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erfinv_test.cpp
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#include "erfinv.h"
#include <cassert>
#include <cmath>
#include <vector>
using namespace std;
////////////////////////////////////////////////////////////////////////////////
// data for testing (computed using wolfram alpha)
// A vector containing (x, expected erfinv, allowed error)
using TABLE = vector<tuple<long double, long double, long double>>;
// Nearly uniform samples of x from [-1, 1]
const TABLE uniform_data = {
{ -0.9999901234567890L, -3.12531209890571959826L, 1e-15L }, // 0
{ -0.9090817727272728L, -1.19541621600439254353L, 1e-16L }, // 1
{ -0.8181735454545455L, -0.94409535430005211436L, 1e-16L }, // 2
{ -0.7272653181818183L, -0.77554525438923442604L, 1e-16L }, // 3
{ -0.6363570909090909L, -0.64236795545430416665L, 1e-16L }, // 4
{ -0.5454488636363637L, -0.52880922364399673143L, 1e-16L }, // 5
{ -0.4545406363636364L, -0.42750127212741209472L, 1e-16L }, // 6
{ -0.3636324090909091L, -0.33430847448420056223L, 1e-16L }, // 7
{ -0.2727241818181818L, -0.24660460627491576384L, 1e-16L }, // 8
{ -0.1818159545454545L, -0.16255059170754568956L, 1e-17L }, // 9
{ -0.0909077272727272L, -0.08073997953126072744L, 1e-17L }, // 10
{ 0.00000050123456789L, 0.00000044420757003182L, 1e-19L }, // 11
{ 0.09090872727272725L, 0.08074087155438624655L, 1e-17L }, // 12
{ 0.18181695454545455L, 0.16255150166321581410L, 1e-17L }, // 13
{ 0.27272518181818184L, 0.24660554806942288638L, 1e-17L }, // 14
{ 0.36363340909090913L, 0.33430946550500629626L, 1e-16L }, // 15
{ 0.45454163636363636L, 0.42750233606374840004L, 1e-16L }, // 16
{ 0.54544986363636364L, 0.52881039581498761461L, 1e-16L }, // 17
{ 0.63635809090909090L, 0.64236929436345064007L, 1e-16L }, // 18
{ 0.72726631818181831L, 0.77554687157823653280L, 1e-16L }, // 19
{ 0.81817454545454562L, 0.94409751522390649338L, 1e-16L }, // 20
{ 0.90908277272727291L, 1.19541991566879908234L, 1e-16L }, // 21
{ 0.99999100123456789L, 3.13950543736986052401L, 1e-15L }, // 22
};
// Values of x very close to the asymptotes at x=+1 and x=-1
const TABLE close_to_1 = {
{ -0.99999999999L, -4.8129240673658227430L, 1e-09L },
{ -0.99999999990L, -4.5728249673894852787L, 1e-10L },
{ -0.99999999900L, -4.3200053849134452862L, 1e-11L },
{ 0.99999999900L, 4.3200053849134452862L, 1e-11L },
{ 0.99999999990L, 4.5728249673894852787L, 1e-10L },
{ 0.99999999999L, 4.8129240673658227430L, 1e-09L },
}; // size = 6
// The implementation uses functions to approximate erfinv in
// various intervals. This table contains the points where two
// different functions come together
const TABLE joining_points = {
{ 0.85000000000L, 1.0179024648320276436L, 1e-16 },
{ -0.85000000000L, -1.0179024648320276436L, 1e-16 },
// |x| is smaller than 1 - 2 * exp(-25)
{ 0.99999999997L, 4.6998353461721558307L, 1e-10 },
{ -0.99999999997L, -4.6998353461721558307L, 1e-10 },
// |x| is slightly larger than 1 - 2 * exp(-25)
{ 0.99999999998L, 4.7418744480446202994L, 1e-09 },
{ -0.99999999998L, -4.7418744480446202994L, 1e-09 },
}; // size = 6
////////////////////////////////////////////////////////////////////////////////
// Unit tests
#define ASSERT_INF(x, sign) \
do { \
