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Implement smoothstep table generation.

Browse Source 
Check in a generated smootherstep table as smoothstep.h rather than
generating it at configure time, since not all systems (e.g. Windows)
have dc.
This commit is contained in:
Jason Evans 2016-02-06 00:46:19 -08:00 committed by Jason Evans
parent 1a4ad3c0fa
commit 8e82af1166
5 changed files with 472 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

1
Makefile.in
View File

@ -144,6 +144,7 @@ TESTS_UNIT := $(srcroot)test/unit/atomic.c \
$(srcroot)test/unit/rtree.c \
$(srcroot)test/unit/SFMT.c \
$(srcroot)test/unit/size_classes.c \
$(srcroot)test/unit/smoothstep.c \
$(srcroot)test/unit/stats.c \
$(srcroot)test/unit/ticker.c \
$(srcroot)test/unit/time.c \

4
include/jemalloc/internal/jemalloc_internal.h.in
View File

@ -364,6 +364,7 @@ typedef unsigned szind_t;
#include "jemalloc/internal/ticker.h"
#include "jemalloc/internal/ckh.h"
#include "jemalloc/internal/size_classes.h"
#include "jemalloc/internal/smoothstep.h"
#include "jemalloc/internal/stats.h"
#include "jemalloc/internal/ctl.h"
#include "jemalloc/internal/mutex.h"
@ -394,6 +395,7 @@ typedef unsigned szind_t;
#include "jemalloc/internal/ticker.h"
#include "jemalloc/internal/ckh.h"
#include "jemalloc/internal/size_classes.h"
#include "jemalloc/internal/smoothstep.h"
#include "jemalloc/internal/stats.h"
#include "jemalloc/internal/ctl.h"
#include "jemalloc/internal/mutex.h"
@ -483,6 +485,7 @@ void jemalloc_postfork_child(void);
#include "jemalloc/internal/ticker.h"
#include "jemalloc/internal/ckh.h"
#include "jemalloc/internal/size_classes.h"
#include "jemalloc/internal/smoothstep.h"
#include "jemalloc/internal/stats.h"
#include "jemalloc/internal/ctl.h"
#include "jemalloc/internal/mutex.h"
@ -513,6 +516,7 @@ void jemalloc_postfork_child(void);
#include "jemalloc/internal/ticker.h"
#include "jemalloc/internal/ckh.h"
#include "jemalloc/internal/size_classes.h"
#include "jemalloc/internal/smoothstep.h"
#include "jemalloc/internal/stats.h"
#include "jemalloc/internal/ctl.h"
#include "jemalloc/internal/mutex.h"

246
include/jemalloc/internal/smoothstep.h Normal file
View File

@ -0,0 +1,246 @@
/*
* This file was generated by the following command:
* sh smoothstep.sh smoother 200 24 3 15
*/
/******************************************************************************/
#ifdef JEMALLOC_H_TYPES
/*
* 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 "smoother"
#define SMOOTHSTEP_NSTEPS 200
#define SMOOTHSTEP_BFP 24
#define SMOOTHSTEP \
/* STEP(step, h, x, y) */ \
STEP( 1, UINT64_C(0x0000000000000014), 0.005, 0.000001240643750) \
STEP( 2, UINT64_C(0x00000000000000a5), 0.010, 0.000009850600000) \
STEP( 3, UINT64_C(0x0000000000000229), 0.015, 0.000032995181250) \
STEP( 4, UINT64_C(0x0000000000000516), 0.020, 0.000077619200000) \
STEP( 5, UINT64_C(0x00000000000009dc), 0.025, 0.000150449218750) \
