HCoop / jackhill / mal.git / blame
| Commit | Line | Data |
|---|---|---|
| f4c8a091 JM |
1 | # |
| 2 | # mal (Make a Lisp) number types | |
| 3 | # | |
| 4 | ||
| 5 | ifndef __mal_numbers_included | |
| 6 | __mal_numbers_included := true | |
| 7 | ||
| 8 | _TOP_DIR := $(dir $(lastword $(MAKEFILE_LIST))) | |
| 9 | include $(_TOP_DIR)util.mk | |
| 10 | ||
| 11 | LIST20_X := x x x x x x x x x x x x x x x x x x x x | |
| 12 | LIST100_X := $(foreach x,$(LIST20_X),X X X X X) | |
| 13 | LIST100_0 := $(foreach x,$(LIST20_X),0 0 0 0 0) | |
| 14 | LIST100_9 := $(foreach x,$(LIST20_X),9 9 9 9 9) | |
| 15 | ||
| 16 | ### | |
| 17 | ### general numeric utility functions | |
| 18 | ### | |
| 19 | ||
| 20 | int_encode = $(strip $(call _reverse,\ | |
| 21 | $(eval __temp := $(1))\ | |
| 4c0073a3 | 22 | $(foreach a,- 0 1 2 3 4 5 6 7 8 9,\ |
| f4c8a091 JM |
23 | $(eval __temp := $$(subst $$a,$$a$$(SPACE),$(__temp))))$(__temp))) |
| 24 | ||
| 25 | int_decode = $(strip $(call _join,$(call _reverse,$(1)))) | |
| 26 | ||
| 27 | # trim extaneous zero digits off the end (front of number) | |
| 28 | _trim_zeros = $(if $(call _EQ,0,$(strip $(1))),0,$(if $(call _EQ,0,$(word 1,$(1))),$(call _trim_zeros,$(wordlist 2,$(words $(1)),$(1))),$(1))) | |
| 4c0073a3 JM |
29 | trim_zeros = $(strip \ |
| 30 | $(if $(call _EQ,0,$(strip $(filter-out -,$(1)))),\ | |
| 31 | $(filter-out -,$(1)),\ | |
| 32 | $(call _reverse,$(call _trim_zeros,$(call _reverse,$(filter-out -,$(1))))))\ | |
| 33 | $(if $(filter -,$(1)), -,)) | |
| f4c8a091 JM |
34 | |
| 35 | # drop the last element of a list of words/digits | |
| 36 | drop_last = $(call _reverse,$(wordlist 2,$(words $(1)),$(call _reverse,$(1)))) | |
| 37 | ||
| 38 | ### utility function tests | |
| 39 | ||
| 40 | #$(info $(filter-out 1,$(filter 1%,1 132 456))) | |
| 41 | #$(info (int_encode 13): [$(call int_encode,13)]) | |
| 42 | #$(info (int_encode 156463): [$(call int_encode,156463)]) | |
| 4c0073a3 | 43 | #$(info (int_encode -156463): [$(call int_encode,-156463)]) |
| f4c8a091 JM |
44 | #$(info (int_decode (int_encode 156463)): [$(call int_decode,$(call int_encode,156463))]) |
| 45 | ||
| 46 | #$(info trim_zeros(0 0 0): [$(call trim_zeros,0 0 0)]) | |
| 4c0073a3 | 47 | #$(info trim_zeros(0 0 0 -): [$(call trim_zeros,0 0 0 -)]) |
| f4c8a091 JM |
48 | |
| 49 | ||
| 50 | ### | |
| 51 | ### comparisons | |
| 52 | ### | |
| 53 | ||
| 54 | # compare two digits and return 'true' if digit 1 is less than or | |
| 55 | # equal to digit 2 | |
| 56 | _lte_digit = $(strip \ | |
| 57 | $(if $(call _EQ,$(1),$(2)),\ | |
| 58 | true,\ | |
| 59 | $(if $(call _EQ,0,$(1)),\ | |
| 60 | true,\ | |
| 61 | $(if $(wordlist $(1),$(2),$(LIST20_X)),\ | |
| 62 | true,\ | |
| 63 | )))) | |
| 64 | ||
| 65 | # compare two lists of digits (MSB->LSB) of equal length and return | |
| 66 | # 'true' if number 1 is less than number 2 | |
| 67 | _lte_digits = $(strip \ | |
| 68 | $(if $(strip $(1)),\ | |
| 69 | $(if $(call _EQ,$(word 1,$(1)),$(word 1,$(2))),\ | |
| 70 | $(call _lte_digits,$(wordlist 2,$(words $(1)),$(1)),$(wordlist 2,$(words $(2)),$(2))),\ | |
| 71 | $(if $(call _lte_digit,$(word 1,$(1)),$(word 1,$(2))),true,)),\ | |
| 72 | true)) | |
| 73 | ||
| 74 | ### lte/less than or equal to | |
| 75 | ||
