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8
src/arith_uint256.h
View file

@ -6,6 +6,7 @@
#ifndef BITCOIN_ARITH_UINT256_H
#define BITCOIN_ARITH_UINT256_H
#include <compare>
#include <cstdint>
#include <cstring>
#include <limits>
@ -212,13 +213,8 @@ public:
friend inline base_uint operator<<(const base_uint& a, int shift) { return base_uint(a) <<= shift; }
friend inline base_uint operator*(const base_uint& a, uint32_t b) { return base_uint(a) *= b; }
friend inline bool operator==(const base_uint& a, const base_uint& b) { return memcmp(a.pn, b.pn, sizeof(a.pn)) == 0; }
friend inline bool operator!=(const base_uint& a, const base_uint& b) { return memcmp(a.pn, b.pn, sizeof(a.pn)) != 0; }
friend inline bool operator>(const base_uint& a, const base_uint& b) { return a.CompareTo(b) > 0; }
friend inline bool operator<(const base_uint& a, const base_uint& b) { return a.CompareTo(b) < 0; }
friend inline bool operator>=(const base_uint& a, const base_uint& b) { return a.CompareTo(b) >= 0; }
friend inline bool operator<=(const base_uint& a, const base_uint& b) { return a.CompareTo(b) <= 0; }
friend inline std::strong_ordering operator<=>(const base_uint& a, const base_uint& b) { return a.CompareTo(b) <=> 0; }
friend inline bool operator==(const base_uint& a, uint64_t b) { return a.EqualTo(b); }
friend inline bool operator!=(const base_uint& a, uint64_t b) { return !a.EqualTo(b); }
/** Hex encoding of the number (with the most significant digits first). */
std::string GetHex() const;

70
src/test/feefrac_tests.cpp
View file

@ -15,7 +15,45 @@ BOOST_AUTO_TEST_CASE(feefrac_operators)
FeeFrac sum{1500, 400};
FeeFrac diff{500, -200};
FeeFrac empty{0, 0};
[[maybe_unused]] FeeFrac zero_fee{0, 1}; // zero-fee allowed
FeeFrac zero_fee{0, 1}; // zero-fee allowed
BOOST_CHECK_EQUAL(zero_fee.EvaluateFeeDown(0), 0);
BOOST_CHECK_EQUAL(zero_fee.EvaluateFeeDown(1), 0);
BOOST_CHECK_EQUAL(zero_fee.EvaluateFeeDown(1000000), 0);
BOOST_CHECK_EQUAL(zero_fee.EvaluateFeeDown(0x7fffffff), 0);
BOOST_CHECK_EQUAL(zero_fee.EvaluateFeeUp(0), 0);
BOOST_CHECK_EQUAL(zero_fee.EvaluateFeeUp(1), 0);
BOOST_CHECK_EQUAL(zero_fee.EvaluateFeeUp(1000000), 0);
BOOST_CHECK_EQUAL(zero_fee.EvaluateFeeUp(0x7fffffff), 0);
BOOST_CHECK_EQUAL(p1.EvaluateFeeDown(0), 0);
BOOST_CHECK_EQUAL(p1.EvaluateFeeDown(1), 10);
BOOST_CHECK_EQUAL(p1.EvaluateFeeDown(100000000), 1000000000);
BOOST_CHECK_EQUAL(p1.EvaluateFeeDown(0x7fffffff), int64_t(0x7fffffff) * 10);
BOOST_CHECK_EQUAL(p1.EvaluateFeeUp(0), 0);
BOOST_CHECK_EQUAL(p1.EvaluateFeeUp(1), 10);
BOOST_CHECK_EQUAL(p1.EvaluateFeeUp(100000000), 1000000000);
BOOST_CHECK_EQUAL(p1.EvaluateFeeUp(0x7fffffff), int64_t(0x7fffffff) * 10);
FeeFrac neg{-1001, 100};
BOOST_CHECK_EQUAL(neg.EvaluateFeeDown(0), 0);
BOOST_CHECK_EQUAL(neg.EvaluateFeeDown(1), -11);
BOOST_CHECK_EQUAL(neg.EvaluateFeeDown(2), -21);
BOOST_CHECK_EQUAL(neg.EvaluateFeeDown(3), -31);
BOOST_CHECK_EQUAL(neg.EvaluateFeeDown(100), -1001);
BOOST_CHECK_EQUAL(neg.EvaluateFeeDown(101), -1012);
