static void EnumerateAllValues()
{
uint MAX = (1u << 12);
var values = new List <float>();
for (uint b = 0; b < MAX; b++)
{
fp12 f = new fp12((ushort)b);
if (f.is_nan || f.is_negative_infinity || f.is_positive_infinity)
{
continue;
}
if (f.__sign == 1)
{
continue;
}
values.Add((float)f);
}
values.Sort();
File.WriteAllText(
"/home/mc/fp12_values.txt",
string.Join(
Environment.NewLine,
values.Select(f => f.ToString("R")).ToArray()));
}
public void negation_works()
{
fp12 a = (fp12)0.01f;
fp12 negA = (fp12)(-0.01f);
Assert.Equal(negA, -a);
}
static void ReciprocalX()
{
// Draw using gnuplot> plot 'recX.txt' using 1:2, "" u 3:4
// set key autotitle columnheader
StringBuilder sb = new StringBuilder();
sb.Append("x float xfp12 fp12").AppendLine();
int POINTS_COUNT = 200;
float X_MIN = 0.01f, X_MAX = 0.3f;
for (int i = 0; i < POINTS_COUNT; i++)
{
float x = X_MIN + i * (X_MAX - X_MIN) / POINTS_COUNT;
// https://en.wikipedia.org/wiki/Chebyshev_polynomials
float r = 1.0f / x;
fp12 X = (fp12)x;
fp12 R = ((fp12)1.0f) / X;
sb.AppendFormat("{0} {1} {2} {3}", x, r, (float)X, (float)R).AppendLine();
}
File.WriteAllText("/home/mc/recX.txt", sb.ToString());
}
static void Chebyshev5()
{
// Draw using gnuplot> plot 'chart.txt' using 1:2, "" u 3:4
StringBuilder sb = new StringBuilder();
sb.Append("x float xfp12 fp12").AppendLine();
int POINTS_COUNT = 100;
for (int i = 0; i < POINTS_COUNT; i++)
{
float x = -1.0f + i * 2.0f / POINTS_COUNT;
// https://en.wikipedia.org/wiki/Chebyshev_polynomials
float c5 = 16 * pow(x, 5) - 20 * pow(x, 3) + 5 * x;
fp12 X = (fp12)x;
fp12 C5 = ((fp12)16.0f) * X * X * X * X * X - ((fp12)20.0f) * X * X * X + ((fp12)5.0f) * X;
sb.AppendFormat("{0} {1} {2} {3}", x, c5, (float)X, (float)C5).AppendLine();
}
File.WriteAllText("/home/mc/chart.txt", sb.ToString());
}
public void negative_infinity_is_recognized_as_negative_infinity()
{
fp12 x = fp12.NEGATIVE_INFINITY;
Assert.False(x.is_nan);
Assert.False(x.is_positive_infinity);
Assert.True(x.is_negative_infinity);
}
public void can_convert_finite_value()
{
fp12 x = (fp12)3.1415f;
float fx = (float)x;
// TODO: Check this is legit
Assert.Equal(3.140625f, fx);
}
public void conversion_should_round_to_next_value()
{
float s3 = -1.98412698298579493134e-04f;
fp12 S3 = (fp12)s3;
Assert.Equal((fp12)(-0.000244140625f), S3);
}
public void can_convert_min_positive_value()
{
fp12 x = fp12.MIN_POSITIVE_VALUE;
float fx = (float)x;
Assert.Equal(0.0001220703125f, fx);
}
public void can_convert_max_positive_value()
