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__MATH_ONE_NUMBERS := 0 1 2 3 4 5 6 7 8 9 29 30math-error = $(call pretty-error,$(1)) 31math-expect := 32math-expect-true := 33math-expect := 34math-expect-error := 35 36# Run the math tests with: 37# make -f ${ANDROID_BUILD_TOP}/build/make/common/math.mk RUN_MATH_TESTS=true 38# $(get_build_var CKATI) -f ${ANDROID_BUILD_TOP}//build/make/common/math.mk RUN_MATH_TESTS=true 39ifdef RUN_MATH_TESTS 40 ifndef empty 41 empty := 42 space := $(empty) $(empty) 43 endif 44 MATH_TEST_FAILURE := 45 MATH_TEST_ERROR := 46 math-error = $(if $(MATH_TEST_ERROR),,$(eval MATH_TEST_ERROR:=$(1))) 47 define math-expect 48 $(eval got:=$$$1) \ 49 $(if $(subst $(got),,$(2))$(subst $(2),,$(got))$(MATH_TEST_ERROR), \ 50 $(if $(MATH_TEST_ERROR),$(warning $(MATH_TEST_ERROR)),$(warning $$$1 '$(got)' != '$(2)')) \ 51 $(eval MATH_TEST_FAILURE := true)) \ 52 $(eval MATH_TEST_ERROR :=) \ 53 $(eval got:=) 54 endef 55 math-expect-true = $(call math-expect,$(1),true) 56 math-expect-false = $(call math-expect,$(1),) 57 58 define math-expect-error 59 $(eval got:=$$$1) \ 60 $(if $(subst $(MATH_TEST_ERROR),,$(2))$(subst $(2),,$(MATH_TEST_ERROR)), \ 61 $(warning '$(MATH_TEST_ERROR)' != '$(2)') \ 62 $(eval MATH_TEST_FAILURE := true)) \ 63 $(eval MATH_TEST_ERROR :=) \ 64 $(eval got:=) 65 endef 66endif 67 68# Returns true if $(1) is a non-negative integer <= 100, otherwise returns nothing. 69define math_is_number_in_100 70$(strip \ 71 $(if $(1),,$(call math-error,Argument missing)) \ 72 $(if $(word 2,$(1)),$(call math-error,Multiple words in a single argument: $(1))) \ 73 $(if $(filter $(1),$(__MATH_NUMBERS)),true)) 74endef 75 76# Same with math_is_number_in_100, but no limit. 77define _math_ext_is_number 78$(strip \ 79 $(if $(1),,$(call math-error,Argument missing)) \ 80 $(if $(word 2,$(1)),$(call math-error,Multiple words in a single argument: $(1))) \ 81 $(eval should_empty:=$(1)) \ 82 $(foreach num,$(__MATH_ONE_NUMBERS),\ 83 $(eval should_empty:=$(subst $(num),$(empty),$(should_empty)))) \ 84 $(if $(should_empty),,true)) 85endef 86 87# Returns true if $(1) is a non-negative integer. 88define math_is_number 89$(strip $(if $(call math_is_number_in_100,$(1)),true,$(call _math_ext_is_number,$(1)))) 90endef 91 92define math_is_zero 93$(strip \ 94 $(if $(word 2,$(1)),$(call math-error,Multiple words in a single argument: $(1))) \ 95 $(if $(filter 0,$(1)),true)) 96endef 97 98$(call math-expect-true,(call math_is_number,0)) 99$(call math-expect-true,(call math_is_number,2)) 100$(call math-expect-true,(call math_is_number,202412)) 101$(call math-expect-false,(call math_is_number,foo)) 102$(call math-expect-false,(call math_is_number,-1)) 103$(call math-expect-error,(call math_is_number,1 2),Multiple words in a single argument: 1 2) 104$(call math-expect-error,(call math_is_number,no 2),Multiple words in a single argument: no 2) 105 106$(call math-expect-true,(call math_is_zero,0)) 107$(call math-expect-false,(call math_is_zero,1)) 108$(call math-expect-false,(call math_is_zero,foo)) 109$(call math-expect-error,(call math_is_zero,1 2),Multiple words in a single argument: 1 2) 110$(call math-expect-error,(call math_is_zero,no 2),Multiple words in a single