formatting pass
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@ -1,9 +1,9 @@
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#include <stdint.h>
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#include <stdlib.h>
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#include <stdio.h>
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#include <float.h> // FLT_MAX, FLT_MIN
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#include <limits.h> // INT_MAX
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#include <math.h>
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#include <stdint.h>
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#include <stdio.h>
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#include <stdlib.h>
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#define VERBOSE 1
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// Errors
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@ -12,150 +12,153 @@
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// https://en.wikipedia.org/wiki/Struct_(C_programming_language)
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// https://www.cs.yale.edu/homes/aspnes/pinewiki/C(2f)Structs.html
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// https://stackoverflow.com/questions/9653072/return-a-struct-from-a-function-in-c
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// options:
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// options:
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// - exit
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// - pass structs
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// to do: reuse more informative printing from build-your-own-lisp?
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struct box {
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int empty;
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float content;
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int empty;
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float content;
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};
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// Example cdf
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float cdf_uniform_0_1(float x){
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if(x < 0){
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return 0;
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} else if (x > 1){
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return 1;
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} else {
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return x;
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}
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float cdf_uniform_0_1(float x)
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{
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if (x < 0) {
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return 0;
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} else if (x > 1) {
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return 1;
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} else {
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return x;
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}
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}
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float cdf_squared_0_1(float x){
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if(x < 0){
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return 0;
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} else if (x > 1){
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return 1;
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} else {
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return x*x;
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}
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float cdf_squared_0_1(float x)
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{
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if (x < 0) {
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return 0;
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} else if (x > 1) {
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return 1;
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} else {
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return x * x;
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}
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}
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float cdf_normal_0_1(float x){
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float mean = 0;
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float std = 1;
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return 0.5 * ( 1 + erf((x-mean)/(std * sqrt(2)) ));
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float cdf_normal_0_1(float x)
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{
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float mean = 0;
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float std = 1;
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return 0.5 * (1 + erf((x - mean) / (std * sqrt(2))));
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}
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// Inverse cdf
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struct box inverse_cdf(float cdf(float), float p){
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// given a cdf: [-Inf, Inf] => [0,1]
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// returns x such that cdf(x) = p
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// to do: add bounds, add error checking
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// [x] maybe return a struct or smth.
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struct box result;
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float low = -1.0;
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float high = 1.0;
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struct box inverse_cdf(float cdf(float), float p)
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{
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// given a cdf: [-Inf, Inf] => [0,1]
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// returns x such that cdf(x) = p
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// to do: add bounds, add error checking
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// [x] maybe return a struct or smth.
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// 1. Make sure that cdf(low) < p < cdf(high)
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// [x] to do: do smth with float min and float max?
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int interval_found = 0;
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while((!interval_found) && (low > -FLT_MAX/4) && (high < FLT_MAX/4)){
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// ^ Using FLT_MIN and FLT_MAX is overkill
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// but it's also the *correct* thing to do.
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struct box result;
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float low = -1.0;
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float high = 1.0;
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int low_condition = (cdf(low) < p);
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int high_condition = (p < cdf(high));
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if( low_condition && high_condition ){
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interval_found = 1;
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}else if(!low_condition){
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low = low * 2;
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}else if (!high_condition){
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high = high * 2 ;
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}
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}
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if(0){
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printf("FLT_MIN = %f, FLT_MAX = %f, INT_MAX = %d\n", -FLT_MAX, FLT_MAX, INT_MAX);
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printf("low: %f, high: %f\n", low, high);
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printf("interval_found? %d\n", interval_found);
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int while_condition = (!interval_found) && (low > FLT_MIN/4) && (high < FLT_MAX/4);
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printf("while condition: %i\n", while_condition);
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}
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if(!interval_found){
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result.empty = 1;
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return result;
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} else{
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// 1. Make sure that cdf(low) < p < cdf(high)
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// [x] to do: do smth with float min and float max?
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int interval_found = 0;
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while ((!interval_found) && (low > -FLT_MAX / 4) && (high < FLT_MAX / 4)) {
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// ^ Using FLT_MIN and FLT_MAX is overkill
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// but it's also the *correct* thing to do.
