Grand test fixup (#138)

* start fixing up tests

* fix up tests + automate with drone

* fiddle with linting

* messing about with drone.yml

* some more fiddling

* hmmm

* add cache

* add vendor directory

* verbose

* ci updates

* update some little things

* update sig

1 files changed, 462 insertions, 0 deletions

diff --git a/vendor/github.com/golang/geo/s1/interval.go b/vendor/github.com/golang/geo/s1/interval.go
new file mode 100644
index 000000000..6fea5221f
--- /dev/null
+++ b/vendor/github.com/golang/geo/s1/interval.go
@@ -0,0 +1,462 @@
+// Copyright 2014 Google Inc. All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package s1
+
+import (
+	"math"
+	"strconv"
+)
+
+// An Interval represents a closed interval on a unit circle (also known
+// as a 1-dimensional sphere). It is capable of representing the empty
+// interval (containing no points), the full interval (containing all
+// points), and zero-length intervals (containing a single point).
+//
+// Points are represented by the angle they make with the positive x-axis in
+// the range [-π, π]. An interval is represented by its lower and upper
+// bounds (both inclusive, since the interval is closed). The lower bound may
+// be greater than the upper bound, in which case the interval is "inverted"
+// (i.e. it passes through the point (-1, 0)).
+//
+// The point (-1, 0) has two valid representations, π and -π. The
+// normalized representation of this point is π, so that endpoints
+// of normal intervals are in the range (-π, π]. We normalize the latter to
+// the former in IntervalFromEndpoints. However, we take advantage of the point
+// -π to construct two special intervals:
+//   The full interval is [-π, π]
+//   The empty interval is [π, -π].
+//
+// Treat the exported fields as read-only.
+type Interval struct {
+	Lo, Hi float64
+}
+
+// IntervalFromEndpoints constructs a new interval from endpoints.
+// Both arguments must be in the range [-π,π]. This function allows inverted intervals
+// to be created.
+func IntervalFromEndpoints(lo, hi float64) Interval {
+	i := Interval{lo, hi}
+	if lo == -math.Pi && hi != math.Pi {
+		i.Lo = math.Pi
+	}
+	if hi == -math.Pi && lo != math.Pi {
+		i.Hi = math.Pi
+	}
+	return i
+}
+
+// IntervalFromPointPair returns the minimal interval containing the two given points.
+// Both arguments must be in [-π,π].
+func IntervalFromPointPair(a, b float64) Interval {
+	if a == -math.Pi {
+		a = math.Pi
+	}
+	if b == -math.Pi {
+		b = math.Pi
+	}
+	if positiveDistance(a, b) <= math.Pi {
+		return Interval{a, b}
+	}
+	return Interval{b, a}
+}
+
+// EmptyInterval returns an empty interval.
+func EmptyInterval() Interval { return Interval{math.Pi, -math.Pi} }
+
+// FullInterval returns a full interval.
+func FullInterval() Interval { return Interval{-math.Pi, math.Pi} }
+
+// IsValid reports whether the interval is valid.
+func (i Interval) IsValid() bool {
+	return (math.Abs(i.Lo) <= math.Pi && math.Abs(i.Hi) <= math.Pi &&
+		!(i.Lo == -math.Pi && i.Hi != math.Pi) &&
+		!(i.Hi == -math.Pi && i.Lo != math.Pi))
+}
+
+// IsFull reports whether the interval is full.
+func (i Interval) IsFull() bool { return i.Lo == -math.Pi && i.Hi == math.Pi }
+
+// IsEmpty reports whether the interval is empty.
+func (i Interval) IsEmpty() bool { return i.Lo == math.Pi && i.Hi == -math.Pi }
+
+// IsInverted reports whether the interval is inverted; that is, whether Lo > Hi.
+func (i Interval) IsInverted() bool { return i.Lo > i.Hi }
+
+// Invert returns the interval with endpoints swapped.
+func (i Interval) Invert() Interval {
+	return Interval{i.Hi, i.Lo}
+}
+
+// Center returns the midpoint of the interval.