BOOST_CHECK_EQUAL(neg.EvaluateFeeDown(100000000), -1001000000);
BOOST_CHECK_EQUAL(neg.EvaluateFeeDown(100000001), -1001000011);
BOOST_CHECK_EQUAL(neg.EvaluateFeeDown(0x7fffffff), -21496311307);
BOOST_CHECK_EQUAL(neg.EvaluateFeeUp(0), 0);
BOOST_CHECK_EQUAL(neg.EvaluateFeeUp(1), -10);
BOOST_CHECK_EQUAL(neg.EvaluateFeeUp(2), -20);
BOOST_CHECK_EQUAL(neg.EvaluateFeeUp(3), -30);
BOOST_CHECK_EQUAL(neg.EvaluateFeeUp(100), -1001);
BOOST_CHECK_EQUAL(neg.EvaluateFeeUp(101), -1011);
BOOST_CHECK_EQUAL(neg.EvaluateFeeUp(100000000), -1001000000);
BOOST_CHECK_EQUAL(neg.EvaluateFeeUp(100000001), -1001000010);
BOOST_CHECK_EQUAL(neg.EvaluateFeeUp(0x7fffffff), -21496311306);
BOOST_CHECK(empty == FeeFrac{}); // same as no-args
@ -67,6 +105,23 @@ BOOST_AUTO_TEST_CASE(feefrac_operators)
BOOST_CHECK(oversized_1 << oversized_2);
BOOST_CHECK(oversized_1 != oversized_2);
BOOST_CHECK_EQUAL(oversized_1.EvaluateFeeDown(0), 0);
BOOST_CHECK_EQUAL(oversized_1.EvaluateFeeDown(1), 1152921);
BOOST_CHECK_EQUAL(oversized_1.EvaluateFeeDown(2), 2305843);
BOOST_CHECK_EQUAL(oversized_1.EvaluateFeeDown(1548031267), 1784758530396540);
BOOST_CHECK_EQUAL(oversized_1.EvaluateFeeUp(0), 0);
BOOST_CHECK_EQUAL(oversized_1.EvaluateFeeUp(1), 1152922);
BOOST_CHECK_EQUAL(oversized_1.EvaluateFeeUp(2), 2305843);
BOOST_CHECK_EQUAL(oversized_1.EvaluateFeeUp(1548031267), 1784758530396541);
// Test cases on the threshold where FeeFrac::Evaluate start using Mul/Div.
BOOST_CHECK_EQUAL(FeeFrac(0x1ffffffff, 123456789).EvaluateFeeDown(98765432), 6871947728);
BOOST_CHECK_EQUAL(FeeFrac(0x200000000, 123456789).EvaluateFeeDown(98765432), 6871947729);
BOOST_CHECK_EQUAL(FeeFrac(0x200000001, 123456789).EvaluateFeeDown(98765432), 6871947730);
BOOST_CHECK_EQUAL(FeeFrac(0x1ffffffff, 123456789).EvaluateFeeUp(98765432), 6871947729);
BOOST_CHECK_EQUAL(FeeFrac(0x200000000, 123456789).EvaluateFeeUp(98765432), 6871947730);
BOOST_CHECK_EQUAL(FeeFrac(0x200000001, 123456789).EvaluateFeeUp(98765432), 6871947731);
// Tests paths that use double arithmetic
FeeFrac busted{(static_cast<int64_t>(INT32_MAX)) + 1, INT32_MAX};
BOOST_CHECK(!(busted < busted));
@ -77,6 +132,19 @@ BOOST_AUTO_TEST_CASE(feefrac_operators)
BOOST_CHECK(max_fee <= max_fee);
BOOST_CHECK(max_fee >= max_fee);
BOOST_CHECK_EQUAL(max_fee.EvaluateFeeDown(0), 0);
BOOST_CHECK_EQUAL(max_fee.EvaluateFeeDown(1), 977888);
BOOST_CHECK_EQUAL(max_fee.EvaluateFeeDown(2), 1955777);
BOOST_CHECK_EQUAL(max_fee.EvaluateFeeDown(3), 2933666);
BOOST_CHECK_EQUAL(max_fee.EvaluateFeeDown(1256796054), 1229006664189047);
BOOST_CHECK_EQUAL(max_fee.EvaluateFeeDown(INT32_MAX), 2100000000000000);
BOOST_CHECK_EQUAL(max_fee.EvaluateFeeUp(0), 0);
BOOST_CHECK_EQUAL(max_fee.EvaluateFeeUp(1), 977889);
BOOST_CHECK_EQUAL(max_fee.EvaluateFeeUp(2), 1955778);
BOOST_CHECK_EQUAL(max_fee.EvaluateFeeUp(3), 2933667);
BOOST_CHECK_EQUAL(max_fee.EvaluateFeeUp(1256796054), 1229006664189048);
BOOST_CHECK_EQUAL(max_fee.EvaluateFeeUp(INT32_MAX), 2100000000000000);
FeeFrac max_fee2{1, 1};
