Alternative Math functions
I discovered that some math functions give different answers depending on which computer I was using. When I went looking for why, I found that certain math functions are directly implemented in the (x86) CPU.
Wikipedia shows some of these instructions.
- https://en.wikipedia.org/wiki/X86_instruction_listings#Original_8087_instructions
- https://en.wikipedia.org/wiki/X86_instruction_listings#Added_with_80387
The ones that caught my eye were the trig functions:
- FPATAN
- FPTAN
- FCOS
- FSIN
- FSINCOS
- FSQRT
- Review functions that are way off (innacurate)
- Do Cross platform testing
- Add more functions
all times in milliseconds
| Processor | Label | Total Time |
|---|---|---|
| AMD Athlon X2 1.7GHz | A | 65251 |
| Intel i3 530 2.93GHz | I | 31358 |
test.TestArcTrig
| Name | Accuracy - A | Speed - A | Accuracy - I | Speed - I |
|---|---|---|---|---|
| AtanSO1 | 0.0136638037737245 | 213.1517 | 0.0136638037737241 | 68.943 |
| AtanMac | 0.0935295762042116 | 3797.3095 | 0.0935295762042112 | 1260.5377 |
| AtanMac-16 | 0.0658025452458658 | 4476.5338 | 0.0658025452458654 | 1455.6221 |
| AtanMac-32 | 0.0569347297414583 | 5217.8095 | 0.0569347297414578 | 1614.5611 |
| AtanActon | 0.00226640192840606 | 1089.9242 | 0.00226640192840601 | 530.4486 |
| AtanActon-16 | 3.45821482145015E-08 | 1900.1575 | 3.45821481589903E-08 | 913.3468 |
| AtanActon-32 | 5.09453590424869E-14 | 3508.7304 | 5.04457586814056E-14 | 1711.377 |
| AtanAms | 5.64583344242475E-08 | 408.148 | 5.64583343687364E-08 | 201.6743 |
| Atanfdlibm | 122.793568849762 | 443.1341 | 122.793568849762 | 220.6983 |
test.TestTrig
| Name | Accuracy - A | Speed - A | Accuracy - I | Speed - I |
|---|---|---|---|---|
| SinSO | 1.10087619858681E-13 | 4249.7292 | 1.09810064102525E-13 | 8500.9257 |
| Sin3 | 78.6051247042265 | 439.1145 | 78.6051247042265 | 231.0808 |
| SinXupremZero | 0.0635031546303115 | 185.9578 | 0.0635031546303115 | 81.8284 |
| SinAms | 3.06749505990386E-08 | 299.0557 | 3.06749508765944E-08 | 127.8584 |
| Sin5 | 4.73341042766662E-05 | 364.5602 | 4.73341042769437E-05 | 175.7506 |
| Sin5-16 | 1.28681912630859E-13 | 548.9695 | 1.28626401479628E-13 | 259.3699 |
| Sin5-32 | 1.93002683562518E-13 | 934.2172 | 1.93058194713749E-13 | 425.5533 |
| Cordic-Sin | 0.301510668694616 | 3747.2538 | 0.301510668694616 | 1464.9103 |
| Cordic-Sin-24 | 4.7274776291645E-06 | 12637.42 | 4.72747762933103E-06 | 4361.2589 |
| SinTaylor | 0.00400130951601307 | 212.638 | 0.00400130951601312 | 100.7131 |
| SinFdlibm | 2.261290882078 | 228.4435 | 2.261290882078 | 106.4183 |
| Sin6 | 14.075154510891 | 381.0937 | 14.075154510891 | 132.8478 |
| Sin6-16 | 6.75028061584193 | 595.37 | 6.75028061584193 | 210.7845 |
| Sin6-32 | 3.30773444231687 | 1046.5789 | 3.30773444231687 | 360.3422 |
| Cos | 4.28993996385435E-08 | 274.9541 | 4.28993995275212E-08 | 111.4881 |
| Cordic-Cos | 0.30451787266993 | 3702.4638 | 0.30451787266993 | 1421.8445 |
| Cordic-Cos-24 | 4.680740490739E-06 | 13189.1135 | 4.68074049085002E-06 | 4274.8336 |