argument: no 2) 111 112define _math_check_valid 113$(if $(call math_is_number_in_100,$(1)),,$(call math-error,Only non-negative integers <= 100 are supported (not $(1)))) 114endef 115 116$(call math-expect,(call _math_check_valid,0)) 117$(call math-expect,(call _math_check_valid,1)) 118$(call math-expect,(call _math_check_valid,100)) 119$(call math-expect-error,(call _math_check_valid,-1),Only non-negative integers <= 100 are supported (not -1)) 120$(call math-expect-error,(call _math_check_valid,101),Only non-negative integers <= 100 are supported (not 101)) 121$(call math-expect-error,(call _math_check_valid,),Argument missing) 122$(call math-expect-error,(call _math_check_valid,1 2),Multiple words in a single argument: 1 2) 123 124# return a list containing integers ranging from [$(1),$(2)] 125define int_range_list 126$(strip \ 127 $(call _math_check_valid,$(1))$(call _math_check_valid,$(2)) \ 128 $(if $(call math_is_zero,$(1)),0)\ 129 $(wordlist $(if $(call math_is_zero,$(1)),1,$(1)),$(2),$(__MATH_POS_NUMBERS))) 130endef 131 132$(call math-expect,(call int_range_list,0,1),0 1) 133$(call math-expect,(call int_range_list,1,1),1) 134$(call math-expect,(call int_range_list,1,2),1 2) 135$(call math-expect,(call int_range_list,2,1),) 136$(call math-expect-error,(call int_range_list,1,101),Only non-negative integers <= 100 are supported (not 101)) 137 138# Split an integer into a list of digits 139define _math_number_to_list 140$(strip \ 141 $(if $(call _math_ext_is_number,$(1)),,\ 142 $(call math-error,Only non-negative integers are supported (not $(1)))) \ 143 $(eval num_list:=$(1)) \ 144 $(foreach num,$(__MATH_ONE_NUMBERS),\ 145 $(eval num_list:=$(subst $(num),$(space)$(num),$(num_list)))) \ 146 $(if $(filter $(words $(num_list)),$(__MATH_ONE_NUMBERS)),,\ 147 $(call math-error,Only non-negative integers with less than 9 digits are supported (not $(1)))) \ 148 $(if $(filter 0,$(word 1,$(num_list))),\ 149 $(call math-error,Only non-negative integers without leading zeros are supported (not $(1)))) \ 150 $(num_list)) 151endef 152 153$(call math-expect,(call _math_number_to_list,123),1 2 3) 154$(call math-expect-error,(call _math_number_to_list,123 456),Multiple words in a single argument: 123 456) 155$(call math-expect-error,(call _math_number_to_list,-123),Only non-negative integers are supported (not -123)) 156$(call math-expect-error,(call _math_number_to_list,002),Only non-negative integers without leading zeros are supported (not 002)) 157$(call math-expect-error,(call _math_number_to_list,1234567890),Only non-negative integers with less than 9 digits are supported (not 1234567890)) 158 159# Compare 1-digit integer $(1) and $(2). 160# Returns 1 if $(1) > $(2), -1 if $(1) < $(2), nothing if equals. 161define _math_1digit_comp 162$(strip \ 163 $(if $(filter $(1),$(2)),,\ 164 $(if $(filter $(1),$(firstword $(filter $(1) $(2),$(__MATH_ONE_NUMBERS)))),-1,1))) 165endef 166 167$(call math-expect,(call _math_1digit_comp,1,1)) 168$(call math-expect,(call _math_1digit_comp,0,9),-1) 169$(call math-expect,(call _math_1digit_comp,3,1),1) 170 171# Compare the same $(3)-digit-length integers $(1) and $(2) that are split into a list of digits. 