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<h1 style="font-family : Courier, monospace; letter-spacing: 8px; margin-bottom: 0px;">fbench</h1>
<h3 style="margin-top: 0px;">
Trigonometry Intense Floating Point Benchmark
</h3>
by <a href="/">John Walker</a><br />
December 1980<br />
Last update: September 24th, 2021
</center>

<hr />

<h3>Introduction</h3>

<p class="j">
<b>Fbench</b> is a complete optical design raytracing algorithm,
shorn of its user interface and recast into portable C. It not only
determines execution speed on an extremely floating point (including
trigonometric functions) intensive real-world application, it checks
accuracy on an algorithm that is exquisitely sensitive to errors. The
performance of this program is typically far more sensitive to
changes in the efficiency of the trigonometric library routines than
the average floating point program.
</p>

<p class="j">
The benchmark may be compiled in two modes. If the symbol
<tt>INTRIG</tt> is defined, built-in trigonometric and square root
routines will be used for all calculations. Timings made with
<tt>INTRIG</tt> defined reflect the machine's basic floating point
performance for the arithmetic operators. If <tt>INTRIG</tt> is not
defined, the system library <tt>&lt;math.h&gt;</tt> functions are used.
Results with <tt>INTRIG</tt> not defined reflect the system's library
performance and/or floating point hardware support for trig
functions and square root. Results with <tt>INTRIG</tt> defined are a
good guide to general floating point performance, while results
with <tt>INTRIG</tt> undefined indicate the performance of an application
which is math function intensive.
</p>

<p class="j">
Special note regarding errors in accuracy: this program has
generated numbers identical to the last digit it formats and
checks on the following machines, floating point
architectures, and languages:
</p>

<center>
<table width="80%" cellpadding="3">
<tr><th bgcolor="#C0C0C0">Machine</th> <th bgcolor="#C0C0C0">Language</th> <th bgcolor="#C0C0C0">Floating Point Format</th></tr>
<tr class="ltgrey">
<td>Marinchip 9900</td> <td>QBASIC</td> <td>IBM 370 double-precision (REAL&nbsp;*&nbsp;8) format</td>
</tr>

<tr class="ltgrey">
<td class="e" rowspan="5">IBM PC /XT/ AT, <br />
    Intel i<em>x</em>86 / Pentium&nbsp;<em>n</em><br />
    Intel/AMD <em>x</em>86_64</td>
<td>Lattice C</td> <td>IEEE 64 bit, 80 bit temporaries</td>
</tr>
<tr class="ltgrey"> <td>High C</td> <td>same, in line 80<em>x</em>87 code</td></tr>
<tr class="ltgrey"> <td class="e">GCC/G++</td> <td>same, native FPU code<br />
                                     <tt>long double</tt> (Intel 80 bit)<br />
                                     <tt>__float128</tt> (128 bit)<br />
                                     GNU MPFR library (128 and 512 bit)</td></tr>
<tr class="ltgrey"> <td>BASICA</td> <td>&ldquo;Double precision&rdquo;</td></tr>
<tr class="ltgrey"> <td>Quick BASIC</td> <td>IEEE double precision, software routines</td></tr>

<tr class="ltgrey">
<td>Sun 3</td> <td>C</td> <td>IEEE 64 bit, 80 bit temporaries,
 in-line 68881 code, in-line FPA code.
</td></tr>

<tr class="ltgrey">
<td>MicroVAX II</td> <td>C</td> <td>VAX &ldquo;G&rdquo; format floating point
</td></tr>

<tr class="ltgrey">
<td>Macintosh Plus</td> <td>MPW C</td> <td>SANE floating point, IEEE 64 bit format
 implemented in ROM.
</td></tr>
</table>
</center>

<p class="j">
Inaccuracies reported by this program should be taken
<strong>very seriously indeed</strong>, as the program has been
demonstrated to be invariant under changes in floating point
format, as long as the format is a recognised double precision
format. If you encounter errors, please remember that they are
just as likely to be in the floating point editing library or
the trigonometric libraries (unless compiled with
<tt>INTRIG</tt> defined) as in the low level operator code.
Now that virtually all computers use IEEE floating point format,
differences in results are almost certainly indicative of errors
in code generation, optimisation, or library routines.
</p>

