entities.put("Iuml", "\u00cf");
        entities.put("ETH", "\u00d0");
        entities.put("Ntilde", "\u00d1");
        entities.put("Ograve", "\u00d2");
        entities.put("Oacute", "\u00d3");
        entities.put("Ocirc", "\u00d4");
        entities.put("Otilde", "\u00d5");
        entities.put("Ouml", "\u00d6");
        entities.put("times", "\u00d7");
        entities.put("Oslash", "\u00d8");

	"⁡":                   "\u2061",
	"Å":                           "\u00c5",
	"𝒜":                            "\U0001d49c",
	"≔":                          "\u2254",
	"Ã":                          "\u00c3",
	"Ä":                            "\u00c4",
	"∖":                       "\u2216",
	"⫧":                            "\u2ae7",
	"⌆":                          "\u2306",

	"Igrave":   "\u00CC",
	"Iacute":   "\u00CD",
	"Icirc":    "\u00CE",
	"Iuml":     "\u00CF",
	"ETH":      "\u00D0",
	"Ntilde":   "\u00D1",
	"Ograve":   "\u00D2",
	"Oacute":   "\u00D3",
	"Ocirc":    "\u00D4",
	"Otilde":   "\u00D5",
	"Ouml":     "\u00D6",
	"times":    "\u00D7",
	"Oslash":   "\u00D8",
	"Ugrave":   "\u00D9",
	"Uacute":   "\u00DA",
	"Ucirc":    "\u00DB",
	"Uuml":     "\u00DC",

package tlog

import (
	"fmt"
	"strconv"
	"strings"
)

// A Tile is a description of a transparency log tile.
// A tile of height H at level L offset N lists W consecutive hashes
// at level H*L of the tree starting at offset N*(2**H).
// A complete tile lists 2**H hashes; a partial tile lists fewer.
// Note that a tile represents the entire subtree of height H
// with those hashes as the leaves. The levels above H*L

	//  T ⊆ ~t == true
	//  T ⊆  T == true
	return !x.tilde || y.tilde
}

// disjoint reports whether x ∩ y == ∅.
// x.typ and y.typ must not be nil.
func (x *term) disjoint(y *term) bool {
	if debug && (x.typ == nil || y.typ == nil) {
		panic("invalid argument(s)")
	}
	ux := x.typ
	if y.tilde {
		ux = under(ux)
	}
	uy := y.typ
	if x.tilde {
		uy = under(uy)
	}
	return !Identical(ux, uy)

    const tpu::TPUCompileMetadataProto& metadata);

// Gets the proper tensor dimension from XLA OpSharding.
// "replicate_on_last_tile_dim" and "last_tile_dims" should be deducted from the
// real Tensor dimensions when tiled.
// For example:
// f32[8,512](sharding={devices=[1,1,2]0,1 last_tile_dims={REPLICATED})
// also means a replicated tensor over all devices.
//
// See xla_data.proto for detailed explanations on the fields.

// term has a tilde. In all other cases coreTerm returns (nil, false).
func coreTerm(tpar *TypeParam) (*term, bool) {
	n := 0
	var single *term // valid if n == 1
	var tilde bool
	tpar.is(func(t *term) bool {
		if t == nil {
			assert(n == 0)
			return false // no terms
		}
		n++
		single = t
		if t.tilde {
			tilde = true
		}
		return true

	return "/" + tile.Path()
}

// readTile reads a single tile, either from the on-disk cache or the server.
func (c *Client) readTile(tile tlog.Tile) ([]byte, error) {
	type cached struct {
		data []byte
		err  error
	}

	result := c.tileCache.Do(tile, func() interface{} {
		// Try the requested tile in on-disk cache.
		data, err := c.ops.ReadCache(c.tileCacheKey(tile))

// term has a tilde. In all other cases coreTerm returns (nil, false).
func coreTerm(tpar *TypeParam) (*term, bool) {
	n := 0
	var single *term // valid if n == 1
	var tilde bool
	tpar.is(func(t *term) bool {
		if t == nil {
			assert(n == 0)
			return false // no terms
		}
		n++
		single = t
		if t.tilde {
			tilde = true
		}
		return true

  }

  return builder->create<mlir::TF::ConcatOp>(
      location, output_type, concat_dimension_op.getOutput(), inputs);
}

// For tile sharded inputs to TPU computation, inject split op between the
// input values and TPU computation so that tiled input values are passed in
// as inputs to TPU computations. If more than one dimension is sharded, then