* lite2: add Start method

There are few reasons to do that:

1) separation of state and dynamics (some users will want to delay
   starting the light client; does not matter we should not allow them
   to create a light client object)
2) less important, but some users might not need autoUpdateRoutine and
   removeNoLongerTrustedHeadersRoutine routines

* lite2: wait till routines are finished in Stop

because they are started in Start, it feels more natural to wait for
them to finish in Stop.

* lite2: add TrustedValidatorSet func

* refactor cleanup code

* changed restore header and val function to handle negative height

* reverted restoreTrustedHeaderAndNextVals() functionality

Co-authored-by: Anton Kaliaev <anton.kalyaev@gmail.com>

Closes #4341

* lite2: add Start method

There are few reasons to do that:

1) separation of state and dynamics (some users will want to delay
   starting the light client; does not matter we should not allow them
   to create a light client object)
2) less important, but some users might not need autoUpdateRoutine and
   removeNoLongerTrustedHeadersRoutine routines

* lite2: wait till routines are finished in Stop

because they are started in Start, it feels more natural to wait for
them to finish in Stop.

* lite2: add TrustedValidatorSet func

* lite2: advance to latest header

without any exponential steps

rename autoUpdate to autoUpdateRoutine

* lite2: wait in Cleanup until goroutines finished running

* lite2: move AutoClient into Client

Most of the users will want auto update feature, so it makes sense to
move it into the Client itself, rather than having a separate
abstraction (it makes the code cleaner, but introduces an extra thing
the user will need to learn).

Also, add `FirstTrustedHeight` func to Client to get first trusted height.

* fix db store tests

* separate examples for auto and manual clients

* AutoUpdate tries to update to latest state

NOT 1 header at a time

* fix errors

* lite2: make Logger an option

remove SetLogger func

* fix lite cmd

* lite2: make concurrency assumptions explicit

* fixes after my own review

* no need for nextHeightFn

sequence func will download intermediate headers

* correct comment

* cmd/lite: switch to new lite2 package

* update changelog

* shorten the trusting period explanation

* rename adjusted to adjacent

Refs https://github.com/tendermint/tendermint/pull/3989#discussion_r352140829

* rename ErrTooMuchChange to ErrNotEnoughVotingPowerSigned

Refs https://github.com/tendermint/tendermint/pull/3989#discussion_r352142785

* verify commit is properly signed

* remove no longer trusted headers

* restore trustedHeader and trustedNextVals

* check trustedHeader using options

Refs https://github.com/tendermint/tendermint/pull/4209#issuecomment-562462165

* use correct var when checking if headers are adjacent

in bisection func
+ replace TODO with a comment

https://github.com/tendermint/tendermint/pull/3989#discussion_r352125455

* return header in VerifyHeaderAtHeight

because that way we avoid DB call

+ add godoc comments
+ check if there are no headers yet in AutoClient

https://github.com/tendermint/tendermint/pull/3989#pullrequestreview-315454506

* TestVerifyAdjacentHeaders: add 2 more test-cases

+ add TestVerifyReturnsErrorIfTrustLevelIsInvalid

* lite: avoid overflow when parsing key in db store!

* lite: rename AutoClient#Err to Errs

* lite: add a test for AutoClient

* lite: fix keyPattern and call itr.Next in db store

* lite: add two tests for db store

* lite: add TestClientRemovesNoLongerTrustedHeaders

* lite: test Client#Cleanup

* lite: test restoring trustedHeader

https://github.com/tendermint/tendermint/pull/4209#issuecomment-562462165

* lite: comment out unused code in test_helpers

* fix TestVerifyReturnsErrorIfTrustLevelIsInvalid after merge

* change defaultRemoveNoLongerTrustedHeadersPeriod

and add docs

* write more doc

* lite: uncomment testable examples

* use stdlog.Fatal to stop AutoClient tests

* make lll linter happy

* separate errors for 2 cases

- the validator set of a skipped header cannot be trusted, i.e. <1/3rd
  of h1 validator set has signed (new error, something like
  ErrNewValSetCantBeTrusted)
- the validator set is trusted but < 2/3rds has signed
  (ErrNewHeaderCantBeTrusted)

https://github.com/tendermint/tendermint/pull/4209#discussion_r360331253

* remove all headers (even the last one) that are outside

of the trusting period. By doing this, we avoid checking the
trustedHeader's hash in checkTrustedHeaderUsingOptions (case #1).

https://github.com/tendermint/tendermint/pull/4209#discussion_r360332460

* explain restoreTrustedHeaderAndNextVals better

https://github.com/tendermint/tendermint/pull/4209#discussion_r360602328

* add ConfirmationFunction option

for optionally prompting for user input Y/n before removing headers

Refs https://github.com/tendermint/tendermint/pull/4209#discussion_r360602945

* make cleaning optional

https://github.com/tendermint/tendermint/pull/4209#discussion_r364838189

* return error when user refused to remove headers

* check for double votes in VerifyCommitTrusting

* leave only ErrNewValSetCantBeTrusted error

to differenciate between h2Vals.VerifyCommit and
h1NextVals.VerifyCommitTrusting

* fix example tests

* remove unnecessary if condition

https://github.com/tendermint/tendermint/pull/4209#discussion_r365171847

It will be handled by the above switch.

