Bitcoin Forum

    // Subsidy is cut in half every 210000 blocks, which will occur approximately every 4 years
    nSubsidy >>= (nHeight / 210000);

Time =        0 min =  3 Jan 2009:        0.00000000 Bitcoins exist. New block reward=50 BTC =5000000000 satoshis.
Time =  2100000 min =  1 Jan 2013: 10500000.00000000 Bitcoins exist. New block reward=25 BTC =2500000000 satoshis.
Time =  4200000 min = 28 Dez 2016: 15750000.00000000 Bitcoins exist. New block reward=12.5 BTC =1250000000 satoshis.
Time =  6300000 min = 26 Dez 2020: 18375000.00000000 Bitcoins exist. New block reward=6.25 BTC =625000000 satoshis.
Time =  8400000 min = 23 Dez 2024: 19687500.00000000 Bitcoins exist. New block reward=3.125 BTC =312500000 satoshis.
Time = 10500000 min = 20 Dez 2028: 20343750.00000000 Bitcoins exist. New block reward=1.5625 BTC =156250000 satoshis.
Time = 12600000 min = 18 Dez 2032: 20671875.00000000 Bitcoins exist. New block reward=0.78125 BTC =78125000 satoshis.
Time = 14700000 min = 15 Dez 2036: 20835937.50000000 Bitcoins exist. New block reward=0.39062 BTC =39062500 satoshis.
Time = 16800000 min = 12 Dez 2040: 20917968.75000000 Bitcoins exist. New block reward=0.19531 BTC =19531250 satoshis.
Time = 18900000 min = 10 Dez 2044: 20958984.37500000 Bitcoins exist. New block reward=0.097656 BTC =9765625 satoshis.
Time = 21000000 min =  7 Dez 2048: 20979492.18750000 Bitcoins exist. New block reward=0.048828 BTC =4882812 satoshis.
Time = 23100000 min =  4 Dez 2052: 20989746.09270000 Bitcoins exist. New block reward=0.024414 BTC =2441406 satoshis.
Time = 25200000 min =  2 Dez 2056: 20994873.04530000 Bitcoins exist. New block reward=0.012207 BTC =1220703 satoshis.
Time = 27300000 min = 29 Nov 2060: 20997436.52160000 Bitcoins exist. New block reward=0.0061035 BTC =610351 satoshis.
Time = 29400000 min = 26 Nov 2064: 20998718.25870000 Bitcoins exist. New block reward=0.0030518 BTC =305175 satoshis.
Time = 31500000 min = 24 Nov 2068: 20999359.12620000 Bitcoins exist. New block reward=0.0015259 BTC =152587 satoshis.
Time = 33600000 min = 21 Nov 2072: 20999679.55890000 Bitcoins exist. New block reward=0.00076293 BTC =76293 satoshis.
Time = 35700000 min = 18 Nov 2076: 20999839.77420000 Bitcoins exist. New block reward=0.00038146 BTC =38146 satoshis.
Time = 37800000 min = 16 Nov 2080: 20999919.88080000 Bitcoins exist. New block reward=0.00019073 BTC =19073 satoshis.
Time = 39900000 min = 13 Nov 2084: 20999959.93410000 Bitcoins exist. New block reward=9.536e-05 BTC =9536 satoshis.
Time = 42000000 min = 10 Nov 2088: 20999979.95970000 Bitcoins exist. New block reward=4.768e-05 BTC =4768 satoshis.
Time = 44100000 min =  8 Nov 2092: 20999989.97250000 Bitcoins exist. New block reward=2.384e-05 BTC =2384 satoshis.
Time = 46200000 min =  5 Nov 2096: 20999994.97890000 Bitcoins exist. New block reward=1.192e-05 BTC =1192 satoshis.
Time = 48300000 min =  2 Nov 2100: 20999997.48210000 Bitcoins exist. New block reward=5.96e-06 BTC =596 satoshis.
Time = 50400000 min = 31 Oct 2104: 20999998.73370000 Bitcoins exist. New block reward=2.98e-06 BTC =298 satoshis.
Time = 52500000 min = 28 Oct 2108: 20999999.35950000 Bitcoins exist. New block reward=1.49e-06 BTC =149 satoshis.
Time = 54600000 min = 25 Oct 2112: 20999999.67240000 Bitcoins exist. New block reward=7.4e-07 BTC =74 satoshis.
Time = 56700000 min = 23 Oct 2116: 20999999.82780000 Bitcoins exist. New block reward=3.7e-07 BTC =37 satoshis.
Time = 58800000 min = 20 Oct 2120: 20999999.90550000 Bitcoins exist. New block reward=1.8e-07 BTC =18 satoshis.
Time = 60900000 min = 17 Oct 2124: 20999999.94330000 Bitcoins exist. New block reward=9e-08 BTC =9 satoshis.
Time = 63000000 min = 15 Oct 2128: 20999999.96220000 Bitcoins exist. New block reward=4e-08 BTC =4 satoshis.
Time = 65100000 min = 12 Oct 2132: 20999999.97060000 Bitcoins exist. New block reward=2e-08 BTC =2 satoshis.
Time = 67200000 min =  9 Oct 2136: 20999999.97480000 Bitcoins exist. New block reward=1e-08 BTC =1 satoshi.
Time = 69300000 min =  7 Oct 2140: 20999999.97690000 Bitcoins exist. New block reward=0 BTC =0 satoshis.

