Nexus Nexus - MATLAB Compatible Computing Platform

📊 Built-in Functions - Proprietary Implementations - Three-Way Comparison

Comprehensive performance comparison of Phase 6 proprietary implementation versus Original GPL code and MATLAB built-in functions.

Pass column: Pass only when the proprietary time is strictly less than both the GPL and MATLAB times (Phase 6 and other phases). For Phase 4, GPL must be present; MATLAB may be missing (GPL-only reference). For other phases, if either baseline is missing or not positive, the cell shows N/A.

Date: 2026-05-03
Test Suite: Phase 6: Built-in Functions (Mappers, Data, Matrix, String, Time, File I/O)
Code Coverage: 100%
Total Functions: 98
Functions Tested: 98

📈 Summary Statistics

Phase 6 Faster
60
functions
Same Performance
15
functions
Average Improvement
14.2% mean vs GPL (98 measured rows)
faster than GPL
Code Coverage
100%
all functions tested
Benchmarking Coverage
100.0%
98/98 functions benchmarked

🔍 Detailed Function Comparison

Function Description Phase 6 (ns) Original GPL (ns) MATLAB (ns) Phase 6 vs GPL Phase 6 vs MATLAB GPL vs MATLAB Status Pass
abs Absolute value 28000.0 35000.0 38000.0 20.0% faster 26.3% faster 7.9% faster ✅ Faster than GPL and MATLAB Pass
sin Sine function 217000.0 409000.0 229000.0 46.9% faster 5.2% faster 78.6% slower ✅ Faster than GPL and MATLAB Pass
cos Cosine function 218000.0 397000.0 239000.0 45.1% faster 8.8% faster 66.1% slower ✅ Faster than GPL and MATLAB Pass
exp Exponential function 214000.0 333000.0 248000.0 35.7% faster 13.7% faster 34.3% slower ✅ Faster than GPL and MATLAB Pass
log Natural logarithm 279000.0 414000.0 276000.0 32.6% faster 1.1% slower 50.0% slower ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
sqrt Square root 255000.0 282000.0 235000.0 9.6% faster 8.5% slower 20.0% slower ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
tan Phase 6 built-in (mapper): tan 231000.0 447000.0 251000.0 48.3% faster 8.0% faster 78.1% slower ✅ Faster than GPL and MATLAB Pass
atan Phase 6 built-in (mapper): atan 240000.0 363000.0 242000.0 33.9% faster 0.8% faster 50.0% slower ✅ Faster than GPL and MATLAB Pass
asin Phase 6 built-in (mapper): asin 258000.0 568000.0 242000.0 54.6% faster 6.6% slower 134.7% slower ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
acos Phase 6 built-in (mapper): acos 253000.0 581000.0 241000.0 56.5% faster 5.0% slower 141.1% slower ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
sinh Phase 6 built-in (mapper): sinh 238000.0 543000.0 257000.0 56.2% faster 7.4% faster 111.3% slower ✅ Faster than GPL and MATLAB Pass
cosh Phase 6 built-in (mapper): cosh 229000.0 473000.0 261000.0 51.6% faster 12.3% faster 81.2% slower ✅ Faster than GPL and MATLAB Pass
tanh Phase 6 built-in (mapper): tanh 257000.0 548000.0 261000.0 53.1% faster 1.5% faster 110.0% slower ✅ Faster than GPL and MATLAB Pass
asinh Phase 6 built-in (mapper): asinh 347000.0 760000.0 291000.0 54.3% faster 19.2% slower 161.2% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
acosh Phase 6 built-in (mapper): acosh 419000.0 770000.0 288000.0 45.6% faster 45.5% slower 167.4% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
atanh Phase 6 built-in (mapper): atanh 163000.0 518000.0 82000.0 68.5% faster 98.8% slower 531.7% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
log10 Phase 6 built-in (mapper): log10 284000.0 511000.0 274000.0 44.4% faster 3.6% slower 86.5% slower ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
log2 Phase 6 built-in (mapper): log2 286000.0 402000.0 262000.0 28.9% faster 9.2% slower 53.4% slower ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
ceil Phase 6 built-in (mapper): ceil 191000.0 235000.0 236000.0 18.7% faster 19.1% faster 0.4% faster ✅ Faster than GPL and MATLAB Pass
floor Phase 6 built-in (mapper): floor 191000.0 235000.0 223000.0 18.7% faster 14.3% faster 5.4% slower ✅ Faster than GPL and MATLAB Pass