| 4c0073a3 JM |
76 | _int_lte_encoded = $(strip \ |
| 77 | $(foreach len1,$(words $(1)),$(foreach len2,$(words $(2)),\ | |
| 78 | $(if $(call _EQ,$(len1),$(len2)),\ | |
| 79 | $(call _lte_digits,$(call _reverse,$(1)),$(call _reverse,$(2))),\ | |
| 80 | $(if $(wordlist $(len1),$(len2),$(LIST100_X)),\ | |
| 81 | true,\ | |
| 82 | ))))) | |
| 83 | ||
| f4c8a091 | 84 | int_lte_encoded = $(strip \ |
| 4c0073a3 JM |
85 | $(if $(filter -,$(1)),\ |
| 86 | $(if $(filter -,$(2)),\ | |
| 87 | $(call _int_lte_encoded,$(filter-out -,$(2)),$(filter-out -,$(1))),\ | |
| 88 | true),\ | |
| 89 | $(if $(filter -,$(2)),\ | |
| 90 | ,\ | |
| 91 | $(call _int_lte_encoded,$(1),$(2))))) | |
| f4c8a091 JM |
92 | |
| 93 | int_lte = $(call int_lte_encoded,$(call int_encode,$(1)),$(call int_encode,$(2))) | |
| 94 | ||
| 95 | ### lt/less than | |
| 96 | ||
| 97 | int_lt_encoded = $(strip \ | |
| 98 | $(if $(call _EQ,$(strip $(1)),$(strip $(2))),\ | |
| 99 | ,\ | |
| 100 | $(call int_lte_encoded,$(1),$(2)))) | |
| 101 | ||
| 102 | int_lt = $(call int_lt_encoded,$(call int_encode,$(1)),$(call int_encode,$(2))) | |
| 103 | ||
| 104 | ### gte/greater than or equal to | |
| 105 | ||
| 106 | int_gte_encoded = $(strip \ | |
| 107 | $(if $(call _EQ,$(strip $(1)),$(strip $(2))),\ | |
| 108 | true,\ | |
| 109 | $(if $(call int_lte_encoded,$(1),$(2)),,true))) | |
| 110 | ||
| 111 | int_gte = $(call int_gte_encoded,$(call int_encode,$(1)),$(call int_encode,$(2))) | |
| 112 | ||
| 113 | ### gt/greater than | |
| 114 | ||
| 115 | int_gt_encoded = $(strip \ | |
| 116 | $(if $(call _EQ,$(strip $(1)),$(strip $(2))),\ | |
| 117 | ,\ | |
| 118 | $(call int_gte_encoded,$(1),$(2)))) | |
| 119 | ||
| 120 | int_gt = $(call int_gt_encoded,$(call int_encode,$(1)),$(call int_encode,$(2))) | |
| 121 | ||
| 122 | #$(info _lte_digit,7,8: [$(call _lte_digit,7,8)]) | |
| 123 | #$(info _lte_digit,8,8: [$(call _lte_digit,8,8)]) | |
| 124 | #$(info _lte_digit,2,1: [$(call _lte_digit,2,1)]) | |
| 125 | #$(info _lte_digit,0,0: [$(call _lte_digit,0,0)]) | |
| 126 | #$(info _lte_digit,0,1: [$(call _lte_digit,0,1)]) | |
| 127 | #$(info _lte_digit,1,0: [$(call _lte_digit,1,0)]) | |
| 128 | ||
| 129 | #$(info _lte_digits,1 2 3,1 2 4: [$(call _lte_digits,1 2 3,1 2 4)]) | |
| 130 | #$(info _lte_digits,1 2 4,1 2 4: [$(call _lte_digits,1 2 4,1 2 4)]) | |
| 131 | #$(info _lte_digits,1 2 5,1 2 4: [$(call _lte_digits,1 2 5,1 2 4)]) | |
| 132 | #$(info _lte_digits,4 1,9 0: [$(call _lte_digits,4 1,9 0)]) | |
| 133 | ||
| 4c0073a3 | 134 | # The main comparison operator (others are built on this) |
| f4c8a091 JM |
135 | #$(info int_lte_encoded,1,1: [$(call int_lte_encoded,1,1)]) |
| 136 | #$(info int_lte_encoded,1,2: [$(call int_lte_encoded,1,2)]) | |
| 137 | #$(info int_lte_encoded,2,1: [$(call int_lte_encoded,2,1)]) | |
| 138 | #$(info int_lte_encoded,0,3: [$(call int_lte_encoded,0,3)]) | |
| 139 | #$(info int_lte_encoded,3,0: [$(call int_lte_encoded,3,0)]) | |
| 140 | #$(info int_lte_encoded,1 4,0 9: [$(call int_lte_encoded,1 4,0 9)]) | |
| 141 | #$(info int_lte_encoded,4 3 2 1,4 3 2 1: [$(call int_lte_encoded,4 3 2 1,4 3 2 1)]) | |
| 142 | #$(info int_lte_encoded,5 3 2 1,4 3 2 1: [$(call int_lte_encoded,5 3 2 1,4 3 2 1)]) | |
