RetroArch/deps/math-neon

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: 	lachlan.ts@gmail.com

PSVITA performances test results:

RUNFAST: Enabled 
------------------------------------------------------------------------------------------------------
MATRIX FUNCTION TESTS 
------------------------------------------------------------------------------------------------------
matmul2_c = 
			|-7.16, 9.42|
			|17.86, -10.70|
matmul2_neon = 
			|-7.16, 9.42|
			|17.86, -10.70|
matmul2: c=183985 	 neon=87480 	 rate=2.10 
matvec2_c = |-7.16, 17.86|
matvec2_neon = |-7.16, 17.86|
matvec2: c=98178 	 neon=66040 	 rate=1.49 
matmul3_c =
			|11.14, -0.78, -3.98|
			|16.56, 17.96, 23.58|
			|8.73, -0.18, 1.57|
matmul3_neon =
			|11.14, -0.78, -3.98|
			|16.56, 17.96, 23.58|
			|8.73, -0.18, 1.57|
matmul3: c=551838 	 neon=340292 	 rate=1.62 
matvec3_c = |11.14, 16.56, 8.73|
matvec3_neon = |11.14, 16.56, 8.73|
matvec3: c=98178 	 neon=66040 	 rate=1.49 
matmul4_c =
			|17.91, -23.96, 1.86, 16.53|
			|4.10, -18.16, 4.17, 29.06|
			|6.92, -1.60, 3.12, 27.81|
			|-15.13, -7.46, -17.91, 22.49|
matmul4_neon =
			|17.91, -23.96, 1.86, 16.53|
			|4.10, -18.16, 4.17, 29.06|
			|6.92, -1.60, 3.12, 27.81|
			|-15.13, -7.46, -17.91, 22.49|
matmul4: c=1316131 	 neon=315444 	 rate=4.17 
matvec4_c = |17.91, 4.10, 6.92, -15.126419|
matvec4_neon = |17.91, 4.10, 6.92, -15.126419|
matvec4: c=98178 	 neon=66040 	 rate=1.49 

dot2_c = 5.804099
dot2_neon = 5.804099
dot2: c=291526 	 neon=307025 	 rate=0.95 
normalize2_c = [0.97, 0.24]
normalize2_neon = [0.97, 0.24]
normalize2: c=1058588 	 neon=965696 	 rate=1.10 

dot3_c = -0.817487
dot3_neon = -0.817487
dot3: c=322094 	 neon=444834 	 rate=0.72 
normalize3_c = [0.50, 0.12, -0.86]
normalize3_neon = [0.50, 0.12, -0.86]
normalize3: c=1257201 	 neon=1134375 	 rate=1.11 
cross3_c = [-13.16, -17.29, -10.19]
cross3_neon = [-13.16, -17.29, -10.19]
cross3: c=705298 	 neon=766477 	 rate=0.92 

dot4_c = -7.880241
dot4_neon = -7.880241
dot4: c=414431 	 neon=506460 	 rate=0.82 
normalize4_c = [0.45, 0.11, -0.77, -0.44]
normalize4_neon = [0.45, 0.11, -0.77, -0.44]
normalize4: c=1410727 	 neon=1102802 	 rate=1.28 