assert(sign != 0); \
auto y = (x); \
if (sign > 0) { \
assert(isinf(y) && !signbit(y)); \
} else if (sign < 0) { \
assert(isinf(y) && signbit(y)); \
} \
} while (0)
#define ASSERT_NAN(x) assert(isnan(x))
void test_out_of_domain_values() {
ASSERT_NAN(erfinv(-2.0L));
ASSERT_INF(erfinv(-1.0L), -1);
ASSERT_INF(erfinv(1.0L), 1);
ASSERT_NAN(erfinv(2.0L));
}
#define ASSERT_ERFINV(table_entry) \
{ \
long double x, y, eps; \
tie(x, y, eps) = table_entry; \
assert(fabsl(erfinv(x) - y) < eps); \
}
void test_values_close_to_asymptotes() {
ASSERT_ERFINV(close_to_1[0]);
ASSERT_ERFINV(close_to_1[1]);
ASSERT_ERFINV(close_to_1[2]);
ASSERT_ERFINV(close_to_1[3]);
ASSERT_ERFINV(close_to_1[4]);
ASSERT_ERFINV(close_to_1[5]);
}
void test_piecewise_boundaries() {
ASSERT_ERFINV(joining_points[0]);
ASSERT_ERFINV(joining_points[1]);
ASSERT_ERFINV(joining_points[2]);
ASSERT_ERFINV(joining_points[3]);
ASSERT_ERFINV(joining_points[4]);
ASSERT_ERFINV(joining_points[5]);
}
void test_uniform_samples() {
ASSERT_ERFINV(uniform_data[0]);
ASSERT_ERFINV(uniform_data[1]);
ASSERT_ERFINV(uniform_data[2]);
ASSERT_ERFINV(uniform_data[3]);
ASSERT_ERFINV(uniform_data[4]);
ASSERT_ERFINV(uniform_data[5]);
ASSERT_ERFINV(uniform_data[6]);
ASSERT_ERFINV(uniform_data[7]);
ASSERT_ERFINV(uniform_data[8]);
ASSERT_ERFINV(uniform_data[9]);
ASSERT_ERFINV(uniform_data[10]);
ASSERT_ERFINV(uniform_data[11]);
ASSERT_ERFINV(uniform_data[12]);
ASSERT_ERFINV(uniform_data[13]);
ASSERT_ERFINV(uniform_data[14]);
ASSERT_ERFINV(uniform_data[15]);
ASSERT_ERFINV(uniform_data[16]);
ASSERT_ERFINV(uniform_data[17]);
ASSERT_ERFINV(uniform_data[18]);
ASSERT_ERFINV(uniform_data[19]);
ASSERT_ERFINV(uniform_data[20]);
ASSERT_ERFINV(uniform_data[21]);
ASSERT_ERFINV(uniform_data[22]);
}
#define DISABLE_ASSERT_ERFINV_WITH_NR(x) (void)0
#define ASSERT_ERFINV_WITH_NR(table_entry) \
{ \
long double x, y, eps; \
tie(x, y, eps) = table_entry; \
assert(fabsl(erfinv_refine(x, 1) - y) < 0.1 * eps); \
}
void test_erfinv_with_newton_raphson() {
// removing points at the extremeties as NR is unable
// to compute a better estimate for those points
DISABLE_ASSERT_ERFINV_WITH_NR(uniform_data[0]);
ASSERT_ERFINV_WITH_NR(uniform_data[1]);
ASSERT_ERFINV_WITH_NR(uniform_data[2]);
ASSERT_ERFINV_WITH_NR(uniform_data[3]);
ASSERT_ERFINV_WITH_NR(uniform_data[4]);
ASSERT_ERFINV_WITH_NR(uniform_data[5]);
ASSERT_ERFINV_WITH_NR(uniform_data[6]);
ASSERT_ERFINV_WITH_NR(uniform_data[7]);
ASSERT_ERFINV_WITH_NR(uniform_data[8]);
ASSERT_ERFINV_WITH_NR(uniform_data[9]);
ASSERT_ERFINV_WITH_NR(uniform_data[10]);
ASSERT_ERFINV_WITH_NR(uniform_data[11]);
ASSERT_ERFINV_WITH_NR(uniform_data[12]);
ASSERT_ERFINV_WITH_NR(uniform_data[13]);
ASSERT_ERFINV_WITH_NR(uniform_data[14]);
ASSERT_ERFINV_WITH_NR(uniform_data[15]);
ASSERT_ERFINV_WITH_NR(uniform_data[16]);
ASSERT_ERFINV_WITH_NR(uniform_data[17]);
ASSERT_ERFINV_WITH_NR(uniform_data[18]);
ASSERT_ERFINV_WITH_NR(uniform_data[19]);
ASSERT_ERFINV_WITH_NR(uniform_data[20]);
ASSERT_ERFINV_WITH_NR(uniform_data[21]);
DISABLE_ASSERT_ERFINV_WITH_NR(uniform_data[22]);
}
int main() {
test_out_of_domain_values();
test_values_close_to_asymptotes();
test_piecewise_boundaries();
test_uniform_samples();
test_erfinv_with_newton_raphson();
return 0;
}