172# Returns 1 if $(1) > $(2), -1 if $(1) < $(2), nothing if equals. 173define _math_list_comp 174$(strip \ 175 $(eval ans:=) \ 176 $(foreach num,$(call int_range_list,1,$(3)),\ 177 $(if $(ans),,$(eval ans:=$(call _math_1digit_comp,$(word $(num),$(1)),$(word $(num),$(2)))))) \ 178 $(ans)) 179endef 180 181# Compare any two non-negative integers $(1) and $(2). 182# Returns 1 if $(1) > $(2), -1 if $(1) < $(2), nothing if equals. 183define _math_ext_comp 184$(strip \ 185 $(eval num_list1:=$(call _math_number_to_list,$(1))) \ 186 $(eval len1:=$(words $(num_list1))) \ 187 $(eval num_list2:=$(call _math_number_to_list,$(2))) \ 188 $(eval len2:=$(words $(num_list2))) \ 189 $(eval comp:=$(call _math_1digit_comp,$(len1),$(len2))) \ 190 $(if $(comp),$(comp),$(call _math_list_comp,$(num_list1),$(num_list2),$(len1)))) 191endef 192 193$(call math-expect,(call _math_ext_comp,5,10),-1) 194$(call math-expect,(call _math_ext_comp,12345,12345)) 195$(call math-expect,(call _math_ext_comp,500,5),1) 196$(call math-expect,(call _math_ext_comp,202404,202504),-1) 197 198# Returns the greater of $1 or $2. 199# If $1 or $2 is not a positive integer, then an error is generated. 200define math_max 201$(strip \ 202 $(if $(filter truetrue,$(call math_is_number_in_100,$(1))$(call math_is_number_in_100,$(2))),\ 203 $(lastword $(filter $(1) $(2),$(__MATH_NUMBERS))),\ 204 $(if $(filter 1,$(call _math_ext_comp,$(1),$(2))),$(1),$(2)))) 205endef 206 207# Returns the lesser of $1 or $2. 208define math_min 209$(strip \ 210 $(if $(filter truetrue,$(call math_is_number_in_100,$(1))$(call math_is_number_in_100,$(2))),\ 211 $(firstword $(filter $(1) $(2),$(__MATH_NUMBERS))),\ 212 $(if $(filter -1,$(call _math_ext_comp,$(1),$(2))),$(1),$(2)))) 213endef 214 215$(call math-expect-error,(call math_max),Argument missing) 216$(call math-expect-error,(call math_max,1),Argument missing) 217$(call math-expect-error,(call math_max,1 2,3),Multiple words in a single argument: 1 2) 218$(call math-expect-error,(call math_min,1,2 3),Multiple words in a single argument: 2 3) 219$(call math-expect,(call math_max,0,1),1) 220$(call math-expect,(call math_max,1,0),1) 221$(call math-expect,(call math_max,1,1),1) 222$(call math-expect,(call math_max,5,42),42) 223$(call math-expect,(call math_max,42,5),42) 224$(call math-expect,(call math_min,0,1),0) 225$(call math-expect,(call math_min,1,0),0) 226$(call math-expect,(call math_min,1,1),1) 227$(call math-expect,(call math_min,7,32),7) 228$(call math-expect,(call math_min,32,7),7) 229 230$(call math-expect,(call math_max,32759,7),32759) 231$(call math-expect,(call math_max,7,32759),32759) 232$(call math-expect,(call math_max,202404,202505),202505) 233$(call math-expect,(call math_max,202404,202404),202404) 234$(call math-expect,(call math_min,8908527,32),32) 235$(call math-expect,(call math_min,32,8908527),32) 236$(call math-expect,(call math_min,202404,202505),202404) 237$(call math-expect,(call math_min,202404,202404),202404) 238 239define math_gt_or_eq 240$(if $(filter $(1),$(call math_max,$(1),$(2))),true) 241endef 242 243define math_gt 244$(if $(call math_gt_or_eq,$(2),$(1)),,true) 245endef 246 247define math_lt_or_eq 248$(if $(call math_gt_or_eq,$(2),$(1)),true) 249endef 250 251define