<p class="j">
The benchmark assumes that results are basically reliable, and
only tests the last result computed against the reference. If
you're running on a suspect system you can compile this program
with <tt>ACCURACY</tt> defined. This will generate a version which
executes as an infinite loop, performing the ray trace and
checking the results on every pass. All incorrect results will
be reported.
</p>

<h3>Benchmark Results for Various Systems</h3>

<p class="j">
Representative timings are given below. All have been
normalised as if run for 1000 iterations.
</p>

<center>
<table width="80%" cellpadding="2" class="results">
<tr><th bgcolor="#C0C0C0" colspan="2"> Time in Seconds</th> <th bgcolor="#C0C0C0" rowspan="2">Computer, Compiler, and Notes</th></tr>
<tr><th bgcolor="#C0C0C0"> Normal</th> <th bgcolor="#C0C0C0">INTRIG</th></tr>

<tr class="ltgrey"> <td class="ct"> 3466.00</td> <td class="ct">4031.00</td> <td class="ccnotes">Commodore 128, 2 MHz 8510 with software floating
 point. Abacus Software/Data-Becker Super-C 128,
 version 3.00, run in fast (2 MHz) mode. Note:
 the results generated by this system differed
 from the reference results in the 8th to 10th
 decimal place.
</td></tr>

<tr class="ltgrey"> <td class="ct"> 3290.00</td> <td class="ct">&nbsp;</td> <td class="ccnotes">IBM PC/AT 6 MHz, Microsoft/IBM BASICA version A3.00.
 Run with the &ldquo;/d&rdquo; switch, software floating point.
</td></tr>

<tr class="ltgrey"> <td class="ct"> 2131.50</td> <td class="ct">&nbsp;</td> <td class="ccnotes">IBM PC/AT 6 MHz, Lattice C version 2.14, small model.
 This version of Lattice compiles subroutine
 calls which either do software floating point
 or use the 80x87. The machine on which I ran
 this had an 80287, but the results were so bad
 I wonder if it was being used.
</td></tr>

<tr class="ltgrey"> <td class="ct"> 1598.00</td> <td class="ct">&nbsp;</td> <td class="ccnotes">Macintosh Plus, MPW C, SANE Software floating point.
</td></tr>

<tr class="ltgrey"> <td class="ct"> 1582.13</td> <td class="ct">&nbsp;</td> <td class="ccnotes">Marinchip 9900 2 MHz, QBASIC compiler with software
 floating point. This was a QBASIC version of the
 program which contained the identical algorithm.
</td></tr>

<tr class="ltgrey"><td class="ct"> 404.00</td> <td class="ct">&nbsp;</td> <td class="ccnotes">IBM PC/AT 6 MHz, Microsoft QuickBASIC version 2.0.
 Software floating point.
</td></tr>

<tr class="ltgrey"><td class="ct"> 165.15</td> <td class="ct">&nbsp;</td> <td class="ccnotes">IBM PC/AT 6 MHz, Metaware High C version 1.3, small
 model. This was compiled to call subroutines for
 floating point, and the machine contained an 80287
 which was used by the subroutines.
</td></tr>

<tr class="ltgrey"><td class="ct"> 143.20</td> <td class="ct">&nbsp;</td> <td class="ccnotes">Macintosh II, MPW C, SANE calls. I was unable to
 determine whether SANE was using the 68881 chip or
 not.
</td></tr>

<tr class="ltgrey"><td class="ct"> 121.80</td> <td class="ct">&nbsp;</td> <td class="ccnotes">Sun 3/160 16 MHz, Sun C
 Compiled with &ldquo;-fsoft&rdquo; switch
 which executes floating point in software.
</td></tr>

<tr class="ltgrey"><td class="ct"> 78.78</td> <td class="ct">110.11</td> <td class="ccnotes">IBM RT PC (Model 6150). IBM AIX 1.0 C compiler
 with &ldquo;-O&rdquo; switch.
</td></tr>

<tr class="ltgrey"><td class="ct"> 75.2</td> <td class="ct">254.0</td> <td class="ccnotes">Microsoft Quick C 1.0, in-line 8087 instructions,
 compiled with 80286 optimisation on. (Switches
 were &ldquo;-Ol -FPi87-G2 -AS&rdquo;). Small memory model.
</td></tr>