BOOST_CHECK(max_fee >= max_fee2);

200
src/test/fuzz/feefrac.cpp
View file

@ -2,54 +2,48 @@
// Distributed under the MIT software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#include <arith_uint256.h>
#include <policy/feerate.h>
#include <util/feefrac.h>
#include <test/fuzz/FuzzedDataProvider.h>
#include <test/fuzz/fuzz.h>
#include <test/fuzz/util.h>
#include <compare>
#include <cmath>
#include <cstdint>
#include <iostream>
namespace {
/** Compute a * b, represented in 4x32 bits, highest limb first. */
std::array<uint32_t, 4> Mul128(uint64_t a, uint64_t b)
/** The maximum absolute value of an int64_t, as an arith_uint256 (2^63). */
const auto MAX_ABS_INT64 = arith_uint256{1} << 63;
/** Construct an arith_uint256 whose value equals abs(x). */
arith_uint256 Abs256(int64_t x)
{
std::array<uint32_t, 4> ret{0, 0, 0, 0};
/** Perform ret += v << (32 * pos), at 128-bit precision. */
auto add_fn = [&](uint64_t v, int pos) {
uint64_t accum{0};
for (int i = 0; i + pos < 4; ++i) {
// Add current value at limb pos in ret.
accum += ret[3 - pos - i];
// Add low or high half of v.
if (i == 0) accum += v & 0xffffffff;
if (i == 1) accum += v >> 32;
// Store lower half of result in limb pos in ret.
ret[3 - pos - i] = accum & 0xffffffff;
// Leave carry in accum.
accum >>= 32;
if (x >= 0) {
// For positive numbers, pass through the value.
return arith_uint256{static_cast<uint64_t>(x)};
} else if (x > std::numeric_limits<int64_t>::min()) {
// For negative numbers, negate first.
return arith_uint256{static_cast<uint64_t>(-x)};
} else {
// Special case for x == -2^63 (for which -x results in integer overflow).
return MAX_ABS_INT64;
}
// Make sure no overflow.
assert(accum == 0);
};
// Multiply the 4 individual limbs (schoolbook multiply, with base 2^32).
add_fn((a & 0xffffffff) * (b & 0xffffffff), 0);
add_fn((a >> 32) * (b & 0xffffffff), 1);
add_fn((a & 0xffffffff) * (b >> 32), 1);
add_fn((a >> 32) * (b >> 32), 2);
return ret;
}
/* comparison helper for std::array */
std::strong_ordering compare_arrays(const std::array<uint32_t, 4>& a, const std::array<uint32_t, 4>& b) {
for (size_t i = 0; i < a.size(); ++i) {
if (a[i] != b[i]) return a[i] <=> b[i];
/** Construct an arith_uint256 whose value equals abs(x), for 96-bit x. */
arith_uint256 Abs256(std::pair<int64_t, uint32_t> x)
{
if (x.first >= 0) {
// x.first and x.second are both non-negative; sum their absolute values.
return (Abs256(x.first) << 32) + Abs256(x.second);
} else {
// x.first is negative and x.second is non-negative; subtract the absolute values.
return (Abs256(x.first) << 32) - Abs256(x.second);
}
return std::strong_ordering::equal;
}
std::strong_ordering MulCompare(int64_t a1, int64_t a2, int64_t b1, int64_t b2)
@ -59,23 +53,14 @@ std::strong_ordering MulCompare(int64_t a1, int64_t a2, int64_t b1, int64_t b2)
int sign_b = (b1 == 0 ? 0 : b1 < 0 ? -1 : 1) * (b2 == 0 ? 0 : b2 < 0 ? -1 : 1);
if (sign_a != sign_b) return sign_a <=> sign_b;
// Compute absolute values.
