Rev | Line | |
---|
[37] | 1 | function f = flops_pow(a)
|
---|
| 2 | % FLOPS_POW Flops for raising to real power.
|
---|
| 3 | % FLOPS_POW(A) returns the number of flops for (X .^ A) where X is scalar.
|
---|
| 4 | % Powers like 0, 1, 2, and 1/2 are handled specially.
|
---|
| 5 |
|
---|
| 6 | flops_div = 8;
|
---|
| 7 | flops_sqrt = 8;
|
---|
| 8 | if nargin < 1
|
---|
| 9 | a = 0.1;
|
---|
| 10 | end
|
---|
| 11 | f = 0;
|
---|
| 12 | if a < 0
|
---|
| 13 | f = f + flops_div;
|
---|
| 14 | a = -a;
|
---|
| 15 | end
|
---|
| 16 | if a == 0 || a == 1
|
---|
| 17 | return;
|
---|
| 18 | end
|
---|
| 19 | if fix(a) == a
|
---|
| 20 | % number of multiplications to raise to integer power
|
---|
| 21 | f = f + floor(log2(a)) + num_bits(a)-1;
|
---|
| 22 | elseif a == 1/2
|
---|
| 23 | % sqrt is built-in function
|
---|
| 24 | f = f + flops_sqrt;
|
---|
| 25 | elseif fix(2*a) == 2*a
|
---|
| 26 | % this handles flops_pow(1/2+1)
|
---|
| 27 | f = f + flops_pow(2*a) - 1 + flops_sqrt;
|
---|
| 28 | elseif a == 1/4
|
---|
| 29 | f = f + 2*flops_sqrt;
|
---|
| 30 | elseif a == 3/4
|
---|
| 31 | f = f + 2*flops_sqrt+1;
|
---|
| 32 | elseif fix(4*a) == 4*a
|
---|
| 33 | % this handles flops_pow(1/4+1)
|
---|
| 34 | f = f + flops_pow(2*a) - 1 + flops_sqrt;
|
---|
| 35 | else
|
---|
| 36 | f = Inf;
|
---|
| 37 | end
|
---|
| 38 |
|
---|
| 39 | % The identities
|
---|
| 40 | % exp(a) = e^a
|
---|
| 41 | % a^b = exp(b*log(a))
|
---|
| 42 | % require that
|
---|
| 43 | % flops_exp < flops_pow < flops_exp+flops_log+1.
|
---|
| 44 | % But in practice, I find that the runtime exceeds this upper bound.
|
---|
| 45 |
|
---|
| 46 | f_upper = 61; % flops_exp+flops_log+1
|
---|
| 47 | if f > f_upper
|
---|
| 48 | f = f_upper;
|
---|
| 49 | end
|
---|
| 50 |
|
---|
| 51 |
|
---|
| 52 | function b = num_bits(x)
|
---|
| 53 | % Returns the number of 1 bits in the binary representation of x.
|
---|
| 54 | % x must be a non-negative integer.
|
---|
| 55 |
|
---|
| 56 | % lookup table for 0-15
|
---|
| 57 | bits = [0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4];
|
---|
| 58 |
|
---|
| 59 | b = 0;
|
---|
| 60 | while(x > 0)
|
---|
| 61 | b = b + bits(mod(x,16)+1);
|
---|
| 62 | x = floor(x/16);
|
---|
| 63 | end
|
---|
Note: See
TracBrowser
for help on using the repository browser.