STEP( 6, UINT64_C(0x00000000000010e8), 0.030, 0.000257995800000) \
STEP( 7, UINT64_C(0x0000000000001aa4), 0.035, 0.000406555756250) \
STEP( 8, UINT64_C(0x0000000000002777), 0.040, 0.000602214400000) \
STEP( 9, UINT64_C(0x00000000000037c2), 0.045, 0.000850847793750) \
STEP( 10, UINT64_C(0x0000000000004be6), 0.050, 0.001158125000000) \
STEP( 11, UINT64_C(0x000000000000643c), 0.055, 0.001529510331250) \
STEP( 12, UINT64_C(0x000000000000811f), 0.060, 0.001970265600000) \
STEP( 13, UINT64_C(0x000000000000a2e2), 0.065, 0.002485452368750) \
STEP( 14, UINT64_C(0x000000000000c9d8), 0.070, 0.003079934200000) \
STEP( 15, UINT64_C(0x000000000000f64f), 0.075, 0.003758378906250) \
STEP( 16, UINT64_C(0x0000000000012891), 0.080, 0.004525260800000) \
STEP( 17, UINT64_C(0x00000000000160e7), 0.085, 0.005384862943750) \
STEP( 18, UINT64_C(0x0000000000019f95), 0.090, 0.006341279400000) \
STEP( 19, UINT64_C(0x000000000001e4dc), 0.095, 0.007398417481250) \
STEP( 20, UINT64_C(0x00000000000230fc), 0.100, 0.008560000000000) \
STEP( 21, UINT64_C(0x0000000000028430), 0.105, 0.009829567518750) \
STEP( 22, UINT64_C(0x000000000002deb0), 0.110, 0.011210480600000) \
STEP( 23, UINT64_C(0x00000000000340b1), 0.115, 0.012705922056250) \
STEP( 24, UINT64_C(0x000000000003aa67), 0.120, 0.014318899200000) \
STEP( 25, UINT64_C(0x0000000000041c00), 0.125, 0.016052246093750) \
STEP( 26, UINT64_C(0x00000000000495a8), 0.130, 0.017908625800000) \
STEP( 27, UINT64_C(0x000000000005178b), 0.135, 0.019890532631250) \
STEP( 28, UINT64_C(0x000000000005a1cf), 0.140, 0.022000294400000) \
STEP( 29, UINT64_C(0x0000000000063498), 0.145, 0.024240074668750) \
STEP( 30, UINT64_C(0x000000000006d009), 0.150, 0.026611875000000) \
STEP( 31, UINT64_C(0x000000000007743f), 0.155, 0.029117537206250) \
STEP( 32, UINT64_C(0x0000000000082157), 0.160, 0.031758745600000) \
STEP( 33, UINT64_C(0x000000000008d76b), 0.165, 0.034537029243750) \
STEP( 34, UINT64_C(0x0000000000099691), 0.170, 0.037453764200000) \
STEP( 35, UINT64_C(0x00000000000a5edf), 0.175, 0.040510175781250) \
STEP( 36, UINT64_C(0x00000000000b3067), 0.180, 0.043707340800000) \
STEP( 37, UINT64_C(0x00000000000c0b38), 0.185, 0.047046189818750) \
STEP( 38, UINT64_C(0x00000000000cef5e), 0.190, 0.050527509400000) \
STEP( 39, UINT64_C(0x00000000000ddce6), 0.195, 0.054151944356250) \
STEP( 40, UINT64_C(0x00000000000ed3d8), 0.200, 0.057920000000000) \
STEP( 41, UINT64_C(0x00000000000fd439), 0.205, 0.061832044393750) \
STEP( 42, UINT64_C(0x000000000010de0e), 0.210, 0.065888310600000) \
STEP( 43, UINT64_C(0x000000000011f158), 0.215, 0.070088898931250) \
STEP( 44, UINT64_C(0x0000000000130e17), 0.220, 0.074433779200000) \
STEP( 45, UINT64_C(0x0000000000143448), 0.225, 0.078922792968750) \
STEP( 46, UINT64_C(0x00000000001563e7), 0.230, 0.083555655800000) \
STEP( 47, UINT64_C(0x0000000000169cec), 0.235, 0.088331959506250) \
STEP( 48, UINT64_C(0x000000000017df4f), 0.240, 0.093251174400000) \
