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POWhat is the fastest way to get the value of π?
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copied!<p>I'm looking for the fastest way to obtain the value of π, as a personal challenge. More specifically, I'm using ways that don't involve using <code>#define</code> constants like <code>M_PI</code>, or hard-coding the number in.</p> <p>The program below tests the various ways I know of. The inline assembly version is, in theory, the fastest option, though clearly not portable. I've included it as a baseline to compare against the other versions. In my tests, with built-ins, the <code>4 * atan(1)</code> version is fastest on GCC 4.2, because it auto-folds the <code>atan(1)</code> into a constant. With <code>-fno-builtin</code> specified, the <code>atan2(0, -1)</code> version is fastest.</p> <p>Here's the main testing program (<code>pitimes.c</code>):</p> <pre class="lang-c prettyprint-override"><code>#include <math.h> #include <stdio.h> #include <time.h> #define ITERS 10000000 #define TESTWITH(x) { \ diff = 0.0; \ time1 = clock(); \ for (i = 0; i < ITERS; ++i) \ diff += (x) - M_PI; \ time2 = clock(); \ printf("%s\t=> %e, time => %f\n", #x, diff, diffclock(time2, time1)); \ } static inline double diffclock(clock_t time1, clock_t time0) { return (double) (time1 - time0) / CLOCKS_PER_SEC; } int main() { int i; clock_t time1, time2; double diff; /* Warmup. The atan2 case catches GCC's atan folding (which would * optimise the ``4 * atan(1) - M_PI'' to a no-op), if -fno-builtin * is not used. */ TESTWITH(4 * atan(1)) TESTWITH(4 * atan2(1, 1)) #if defined(__GNUC__) && (defined(__i386__) || defined(__amd64__)) extern double fldpi(); TESTWITH(fldpi()) #endif /* Actual tests start here. */ TESTWITH(atan2(0, -1)) TESTWITH(acos(-1)) TESTWITH(2 * asin(1)) TESTWITH(4 * atan2(1, 1)) TESTWITH(4 * atan(1)) return 0; } </code></pre> <p>And the inline assembly stuff (<code>fldpi.c</code>) that will only work for x86 and x64 systems:</p> <pre class="lang-c prettyprint-override"><code>double fldpi() { double pi; asm("fldpi" : "=t" (pi)); return pi; } </code></pre> <p>And a build script that builds all the configurations I'm testing (<code>build.sh</code>):</p> <pre><code>#!/bin/sh gcc -O3 -Wall -c -m32 -o fldpi-32.o fldpi.c gcc -O3 -Wall -c -m64 -o fldpi-64.o fldpi.c gcc -O3 -Wall -ffast-math -m32 -o pitimes1-32 pitimes.c fldpi-32.o gcc -O3 -Wall -m32 -o pitimes2-32 pitimes.c fldpi-32.o -lm gcc -O3 -Wall -fno-builtin -m32 -o pitimes3-32 pitimes.c fldpi-32.o -lm gcc -O3 -Wall -ffast-math -m64 -o pitimes1-64 pitimes.c fldpi-64.o -lm gcc -O3 -Wall -m64 -o pitimes2-64 pitimes.c fldpi-64.o -lm gcc -O3 -Wall -fno-builtin -m64 -o pitimes3-64 pitimes.c fldpi-64.o -lm </code></pre> <p>Apart from testing between various compiler flags (I've compared 32-bit against 64-bit too, because the optimisations are different), I've also tried switching the order of the tests around. But still, the <code>atan2(0, -1)</code> version still comes out on top every time.</p>

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