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1#
2# Copyright (C) 2017 The Android Open Source Project
3#
4# Licensed under the Apache License, Version 2.0 (the "License");
5# you may not use this file except in compliance with the License.
6# You may obtain a copy of the License at
7#
8#      http://www.apache.org/licenses/LICENSE-2.0
9#
10# Unless required by applicable law or agreed to in writing, software
11# distributed under the License is distributed on an "AS IS" BASIS,
12# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13# See the License for the specific language governing permissions and
14# limitations under the License.
15#
16
17###########################################################
18# Basic math functions for non-negative integers <= 100
19#
20# (SDK versions for example)
21###########################################################
22__MATH_POS_NUMBERS :=  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 \
23                      21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 \
24                      41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 \
25                      61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 \
26                      81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
27__MATH_NUMBERS := 0 $(__MATH_POS_NUMBERS)
28
29math-error = $(call pretty-error,$(1))
30math-expect :=
31math-expect-true :=
32math-expect :=
33math-expect-error :=
34
35# Run the math tests with:
36#  make -f ${ANDROID_BUILD_TOP}/build/make/core/math.mk RUN_MATH_TESTS=true
37#  $(get_build_var CKATI) -f ${ANDROID_BUILD_TOP}//build/make/core/math.mk RUN_MATH_TESTS=true
38ifdef RUN_MATH_TESTS
39  MATH_TEST_FAILURE :=
40  MATH_TEST_ERROR :=
41  math-error = $(if $(MATH_TEST_ERROR),,$(eval MATH_TEST_ERROR:=$(1)))
42  define math-expect
43    $(eval got:=$$$1) \
44    $(if $(subst $(got),,$(2))$(subst $(2),,$(got))$(MATH_TEST_ERROR), \
45      $(if $(MATH_TEST_ERROR),$(warning $(MATH_TEST_ERROR)),$(warning $$$1 '$(got)' != '$(2)')) \
46      $(eval MATH_TEST_FAILURE := true)) \
47    $(eval MATH_TEST_ERROR :=) \
48    $(eval got:=)
49  endef
50  math-expect-true = $(call math-expect,$(1),true)
51  math-expect-false = $(call math-expect,$(1),)
52
53  define math-expect-error
54    $(eval got:=$$$1) \
55    $(if $(subst $(MATH_TEST_ERROR),,$(2))$(subst $(2),,$(MATH_TEST_ERROR)), \
56      $(warning '$(MATH_TEST_ERROR)' != '$(2)') \
57      $(eval MATH_TEST_FAILURE := true)) \
58    $(eval MATH_TEST_ERROR :=) \
59    $(eval got:=)
60  endef
61endif
62
63# Returns true if $(1) is a non-negative integer <= 100, otherwise returns nothing.
64define math_is_number
65$(strip \
66  $(if $(1),,$(call math-error,Argument missing)) \
67  $(if $(word 2,$(1)),$(call math-error,Multiple words in a single argument: $(1))) \
68  $(if $(filter $(1),$(__MATH_NUMBERS)),true))
69endef
70
71define math_is_zero
72$(strip \
73  $(if $(word 2,$(1)),$(call math-error,Multiple words in a single argument: $(1))) \
74  $(if $(filter 0,$(1)),true))
75endef
76
77$(call math-expect-true,(call math_is_number,0))
78$(call math-expect-true,(call math_is_number,2))
79$(call math-expect-false,(call math_is_number,foo))
80$(call math-expect-false,(call math_is_number,-1))
81$(call math-expect-error,(call math_is_number,1 2),Multiple words in a single argument: 1 2)
82$(call math-expect-error,(call math_is_number,no 2),Multiple words in a single argument: no 2)
83
84$(call math-expect-true,(call math_is_zero,0))
85$(call math-expect-false,(call math_is_zero,1))
86$(call math-expect-false,(call math_is_zero,foo))
87$(call math-expect-error,(call math_is_zero,1 2),Multiple words in a single argument: 1 2)
88$(call math-expect-error,(call math_is_zero,no 2),Multiple words in a single argument: no 2)
89
90define _math_check_valid
91$(if $(call math_is_number,$(1)),,$(call math-error,Only non-negative integers <= 100 are supported (not $(1))))