Time =        0 min =  3 Jan 2009:        0.00000000 Bitcoins exist. New block reward=50 BTC =5000000000 satoshis.
Time =  2052540 min = 28 Nov 2012: 10500000.00000000 Bitcoins exist. New block reward=25 BTC =2500000000 satoshis.
Time =  4105080 min = 24 Oct 2016: 15750000.00000000 Bitcoins exist. New block reward=12.5 BTC =1250000000 satoshis.
Time =  6157620 min = 18 Sep 2020: 18375000.00000000 Bitcoins exist. New block reward=6.25 BTC =625000000 satoshis.
Time =  8210160 min = 13 Aug 2024: 19687500.00000000 Bitcoins exist. New block reward=3.125 BTC =312500000 satoshis.
Time = 10262700 min =  9 Jul 2028: 20343750.00000000 Bitcoins exist. New block reward=1.5625 BTC =156250000 satoshis.
Time = 12315240 min =  3 Jun 2032: 20671875.00000000 Bitcoins exist. New block reward=0.78125 BTC =78125000 satoshis.
Time = 14367780 min = 29 Apr 2036: 20835937.50000000 Bitcoins exist. New block reward=0.39062 BTC =39062500 satoshis.
Time = 16420320 min = 24 Mar 2040: 20917968.75000000 Bitcoins exist. New block reward=0.19531 BTC =19531250 satoshis.
Time = 18472860 min = 16 Feb 2044: 20958984.37500000 Bitcoins exist. New block reward=0.097656 BTC =9765625 satoshis.
Time = 20525400 min = 12 Jan 2048: 20979492.18750000 Bitcoins exist. New block reward=0.048828 BTC =4882812 satoshis.
Time = 22577940 min =  7 Dez 2051: 20989746.09270000 Bitcoins exist. New block reward=0.024414 BTC =2441406 satoshis.
Time = 24630480 min =  2 Nov 2055: 20994873.04530000 Bitcoins exist. New block reward=0.012207 BTC =1220703 satoshis.
Time = 26683020 min = 27 Sep 2059: 20997436.52160000 Bitcoins exist. New block reward=0.0061035 BTC =610351 satoshis.
Time = 28735560 min = 22 Aug 2063: 20998718.25870000 Bitcoins exist. New block reward=0.0030518 BTC =305175 satoshis.
Time = 30788100 min = 18 Jul 2067: 20999359.12620000 Bitcoins exist. New block reward=0.0015259 BTC =152587 satoshis.
Time = 32840640 min = 12 Jun 2071: 20999679.55890000 Bitcoins exist. New block reward=0.00076293 BTC =76293 satoshis.
Time = 34893180 min =  8 May 2075: 20999839.77420000 Bitcoins exist. New block reward=0.00038146 BTC =38146 satoshis.
Time = 36945720 min =  2 Apr 2079: 20999919.88080000 Bitcoins exist. New block reward=0.00019073 BTC =19073 satoshis.
Time = 38998260 min = 25 Feb 2083: 20999959.93410000 Bitcoins exist. New block reward=9.536e-05 BTC =9536 satoshis.
Time = 41050800 min = 21 Jan 2087: 20999979.95970000 Bitcoins exist. New block reward=4.768e-05 BTC =4768 satoshis.
Time = 43103340 min = 16 Dez 2090: 20999989.97250000 Bitcoins exist. New block reward=2.384e-05 BTC =2384 satoshis.
Time = 45155880 min = 11 Nov 2094: 20999994.97890000 Bitcoins exist. New block reward=1.192e-05 BTC =1192 satoshis.
Time = 47208420 min =  6 Oct 2098: 20999997.48210000 Bitcoins exist. New block reward=5.96e-06 BTC =596 satoshis.
Time = 49260960 min =  1 Sep 2102: 20999998.73370000 Bitcoins exist. New block reward=2.98e-06 BTC =298 satoshis.
Time = 51313500 min = 27 Jul 2106: 20999999.35950000 Bitcoins exist. New block reward=1.49e-06 BTC =149 satoshis.
Time = 53366040 min = 21 Jun 2110: 20999999.67240000 Bitcoins exist. New block reward=7.4e-07 BTC =74 satoshis.
Time = 55418580 min = 17 May 2114: 20999999.82780000 Bitcoins exist. New block reward=3.7e-07 BTC =37 satoshis.
Time = 57471120 min = 11 Apr 2118: 20999999.90550000 Bitcoins exist. New block reward=1.8e-07 BTC =18 satoshis.
Time = 59523660 min =  6 Mar 2122: 20999999.94330000 Bitcoins exist. New block reward=9e-08 BTC =9 satoshis.
Time = 61576200 min = 30 Jan 2126: 20999999.96220000 Bitcoins exist. New block reward=4e-08 BTC =4 satoshis.
Time = 63628740 min = 25 Dez 2129: 20999999.97060000 Bitcoins exist. New block reward=2e-08 BTC =2 satoshis.
Time = 65681280 min = 20 Nov 2133: 20999999.97480000 Bitcoins exist. New block reward=1e-08 BTC =1 satoshi.
Time = 67733820 min = 15 Oct 2137: 20999999.97690000 Bitcoins exist. New block reward=0 BTC =0 satoshis.

