# Example 807 — The amounts were summed at each days rate `the_amounts_were_summed_at_each_days_rate.eml` - The multi-currency balance is summed correctly to a single dollar figure, and each conversion is right. What rate each line was converted at is computed below. ## EML ```eml # Self-authored for the EML case corpus (no external origin). The multi-currency # balance is summed correctly to a single dollar figure, and each conversion is # right. What rate each line was converted at is computed below. # # The conversion is done properly per line. Each amount is converted with the # official rate for its own booking day; the rate source is the same for every # currency; no line is dropped; and the arithmetic is exact to the cent. # # Each line keeps the rate of the day it was booked, and the sum mixes them. 12040000 => reported_total_usd_cents 11890000 => total_at_one_month_end_rate_usd_cents 3 => currencies 0 => lines_dropped reported_total_usd_cents - total_at_one_month_end_rate_usd_cents => difference_from_mixing_rates_cents int(difference_from_mixing_rates_cents * 10000 / total_at_one_month_end_rate_usd_cents) => difference_per_myriad int(reported_total_usd_cents / 100) => reported_total_usd_dollars "reported total (each day's rate): " + str(reported_total_usd_cents) + " cents" ^0 "total at one month-end rate : " + str(total_at_one_month_end_rate_usd_cents) + " cents" ^0 " difference from mixing rates : " + str(difference_from_mixing_rates_cents) + " cents" ^0 " as a share of the total : " + str(difference_per_myriad) + " per ten thousand" ^0 "currencies : " + str(currencies) ^0 "lines dropped : " + str(lines_dropped) ^0 "reported total in dollars : " + str(reported_total_usd_dollars) ^0 "" ^0 # ---- what the conversion verified ---- "the per-line conversion" ^0 " rate used : the official rate for the line's booking" ^0 " day" ^0 " rate source : the same for every currency" ^0 " lines dropped : " + str(lines_dropped) ^0 " arithmetic : exact to the cent" ^0 " lines converted correctly : all of them" ^0 " verdict : EACH LINE CORRECT" ^0 "" ^0 " one rate source across all currencies is the part done" ^0 " right here, and it is why no line used a stray quote" ^0 "" ^0 # ---- what the sum mixes ---- "the total" ^0 " how it was formed : the per-day conversions, added" ^0 " what each conversion fixes : the value on its own day" ^0 " what the market did across the month : moved" ^0 " so the sum : mixes rates from different days into one" ^0 " figure" ^0 " what it is the value of : no single day's holdings" ^0 "" ^0 # ---- what a reader of the balance assumes ---- "the reader of the balance" ^0 " what they take it to be : what the holdings are worth" ^0 " now" ^0 " what it is : a sum of what each line was worth on its" ^0 " own day" ^0 " the gap at one consistent rate : " ^0 " " + str(difference_from_mixing_rates_cents) + " cents" ^0 " is any line wrong : no; each is exact on its day" ^0 " is the total a valuation : not at any one date" ^0 "" ^0 # ---- null control ---- # The same lines, all converted at a single month-end rate so the total is a # valuation at one instant. 12040000 => nc_each_days_rate_cents 11890000 => nc_one_rate_cents 0 => nc_lines_changed "null control - one rate for the whole balance" ^0 " summed at each day's rate : " + str(nc_each_days_rate_cents) + ", unchanged" ^0 " summed at one month-end rate : " + str(nc_one_rate_cents) + " cents" ^0 " lines changed : " + str(nc_lines_changed) ^0 " no amount and no booking date changed; the rates" ^0 " stopped being mixed across a moving month" ^0 "" ^0 # ---- the rule ---- "what a correct multi-currency total guarantees" ^0 " each line is converted at its own day's official rate :" ^0 " exactly, one source, nothing dropped, to the cent" ^0 " the total is what the holdings are worth now : not" ^0 " addressed; each line was converted on its booking day," ^0 " so the sum mixes rates across a moving month and is not" ^0 " any single day's valuation - at one rate it is " ^0 " " + str(total_at_one_month_end_rate_usd_cents) ^0 "" ^0 "a valuation is taken at an instant, and a sum of conversions taken at different" ^0 "instants belongs to no instant; each term is right on its day and the total is" ^0 "a date that never happened" ^0 "" ^0 "Each line uses its booking day's official rate, one source, exact to the cent -" ^0 "no line wrong. The sum mixes rates across a moving month, so it is not a" ^0 "valuation at any date: at one month-end rate it is " + str(total_at_one_month_end_rate_usd_cents) + " cents, " ^0 "" + str(difference_from_mixing_rates_cents) + " from the reported " + str(reported_total_usd_cents) + ", " + str(difference_per_myriad) + " per ten thousand." ^0 ``` ## Python (deterministic transpilation) ```python reported_total_usd_cents = 12040000 total_at_one_month_end_rate_usd_cents = 11890000 currencies = 3 lines_dropped = 0 difference_from_mixing_rates_cents = reported_total_usd_cents - total_at_one_month_end_rate_usd_cents difference_per_myriad = int(difference_from_mixing_rates_cents * 10000 / total_at_one_month_end_rate_usd_cents) reported_total_usd_dollars = int(reported_total_usd_cents / 100) print("reported total (each day's rate): " + str(reported_total_usd_cents) + " cents") print("total at one month-end rate : " + str(total_at_one_month_end_rate_usd_cents) + " cents") print(" difference from mixing rates : " + str(difference_from_mixing_rates_cents) + " cents") print(" as a share of the total : " + str(difference_per_myriad) + " per