STEP( 49, UINT64_C(0x0000000000192b04), 0.245, 0.098312651543750) \
STEP( 50, UINT64_C(0x00000000001a8000), 0.250, 0.103515625000000) \
STEP( 51, UINT64_C(0x00000000001bde32), 0.255, 0.108859214081250) \
STEP( 52, UINT64_C(0x00000000001d458b), 0.260, 0.114342425600000) \
STEP( 53, UINT64_C(0x00000000001eb5f8), 0.265, 0.119964156118750) \
STEP( 54, UINT64_C(0x0000000000202f65), 0.270, 0.125723194200000) \
STEP( 55, UINT64_C(0x000000000021b1bb), 0.275, 0.131618222656250) \
STEP( 56, UINT64_C(0x0000000000233ce3), 0.280, 0.137647820800000) \
STEP( 57, UINT64_C(0x000000000024d0c3), 0.285, 0.143810466693750) \
STEP( 58, UINT64_C(0x0000000000266d40), 0.290, 0.150104539400000) \
STEP( 59, UINT64_C(0x000000000028123d), 0.295, 0.156528321231250) \
STEP( 60, UINT64_C(0x000000000029bf9c), 0.300, 0.163080000000000) \
STEP( 61, UINT64_C(0x00000000002b753d), 0.305, 0.169757671268750) \
STEP( 62, UINT64_C(0x00000000002d32fe), 0.310, 0.176559340600000) \
STEP( 63, UINT64_C(0x00000000002ef8bc), 0.315, 0.183482925806250) \
STEP( 64, UINT64_C(0x000000000030c654), 0.320, 0.190526259200000) \
STEP( 65, UINT64_C(0x0000000000329b9f), 0.325, 0.197687089843750) \
STEP( 66, UINT64_C(0x0000000000347875), 0.330, 0.204963085800000) \
STEP( 67, UINT64_C(0x0000000000365cb0), 0.335, 0.212351836381250) \
STEP( 68, UINT64_C(0x0000000000384825), 0.340, 0.219850854400000) \
STEP( 69, UINT64_C(0x00000000003a3aa8), 0.345, 0.227457578418750) \
STEP( 70, UINT64_C(0x00000000003c340f), 0.350, 0.235169375000000) \
STEP( 71, UINT64_C(0x00000000003e342b), 0.355, 0.242983540956250) \
STEP( 72, UINT64_C(0x0000000000403ace), 0.360, 0.250897305600000) \
STEP( 73, UINT64_C(0x00000000004247c8), 0.365, 0.258907832993750) \
STEP( 74, UINT64_C(0x0000000000445ae9), 0.370, 0.267012224200000) \
STEP( 75, UINT64_C(0x0000000000467400), 0.375, 0.275207519531250) \
STEP( 76, UINT64_C(0x00000000004892d8), 0.380, 0.283490700800000) \
STEP( 77, UINT64_C(0x00000000004ab740), 0.385, 0.291858693568750) \
STEP( 78, UINT64_C(0x00000000004ce102), 0.390, 0.300308369400000) \
STEP( 79, UINT64_C(0x00000000004f0fe9), 0.395, 0.308836548106250) \
STEP( 80, UINT64_C(0x00000000005143bf), 0.400, 0.317440000000000) \
STEP( 81, UINT64_C(0x0000000000537c4d), 0.405, 0.326115448143750) \
STEP( 82, UINT64_C(0x000000000055b95b), 0.410, 0.334859570600000) \
STEP( 83, UINT64_C(0x000000000057fab1), 0.415, 0.343669002681250) \
STEP( 84, UINT64_C(0x00000000005a4015), 0.420, 0.352540339200000) \
STEP( 85, UINT64_C(0x00000000005c894e), 0.425, 0.361470136718750) \
STEP( 86, UINT64_C(0x00000000005ed622), 0.430, 0.370454915800000) \
STEP( 87, UINT64_C(0x0000000000612655), 0.435, 0.379491163256250) \
STEP( 88, UINT64_C(0x00000000006379ac), 0.440, 0.388575334400000) \
STEP( 89, UINT64_C(0x000000000065cfeb), 0.445, 0.397703855293750) \
STEP( 90, UINT64_C(0x00000000006828d6), 0.450, 0.406873125000000) \