{
fp12 x = fp12.MAX_POSITIVE_VALUE;
float fx = (float)x;
Assert.Equal(255f, fx);
}
public void zero_converts_to_zero()
{
fp12 x = fp12.POSITIVE_ZERO;
float fx = (float)x;
Assert.Equal(0.0f, fx);
}
public void nan_is_recognized_as_nan()
{
fp12 x = fp12.NaN;
Assert.True(x.is_nan);
Assert.False(x.is_positive_infinity);
Assert.False(x.is_negative_infinity);
}
static void SinePolynomial()
{
float s1 = -1.66666666666666324348e-01f;
float s2 = 8.33333333332248946124e-03f;
float s3 = -1.98412698298579493134e-04f;
fp12 S1 = (fp12)s1;
fp12 S2 = (fp12)s2;
fp12 S3 = (fp12)s3;
S3 = fp12.POSITIVE_ZERO;
// x in [-pi/4; pi/4]
fp12 sine(fp12 x)
{
fp12 x2 = x * x;
fp12 x3 = x2 * x;
fp12 sine_aprox = x + x3 * (S1 + x2 * (S2 + x2 * S3));
return(sine_aprox);
}
float sine_float(float x)
{
float x2 = x * x;
float x3 = x2 * x;
float sine_aprox = x + x3 * (s1 + x2 * (s2 + x2 * s3));
return(sine_aprox);
}
StringBuilder sb = new StringBuilder();
sb.Append("x float xfp12 fp12").AppendLine();
int POINTS_COUNT = 200;
float X_MIN = -0.7854f, X_MAX = 0.7854f * 2;
for (int i = 0; i < POINTS_COUNT; i++)
{
float x = X_MIN + i * (X_MAX - X_MIN) / POINTS_COUNT;
// https://en.wikipedia.org/wiki/Chebyshev_polynomials
float sin = sine_float(x);
fp12 X = (fp12)x;
fp12 R = sine(X);
sb.AppendFormat("{0} {1} {2} {3}", x, sin, (float)X, (float)R).AppendLine();
}
File.WriteAllText("/home/mc/sine.txt", sb.ToString());
}
public void abs_works()
{
fp12 m3 = (fp12)(-3.0f);
fp12 m3abs = m3.abs();
Assert.Equal((fp12)3.0f, m3abs);
m3abs = m3abs.abs();
Assert.Equal((fp12)3.0f, m3abs);
}
public void bug_wrong_normalization_after_addition()
{
fp12 a = (fp12)0.01f;
fp12 b = (fp12)0.00390625f;
fp12 result = a + b;
fp12 expected = (fp12)0.01390625f;
Assert.Equal(expected, result);
}
public void division_bug()
{
// x 1/x fpX fp1/X
// 0.0303 33.0033 0.03027344 48.5
// 0.03175 31.49606 0.03173828 31.75
fp12 x = (fp12)0.0303f;
fp12 one = ((fp12)1.0f);
fp12 rx = one / x;
Assert.True(rx < ((fp12)35.0f));
}
public void subtraction_works()
{
fp12 n1 = (fp12)1.0f;
fp12 n2 = (fp12)2.0f;
fp12 n3 = (fp12)3.0f;
fp12 n8 = (fp12)8.0f;
fp12 n9 = (fp12)9.0f;
Assert.Equal(n1, n2 - n1);
Assert.Equal(n3, n8 - n3 - n2);
Assert.Equal(n8, n9 - n1);
Assert.Equal(fp12.POSITIVE_ZERO, n9 - n3 - n2 - n1 - n2 - n1);
}
public void operator_plus_works()
{
fp12 n1 = (fp12)1.0f;
fp12 n2 = (fp12)2.0f;
fp12 n3 = (fp12)3.0f;
fp12 n8 = (fp12)8.0f;
fp12 n9 = (fp12)9.0f;
Assert.Equal(n3, n1 + n2);
Assert.Equal(n3, n1 + n1 + n1);
