Make: refactor number type. Support large numbers.

- Can support numbers up to 100 decimal digits in length.
- Still no support for negative numbers or floating point.
- Change time-secs to time-ms and remove conditional in perf.mal

1 files changed, 409 insertions, 0 deletions

diff --git a/make/numbers.mk b/make/numbers.mk
new file mode 100644
index 0000000..b0fa29a
--- /dev/null
+++ b/make/numbers.mk
@@ -0,0 +1,409 @@
+#
+# mal (Make a Lisp) number types
+#
+
+ifndef __mal_numbers_included
+__mal_numbers_included := true
+
+_TOP_DIR := $(dir $(lastword $(MAKEFILE_LIST)))
+include $(_TOP_DIR)util.mk
+
+LIST20_X := x x x x x x x x x x x x x x x x x x x x
+LIST100_X := $(foreach x,$(LIST20_X),X X X X X)
+LIST100_0 := $(foreach x,$(LIST20_X),0 0 0 0 0)
+LIST100_9 := $(foreach x,$(LIST20_X),9 9 9 9 9)
+
+###
+### general numeric utility functions
+###
+
+int_encode = $(strip $(call _reverse,\
+               $(eval __temp := $(1))\
+               $(foreach a,0 1 2 3 4 5 6 7 8 9,\
+                 $(eval __temp := $$(subst $$a,$$a$$(SPACE),$(__temp))))$(__temp)))
+
+int_decode = $(strip $(call _join,$(call _reverse,$(1))))
+
+# trim extaneous zero digits off the end (front of number)
+_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)))
+trim_zeros = $(strip $(if $(call _EQ,0,$(strip $(1))),$(1),$(call _reverse,$(call _trim_zeros,$(call _reverse,$(1))))))
+
+# drop the last element of a list of words/digits
+drop_last = $(call _reverse,$(wordlist 2,$(words $(1)),$(call _reverse,$(1))))
+
+### utility function tests
+
+#$(info $(filter-out 1,$(filter 1%,1 132 456)))
+#$(info (int_encode 13): [$(call int_encode,13)])
+#$(info (int_encode 156463): [$(call int_encode,156463)])
+#$(info (int_decode (int_encode 156463)): [$(call int_decode,$(call int_encode,156463))])
+
+#$(info trim_zeros(0 0 0): [$(call trim_zeros,0 0 0)])
+
+
+### 
+### comparisons
+###
+
+# compare two digits and return 'true' if digit 1 is less than or
+# equal to digit 2
+_lte_digit = $(strip \
+              $(if $(call _EQ,$(1),$(2)),\
+                true,\
+                $(if $(call _EQ,0,$(1)),\
+                  true,\
+                  $(if $(wordlist $(1),$(2),$(LIST20_X)),\
+                    true,\
+                    ))))
+
+# compare two lists of digits (MSB->LSB) of equal length and return
+# 'true' if number 1 is less than number 2
+_lte_digits = $(strip \
+                $(if $(strip $(1)),\
+                  $(if $(call _EQ,$(word 1,$(1)),$(word 1,$(2))),\
+                    $(call _lte_digits,$(wordlist 2,$(words $(1)),$(1)),$(wordlist 2,$(words $(2)),$(2))),\
+                    $(if $(call _lte_digit,$(word 1,$(1)),$(word 1,$(2))),true,)),\
+                  true))
+
+### lte/less than or equal to
+
+int_lte_encoded = $(strip \
+                    $(foreach len1,$(words $(1)),$(foreach len2,$(words $(2)),\
+                      $(if $(call _EQ,$(len1),$(len2)),\
+                        $(call _lte_digits,$(call _reverse,$(1)),$(call _reverse,$(2))),\
+                        $(if $(wordlist $(len1),$(len2),$(LIST100_X)),\
+                          true,\
+                          )))))
+
+int_lte = $(call int_lte_encoded,$(call int_encode,$(1)),$(call int_encode,$(2)))
+
+### lt/less than
+
+int_lt_encoded = $(strip \
+                   $(if $(call _EQ,$(strip $(1)),$(strip $(2))),\