math_lt 252$(if $(call math_gt_or_eq,$(1),$(2)),,true) 253endef 254 255$(call math-expect-true,(call math_gt_or_eq, 2, 1)) 256$(call math-expect-true,(call math_gt_or_eq, 1, 1)) 257$(call math-expect-false,(call math_gt_or_eq, 1, 2)) 258$(call math-expect-true,(call math_gt, 4, 3)) 259$(call math-expect-false,(call math_gt, 5, 5)) 260$(call math-expect-false,(call math_gt, 6, 7)) 261$(call math-expect-true,(call math_lt_or_eq, 11, 11)) 262$(call math-expect-false,(call math_lt_or_eq, 25, 15)) 263$(call math-expect-true,(call math_lt_or_eq, 9, 16)) 264$(call math-expect-false,(call math_lt, 1, 0)) 265$(call math-expect-false,(call math_lt, 8, 8)) 266$(call math-expect-true,(call math_lt, 10, 11)) 267 268$(call math-expect-true,(call math_gt_or_eq, 2573904, 2573900)) 269$(call math-expect-true,(call math_gt_or_eq, 12345, 12345)) 270$(call math-expect-false,(call math_gt_or_eq, 56, 2780)) 271 272# $1 is the variable name to increment 273define inc_and_print 274$(strip $(eval $(1) := $($(1)) .)$(words $($(1)))) 275endef 276 277ifdef RUN_MATH_TESTS 278a := 279$(call math-expect,(call inc_and_print,a),1) 280$(call math-expect,(call inc_and_print,a),2) 281$(call math-expect,(call inc_and_print,a),3) 282$(call math-expect,(call inc_and_print,a),4) 283endif 284 285# Returns the words in $2 that are numbers and are less than $1 286define numbers_less_than 287$(strip \ 288 $(foreach n,$2, \ 289 $(if $(call math_is_number,$(n)), \ 290 $(if $(call math_lt,$(n),$(1)), \ 291 $(n))))) 292endef 293 294$(call math-expect,(call numbers_less_than,0,0 1 2 3),) 295$(call math-expect,(call numbers_less_than,1,0 2 1 3),0) 296$(call math-expect,(call numbers_less_than,2,0 2 1 3),0 1) 297$(call math-expect,(call numbers_less_than,3,0 2 1 3),0 2 1) 298$(call math-expect,(call numbers_less_than,4,0 2 1 3),0 2 1 3) 299$(call math-expect,(call numbers_less_than,3,0 2 1 3 2),0 2 1 2) 300$(call math-expect,(call numbers_less_than,100,0 1000 50 101 100),0 50) 301 302# Returns the words in $2 that are numbers and are greater or equal to $1 303define numbers_greater_or_equal_to 304$(strip \ 305 $(foreach n,$2, \ 306 $(if $(call math_is_number,$(n)), \ 307 $(if $(call math_gt_or_eq,$(n),$(1)), \ 308 $(n))))) 309endef 310 311$(call math-expect,(call numbers_greater_or_equal_to,4,0 1 2 3),) 312$(call math-expect,(call numbers_greater_or_equal_to,3,0 2 1 3),3) 313$(call math-expect,(call numbers_greater_or_equal_to,2,0 2 1 3),2 3) 314$(call math-expect,(call numbers_greater_or_equal_to,1,0 2 1 3),2 1 3) 315$(call math-expect,(call numbers_greater_or_equal_to,0,0 2 1 3),0 2 1 3) 316$(call math-expect,(call numbers_greater_or_equal_to,1,0 2 1 3 2),2 1 3 2) 317 318_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,\ 319 $(foreach c,x x x x x x x x x x x x x x x x,x x x x x x x x x x x x x x x x))) 320 321define _int_encode 322$(if $(filter $(words x $(_INT_LIMIT_WORDS)),$(words $(wordlist 1,$(1),x $(_INT_LIMIT_WORDS)))),\ 323 $(call math-error,integer greater than $(words $(_INT_LIMIT_WORDS)) is not supported!),\ 324 $(wordlist 1,$(1),$(_INT_LIMIT_WORDS))) 325endef 326 327# _int_max returns the maximum of the two arguments 328# input: two (x) lists; output: one (x) list 329# integer cannot be passed in directly. It has to be converted using _int_encode. 