Exp, Log & Pow - Java-Gaming.org

Sorry. 32-bit floats only.

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public final class FloatMath
{
  private FloatMath() {}
  
  // 3rd order: 14 good bits
  /**
  private static final float EXP2_0 = 0xf.ff8fcp-4f;
  private static final float EXP2_1 = 0xb.24b09p-4f;
  private static final float EXP2_2 = 0x3.96e3dp-4f;
  private static final float EXP2_3 = 0x1.446bap-4f;
  */
  
  // 4th order: 17 good bits
  /**
  private static final float EXP2_0 = 0x1.00002cp0f;
  private static final float EXP2_1 = 0x1.62d166p-1f;
  private static final float EXP2_2 = 0x1.ee798ap-3f;
  private static final float EXP2_3 = 0x1.aa13fp-5f;
  private static final float EXP2_4 = 0x1.bb7cd4p-7f;
  */

  
  // 5th order: 21 good bits
  private static final float EXP2_0 = 0xf.ffffep-4f;
  private static final float EXP2_1 = 0xb.1729ap-4f;
  private static final float EXP2_2 = 0x3.d79c1p-4f;
  private static final float EXP2_3 = 0xe.4d4cp-8f;
  private static final float EXP2_4 = 0x2.4a14p-8f;
  private static final float EXP2_5 = 0x7.c45p-12f;
 
  
  /**
   * Calculates: 2<sup>x</sup>
   */
 
  public static final float exp2(float x)
  {
    int   a = (int)x;
    float b = x-a;
    float r = 0;
    
  //r = b*(r + EXP2_6);
    r = b*(r + EXP2_5);
    r = b*(r + EXP2_4);
    r = b*(r + EXP2_3);
    r = b*(r + EXP2_2);
    r = b*(r + EXP2_1);
    r =   (r + EXP2_0);

    return exp2(a)*r;
  }
  
  
  // Result accurate to 22 bits (on primary range).
  private static final float LOG2_1 = 0x1.71547ap1f;
  private static final float LOG2_2 = 0x1.ec554ep-1f;
  private static final float LOG2_3 = 0x1.310a2cp-1f;
  
  
  /**
   * Calculates: Log<sub>2</sub> x
   * <p>
   * Accuracy: 22 bits (in normal range)
   */
  
  public static final float log2(float x)
  {
    int   i = Float.floatToRawIntBits(x);
    int   e = ((i >>> 23) & 0xff)-127;
    float y = Float.intBitsToFloat(i - (e<<23));
    float r = (y-sqrtOf2f)/(y+sqrtOf2f);
    float b = r * r;
    float a;
    
    // Approximate via ArcTanh:
    a = r*(LOG2_1 + b*(LOG2_2 + b*LOG2_3));
    
    return 0.5f + e + a;
  }
  
  
  // change to pre-calculated correctly round hex constant
  private static final float oneOverLog2 = (float)(1.0/Math.log(2));
  
  /**
   * Calculates: e<sup>x</sup>
   * <p>
   */
  public static final float exp(float x)
  {
    return exp2(x * oneOverLog2);
  }
  
  /**
   * Calculates: x<sup>y</sup>
   */
  public static final float powf(float x, float y)
  {
    return exp2(y * log2(x));
  }

  /**
   * Calculates: x<sup>n</sup>
   */
  
  public static final float pow(float x, int n)
  {
    float r = 1.f;
    int   e = n;
    
    if (n < 0)
      e = -n;

    do {
      if ((e & 1) != 0) r *= x;
      
      e >>>= 1;
      
      if (e != 0) {
        x *= x;
        continue;
      }
      
      if (n >= 0)
        return r;
      
      return 1/r;
      
    } while(true);
  }
  
  // hastings style
  private static final float sqrtOf2f = (float)Math.sqrt(2);
  

  
  // TODO: change to precalculated exact constant
  private static final float logOf2 = (float)Math.log(2);
  
  /**
   * Calculates: Log x
   */
  public static final float log(float x)
  {
    return log2(x) * logOf2;
  }
  
  // Log[2]/Log[10]
  private static final float log10Convert = 0x1.344136p-2f;
  
  /**
   * Calculates: Log<sub>10</sub> x
   */
  public static final float log10(float x)
  {
    return log2(x) * log10Convert;
  }
  
  /**
   * Calculates: 2<sup>x</sup> for inputs on [-127, 128].
   * <p>
   * The result is exact for valid input values,
   * otherwise the result is undefined.
   */
  public static final float exp2(int x)
  {
    return Float.intBitsToFloat((x+127)<<23);
  }
  

}