Various methods of calculating cosine without math.h.
See the explanation and benchmarks at http://austinhenley.com/blog/cosine.html
For educational purposes only :)
clang -O3 -mavx benchmarks.c -o benchmarks -lm
./benchmarks -h
Usage: ./benchmarks [-na] [-nt] [-t <testname>]
-na - Don't run accuracy tests
-nt - Don't run speed tests.
-t <testname> - Run a particular test instead of all tests.
-p - Print all test names.
There are four types of tests:
- Taylor series with literal values
- Taylor series with running values
- Table lookup with clamp to nearest
- Table lookup with linear interpolation (LERP)
Table tests have the following properties
- cos_table_1 - a cosine table with 1 value per radian
- cos_table_0_1 - a cosine table with 10 values per radian
- cos_table_0_01 - a cosine table with 100 values per radian
- cos_table_0_001 - a cosine table with 1000 values per radian
- cos_table_0_0001 - a cosine table with 10,000 values per radian
cos_taylor_literal_4terms_naive
cos_taylor_literal_6terms_naive
cos_taylor_literal_6terms_2pi
cos_taylor_literal_6terms_pi
cos_taylor_literal_6terms
cos_taylor_literal_10terms
cos_taylor_running_6terms
cos_taylor_running_8terms
cos_taylor_running_10terms
cos_taylor_running_16terms
cos_table_1
cos_table_0_1
cos_table_0_01
cos_table_0_001
cos_table_0_0001
cos_table_1_LERP
cos_table_0_1_LERP
cos_table_0_01_LERP
cos_table_0_001_LERP
cos_table_0_0001_LERP
cos_math_h
You can run a particular test by using the -t switch:
./benchmarks -t cos_table_1_LERP
ACCURACY
cos_table_1_LERP 0.1147496616359112
TIME
cos_table_1_LERP 1.3534999999999999
Or run all tests with no arguments.
./benchmarks
Cosine benchmark
ACCURACY
cos_taylor_literal_4terms_naive 19.9880092736029695
cos_taylor_literal_6terms_naive 1.4652889617438571
cos_taylor_literal_6terms_2pi 1.4652889617438571
cos_taylor_literal_6terms_pi 0.0001004702941281
cos_taylor_literal_6terms 0.0001004702941279
cos_taylor_literal_10terms 0.0000000000756514
cos_taylor_running_6terms 0.0001004702941287
cos_taylor_running_8terms 0.0000001352604422
cos_taylor_running_10terms 0.0000000000756513
cos_taylor_running_16terms 0.0000000000000009
cos_table_1 0.4944578886434219
cos_table_0_1 0.0499943500331001
cos_table_0_01 0.0049999938268771
cos_table_0_001 0.0004999999109268
cos_table_0_0001 0.0000499999164148
cos_table_1_LERP 0.1147496616359112
cos_table_0_1_LERP 0.0012496954434600
cos_table_0_01_LERP 0.0000124999013960
cos_table_0_001_LERP 0.0000001249999969
cos_table_0_0001_LERP 0.0000000012500020
cos_math_h 0.0000000000000000
TIME
cos_taylor_literal_4terms_naive 1.2767610000000000
cos_taylor_literal_6terms_naive 1.8665570000000000
cos_taylor_literal_6terms_2pi 2.7213579999999999
cos_taylor_literal_6terms_pi 3.0191659999999998
cos_taylor_literal_6terms 2.7813910000000002
cos_taylor_literal_10terms 4.3346099999999996
cos_taylor_running_6terms 2.7858489999999998
cos_taylor_running_8terms 3.6085900000000000
cos_taylor_running_10terms 4.5931400000000000
cos_taylor_running_16terms 6.5223639999999996
cos_table_1 0.9697160000000000
cos_table_0_1 1.0025700000000000
cos_table_0_01 1.0026360000000001
cos_table_0_001 1.0028140000000001
cos_table_0_0001 1.0027860000000000
cos_table_1_LERP 1.3534610000000000
cos_table_0_1_LERP 1.4333030000000000
cos_table_0_01_LERP 1.4268099999999999
cos_table_0_001_LERP 1.4344870000000001
cos_table_0_0001_LERP 1.4317990000000000
cos_math_h 3.3061980000000002
Done
Your results will differ.