src/jemalloc/include/jemalloc/internal/smoothstep.sh

   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
  18 cmd="sh smoothstep.sh $*"
  19 variant=$1
  20 nsteps=$2
  21 bfp=$3
  22 xprec=$4
  23 yprec=$5
  24
  25 case "${variant}" in
  26   smooth)
  27     ;;
  28   smoother)
  29     ;;
  30   smoothest)
  31     ;;
  32   *)
  33     echo "Unsupported variant"
  34     exit 1
  35     ;;
  36 esac
  37
  38 smooth() {
  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
  44 smoother() {
  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
  50 smoothest() {
  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
  56 cat <<EOF
  57 /*
  58  * This file was generated by the following command:
  59  *   $cmd
  60  */
  61 /******************************************************************************/
  62 #ifdef JEMALLOC_H_TYPES
  63
  64 /*
  65  * This header defines a precomputed table based on the smoothstep family of
  66  * sigmoidal curves (https://en.wikipedia.org/wiki/Smoothstep) that grow from 0
  67  * to 1 in 0 <= x <= 1.  The table is stored as integer fixed point values so
  68  * that floating point math can be avoided.
  69  *
  70  *                      3     2
  71  *   smoothstep(x) = -2x  + 3x
  72  *
  73  *                       5      4      3
  74  *   smootherstep(x) = 6x  - 15x  + 10x
  75  *
  76  *                          7      6      5      4
  77  *   smootheststep(x) = -20x  + 70x  - 84x  + 35x
  78  */
  79
  80 #define SMOOTHSTEP_VARIANT      "${variant}"
  81 #define SMOOTHSTEP_NSTEPS       ${nsteps}
  82 #define SMOOTHSTEP_BFP          ${bfp}
  83 #define SMOOTHSTEP \\
  84  /* STEP(step, h,                            x,     y) */ \\
  85 EOF
  86
  87 s=1
  88 while [ $s -le $nsteps ] ; do
  89   $variant ${s}
  90   x=`echo ${xprec} k ${s} ${nsteps} / p | dc | tr -d '\\\\\n' | sed -e 's#^\.#0.#g'`
  91   printf '    STEP(%4d, UINT64_C(0x%016x), %s, %s) \\\n' ${s} ${h} ${x} ${y}
  92
  93   s=$((s+1))
  94 done
  95 echo
  96
  97 cat <<EOF
  98 #endif /* JEMALLOC_H_TYPES */
  99 /******************************************************************************/
 100 #ifdef JEMALLOC_H_STRUCTS
 101
 102
 103 #endif /* JEMALLOC_H_STRUCTS */
 104 /******************************************************************************/
 105 #ifdef JEMALLOC_H_EXTERNS
 106
 107
 108 #endif /* JEMALLOC_H_EXTERNS */
 109 /******************************************************************************/
 110 #ifdef JEMALLOC_H_INLINES
 111
 112
 113 #endif /* JEMALLOC_H_INLINES */
 114 /******************************************************************************/
 115 EOF