| 143 | #$(info int_lte_encoded,4 3 2 1,5 3 2 1: [$(call int_lte_encoded,4 3 2 1,5 3 2 1)]) | |
| 4c0073a3 JM |
144 | # negative numbers |
| 145 | #$(info int_lte_encoded,7 -,7: [$(call int_lte_encoded,7 -,7)]) | |
| 146 | #$(info int_lte_encoded,7,7 -: [$(call int_lte_encoded,7,7 -)]) | |
| 147 | #$(info int_lte_encoded,7 -,7 -: [$(call int_lte_encoded,7 -,7 -)]) | |
| 148 | #$(info int_lte_encoded,1 7 -,0 7: [$(call int_lte_encoded,1 7 -,0 7)]) | |
| 149 | #$(info int_lte_encoded,1 7,0 7 -: [$(call int_lte_encoded,1 7,0 7 -)]) | |
| 150 | #$(info int_lte_encoded,1 7 -,0 7 -: [$(call int_lte_encoded,1 7 -,0 7 -)]) | |
| 151 | #$(info int_lte_encoded,4 3 2 1 -,4 3 2 1: [$(call int_lte_encoded,4 3 2 1 -,4 3 2 1)]) | |
| 152 | #$(info int_lte_encoded,4 3 2 1,4 3 2 1 -: [$(call int_lte_encoded,4 3 2 1,4 3 2 1 -)]) | |
| 153 | #$(info int_lte_encoded,4 3 2 1 -,4 3 2 1 -: [$(call int_lte_encoded,4 3 2 1 -,4 3 2 1 -)]) | |
| f4c8a091 JM |
154 | |
| 155 | #$(info int_lte,1,1: [$(call int_lte,1,1)]) | |
| 156 | #$(info int_lte,1,2: [$(call int_lte,1,2)]) | |
| 157 | #$(info int_lte,2,1: [$(call int_lte,2,1)]) | |
| 158 | #$(info int_lte,0,3: [$(call int_lte,0,3)]) | |
| 159 | #$(info int_lte,3,0: [$(call int_lte,3,0)]) | |
| 160 | #$(info int_lte,1234,1234: [$(call int_lte,1234,1234)]) | |
| 161 | #$(info int_lte,1235,1234: [$(call int_lte,1235,1234)]) | |
| 162 | #$(info int_lte,1234,1235: [$(call int_lte,1234,1235)]) | |
| 4c0073a3 JM |
163 | #$(info int_lte,-1234,1235: [$(call int_lte,-1234,1235)]) |
| 164 | #$(info int_lte,1234,-1235: [$(call int_lte,1234,-1235)]) | |
| 165 | #$(info int_lte,-1234,-1235: [$(call int_lte,-1234,-1235)]) | |
| 166 | ||
| f4c8a091 JM |
167 | #$(info int_lt,1,1: [$(call int_lt,1,1)]) |
| 168 | #$(info int_lt,1,2: [$(call int_lt,1,2)]) | |
| 169 | #$(info int_lt,2,1: [$(call int_lt,2,1)]) | |
| 170 | #$(info int_lt,0,3: [$(call int_lt,0,3)]) | |
| 171 | #$(info int_lt,3,0: [$(call int_lt,3,0)]) | |
| 172 | #$(info int_lt,1234,1234: [$(call int_lt,1234,1234)]) | |
| 173 | #$(info int_lt,1235,1234: [$(call int_lt,1235,1234)]) | |
| 174 | #$(info int_lt,1234,1235: [$(call int_lt,1234,1235)]) | |
| 175 | # | |
| 176 | #$(info int_gte,1,1: [$(call int_gte,1,1)]) | |
| 177 | #$(info int_gte,1,2: [$(call int_gte,1,2)]) | |
| 178 | #$(info int_gte,2,1: [$(call int_gte,2,1)]) | |
| 179 | #$(info int_gte,0,3: [$(call int_gte,0,3)]) | |
| 180 | #$(info int_gte,3,0: [$(call int_gte,3,0)]) | |
| 181 | #$(info int_gte,1234,1234: [$(call int_gte,1234,1234)]) | |
| 182 | #$(info int_gte,1235,1234: [$(call int_gte,1235,1234)]) | |
| 183 | #$(info int_gte,1234,1235: [$(call int_gte,1234,1235)]) | |
| 184 | # | |
| 185 | #$(info int_gt,1,1: [$(call int_gt,1,1)]) | |
| 186 | #$(info int_gt,1,2: [$(call int_gt,1,2)]) | |
| 187 | #$(info int_gt,2,1: [$(call int_gt,2,1)]) | |
| 188 | #$(info int_gt,0,3: [$(call int_gt,0,3)]) | |
| 189 | #$(info int_gt,3,0: [$(call int_gt,3,0)]) | |
| 190 | #$(info int_gt,1234,1234: [$(call int_gt,1234,1234)]) | |
| 191 | #$(info int_gt,1235,1234: [$(call int_gt,1235,1234)]) | |
| 192 | #$(info int_gt,1234,1235: [$(call int_gt,1234,1235)]) | |
| 4c0073a3 JM |
193 | #$(info int_gt,-1234,1235: [$(call int_gt,-1234,1235)]) |
| 194 | #$(info int_gt,-1234,-1235: [$(call int_gt,-1234,-1235)]) | |