uint64_t abs_a1 = static_cast<uint64_t>(a1), abs_a2 = static_cast<uint64_t>(a2);
uint64_t abs_b1 = static_cast<uint64_t>(b1), abs_b2 = static_cast<uint64_t>(b2);
// Use (~x + 1) instead of the equivalent (-x) to silence the linter; mod 2^64 behavior is
// intentional here.
if (a1 < 0) abs_a1 = ~abs_a1 + 1;
if (a2 < 0) abs_a2 = ~abs_a2 + 1;
if (b1 < 0) abs_b1 = ~abs_b1 + 1;
if (b2 < 0) abs_b2 = ~abs_b2 + 1;
// Compute absolute values of products.
auto mul_abs_a = Abs256(a1) * Abs256(a2), mul_abs_b = Abs256(b1) * Abs256(b2);
// Compute products of absolute values.
auto mul_abs_a = Mul128(abs_a1, abs_a2);
auto mul_abs_b = Mul128(abs_b1, abs_b2);
if (sign_a < 0) {
return compare_arrays(mul_abs_b, mul_abs_a);
return mul_abs_b <=> mul_abs_a;
} else {
return compare_arrays(mul_abs_a, mul_abs_b);
return mul_abs_a <=> mul_abs_b;
}
}
@ -121,3 +106,128 @@ FUZZ_TARGET(feefrac)
assert((fr1 == fr2) == std::is_eq(cmp_total));
assert((fr1 != fr2) == std::is_neq(cmp_total));
}
FUZZ_TARGET(feefrac_div_fallback)
{
// Verify the behavior of FeeFrac::DivFallback over all possible inputs.
// Construct a 96-bit signed value num, a positive 31-bit value den, and rounding mode.
FuzzedDataProvider provider(buffer.data(), buffer.size());
auto num_high = provider.ConsumeIntegral<int64_t>();
auto num_low = provider.ConsumeIntegral<uint32_t>();
std::pair<int64_t, uint32_t> num{num_high, num_low};
auto den = provider.ConsumeIntegralInRange<int32_t>(1, std::numeric_limits<int32_t>::max());
auto round_down = provider.ConsumeBool();
// Predict the sign of the actual result.
bool is_negative = num_high < 0;
// Evaluate absolute value using arith_uint256. If the actual result is negative and we are
// rounding down, or positive and we are rounding up, the absolute value of the quotient is
// the rounded-up quotient of the absolute values.
auto num_abs = Abs256(num);
auto den_abs = Abs256(den);
auto quot_abs = (is_negative == round_down) ?
(num_abs + den_abs - 1) / den_abs :
num_abs / den_abs;
// If the result is not representable by an int64_t, bail out.
if ((is_negative && quot_abs > MAX_ABS_INT64) || (!is_negative && quot_abs >= MAX_ABS_INT64)) {
return;
}
// Verify the behavior of FeeFrac::DivFallback.
auto res = FeeFrac::DivFallback(num, den, round_down);
assert(res == 0 || (res < 0) == is_negative);
assert(Abs256(res) == quot_abs);
// Compare approximately with floating-point.
long double expect = round_down ? std::floor(num_high * 4294967296.0L + num_low) / den
: std::ceil(num_high * 4294967296.0L + num_low) / den;
// Expect to be accurate within 50 bits of precision, +- 1 sat.
if (expect == 0.0L) {
assert(res >= -1 && res <= 1);
} else if (expect > 0.0L) {
assert(res >= expect * 0.999999999999999L - 1.0L);
assert(res <= expect * 1.000000000000001L + 1.0L);
} else {
assert(res >= expect * 1.000000000000001L - 1.0L);
assert(res <= expect * 0.999999999999999L + 1.0L);
}
}
FUZZ_TARGET(feefrac_mul_div)
{
// Verify the behavior of:
// - The combination of FeeFrac::Mul + FeeFrac::Div.
// - The combination of FeeFrac::MulFallback + FeeFrac::DivFallback.
// - FeeFrac::Evaluate.
