> *I am asking you to do some performance analysis. Specifically, would*
> *you** please profile a curve and a straight segment to compare?*
Sure, here is the average of 1 million iteration of computing shortest
distance from a point to both types of curves and line segments:
(using -O3 optimization, measured using chrono library)
A) Line Segment: ~0.32 microseconds
B) Conic Bezier: ~1.08 microseconds
C) Cubic Bezier: ~1.25 microseconds
[I have also attached the gprof output in case you are interested. Note
that the gprof output is without any compiler optimization]
> *We need to know if it is worth simply splitting the curve into a large*
> *number of straight segments. How many straight segments we can afford*
> *and still beat the exact solution.*
In my opinion it's not worth splitting the curves into line segments.
But if there is a way to not check each and every line segment, then
it might be worth giving it a try.
> *Sure, but please use your dedicated branch.*
Yes, I will do that.
Anuj
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls us/call us/call name
57.03 1.38 1.38 8378453 0.16 0.16 ft_trig_pseudo_polarize
16.12 1.77 0.39 1000000 0.39 2.38 get_min_distance [for
cubic curves]
13.64 2.10 0.33 153570100 0.00 0.00 FT_MulFix_x86_64
4.55 2.21 0.11 1000000 0.11 0.11 FT_Vector_NormLen
2.89 2.28 0.07 8378453 0.01 0.01 ft_trig_prenorm
1.86 2.33 0.05 7378505 0.01 0.01 FT_DivFix
1.65 2.37 0.04 8378505 0.00 0.18 FT_Vector_Length
1.24 2.40 0.03 main
0.41 2.41 0.01 8378453 0.00 0.00 ft_trig_downscale
0.41 2.42 0.01 FT_Vector_Rotate
0.21 2.42 0.01 FT_MulFix
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2020 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.41% of 2.42 seconds
index % time self children called name
<spontaneous>
[1] 99.4 0.03 2.38 main [1]
0.39 1.99 1000000/1000000 get_min_distance [2]
-----------------------------------------------
0.39 1.99 1000000/1000000 main [1]
[2] 98.1 0.39 1.99 1000000 get_min_distance [2]
0.04 1.46 8378505/8378505 FT_Vector_Length [3]
0.33 0.00 153570100/153570100 FT_MulFix_x86_64 [5]
0.11 0.00 1000000/1000000 FT_Vector_NormLen [6]
0.05 0.00 7378505/7378505 FT_DivFix [8]
-----------------------------------------------
0.04 1.46 8378505/8378505 get_min_distance [2]
[3] 62.0 0.04 1.46 8378505 FT_Vector_Length [3]
1.38 0.00 8378453/8378453 ft_trig_pseudo_polarize [4]
0.07 0.00 8378453/8378453 ft_trig_prenorm [7]
0.01 0.00 8378453/8378453 ft_trig_downscale [9]
-----------------------------------------------
1.38 0.00 8378453/8378453 FT_Vector_Length [3]
[4] 57.0 1.38 0.00 8378453 ft_trig_pseudo_polarize [4]
-----------------------------------------------
0.33 0.00 153570100/153570100 get_min_distance [2]
[5] 13.6 0.33 0.00 153570100 FT_MulFix_x86_64 [5]
-----------------------------------------------
0.11 0.00 1000000/1000000 get_min_distance [2]
[6] 4.5 0.11 0.00 1000000 FT_Vector_NormLen [6]
-----------------------------------------------
0.07 0.00 8378453/8378453 FT_Vector_Length [3]
[7] 2.9 0.07 0.00 8378453 ft_trig_prenorm [7]
-----------------------------------------------
0.05 0.00 7378505/7378505 get_min_distance [2]
[8] 1.9 0.05 0.00 7378505 FT_DivFix [8]
-----------------------------------------------
0.01 0.00 8378453/8378453 FT_Vector_Length [3]