<tr class="ltgrey"><td class="ct"> 69.50</td> <td class="ct">&nbsp;</td> <td class="ccnotes">IBM PC/AT 6 MHz, Borland Turbo BASIC 1.0. Compiled
 in &ldquo;8087 required&rdquo; mode to generate in-line
 code for the math coprocessor.
</td></tr>

<tr class="ltgrey"><td class="ct"> 66.96</td> <td class="ct">&nbsp;</td> <td class="ccnotes">IBM PC/AT 6 MHz, Microsoft QuickBASIC 4.0. This
 release of QuickBASIC compiles code for the
 80287 math coprocessor.
</td></tr>

<tr class="ltgrey"><td class="ct"> 66.36</td> <td class="ct">206.35</td> <td class="ccnotes">IBM PC/AT 6 MHz, Metaware High C version 1.3, small
 model. This was compiled with in-line code for the
 80287 math coprocessor. Trig functions still call
 library routines.
</td></tr>

<tr class="ltgrey"><td class="ct"> 63.07</td> <td class="ct">220.43</td> <td class="ccnotes">IBM PC/AT, 6 MHz, Borland Turbo C, in-line 8087 code,
 small model, word alignment, no stack checking,
 8086 code mode.
</td></tr>

<tr class="ltgrey"><td class="ct"> 17.18</td> <td class="ct">&nbsp;</td> <td class="ccnotes">Apollo DN-3000, 12 MHz 68020 with 68881, compiled
 with in-line code for the 68881 coprocessor.
 According to Apollo, the library routines are chosen
 at runtime based on coprocessor presence. Since the
 coprocessor was present, the library is supposed to
 use in-line floating point code.
</td></tr>

<tr class="ltgrey"><td class="ct"> 15.55</td> <td class="ct">27.56</td> <td class="ccnotes">VAXstation II GPX. Compiled and executed under
 VAX/VMS C.
</td></tr>

<tr class="ltgrey"><td class="ct"> 15.14</td> <td class="ct">37.93</td> <td class="ccnotes">Macintosh II, Unix system V. Green Hills 68020
 Unix compiler with in-line code for the 68881
 coprocessor (&ldquo;-O -ZI&rdquo; switches).
</td></tr>

<tr class="ltgrey"><td class="ct"> 12.69</td> <td class="ct">&nbsp;</td> <td class="ccnotes">Sun 3/160 16 MHz, Sun C.
 Compiled with &ldquo;-fswitch&rdquo;,
 which calls a subroutine to select the fastest
 floating point processor. This was using the 68881.
</td></tr>

<tr class="ltgrey"><td class="ct"> 11.74</td> <td class="ct">26.73</td> <td class="ccnotes">Compaq Deskpro 386, 16 MHz 80386 with 16 MHz 80387.
 Metaware High C version 1.3, compiled with in-line
 for the math coprocessor (but not optimised for the
 80386/80387). Trig functions still call library
 routines.
</td></tr>

<tr class="ltgrey"><td class="ct"> 8.43</td> <td class="ct">30.49</td> <td class="ccnotes">Sun 3/160 16 MHz, Sun C.
 Compiled with &ldquo;-f68881&rdquo;,
 generating in-line MC68881 instructions. Trig
 functions still call library routines.
</td></tr>

<tr class="ltgrey"><td class="ct"> 6.29</td> <td class="ct">25.17</td> <td class="ccnotes">Sun 3/260 25 MHz, Sun C.
 Compiled with &ldquo;-f68881&rdquo;,
 generating in-line MC68881 instructions. Trig
 functions still call library routines.
</td></tr>

<tr class="ltgrey"><td class="ct"> 4.57</td> <td class="ct">&nbsp;</td> <td class="ccnotes">Sun 3/260 25 MHz, Sun FORTRAN 77. Compiled with
 &ldquo;-O -f68881&rdquo;, generating in-line MC68881 instructions.
 Trig functions are compiled in-line. This used
 the FORTRAN 77 version of the program, FBFORT77.F.
</td></tr>

<tr class="ltgrey"><td class="ct"> 4.00</td> <td class="ct">14.20</td> <td class="ccnotes">Sun386i/25 MHz model 250, Sun C compiler.
</td></tr>