92endef
93
94$(call math-expect,(call _math_check_valid,0))
95$(call math-expect,(call _math_check_valid,1))
96$(call math-expect,(call _math_check_valid,100))
97$(call math-expect-error,(call _math_check_valid,-1),Only non-negative integers <= 100 are supported (not -1))
98$(call math-expect-error,(call _math_check_valid,101),Only non-negative integers <= 100 are supported (not 101))
99$(call math-expect-error,(call _math_check_valid,),Argument missing)
100$(call math-expect-error,(call _math_check_valid,1 2),Multiple words in a single argument: 1 2)
101
102# return a list containing integers ranging from [$(1),$(2)]
103define int_range_list
104$(strip \
105  $(call _math_check_valid,$(1))$(call _math_check_valid,$(2)) \
106  $(if $(call math_is_zero,$(1)),0)\
107  $(wordlist $(if $(call math_is_zero,$(1)),1,$(1)),$(2),$(__MATH_POS_NUMBERS)))
108endef
109
110$(call math-expect,(call int_range_list,0,1),0 1)
111$(call math-expect,(call int_range_list,1,1),1)
112$(call math-expect,(call int_range_list,1,2),1 2)
113$(call math-expect,(call int_range_list,2,1),)
114$(call math-expect-error,(call int_range_list,1,101),Only non-negative integers <= 100 are supported (not 101))
115
116
117# Returns the greater of $1 or $2.
118# If $1 or $2 is not a positive integer <= 100, then an error is generated.
119define math_max
120$(strip $(call _math_check_valid,$(1)) $(call _math_check_valid,$(2)) \
121  $(lastword $(filter $(1) $(2),$(__MATH_NUMBERS))))
122endef
123
124$(call math-expect-error,(call math_max),Argument missing)
125$(call math-expect-error,(call math_max,1),Argument missing)
126$(call math-expect-error,(call math_max,1 2,3),Multiple words in a single argument: 1 2)
127$(call math-expect,(call math_max,0,1),1)
128$(call math-expect,(call math_max,1,0),1)
129$(call math-expect,(call math_max,1,1),1)
130$(call math-expect,(call math_max,5,42),42)
131$(call math-expect,(call math_max,42,5),42)
132
133define math_gt_or_eq
134$(if $(filter $(1),$(call math_max,$(1),$(2))),true)
135endef
136
137define math_lt
138$(if $(call math_gt_or_eq,$(1),$(2)),,true)
139endef
140
141$(call math-expect-true,(call math_gt_or_eq, 2, 1))
142$(call math-expect-true,(call math_gt_or_eq, 1, 1))
143$(call math-expect-false,(call math_gt_or_eq, 1, 2))
144
145# $1 is the variable name to increment
146define inc_and_print
147$(strip $(eval $(1) := $($(1)) .)$(words $($(1))))
148endef
149
150ifdef RUN_MATH_TESTS
151a :=
152$(call math-expect,(call inc_and_print,a),1)
153$(call math-expect,(call inc_and_print,a),2)
154$(call math-expect,(call inc_and_print,a),3)
155$(call math-expect,(call inc_and_print,a),4)
156endif
157
158# Returns the words in $2 that are numbers and are less than $1
159define numbers_less_than
160$(strip \
161  $(foreach n,$2, \
162    $(if $(call math_is_number,$(n)), \
163      $(if $(call math_lt,$(n),$(1)), \
164        $(n)))))
165endef
166
167$(call math-expect,(call numbers_less_than,0,0 1 2 3),)
168$(call math-expect,(call numbers_less_than,1,0 2 1 3),0)
169$(call math-expect,(call numbers_less_than,2,0 2 1 3),0 1)
170$(call math-expect,(call numbers_less_than,3,0 2 1 3),0 2 1)
171$(call math-expect,(call numbers_less_than,4,0 2 1 3),0 2 1 3)
172$(call math-expect,(call numbers_less_than,3,0 2 1 3 2),0 2 1 2)
173
174_INT_LIMIT_WORDS := $(foreach a,x x,$(foreach b,x x x x x x x x x x x x x x x x,\
175  $(foreach c,x x x x x x x x x x x x x x x x,x x x x x x x x x x x x x x x x)))
176
177define _int_encode
178$(if $(filter $(words x $(_INT_LIMIT_WORDS)),$(words $(wordlist 1,$(1),x $(_INT_LIMIT_WORDS)))),\
179  $(call math-error,integer greater than $(words $(_INT_LIMIT_WORDS)) is not supported!),\
180    $(wordlist 1,$(1),$(_INT_LIMIT_WORDS)))
181endef
182
183# _int_max returns the maximum of the two arguments
184# input: two (x) lists; output: one (x) list
185# integer cannot be passed in directly. It has to be converted using _int_encode.