[9] 0.4 0.01 0.00 8378453 ft_trig_downscale [9]
-----------------------------------------------
<spontaneous>
[10] 0.4 0.01 0.00 FT_Vector_Rotate [10]
-----------------------------------------------
<spontaneous>
[11] 0.2 0.01 0.00 FT_MulFix [11]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2020 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[8] FT_DivFix [6] FT_Vector_NormLen (ftcalc.c) [4]
ft_trig_pseudo_polarize (fttrigon.c)
[11] FT_MulFix [10] FT_Vector_Rotate [2] get_min_distance
[5] FT_MulFix_x86_64 (ftcalc.h) [9] ft_trig_downscale (fttrigon.c) [1] main
[3] FT_Vector_Length [7] ft_trig_prenorm (fttrigon.c)
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls ns/call ns/call name
57.79 0.26 0.26 1999998 130.02 130.02 ft_trig_pseudo_polarize
31.12 0.40 0.14 2000000 70.01 70.01 FT_Vector_NormLen
6.67 0.43 0.03 1000000 30.00 30.00 FT_DivFix
2.22 0.44 0.01 4000000 2.50 2.50 FT_MulFix_x86_64
2.22 0.45 0.01 1999998 5.00 5.00 ft_trig_prenorm
0.00 0.45 0.00 2000000 0.00 135.02 FT_Vector_Length
0.00 0.45 0.00 1999998 0.00 0.00 ft_trig_downscale
0.00 0.45 0.00 1000000 0.00 450.06 get_min_distance [for
line segments]
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2020 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 2.22% of 0.45 seconds
index % time self children called name
0.00 0.45 1000000/1000000 main [2]
[1] 100.0 0.00 0.45 1000000 get_min_distance [1]
0.00 0.27 2000000/2000000 FT_Vector_Length [3]
0.14 0.00 2000000/2000000 FT_Vector_NormLen [5]
0.03 0.00 1000000/1000000 FT_DivFix [6]
0.01 0.00 4000000/4000000 FT_MulFix_x86_64 [7]
-----------------------------------------------
<spontaneous>
[2] 100.0 0.00 0.45 main [2]
0.00 0.45 1000000/1000000 get_min_distance [1]
-----------------------------------------------
0.00 0.27 2000000/2000000 get_min_distance [1]
[3] 60.0 0.00 0.27 2000000 FT_Vector_Length [3]
0.26 0.00 1999998/1999998 ft_trig_pseudo_polarize [4]
0.01 0.00 1999998/1999998 ft_trig_prenorm [8]
0.00 0.00 1999998/1999998 ft_trig_downscale [9]
-----------------------------------------------
0.26 0.00 1999998/1999998 FT_Vector_Length [3]
[4] 57.8 0.26 0.00 1999998 ft_trig_pseudo_polarize [4]
-----------------------------------------------
0.14 0.00 2000000/2000000 get_min_distance [1]
[5] 31.1 0.14 0.00 2000000 FT_Vector_NormLen [5]
-----------------------------------------------
0.03 0.00 1000000/1000000 get_min_distance [1]
[6] 6.7 0.03 0.00 1000000 FT_DivFix [6]
-----------------------------------------------
0.01 0.00 4000000/4000000 get_min_distance [1]
[7] 2.2 0.01 0.00 4000000 FT_MulFix_x86_64 [7]
-----------------------------------------------
0.01 0.00 1999998/1999998 FT_Vector_Length [3]
[8] 2.2 0.01 0.00 1999998 ft_trig_prenorm [8]
-----------------------------------------------
0.00 0.00 1999998/1999998 FT_Vector_Length [3]
[9] 0.0 0.00 0.00 1999998 ft_trig_downscale [9]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2020 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[6] FT_DivFix [5] FT_Vector_NormLen (ftcalc.c) [4]
ft_trig_pseudo_polarize (fttrigon.c)
[7] FT_MulFix_x86_64 (ftcalc.h) [9] ft_trig_downscale (fttrigon.c) [1]
get_min_distance
[3] FT_Vector_Length [8] ft_trig_prenorm (fttrigon.c)
Flat profile:
Each sample counts as 0.01 seconds.
