i/test3
 Home Manual Packages Global Index Keywords Quick Reference ``` /* TEST3.I Pure scalar math problem for timing Yorick. \$Id: test3.i,v 1.1 1993/08/27 18:50:06 munro Exp \$ */ /* Copyright (c) 1994. The Regents of the University of California. All rights reserved. */ func test3 (npass) /* DOCUMENT test3 or test3, npass Computes the ratio r which solves 1 + r^2 + r^3 +...+ r^n = s, given n and s. If NPASS is given, the calculation is repeated that many times (actually the equation is solved many times for each pass). The worker routine invgeom can actually be vectorized; the vector version is gseries_r in series.i. */ { if (is_void(npass) || npass<=0) npass= 1; extern s, n, answer; nsums= numberof(answer); r= 0.0*answer; now= split= array(0.0, 3); timer, now; m= npass; while (m--) { for (i=1 ; i<=nsums ; i++) r(i)= invgeom(s(i), n); } timer, now, split; timer_print, "Time per pass", split/npass, "Total time", split; if (anyof(abs(r-answer)>1.e-9*answer)) write, "***WARNING*** values returned by invgeom are not correct"; } #if 0 CPU seconds per pass: IDL Yorick Basis DAP HP730 - 0.11 5.08 5.00 Solbourne 0.31 0.21 11.8 13.7 (varies by ~10%) forum[10] yorick Yorick ready. For help type 'help' > #include "/home/miggle/munro/Yorick/include/test3.i" > test3,1 Timing Category CPU sec System sec Wall sec Time per pass 0.190 0.000 0.230 Total time 0.190 0.000 0.230 > test3,51 Timing Category CPU sec System sec Wall sec Time per pass 0.206 0.000 0.207 Total time 10.520 0.000 10.560 forum[6] time idl IDL> .rnew /home/miggle/munro/Yorick/include/test3 % Compiled module: INVGEOM. % Compiled module: TEST3. % Compiled module: SPAN. % Compiled module: \$MAIN\$. IDL> test3,1 IDL> exit 0.5u 0.3s 0:08 11% 0+928k 0+2io 0pf+0w forum[7] time idl IDL> .rnew /home/miggle/munro/Yorick/include/test3 % Compiled module: INVGEOM. % Compiled module: TEST3. % Compiled module: SPAN. % Compiled module: \$MAIN\$. IDL> test3,51 IDL> exit 16.0u 0.4s 0:41 39% 0+1400k 0+0io 0pf+0w forum[13] basis Initializing Basis System Basis 7.0 Initializing EZCURVE/NCAR Graphics Ezcurve/NCAR 2.0 Basis> echo=0 Basis> read /home/miggle/munro/Yorick/include/test3.bas End of input file /home/miggle/munro/Yorick/include/test3.bas Resuming input from TERMINAL Basis> test3(1) CPU (sec) SYS (sec) 11.817 0.017 forum[14] dap DAP> echo=0 DAP> read /home/miggle/munro/Yorick/include/test3.bas DAP> test3(1) CPU (sec) SYS (sec) 13.700 0.033 #endif /* invgeom(s, n) returns the ratio r of the finite geometric series, given the sum s: 1 + r + r^2 + r^3 + ... + r^n = s */ func invgeom (s, n) { nn= n+1; if (nn<2) return s-1.0; /* compute an approximate result which has exact values and derivatives at s==1, s==n, and s->infinity */ /* different approximations apply for s>nn and snn) { pow= 1.0/n; npow= nn^pow - 1.0; n2r= 1.0/(nn-2.0); A= (2.0-nn*npow)*n2r; B= (2.0*npow-nn*pow)*nn*n2r; r= s^pow - pow + A*(nn/s)^pow + B/s; } else { sn= (s-1.0)/n; n2r= 1.0/(nn*nn); r= 1.0 - 1.0/s + n2r*sn*sn*(nn+1.0 - sn); } /* Polish the approximation using Newton-Raphson iterations. */ for (;;) { rr= r-1.0; rn= r^(nn-1); delta= rr*s - (r*rn-1.0); if (abs(delta)<=1.e-9*abs(rr*s)) break; r+= delta/(nn*rn-s); } /* try to get it to machine precision */ if (delta) r+= delta/(nn*rn-s); return r; } /* Set up a bunch of values to compute. */ answer= span(0.0, 2.0, 200); /* number must be even to avoid 1.0000 */ n= 100; s= (answer^(n+1)-1.0)/(answer-1.0); ```