// Construct a 32-bit signed multiplicand, a 64-bit signed multiplicand, a positive 31-bit
// divisor, and a rounding mode.
FuzzedDataProvider provider(buffer.data(), buffer.size());
auto mul32 = provider.ConsumeIntegral<int32_t>();
auto mul64 = provider.ConsumeIntegral<int64_t>();
auto div = provider.ConsumeIntegralInRange<int32_t>(1, std::numeric_limits<int32_t>::max());
auto round_down = provider.ConsumeBool();
// Predict the sign of the overall result.
bool is_negative = ((mul32 < 0) && (mul64 > 0)) || ((mul32 > 0) && (mul64 < 0));
// Evaluate absolute value using arith_uint256. If the actual result is negative and we are
// rounding down or positive and we rounding up, the absolute value of the quotient is the
// rounded-up quotient of the absolute values.
auto prod_abs = Abs256(mul32) * Abs256(mul64);
auto div_abs = Abs256(div);
auto quot_abs = (is_negative == round_down) ?
(prod_abs + div_abs - 1) / div_abs :
prod_abs / div_abs;
// If the result is not representable by an int64_t, bail out.
if ((is_negative && quot_abs > MAX_ABS_INT64) || (!is_negative && quot_abs >= MAX_ABS_INT64)) {
// If 0 <= mul32 <= div, then the result is guaranteed to be representable. In the context
// of the Evaluate{Down,Up} calls below, this corresponds to 0 <= at_size <= feefrac.size.
assert(mul32 < 0 || mul32 > div);
return;
}
// Verify the behavior of FeeFrac::Mul + FeeFrac::Div.
auto res = FeeFrac::Div(FeeFrac::Mul(mul64, mul32), div, round_down);
assert(res == 0 || (res < 0) == is_negative);
assert(Abs256(res) == quot_abs);
// Verify the behavior of FeeFrac::MulFallback + FeeFrac::DivFallback.
auto res_fallback = FeeFrac::DivFallback(FeeFrac::MulFallback(mul64, mul32), div, round_down);
assert(res == res_fallback);
// Compare approximately with floating-point.
long double expect = round_down ? std::floor(static_cast<long double>(mul32) * mul64 / div)
: std::ceil(static_cast<long double>(mul32) * mul64 / div);
// Expect to be accurate within 50 bits of precision, +- 1 sat.
if (expect == 0.0L) {
assert(res >= -1 && res <= 1);
} else if (expect > 0.0L) {
assert(res >= expect * 0.999999999999999L - 1.0L);
assert(res <= expect * 1.000000000000001L + 1.0L);
} else {
assert(res >= expect * 1.000000000000001L - 1.0L);
assert(res <= expect * 0.999999999999999L + 1.0L);
}
// Verify the behavior of FeeFrac::Evaluate{Down,Up}.
if (mul32 >= 0) {
auto res_fee = round_down ?
FeeFrac{mul64, div}.EvaluateFeeDown(mul32) :
FeeFrac{mul64, div}.EvaluateFeeUp(mul32);
assert(res == res_fee);
// Compare approximately with CFeeRate.
if (mul64 <= std::numeric_limits<int64_t>::max() / 1000 &&
mul64 >= std::numeric_limits<int64_t>::min() / 1000 &&
quot_abs <= arith_uint256{std::numeric_limits<int64_t>::max() / 1000}) {
CFeeRate feerate(mul64, (uint32_t)div);
CAmount feerate_fee{feerate.GetFee(mul32)};
auto allowed_gap = static_cast<int64_t>(mul32 / 1000 + 3 + round_down);
assert(feerate_fee - res_fee >= -allowed_gap);
assert(feerate_fee - res_fee <= allowed_gap);
}
}
}

89
src/util/feefrac.h
View file

@ -37,27 +37,69 @@
*/
struct FeeFrac
{
/** Fallback version for Mul (see below).
*
* Separate to permit testing on platforms where it isn't actually needed.
*/
/** Helper function for 32*64 signed multiplication, returning an unspecified but totally
* ordered type. This is a fallback version, separate so it can be tested on platforms where
* it isn't actually needed. */
static inline std::pair<int64_t, uint32_t> MulFallback(int64_t a, int32_t b) noexcept
{
// Otherwise, emulate 96-bit multiplication using two 64-bit multiplies.
int64_t low = int64_t{static_cast<uint32_t>(a)} * b;
int64_t high = (a >> 32) * b;
return {high + (low >> 32), static_cast<uint32_t>(low)};
}
// Compute a * b, returning an unspecified but totally ordered type.