% cumulative self self total
time seconds seconds calls us/call us/call name
30.14 0.44 0.44 3818733 0.12 0.12 ft_trig_pseudo_polarize
28.77 0.86 0.42 4999885 0.08 0.08 square_root
9.59 1.00 0.14 51985248 0.00 0.00 FT_MulFix_x86_64
9.59 1.14 0.14 2000000 0.07 0.07 FT_Vector_NormLen
6.17 1.23 0.09 1000000 0.09 1.44 get_min_distance [for
conic curves]
4.11 1.29 0.06 1999946 0.03 0.25 cube_root
3.43 1.34 0.05 3999998 0.01 0.13 FT_Vector_Length
2.74 1.38 0.04 11995084 0.00 0.00 FT_DivFix
2.74 1.42 0.04 1000000 0.04 0.65 solve_cubic_equation
1.37 1.44 0.02 3818733 0.01 0.01 ft_trig_prenorm
1.37 1.46 0.02 main
0.00 1.46 0.00 3818733 0.00 0.00 ft_trig_downscale
0.00 1.46 0.00 27 0.00 0.08 solve_quadratic_equation
% the percentage of the total running time of the
time program used by this function.
cumulative a running sum of the number of seconds accounted
seconds for by this function and those listed above it.
self the number of seconds accounted for by this
seconds function alone. This is the major sort for this
listing.
calls the number of times this function was invoked, if
this function is profiled, else blank.
self the average number of milliseconds spent in this
ms/call function per call, if this function is profiled,
else blank.
total the average number of milliseconds spent in this
ms/call function and its descendents per call, if this
function is profiled, else blank.
name the name of the function. This is the minor sort
for this listing. The index shows the location of
the function in the gprof listing. If the index is
in parenthesis it shows where it would appear in
the gprof listing if it were to be printed.
Copyright (C) 2012-2020 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Call graph (explanation follows)
granularity: each sample hit covers 2 byte(s) for 0.68% of 1.46 seconds
index % time self children called name
<spontaneous>
[1] 100.0 0.02 1.44 main [1]
0.09 1.35 1000000/1000000 get_min_distance [2]
-----------------------------------------------
0.09 1.35 1000000/1000000 main [1]
[2] 98.6 0.09 1.35 1000000 get_min_distance [2]
0.04 0.61 1000000/1000000 solve_cubic_equation [3]
0.05 0.46 3999998/3999998 FT_Vector_Length [4]
0.14 0.00 2000000/2000000 FT_Vector_NormLen [9]
0.05 0.00 19000013/51985248 FT_MulFix_x86_64 [8]
-----------------------------------------------
0.04 0.61 1000000/1000000 get_min_distance [2]
[3] 44.4 0.04 0.61 1000000 solve_cubic_equation [3]
0.06 0.44 1999946/1999946 cube_root [5]
0.08 0.00 999972/4999885 square_root [7]
0.02 0.00 5999838/51985248 FT_MulFix_x86_64 [8]
0.01 0.00 2999919/11995084 FT_DivFix [10]
0.00 0.00 27/27 solve_quadratic_equation [12]
-----------------------------------------------
0.05 0.46 3999998/3999998 get_min_distance [2]
[4] 34.9 0.05 0.46 3999998 FT_Vector_Length [4]
0.44 0.00 3818733/3818733 ft_trig_pseudo_polarize [6]
0.02 0.00 3818733/3818733 ft_trig_prenorm [11]
0.00 0.00 3818733/3818733 ft_trig_downscale [13]
-----------------------------------------------
0.06 0.44 1999946/1999946 solve_cubic_equation [3]
[5] 34.2 0.06 0.44 1999946 cube_root [5]
0.34 0.00 3999890/4999885 square_root [7]
0.07 0.00 26985351/51985248 FT_MulFix_x86_64 [8]
0.03 0.00 8995117/11995084 FT_DivFix [10]
-----------------------------------------------
0.44 0.00 3818733/3818733 FT_Vector_Length [4]
[6] 30.1 0.44 0.00 3818733 ft_trig_pseudo_polarize [6]
-----------------------------------------------
0.00 0.00 23/4999885 solve_quadratic_equation [12]
0.08 0.00 999972/4999885 solve_cubic_equation [3]
0.34 0.00 3999890/4999885 cube_root [5]
[7] 28.8 0.42 0.00 4999885 square_root [7]
-----------------------------------------------
0.00 0.00 46/51985248 solve_quadratic_equation [12]
0.02 0.00 5999838/51985248 solve_cubic_equation [3]
0.05 0.00 19000013/51985248 get_min_distance [2]
0.07 0.00 26985351/51985248 cube_root [5]
[8] 9.6 0.14 0.00 51985248 FT_MulFix_x86_64 [8]
-----------------------------------------------
0.14 0.00 2000000/2000000 get_min_distance [2]
[9] 9.6 0.14 0.00 2000000 FT_Vector_NormLen [9]
-----------------------------------------------
0.00 0.00 48/11995084 solve_quadratic_equation [12]
0.01 0.00 2999919/11995084 solve_cubic_equation [3]
0.03 0.00 8995117/11995084 cube_root [5]
[10] 2.7 0.04 0.00 11995084 FT_DivFix [10]