+                     ,\
+                     $(call int_lte_encoded,$(1),$(2))))
+
+int_lt = $(call int_lt_encoded,$(call int_encode,$(1)),$(call int_encode,$(2)))
+
+### gte/greater than or equal to
+
+int_gte_encoded = $(strip \
+                $(if $(call _EQ,$(strip $(1)),$(strip $(2))),\
+                  true,\
+                  $(if $(call int_lte_encoded,$(1),$(2)),,true)))
+
+int_gte = $(call int_gte_encoded,$(call int_encode,$(1)),$(call int_encode,$(2)))
+
+### gt/greater than
+
+int_gt_encoded = $(strip \
+               $(if $(call _EQ,$(strip $(1)),$(strip $(2))),\
+                 ,\
+                 $(call int_gte_encoded,$(1),$(2))))
+
+int_gt = $(call int_gt_encoded,$(call int_encode,$(1)),$(call int_encode,$(2)))
+
+#$(info _lte_digit,7,8: [$(call _lte_digit,7,8)])
+#$(info _lte_digit,8,8: [$(call _lte_digit,8,8)])
+#$(info _lte_digit,2,1: [$(call _lte_digit,2,1)])
+#$(info _lte_digit,0,0: [$(call _lte_digit,0,0)])
+#$(info _lte_digit,0,1: [$(call _lte_digit,0,1)])
+#$(info _lte_digit,1,0: [$(call _lte_digit,1,0)])
+
+#$(info _lte_digits,1 2 3,1 2 4: [$(call _lte_digits,1 2 3,1 2 4)])
+#$(info _lte_digits,1 2 4,1 2 4: [$(call _lte_digits,1 2 4,1 2 4)])
+#$(info _lte_digits,1 2 5,1 2 4: [$(call _lte_digits,1 2 5,1 2 4)])
+#$(info _lte_digits,4 1,9 0: [$(call _lte_digits,4 1,9 0)])
+
+#$(info int_lte_encoded,1,1: [$(call int_lte_encoded,1,1)])
+#$(info int_lte_encoded,1,2: [$(call int_lte_encoded,1,2)])
+#$(info int_lte_encoded,2,1: [$(call int_lte_encoded,2,1)])
+#$(info int_lte_encoded,0,3: [$(call int_lte_encoded,0,3)])
+#$(info int_lte_encoded,3,0: [$(call int_lte_encoded,3,0)])
+#$(info int_lte_encoded,1 4,0 9: [$(call int_lte_encoded,1 4,0 9)])
+#$(info int_lte_encoded,4 3 2 1,4 3 2 1: [$(call int_lte_encoded,4 3 2 1,4 3 2 1)])
+#$(info int_lte_encoded,5 3 2 1,4 3 2 1: [$(call int_lte_encoded,5 3 2 1,4 3 2 1)])
+#$(info int_lte_encoded,4 3 2 1,5 3 2 1: [$(call int_lte_encoded,4 3 2 1,5 3 2 1)])
+
+#$(info int_lte,1,1: [$(call int_lte,1,1)])
+#$(info int_lte,1,2: [$(call int_lte,1,2)])
+#$(info int_lte,2,1: [$(call int_lte,2,1)])
+#$(info int_lte,0,3: [$(call int_lte,0,3)])
+#$(info int_lte,3,0: [$(call int_lte,3,0)])
+#$(info int_lte,1234,1234: [$(call int_lte,1234,1234)])
+#$(info int_lte,1235,1234: [$(call int_lte,1235,1234)])
+#$(info int_lte,1234,1235: [$(call int_lte,1234,1235)])
+#
+#$(info int_lt,1,1: [$(call int_lt,1,1)])
+#$(info int_lt,1,2: [$(call int_lt,1,2)])
+#$(info int_lt,2,1: [$(call int_lt,2,1)])
+#$(info int_lt,0,3: [$(call int_lt,0,3)])
+#$(info int_lt,3,0: [$(call int_lt,3,0)])
+#$(info int_lt,1234,1234: [$(call int_lt,1234,1234)])
+#$(info int_lt,1235,1234: [$(call int_lt,1235,1234)])
+#$(info int_lt,1234,1235: [$(call int_lt,1234,1235)])
+#
+#$(info int_gte,1,1: [$(call int_gte,1,1)])
+#$(info int_gte,1,2: [$(call int_gte,1,2)])
+#$(info int_gte,2,1: [$(call int_gte,2,1)])
+#$(info int_gte,0,3: [$(call int_gte,0,3)])
+#$(info int_gte,3,0: [$(call int_gte,3,0)])
+#$(info int_gte,1234,1234: [$(call int_gte,1234,1234)])
+#$(info int_gte,1235,1234: [$(call int_gte,1235,1234)])
+#$(info int_gte,1234,1235: [$(call int_gte,1234,1235)])
+#
+#$(info int_gt,1,1: [$(call int_gt,1,1)])
+#$(info int_gt,1,2: [$(call int_gt,1,2)])
+#$(info int_gt,2,1: [$(call int_gt,2,1)])
+#$(info int_gt,0,3: [$(call int_gt,0,3)])
+#$(info int_gt,3,0: [$(call int_gt,3,0)])