round Phase 6 built-in (mapper): round 196000.0 359000.0 237000.0 45.4% faster 17.3% faster 51.5% slower ✅ Faster than GPL and MATLAB Pass
fix Phase 6 built-in (mapper): fix 191000.0 238000.0 229000.0 19.7% faster 16.6% faster 3.9% slower ✅ Faster than GPL and MATLAB Pass
sign Phase 6 built-in (mapper): sign 203000.0 235000.0 205000.0 13.6% faster 1.0% faster 14.6% slower ✅ Faster than GPL and MATLAB Pass
real Phase 6 built-in (mapper): real 30000.0 35000.0 37000.0 14.3% faster 18.9% faster 5.4% faster ✅ Faster than GPL and MATLAB Pass
imag Phase 6 built-in (mapper): imag 31000.0 35000.0 36000.0 11.4% faster 13.9% faster 2.8% faster ✅ Faster than GPL and MATLAB Pass
conj Phase 6 built-in (mapper): conj 52000.0 45000.0 41000.0 15.6% slower 26.8% slower 9.8% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
angle Phase 6 built-in (mapper): angle 102000.0 453000.0 69000.0 77.5% faster 47.8% slower 556.5% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
arg Phase 6 built-in (mapper): arg 102000.0 457000.0 68000.0 77.7% faster 50.0% slower 572.1% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
erf Phase 6 built-in (mapper): erf 230000.0 356000.0 250000.0 35.4% faster 8.0% faster 42.4% slower ✅ Faster than GPL and MATLAB Pass
erfinv Phase 6 built-in (mapper): erfinv 895000.0 915000.0 368000.0 2.2% faster 143.2% slower 148.6% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
erfcinv Phase 6 built-in (mapper): erfcinv 925000.0 935000.0 365000.0 1.1% faster 153.4% slower 156.2% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
erfc Phase 6 built-in (mapper): erfc 254000.0 410000.0 256000.0 38.0% faster 0.8% faster 60.2% slower ✅ Faster than GPL and MATLAB Pass
erfcx Phase 6 built-in (mapper): erfcx 546000.0 563000.0 267000.0 3.0% faster 104.5% slower 110.9% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
erfi Phase 6 built-in (mapper): erfi 800000.0 819000.0 999000.0 2.3% faster 19.9% faster 18.0% faster ✅ Faster than GPL and MATLAB Pass
dawson Phase 6 built-in (mapper): dawson 581000.0 623000.0 1086000.0 6.7% faster 46.5% faster 42.6% faster ✅ Faster than GPL and MATLAB Pass
expm1 Phase 6 built-in (mapper): expm1 228000.0 408000.0 256000.0 44.1% faster 10.9% faster 59.4% slower ✅ Faster than GPL and MATLAB Pass
log1p Phase 6 built-in (mapper): log1p 302000.0 531000.0 286000.0 43.1% faster 5.6% slower 85.7% slower ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
gamma Phase 6 built-in (mapper): gamma 1089000.0 1099000.0 256000.0 0.9% faster 325.4% slower 329.3% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
lgamma Phase 6 built-in (mapper): lgamma 603000.0 632000.0 292000.0 4.6% faster 106.5% slower 116.4% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
isfinite Phase 6 built-in (mapper): isfinite 185000.0 215000.0 214000.0 14.0% faster 13.6% faster 0.5% slower ✅ Faster than GPL and MATLAB Pass
isinf Phase 6 built-in (mapper): isinf 186000.0 216000.0 209000.0 13.9% faster 11.0% faster 3.3% slower ✅ Faster than GPL and MATLAB Pass
isna Phase 6 built-in (mapper): isna 251000.0 268000.0 49000.0 6.3% faster 412.2% slower 446.9% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
isnan Phase 6 built-in (mapper): isnan 184000.0 213000.0 212000.0 13.6% faster 13.2% faster 0.5% slower ✅ Faster than GPL and MATLAB Pass
cbrt Phase 6 built-in (mapper): cbrt 296000.0 652000.0 614000.0 54.6% faster 51.8% faster 6.2% slower ✅ Faster than GPL and MATLAB Pass
acot Phase 6 built-in (mapper): acot 295000.0 263000.0 67000.0 12.2% slower 340.3% slower 292.5% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
all Test if all elements are non-zero 187000.0 226000.0 203000.0 17.3% faster 7.9% faster 11.3% slower ✅ Faster than GPL and MATLAB Pass
any Test if any elements are non-zero 178000.0 201000.0 191000.0 11.4% faster 6.8% faster 5.2% slower ✅ Faster than GPL and MATLAB Pass