| f4c8a091 JM |
195 | |
| 196 | ||
| 197 | ### | |
| 198 | ### addition | |
| 199 | ### | |
| 200 | ||
| 201 | ||
| 202 | # add_digits_with_carry | |
| 203 | _add_digit = $(words $(if $(strip $(1)),$(wordlist 1,$(1),$(LIST20_X)),) \ | |
| 204 | $(if $(strip $(2)),$(wordlist 1,$(2),$(LIST20_X)),)) | |
| 205 | ||
| 206 | # add one to a single digit | |
| 207 | _inc_digit = $(words $(wordlist 1,$(if $(1),$(1),0),$(LIST20_X)) x) | |
| 208 | ||
| 209 | # add two encoded numbers digit by digit without resolving carries | |
| 210 | # (each digit will be larger than 9 if there is a carry value) | |
| 211 | _add = $(if $(1)$(2),$(call _add_digit,$(word 1,$(1)),$(word 1,$(2))) $(call _add,$(wordlist 2,$(words $(1)),$(1)),$(wordlist 2,$(words $(2)),$(2))),) | |
| 212 | ||
| 213 | # take the result of _add and resolve the carry values digit by digit | |
| 214 | _resolve_carries = $(strip \ | |
| 215 | $(if $(1),\ | |
| 216 | $(foreach num,$(word 1,$(1)),\ | |
| 217 | $(if $(filter-out 1,$(filter 1%,$(num))),\ | |
| 218 | $(call _resolve_carries,$(call _inc_digit,$(word 2,$(1))) $(wordlist 3,$(words $(1)),$(1)),$(2) $(patsubst 1%,%,$(num))),\ | |
| 219 | $(call _resolve_carries,$(wordlist 2,$(words $(1)),$(1)),$(2) $(num)))),\ | |
| 220 | $(2))) | |
| 221 | ||
| 4c0073a3 JM |
222 | _negate = $(strip \ |
| 223 | $(if $(call _EQ,0,$(strip $(1))),\ | |
| 224 | 0,\ | |
| 225 | $(if $(filter -,$(1)),$(filter-out -,$(1)),$(1) -))) | |
| 226 | ||
| f4c8a091 | 227 | # add two encoded numbers, returns encoded number |
| 4c0073a3 JM |
228 | _int_add_encoded = $(call _resolve_carries,$(call _add,$(1),$(2))) |
| 229 | ||
| 230 | int_add_encoded = $(strip \ | |
| 231 | $(if $(filter -,$(1)),\ | |
| 232 | $(if $(filter -,$(2)),\ | |
| 233 | $(call _negate,$(call _int_add_encoded,$(filter-out -,$(1)),$(filter-out -,$(2)))),\ | |
| 234 | $(call int_sub_encoded,$(2),$(filter-out -,$(1)))),\ | |
| 235 | $(if $(filter -,$(2)),\ | |
| 236 | $(call int_sub_encoded,$(1),$(filter-out -,$(2))),\ | |
| 237 | $(call _int_add_encoded,$(1),$(2))))) | |
| f4c8a091 JM |
238 | |
| 239 | # add two unencoded numbers, returns unencoded number | |
| 240 | int_add = $(call int_decode,$(call int_add_encoded,$(call int_encode,$(1)),$(call int_encode,$(2)))) | |
| 241 | ||
| 242 | ### addition tests | |
| 243 | ||
| 244 | #$(info _add_digit(7,6,1): [$(call _add_digit,7,6,1)]) | |
| 245 | #$(info _add_digit(7,6,0): [$(call _add_digit,7,6,0)]) | |
| 246 | #$(info _add_digit(7,6,0): [$(call _add_digit,7,6,0)]) | |
| 247 | #$(info _carries(12 14 15): [$(call _carries,12 14 15)]) | |
| 248 | #$(info _inc_digit(0): $(call _inc_digit,0)) | |
| 249 | #$(info _inc_digit(1): $(call _inc_digit,1)) | |
| 250 | #$(info _inc_digit(9): $(call _inc_digit,9)) | |
| 251 | #$(info _inc_digit(18): $(call _inc_digit,18)) | |
| 252 | #$(info int_add_encoded(0,0): [$(call int_add_encoded,0,0)]) | |
| 253 | ||
| 254 | #$(info int_add(1,2): [$(call int_add,1,2)]) | |
| 255 | #$(info int_add(9,9): [$(call int_add,9,9)]) | |
| 256 | #$(info int_add(0,9): [$(call int_add,0,9)]) | |
| 257 | #$(info int_add(9,0): [$(call int_add,9,0)]) | |
| 258 | #$(info int_add(0,0): [$(call int_add,0,0)]) | |
| 259 | #$(info int_add(123,456): [$(call int_add,123,456)]) | |