+#$(info int_gt,1234,1234: [$(call int_gt,1234,1234)])
+#$(info int_gt,1235,1234: [$(call int_gt,1235,1234)])
+#$(info int_gt,1234,1235: [$(call int_gt,1234,1235)])
+
+
+###
+### addition
+###
+
+
+# add_digits_with_carry
+_add_digit = $(words $(if $(strip $(1)),$(wordlist 1,$(1),$(LIST20_X)),) \
+                     $(if $(strip $(2)),$(wordlist 1,$(2),$(LIST20_X)),))
+
+# add one to a single digit
+_inc_digit = $(words $(wordlist 1,$(if $(1),$(1),0),$(LIST20_X)) x)
+
+# add two encoded numbers digit by digit without resolving carries
+# (each digit will be larger than 9 if there is a carry value)
+_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))),)
+
+# take the result of _add and resolve the carry values digit by digit
+_resolve_carries = $(strip \
+             $(if $(1),\
+               $(foreach num,$(word 1,$(1)),\
+                 $(if $(filter-out 1,$(filter 1%,$(num))),\
+                   $(call _resolve_carries,$(call _inc_digit,$(word 2,$(1))) $(wordlist 3,$(words $(1)),$(1)),$(2) $(patsubst 1%,%,$(num))),\
+                   $(call _resolve_carries,$(wordlist 2,$(words $(1)),$(1)),$(2) $(num)))),\
+               $(2)))
+
+# add two encoded numbers, returns encoded number
+int_add_encoded = $(call _resolve_carries,$(call _add,$(1),$(2)))
+
+# add two unencoded numbers, returns unencoded number
+int_add = $(call int_decode,$(call int_add_encoded,$(call int_encode,$(1)),$(call int_encode,$(2))))
+
+### addition tests
+
+#$(info _add_digit(7,6,1): [$(call _add_digit,7,6,1)])
+#$(info _add_digit(7,6,0): [$(call _add_digit,7,6,0)])
+#$(info _add_digit(7,6,0): [$(call _add_digit,7,6,0)])
+#$(info _carries(12 14 15): [$(call _carries,12 14 15)])
+#$(info _inc_digit(0): $(call _inc_digit,0))
+#$(info _inc_digit(1): $(call _inc_digit,1))
+#$(info _inc_digit(9): $(call _inc_digit,9))
+#$(info _inc_digit(18): $(call _inc_digit,18))
+#$(info int_add_encoded(0,0): [$(call int_add_encoded,0,0)])
+
+#$(info int_add(1,2): [$(call int_add,1,2)])
+#$(info int_add(9,9): [$(call int_add,9,9)])
+#$(info int_add(0,9): [$(call int_add,0,9)])
+#$(info int_add(9,0): [$(call int_add,9,0)])
+#$(info int_add(0,0): [$(call int_add,0,0)])
+#$(info int_add(123,456): [$(call int_add,123,456)])
+#$(info int_add(678,789): [$(call int_add,678,789)])
+#$(info int_add(1,12): [$(call int_add,1,12)])
+#$(info int_add(123,5): [$(call int_add,123,5)])
+#$(info int_add(123456,9): [$(call int_add,123456,9)])
+#$(info int_add(999999991,9): [$(call int_add,999999991,9)])
+
+###
+### subtraction
+###
+
+_get_zeros = $(if $(call _EQ,0,$(word 1,$(1))),$(call _get_zeros,$(wordlist 2,$(words $(1)),$(1)),$(2) 0),$(2))
+
+# return a 9's complement of a single digit
+_complement9 = $(strip \
+                 $(if $(call _EQ,0,$(1)),9,\
+                 $(if $(call _EQ,1,$(1)),8,\
+                 $(if $(call _EQ,2,$(1)),7,\
+                 $(if $(call _EQ,3,$(1)),6,\
+                 $(if $(call _EQ,4,$(1)),5,\
+                 $(if $(call _EQ,5,$(1)),4,\
+                 $(if $(call _EQ,6,$(1)),3,\
+                 $(if $(call _EQ,7,$(1)),2,\
+                 $(if $(call _EQ,8,$(1)),1,\
+                 $(if $(call _EQ,9,$(1)),0)))))))))))
+
+# return a 10's complement of a single digit
+_complement10 = $(call _inc_digit,$(call _complement9,$(1)))
+
+# 
+_complement_rest = $(if $(strip $(1)),\
