How are exponents calculated?

by

I’ve had a chance to look at fdlibm’s implementation. The comments describe the algorithm used:

 *                    n
 * Method:  Let x =  2   * (1+f)
 *      1. Compute and return log2(x) in two pieces:
 *              log2(x) = w1 + w2,
 *         where w1 has 53-24 = 29 bit trailing zeros.
 *      2. Perform y*log2(x) = n+y' by simulating muti-precision
 *         arithmetic, where |y'|<=0.5.
 *      3. Return x**y = 2**n*exp(y'*log2)

followed by a listing of all the special cases handled (0, 1, inf, nan).

The most intense sections of the code, after all the special-case handling, involve the log2 and 2** calculations. And there are no loops in either of those. So, the complexity of floating-point primitives notwithstanding, it looks like a asymptotically constant-time algorithm.

Floating-point experts (of which I’m not one) are welcome to comment. 🙂

More Related Contents:

  1. Why can’t decimal numbers be represented exactly in binary?
  2. How can i produce multi point linear interpolation? [closed]
  3. How to determine if a list of polygon points are in clockwise order?
  4. Turning a cylinder into a sphere without pinching at the poles
  5. Cone to box collision
  6. How to convert latitude or longitude to meters?
  7. Changing a matrix from right-handed to left-handed coordinate system
  8. How do I combine complex polygons?
  9. Smart design of a math parser?
  10. Using atan2 to find angle between two vectors
  11. What does the ^ (XOR) operator do? [duplicate]
  12. How to test randomness (case in point – Shuffling)
  13. What is “entropy and information gain”?
  14. Signed angle between two 3D vectors with same origin within the same plane
  15. How do I detect intersections between a circle and any other circle in the same plane?
  16. How to distribute points evenly on the surface of hyperspheres in higher dimensions?
  17. How to calculate Tangent and Binormal?
  18. Can a IEEE 754 real number “cover” all integers within its range?
  19. Calculating bounding box a certain distance away from a lat/long coordinate in Java
  20. Plotting a point on the edge of a sphere
  21. How does the CPU do subtraction?
  22. Handling errors in math functions
  23. Do not want scientific notation on plot axis
  24. Designing function f(f(n)) == -n
  25. Why use softmax as opposed to standard normalization?
  26. How to perform division in Go
  27. How to best approximate a geometrical arc with a Bezier curve?
  28. Difference between some operators “|”, “^”, “&”, “&^”. Golang
  29. What is the difference between ‘precision’ and ‘accuracy’? [closed]
  30. Get direction (compass) with two longitude/latitude points

Leave a Comment