Adjust various CLI display ratios to arbitrary precision

Originally the deviations from using float64 were insignificant, but at
exabyte scale they start to show up. Cleanup all displays, and clarify
the expectation text, adding an extra 99.9% probability calculator to
`lotus-miner info`

testplans/lotus-soup/rfwp/chain_state.go

@@ -7,6 +7,8 @@ import (
 	"encoding/json"
 	"fmt"
 	"io"
+	"math"
+	corebig "math/big"
 	"os"
 	"sort"
 	"text/tabwriter"
@@ -27,6 +29,7 @@ import (
 	"github.com/filecoin-project/go-state-types/abi"
 	sealing "github.com/filecoin-project/lotus/extern/storage-sealing"
 
+	"github.com/filecoin-project/lotus/chain/actors/builtin"
 	"github.com/filecoin-project/lotus/chain/actors/builtin/miner"
 	tstats "github.com/filecoin-project/lotus/tools/stats"
 )
@@ -581,18 +584,24 @@ func (i *MinerInfo) MarshalPlainText() ([]byte, error) {
 	fmt.Fprintf(w, "Sector Size: %s\n", i.SectorSize)
 
 	pow := i.MinerPower
-	rpercI := types.BigDiv(types.BigMul(pow.MinerPower.RawBytePower, types.NewInt(1000000)), pow.TotalPower.RawBytePower)
-	qpercI := types.BigDiv(types.BigMul(pow.MinerPower.QualityAdjPower, types.NewInt(1000000)), pow.TotalPower.QualityAdjPower)
 
 	fmt.Fprintf(w, "Byte Power:   %s / %s (%0.4f%%)\n",
 		types.SizeStr(pow.MinerPower.RawBytePower),
 		types.SizeStr(pow.TotalPower.RawBytePower),
-		float64(rpercI.Int64())/10000)
+		types.BigDivFloat(
+			types.BigMul(pow.MinerPower.RawBytePower, big.NewInt(100)),
+			pow.TotalPower.RawBytePower,
+		),
+	)
 
 	fmt.Fprintf(w, "Actual Power: %s / %s (%0.4f%%)\n",
 		types.DeciStr(pow.MinerPower.QualityAdjPower),
 		types.DeciStr(pow.TotalPower.QualityAdjPower),
-		float64(qpercI.Int64())/10000)
+		types.BigDivFloat(
+			types.BigMul(pow.MinerPower.QualityAdjPower, big.NewInt(100)),
+			pow.TotalPower.QualityAdjPower,
+		),
+	)
 
 	fmt.Fprintf(w, "\tCommitted: %s\n", types.SizeStr(i.CommittedBytes))
 
@@ -608,16 +617,43 @@ func (i *MinerInfo) MarshalPlainText() ([]byte, error) {
 	if !i.MinerPower.HasMinPower {
 		fmt.Fprintf(w, "Below minimum power threshold, no blocks will be won\n")
 	} else {
-		expWinChance := float64(types.BigMul(qpercI, types.NewInt(build.BlocksPerEpoch)).Int64()) / 1000000
-		if expWinChance > 0 {
-			if expWinChance > 1 {
-				expWinChance = 1
-			}
-			winRate := time.Duration(float64(time.Second*time.Duration(build.BlockDelaySecs)) / expWinChance)
-			winPerDay := float64(time.Hour*24) / float64(winRate)
 
-			fmt.Fprintln(w, "Expected block win rate: ")
-			fmt.Fprintf(w, "%.4f/day (every %s)\n", winPerDay, winRate.Truncate(time.Second))
+		winRatio := new(corebig.Rat).Mul(
+			new(corebig.Rat).SetFrac(
+				types.BigMul(pow.MinerPower.QualityAdjPower, types.NewInt(build.BlocksPerEpoch)).Int,
+				pow.TotalPower.QualityAdjPower.Int,
+			),
+			// decrease the rate ever-so-slightly to very roughly account for the multi-win poisson distribution
+			// FIXME - this is not a scientifically derived number... like at all
+			corebig.NewRat(99997, 100000),
+		)
+
+		if winRatioFloat, _ := winRatio.Float64(); winRatioFloat > 0 {
+
+			weekly, _ := new(corebig.Rat).Mul(
+				winRatio,
+				new(corebig.Rat).SetInt64(7*builtin.EpochsInDay),
+			).Float64()
+
+			avgDuration, _ := new(corebig.Rat).Mul(
+				new(corebig.Rat).SetInt64(builtin.EpochDurationSeconds),
+				new(corebig.Rat).Inv(winRatio),
+			).Float64()
+
+			fmt.Fprintf(w, "Projected average block win rate: %.02f/week (every %s)\n",
+				weekly,
+				(time.Second * time.Duration(avgDuration)).Truncate(time.Second).String(),
+			)
+
+			// Geometric distribution calculated as described in https://en.wikipedia.org/wiki/Geometric_distribution#Probability_Outcomes_Examples
+			// https://www.wolframalpha.com/input/?i=c%3D99%3B+p%3D188809111007232%3B+n%3D5740343177447735296%3B+%281-%284.99*p%2Fn%29%29%5E%28t*2880%29%3D%281-%28c%2F100%29%29
+			fmt.Fprintf(w, "Projected block win with 99.9%% probability every %s\n",
+				(time.Second * time.Duration(
+					builtin.EpochDurationSeconds*math.Log(1-0.999)/
+						math.Log(1-winRatioFloat),
+				)).Truncate(time.Second).String(),
+			)
+			fmt.Fprintln(w, "(projections DO NOT account for future network and miner growth)")
 		}
 	}