| 260 | #$(info int_add(678,789): [$(call int_add,678,789)]) | |
| 261 | #$(info int_add(1,12): [$(call int_add,1,12)]) | |
| 262 | #$(info int_add(123,5): [$(call int_add,123,5)]) | |
| 263 | #$(info int_add(123456,9): [$(call int_add,123456,9)]) | |
| 264 | #$(info int_add(999999991,9): [$(call int_add,999999991,9)]) | |
| 4c0073a3 JM |
265 | # negative numbers |
| 266 | #$(info int_add(-2,2): [$(call int_add,-2,2)]) | |
| 267 | #$(info int_add(-1,2): [$(call int_add,-1,2)]) | |
| 268 | #$(info int_add(1,-2): [$(call int_add,1,-2)]) | |
| 269 | #$(info int_add(-1,-2): [$(call int_add,-1,-2)]) | |
| f4c8a091 JM |
270 | |
| 271 | ### | |
| 272 | ### subtraction | |
| 273 | ### | |
| 274 | ||
| 275 | _get_zeros = $(if $(call _EQ,0,$(word 1,$(1))),$(call _get_zeros,$(wordlist 2,$(words $(1)),$(1)),$(2) 0),$(2)) | |
| 276 | ||
| 277 | # return a 9's complement of a single digit | |
| 278 | _complement9 = $(strip \ | |
| 279 | $(if $(call _EQ,0,$(1)),9,\ | |
| 280 | $(if $(call _EQ,1,$(1)),8,\ | |
| 281 | $(if $(call _EQ,2,$(1)),7,\ | |
| 282 | $(if $(call _EQ,3,$(1)),6,\ | |
| 283 | $(if $(call _EQ,4,$(1)),5,\ | |
| 284 | $(if $(call _EQ,5,$(1)),4,\ | |
| 285 | $(if $(call _EQ,6,$(1)),3,\ | |
| 286 | $(if $(call _EQ,7,$(1)),2,\ | |
| 287 | $(if $(call _EQ,8,$(1)),1,\ | |
| 288 | $(if $(call _EQ,9,$(1)),0))))))))))) | |
| 289 | ||
| 290 | # return a 10's complement of a single digit | |
| 291 | _complement10 = $(call _inc_digit,$(call _complement9,$(1))) | |
| 292 | ||
| 293 | # | |
| 294 | _complement_rest = $(if $(strip $(1)),\ | |
| 295 | $(strip \ | |
| 296 | $(call _complement10,$(word 1,$(1))) \ | |
| 297 | $(foreach digit,$(wordlist 2,$(words $(1)),$(1)),\ | |
| 298 | $(call _complement9,$(digit)))),) | |
| 299 | ||
| 300 | # return the complement of a number | |
| 301 | _complement = $(strip $(call _get_zeros,$(1)) \ | |
| 302 | $(call _complement_rest,$(wordlist $(call _inc_digit,$(words $(call _get_zeros,$(1)))),$(words $(1)),$(1)))) | |
| 303 | ||
| 304 | # subtracted encoded number 2 from encoded number 1 and return and | |
| 4c0073a3 JM |
305 | # encoded number result. both numbers must be positive but may have |
| 306 | # a negative result | |
| 307 | __int_sub_encoded = $(strip \ | |
| f4c8a091 JM |
308 | $(call trim_zeros,\ |
| 309 | $(call drop_last,\ | |
| 310 | $(call int_add_encoded,\ | |
| 311 | $(1),\ | |
| 4c0073a3 JM |
312 | $(wordlist 1,$(words $(1)),$(call _complement,$(2)) $(LIST100_9)))))) |
| 313 | ||
| 314 | _int_sub_encoded = $(strip \ | |
| 315 | $(if $(call _EQ,0,$(strip $(2))),\ | |
| 316 | $(1),\ | |
| 317 | $(if $(call _int_lte_encoded,$(2),$(1)),\ | |
| 318 | $(call __int_sub_encoded,$(1),$(2)),\ | |
| 319 | $(call _negate,$(call __int_sub_encoded,$(2),$(1)))))) | |
| 320 | ||
| 321 | int_sub_encoded = $(strip \ | |
| 322 | $(if $(filter -,$(1)),\ | |
| 323 | $(if $(filter -,$(2)),\ | |
| 324 | $(call _int_sub_encoded,$(filter-out -,$(2)),$(filter-out -,$(1))),\ | |
| 325 | $(call _negate,$(call _int_add_encoded,$(filter-out -,$(1)),$(2)))),\ | |
| 326 | $(if $(filter -,$(2)),\ | |
| 327 | $(call _int_add_encoded,$(1),$(filter-out -,$(2))),\ | |
| 328 | $(call _int_sub_encoded,$(1),$(2))))) | |
| f4c8a091 JM |
329 | |
