1#!/bin/sh
2#
3# Generate a discrete lookup table for a sigmoid function in the smoothstep
4# family (https://en.wikipedia.org/wiki/Smoothstep), where the lookup table
5# entries correspond to x in [1/nsteps, 2/nsteps, ..., nsteps/nsteps].  Encode
6# the entries using a binary fixed point representation.
7#
8# Usage: smoothstep.sh <variant> <nsteps> <bfp> <xprec> <yprec>
9#
10#        <variant> is in {smooth, smoother, smoothest}.
11#        <nsteps> must be greater than zero.
12#        <bfp> must be in [0..62]; reasonable values are roughly [10..30].
13#        <xprec> is x decimal precision.
14#        <yprec> is y decimal precision.
15
16#set -x
17
18cmd="sh smoothstep.sh $*"
19variant=$1
20nsteps=$2
21bfp=$3
22xprec=$4
23yprec=$5
24
25case "${variant}" in
26  smooth)
27    ;;
28  smoother)
29    ;;
30  smoothest)
31    ;;
32  *)
33    echo "Unsupported variant"
34    exit 1
35    ;;
36esac
37
38smooth() {
39  step=$1
40  y=`echo ${yprec} k ${step} ${nsteps} / sx _2 lx 3 ^ '*' 3 lx 2 ^ '*' + p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g'`
41  h=`echo ${yprec} k 2 ${bfp} ^ ${y} '*' p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g' | tr '.' ' ' | awk '{print $1}' `
42}
43
44smoother() {
45  step=$1
46  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'`
47  h=`echo ${yprec} k 2 ${bfp} ^ ${y} '*' p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g' | tr '.' ' ' | awk '{print $1}' `
48}
49
50smoothest() {
51  step=$1
52  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'`
53  h=`echo ${yprec} k 2 ${bfp} ^ ${y} '*' p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g' | tr '.' ' ' | awk '{print $1}' `
54}
55
56cat <<EOF
57#ifndef JEMALLOC_INTERNAL_SMOOTHSTEP_H
58#define JEMALLOC_INTERNAL_SMOOTHSTEP_H
59
60/*
61 * This file was generated by the following command:
62 *   $cmd
63 */
64/******************************************************************************/
65
66/*
67 * This header defines a precomputed table based on the smoothstep family of
68 * sigmoidal curves (https://en.wikipedia.org/wiki/Smoothstep) that grow from 0
69 * to 1 in 0 <= x <= 1.  The table is stored as integer fixed point values so
70 * that floating point math can be avoided.
71 *
72 *                      3     2
73 *   smoothstep(x) = -2x  + 3x
74 *
75 *                       5      4      3
76 *   smootherstep(x) = 6x  - 15x  + 10x
77 *
78 *                          7      6      5      4
79 *   smootheststep(x) = -20x  + 70x  - 84x  + 35x
80 */
81
82#define SMOOTHSTEP_VARIANT	"${variant}"
83#define SMOOTHSTEP_NSTEPS	${nsteps}
84#define SMOOTHSTEP_BFP		${bfp}
85#define SMOOTHSTEP \\
86 /* STEP(step, h,                            x,     y) */ \\
87EOF
88
89s=1
90while [ $s -le $nsteps ] ; do
91  $variant ${s}
92  x=`echo ${xprec} k ${s} ${nsteps} / p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g'`
93  printf '    STEP(%4d, UINT64_C(0x%016x), %s, %s) \\\n' ${s} ${h} ${x} ${y}
94
95  s=$((s+1))
96done
97echo
98
99cat <<EOF
100#endif /* JEMALLOC_INTERNAL_SMOOTHSTEP_H */
101EOF
102