<tr class="ltgrey"><td class="ct"> 4.00</td> <td class="ct">14.00</td> <td class="ccnotes">Sun386i/25 MHz model 250, Metaware C.
</td></tr>

<tr class="ltgrey"><td class="ct"> 3.10</td> <td class="ct">12.00</td> <td class="ccnotes">Compaq 386/387 25 MHz running SCO Xenix 2.
 Compiled with Metaware HighC 386, optimised
 for 386.
</td></tr>

<tr class="ltgrey"><td class="ct"> 3.00</td> <td class="ct">12.00</td> <td class="ccnotes">Compaq 386/387 25 MHz optimised for 386/387.
</td></tr>

<tr class="ltgrey"><td class="ct"> 2.96</td> <td class="ct">5.17</td> <td class="ccnotes">Sun 4/260, Sparc RISC processor. Sun C,
 compiled with the &ldquo;-O2&rdquo; switch for global
 optimisation.
</td></tr>

<tr class="ltgrey"><td class="ct"> 2.47</td> <td class="ct">&nbsp;</td> <td class="ccnotes">COMPAQ 486/25, secondary cache disabled, High C,
 486/387, inline f.p., small memory model.
</td></tr>

<tr class="ltgrey"><td class="ct"> 2.20</td> <td class="ct">3.40</td> <td class="ccnotes">Data General Motorola 88000, 16 MHz, Gnu C.
</td></tr>

<tr class="ltgrey"><td class="ct"> 1.56</td> <td class="ct">&nbsp;</td> <td class="ccnotes">COMPAQ 486/25, 128K secondary cache, High C, 486/387,
 inline f.p., small memory model.
</td></tr>

<tr class="ltgrey"><td class="ct"> 0.66</td> <td class="ct">1.50</td> <td class="ccnotes">DEC Pmax, MIPS processor.
</td></tr>

<tr class="ltgrey"><td class="ct"> 0.63</td> <td class="ct">0.91</td> <td class="ccnotes">Sun SparcStation 2, Sun C (SunOS 4.1.1) with
 &ldquo;-O4&rdquo; optimisation and &ldquo;/usr/lib/libm.il&rdquo; inline
 floating point.
</td></tr>

<tr class="ltgrey"><td class="ct"> 0.60</td> <td class="ct">1.07</td> <td class="ccnotes">Intel 860 RISC processor, 33 MHz, Greenhills
 C compiler.
</td></tr>

<tr class="ltgrey"><td class="ct"> 0.40</td> <td class="ct">0.90</td> <td class="ccnotes">Dec 3MAX,
 MIPS 3000 processor, &ldquo;-O4&rdquo;.
</td></tr>

<tr class="ltgrey"><td class="ct"> 0.31</td> <td class="ct">0.90</td> <td class="ccnotes">IBM RS/6000, &ldquo;-O&rdquo;.
</td></tr>

<tr class="ltgrey"><td class="ct"> 0.1129</td> <td class="ct">0.2119</td> <td class="ccnotes">Dell Dimension XPS P133c, Pentium 133 MHz,
 Windows 95, Microsoft Visual C 5.0.
</td></tr>

<tr class="ltgrey"><td class="ct"> 0.0883</td> <td class="ct">0.2166</td> <td class="ccnotes">Silicon
    Graphics Indigo&sup2;, MIPS R4400,
    175 MHz, &ldquo;-O3&rdquo;.
</td></tr>

<tr class="ltgrey"><td class="ct"> 0.0351</td> <td class="ct">0.0561</td> <td class="ccnotes">Dell Dimension XPS R100, Pentium II 400 MHz,
 Windows 98, Microsoft Visual C 5.0.
</td></tr>

<tr class="ltgrey"><td class="ct"> 0.0312</td> <td class="ct">0.0542</td> <td class="ccnotes">Sun Ultra 2, UltraSPARC V9, 300 MHz, Solaris
 2.5.1.
</td></tr>

<tr class="ltgrey"><td class="ct"> 0.0141</td> <td class="ct">0.0157</td> <td class="ccnotes">Raspberry Pi 3, ARMv8 Cortex-A53, 1.2 GHz, Raspbian, GCC 4.9.2 &ldquo;-O3&rdquo;
</td></tr>

