Fastest sqrt?

[daydreamer]

Fastest sqrt?
Fsqrt with real4,real8,REAL10
SSE sqrtss
SSE2 sqrtds
Rcpsqrt followed by rcpss?
Sqrt LUT 0-255 range = 0-65535 words
https://stackoverflow.com/questions/7724061/how-slow-how-many-cycles-is-calculating-a-square-root
SSE Reciprocal square root enough for calculate per bcd digit?
Probably good enough for student task of calculate phytagoras only output 2-3 decimals

SSE Reciprocal square root with newton-raphson calculated more times than fewer times with real8 together with newton raphson?

[jj2007]

Fsqrt with real4,real8,REAL10

fsqrt in REAL10 precision costs only 5-6 cycles.

Clever tricks make sense for slow complex functions like the Bessel function.

[jack]

you might want to play with inverse square root approximation https://stackoverflow.com/questions/11644441/fast-inverse-square-root-on-x64

[jj2007]

you might want to play with inverse square root approximation

I love it when C++ fans try to be fast

Code Select Expand

AMD Athlon Gold 3150U with Radeon Graphics      (SSE4)
67 µs for initialising FastLog10

1927    cycles for 100 * Log10 (Guga)
4961    cycles for 100 * MasmBasic Log10
1246    cycles for 100 * FastMath Log10
541    cycles for 100 * fsqrt (good ol' FPU)
1246    cycles for 100 * FastSqrt
645    cycles for 100 * SqrtSSE

1948    cycles for 100 * Log10 (Guga)
4917    cycles for 100 * MasmBasic Log10
1242    cycles for 100 * FastMath Log10
538    cycles for 100 * fsqrt (good ol' FPU)
1242    cycles for 100 * FastSqrt
618    cycles for 100 * SqrtSSE

1944    cycles for 100 * Log10 (Guga)
4915    cycles for 100 * MasmBasic Log10
1242    cycles for 100 * FastMath Log10
575    cycles for 100 * fsqrt (good ol' FPU)
1258    cycles for 100 * FastSqrt
614    cycles for 100 * SqrtSSE

2634    cycles for 100 * Log10 (Guga)
4939    cycles for 100 * MasmBasic Log10
1270    cycles for 100 * FastMath Log10
541    cycles for 100 * fsqrt (good ol' FPU)
1242    cycles for 100 * FastSqrt
616    cycles for 100 * SqrtSSE

1883    cycles for 100 * Log10 (Guga)
4929    cycles for 100 * MasmBasic Log10
1269    cycles for 100 * FastMath Log10
548    cycles for 100 * fsqrt (good ol' FPU)
1242    cycles for 100 * FastSqrt
610    cycles for 100 * SqrtSSE

516    bytes for Log10 (Guga)
16      bytes for MasmBasic Log10
67      bytes for FastMath Log10
14      bytes for fsqrt (good ol' FPU)
67      bytes for FastSqrt
30      bytes for SqrtSSE

Real8  0.6989700043360187465
Real8  0.6989700043360188575
Real8  0.6989700043360188575
Real8  2.236067977499789805
Real8  2.236067977499789805
Real8  2.236328125000000000
Note the reduced precision for SqrtSSE: 2.236328125000000000

[TimoVJL]

you might want to play with inverse square root approximation

I love it when C++ fans try to be fast

also when we need 32 / 64 bit and ARM versions 

Fastest squirts are also interesting 

[HSE]

you might want to play with inverse square root approximation https://stackoverflow.com/questions/11644441/fast-inverse-square-root-on-x64

Not so exact, I'm afraid:

Code Select Expand

sqrt fast?

aprox    5.635775715649263800000e-001

FPU      5.638032088398418100000e-001

Press any key to continue...


[HSE]

   For more precision, more cycles (and perhaps no longer faster)

Code Select Expand

inv sqrt fast?

aprox(4)  5.638032088398418100000e-001

FPU       5.638032088398418100000e-001

Press any key to continue...


[daydreamer]

thanks jochen,hector,jack 
Hector for the purpose of user enter number of decimals like in raymonds 10000 decimals,user wants between 1-3 decimals and real8 ,use approximation
for 10000 decimals how many repeated real8 calculation is needed ?
 

[HSE]

If user decide number of decimals that is arbitrary presicion