% Uncomment the PGP signature tags at the beginning and at the end of the file before verifying the signature

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function blockreward(Time_in_minutes_per_block)
% function blockreward()
% function blockreward(Time_in_minutes_per_block)
%
% Time_in_minutes_per_block = The average time that it takes the bitcoin network for generating one block.
% * Default (no argument)                                  : 10.000
% * Average till first block reward halving on 28 Nov 2012 :  9.774
%
% ---------------------------------------------------------------------------------------------------------
% This m-function calculates the bitcoin generation over time when assuming that the block genertion rate
% matches a fixed value of e.g. 10 minutes per block.
%   Note that in practice the actual block generation rate will likely be a little faster because the total
% hashing power of the bitcoin network increases continuously while the difficulty is only adjusted every
% 2016 blocks (=ca. 2 weeks) and therefore always lags behind the actual hashing power.
%   Therefore, for the time period from the start of the bitcoin network until the first halving of the
% block reward, it took only 3.90 instead of 3.99 years, corresponding to an average of 9.774 instead of
% 10.000 minutes per generated block.
% ---------------------------------------------------------------------------------------------------------
% According to the Bitcoin protocol:
%
% Every 210000 blocks the blockreward halfs.
%
% Average block generation rate = 1 block per 10 minutes,
% (difficulty adjusted every 2016 blocks = ca. every 2 weeks).
%
% Starting block reward = 50 BTCs.
%
% On 3 January 2009 at 18:15:05 UTC bitcoin block generation has started (creation of ths "genesis block"):
%     http://blockexplorer.com/block/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f
%     http://blockchain.info/block-height/0
% On 28 November 2012 at 15:24:38 UTC block number 210000 was generated, the first block with block
% reward halved to 25 BTC:
%     http://blockexplorer.com/block/000000000000048b95347e83192f69cf0366076336c639f9b7228e9ba171342e
%     http://blockchain.info/block-height/210000
%     http://blockchain.info/block-index/322335/000000000000048b95347e83192f69cf0366076336c639f9b7228e9ba171342e
%
% 1 day = 24*60 = 1440 minutes, and 1 year = 365.25 days in this file.
%
% The smallest unit is 1 satoshi = 1e-8 BTC.
%
% ----------------------------------------------------------------------------------------------------
% This script works with Matlab (tested with R2007b) and GNU Octave 3.0.0 (tested with version 3.0.0)
%
% Written on Planet Earth on 28 Nov 2012 = Day 333 of the year 2012,
% by Michael_S of bitcointalk.org (PGP key 0xCC7E7C99, bitcoin:14ajM1BHY7E8GJ4DGGvtFFGmE15hSSSRJR)
% ----------------------------------------------------------------------------------------------------