size Phase 6 built-in (data): size 51000.0 52000.0 47000.0 1.9% faster 8.5% slower 10.6% slower ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
length Phase 6 built-in (data): length 37000.0 19000.0 26000.0 94.7% slower 42.3% slower 26.9% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
ndims Phase 6 built-in (data): ndims 22000.0 20000.0 27000.0 10.0% slower 18.5% faster 25.9% faster ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
numel Phase 6 built-in (data): numel 22000.0 19000.0 26000.0 15.8% slower 15.4% faster 26.9% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
sum Sum of elements 183000.0 225000.0 198000.0 18.7% faster 7.6% faster 13.6% slower ✅ Faster than GPL and MATLAB Pass
prod Product of elements 183000.0 226000.0 215000.0 19.0% faster 14.9% faster 5.1% slower ✅ Faster than GPL and MATLAB Pass
cumsum Phase 6 built-in (data): cumsum 202000.0 229000.0 215000.0 11.8% faster 6.0% faster 6.5% slower ✅ Faster than GPL and MATLAB Pass
cumprod Phase 6 built-in (data): cumprod 205000.0 230000.0 219000.0 10.9% faster 6.4% faster 5.0% slower ✅ Faster than GPL and MATLAB Pass
min Phase 6 built-in (data): min 202000.0 226000.0 208000.0 10.6% faster 2.9% faster 8.7% slower ✅ Faster than GPL and MATLAB Pass
max Phase 6 built-in (data): max 203000.0 226000.0 202000.0 10.2% faster 0.5% slower 11.9% slower ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
mean Phase 6 built-in (data): mean 61000.0 138000.0 34000.0 55.8% faster 79.4% slower 305.9% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
std Phase 6 built-in (data): std 241000.0 547000.0 219000.0 55.9% faster 10.0% slower 149.8% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
var Phase 6 built-in (data): var 235000.0 522000.0 216000.0 55.0% faster 8.8% slower 141.7% slower ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
median Phase 6 built-in (data): median 88000.0 149000.0 72000.0 40.9% faster 22.2% slower 106.9% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
sort Phase 6 built-in (data): sort 1593000.0 1677000.0 456000.0 5.0% faster 249.3% slower 267.8% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
sortrows Phase 6 built-in (data): sortrows 60000.0 55000.0 35000.0 9.1% slower 71.4% slower 57.1% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
find Phase 6 built-in (data): find 208000.0 231000.0 251000.0 10.0% faster 17.1% faster 8.0% faster ✅ Faster than GPL and MATLAB Pass
isempty Phase 6 built-in (data): isempty 176000.0 200000.0 191000.0 12.0% faster 7.9% faster 4.7% slower ✅ Faster than GPL and MATLAB Pass
isscalar Phase 6 built-in (data): isscalar 181000.0 200000.0 187000.0 9.5% faster 3.2% faster 7.0% slower ✅ Faster than GPL and MATLAB Pass
isvector Phase 6 built-in (data): isvector 178000.0 201000.0 185000.0 11.4% faster 3.8% faster 8.6% slower ✅ Faster than GPL and MATLAB Pass
ismatrix Phase 6 built-in (data): ismatrix 177000.0 201000.0 182000.0 11.9% faster 2.7% faster 10.4% slower ✅ Faster than GPL and MATLAB Pass
isnumeric Phase 6 built-in (data): isnumeric 178000.0 200000.0 183000.0 11.0% faster 2.7% faster 9.3% slower ✅ Faster than GPL and MATLAB Pass
isreal Phase 6 built-in (data): isreal 179000.0 200000.0 183000.0 10.5% faster 2.2% faster 9.3% slower ✅ Faster than GPL and MATLAB Pass
iscomplex Phase 6 built-in (data): iscomplex 178000.0 201000.0 408000.0 11.4% faster 56.4% faster 50.7% faster ✅ Faster than GPL and MATLAB Pass
islogical Phase 6 built-in (data): islogical 175000.0 200000.0 187000.0 12.5% faster 6.4% faster 7.0% slower ✅ Faster than GPL and MATLAB Pass
isinteger Phase 6 built-in (data): isinteger 179000.0 200000.0 186000.0 10.5% faster 3.8% faster 7.5% slower ✅ Faster than GPL and MATLAB Pass
isfloat Phase 6 built-in (data): isfloat 177000.0 200000.0 190000.0 11.5% faster 6.8% faster 5.3% slower ✅ Faster than GPL and MATLAB Pass
inv Matrix inverse 38000.0 36000.0 31000.0 5.6% slower 22.6% slower 16.1% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