+// It is undefined for full and empty intervals.
+func (i Interval) Center() float64 {
+	c := 0.5 * (i.Lo + i.Hi)
+	if !i.IsInverted() {
+		return c
+	}
+	if c <= 0 {
+		return c + math.Pi
+	}
+	return c - math.Pi
+}
+
+// Length returns the length of the interval.
+// The length of an empty interval is negative.
+func (i Interval) Length() float64 {
+	l := i.Hi - i.Lo
+	if l >= 0 {
+		return l
+	}
+	l += 2 * math.Pi
+	if l > 0 {
+		return l
+	}
+	return -1
+}
+
+// Assumes p ∈ (-π,π].
+func (i Interval) fastContains(p float64) bool {
+	if i.IsInverted() {
+		return (p >= i.Lo || p <= i.Hi) && !i.IsEmpty()
+	}
+	return p >= i.Lo && p <= i.Hi
+}
+
+// Contains returns true iff the interval contains p.
+// Assumes p ∈ [-π,π].
+func (i Interval) Contains(p float64) bool {
+	if p == -math.Pi {
+		p = math.Pi
+	}
+	return i.fastContains(p)
+}
+
+// ContainsInterval returns true iff the interval contains oi.
+func (i Interval) ContainsInterval(oi Interval) bool {
+	if i.IsInverted() {
+		if oi.IsInverted() {
+			return oi.Lo >= i.Lo && oi.Hi <= i.Hi
+		}
+		return (oi.Lo >= i.Lo || oi.Hi <= i.Hi) && !i.IsEmpty()
+	}
+	if oi.IsInverted() {
+		return i.IsFull() || oi.IsEmpty()
+	}
+	return oi.Lo >= i.Lo && oi.Hi <= i.Hi
+}
+
+// InteriorContains returns true iff the interior of the interval contains p.
+// Assumes p ∈ [-π,π].
+func (i Interval) InteriorContains(p float64) bool {
+	if p == -math.Pi {
+		p = math.Pi
+	}
+	if i.IsInverted() {
+		return p > i.Lo || p < i.Hi
+	}
+	return (p > i.Lo && p < i.Hi) || i.IsFull()
+}
+
+// InteriorContainsInterval returns true iff the interior of the interval contains oi.
+func (i Interval) InteriorContainsInterval(oi Interval) bool {
+	if i.IsInverted() {
+		if oi.IsInverted() {
+			return (oi.Lo > i.Lo && oi.Hi < i.Hi) || oi.IsEmpty()
+		}
+		return oi.Lo > i.Lo || oi.Hi < i.Hi
+	}
+	if oi.IsInverted() {
+		return i.IsFull() || oi.IsEmpty()
+	}
+	return (oi.Lo > i.Lo && oi.Hi < i.Hi) || i.IsFull()
+}
+
+// Intersects returns true iff the interval contains any points in common with oi.
+func (i Interval) Intersects(oi Interval) bool {
+	if i.IsEmpty() || oi.IsEmpty() {
+		return false
+	}
+	if i.IsInverted() {
+		return oi.IsInverted() || oi.Lo <= i.Hi || oi.Hi >= i.Lo
+	}
+	if oi.IsInverted() {
+		return oi.Lo <= i.Hi || oi.Hi >= i.Lo
+	}
+	return oi.Lo <= i.Hi && oi.Hi >= i.Lo
+}
+
+// InteriorIntersects returns true iff the interior of the interval contains any points in common with oi, including the latter's boundary.
+func (i Interval) InteriorIntersects(oi Interval) bool {
+	if i.IsEmpty() || oi.IsEmpty() || i.Lo == i.Hi {
+		return false
+	}
+	if i.IsInverted() {
+		return oi.IsInverted() || oi.Lo < i.Hi || oi.Hi > i.Lo
+	}
+	if oi.IsInverted() {
+		return oi.Lo < i.Hi || oi.Hi > i.Lo
+	}
+	return (oi.Lo < i.Hi && oi.Hi > i.Lo) || i.IsFull()
+}
+
+// Compute distance from a to b in [0,2π], in a numerically stable way.
+func positiveDistance(a, b float64) float64 {
+	d := b - a
+	if d >= 0 {
+		return d
+	}
+	return (b + math.Pi) - (a - math.Pi)
+}
+
+// Union returns the smallest interval that contains both the interval and oi.
+func (i Interval) Union(oi Interval) Interval {
+	if oi.IsEmpty() {
+		return i
+	}
+	if i.fastContains(oi.Lo) {
+		if i.fastContains(oi.Hi) {
+			// Either oi ⊂ i, or i ∪ oi is the full interval.
+			if i.ContainsInterval(oi) {
+				return i
+			}
+			return FullInterval()
+		}
+		return Interval{i.Lo, oi.Hi}
+	}
+	if i.fastContains(oi.Hi) {
+		return Interval{oi.Lo, i.Hi}
+	}
+
+	// Neither endpoint of oi is in i. Either i ⊂ oi, or i and oi are disjoint.
+	if i.IsEmpty() || oi.fastContains(i.Lo) {
