Add Pow and Ln functions

Author: Bartl

LICENSE.txt

@@ -19,4 +19,16 @@ Permission is hereby granted, free of charge, to any person obtaining a copy of
 
 The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
 
-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+This project uses code from the log2fix library, which is under the following license:
+
+The MIT License (MIT)
+
+Copyright (c) 2015 Dan Moulding
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

src/Fix64.cs

@@ -2,8 +2,7 @@
 using System.IO;
 using System.Runtime.CompilerServices;
 
-namespace FixMath.NET
-{
+namespace FixMath.NET {
 
     /// <summary>
     /// Represents a Q31.32 fixed-point number.
@@ -25,6 +24,9 @@ public partial struct Fix64 : IEquatable<Fix64>, IComparable<Fix64> {
         public static readonly Fix64 PiTimes2 = new Fix64(PI_TIMES_2);
         public static readonly Fix64 PiInv = (Fix64)0.3183098861837906715377675267M;
         public static readonly Fix64 PiOver2Inv = (Fix64)0.6366197723675813430755350535M;
+        static readonly Fix64 Log2Max = new Fix64(LOG2MAX);
+        static readonly Fix64 Log2Min = new Fix64(LOG2MIN);
+        static readonly Fix64 Ln2 = new Fix64(LN2);
 
         static readonly Fix64 LutInterval = (Fix64)(LUT_SIZE - 1) / PiOver2;
         const long MAX_VALUE = long.MaxValue;
@@ -35,6 +37,9 @@ public partial struct Fix64 : IEquatable<Fix64>, IComparable<Fix64> {
         const long PI_TIMES_2 = 0x6487ED511;
         const long PI = 0x3243F6A88;
         const long PI_OVER_2 = 0x1921FB544;
+        const long LN2 = 0xB17217F7;
+        const long LOG2MAX = 0x1F00000000;
+        const long LOG2MIN = -0x2000000000;
         const int LUT_SIZE = (int)(PI_OVER_2 >> 15);
 
         /// <summary>
@@ -206,7 +211,7 @@ static long AddOverflowHelper(long x, long y, ref bool overflow) {
             // then this means the result overflowed.
             var topCarry = hihi >> FRACTIONAL_PLACES;
             if (topCarry != 0 && topCarry != -1 /*&& xl != -17 && yl != -17*/) {
-                return opSignsEqual ? MaxValue : MinValue; 
+                return opSignsEqual ? MaxValue : MinValue;
             }
 
             // If signs differ, both operands' magnitudes are greater than 1,
@@ -257,7 +262,7 @@ public static Fix64 FastMul(Fix64 x, Fix64 y) {
             return new Fix64(sum);
         }
 
-        [MethodImpl(MethodImplOptions.AggressiveInlining)] 
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
         static int CountLeadingZeroes(ulong x) {
             int result = 0;
             while ((x & 0xF000000000000000) == 0) { result += 4; x <<= 4; }
@@ -318,7 +323,7 @@ static int CountLeadingZeroes(ulong x) {
 
         public static Fix64 operator %(Fix64 x, Fix64 y) {
             return new Fix64(
-                x.m_rawValue == MIN_VALUE & y.m_rawValue == -1 ? 
+                x.m_rawValue == MIN_VALUE & y.m_rawValue == -1 ?
                 0 :
                 x.m_rawValue % y.m_rawValue);
         }
@@ -359,6 +364,141 @@ public static Fix64 FastMod(Fix64 x, Fix64 y) {
             return x.m_rawValue <= y.m_rawValue;
         }
 