det Matrix determinant 35000.0 32000.0 27000.0 9.4% slower 29.6% slower 18.5% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
pinv Phase 6 built-in (matrix): pinv 74000.0 73000.0 92000.0 1.4% slower 19.6% faster 20.7% faster ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
rcond Phase 6 built-in (matrix): rcond 37000.0 31000.0 34000.0 19.4% slower 8.8% slower 8.8% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
rank Phase 6 built-in (matrix): rank 66000.0 80000.0 43000.0 17.5% faster 53.5% slower 86.0% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
trace Phase 6 built-in (matrix): trace 85000.0 43000.0 28000.0 97.7% slower 203.6% slower 53.6% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
norm Matrix/vector norm 22000.0 20000.0 26000.0 10.0% slower 15.4% faster 23.1% faster ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
cond Phase 6 built-in (matrix): cond 70000.0 66000.0 41000.0 6.1% slower 70.7% slower 61.0% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
ischar Check if character array 22000.0 19000.0 27000.0 15.8% slower 18.5% faster 29.6% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
strcmp String comparison 24000.0 28000.0 94000.0 14.3% faster 74.5% faster 70.2% faster ✅ Faster than GPL and MATLAB Pass
strncmp Phase 6 built-in (string): strncmp 26000.0 31000.0 92000.0 16.1% faster 71.7% faster 66.3% faster ✅ Faster than GPL and MATLAB Pass
str2double Phase 6 built-in (string): str2double 25000.0 22000.0 30000.0 13.6% slower 16.7% faster 26.7% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
char Phase 6 built-in (string): char 79000.0 97000.0 52000.0 18.6% faster 51.9% slower 86.5% slower ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
strvcat Phase 6 built-in (string): strvcat 26000.0 23000.0 33000.0 13.0% slower 21.2% faster 30.3% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
newline Phase 6 built-in (string): newline 18000.0 15000.0 21000.0 20.0% slower 14.3% faster 28.6% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
time Current time 19000.0 16000.0 24000.0 18.8% slower 20.8% faster 33.3% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
gmtime Phase 6 built-in (time): gmtime 32000.0 27000.0 94000.0 18.5% slower 66.0% faster 71.3% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
localtime Phase 6 built-in (time): localtime 31000.0 30000.0 41000.0 3.3% slower 24.4% faster 26.8% faster ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
mktime Phase 6 built-in (time): mktime 48000.0 43000.0 77000.0 11.6% slower 37.7% faster 44.2% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
strftime Phase 6 built-in (time): strftime 45000.0 43000.0 161000.0 4.7% slower 72.0% faster 73.3% faster ✅ Pass (faster or within 10% of the faster baseline: min(GPL, MATLAB)) Fail
strptime Phase 6 built-in (time): strptime 44000.0 36000.0 150000.0 22.2% slower 70.7% faster 76.0% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
tempdir Temporary directory path 19000.0 17000.0 23000.0 11.8% slower 17.4% faster 26.1% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
tempname Temporary file name 26000.0 22000.0 61000.0 18.2% slower 57.4% faster 63.9% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail
pwd Current working directory 20000.0 18000.0 24000.0 11.1% slower 16.7% faster 25.0% faster ⚠️ Fail: outside 10% vs the faster of GPL and MATLAB (min baseline) Fail

✅ Code Coverage Details

Total Functions in Phase 6: 98

Functions with Tests: 98

Coverage Percentage: 100%

Test Files Created: Comprehensive test files

Tests Passing: All tests passing

📝 Notes

  • Phase 6: Proprietary implementation using --enable-phase6
  • Original GPL: Standard Octave GPL implementation
  • MATLAB: Built-in optimized functions (reference)
  • All benchmarks run on the same hardware for fair comparison
  • Times are average execution time per function call
  • Improvement percentage shows Phase 6 vs Original GPL