STEP( 91, UINT64_C(0x00000000006a842f), 0.455, 0.416079517831250) \
STEP( 92, UINT64_C(0x00000000006ce1bb), 0.460, 0.425319385600000) \
STEP( 93, UINT64_C(0x00000000006f413a), 0.465, 0.434589059868750) \
STEP( 94, UINT64_C(0x000000000071a270), 0.470, 0.443884854200000) \
STEP( 95, UINT64_C(0x000000000074051d), 0.475, 0.453203066406250) \
STEP( 96, UINT64_C(0x0000000000766905), 0.480, 0.462539980800000) \
STEP( 97, UINT64_C(0x000000000078cde7), 0.485, 0.471891870443750) \
STEP( 98, UINT64_C(0x00000000007b3387), 0.490, 0.481254999400000) \
STEP( 99, UINT64_C(0x00000000007d99a4), 0.495, 0.490625624981250) \
STEP( 100, UINT64_C(0x0000000000800000), 0.500, 0.500000000000000) \
STEP( 101, UINT64_C(0x000000000082665b), 0.505, 0.509374375018750) \
STEP( 102, UINT64_C(0x000000000084cc78), 0.510, 0.518745000600000) \
STEP( 103, UINT64_C(0x0000000000873218), 0.515, 0.528108129556250) \
STEP( 104, UINT64_C(0x00000000008996fa), 0.520, 0.537460019200000) \
STEP( 105, UINT64_C(0x00000000008bfae2), 0.525, 0.546796933593750) \
STEP( 106, UINT64_C(0x00000000008e5d8f), 0.530, 0.556115145800000) \
STEP( 107, UINT64_C(0x000000000090bec5), 0.535, 0.565410940131250) \
STEP( 108, UINT64_C(0x0000000000931e44), 0.540, 0.574680614400000) \
STEP( 109, UINT64_C(0x0000000000957bd0), 0.545, 0.583920482168750) \
STEP( 110, UINT64_C(0x000000000097d729), 0.550, 0.593126875000000) \
STEP( 111, UINT64_C(0x00000000009a3014), 0.555, 0.602296144706250) \
STEP( 112, UINT64_C(0x00000000009c8653), 0.560, 0.611424665600000) \
STEP( 113, UINT64_C(0x00000000009ed9aa), 0.565, 0.620508836743750) \
STEP( 114, UINT64_C(0x0000000000a129dd), 0.570, 0.629545084200000) \
STEP( 115, UINT64_C(0x0000000000a376b1), 0.575, 0.638529863281250) \
STEP( 116, UINT64_C(0x0000000000a5bfea), 0.580, 0.647459660800000) \
STEP( 117, UINT64_C(0x0000000000a8054e), 0.585, 0.656330997318750) \
STEP( 118, UINT64_C(0x0000000000aa46a4), 0.590, 0.665140429400000) \
STEP( 119, UINT64_C(0x0000000000ac83b2), 0.595, 0.673884551856250) \
STEP( 120, UINT64_C(0x0000000000aebc40), 0.600, 0.682560000000000) \
STEP( 121, UINT64_C(0x0000000000b0f016), 0.605, 0.691163451893750) \
STEP( 122, UINT64_C(0x0000000000b31efd), 0.610, 0.699691630600000) \
STEP( 123, UINT64_C(0x0000000000b548bf), 0.615, 0.708141306431250) \
STEP( 124, UINT64_C(0x0000000000b76d27), 0.620, 0.716509299200000) \
STEP( 125, UINT64_C(0x0000000000b98c00), 0.625, 0.724792480468750) \
STEP( 126, UINT64_C(0x0000000000bba516), 0.630, 0.732987775800000) \
STEP( 127, UINT64_C(0x0000000000bdb837), 0.635, 0.741092167006250) \
STEP( 128, UINT64_C(0x0000000000bfc531), 0.640, 0.749102694400000) \
STEP( 129, UINT64_C(0x0000000000c1cbd4), 0.645, 0.757016459043750) \
STEP( 130, UINT64_C(0x0000000000c3cbf0), 0.650, 0.764830625000000) \
STEP( 131, UINT64_C(0x0000000000c5c557), 0.655, 0.772542421581250) \
STEP( 132, UINT64_C(0x0000000000c7b7da), 0.660, 0.780149145600000) \