Assert.Equal(n9, n8 + n1);
Assert.Equal(n9, n3 + n2 + n1 + n2 + n1);
}
public void sign_changes_are_properly_handled()
{
Assert.Equal((fp12)1.0f, (fp12)(-0.5f) - (fp12)(-1.5));
float x = -0.5f;
fp12 xfp12 = (fp12)x;
fp12 _4_x3 = ((fp12)4.0f) * xfp12 * xfp12 * xfp12;
Assert.Equal((fp12)(-0.5f), _4_x3);
fp12 _3x = ((fp12)3.0f) * xfp12;
Assert.Equal((fp12)(-1.5f), _3x);
fp12 c3fp12 = _4_x3 - _3x;
Assert.Equal((fp12)1f, c3fp12);
}
public void equals_works()
{
fp12 pi = (fp12)3.14159;
fp12 pi2 = (fp12)3.14159;
fp12 e = (fp12)2.7183;
Assert.True(pi == pi2);
Assert.True(e == e);
Assert.False(e == pi);
Assert.False(pi == e);
Assert.False(pi == fp12.NaN);
Assert.False(fp12.NaN == fp12.NaN);
Assert.True(fp12.POSTIVE_INFINITY == fp12.POSTIVE_INFINITY);
Assert.False(fp12.POSTIVE_INFINITY == fp12.NEGATIVE_INFINITY);
Assert.True(fp12.POSITIVE_ZERO == fp12.POSITIVE_ZERO);
}
public void division_works()
{
fp12 n1 = (fp12)1.0f;
fp12 n2 = (fp12)2.0f;
fp12 n4 = (fp12)4.0f;
fp12 n0_5 = (fp12)0.5f;
fp12 n0_25 = (fp12)0.25f;
Assert.Equal(n1, n1 / n1);
Assert.Equal(n1, n1 / n1 / n1 / n1 / n1);
Assert.Equal(n2, n4 / n2);
Assert.Equal(n2, n4 / n1 / n2);
Assert.Equal(n1, n4 / n4);
Assert.Equal(n0_25, n1 / n4);
Assert.Equal(n2, n0_5 / n0_25);
Assert.Equal(n4, n1 / n0_25);
}
public void multiplication_works()
{
fp12 n1 = (fp12)1.0f;
fp12 n2 = (fp12)2.0f;
fp12 n4 = (fp12)4.0f;
fp12 n0_5 = (fp12)0.5f;
fp12 n0_25 = (fp12)0.25f;
Assert.Equal(n1, n1 * n1);
Assert.Equal(n1, n1 * n1 * n1 * n1 * n1);
Assert.Equal(n4, n2 * n2);
Assert.Equal(n4, n2 * n1 * n2);
Assert.Equal(n4, n4 * n1);
Assert.Equal(n4, n1 * n4);
Assert.Equal(n0_25, n0_5 * n0_5);
Assert.Equal(n1, n0_25 * n4);
}
public void sin_bug()
{
// 1.382304 0.9822379 1.375 0.96875
// 1.394085 0.9843733 1.390625 0.9921875
float x = 1.375f;
fp12 X = (fp12)x;
float x2 = x * x;
fp12 X2 = X * X;
float x3 = x * x2;
fp12 X3 = X * X2;
fp12 EXPECTED_X3 = (fp12)2.59960938f;
float s1 = -1.66666666666666324348e-01f;
float s2 = 8.33333333332248946124e-03f;
float s3 = -1.98412698298579493134e-04f;
fp12 S1 = (fp12)s1;
fp12 S2 = (fp12)s2;
fp12 S3 = (fp12)s3;
S1 = (fp12)(-0.166992188f);
var step1 = s2 + x2 * s3;
var STEP1 = S2 + X2 * S3;
var step2 = s1 + x2 * step1;
var STEP2 = S1 + X2 * STEP1;
var step3 = x + x3 * step2;
var STEP3 = X + X3 * STEP2;
Assert.Equal(0.980845451f, step3);
Assert.Equal(fp12.POSITIVE_ZERO, STEP3);
}
public void bug_small_value_converted_to_infinity()
{
fp12 b = (fp12)0.00390625559f;
Assert.False(b.is_positive_infinity);
}