/** Helper function for 96/32 signed division, rounding towards negative infinity (if
* round_down) or positive infinity (if !round_down). This is a fallback version, separate so
* that it can be tested on platforms where it isn't actually needed.
*
* The exact behavior with negative n does not really matter, but this implementation chooses
* to be consistent for testability reasons.
*
* The result must fit in an int64_t, and d must be strictly positive. */
static inline int64_t DivFallback(std::pair<int64_t, uint32_t> n, int32_t d, bool round_down) noexcept
{
Assume(d > 0);
// Compute quot_high = n.first / d, so the result becomes
// (n.second + (n.first - quot_high * d) * 2**32) / d + (quot_high * 2**32), or
// (n.second + (n.first % d) * 2**32) / d + (quot_high * 2**32).
int64_t quot_high = n.first / d;
// Evaluate the parenthesized expression above, so the result becomes
// n_low / d + (quot_high * 2**32)
int64_t n_low = ((n.first % d) << 32) + n.second;
// Evaluate the division so the result becomes quot_low + quot_high * 2**32. It is possible
// that the / operator here rounds in the wrong direction (if n_low is not a multiple of
// size, and is (if round_down) negative, or (if !round_down) positive). If so, make a
// correction.
int64_t quot_low = n_low / d;
int32_t mod_low = n_low % d;
quot_low += (mod_low > 0) - (mod_low && round_down);
// Combine and return the result
return (quot_high << 32) + quot_low;
}
#ifdef __SIZEOF_INT128__
/** Helper function for 32*64 signed multiplication, returning an unspecified but totally
* ordered type. This is a version relying on __int128. */
static inline __int128 Mul(int64_t a, int32_t b) noexcept
{
// If __int128 is available, use 128-bit wide multiply.
return __int128{a} * b;
}
/** Helper function for 96/32 signed division, rounding towards negative infinity. This is a
* version relying on __int128.
*
* The result must fit in an int64_t, and d must be strictly positive. */
static inline int64_t Div(__int128 n, int32_t d, bool round_down) noexcept
{
Assume(d > 0);
// Compute the division.
int64_t quot = n / d;
int32_t mod = n % d;
// Correct result if the / operator above rounded in the wrong direction.
return quot + (mod > 0) - (mod && round_down);
}
#else
static constexpr auto Mul = MulFallback;
static constexpr auto Div = DivFallback;
#endif
int64_t fee;
@ -144,6 +186,39 @@ struct FeeFrac
std::swap(a.fee, b.fee);
std::swap(a.size, b.size);
}
/** Compute the fee for a given size `at_size` using this object's feerate.
*
* This effectively corresponds to evaluating (this->fee * at_size) / this->size, with the
* result rounded towards negative infinity (if RoundDown) or towards positive infinity
* (if !RoundDown).
*
* Requires this->size > 0, at_size >= 0, and that the correct result fits in a int64_t. This
* is guaranteed to be the case when 0 <= at_size <= this->size.
*/
template<bool RoundDown>
int64_t EvaluateFee(int32_t at_size) const noexcept
{
Assume(size > 0);
Assume(at_size >= 0);
if (fee >= 0 && fee < 0x200000000) [[likely]] {
// Common case where (this->fee * at_size) is guaranteed to fit in a uint64_t.
if constexpr (RoundDown) {
return (uint64_t(fee) * at_size) / uint32_t(size);
} else {
return (uint64_t(fee) * at_size + size - 1U) / uint32_t(size);
}
} else {
// Otherwise, use Mul and Div.
return Div(Mul(fee, at_size), size, RoundDown);
}
}
public:
/** Compute the fee for a given size `at_size` using this object's feerate, rounding down. */
int64_t EvaluateFeeDown(int32_t at_size) const noexcept { return EvaluateFee<true>(at_size); }
/** Compute the fee for a given size `at_size` using this object's feerate, rounding up. */
int64_t EvaluateFeeUp(int32_t at_size) const noexcept { return EvaluateFee<false>(at_size); }
};
/** Compare the feerate diagrams implied by the provided sorted chunks data.