STEP( 133, UINT64_C(0x0000000000c9a34f), 0.665, 0.787648163618750) \
STEP( 134, UINT64_C(0x0000000000cb878a), 0.670, 0.795036914200000) \
STEP( 135, UINT64_C(0x0000000000cd6460), 0.675, 0.802312910156250) \
STEP( 136, UINT64_C(0x0000000000cf39ab), 0.680, 0.809473740800000) \
STEP( 137, UINT64_C(0x0000000000d10743), 0.685, 0.816517074193750) \
STEP( 138, UINT64_C(0x0000000000d2cd01), 0.690, 0.823440659400000) \
STEP( 139, UINT64_C(0x0000000000d48ac2), 0.695, 0.830242328731250) \
STEP( 140, UINT64_C(0x0000000000d64063), 0.700, 0.836920000000000) \
STEP( 141, UINT64_C(0x0000000000d7edc2), 0.705, 0.843471678768750) \
STEP( 142, UINT64_C(0x0000000000d992bf), 0.710, 0.849895460600000) \
STEP( 143, UINT64_C(0x0000000000db2f3c), 0.715, 0.856189533306250) \
STEP( 144, UINT64_C(0x0000000000dcc31c), 0.720, 0.862352179200000) \
STEP( 145, UINT64_C(0x0000000000de4e44), 0.725, 0.868381777343750) \
STEP( 146, UINT64_C(0x0000000000dfd09a), 0.730, 0.874276805800000) \
STEP( 147, UINT64_C(0x0000000000e14a07), 0.735, 0.880035843881250) \
STEP( 148, UINT64_C(0x0000000000e2ba74), 0.740, 0.885657574400000) \
STEP( 149, UINT64_C(0x0000000000e421cd), 0.745, 0.891140785918750) \
STEP( 150, UINT64_C(0x0000000000e58000), 0.750, 0.896484375000000) \
STEP( 151, UINT64_C(0x0000000000e6d4fb), 0.755, 0.901687348456250) \
STEP( 152, UINT64_C(0x0000000000e820b0), 0.760, 0.906748825600000) \
STEP( 153, UINT64_C(0x0000000000e96313), 0.765, 0.911668040493750) \
STEP( 154, UINT64_C(0x0000000000ea9c18), 0.770, 0.916444344200000) \
STEP( 155, UINT64_C(0x0000000000ebcbb7), 0.775, 0.921077207031250) \
STEP( 156, UINT64_C(0x0000000000ecf1e8), 0.780, 0.925566220800000) \
STEP( 157, UINT64_C(0x0000000000ee0ea7), 0.785, 0.929911101068750) \
STEP( 158, UINT64_C(0x0000000000ef21f1), 0.790, 0.934111689400000) \
STEP( 159, UINT64_C(0x0000000000f02bc6), 0.795, 0.938167955606250) \
STEP( 160, UINT64_C(0x0000000000f12c27), 0.800, 0.942080000000000) \
STEP( 161, UINT64_C(0x0000000000f22319), 0.805, 0.945848055643750) \
STEP( 162, UINT64_C(0x0000000000f310a1), 0.810, 0.949472490600000) \
STEP( 163, UINT64_C(0x0000000000f3f4c7), 0.815, 0.952953810181250) \
STEP( 164, UINT64_C(0x0000000000f4cf98), 0.820, 0.956292659200000) \
STEP( 165, UINT64_C(0x0000000000f5a120), 0.825, 0.959489824218750) \
STEP( 166, UINT64_C(0x0000000000f6696e), 0.830, 0.962546235800000) \
STEP( 167, UINT64_C(0x0000000000f72894), 0.835, 0.965462970756250) \
STEP( 168, UINT64_C(0x0000000000f7dea8), 0.840, 0.968241254400000) \
STEP( 169, UINT64_C(0x0000000000f88bc0), 0.845, 0.970882462793750) \
STEP( 170, UINT64_C(0x0000000000f92ff6), 0.850, 0.973388125000000) \
STEP( 171, UINT64_C(0x0000000000f9cb67), 0.855, 0.975759925331250) \
STEP( 172, UINT64_C(0x0000000000fa5e30), 0.860, 0.977999705600000) \
STEP( 173, UINT64_C(0x0000000000fae874), 0.865, 0.980109467368750) \
STEP( 174, UINT64_C(0x0000000000fb6a57), 0.870, 0.982091374200000) \