+        /// <summary>
+        /// Returns 2 raised to the specified power.
+        /// Provides at least 6 decimals of accuracy.
+        /// </summary>
+        internal static Fix64 Pow2(Fix64 x) {
+            if (x.RawValue == 0) {
+                return One;
+            }
+
+            // Avoid negative arguments by exploiting that exp(-x) = 1/exp(x).
+            bool neg = x.RawValue < 0;
+            if (neg) {
+                x = -x;
+            }
+
+            if (x == One) {
+                return neg ? One / (Fix64)2 : (Fix64)2;
+            }
+            if (x >= Log2Max) {
+                return neg ? One / MaxValue : MaxValue;
+            }
+            if (x <= Log2Min) {
+                return neg ? MaxValue : Zero;
+            }
+
+            /* The algorithm is based on the power series for exp(x):
+             * http://en.wikipedia.org/wiki/Exponential_function#Formal_definition
+             * 
+             * From term n, we get term n+1 by multiplying with x/n.
+             * When the sum term drops to zero, we can stop summing.
+             */
+
+            int integerPart = (int)Floor(x);
+            // Take fractional part of exponent
+            x = new Fix64(x.m_rawValue & 0x00000000FFFFFFFF);
+
+            var result = One;
+            var term = One;
+            int i = 1;
+            while (term.m_rawValue != 0) {
+                term = FastMul(FastMul(x, term), Ln2) / (Fix64)i;
+                result += term;
+                i++;
+            }
+
+            result = FromRaw(result.m_rawValue << integerPart);
+            if (neg) {
+                result = One / result;
+            }
+
+            return result;
+        }
+
+        /// <summary>
+        /// Returns the base-2 logarithm of a specified number.
+        /// Provides at least 9 decimals of accuracy.
+        /// </summary>
+        /// <exception cref="ArgumentOutOfRangeException">
+        /// The argument was non-positive
+        /// </exception>
+        internal static Fix64 Log2(Fix64 x) {
+            if (x.RawValue <= 0) {
+                throw new ArgumentOutOfRangeException("Non-positive value passed to Ln", "x");
+            }
+
+            // This implementation is based on Clay. S. Turner's fast binary logarithm
+            // algorithm (C. S. Turner,  "A Fast Binary Logarithm Algorithm", IEEE Signal
+            //     Processing Mag., pp. 124,140, Sep. 2010.)
+
+            long b = 1U << (FRACTIONAL_PLACES - 1);
+            long y = 0;
+
+            long rawX = x.m_rawValue;
+            while (rawX < ONE) {
+                rawX <<= 1;
+                y -= ONE;
+            }
+
+            while (rawX >= (ONE << 1)) {
+                rawX >>= 1;
+                y += ONE;
+            }
+
+            var z = new Fix64(rawX);
+
+            for (int i = 0; i < FRACTIONAL_PLACES; i++) {
+                z = FastMul(z, z);
+                if (z.m_rawValue >= (ONE << 1)) {
+                    z = new Fix64(z.m_rawValue >> 1);
+                    y += b;
+                }
+                b >>= 1;
+            }
+
+            return new Fix64(y);
+        }
+
+        /// <summary>
+        /// Returns the natural logarithm of a specified number.
+        /// Provides at least 7 decimals of accuracy.
+        /// </summary>
+        /// <exception cref="ArgumentOutOfRangeException">
+        /// The argument was non-positive
+        /// </exception>
+        public static Fix64 Ln(Fix64 x) {
+            return FastMul(Log2(x), Ln2);
+        }
+
+        /// <summary>
+        /// Returns a specified number raised to the specified power.
+        /// Provides about 5 digits of accuracy for the result.
+        /// </summary>
+        /// <exception cref="DivideByZeroException">
+        /// The base was zero, with a negative exponent
+        /// </exception>
+        /// <exception cref="ArgumentOutOfRangeException">
+        /// The base was negative, with a non-zero exponent
+        /// </exception>
+        public static Fix64 Pow(Fix64 b, Fix64 exp) {
+            if (b == One) {
+                return One;
+            }
+            if (exp.m_rawValue == 0) {
+                return One;
+            }
+            if (b.m_rawValue == 0) {
+                if (exp.m_rawValue < 0) {
+                    throw new DivideByZeroException();
+                }
+                return Zero;
+            }
+
+            Fix64 log2 = Log2(b);
+            return Pow2(exp * log2);
+        }
 
         /// <summary>
         /// Returns the square root of a specified number.
@@ -438,14 +578,14 @@ public static Fix64 Sin(Fix64 x) {
             // Find the two closest values in the LUT and perform linear interpolation
             // This is what kills the performance of this function on x86 - x64 is fine though
             var rawIndex = FastMul(clamped, LutInterval);
-            var roundedIndex = Round(rawIndex); 
+            var roundedIndex = Round(rawIndex);
             var indexError = FastSub(rawIndex, roundedIndex);
 
-            var nearestValue = new Fix64(SinLut[flipHorizontal ? 
-                SinLut.Length - 1 - (int)roundedIndex : 
+            var nearestValue = new Fix64(SinLut[flipHorizontal ?
+                SinLut.Length - 1 - (int)roundedIndex :
                 (int)roundedIndex]);
-            var secondNearestValue = new Fix64(SinLut[flipHorizontal ? 
-                SinLut.Length - 1 - (int)roundedIndex - Sign(indexError) : 
+            var secondNearestValue = new Fix64(SinLut[flipHorizontal ?
+                SinLut.Length - 1 - (int)roundedIndex - Sign(indexError) :
                 (int)roundedIndex + Sign(indexError)]);
 
             var delta = FastMul(indexError, FastAbs(FastSub(nearestValue, secondNearestValue))).m_rawValue;
@@ -475,7 +615,7 @@ public static Fix64 FastSin(Fix64 x) {
             return new Fix64(flipVertical ? -nearestValue : nearestValue);
         }
 
