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