+                     $(strip \
+                       $(call _complement10,$(word 1,$(1))) \
+                       $(foreach digit,$(wordlist 2,$(words $(1)),$(1)),\
+                         $(call _complement9,$(digit)))),)
+
+# return the complement of a number
+_complement = $(strip $(call _get_zeros,$(1)) \
+                      $(call _complement_rest,$(wordlist $(call _inc_digit,$(words $(call _get_zeros,$(1)))),$(words $(1)),$(1))))
+
+# subtracted encoded number 2 from encoded number 1 and return and
+# encoded number result
+int_sub_encoded = $(strip \
+                $(if $(call _EQ,0,$(strip $(2))),\
+                  $(1),\
+                  $(call trim_zeros,\
+                    $(call drop_last,\
+                      $(call int_add_encoded,\
+                        $(1),\
+                        $(wordlist 1,$(words $(1)),$(call _complement,$(2)) $(LIST100_9)))))))
+
+# subtract unencoded number 2 from unencoded number 1 and return
+# unencoded result
+int_sub = $(call int_decode,$(call int_sub_encoded,$(call int_encode,$(1)),$(call int_encode,$(2))))
+
+### subtraction tests
+
+#$(info _get_zeros(5 7): [$(call _get_zeros,5 7)])
+#$(info _get_zeros(0 0 0 2): [$(call _get_zeros,0 0 0 2)])
+#$(info _get_zeros(0 0 0 2 5): [$(call _get_zeros,0 0 0 2 5)])
+
+#$(info _complement(0): [$(call _complement,0)])
+#$(info _complement(1): [$(call _complement,1)])
+#$(info _complement(9): [$(call _complement,9)])
+#$(info _complement(5 7): [$(call _complement,5 7)])
+#$(info _complement(0 0 0 2): [$(call _complement,0 0 0 2)])
+#$(info _complement(0 0 0 5 4 3 2 1): [$(call _complement,0 0 0 5 4 3 2 1)])
+
+#$(info int_sub_encoded(0 0 1, 3 1): [$(call int_sub_encoded,0 0 1,3 1)])
+#$(info int_sub_encoded(2, 2): [$(call int_sub_encoded,2,2)])
+
+#$(info int_sub(2,1): [$(call int_sub,2,1)])
+#$(info int_sub(2,0): [$(call int_sub,2,0)])
+#$(info int_sub(2,2): [$(call int_sub,2,2)])
+#$(info int_sub(100,13): [$(call int_sub,100,13)])
+#$(info int_sub(100,99): [$(call int_sub,100,99)])
+#$(info int_sub(91,19): [$(call int_sub,91,19)])
+
+
+###
+### multiplication
+###
+
+# multiply two digits
+#_mult_digit = $(words $(foreach x,$(1),$(2)))
+_mult_digit = $(strip \
+                $(words $(foreach x,$(wordlist 1,$(1),$(LIST20_X)),\
+                        $(wordlist 1,$(2),$(LIST20_X)))))
+
+# multipy every digit of number 1 with number 2
+# params: digits, digit, indent_zeros, results
+_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))
+
+# multiply every digit of number 2 with every digit of number 1 adding
+# correct zero padding to the end of each result
+# params: digits, digits, indent_zeros, results
+_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))
+
+# add up a bunch of unencoded numbers. Basically reduce into the first number
+_add_many = $(if $(word 2,$(1)),$(call _add_many,$(call int_add,$(word 1,$(1)),$(word 2,$(1))) $(wordlist  3,$(words $(1)),$(1))),$(1))
+
+# multiply two encoded numbers, returns encoded number
+int_mult_encoded = $(call trim_zeros,$(call int_encode,$(call _add_many,$(call _mult_each,$(1),$(2)))))
+
+# multiply two unencoded numbers, returns unencoded number
+int_mult = $(call int_decode,$(call int_mult_encoded,$(call int_encode,$(1)),$(call int_encode,$(2))))
+
+#$(info _mult_digit(8,6): [$(call _mult_digit,8,6)])