-        
+
         static long ClampSinValue(long angle, out bool flipHorizontal, out bool flipVertical) {
             var largePI = 7244019458077122842;
             // Obtained from ((Fix64)1686629713.065252369824872831112M).m_rawValue
@@ -486,8 +626,7 @@ static long ClampSinValue(long angle, out bool flipHorizontal, out bool flipVert
             // Whereas simply doing x % PI_TIMES_2 is the 2e-3 range.
 
             var clamped2Pi = angle;
-            for (int i = 0; i < 29; ++i)
-            {
+            for (int i = 0; i < 29; ++i) {
                 clamped2Pi %= (largePI >> i);
             }
             if (angle < 0) {

src/Properties/AssemblyInfo.cs

@@ -34,3 +34,6 @@
 // [assembly: AssemblyVersion("1.0.*")]
 [assembly: AssemblyVersion("1.0.0.0")]
 [assembly: AssemblyFileVersion("1.0.0.0")]
+
+// Allow internal methods to be tested
+[assembly: InternalsVisibleTo("Tests")]

tests/Fix64Tests.cs

@@ -361,6 +361,106 @@ public void Sqrt()
             }
         }
 
+        [Fact]
+        public void Log2()
+        {
+            double maxDelta = (double)(Fix64.Precision * 4);
+
+            for (int j = 0; j < m_testCases.Length; ++j)
+            {
+                var b = Fix64.FromRaw(m_testCases[j]);
+
+                if (b <= Fix64.Zero)
+                {
+                    Assert.Throws<ArgumentOutOfRangeException>(() => Fix64.Log2(b));
+                }
+                else
+                {
+                    var expected = Math.Log((double)b)/Math.Log(2);
+                    var actual = (double)Fix64.Log2(b);
+                    var delta = Math.Abs(expected - actual);
+
+                    Assert.True(delta <= maxDelta, string.Format("Ln({0}) = expected {1} but got {2}", b, expected, actual));
+                }
+            }
+        }
+
+        [Fact]
+        public void Ln()
+        {
+            double maxDelta = 0.00000001;
+
+            for (int j = 0; j < m_testCases.Length; ++j)
+            {
+                var b = Fix64.FromRaw(m_testCases[j]);
+
+                if (b <= Fix64.Zero)
+                {
+                    Assert.Throws<ArgumentOutOfRangeException>(() => Fix64.Ln(b));
+                }
+                else
+                {
+                    var expected = Math.Log((double)b);
+                    var actual = (double)Fix64.Ln(b);
+                    var delta = Math.Abs(expected - actual);
+
+                    Assert.True(delta <= maxDelta, string.Format("Ln({0}) = expected {1} but got {2}", b, expected, actual));
+                }
+            }
+        }
+
+        [Fact]
+        public void Pow2()
+        {
+            double maxDelta = 0.0000001;
+            for (int i = 0; i < m_testCases.Length; ++i)
+            {
+                var e = Fix64.FromRaw(m_testCases[i]);
+
+                var expected = Math.Min(Math.Pow(2, (double)e), (double)Fix64.MaxValue);
+                var actual = (double)Fix64.Pow2(e);
+                var delta = Math.Abs(expected - actual);
+
+                Assert.True(delta <= maxDelta, string.Format("Pow2({0}) = expected {1} but got {2}", e, expected, actual));
+            }
+        }
+
+        [Fact]
+        public void Pow()
+        {
+            for (int i = 0; i < m_testCases.Length; ++i)
+            {
+                var b = Fix64.FromRaw(m_testCases[i]);
+
+                for (int j = 0; j < m_testCases.Length; ++j)
+                {
+                    var e = Fix64.FromRaw(m_testCases[j]);
+
+                    if (b == Fix64.Zero && e < Fix64.Zero)
+                    {
+                        Assert.Throws<DivideByZeroException>(() => Fix64.Pow(b, e));
+                    }
+                    else if (b < Fix64.Zero && e != Fix64.Zero)
+                    {
+                        Assert.Throws<ArgumentOutOfRangeException>(() => Fix64.Pow(b, e));
+                    }
+                    else
+                    {
+                        var expected = e == Fix64.Zero ? 1 : b == Fix64.Zero ? 0 : Math.Min(Math.Pow((double)b, (double)e), (double)Fix64.MaxValue);
+
+                        // Absolute precision deteriorates with large result values, take this into account
+                        // Similarly, large exponents reduce precision, even if result is small.
+                        double maxDelta = Math.Abs((double)e) > 100000000 ? 0.5 : expected > 100000000 ? 10 : expected > 1000 ? 0.5 : 0.00001;
+
+                        var actual = (double)Fix64.Pow(b, e);
+                        var delta = Math.Abs(expected - actual);
+
+                        Assert.True(delta <= maxDelta, string.Format("Pow({0}, {1}) = expected {2} but got {3}", b, e, expected, actual));
+                    }
+                }
+            }
+        }
+
         [Fact]
         public void Modulus()
         {