	//
	// ExportObjectFact panics if it is called after the pass is
	// complete, or if obj does not belong to the package being analyzed.
	// ExportObjectFact is not concurrency-safe.
	ExportObjectFact func(obj types.Object, fact Fact)

	check(mul(gen(3), zero()), 0)
	check(mul(zero(), gen(4)), 0)
	check(mul(gen(3), add1(zero())), 3)
	check(mul(add1(zero()), gen(4)), 4)
	check(mul(gen(3), gen(4)), 12)

	check(fact(zero()), 1)
	check(fact(add1(zero())), 1)
	check(fact(gen(5)), 120)
}

// -------------------------------------
// Factorial

var results = [...]int{
	1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800,
	39916800, 479001600,

// that the Doc is not empty;
// that the Run is non-nil;
// that the Requires graph is acyclic;
// that analyzer fact types are unique;
// that each fact type is a pointer.
//
// Analyzer names need not be unique, though this may be confusing.
func Validate(analyzers []*Analyzer) error {
	// Map each fact type to its sole generating analyzer.
	factTypes := make(map[reflect.Type]*Analyzer)

package main

import (
	"./a"
	"fmt"
)

func main() {
	const want = 120

	if got := a.Fact(5); got != want {
		panic(fmt.Sprintf("got %d, want %d", got, want))
	}

	if got := a.Fact[int64](5); got != want {
		panic(fmt.Sprintf("got %d, want %d", got, want))
	}

	if got := a.Fact(5.0); got != want {
		panic(fmt.Sprintf("got %f, want %f", got, want))
	}