186define _int_max
187$(subst xx,x,$(join $(1),$(2)))
188endef
189
190# first argument is greater than second argument
191# output: non-empty if true
192# integer cannot be passed in directly. It has to be converted using _int_encode.
193define _int_greater-than
194$(filter-out $(words $(2)),$(words $(call _int_max,$(1),$(2))))
195endef
196
197# first argument equals to second argument
198# output: non-empty if true
199# integer cannot be passed in directly. It has to be converted using _int_encode.
200define _int_equal
201$(filter $(words $(1)),$(words $(2)))
202endef
203
204# first argument is greater than or equal to second argument
205# output: non-empty if true
206# integer cannot be passed in directly. It has to be converted using _int_encode.
207define _int_greater-or-equal
208$(call _int_greater-than,$(1),$(2))$(call _int_equal,$(1),$(2))
209endef
210
211define int_plus
212$(words $(call _int_encode,$(1)) $(call _int_encode,$(2)))
213endef
214
215$(call math-expect,(call int_plus,0,0),0)
216$(call math-expect,(call int_plus,0,1),1)
217$(call math-expect,(call int_plus,1,0),1)
218$(call math-expect,(call int_plus,1,100),101)
219$(call math-expect,(call int_plus,100,100),200)
220
221define int_subtract
222$(strip \
223  $(if $(call _int_greater-or-equal,$(call _int_encode,$(1)),$(call _int_encode,$(2))),\
224  $(words $(filter-out xx,$(join $(call _int_encode,$(1)),$(call _int_encode,$(2))))),\
225    $(call math-error,subtract underflow $(1) - $(2))))
226endef
227
228$(call math-expect,(call int_subtract,0,0),0)
229$(call math-expect,(call int_subtract,1,0),1)
230$(call math-expect,(call int_subtract,1,1),0)
231$(call math-expect,(call int_subtract,100,1),99)
232$(call math-expect,(call int_subtract,200,100),100)
233$(call math-expect-error,(call int_subtract,0,1),subtract underflow 0 - 1)
234
235define int_multiply
236$(words $(foreach a,$(call _int_encode,$(1)),$(call _int_encode,$(2))))
237endef
238
239$(call math-expect,(call int_multiply,0,0),0)
240$(call math-expect,(call int_multiply,1,0),0)
241$(call math-expect,(call int_multiply,1,1),1)
242$(call math-expect,(call int_multiply,100,1),100)
243$(call math-expect,(call int_multiply,1,100),100)
244$(call math-expect,(call int_multiply,4,100),400)
245$(call math-expect,(call int_multiply,100,4),400)
246
247define int_divide
248$(if $(filter 0,$(2)),$(call math-error,division by zero is not allowed!),$(strip \
249  $(if $(call _int_greater-or-equal,$(call _int_encode,$(1)),$(call _int_encode,$(2))), \
250    $(call int_plus,$(call int_divide,$(call int_subtract,$(1),$(2)),$(2)),1),0)))
251endef
252
253$(call math-expect,(call int_divide,1,1),1)
254$(call math-expect,(call int_divide,200,1),200)
255$(call math-expect,(call int_divide,200,3),66)
256$(call math-expect,(call int_divide,1,2),0)
257$(call math-expect-error,(call int_divide,0,0),division by zero is not allowed!)
258$(call math-expect-error,(call int_divide,1,0),division by zero is not allowed!)
259
260ifdef RUN_MATH_TESTS
261  ifdef MATH_TEST_FAILURE
262    math-tests:
263	@echo FAIL
264	@false
265  else
266    math-tests:
267	@echo PASS
268  endif
269  .PHONY: math-tests
270endif
271