ten thousand") print("currencies : " + str(currencies)) print("lines dropped : " + str(lines_dropped)) print("reported total in dollars : " + str(reported_total_usd_dollars)) print("") print("the per-line conversion") print(" rate used : the official rate for the line's booking") print(" day") print(" rate source : the same for every currency") print(" lines dropped : " + str(lines_dropped)) print(" arithmetic : exact to the cent") print(" lines converted correctly : all of them") print(" verdict : EACH LINE CORRECT") print("") print(" one rate source across all currencies is the part done") print(" right here, and it is why no line used a stray quote") print("") print("the total") print(" how it was formed : the per-day conversions, added") print(" what each conversion fixes : the value on its own day") print(" what the market did across the month : moved") print(" so the sum : mixes rates from different days into one") print(" figure") print(" what it is the value of : no single day's holdings") print("") print("the reader of the balance") print(" what they take it to be : what the holdings are worth") print(" now") print(" what it is : a sum of what each line was worth on its") print(" own day") print(" the gap at one consistent rate : ") print(" " + str(difference_from_mixing_rates_cents) + " cents") print(" is any line wrong : no; each is exact on its day") print(" is the total a valuation : not at any one date") print("") nc_each_days_rate_cents = 12040000 nc_one_rate_cents = 11890000 nc_lines_changed = 0 print("null control - one rate for the whole balance") print(" summed at each day's rate : " + str(nc_each_days_rate_cents) + ", unchanged") print(" summed at one month-end rate : " + str(nc_one_rate_cents) + " cents") print(" lines changed : " + str(nc_lines_changed)) print(" no amount and no booking date changed; the rates") print(" stopped being mixed across a moving month") print("") print("what a correct multi-currency total guarantees") print(" each line is converted at its own day's official rate :") print(" exactly, one source, nothing dropped, to the cent") print(" the total is what the holdings are worth now : not") print(" addressed; each line was converted on its booking day,") print(" so the sum mixes rates across a moving month and is not") print(" any single day's valuation - at one rate it is ") print(" " + str(total_at_one_month_end_rate_usd_cents)) print("") print("a valuation is taken at an instant, and a sum of conversions taken at different") print("instants belongs to no instant; each term is right on its day and the total is") print("a date that never happened") print("") print("Each line uses its booking day's official rate, one source, exact to the cent -") print("no line wrong. The sum mixes rates across a moving month, so it is not a") print("valuation at any date: at one month-end rate it is " + str(total_at_one_month_end_rate_usd_cents) + " cents, ") print("" + str(difference_from_mixing_rates_cents) + " from the reported " + str(reported_total_usd_cents) + ", " + str(difference_per_myriad) + " per ten thousand.") ``` ## stdout (executed) ```text reported total (each day's rate): 12040000 cents total at one month-end rate : 11890000 cents difference from mixing rates : 150000 cents as a share of the total : 126 per ten thousand currencies : 3 lines dropped : 0 reported total in dollars : 120400 the per-line conversion rate used : the official rate for the line's booking day rate source : the same for every currency lines dropped : 0 arithmetic : exact to the cent lines converted correctly : all of them verdict : EACH LINE CORRECT one rate source across all currencies is the part done right here, and it is why no line used a stray quote the total how it was formed : the per-day conversions, added what each conversion fixes : the value on its own day what the market did across the month : moved so the sum : mixes rates from different days into one figure what it is the value of : no single day's holdings the reader of the balance what they take it to be : what the holdings are worth now what it is : a sum of what each line was worth on its own day the gap at one consistent rate : 150000 cents is any line wrong : no; each is exact on its day is the total a valuation : not at any one date null control - one rate for the whole balance summed at each day's rate : 12040000, unchanged summed at one month-end rate : 11890000 cents lines changed : 0 no amount and no booking date changed; the rates stopped being mixed across a moving month what a correct multi-currency total guarantees each line is converted at its own day's official rate : exactly, one source, nothing dropped, to the cent the total is what the holdings are worth now : not addressed; each line was converted on its booking day, so the sum mixes rates across a moving month and is not any single day's valuation - at one rate it is 11890000 a valuation is taken at an instant, and a sum of conversions taken at different instants belongs to no instant; each term is right on its day and the total is a date that never happened Each line uses its booking day's official rate, one source, exact to the cent - no line wrong. The sum mixes rates across a moving month, so it is not a valuation at any date: at one month-end rate it is 11890000 cents, 150000 from the reported 12040000, 126 per ten thousand. ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:assign · eml:output · eml:run:done