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#!/bin/sh
#
# Generate a discrete lookup table for a sigmoid function in the smoothstep
# family (https://en.wikipedia.org/wiki/Smoothstep), where the lookup table
# entries correspond to x in [1/nsteps, 2/nsteps, ..., nsteps/nsteps]. Encode
# the entries using a binary fixed point representation.
#
# Usage: smoothstep.sh <variant> <nsteps> <bfp> <xprec> <yprec>
#
# <variant> is in {smooth, smoother, smoothest}.
# <nsteps> must be greater than zero.
# <bfp> must be in [0..62]; reasonable values are roughly [10..30].
# <xprec> is x decimal precision.
# <yprec> is y decimal precision.
#set -x
cmd="sh smoothstep.sh $*"
variant=$1
nsteps=$2
bfp=$3
xprec=$4
yprec=$5
case "${variant}" in
smooth)
;;
smoother)
;;
smoothest)
;;
*)
echo "Unsupported variant"
exit 1
;;
esac
smooth() {
step=$1
y=`echo ${yprec} k ${step} ${nsteps} / sx _2 lx 3 ^ '*' 3 lx 2 ^ '*' + p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g'`
h=`echo ${yprec} k 2 ${bfp} ^ ${y} '*' p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g' | tr '.' ' ' | awk '{print $1}' `
}
smoother() {
step=$1
y=`echo ${yprec} k ${step} ${nsteps} / sx 6 lx 5 ^ '*' _15 lx 4 ^ '*' + 10 lx 3 ^ '*' + p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g'`
h=`echo ${yprec} k 2 ${bfp} ^ ${y} '*' p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g' | tr '.' ' ' | awk '{print $1}' `
}
smoothest() {
step=$1
y=`echo ${yprec} k ${step} ${nsteps} / sx _20 lx 7 ^ '*' 70 lx 6 ^ '*' + _84 lx 5 ^ '*' + 35 lx 4 ^ '*' + p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g'`
h=`echo ${yprec} k 2 ${bfp} ^ ${y} '*' p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g' | tr '.' ' ' | awk '{print $1}' `
}
cat <<EOF
#ifndef JEMALLOC_INTERNAL_SMOOTHSTEP_H
#define JEMALLOC_INTERNAL_SMOOTHSTEP_H
/*
* This file was generated by the following command:
* $cmd
*/
/******************************************************************************/
/*
* This header defines a precomputed table based on the smoothstep family of
* sigmoidal curves (https://en.wikipedia.org/wiki/Smoothstep) that grow from 0
* to 1 in 0 <= x <= 1. The table is stored as integer fixed point values so
* that floating point math can be avoided.
*
* 3 2
* smoothstep(x) = -2x + 3x
*
* 5 4 3
* smootherstep(x) = 6x - 15x + 10x
*
* 7 6 5 4
* smootheststep(x) = -20x + 70x - 84x + 35x
*/
#define SMOOTHSTEP_VARIANT "${variant}"
#define SMOOTHSTEP_NSTEPS ${nsteps}
#define SMOOTHSTEP_BFP ${bfp}
#define SMOOTHSTEP \\
/* STEP(step, h, x, y) */ \\
EOF
s=1
while [ $s -le $nsteps ] ; do
$variant ${s}
x=`echo ${xprec} k ${s} ${nsteps} / p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g'`
printf ' STEP(%4d, UINT64_C(0x%016x), %s, %s) \\\n' ${s} ${h} ${x} ${y}
s=$((s+1))
done
echo
cat <<EOF
#endif /* JEMALLOC_INTERNAL_SMOOTHSTEP_H */
EOF
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