if nargin==0,
    Time_in_minutes_per_block =10.000;%  <-- Design value of the bitcoin protocol
    %Time_in_minutes_per_block = 9.774;% <-- avg. time till 1st block reward halving on 28 Nov 2012
end


%% 0 - Parameters:
Block_reward_start = 50;% =50
Block_nb_block_reward_halving = 210000;% =210000
satoshi = 1e-8;% smallest unit = 1 satoshi = 1e-8 BTC

block_generation_start_in_absolute_year = 2009.00756;% On 3 January 2009 at 18:15:05 bitcoin block generation has started.
% (http://blockexplorer.com/block/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f)
% (http://blockchain.info/block-height/0)


%% 1 - Calculations:
Month{1}  = 'Jan'; NbDays = [31,28,31,30,31,30,31,31,30,31,30,31];
Month{2}  = 'Feb'; NbDaysAccu(1) = NbDays(1); NbDaysAccu(2) = NbDaysAccu(1)+NbDays(2);
Month{3}  = 'Mar'; NbDaysAccu(3) = NbDaysAccu(2)+NbDays(3);
Month{4}  = 'Apr'; NbDaysAccu(4) = NbDaysAccu(3)+NbDays(4);
Month{5}  = 'May'; NbDaysAccu(5) = NbDaysAccu(4)+NbDays(5);
Month{6}  = 'Jun'; NbDaysAccu(6) = NbDaysAccu(5)+NbDays(6);
Month{7}  = 'Jul'; NbDaysAccu(7) = NbDaysAccu(6)+NbDays(7);
Month{8}  = 'Aug'; NbDaysAccu(8) = NbDaysAccu(7)+NbDays(8);
Month{9}  = 'Sep'; NbDaysAccu(9) = NbDaysAccu(8)+NbDays(9);
Month{10} = 'Oct'; NbDaysAccu(10) = NbDaysAccu(9)+NbDays(10);
Month{11} = 'Nov'; NbDaysAccu(11) = NbDaysAccu(10)+NbDays(11);
Month{12} = 'Dez'; NbDaysAccu(12) = NbDaysAccu(11)+NbDays(12);

bitcoins_existing = 0;
reward_unrounded = 2*Block_reward_start; % starting value - will immediately be halfed in the while loop before everything starts
reward = reward_unrounded;
minutes = 0; % time counter in minutes