------------------------------------------------------------------------------------------------------
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	647042739	x1.00	
sinf_c     	[-3.14, 3.14]	500000	7.75e-07	1.00e+02%	4.09e-07	646276691	x1.00	
sinf_neon  	[-3.14, 3.14]	500000	1.00e+00	1.00e+02%	7.07e-01	645546381	x1.00	
cosf       	[-3.14, 3.14]	500000	0.00e+00	0.00e+00%	0.00e+00	644742077	x1.00	
cosf_c     	[-3.14, 3.14]	500000	7.75e-07	6.74e-01%	4.15e-07	643957358	x1.00	
cosf_neon  	[-3.14, 3.14]	500000	1.00e+00	1.00e+02%	7.06e-01	643211256	x1.00	
tanf       	[-0.79, 0.79]	500000	0.00e+00	0.00e+00%	0.00e+00	642444112	x1.00	
tanf_c     	[-0.79, 0.79]	500000	2.98e-06	7.94e-04%	1.31e-06	641628507	x1.00	
tanf_neon  	[-0.79, 0.79]	500000	1.00e+00	1.00e+02%	nan	640740514	x1.00	
asinf      	[-1.00, 1.00]	500000	0.00e+00	0.00e+00%	0.00e+00	639560380	x1.00	
asinf_c    	[-1.00, 1.00]	500000	5.54e-05	1.06e-02%	nan	638453383	x1.00	
asinf_neon 	[-1.00, 1.00]	500000	1.57e+00	1.00e+02%	6.84e-01	637349653	x1.00	
acosf      	[-1.00, 1.00]	500000	0.00e+00	0.00e+00%	0.00e+00	636078992	x1.00	
acosf_c    	[-1.00, 1.00]	500000	5.56e-05	6.46e-03%	nan	634934201	x1.00	
acosf_neon 	[-1.00, 1.00]	500000	1.57e+00	1.02e+05%	6.84e-01	633793585	x1.00	
atanf      	[-1.00, 1.00]	500000	0.00e+00	0.00e+00%	0.00e+00	632835241	x1.00	
atanf_c    	[-1.00, 1.00]	500000	1.67e-04	2.12e-02%	7.40e-05	632142823	x1.00	
atanf_neon 	[-1.00, 1.00]	500000	7.85e-01	0.00e+00%	nan	631387330	x1.00	
sinhf       	[-3.14, 3.14]	500000	0.00e+00	0.00e+00%	0.00e+00	630142014	x1.00	
sinhf_c     	[-3.14, 3.14]	500000	1.91e-06	1.52e-01%	1.85e-07	628992714	x1.00	
sinhf_neon  	[-3.14, 3.14]	500000	1.15e+01	1.00e+02%	4.55e+00	627998454	x1.00	
coshf       	[-3.14, 3.14]	500000	0.00e+00	0.00e+00%	0.00e+00	626869866	x1.00	
coshf_c     	[-3.14, 3.14]	500000	9.54e-07	2.38e-05%	1.64e-07	625829657	x1.00	
coshf_neon  	[-3.14, 3.14]	500000	1.06e+01	9.14e+01%	3.92e+00	624873969	x1.00	
tanhf       	[-3.14, 3.14]	500000	0.00e+00	0.00e+00%	0.00e+00	623689093	x1.00	
tanhf_c     	[-3.14, 3.14]	500000	1.20e-05	2.48e-01%	5.48e-06	622547097	x1.00	
tanhf_neon  	[-3.14, 3.14]	500000	9.96e-01	1.00e+02%	8.26e-01	621506812	x1.00	
expf       	[0.00, 10.00]	500000	0.00e+00	0.00e+00%	0.00e+00	620497304	x1.00	
expf_c     	[0.00, 10.00]	500000	9.77e-03	6.15e-05%	1.64e-03	619569554	x1.00	
expf_neon  	[0.00, 10.00]	500000	2.20e+04	1.00e+02%	4.92e+03	618761400	x1.00	
logf       	[1.00, 1000.00]	500000	0.00e+00	0.00e+00%	0.00e+00	617882765	x1.00	
logf_c     	[1.00, 1000.00]	500000	6.20e-06	1.62e-02%	9.83e-07	617087810	x1.00	
logf_neon  	[1.00, 1000.00]	500000	9.49e+01	inf%	9.39e+01	616388420	x1.00	
log10f       	[1.00, 1000.00]	500000	0.00e+00	0.00e+00%	0.00e+00	615405364	x1.00	
log10f_c     	[1.00, 1000.00]	500000	2.86e-06	6.68e-03%	4.79e-07	614442585	x1.00	
log10f_neon  	[1.00, 1000.00]	500000	4.12e+01	inf%	4.07e+01	613671782	x1.00	
floorf     	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	611113689	x1.00	
floorf_c   	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	608159325	x1.00	
floorf_neon	[1.00, 1000.00]	5000000	2.00e+00	2.00e+02%	1.42e-02	604769008	x1.01	
ceilf     	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	601342443	x1.00	
ceilf_c   	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	598387998	x1.00	
ceilf_neon	[1.00, 1000.00]	5000000	2.00e+00	1.00e+02%	1.02e+00	594959710	x1.01	
fabsf     	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	592068236	x1.00	
fabsf_c   	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	589808748	x1.00	
fabsf_neon	[1.00, 1000.00]	5000000	0.00e+00	0.00e+00%	0.00e+00	587712180	x1.01	
sqrtf      	[1.00, 1000.00]	500000	0.00e+00	0.00e+00%	0.00e+00	586496654	x1.00	
sqrtf_c    	[1.00, 1000.00]	500000	2.33e-04	1.06e-03%	8.69e-05	585470866	x1.00	
sqrtf_neon 	[1.00, 1000.00]	500000	0.00e+00	0.00e+00%	nan	584594551	x1.00	
invsqrtf      	[1.00, 1000.00]	500000	0.00e+00	0.00e+00%	0.00e+00	583492213	x1.00	
invsqrtf_c    	[1.00, 1000.00]	500000	4.35e-06	4.78e-04%	2.00e-07	582448164	x1.00	
invsqrtf_neon 	[1.00, 1000.00]	500000	0.00e+00	0.00e+00%	nan	581642365	x1.00	
atan2f       	[0.10, 10.00]	10000	0.00e+00	0.00e+00%	0.00e+00	83594269	x1.00	
atan2f_c     	[0.10, 10.00]	10000	1.73e-04	2.23e-02%	0.00e+00	85383651	x0.98	
atan2f_neon  	[0.10, 10.00]	10000	0.00e+00	0.00e+00%	0.00e+00	87387055	x0.96	
powf       	[1.00, 10.00]	10000	0.00e+00	0.00e+00%	0.00e+00	93430489	x1.00	
powf_c     	[1.00, 10.00]	10000	1.08e+05	4.37e-03%	0.00e+00	96726976	x0.97	
powf_neon  	[1.00, 10.00]	10000	9.97e+09	1.00e+02%	0.00e+00	100185753	x0.93	
fmodf       	[1.00, 10.00]	10000	0.00e+00	0.00e+00%	0.00e+00	101653673	x1.00	
fmodf_c     	[1.00, 10.00]	10000	9.90e+00	8.06e-02%	0.00e+00	103177551	x0.99	
fmodf_neon  	[1.00, 10.00]	10000	9.99e+00	1.00e+02%	0.00e+00	104771240	x0.97