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/common/math.mk RUN_MATH_TESTS=true
37#  $(get_build_var CKATI) -f ${ANDROID_BUILD_TOP}//build/make/common/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_gt
138$(if $(call math_gt_or_eq,$(2),$(1)),,true)
139endef
140
141define math_lt
142$(if $(call math_gt_or_eq,$(1),$(2)),,true)
143endef
144
145$(call math-expect-true,(call math_gt_or_eq, 2, 1))
146$(call math-expect-true,(call math_gt_or_eq, 1, 1))
147$(call math-expect-false,(call math_gt_or_eq, 1, 2))
148$(call math-expect-true,(call math_gt, 4, 3))
149$(call math-expect-false,(call math_gt, 5, 5))
150$(call math-expect-false,(call math_gt, 6, 7))
151$(call math-expect-false,(call math_lt, 1, 0))
152$(call math-expect-false,(call math_lt, 8, 8))
153$(call math-expect-true,(call math_lt, 10, 11))
154
155# $1 is the variable name to increment
156define inc_and_print
157$(strip $(eval $(1) := $($(1)) .)$(words $($(1))))
158endef
159
160ifdef RUN_MATH_TESTS
161a :=
162$(call math-expect,(call inc_and_print,a),1)
163$(call math-expect,(call inc_and_print,a),2)
164$(call math-expect,(call inc_and_print,a),3)
165$(call math-expect,(call inc_and_print,a),4)
166endif
167
168# Returns the words in $2 that are numbers and are less than $1
169define numbers_less_than
170$(strip \
171  $(foreach n,$2, \
172    $(if $(call math_is_number,$(n)), \
173      $(if $(call math_lt,$(n),$(1)), \
174        $(n)))))
175endef
176
177$(call math-expect,(call numbers_less_than,0,0 1 2 3),)
178$(call math-expect,(call numbers_less_than,1,0 2 1 3),0)
179$(call math-expect,(call numbers_less_than,2,0 2 1 3),0 1)
180$(call math-expect,(call numbers_less_than,3,0 2 1 3),0 2 1)
181$(call math-expect,(call numbers_less_than,4,0 2 1 3),0 2 1 3)
182$(call math-expect,(call numbers_less_than,3,0 2 1 3 2),0 2 1 2)
183
184_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,\
185  $(foreach c,x x x x x x x x x x x x x x x x,x x x x x x x x x x x x x x x x)))
186
187define _int_encode
188$(if $(filter $(words x $(_INT_LIMIT_WORDS)),$(words $(wordlist 1,$(1),x $(_INT_LIMIT_WORDS)))),\
189  $(call math-error,integer greater than $(words $(_INT_LIMIT_WORDS)) is not supported!),\
190    $(wordlist 1,$(1),$(_INT_LIMIT_WORDS)))
191endef
192
193# _int_max returns the maximum of the two arguments
194# input: two (x) lists; output: one (x) list
195# integer cannot be passed in directly. It has to be converted using _int_encode.
196define _int_max
197$(subst xx,x,$(join $(1),$(2)))
198endef
199
200# first argument is greater than second argument
201# output: non-empty if true
202# integer cannot be passed in directly. It has to be converted using _int_encode.
203define _int_greater-than
204$(filter-out $(words $(2)),$(words $(call _int_max,$(1),$(2))))
205endef
206
207# first argument equals to second argument
208# output: non-empty if true
209# integer cannot be passed in directly. It has to be converted using _int_encode.
210define _int_equal
211$(filter $(words $(1)),$(words $(2)))
212endef
213
214# first argument is greater than or equal to second argument
215# output: non-empty if true
216# integer cannot be passed in directly. It has to be converted using _int_encode.
217define _int_greater-or-equal
218$(call _int_greater-than,$(1),$(2))$(call _int_equal,$(1),$(2))
219endef
220
221define int_plus
222$(words $(call _int_encode,$(1)) $(call _int_encode,$(2)))
223endef
224
225$(call math-expect,(call int_plus,0,0),0)
226$(call math-expect,(call int_plus,0,1),1)
227$(call math-expect,(call int_plus,1,0),1)
228$(call math-expect,(call int_plus,1,100),101)
229$(call math-expect,(call int_plus,100,100),200)
230
231define int_subtract
232$(strip \
233  $(if $(call _int_greater-or-equal,$(call _int_encode,$(1)),$(call _int_encode,$(2))),\
234  $(words $(filter-out xx,$(join $(call _int_encode,$(1)),$(call _int_encode,$(2))))),\
235    $(call math-error,subtract underflow $(1) - $(2))))
236endef
237
238$(call math-expect,(call int_subtract,0,0),0)
239$(call math-expect,(call int_subtract,1,0),1)
240$(call math-expect,(call int_subtract,1,1),0)
241$(call math-expect,(call int_subtract,100,1),99)
242$(call math-expect,(call int_subtract,200,100),100)
243$(call math-expect-error,(call int_subtract,0,1),subtract underflow 0 - 1)
244
245define int_multiply
246$(words $(foreach a,$(call _int_encode,$(1)),$(call _int_encode,$(2))))
247endef
248
249$(call math-expect,(call int_multiply,0,0),0)
250$(call math-expect,(call int_multiply,1,0),0)
251$(call math-expect,(call int_multiply,1,1),1)
252$(call math-expect,(call int_multiply,100,1),100)
253$(call math-expect,(call int_multiply,1,100),100)
254$(call math-expect,(call int_multiply,4,100),400)
255$(call math-expect,(call int_multiply,100,4),400)
256
257define int_divide
258$(if $(filter 0,$(2)),$(call math-error,division by zero is not allowed!),$(strip \
259  $(if $(call _int_greater-or-equal,$(call _int_encode,$(1)),$(call _int_encode,$(2))), \
260    $(call int_plus,$(call int_divide,$(call int_subtract,$(1),$(2)),$(2)),1),0)))
261endef
262
263$(call math-expect,(call int_divide,1,1),1)
264$(call math-expect,(call int_divide,200,1),200)
265$(call math-expect,(call int_divide,200,3),66)
266$(call math-expect,(call int_divide,1,2),0)
267$(call math-expect-error,(call int_divide,0,0),division by zero is not allowed!)
268$(call math-expect-error,(call int_divide,1,0),division by zero is not allowed!)
269
270ifdef RUN_MATH_TESTS
271  ifdef MATH_TEST_FAILURE
272    math-tests:
273	@echo FAIL
274	@false
275  else
276    math-tests:
277	@echo PASS
278  endif
279  .PHONY: math-tests
280endif
281