+		return oi
+	}
+
+	// This is the only hard case where we need to find the closest pair of endpoints.
+	if positiveDistance(oi.Hi, i.Lo) < positiveDistance(i.Hi, oi.Lo) {
+		return Interval{oi.Lo, i.Hi}
+	}
+	return Interval{i.Lo, oi.Hi}
+}
+
+// Intersection returns the smallest interval that contains the intersection of the interval and oi.
+func (i Interval) Intersection(oi Interval) Interval {
+	if oi.IsEmpty() {
+		return EmptyInterval()
+	}
+	if i.fastContains(oi.Lo) {
+		if i.fastContains(oi.Hi) {
+			// Either oi ⊂ i, or i and oi intersect twice. Neither are empty.
+			// In the first case we want to return i (which is shorter than oi).
+			// In the second case one of them is inverted, and the smallest interval
+			// that covers the two disjoint pieces is the shorter of i and oi.
+			// We thus want to pick the shorter of i and oi in both cases.
+			if oi.Length() < i.Length() {
+				return oi
+			}
+			return i
+		}
+		return Interval{oi.Lo, i.Hi}
+	}
+	if i.fastContains(oi.Hi) {
+		return Interval{i.Lo, oi.Hi}
+	}
+
+	// Neither endpoint of oi is in i. Either i ⊂ oi, or i and oi are disjoint.
+	if oi.fastContains(i.Lo) {
+		return i
+	}
+	return EmptyInterval()
+}
+
+// AddPoint returns the interval expanded by the minimum amount necessary such
+// that it contains the given point "p" (an angle in the range [-π, π]).
+func (i Interval) AddPoint(p float64) Interval {
+	if math.Abs(p) > math.Pi {
+		return i
+	}
+	if p == -math.Pi {
+		p = math.Pi
+	}
+	if i.fastContains(p) {
+		return i
+	}
+	if i.IsEmpty() {
+		return Interval{p, p}
+	}
+	if positiveDistance(p, i.Lo) < positiveDistance(i.Hi, p) {
+		return Interval{p, i.Hi}
+	}
+	return Interval{i.Lo, p}
+}
+
+// Define the maximum rounding error for arithmetic operations. Depending on the
+// platform the mantissa precision may be different than others, so we choose to
+// use specific values to be consistent across all.
+// The values come from the C++ implementation.
+var (
+	// epsilon is a small number that represents a reasonable level of noise between two
+	// values that can be considered to be equal.
+	epsilon = 1e-15
+	// dblEpsilon is a smaller number for values that require more precision.
+	dblEpsilon = 2.220446049e-16
+)
+
+// Expanded returns an interval that has been expanded on each side by margin.
+// If margin is negative, then the function shrinks the interval on
+// each side by margin instead. The resulting interval may be empty or
+// full. Any expansion (positive or negative) of a full interval remains
+// full, and any expansion of an empty interval remains empty.
+func (i Interval) Expanded(margin float64) Interval {
+	if margin >= 0 {
+		if i.IsEmpty() {
+			return i
+		}
+		// Check whether this interval will be full after expansion, allowing
+		// for a rounding error when computing each endpoint.
+		if i.Length()+2*margin+2*dblEpsilon >= 2*math.Pi {
+			return FullInterval()
+		}
+	} else {
+		if i.IsFull() {
+			return i
+		}
+		// Check whether this interval will be empty after expansion, allowing
+		// for a rounding error when computing each endpoint.
+		if i.Length()+2*margin-2*dblEpsilon <= 0 {
+			return EmptyInterval()
+		}
+	}
+	result := IntervalFromEndpoints(
+		math.Remainder(i.Lo-margin, 2*math.Pi),
+		math.Remainder(i.Hi+margin, 2*math.Pi),
+	)
+	if result.Lo <= -math.Pi {
+		result.Lo = math.Pi
+	}
+	return result
+}
+
+// ApproxEqual reports whether this interval can be transformed into the given
+// interval by moving each endpoint by at most ε, without the
+// endpoints crossing (which would invert the interval). Empty and full
