#!/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 <

#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 <

#endif /* JEMALLOC_INTERNAL_SMOOTHSTEP_H */

EOF