+/*-
+ * Copyright (c) 1982, 1986, 1990, 1991, 1993
+ * The Regents of the University of California. All rights reserved.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ * must display the following acknowledgement:
+ * This product includes software developed by the University of
+ * California, Berkeley and its contributors.
+ * 4. Neither the name of the University nor the names of its contributors
+ * may be used to endorse or promote products derived from this software
+ * without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ *
+ * @(#)kern_synch.c 8.1 (Berkeley) 6/10/93
+ */
+
+#include <sys/param.h>
+#include <sys/systm.h>
+#include <sys/proc.h>
+#include <sys/kernel.h>
+#include <sys/buf.h>
+#include <sys/signalvar.h>
+#include <sys/resourcevar.h>
+#include <sys/vmmeter.h>
+#ifdef KTRACE
+#include <sys/ktrace.h>
+#endif
+
+#include <machine/cpu.h>
+
+u_char curpri; /* usrpri of curproc */
+int lbolt; /* once a second sleep address */
+
+/*
+ * Force switch among equal priority processes every 100ms.
+ */
+/* ARGSUSED */
+void
+roundrobin(arg)
+ void *arg;
+{
+
+ need_resched();
+ timeout(roundrobin, (void *)0, hz / 10);
+}
+
+/*
+ * constants for digital decay and forget
+ * 90% of (p_cpu) usage in 5*loadav time
+ * 95% of (p_pctcpu) usage in 60 seconds (load insensitive)
+ * Note that, as ps(1) mentions, this can let percentages
+ * total over 100% (I've seen 137.9% for 3 processes).
+ *
+ * Note that hardclock updates p_cpu and p_cpticks independently.
+ *
+ * We wish to decay away 90% of p_cpu in (5 * loadavg) seconds.
+ * That is, the system wants to compute a value of decay such
+ * that the following for loop:
+ * for (i = 0; i < (5 * loadavg); i++)
+ * p_cpu *= decay;
+ * will compute
+ * p_cpu *= 0.1;
+ * for all values of loadavg:
+ *
+ * Mathematically this loop can be expressed by saying:
+ * decay ** (5 * loadavg) ~= .1
+ *
+ * The system computes decay as:
+ * decay = (2 * loadavg) / (2 * loadavg + 1)
+ *
+ * We wish to prove that the system's computation of decay
+ * will always fulfill the equation:
+ * decay ** (5 * loadavg) ~= .1
+ *
+ * If we compute b as:
+ * b = 2 * loadavg
+ * then
+ * decay = b / (b + 1)
+ *
+ * We now need to prove two things:
+ * 1) Given factor ** (5 * loadavg) ~= .1, prove factor == b/(b+1)
+ * 2) Given b/(b+1) ** power ~= .1, prove power == (5 * loadavg)
+ *
+ * Facts:
+ * For x close to zero, exp(x) =~ 1 + x, since
+ * exp(x) = 0! + x**1/1! + x**2/2! + ... .
+ * therefore exp(-1/b) =~ 1 - (1/b) = (b-1)/b.
+ * For x close to zero, ln(1+x) =~ x, since
+ * ln(1+x) = x - x**2/2 + x**3/3 - ... -1 < x < 1
+ * therefore ln(b/(b+1)) = ln(1 - 1/(b+1)) =~ -1/(b+1).
+ * ln(.1) =~ -2.30
+ *
+ * Proof of (1):
+ * Solve (factor)**(power) =~ .1 given power (5*loadav):
+ * solving for factor,
+ * ln(factor) =~ (-2.30/5*loadav), or
+ * factor =~ exp(-1/((5/2.30)*loadav)) =~ exp(-1/(2*loadav)) =
+ * exp(-1/b) =~ (b-1)/b =~ b/(b+1). QED
+ *
+ * Proof of (2):
+ * Solve (factor)**(power) =~ .1 given factor == (b/(b+1)):
+ * solving for power,
+ * power*ln(b/(b+1)) =~ -2.30, or
+ * power =~ 2.3 * (b + 1) = 4.6*loadav + 2.3 =~ 5*loadav. QED
+ *
+ * Actual power values for the implemented algorithm are as follows:
+ * loadav: 1 2 3 4
+ * power: 5.68 10.32 14.94 19.55
+ */
+
+/* calculations for digital decay to forget 90% of usage in 5*loadav sec */
+#define loadfactor(loadav) (2 * (loadav))
+#define decay_cpu(loadfac, cpu) (((loadfac) * (cpu)) / ((loadfac) + FSCALE))