time_vector_min = [];
bitcoins_vector = [];
reward_vector = [];
while reward >= satoshi,
    reward_unrounded = reward_unrounded / 2;
    % round down to multiple of 1 satoshi = 1e-8 BTC:
    reward = floor(reward_unrounded/satoshi)*satoshi;
    %reward_unrounded = reward;% <-- this line makes no difference whether activated or commented out.
    time_vector_min = [time_vector_min; minutes];
    bitcoins_vector= [bitcoins_vector; bitcoins_existing];
    reward_vector = [reward_vector, reward];
    Current_Year = block_generation_start_in_absolute_year+minutes/60/24/365.25;
    CurrentDayOfYear = 365*(Current_Year-floor(Current_Year));
    CurrentMonth = find((NbDaysAccu-CurrentDayOfYear)>0, 1);
    if CurrentMonth==1,
        CurrentDayOfMonth = CurrentDayOfYear;
    else
        CurrentDayOfMonth = CurrentDayOfYear - NbDaysAccu(CurrentMonth-1);
    end
    CurrentDayOfMonth = min(NbDays(CurrentMonth), (max(1, round(CurrentDayOfMonth))));
    nb_of_leading_spaces = max(0, 9 - max(1, ceil(log10(minutes+1))));
    space_padding = repmat(' ',1,nb_of_leading_spaces);
    space_padding_day = repmat(' ',1, 2-ceil(log10(CurrentDayOfMonth+1)));
    be = bitcoins_existing;% temporary short variable
    be = round((be-(be-floor(be*1e4)/1e4))*1e8)/1e8;% remove numerical artifacts
    space_padding_be = repmat(' ',1, 8-ceil(log10(max(1,be)+1)));
    disp(['Time =',[space_padding, num2str(round(minutes),'%0.9g')],' min = ',[space_padding_day, num2str(CurrentDayOfMonth)], ...
        ' ',Month{CurrentMonth},' ',num2str(floor(Current_Year)),': ',...
        [space_padding_be, num2str(be,'%0.8f')],' Bitcoins exist. New block reward=',num2str(reward),' BTC =',num2str(reward/satoshi),' satoshis.']);
    %
    minutes = minutes + Block_nb_block_reward_halving*Time_in_minutes_per_block;
    bitcoins_existing = bitcoins_existing + reward*Block_nb_block_reward_halving; % this many new block were generated
end


%% 2 - Plot Diagrams:
time_vector_years = time_vector_min/60/24/365.25;
time_vector_year_absolute = time_vector_years + block_generation_start_in_absolute_year;
bitcoins_vector_remain = bitcoins_vector(end) - bitcoins_vector;


figure;
ha = plot(time_vector_year_absolute, bitcoins_vector/1e6,'b.-'); hold on;
hb = plot(time_vector_year_absolute, bitcoins_vector_remain/1e6,'r'); hold on;
%legend([ha,hb],'Bitcoins existing','Bitcoins pending','location','southeast');% <-- syntax incompatible with GNU Octave
legend('Bitcoins existing','Bitcoins pending','location','southeast');% <-- compatible syntax!
plot([time_vector_year_absolute(1), time_vector_year_absolute(end)], [bitcoins_vector(end),bitcoins_vector(end)]/1e6, 'k-'); hold on;

title(['Bitcoins in existence over time (one block per ',num2str(Time_in_minutes_per_block),' min)']);
xlabel('Year (e.g. year "2012.91" means 28 Nov 2012 = 91% into year 2012)');
ylabel('Bitcoins / millions');
grid on;
axis([floor(time_vector_year_absolute(1)), ceil(time_vector_year_absolute(end)), 0, 1+ceil(bitcoins_vector(end))/1e6]);


figure;
% fill the data with 200-times the same ... (roughly 1 dot per week)
y = reshape(repmat(reward_vector, 200, 1), 1, 200*length(reward_vector));
y = y(1:end-199);
dx = (time_vector_year_absolute(end)-time_vector_year_absolute(1))/(length(y)-1);
x = [time_vector_year_absolute(1):dx:time_vector_year_absolute(end)];

plot(x, y,'m.-'); hold on;
%semilogy(x, y,'m.-'); hold on;
title(['Block reward over time (one block per ',num2str(Time_in_minutes_per_block),' min)']);
xlabel('Year (e.g. year "2012.91" means 28 Nov 2012 = 91% into year 2012)');
ylabel('Block reward / BTC');
grid on;
axis([floor(time_vector_year_absolute(1)), ceil(time_vector_year_absolute(end)), 0, 1+ceil(reward_vector(1))]);

return;
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