Fast logarithm calculation

Question

All the code was run on the same machine on linux.

In python:

import numpy as np
drr = abs(np.random.randn(100000,50))
%timeit np.log2(drr)

Answer 1

Note that ALL below are float32, not double precision.

UPDATE: I've ditched gcc completely in favour of Intel's icc. It makes ALL the difference when performance is critical and when you don't have time to fine-tune your "compiler hints" to enforce gcc vectorization (see, e.g. here)

log_omp.c,

GCC: gcc -o log_omp.so -fopenmp log_omp.c -lm -O3 -fPIC -shared -std=c99

ICC: icc -o log_omp.so -openmp loge_omp.c -lm -O3 -fPIC -shared -std=c99 -vec-report1 -xAVX -I/opt/intel/composer/mkl/include

#include <math.h>
#include "omp.h"
#include "mkl_vml.h"

#define restrict __restrict

inline void log_omp(int m, float * restrict a, float * restrict c);

void log_omp(int m, float * restrict a, float * restrict c)
{
   int i;
#pragma omp parallel for default(none) shared(m,a,c) private(i)
   for (i=0; i<m; i++) {
      a[i] = log(c[i]);
   }
}

// VML / icc only:
void log_VML(int m, float * restrict a, float * restrict c)
{
   int i;
   int split_to = 14;
   int iter = m / split_to;
   int additional = m % split_to;

//   vsLn(m, c, a);
#pragma omp parallel for default(none) shared(m,a,c, additional, iter) private(i) num_threads(split_to)
   for (i=0;i < (m-additional); i+=iter)
     vsLog10(iter,c+i,a+i);
     //vmsLn(iter,c+i,a+i, VML_HA);

   if (additional > 0)
     vsLog10(additional, c+m-additional, a+m-additional);
     //vmsLn(additional, c+m-additional, a+m-additional, VML_HA);
}

in python:

from ctypes import CDLL, c_int, c_void_p
def log_omp(xs, out):
    lib = CDLL('./log_omp.so')
    lib.log_omp.argtypes = [c_int, np.ctypeslib.ndpointer(dtype=np.float32), np.ctypeslib.ndpointer(dtype=np.float32)]
    lib.log_omp.restype  = c_void_p
    n = xs.shape[0]
    out = np.empty(n, np.float32)
    lib.log_omp(n, out, xs)
    return out

Cython code (in ipython notebook, hence the %% magic):

%%cython --compile-args=-fopenmp --link-args=-fopenmp
import  numpy as np
cimport numpy as np
from libc.math cimport log

from cython.parallel cimport prange
import cython

@cython.boundscheck(False)
def cylog(np.ndarray[np.float32_t, ndim=1] a not None,
        np.ndarray[np.float32_t, ndim=1] out=None):
    if out is None:
        out = np.empty((a.shape[0]), dtype=a.dtype)
    cdef Py_ssize_t i
    with nogil:
        for i in prange(a.shape[0]):
            out[i] = log(a[i])
    return out

Timings:

numexpr.detect_number_of_cores() // 2
28

%env OMP_NUM_THREADS=28
x = np.abs(np.random.randn(50000000).astype('float32'))
y = x.copy()

# GCC
%timeit log_omp(x, y)
10 loops, best of 3: 21.6 ms per loop
# ICC
%timeit log_omp(x, y)
100 loops, best of 3: 9.6 ms per loop
%timeit log_VML(x, y)
100 loops, best of 3: 10 ms per loop

%timeit cylog(x, out=y)
10 loops, best of 3: 21.7 ms per loop

numexpr.set_num_threads(28)
%timeit out = numexpr.evaluate('log(x)')
100 loops, best of 3: 13 ms per loop

So numexpr seems to be doing a better job than (poorly) compiled gcc code, but icc wins.

Some resources I found useful and shamefully used code from:

http://people.duke.edu/~ccc14/sta-663/Optimization_Bakeoff.html

https://gist.github.com/zed/2051661