<tr class="ltgrey"><td class="ct"> 0.00862</td> <td class="ct">0.01074</td> <td class="ccnotes">Dell Inspiron 9100,
 Pentium 4, 3.4 GHz, GCC 3.2.3 &ldquo;-O3&rdquo;.
</td></tr>
</table>
</center>

<blockquote>
<p class="j">
<small>
All brand and product names are trademarks or registered trademarks of
their respective companies.  Results of this benchmark may or may not be
representative of the performance of listed systems for other
programs and workloads.  Lawyers burn spontaneously in an atmosphere
of fluorine.
</small>
</p>
</blockquote>

<h3>Comparing Languages</h3>

<p class="j">
This benchmark was created primarily to compare the performance of
different computers and implementations of the C language.  Over the
years, however, the benchmark has been ported to a variety of
different programming languages.  The following table compares the
relative performance of these languages taking the run time of the C
version as 1.  For example, a language with a &ldquo;Relative Time
&rdquo; of 5 will take five times as long to complete the benchmark
as the reference C implementation.  Language benchmarks were
compared to the run time of the C implementation on the same
machine, with the iteration count of both adjusted to run about five
minutes. Relative performance was then calculated as the ratio of
time per iteration.  None of the primary results for
language implementations tested exploit the thread-level parallelism
implemented in modern processors.  All of these runs produced
precisely the <a href="#results">expected results</a>.
</p>

<center>
<table width="80%" cellpadding="2">
<tr>
    <th class="d">Language</th>
    <th class="d">Relative<br /> Time</th>
    <th class="d">Details</th>
</tr>

<tr>
    <th class="e">C</th>
    <td class="ec">1</td>
    <td class="e">GCC 3.2.3 <tt>-O3</tt>, Linux</td>
</tr>

<tr>
    <th class="e">JavaScript</th>
    <td class="ec">0.372 <br />
                   0.424 <br />
                   1.334 <br />
                   1.378 <br />
                   1.386 <br />
                   1.495 </td>
    <td class="e">Mozilla Firefox 55.0.2, Linux<br />
                  Safari 11.0, MacOS X<br />
                  Brave 0.18.36, Linux<br />
                  Google Chrome 61.0.3163.91, Linux<br />
                  Chromium 60.0.3112.113, Linux<br />
                  Node.js v6.11.3, Linux</td>
</tr>

<tr>
    <th class="e">Chapel</th>
    <td class="ec">0.528<br />
                   0.0314</td>
    <td class="e">Chapel 1.16.0, <tt>-fast</tt>, Linux<br />
                  Parallel, 64 threads</td>
</tr>

<tr>
    <th class="e">Visual Basic .NET</th>
    <td class="ec">0.866</td>
    <td class="e">All optimisations, Windows XP</td>
</tr>

<tr>
    <th class="e">C++</th>
    <td class="ec">0.939<br />
                   0.964<br />
                   31.00<br />
                   189.7<br />
                   499.9</td>
    <td class="e">G++ 5.4.0, <tt>-O3</tt>,
                  Linux, <tt>double</tt><br />
                  <tt>long double</tt> (80 bit)<br />
                  <tt>__float128</tt> (128 bit)<br />
                  MPFR (128 bit)<br />
                  MPFR (512 bit)</td>
</tr>

<tr>
    <th class="e">Modula-2</th>
    <td class="ec">0.941</td>
    <td class="e">GNU Modula-2 gm2-1.6.4 <tt>-O3</tt>, Linux</td>
</tr>

<tr>
    <th class="e">FORTRAN</th>
    <td class="ec">1.008</td>
    <td class="e">GNU Fortran (g77) 3.2.3 <tt>-O3</tt>, Linux</td>
</tr>

<tr>
    <th class="e">Pascal</th>
    <td class="ec">1.027<br />
                   1.077</td>
    <td class="e">Free Pascal 2.2.0 <tt>-O3</tt>, Linux<br />
                  GNU Pascal 2.1 (GCC 2.95.2) <tt>-O3</tt>, Linux</td>
</tr>

