Changeset 97e6d3c in sasmodels for sasmodels/models/hardsphere.py

Timestamp:

Feb 26, 2016 10:22:00 AM (8 years ago)

Author:

richardh

Branches:

master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

e4d8726

Parents:

093f754

Message:

made hardsphere faster

File:

• sasmodels/models/hardsphere.py (modified) (2 diffs)

sasmodels/models/hardsphere.py

@@ -69 +69 @@
                return(HARDSPH);
       }
-      D=pow((1.-volfraction),2);
-      A=pow((1.+2.*volfraction)/D, 2);
+      // removing use of pow(xxx,2) and rearranging the calcs of A, B & G cut ~40% off execution time ( 0.5 to 0.3 msec)
+      X = 1.0/( 1.0 -volfraction);
+      D= X*X;
+      A= (1.+2.*volfraction)*D;
+      A *=A;
       X=fabs(q*effect_radius*2.0);
 
@@ -77 +80 @@
                  return(HARDSPH);
       }
-      X2=pow(X,2);
-      X4=pow(X2,2);
-      B=-6.*volfraction* pow((1.+0.5*volfraction)/D ,2);
+      X2 =X*X;
+      B = (1.0 +0.5*volfraction)*D;
+      B *= B;
+      B *= -6.*volfraction;
       G=0.5*volfraction*A;
 
       if(X < 0.2) {
-      // use Taylor series expansion for small X, IT IS VERY PICKY ABOUT THE X CUT OFF VALUE, ought to be lower in double. 
-      // No obvious way to rearrange the equations to avoid needing a very high number of significant figures. 
+      // RKH Feb 2016, use Taylor series expansion for small X, IT IS VERY PICKY ABOUT THE X CUT OFF VALUE, ought to be lower in double. 
+      // else no obvious way to rearrange the equations to avoid needing a very high number of significant figures. 
       // Series expansion found using Mathematica software. Numerical test in .xls showed terms to X^2 are sufficient 
-      // for 5 or 6 significant figures but I put the X^4 one in anyway 
-            FF = 8*A +6*B + 4*G - (0.8*A +2.0*B/3.0 +0.5*G)*X2 +(A/35. +B/40. +G/50.)*X4;
+      // for 5 or 6 significant figures, but I put the X^4 one in anyway 
+            //FF = 8*A +6*B + 4*G - (0.8*A +2.0*B/3.0 +0.5*G)*X2 +(A/35. +B/40. +G/50.)*X4;
+            // refactoring the polynomial makes it very slightly faster (0.5 not 0.6 msec)
+            //FF = 8*A +6*B + 4*G + ( -0.8*A -2.0*B/3.0 -0.5*G +(A/35. +B/40. +G/50.)*X2)*X2;
+
+            FF = 8.0*A +6.0*B + 4.0*G + ( -0.8*A -B/1.5 -0.5*G +(A/35. +0.0125*B +0.02*G)*X2)*X2;
+
             // combining the terms makes things worse at smallest Q in single precision
             //FF = (8-0.8*X2)*A +(3.0-X2/3.)*2*B + (4+0.5*X2)*G +(A/35. +B/40. +G/50.)*X4;
             // note that G = -volfraction*A/2, combining this makes no further difference at smallest Q
-            //FF = (8 +2.*volfraction + ( volfraction/4. -0.8 +(volfraction/100. -1./35.)*X2 )*X2 )*A  + (3.0 -X2/3. +X4/40)*2*B;
+            //FF = (8 +2.*volfraction + ( volfraction/4. -0.8 +(volfraction/100. -1./35.)*X2 )*X2 )*A  + (3.0 -X2/3. +X4/40.)*2.*B;
             HARDSPH= 1./(1. + volfraction*FF );
             return(HARDSPH);
       }
+      X4=X2*X2;
       SINCOS(X,S,C);
 
-// RKH Feb 2016, use version from FISH code as it is better than original sasview one at small Q in single precision
-      FF=A*(S-X*C)/X + B*(2.*X*S -(X2-2.)*C -2.)/X2 + G*( (4.*X2*X -24.*X)*S -(X4 -12.*X2 +24.)*C +24. )/X4;
+// RKH Feb 2016, use version FISH code as is better than original sasview one at small Q in single precision, and more than twice as fast in double.
+      //FF=A*(S-X*C)/X + B*(2.*X*S -(X2-2.)*C -2.)/X2 + G*( (4.*X2*X -24.*X)*S -(X4 -12.*X2 +24.)*C +24. )/X4;
+      // refactoring the polynomial here & above makes it slightly faster
+
+      FF=  (( G*( (4.*X2 -24.)*X*S -(X4 -12.*X2 +24.)*C +24. )/X2 + B*(2.*X*S -(X2-2.)*C -2.) )/X + A*(S-X*C))/X ;
       HARDSPH= 1./(1. + 24.*volfraction*FF/X2 );
 
-// rearrange the terms, is now about same as sasmodels
+      // changing /X and /X2 to *MX1 and *MX2, no significantg difference?
+      //MX=1.0/X;
+      //MX2=MX*MX;
+      //FF=  (( G*( (4.*X2 -24.)*X*S -(X4 -12.*X2 +24.)*C +24. )*MX2 + B*(2.*X*S -(X2-2.)*C -2.) )*MX + A*(S-X*C)) ;
+      //HARDSPH= 1./(1. + 24.*volfraction*FF*MX2*MX );
+
+// grouping the terms, was about same as sasmodels for single precision issues
 //     FF=A*(S/X-C) + B*(2.*S/X - C +2.0*(C-1.0)/X2) + G*( (4./X -24./X3)*S -(1.0 -12./X2 +24./X4)*C +24./X4 );
 //     HARDSPH= 1./(1. + 24.*volfraction*FF/X2 );