| 330 | # subtract unencoded number 2 from unencoded number 1 and return | |
| 331 | # unencoded result | |
| 332 | int_sub = $(call int_decode,$(call int_sub_encoded,$(call int_encode,$(1)),$(call int_encode,$(2)))) | |
| 333 | ||
| 334 | ### subtraction tests | |
| 335 | ||
| 336 | #$(info _get_zeros(5 7): [$(call _get_zeros,5 7)]) | |
| 337 | #$(info _get_zeros(0 0 0 2): [$(call _get_zeros,0 0 0 2)]) | |
| 338 | #$(info _get_zeros(0 0 0 2 5): [$(call _get_zeros,0 0 0 2 5)]) | |
| 339 | ||
| 340 | #$(info _complement(0): [$(call _complement,0)]) | |
| 341 | #$(info _complement(1): [$(call _complement,1)]) | |
| 342 | #$(info _complement(9): [$(call _complement,9)]) | |
| 343 | #$(info _complement(5 7): [$(call _complement,5 7)]) | |
| 344 | #$(info _complement(0 0 0 2): [$(call _complement,0 0 0 2)]) | |
| 345 | #$(info _complement(0 0 0 5 4 3 2 1): [$(call _complement,0 0 0 5 4 3 2 1)]) | |
| 346 | ||
| 347 | #$(info int_sub_encoded(0 0 1, 3 1): [$(call int_sub_encoded,0 0 1,3 1)]) | |
| 348 | #$(info int_sub_encoded(2, 2): [$(call int_sub_encoded,2,2)]) | |
| 349 | ||
| 350 | #$(info int_sub(2,1): [$(call int_sub,2,1)]) | |
| 351 | #$(info int_sub(2,0): [$(call int_sub,2,0)]) | |
| 352 | #$(info int_sub(2,2): [$(call int_sub,2,2)]) | |
| 353 | #$(info int_sub(100,13): [$(call int_sub,100,13)]) | |
| 354 | #$(info int_sub(100,99): [$(call int_sub,100,99)]) | |
| 355 | #$(info int_sub(91,19): [$(call int_sub,91,19)]) | |
| 4c0073a3 JM |
356 | # negative numbers |
| 357 | #$(info int_sub(1,2): [$(call int_sub,1,2)]) | |
| 358 | #$(info int_sub(-1,2): [$(call int_sub,-1,2)]) | |
| 359 | #$(info int_sub(1,-2): [$(call int_sub,1,-2)]) | |
| 360 | #$(info int_sub(-1,-2): [$(call int_sub,-1,-2)]) | |
| 361 | #$(info int_sub(-2,-1): [$(call int_sub,-2,-1)]) | |
| 362 | #$(info int_sub(19,91): [$(call int_sub,19,91)]) | |
| 363 | #$(info int_sub(91,-19): [$(call int_sub,91,-19)]) | |
| 364 | #$(info int_sub(-91,19): [$(call int_sub,-91,19)]) | |
| 365 | #$(info int_sub(-91,-19): [$(call int_sub,-91,-19)]) | |
| f4c8a091 JM |
366 | |
| 367 | ||
| 368 | ### | |
| 369 | ### multiplication | |
| 370 | ### | |
| 371 | ||
| 372 | # multiply two digits | |
| 373 | #_mult_digit = $(words $(foreach x,$(1),$(2))) | |
| 374 | _mult_digit = $(strip \ | |
| 375 | $(words $(foreach x,$(wordlist 1,$(1),$(LIST20_X)),\ | |
| 376 | $(wordlist 1,$(2),$(LIST20_X))))) | |
| 377 | ||
| 378 | # multipy every digit of number 1 with number 2 | |
| 379 | # params: digits, digit, indent_zeros, results | |
| 380 | _mult_row = $(if $(strip $(1)),$(call _mult_row,$(wordlist 2,$(words $(1)),$(1)),$(2),$(3)0,$(4) $(call _mult_digit,$(word 1,$(1)),$(2))$(3)),$(4)) | |
| 381 | ||
| 382 | # multiply every digit of number 2 with every digit of number 1 adding | |
| 383 | # correct zero padding to the end of each result | |
| 384 | # params: digits, digits, indent_zeros, results | |
| 385 | _mult_each = $(if $(strip $(2)),$(call _mult_each,$(1),$(wordlist 2,$(words $(2)),$(2)),$(3)0,$(4) $(call _mult_row,$(1),$(word 1,$(2)),$(3))),$(4)) | |
| 386 | ||
| 387 | # add up a bunch of unencoded numbers. Basically reduce into the first number | |
| 388 | _add_many = $(if $(word 2,$(1)),$(call _add_many,$(call int_add,$(word 1,$(1)),$(word 2,$(1))) $(wordlist 3,$(words $(1)),$(1))),$(1)) | |