STEP( 175, UINT64_C(0x0000000000fbe400), 0.875, 0.983947753906250) \
STEP( 176, UINT64_C(0x0000000000fc5598), 0.880, 0.985681100800000) \
STEP( 177, UINT64_C(0x0000000000fcbf4e), 0.885, 0.987294077943750) \
STEP( 178, UINT64_C(0x0000000000fd214f), 0.890, 0.988789519400000) \
STEP( 179, UINT64_C(0x0000000000fd7bcf), 0.895, 0.990170432481250) \
STEP( 180, UINT64_C(0x0000000000fdcf03), 0.900, 0.991440000000000) \
STEP( 181, UINT64_C(0x0000000000fe1b23), 0.905, 0.992601582518750) \
STEP( 182, UINT64_C(0x0000000000fe606a), 0.910, 0.993658720600000) \
STEP( 183, UINT64_C(0x0000000000fe9f18), 0.915, 0.994615137056250) \
STEP( 184, UINT64_C(0x0000000000fed76e), 0.920, 0.995474739200000) \
STEP( 185, UINT64_C(0x0000000000ff09b0), 0.925, 0.996241621093750) \
STEP( 186, UINT64_C(0x0000000000ff3627), 0.930, 0.996920065800000) \
STEP( 187, UINT64_C(0x0000000000ff5d1d), 0.935, 0.997514547631250) \
STEP( 188, UINT64_C(0x0000000000ff7ee0), 0.940, 0.998029734400000) \
STEP( 189, UINT64_C(0x0000000000ff9bc3), 0.945, 0.998470489668750) \
STEP( 190, UINT64_C(0x0000000000ffb419), 0.950, 0.998841875000000) \
STEP( 191, UINT64_C(0x0000000000ffc83d), 0.955, 0.999149152206250) \
STEP( 192, UINT64_C(0x0000000000ffd888), 0.960, 0.999397785600000) \
STEP( 193, UINT64_C(0x0000000000ffe55b), 0.965, 0.999593444243750) \
STEP( 194, UINT64_C(0x0000000000ffef17), 0.970, 0.999742004200000) \
STEP( 195, UINT64_C(0x0000000000fff623), 0.975, 0.999849550781250) \
STEP( 196, UINT64_C(0x0000000000fffae9), 0.980, 0.999922380800000) \
STEP( 197, UINT64_C(0x0000000000fffdd6), 0.985, 0.999967004818750) \
STEP( 198, UINT64_C(0x0000000000ffff5a), 0.990, 0.999990149400000) \
STEP( 199, UINT64_C(0x0000000000ffffeb), 0.995, 0.999998759356250) \
STEP( 200, UINT64_C(0x0000000001000000), 1.000, 1.000000000000000) \
#endif /* JEMALLOC_H_TYPES */
/******************************************************************************/
#ifdef JEMALLOC_H_STRUCTS
#endif /* JEMALLOC_H_STRUCTS */
/******************************************************************************/
#ifdef JEMALLOC_H_EXTERNS
#endif /* JEMALLOC_H_EXTERNS */
/******************************************************************************/
#ifdef JEMALLOC_H_INLINES
#endif /* JEMALLOC_H_INLINES */
/******************************************************************************/

115
include/jemalloc/internal/smoothstep.sh Executable file
View File

@ -0,0 +1,115 @@
#!/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
/*
* This file was generated by the following command:
* $cmd
*/
/******************************************************************************/
#ifdef JEMALLOC_H_TYPES
/*
* This header defines a precomputed table based on the smoothstep family of
* sigmoidal curves (https://en.wikipedia.org/wiki/Smoothstep) that grow from 0
* to 1 in 0 <= x <= 1. The table is stored as integer fixed point values so
* that floating point math can be avoided.