* verifyCommitBasic does not depend on vals

Co-authored-by: Marko <marbar3778@yahoo.com>

* lint: golint issue fixes

- on my local machine golint is a lot stricter than the bot so slowly going through and fixing things.

Signed-off-by: Marko Baricevic <marbar3778@yahoo.com>

* more fixes from golint

* remove isPeerPersistentFn

* add changelog entry

* libs/common: Refactor libs/common 5

- move mathematical functions and types out of `libs/common` to math pkg
- move net functions out of `libs/common` to net pkg
- move string functions out of `libs/common` to strings pkg
- move async functions out of `libs/common` to async pkg
- move bit functions out of `libs/common` to bits pkg
- move cmap functions out of `libs/common` to cmap pkg
- move os functions out of `libs/common` to os pkg

Signed-off-by: Marko Baricevic <marbar3778@yahoo.com>

* fix testing issues

* fix tests

closes #41417

woooooooooooooooooo kill the cmn pkg

Signed-off-by: Marko Baricevic <marbar3778@yahoo.com>

* add changelog entry

* fix goimport issues

* run gofmt

* libs/common: refactor libs/common 2

- move random function to there own pkg

Signed-off-by: Marko Baricevic <marbar3778@yahoo.com>

* change imports and usage throughout repo

* fix goimports

* add changelog entry

Refs #1771

ADR: https://github.com/tendermint/tendermint/blob/master/docs/architecture/adr-044-lite-client-with-weak-subjectivity.md

## Commits:

* add Verifier and VerifyCommitTrusting

* add two more checks

make trustLevel an option

* float32 for trustLevel

* check newHeader time

* started writing lite Client

* unify Verify methods

* ensure h2.Header.bfttime < h1.Header.bfttime + tp

* move trust checks into Verify function

* add more comments

* more docs

* started writing tests

* unbonding period failures

* tests are green

* export ErrNewHeaderTooFarIntoFuture

* make golangci happy

* test for non-adjusted headers

* more precision

* providers and stores

* VerifyHeader and VerifyHeaderAtHeight funcs

* fix compile errors

* remove lastVerifiedHeight, persist new trusted header

* sequential verification

* remove TrustedStore option

* started writing tests for light client

* cover basic cases for linear verification

* bisection tests PASS

* rename BisectingVerification to SkippingVerification

* refactor the code

* add TrustedHeader method

* consolidate sequential verification tests

* consolidate skipping verification tests

* rename trustedVals to trustedNextVals

* start writing docs

* ValidateTrustLevel func and ErrOldHeaderExpired error

* AutoClient and example tests

* fix errors

* update doc

* remove ErrNewHeaderTooFarIntoFuture

This check is unnecessary given existing a) ErrOldHeaderExpired b)
h2.Time > now checks.

* return an error if we're at more recent height

* add comments

* add LastSignedHeaderHeight method to Store

I think it's fine if Store tracks last height

* copy over proxy from old lite package

* make TrustedHeader return latest if height=0

* modify LastSignedHeaderHeight to return an error if no headers exist

* copy over proxy impl

* refactor proxy and start http lite client

* Tx and BlockchainInfo methods

* Block method

* commit method

* code compiles again

* lite client compiles

* extract updateLiteClientIfNeededTo func

* move final parts

* add placeholder for tests

* force usage of lite http client in proxy

* comment out query tests for now

* explicitly mention tp: trusting period

* verify nextVals in VerifyHeader

* refactor bisection

* move the NextValidatorsHash check into updateTrustedHeaderAndVals

+ update the comment

* add ConsensusParams method to RPC client

* add ConsensusParams to rpc/mock/client

* change trustLevel type to a new cmn.Fraction type

+ update SkippingVerification comment

* stress out trustLevel is only used for non-adjusted headers

* fixes after Fede's review

Co-authored-by: Federico Kunze <31522760+fedekunze@users.noreply.github.com>

* compare newHeader with a header from an alternative provider

* save pivot header

Refs https://github.com/tendermint/tendermint/pull/3989#discussion_r349122824

* check header can still be trusted in TrustedHeader

Refs https://github.com/tendermint/tendermint/pull/3989#discussion_r349101424

* lite: update Validators and Block endpoints

- Block no longer contains BlockMeta
- Validators now accept two additional params: page and perPage

* make linter happy