<tr>
    <th class="e">Swift</th>
    <td class="ec">1.054</td>
    <td class="e">Swift 3.0.1, <tt>-O</tt>, Linux</td>
</tr>

<tr>
    <th class="e">Java</th>
    <td class="ec">1.121</td>
    <td class="e">Sun JDK 1.5.0_04-b05, Linux</td>
</tr>

<tr>
    <th class="e">Visual Basic 6</th>
    <td class="ec">1.132</td>
    <td class="e">All optimisations, Windows XP</td>
</tr>

<tr>
    <th class="e">Rust</th>
    <td class="ec">1.148</td>
    <td class="e">Rust 1.43.0, <tt>--release</tt>, Linux</td>
</tr>

<tr>
    <th class="e">Haskell</th>
    <td class="ec">1.223</td>
    <td class="e">GHC 7.4.1 <tt>-O2 -funbox-strict-fields</tt>, Linux</td>
</tr>

<tr>
    <th class="e">Scala</th>
    <td class="ec">1.263</td>
    <td class="e">Scala 2.12.3, OpenJDK 9, Linux</td>
</tr>

<tr>
    <th class="e">FreeBASIC</th>
    <td class="ec">1.306</td>
    <td class="e">FreeBASIC 1.05.0, Linux</td>
</tr>

<tr>
    <th class="e">Ada</th>
    <td class="ec">1.401</td>
    <td class="e">GNAT/GCC 3.4.4 <tt>-O3</tt>, Linux</td>
</tr>

<tr>
    <th class="e">Go</th>
    <td class="ec">1.481</td>
    <td class="e">Go version go1.1.1 linux/amd64, Linux</td>
</tr>

<tr>
    <th class="e">Julia</th>
    <td class="ec">1.501</td>
    <td class="e">Julia version 0.6.1 64-bit <tt>-O2 --check-bounds=no</tt>, Linux</td>
</tr>

<tr>
    <th class="e">Simula</th>
    <td class="ec">2.099</td>
    <td class="e">GNU Cim 5.1, GCC 4.8.1 -O2, Linux</td>
</tr>

<tr>
    <th class="e">Lua</th>
    <td class="ec">2.515<br />
                   22.7</td>
    <td class="e">LuaJIT 2.0.3, Linux<br />
                  Lua 5.2.3, Linux</td>
</tr>

<tr>
    <th class="e">Python</th>
    <td class="ec">2.633<br />
                   30.0</td>
    <td class="e">PyPy 2.2.1 (Python 2.7.3), Linux<br />
                  Python 2.7.6, Linux</td>
</tr>

<tr>
    <th class="e">Erlang</th>
    <td class="ec">3.663<br />
                   9.335</td>
    <td class="e">Erlang/OTP 17, emulator 6.0, HiPE [native, {hipe, [o3]}]<br />
                  Byte code (BEAM), Linux</td>
</tr>

 <tr>
    <th class="e">ALGOL 60</th>
    <td class="ec">3.951</td>
    <td class="e">MARST 2.7, GCC 4.8.1 -O3, Linux</td>
</tr>

 <tr>
    <th class="e">PHP</th>
    <td class="ec">5.033</td>
    <td class="e">PHP (cli) 7.0.22, Linux</td>
</tr>

 <tr>
    <th class="e">PL/I</th>
    <td class="ec">5.667</td>
    <td class="e">Iron Spring PL/I 0.9.9b beta, Linux</td>
</tr>

<tr>
    <th class="e">Lisp</th>
    <td class="ec">7.41 <br />
                   19.8</td>
    <td class="e">GNU Common Lisp 2.6.7, Compiled, Linux<br />
                  GNU Common Lisp 2.6.7, Interpreted, Linux</td>
</tr>

<tr>
    <th class="e">Smalltalk</th>
    <td class="ec">7.59</td>
    <td class="e">GNU Smalltalk 2.3.5, Linux</td>
</tr>

<tr>
    <th class="e">Ruby</th>
    <td class="ec">7.832</td>
    <td class="e">Ruby 2.4.2p198, Linux</td>
</tr>

<tr>
    <th class="e">Forth</th>
    <td class="ec">9.92</td>
    <td class="e">Gforth 0.7.0, Linux</td>
</tr>