+// intervals are considered to start at an arbitrary point on the unit circle,
+// so any interval with (length <= 2*ε) matches the empty interval, and
+// any interval with (length >= 2*π - 2*ε) matches the full interval.
+func (i Interval) ApproxEqual(other Interval) bool {
+	// Full and empty intervals require special cases because the endpoints
+	// are considered to be positioned arbitrarily.
+	if i.IsEmpty() {
+		return other.Length() <= 2*epsilon
+	}
+	if other.IsEmpty() {
+		return i.Length() <= 2*epsilon
+	}
+	if i.IsFull() {
+		return other.Length() >= 2*(math.Pi-epsilon)
+	}
+	if other.IsFull() {
+		return i.Length() >= 2*(math.Pi-epsilon)
+	}
+
+	// The purpose of the last test below is to verify that moving the endpoints
+	// does not invert the interval, e.g. [-1e20, 1e20] vs. [1e20, -1e20].
+	return (math.Abs(math.Remainder(other.Lo-i.Lo, 2*math.Pi)) <= epsilon &&
+		math.Abs(math.Remainder(other.Hi-i.Hi, 2*math.Pi)) <= epsilon &&
+		math.Abs(i.Length()-other.Length()) <= 2*epsilon)
+
+}
+
+func (i Interval) String() string {
+	// like "[%.7f, %.7f]"
+	return "[" + strconv.FormatFloat(i.Lo, 'f', 7, 64) + ", " + strconv.FormatFloat(i.Hi, 'f', 7, 64) + "]"
+}
+
+// Complement returns the complement of the interior of the interval. An interval and
+// its complement have the same boundary but do not share any interior
+// values. The complement operator is not a bijection, since the complement
+// of a singleton interval (containing a single value) is the same as the
+// complement of an empty interval.
+func (i Interval) Complement() Interval {
+	if i.Lo == i.Hi {
+		// Singleton. The interval just contains a single point.
+		return FullInterval()
+	}
+	// Handles empty and full.
+	return Interval{i.Hi, i.Lo}
+}
+
+// ComplementCenter returns the midpoint of the complement of the interval. For full and empty
+// intervals, the result is arbitrary. For a singleton interval (containing a
+// single point), the result is its antipodal point on S1.
+func (i Interval) ComplementCenter() float64 {
+	if i.Lo != i.Hi {
+		return i.Complement().Center()
+	}
+	// Singleton. The interval just contains a single point.
+	if i.Hi <= 0 {
+		return i.Hi + math.Pi
+	}
+	return i.Hi - math.Pi
+}
+
+// DirectedHausdorffDistance returns the Hausdorff distance to the given interval.
+// For two intervals i and y, this distance is defined by
+//     h(i, y) = max_{p in i} min_{q in y} d(p, q),
+// where d(.,.) is measured along S1.
+func (i Interval) DirectedHausdorffDistance(y Interval) Angle {
+	if y.ContainsInterval(i) {
+		return 0 // This includes the case i is empty.
+	}
+	if y.IsEmpty() {
+		return Angle(math.Pi) // maximum possible distance on s1.
+	}
+	yComplementCenter := y.ComplementCenter()
+	if i.Contains(yComplementCenter) {
+		return Angle(positiveDistance(y.Hi, yComplementCenter))
+	}
+
+	// The Hausdorff distance is realized by either two i.Hi endpoints or two
+	// i.Lo endpoints, whichever is farther apart.
+	hiHi := 0.0
+	if IntervalFromEndpoints(y.Hi, yComplementCenter).Contains(i.Hi) {
+		hiHi = positiveDistance(y.Hi, i.Hi)
+	}
+
+	loLo := 0.0
+	if IntervalFromEndpoints(yComplementCenter, y.Lo).Contains(i.Lo) {
+		loLo = positiveDistance(i.Lo, y.Lo)
+	}
+
+	return Angle(math.Max(hiHi, loLo))
+}
+
+// Project returns the closest point in the interval to the given point p.
+// The interval must be non-empty.
+func (i Interval) Project(p float64) float64 {
+	if p == -math.Pi {
+		p = math.Pi
+	}
+	if i.fastContains(p) {
+		return p
+	}
+	// Compute distance from p to each endpoint.
+	dlo := positiveDistance(p, i.Lo)
+	dhi := positiveDistance(i.Hi, p)
+	if dlo < dhi {
+		return i.Lo
+	}
+	return i.Hi
+}