xirdigh / math-neon Goto Github PK

Library: 	MATH-NEON
By:			Lachlan Tychsen-Smith
Licence:	MIT (expat)
=======================================================================================
This project implements the cmath functions and some optimised matrix functions 
with the aim of increasing the floating point performance of ARM Cortex A-8
based platforms. As well as implementing the functions in ARM NEON assembly, 
they sacrifice error checking and some accuracy to achieve better performance.

Function Errors:
=======================================================================================
The measurement and characterisations of the inaccuracies present within these 
functions is really a field within itself. For the benchmark i provide the 
maximum absolute, maximum relative and root mean squared error compared to the
cmath implementations over the specified range. However these values can be 
misleading, especially for functions which quickly go to infinity. So its always a 
good idea to test it within your actual program. In general, this library will not 
be as accurate as cmath, however for many functions it is close enough to be
negilible. 
	
Notes:
=======================================================================================
- The *_c functions are c implementations of the *_neon code.
- Like cmath, The errors present in the functions are very dependent on the 
  range which your operating in. So you should test them first.
- Look in the "math_neon.h" file for discriptions of the functions. In some 
  function files there are also notes on the specific implementation.
- The *_neon functions make certain assumptions about the location of arguments 
  that is incompatible with inlining. 
	  
Contact:
=======================================================================================
Name: 	Lachlan Tychsen-Smith 
Email: 	[email protected]

PSVITA performances test results:

RUNFAST: Disabled 
------------------------------------------------------------------------------------------------------
MATRIX FUNCTION TESTS 
------------------------------------------------------------------------------------------------------
matmul2_c = 
			|-14.56, 5.96|
			|-15.35, 10.50|
matmul2_neon = 
			|-14.56, 5.96|
			|-15.35, 10.50|
matmul2: c=174924 	 neon=64490 	 rate=2.71 
matvec2_c = |-14.56, -15.35|
matvec2_neon = |-14.56, -15.35|
matvec2: c=88957 	 neon=58337 	 rate=1.52 
matmul3_c =
			|-21.39, -4.68, -1.74|
			|-8.66, -8.97, 1.83|
			|15.88, 0.30, -2.23|
matmul3_neon =
			|-21.39, -4.68, -1.74|
			|-8.66, -8.97, 1.83|
			|15.88, 0.30, -2.23|
matmul3: c=552486 	 neon=297268 	 rate=1.86 
matvec3_c = |-21.39, -8.66, 15.88|
matvec3_neon = |-21.39, -8.66, 15.88|
matvec3: c=184104 	 neon=128780 	 rate=1.43 
matmul4_c =
			|-13.65, -1.80, -12.92, 6.56|
			|-10.21, 9.47, 2.73, 14.79|
			|0.97, 11.69, -0.64, -12.87|
			|20.06, 6.77, 35.61, -0.02|
matmul4_neon =
			|-13.65, -1.80, -12.92, 6.56|
			|-10.21, 9.47, 2.73, 14.79|
			|0.97, 11.69, -0.64, -12.87|
			|20.06, 6.77, 35.61, -0.02|
matmul4: c=1315568 	 neon=254227 	 rate=5.17 
matvec4_c = |-13.65, -10.21, 0.97, 20.058556|
matvec4_neon = |-13.65, -10.21, 0.97, 20.058556|
matvec4: c=331712 	 neon=147196 	 rate=2.25 

dot2_c = -10.903330
dot2_neon = -10.903330
dot2: c=230295 	 neon=168799 	 rate=1.36 
normalize2_c = [-0.74, 0.67]
normalize2_neon = [-0.74, 0.67]
normalize2: c=950716 	 neon=965780 	 rate=0.98 

dot3_c = -4.226746
dot3_neon = -4.226746
dot3: c=306957 	 neon=337316 	 rate=0.91 
normalize3_c = [-0.69, 0.62, -0.38]
normalize3_neon = [-0.69, 0.62, -0.38]
normalize3: c=1180950 	 neon=1134557 	 rate=1.04 
cross3_c = [-9.67, -19.39, -14.24]
cross3_neon = [-9.67, -19.39, -14.24]
cross3: c=659558 	 neon=766896 	 rate=0.86 

dot4_c = 2.782796
dot4_neon = 2.782796
dot4: c=414233 	 neon=276068 	 rate=1.50 
normalize4_c = [-0.59, 0.53, -0.32, -0.52]
normalize4_neon = [-0.59, 0.53, -0.32, -0.52]
normalize4: c=1364294 	 neon=1103327 	 rate=1.24 