<tr>
    <th class="e">Prolog</th>
    <td class="ec">11.72<br />
                   5.747</td>
    <td class="e">SWI-Prolog 7.6.0-rc2, Linux<br />
                  GNU Prolog 1.4.4, Linux, (limited iterations)</td>
</tr>

<tr>
    <th class="e">COBOL</th>
    <td class="ec">12.5<br />
                                   46.3</td>
    <td class="e">Micro Focus Visual COBOL 2010, Windows 7<br />
                  Fixed decimal instead of <tt>computational-2</tt></td>
</tr>

<tr>
    <th class="e">Algol 68</th>
    <td class="ec">15.2</td>
    <td class="e">Algol 68 Genie 2.4.1 <tt>-O3</tt>, Linux</td>
</tr>

<tr>
    <th class="e">Perl</th>
    <td class="ec">23.6</td>
    <td class="e">Perl v5.8.0, Linux</td>
</tr>

<tr>
    <th class="e">BASICA/GW-BASIC</th>
    <td class="ec">53.42</td>
    <td class="e">Bas 2.4, Linux</td>
</tr>

<tr>
    <th class="e">QBasic</th>
    <td class="ec">148.3</td>
    <td class="e">MS-DOS QBasic 1.1, Windows XP Console</td>
</tr>

<tr>
    <th class="e">Raku</th>
    <td class="ec">205.6<br />
                   735.3</td>
    <td class="e">Rakudo v2021.09/v6.d, Linux, object-oriented rewrite<br />
                  Minimal port of Perl version</td>
</tr>

<tr>
    <th class="e">Mathematica</th>
    <td class="ec">391.6</td>
    <td class="e">Mathematica 10.3.1.0, Raspberry Pi 3, Raspbian</td>
</tr>

</table>
</center>

<p class="j">
These results should <em>not</em> be interpreted as representative of
the overall performance of the various languages for a broad variety
of tasks.  Each language port is a straightforward translation of the
reference C algorithm, and does not exploit additional
features (such as vector and matrix operations) which may be present
in the target language.  However, the nature of the algorithm does
not lend itself to such optimisations.
</p>

<p class="j">
Special thanks to Jim White
(&ldquo;<a href="mailto:mathimagics@yahoo.co.uk">mathimagics</a>&rdquo;)&mdash;approach
with extreme caution, known to be in possession of weapons of math
instruction&mdash;who ported the benchmark to Visual Basic 6, Java,
and Scilab; and to
<a href="http://www.animats.com/" target="_blank">John Nagle</a>,
who ported the benchmark to Go.
</p>

<h3><a class="i" name="results">Expected Numerical Results</a></h3>

<p class="j">
The C language version of this benchmark contains code which
automatically verifies the results of the computation with those
expected.  Implementations in some other languages may simply print
the results and leave it up to you to check that they are correct.
The following is the output from a correct execution of <b>fbench</b>
in the other languages.  There may be slight differences in the
annotations and formatting, but the numbers should be absolutely
identical.
</p>

<pre style="padding: 6px; background-color: #FFFFC0;">
                       Focal Length          Angle to Axis
Marginal ray         47.09479120920          0.04178472683
Paraxial ray         47.08372160249          0.04177864821

Longitudinal spherical aberration:        -0.01106960671
  (Maximum permissible):                   0.05306749907
                                             Acceptable

Offense against sine condition (coma):     0.00008954761
    (Maximum permissible):                 0.00250000000
                                             Acceptable

Axial chromatic aberration:                0.00448229032
    (Maximum permissible):                 0.05306749907
                                             Acceptable
</pre>

<p class="j">
Don't worry about the terminology&mdash;unless you're an optical
designer it'll probably make no sense whatsoever.  What's
important is that the numbers agree to the last decimal place;
if they don't, it's a sign something is amiss.  If you've
compiled the benchmark with aggressive optimisation,
you might try more conservative settings to see if that
corrects the results.
</p>

<h3 class="nav"><a href="ffbench.html">FFBENCH</a>: Fast Fourier Transform Benchmark</h3>
<h3 class="nav"><a href="./">Floating Point Benchmarks</a></h3>
<h3 class="nav"><a href="/">Fourmilab Home Page</a></h3>

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<a href="/">by John Walker</a><br />
September 24th, 2021
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