+#$(info _mult_digit(7,6): [$(call _mult_digit,7,6)])
+#$(info _mult_row(8,6): [$(call _mult_row,8,6)])
+#$(info _mult_row(8 7,6): [$(call _mult_row,8 7,6)])
+#$(info _mult_row(8 7 3,6): [$(call _mult_row,8 7 3,6)])
+#$(info _mult_each(8 7 6, 4 3 2): [$(call _mult_each,8 7 6,4 3 2)])
+#$(info _add_many(123 234 345 456): [$(call _add_many,123 234 345 456)])
+
+#$(info int_mult_encoded(8 7 3,6): [$(call int_mult_encoded,8 7 3,6)])
+#$(info int_mult_encoded(8 7 3,0): [$(call int_mult_encoded,8 7 3,0)])
+
+#$(info int_mult(378,6): [$(call int_mult,378,6)])
+#$(info int_mult(678,234): [$(call int_mult,678,234)])
+#$(info int_mult(1,23456): [$(call int_mult,1,23456)])
+#$(info int_mult(0,23456): [$(call int_mult,0,23456)])
+#$(info int_mult(0,0): [$(call int_mult,0,0)])
+
+###
+### division
+###
+
+# return list of zeros needed to pad number 2 to the same length as number 1
+_zero_pad = $(strip $(wordlist 1,$(call int_sub,$(words $(1)),$(words $(2))),$(LIST100_0)))
+
+# num1, num2, zero pad, result_accumulator
+# algorithm:
+# - B = pad with zeros to make same digit length as A
+# - loop
+#    - if (B <= A)
+#        - A = subtract B from A
+#        - C = C + 10^(B pad.length)
+#    - else
+#        - if B.length < origin B.length: break
+#        - chop least significant digit of B
+_div = $(strip \
+         $(if $(call int_lte_encoded,$(3) $(2),$(1)),\
+           $(call _div,$(call int_sub_encoded,$(1),$(3) $(2)),$(2),$(3),$(call int_add_encoded,$(4),$(3) 1)),\
+           $(if $(3),\
+             $(call _div,$(1),$(2),$(wordlist 2,$(words $(3)),$(3)),$(4)),\
+             $(4))))
+
+# divide two encoded numbers, returns encoded number
+int_div_encoded = $(strip \
+                $(if $(call _EQ,0,$(1)),\
+                  0,\
+                  $(if $(call _EQ,$(1),$(2)),\
+                    1,\
+                    $(if $(call int_gt_encoded,$(2),$(1)),\
+                      0,\
+                      $(call _div,$(1),$(2),$(call _zero_pad,$(1),$(2)),0)))))
+
+# divide two unencoded numbers, returns unencoded number
+int_div = $(call int_decode,$(call int_div_encoded,$(call int_encode,$(1)),$(call int_encode,$(2))))
+
+### division tests
+
+#$(info _zero_pad(1 2 3 4,1 3): [$(call _zero_pad,1 2 3 4,1 3)])
+#$(info _zero_pad(1 2,1 3): [$(call _zero_pad,1 2,1 3)])
+#$(info _zero_pad(2,1 3): [$(call _zero_pad,1 2,1 3)])
+#
+#$(info int_div_encoded(2,1): [$(call int_div_encoded,2,1)])
+#$(info int_div_encoded(3,1): [$(call int_div_encoded,3,1)])
+#$(info int_div_encoded(3,2): [$(call int_div_encoded,3,2)])
+#$(info int_div_encoded(0,7): [$(call int_div_encoded,0,7)])
+#$(info int_div_encoded(0 3,0 2): [$(call int_div_encoded,0 3,0 2)])
+#$(info int_div_encoded(0 3,5): [$(call int_div_encoded,0 3,5)])
+#
+#$(info int_div(5,1): [$(call int_div,5,1)])
+#$(info int_div(5,2): [$(call int_div,5,2)])
+#$(info int_div(123,7): [$(call int_div,123,7)])
+#$(info int_div(100,7): [$(call int_div,100,7)])
+
+
+### combination tests
+
+# (/ (- (+ 515 (* 222 311)) 300) 41)
+#$(info int_mult,222,311: [$(call int_mult,222,311)])
+#$(info int_add(515,69042): [$(call int_add,515,69042)])
+#$(info int_sub(69557,300): [$(call int_sub,69557,300)])
+#$(info int_div(69257,41): [$(call int_div,69257,41)])
+
+###############################################################
+
+all:
+	@true
+
+endif
+
+# vim: ts=2 et