------------------------------------------------------------------------------------------------------
CMATH FUNCTION TESTS 
------------------------------------------------------------------------------------------------------
Function	Range		Number	ABS Max Error	REL Max Error	RMS Error	Time	Rate
------------------------------------------------------------------------------------------------------
sinf       	[-3.14, 3.14]	500000	0.00e+00	0.00e+00%	0.00e+00	1394459996	x1.00	
sinf_c     	[-3.14, 3.14]	500000	7.75e-07	1.00e+02%	4.09e-07	1395128226	x1.00	
sinf_neon  	[-3.14, 3.14]	500000	8.34e-07	1.00e+02%	4.09e-07	1395853554	x1.00	
cosf       	[-3.14, 3.14]	500000	0.00e+00	0.00e+00%	0.00e+00	1396644271	x1.00	
cosf_c     	[-3.14, 3.14]	500000	7.75e-07	6.74e-01%	4.15e-07	1397360321	x1.00	
cosf_neon  	[-3.14, 3.14]	500000	8.34e-07	6.74e-01%	4.16e-07	1398126872	x1.00	
tanf       	[-0.79, 0.79]	500000	0.00e+00	0.00e+00%	0.00e+00	1398889596	x1.00	
tanf_c     	[-0.79, 0.79]	500000	2.98e-06	7.94e-04%	1.31e-06	1399704712	x1.00	
tanf_neon  	[-0.79, 0.79]	500000	1.91e-06	3.62e-04%	6.66e-07	1400612899	x1.00	
asinf      	[-1.00, 1.00]	500000	0.00e+00	0.00e+00%	0.00e+00	1401838993	x1.00	
asinf_c    	[-1.00, 1.00]	500000	5.54e-05	1.06e-02%	nan	1402745512	x1.00	
asinf_neon 	[-1.00, 1.00]	500000	4.66e-05	8.90e-03%	nan	1403967661	x1.00	
acosf      	[-1.00, 1.00]	500000	0.00e+00	0.00e+00%	0.00e+00	1405317842	x1.00	
acosf_c    	[-1.00, 1.00]	500000	5.56e-05	6.46e-03%	nan	1406294753	x1.00	
acosf_neon 	[-1.00, 1.00]	500000	4.67e-05	6.35e-03%	nan	1407598039	x1.00	
atanf      	[-1.00, 1.00]	500000	0.00e+00	0.00e+00%	0.00e+00	1408314869	x1.00	
atanf_c    	[-1.00, 1.00]	500000	1.67e-04	2.12e-02%	7.40e-05	1408872421	x1.00	
atanf_neon 	[-1.00, 1.00]	500000	1.67e-04	2.12e-02%	7.40e-05	1409736652	x1.00	
sinhf       	[-3.14, 3.14]	500000	0.00e+00	0.00e+00%	0.00e+00	1411101066	x1.00	
sinhf_c     	[-3.14, 3.14]	500000	1.91e-06	1.52e-01%	1.85e-07	1412173492	x1.00	
sinhf_neon  	[-3.14, 3.14]	500000	1.91e-06	1.52e-01%	1.90e-07	1413205410	x1.00	
coshf       	[-3.14, 3.14]	500000	0.00e+00	0.00e+00%	0.00e+00	1414417802	x1.00	
coshf_c     	[-3.14, 3.14]	500000	9.54e-07	2.38e-05%	1.64e-07	1415426083	x1.00	
coshf_neon  	[-3.14, 3.14]	500000	1.91e-06	2.22e-05%	1.68e-07	1416412636	x1.00	
tanhf       	[-3.14, 3.14]	500000	0.00e+00	0.00e+00%	0.00e+00	1417684273	x1.00	
tanhf_c     	[-3.14, 3.14]	500000	1.20e-05	2.48e-01%	5.48e-06	1418659628	x1.00	
tanhf_neon  	[-3.14, 3.14]	500000	2.38e-07	2.47e-01%	5.40e-08	1419650721	x1.00	
expf       	[0.00, 10.00]	500000	0.00e+00	0.00e+00%	0.00e+00	1420706074	x1.00	