330define _int_max 331$(subst xx,x,$(join $(1),$(2))) 332endef 333 334# first argument is greater than second argument 335# output: non-empty if true 336# integer cannot be passed in directly. It has to be converted using _int_encode. 337define _int_greater-than 338$(filter-out $(words $(2)),$(words $(call _int_max,$(1),$(2)))) 339endef 340 341# first argument equals to second argument 342# output: non-empty if true 343# integer cannot be passed in directly. It has to be converted using _int_encode. 344define _int_equal 345$(filter $(words $(1)),$(words $(2))) 346endef 347 348# first argument is greater than or equal to second argument 349# output: non-empty if true 350# integer cannot be passed in directly. It has to be converted using _int_encode. 351define _int_greater-or-equal 352$(call _int_greater-than,$(1),$(2))$(call _int_equal,$(1),$(2)) 353endef 354 355define int_plus 356$(words $(call _int_encode,$(1)) $(call _int_encode,$(2))) 357endef 358 359$(call math-expect,(call int_plus,0,0),0) 360$(call math-expect,(call int_plus,0,1),1) 361$(call math-expect,(call int_plus,1,0),1) 362$(call math-expect,(call int_plus,1,100),101) 363$(call math-expect,(call int_plus,100,100),200) 364 365define int_subtract 366$(strip \ 367 $(if $(call _int_greater-or-equal,$(call _int_encode,$(1)),$(call _int_encode,$(2))),\ 368 $(words $(filter-out xx,$(join $(call _int_encode,$(1)),$(call _int_encode,$(2))))),\ 369 $(call math-error,subtract underflow $(1) - $(2)))) 370endef 371 372$(call math-expect,(call int_subtract,0,0),0) 373$(call math-expect,(call int_subtract,1,0),1) 374$(call math-expect,(call int_subtract,1,1),0) 375$(call math-expect,(call int_subtract,100,1),99) 376$(call math-expect,(call int_subtract,200,100),100) 377$(call math-expect-error,(call int_subtract,0,1),subtract underflow 0 - 1) 378 379define int_multiply 380$(words $(foreach a,$(call _int_encode,$(1)),$(call _int_encode,$(2)))) 381endef 382 383$(call math-expect,(call int_multiply,0,0),0) 384$(call math-expect,(call int_multiply,1,0),0) 385$(call math-expect,(call int_multiply,1,1),1) 386$(call math-expect,(call int_multiply,100,1),100) 387$(call math-expect,(call int_multiply,1,100),100) 388$(call math-expect,(call int_multiply,4,100),400) 389$(call math-expect,(call int_multiply,100,4),400) 390 391define int_divide 392$(if $(filter 0,$(2)),$(call math-error,division by zero is not allowed!),$(strip \ 393 $(if $(call _int_greater-or-equal,$(call _int_encode,$(1)),$(call _int_encode,$(2))), \ 394 $(call int_plus,$(call int_divide,$(call int_subtract,$(1),$(2)),$(2)),1),0))) 395endef 396 397$(call math-expect,(call int_divide,1,1),1) 398$(call math-expect,(call int_divide,200,1),200) 399$(call math-expect,(call int_divide,200,3),66) 400$(call math-expect,(call int_divide,1,2),0) 401$(call math-expect-error,(call int_divide,0,0),division by zero is not allowed!) 402$(call math-expect-error,(call int_divide,1,0),division by zero is not allowed!) 403 404ifdef RUN_MATH_TESTS 405 ifdef MATH_TEST_FAILURE 406 math-tests: 407 @echo FAIL 408 @false 409 else 410 math-tests: 411 @echo PASS 412 endif 413 .PHONY: math-tests 414endif 415