| 389 | ||
| 390 | # multiply two encoded numbers, returns encoded number | |
| 4c0073a3 JM |
391 | _int_mult_encoded = $(call trim_zeros,$(call int_encode,$(call _add_many,$(call _mult_each,$(1),$(2))))) |
| 392 | ||
| 393 | int_mult_encoded = $(strip \ | |
| 394 | $(if $(filter -,$(1)),\ | |
| 395 | $(if $(filter -,$(2)),\ | |
| 396 | $(call _int_mult_encoded,$(filter-out -,$(1)),$(filter-out -,$(2))),\ | |
| 397 | $(call _negate,$(call _int_mult_encoded,$(filter-out -,$(1)),$(2)))),\ | |
| 398 | $(if $(filter -,$(2)),\ | |
| 399 | $(call _negate,$(call _int_mult_encoded,$(1),$(filter-out -,$(2)))),\ | |
| 400 | $(call _int_mult_encoded,$(1),$(2))))) | |
| f4c8a091 JM |
401 | |
| 402 | # multiply two unencoded numbers, returns unencoded number | |
| 403 | int_mult = $(call int_decode,$(call int_mult_encoded,$(call int_encode,$(1)),$(call int_encode,$(2)))) | |
| 404 | ||
| 405 | #$(info _mult_digit(8,6): [$(call _mult_digit,8,6)]) | |
| 406 | #$(info _mult_digit(7,6): [$(call _mult_digit,7,6)]) | |
| 407 | #$(info _mult_row(8,6): [$(call _mult_row,8,6)]) | |
| 408 | #$(info _mult_row(8 7,6): [$(call _mult_row,8 7,6)]) | |
| 409 | #$(info _mult_row(8 7 3,6): [$(call _mult_row,8 7 3,6)]) | |
| 410 | #$(info _mult_each(8 7 6, 4 3 2): [$(call _mult_each,8 7 6,4 3 2)]) | |
| 411 | #$(info _add_many(123 234 345 456): [$(call _add_many,123 234 345 456)]) | |
| 412 | ||
| 413 | #$(info int_mult_encoded(8 7 3,6): [$(call int_mult_encoded,8 7 3,6)]) | |
| 414 | #$(info int_mult_encoded(8 7 3,0): [$(call int_mult_encoded,8 7 3,0)]) | |
| 415 | ||
| 416 | #$(info int_mult(378,6): [$(call int_mult,378,6)]) | |
| 417 | #$(info int_mult(678,234): [$(call int_mult,678,234)]) | |
| 418 | #$(info int_mult(1,23456): [$(call int_mult,1,23456)]) | |
| 419 | #$(info int_mult(0,23456): [$(call int_mult,0,23456)]) | |
| 420 | #$(info int_mult(0,0): [$(call int_mult,0,0)]) | |
| 4c0073a3 JM |
421 | # negative numbers |
| 422 | #$(info int_mult(-378,6): [$(call int_mult,-378,6)]) | |
| 423 | #$(info int_mult(678,-234): [$(call int_mult,678,-234)]) | |
| 424 | #$(info int_mult(-1,-23456): [$(call int_mult,-1,-23456)]) | |
| 425 | #$(info int_mult(0,-23456): [$(call int_mult,0,-23456)]) | |
| f4c8a091 JM |
426 | |
| 427 | ### | |
| 428 | ### division | |
| 429 | ### | |
| 430 | ||
| 431 | # return list of zeros needed to pad number 2 to the same length as number 1 | |
| 432 | _zero_pad = $(strip $(wordlist 1,$(call int_sub,$(words $(1)),$(words $(2))),$(LIST100_0))) | |
| 433 | ||
| 434 | # num1, num2, zero pad, result_accumulator | |
| 435 | # algorithm: | |
| 436 | # - B = pad with zeros to make same digit length as A | |
| 437 | # - loop | |
| 438 | # - if (B <= A) | |
| 439 | # - A = subtract B from A | |
| 440 | # - C = C + 10^(B pad.length) | |
| 441 | # - else | |
| 442 | # - if B.length < origin B.length: break | |
| 443 | # - chop least significant digit of B | |
| 444 | _div = $(strip \ | |
| 445 | $(if $(call int_lte_encoded,$(3) $(2),$(1)),\ | |
| 446 | $(call _div,$(call int_sub_encoded,$(1),$(3) $(2)),$(2),$(3),$(call int_add_encoded,$(4),$(3) 1)),\ | |
| 447 | $(if $(3),\ | |
| 448 | $(call _div,$(1),$(2),$(wordlist 2,$(words $(3)),$(3)),$(4)),\ | |
| 449 | $(4)))) | |
