This gives a reduction of roughly 2.5 million instructions in the execution
trace of example4.
genann_act_sigmoid_cached() previously divided by interval to calculate the
lookup index. Divide is a expensive operation, so instead use the reciprocal of
the existing interval calculation to reduce the divide to a multiply.
Building with the following configuration:
```
$ head /proc/cpuinfo
processor : 0
vendor_id : GenuineIntel
cpu family : 6
model : 61
model name : Intel(R) Core(TM) i7-5600U CPU @ 2.60GHz
stepping : 4
microcode : 0x25
cpu MHz : 2593.871
cache size : 4096 KB
physical id : 0
$ cat /etc/os-release
NAME="Ubuntu"
VERSION="17.10 (Artful Aardvark)"
ID=ubuntu
ID_LIKE=debian
PRETTY_NAME="Ubuntu 17.10"
VERSION_ID="17.10"
HOME_URL="https://www.ubuntu.com/"
SUPPORT_URL="https://help.ubuntu.com/"
BUG_REPORT_URL="https://bugs.launchpad.net/ubuntu/"
PRIVACY_POLICY_URL="https://www.ubuntu.com/legal/terms-and-policies/privacy-policy"
VERSION_CODENAME=artful
UBUNTU_CODENAME=artful
$ cc --version
gcc (Ubuntu 7.2.0-8ubuntu3) 7.2.0
Copyright (C) 2017 Free Software Foundation, Inc.
This is free software; see the source for copying conditions. There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
```
on my Lenovo X1 Carbon Gen 3 machine sees the following:
```
$ make CFLAGS="-g -O3 -march=native -DNDEBUG"
cc -g -O3 -march=native -DNDEBUG -c -o test.o test.c
cc -g -O3 -march=native -DNDEBUG -c -o genann.o genann.c
cc -g -O3 -march=native -DNDEBUG -c -o example1.o example1.c
cc -g -O3 -march=native -DNDEBUG -c -o example2.o example2.c
cc -g -O3 -march=native -DNDEBUG -c -o example3.o example3.c
cc -g -O3 -march=native -DNDEBUG -c -o example4.o example4.c
cc -g -O3 -march=native -DNDEBUG -c -o strings.o strings.c
cc test.o genann.o -lm -o test
cc example1.o genann.o -lm -o example1
cc example4.o genann.o -lm -o example4
cc example3.o genann.o -lm -o example3
cc example2.o genann.o -lm -o example2
cc strings.o genann.o -lm -o strings
$ for i in `seq 0 10`; do ./example4 > /dev/null; done; sudo perf stat record ./example4
GENANN example 4.
Train an ANN on the IRIS dataset using backpropagation.
Loading 150 data points from example/iris.data
Training for 5000 loops over data.
147/150 correct (98.0%).
Performance counter stats for './example4':
101.369081 task-clock (msec) # 0.998 CPUs utilized
1 context-switches # 0.010 K/sec
0 cpu-migrations # 0.000 K/sec
79 page-faults # 0.779 K/sec
320,197,883 cycles # 3.159 GHz
1,121,174,423 instructions # 3.50 insn per cycle
223,257,752 branches # 2202.425 M/sec
62,680 branch-misses # 0.03% of all branches
0.101595114 seconds time elapsed
```
Prior to the change, we see something like:
```
$ make CFLAGS="-g -O3 -march=native"
cc -g -O3 -march=native -c -o test.o test.c
cc -g -O3 -march=native -c -o genann.o genann.c
cc -g -O3 -march=native -c -o example1.o example1.c
cc -g -O3 -march=native -c -o example2.o example2.c
cc -g -O3 -march=native -c -o example3.o example3.c
cc -g -O3 -march=native -c -o example4.o example4.c
cc -g -O3 -march=native -c -o strings.o strings.c
cc test.o genann.o -lm -o test
cc example1.o genann.o -lm -o example1
cc example3.o genann.o -lm -o example3
cc example4.o genann.o -lm -o example4
cc strings.o genann.o -lm -o strings
cc example2.o genann.o -lm -o example2
$ for i in `seq 0 10`; do ./example4 > /dev/null; done; sudo perf stat record ./example4
GENANN example 4.
Train an ANN on the IRIS dataset using backpropagation.
Loading 150 data points from example/iris.data
Training for 5000 loops over data.
147/150 correct (98.0%).
Performance counter stats for './example4':
104.644198 task-clock (msec) # 0.998 CPUs utilized
0 context-switches # 0.000 K/sec
0 cpu-migrations # 0.000 K/sec
79 page-faults # 0.755 K/sec
330,340,554 cycles # 3.157 GHz
1,123,669,767 instructions # 3.40 insn per cycle
215,441,809 branches # 2058.803 M/sec
62,406 branch-misses # 0.03% of all branches
0.104891323 seconds time elapsed
```
Signed-off-by: Andrew Jeffery <andrew@aj.id.au>
Jose Fernando Lopez Fernandez