expf_c     	[0.00, 10.00]	500000	9.77e-03	6.15e-05%	1.64e-03	1421444150	x1.00	
expf_neon  	[0.00, 10.00]	500000	9.77e-03	6.58e-05%	1.64e-03	1422203499	x1.00	
logf       	[1.00, 1000.00]	500000	0.00e+00	0.00e+00%	0.00e+00	1423106698	x1.00	
logf_c     	[1.00, 1000.00]	500000	6.20e-06	1.62e-02%	9.83e-07	1423735174	x1.00	
logf_neon  	[1.00, 1000.00]	500000	7.63e-06	1.03e-02%	1.07e-06	1424434406	x1.00	
log10f       	[1.00, 1000.00]	500000	0.00e+00	0.00e+00%	0.00e+00	1425516892	x1.00	
log10f_c     	[1.00, 1000.00]	500000	2.86e-06	6.68e-03%	4.79e-07	1426200368	x1.00	
log10f_neon  	[1.00, 1000.00]	500000	3.34e-06	6.68e-03%	4.84e-07	1426966844	x1.00	
floorf     	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	1429081993	x1.00	
floorf_c   	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	1430839273	x1.00	
floorf_neon	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	1433474766	x1.00	
ceilf     	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	1435602956	x1.00	
ceilf_c   	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	1437403711	x1.00	
ceilf_neon	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	1440044970	x1.00	
fabsf     	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	1441265630	x1.00	
fabsf_c   	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	1442491716	x1.00	
fabsf_neon	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	1443680744	x1.00	
sqrtf      	[1.00, 1000.00]	500000	0.00e+00	0.00e+00%	0.00e+00	1444844144	x1.00	
sqrtf_c    	[1.00, 1000.00]	500000	2.33e-04	1.06e-03%	8.69e-05	1445710342	x1.00	
sqrtf_neon 	[1.00, 1000.00]	500000	7.63e-06	2.91e-05%	1.60e-06	1446544637	x1.00	
invsqrtf      	[1.00, 1000.00]	500000	0.00e+00	0.00e+00%	0.00e+00	1446995307	x1.00	
invsqrtf_c    	[1.00, 1000.00]	500000	4.35e-06	4.78e-04%	2.00e-07	1447471977	x1.00	
invsqrtf_neon 	[1.00, 1000.00]	500000	1.19e-07	2.12e-05%	4.81e-09	1447987675	x1.00	
atan2f       	[0.10, 10.00]	10000	0.00e+00	0.00e+00%	0.00e+00	1449713108	x1.00	
atan2f_c     	[0.10, 10.00]	10000	1.73e-04	2.23e-02%	0.00e+00	1451276575	x1.00	
atan2f_neon  	[0.10, 10.00]	10000	1.67e-04	2.12e-02%	0.00e+00	1453093260	x1.00	
powf       	[1.00, 10.00]	10000	0.00e+00	0.00e+00%	0.00e+00	1458606663	x1.00	
powf_c     	[1.00, 10.00]	10000	1.08e+05	4.37e-03%	0.00e+00	1461584933	x1.00	
powf_neon  	[1.00, 10.00]	10000	1.36e+05	5.88e-03%	0.00e+00	1464702743	x1.00	
fmodf       	[1.00, 10.00]	10000	0.00e+00	0.00e+00%	0.00e+00	1466022029	x1.00	
fmodf_c     	[1.00, 10.00]	10000	9.90e+00	8.06e-02%	0.00e+00	1467403015	x1.00	
fmodf_neon  	[1.00, 10.00]	10000	9.97e+00	8.06e-02%	0.00e+00	1468767755	x1.00