-----------------------------------------------
0.02 0.00 3818733/3818733 FT_Vector_Length [4]
[11] 1.4 0.02 0.00 3818733 ft_trig_prenorm [11]
-----------------------------------------------
0.00 0.00 27/27 solve_cubic_equation [3]
[12] 0.0 0.00 0.00 27 solve_quadratic_equation [12]
0.00 0.00 23/4999885 square_root [7]
0.00 0.00 48/11995084 FT_DivFix [10]
0.00 0.00 46/51985248 FT_MulFix_x86_64 [8]
-----------------------------------------------
0.00 0.00 3818733/3818733 FT_Vector_Length [4]
[13] 0.0 0.00 0.00 3818733 ft_trig_downscale [13]
-----------------------------------------------
This table describes the call tree of the program, and was sorted by
the total amount of time spent in each function and its children.
Each entry in this table consists of several lines. The line with the
index number at the left hand margin lists the current function.
The lines above it list the functions that called this function,
and the lines below it list the functions this one called.
This line lists:
index A unique number given to each element of the table.
Index numbers are sorted numerically.
The index number is printed next to every function name so
it is easier to look up where the function is in the table.
% time This is the percentage of the `total' time that was spent
in this function and its children. Note that due to
different viewpoints, functions excluded by options, etc,
these numbers will NOT add up to 100%.
self This is the total amount of time spent in this function.
children This is the total amount of time propagated into this
function by its children.
called This is the number of times the function was called.
If the function called itself recursively, the number
only includes non-recursive calls, and is followed by
a `+' and the number of recursive calls.
name The name of the current function. The index number is
printed after it. If the function is a member of a
cycle, the cycle number is printed between the
function's name and the index number.
For the function's parents, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the function into this parent.
children This is the amount of time that was propagated from
the function's children into this parent.
called This is the number of times this parent called the
function `/' the total number of times the function
was called. Recursive calls to the function are not
included in the number after the `/'.
name This is the name of the parent. The parent's index
number is printed after it. If the parent is a
member of a cycle, the cycle number is printed between
the name and the index number.
If the parents of the function cannot be determined, the word
`<spontaneous>' is printed in the `name' field, and all the other
fields are blank.
For the function's children, the fields have the following meanings:
self This is the amount of time that was propagated directly
from the child into the function.
children This is the amount of time that was propagated from the
child's children to the function.
called This is the number of times the function called
this child `/' the total number of times the child
was called. Recursive calls by the child are not
listed in the number after the `/'.
name This is the name of the child. The child's index
number is printed after it. If the child is a
member of a cycle, the cycle number is printed
between the name and the index number.
If there are any cycles (circles) in the call graph, there is an
entry for the cycle-as-a-whole. This entry shows who called the
cycle (as parents) and the members of the cycle (as children.)
The `+' recursive calls entry shows the number of function calls that
were internal to the cycle, and the calls entry for each member shows,
for that member, how many times it was called from other members of
the cycle.
Copyright (C) 2012-2020 Free Software Foundation, Inc.
Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.
Index by function name
[10] FT_DivFix [13] ft_trig_downscale (fttrigon.c) [3]
solve_cubic_equation
[8] FT_MulFix_x86_64 (ftcalc.h) [11] ft_trig_prenorm (fttrigon.c) [12]
solve_quadratic_equation
[4] FT_Vector_Length [6] ft_trig_pseudo_polarize (fttrigon.c) [7]
square_root (ext.h)
[9] FT_Vector_NormLen (ftcalc.c) [2] get_min_distance
[5] cube_root (ext.h) [1] main