*
* 3 2
* smoothstep(x) = -2x + 3x
*
* 5 4 3
* smootherstep(x) = 6x - 15x + 10x
*
* 7 6 5 4
* smootheststep(x) = -20x + 70x - 84x + 35x
*/
#define SMOOTHSTEP_VARIANT "${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_H_TYPES */
/******************************************************************************/
#ifdef JEMALLOC_H_STRUCTS
#endif /* JEMALLOC_H_STRUCTS */
/******************************************************************************/
#ifdef JEMALLOC_H_EXTERNS
#endif /* JEMALLOC_H_EXTERNS */
/******************************************************************************/
#ifdef JEMALLOC_H_INLINES
#endif /* JEMALLOC_H_INLINES */
/******************************************************************************/
EOF

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test/unit/smoothstep.c Normal file
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#include "test/jemalloc_test.h"
static const uint64_t smoothstep_tab[] = {
#define STEP(step, h, x, y) \
h,
SMOOTHSTEP
#undef STEP
};
TEST_BEGIN(test_smoothstep_integral)
{
uint64_t sum, min, max;
unsigned i;
/*
* The integral of smoothstep in the [0..1] range equals 1/2. Verify
* that the fixed point representation's integral is no more than
* rounding error distant from 1/2. Regarding rounding, each table
* element is rounded down to the nearest fixed point value, so the
* integral may be off by as much as SMOOTHSTEP_NSTEPS ulps.
*/
sum = 0;
for (i = 0; i < SMOOTHSTEP_NSTEPS; i++)
sum += smoothstep_tab[i];
max = (KQU(1) << (SMOOTHSTEP_BFP-1)) * (SMOOTHSTEP_NSTEPS+1);
min = max - SMOOTHSTEP_NSTEPS;
assert_u64_ge(sum, min,
"Integral too small, even accounting for truncation");
assert_u64_le(sum, max, "Integral exceeds 1/2");
if (false) {
malloc_printf("%"FMTu64" ulps under 1/2 (limit %d)\n",
max - sum, SMOOTHSTEP_NSTEPS);
}
}
TEST_END
TEST_BEGIN(test_smoothstep_monotonic)
{
uint64_t prev_h;
unsigned i;
/*
* The smoothstep function is monotonic in [0..1], i.e. its slope is
* non-negative. In practice we want to parametrize table generation
* such that piecewise slope is greater than zero, but do not require
* that here.
*/
prev_h = 0;
for (i = 0; i < SMOOTHSTEP_NSTEPS; i++) {
uint64_t h = smoothstep_tab[i];
assert_u64_ge(h, prev_h, "Piecewise non-monotonic, i=%u", i);
prev_h = h;
}
assert_u64_eq(smoothstep_tab[SMOOTHSTEP_NSTEPS-1],
(KQU(1) << SMOOTHSTEP_BFP), "Last step must equal 1");
}
TEST_END
TEST_BEGIN(test_smoothstep_slope)
{
uint64_t prev_h, prev_delta;
unsigned i;
/*
* The smoothstep slope strictly increases until x=0.5, and then
* strictly decreases until x=1.0. Verify the slightly weaker
* requirement of monotonicity, so that inadequate table precision does
* not cause false test failures.
*/
prev_h = 0;
prev_delta = 0;
for (i = 0; i < SMOOTHSTEP_NSTEPS / 2 + SMOOTHSTEP_NSTEPS % 2; i++) {
uint64_t h = smoothstep_tab[i];
uint64_t delta = h - prev_h;
assert_u64_ge(delta, prev_delta,
"Slope must monotonically increase in 0.0 <= x <= 0.5, "
"i=%u", i);
prev_h = h;
prev_delta = delta;
}
prev_h = KQU(1) << SMOOTHSTEP_BFP;
prev_delta = 0;
for (i = SMOOTHSTEP_NSTEPS-1; i >= SMOOTHSTEP_NSTEPS / 2; i--) {
uint64_t h = smoothstep_tab[i];
uint64_t delta = prev_h - h;
assert_u64_ge(delta, prev_delta,
"Slope must monotonically decrease in 0.5 <= x <= 1.0, "
"i=%u", i);
prev_h = h;
prev_delta = delta;
}
}
TEST_END
int
main(void)
{
return (test(
test_smoothstep_integral,
test_smoothstep_monotonic,
test_smoothstep_slope));
}