| 450 | ||
| 451 | # divide two encoded numbers, returns encoded number | |
| 4c0073a3 | 452 | _int_div_encoded = $(strip \ |
| f4c8a091 JM |
453 | $(if $(call _EQ,0,$(1)),\ |
| 454 | 0,\ | |
| 455 | $(if $(call _EQ,$(1),$(2)),\ | |
| 456 | 1,\ | |
| 457 | $(if $(call int_gt_encoded,$(2),$(1)),\ | |
| 458 | 0,\ | |
| 459 | $(call _div,$(1),$(2),$(call _zero_pad,$(1),$(2)),0))))) | |
| 460 | ||
| 4c0073a3 JM |
461 | int_div_encoded = $(strip \ |
| 462 | $(if $(filter -,$(1)),\ | |
| 463 | $(if $(filter -,$(2)),\ | |
| 464 | $(call _int_div_encoded,$(filter-out -,$(1)),$(filter-out -,$(2))),\ | |
| 465 | $(call _negate,$(call _int_div_encoded,$(filter-out -,$(1)),$(2)))),\ | |
| 466 | $(if $(filter -,$(2)),\ | |
| 467 | $(call _negate,$(call _int_div_encoded,$(1),$(filter-out -,$(2)))),\ | |
| 468 | $(call _int_div_encoded,$(1),$(2))))) | |
| 469 | ||
| f4c8a091 JM |
470 | # divide two unencoded numbers, returns unencoded number |
| 471 | int_div = $(call int_decode,$(call int_div_encoded,$(call int_encode,$(1)),$(call int_encode,$(2)))) | |
| 472 | ||
| 473 | ### division tests | |
| 474 | ||
| 475 | #$(info _zero_pad(1 2 3 4,1 3): [$(call _zero_pad,1 2 3 4,1 3)]) | |
| 476 | #$(info _zero_pad(1 2,1 3): [$(call _zero_pad,1 2,1 3)]) | |
| 477 | #$(info _zero_pad(2,1 3): [$(call _zero_pad,1 2,1 3)]) | |
| 478 | # | |
| 479 | #$(info int_div_encoded(2,1): [$(call int_div_encoded,2,1)]) | |
| 480 | #$(info int_div_encoded(3,1): [$(call int_div_encoded,3,1)]) | |
| 481 | #$(info int_div_encoded(3,2): [$(call int_div_encoded,3,2)]) | |
| 482 | #$(info int_div_encoded(0,7): [$(call int_div_encoded,0,7)]) | |
| 483 | #$(info int_div_encoded(0 3,0 2): [$(call int_div_encoded,0 3,0 2)]) | |
| 484 | #$(info int_div_encoded(0 3,5): [$(call int_div_encoded,0 3,5)]) | |
| 485 | # | |
| 486 | #$(info int_div(5,1): [$(call int_div,5,1)]) | |
| 487 | #$(info int_div(5,2): [$(call int_div,5,2)]) | |
| 488 | #$(info int_div(123,7): [$(call int_div,123,7)]) | |
| 489 | #$(info int_div(100,7): [$(call int_div,100,7)]) | |
| 4c0073a3 JM |
490 | # negative numbers |
| 491 | #$(info int_div(-5,1): [$(call int_div,-5,1)]) | |
| 492 | #$(info int_div(5,-2): [$(call int_div,5,-2)]) | |
| 493 | #$(info int_div(-123,-7): [$(call int_div,-123,-7)]) | |
| f4c8a091 JM |
494 | |
| 495 | ||
| 496 | ### combination tests | |
| 497 | ||
| 4c0073a3 | 498 | # (/ (- (+ 515 (* 222 311)) 300) 41) = 1689 |
| f4c8a091 JM |
499 | #$(info int_mult,222,311: [$(call int_mult,222,311)]) |
| 500 | #$(info int_add(515,69042): [$(call int_add,515,69042)]) | |
| 501 | #$(info int_sub(69557,300): [$(call int_sub,69557,300)]) | |
| 502 | #$(info int_div(69257,41): [$(call int_div,69257,41)]) | |
| 4c0073a3 JM |
503 | # (/ (- (+ 515 (* -222 311)) 300) 41) = -1678 |
| 504 | #$(info int_mult,-222,311: [$(call int_mult,-222,311)]) | |
| 505 | #$(info int_add(515,-69042): [$(call int_add,515,-69042)]) | |
| 506 | #$(info int_sub(-68527,300): [$(call int_sub,-68527,300)]) | |
| 507 | #$(info int_div(-68827,41): [$(call int_div,-68827,41)]) | |
| f4c8a091 JM |
508 | |
| 509 | ############################################################### | |
| 510 | ||
| 511 | all: | |
| 512 | @true | |
| 513 | ||
| 514 | endif | |
| 515 | ||
| 516 | # vim: ts=2 et |