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int convergence_condition = 0;
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int count = 0;
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while(!convergence_condition && (count < (INT_MAX/2) )){
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float mid = (high + low)/2;
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int mid_not_new = (mid == low) || (mid == high);
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if(0){
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printf("while loop\n");
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printf("low: %f, high: %f\n", low, high);
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printf("mid: %f\n", mid);
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}
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int low_condition = (cdf(low) < p);
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int high_condition = (p < cdf(high));
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if (low_condition && high_condition) {
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interval_found = 1;
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} else if (!low_condition) {
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low = low * 2;
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} else if (!high_condition) {
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high = high * 2;
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}
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}
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if (0) {
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printf("FLT_MIN = %f, FLT_MAX = %f, INT_MAX = %d\n", -FLT_MAX, FLT_MAX, INT_MAX);
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printf("low: %f, high: %f\n", low, high);
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printf("interval_found? %d\n", interval_found);
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int while_condition = (!interval_found) && (low > FLT_MIN / 4) && (high < FLT_MAX / 4);
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printf("while condition: %i\n", while_condition);
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}
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if(mid_not_new){
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convergence_condition = 1;
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} else{
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float mid_sign = cdf(mid) - p;
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if(mid_sign < 0){
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low = mid;
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} else if (mid_sign > 0){
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high = mid;
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} else if (mid_sign == 0){
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low = mid;
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high = mid;
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}
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}
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if (!interval_found) {
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result.empty = 1;
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return result;
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} else {
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}
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if(convergence_condition){
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result.content = low;
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result.empty = 0;
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} else{
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result.empty = 1;
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}
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int convergence_condition = 0;
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int count = 0;
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while (!convergence_condition && (count < (INT_MAX / 2))) {
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float mid = (high + low) / 2;
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int mid_not_new = (mid == low) || (mid == high);
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if (0) {
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printf("while loop\n");
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printf("low: %f, high: %f\n", low, high);
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printf("mid: %f\n", mid);
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}
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return result;
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}
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if (mid_not_new) {
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convergence_condition = 1;
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} else {
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float mid_sign = cdf(mid) - p;
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if (mid_sign < 0) {
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low = mid;
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} else if (mid_sign > 0) {
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high = mid;
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} else if (mid_sign == 0) {
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low = mid;
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high = mid;
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}
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}
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}
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if (convergence_condition) {
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result.content = low;
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result.empty = 0;
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} else {
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result.empty = 1;
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}
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return result;
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}
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}
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// Get random number between 0 and 1
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uint32_t xorshift32
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(uint32_t* seed)
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uint32_t xorshift32(uint32_t* seed)
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{
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// Algorithm "xor" from p. 4 of Marsaglia, "Xorshift RNGs"
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// See <https://stackoverflow.com/questions/53886131/how-does-xorshift32-works>
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// https://en.wikipedia.org/wiki/Xorshift
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// Also some drama: <https://www.pcg-random.org/posts/on-vignas-pcg-critique.html>, <https://prng.di.unimi.it/>
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// Algorithm "xor" from p. 4 of Marsaglia, "Xorshift RNGs"
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// See <https://stackoverflow.com/questions/53886131/how-does-xorshift32-works>
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// https://en.wikipedia.org/wiki/Xorshift
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// Also some drama: <https://www.pcg-random.org/posts/on-vignas-pcg-critique.html>, <https://prng.di.unimi.it/>
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uint32_t x = *seed;
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x ^= x << 13;
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x ^= x >> 17;
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x ^= x << 5;
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return *seed = x;
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uint32_t x = *seed;
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x ^= x << 13;
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x ^= x >> 17;
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x ^= x << 5;
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return *seed = x;
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}
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// Distribution & sampling functions
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float rand_0_to_1(uint32_t* seed){
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return ((float) xorshift32(seed)) / ((float) UINT32_MAX);
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float rand_0_to_1(uint32_t* seed)
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{
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return ((float)xorshift32(seed)) / ((float)UINT32_MAX);
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}
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// sampler based on inverse cdf
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struct box sampler(float cdf(float), uint32_t* seed){
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struct box result;
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float p = rand_0_to_1(seed);
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result = inverse_cdf(cdf, p);
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return result;
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struct box sampler(float cdf(float), uint32_t* seed)
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{
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struct box result;
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float p = rand_0_to_1(seed);
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result = inverse_cdf(cdf, p);
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return result;
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}
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// ~~[-] to-do: integrals => beta distribution~~
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// <https://github.com/codeplea/incbeta>
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// main with an example
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int main(){
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int main()
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{
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// Uniform:
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struct box result_1 = inverse_cdf(cdf_uniform_0_1, 0.5);
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char* name_1 = "cdf_uniform_0_1";
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if(result_1.empty){
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printf("Inverse for %s not calculated\n", name_1);
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exit(1);
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}else{
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printf("Inverse of %s at %f is: %f\n", name_1, 0.5, result_1.content);
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}
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// Uniform:
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struct box result_1 = inverse_cdf(cdf_uniform_0_1, 0.5);
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char* name_1 = "cdf_uniform_0_1";
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if (result_1.empty) {
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printf("Inverse for %s not calculated\n", name_1);
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exit(1);
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} else {
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printf("Inverse of %s at %f is: %f\n", name_1, 0.5, result_1.content);
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}
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// Squared cdf
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struct box result_2 = inverse_cdf(cdf_squared_0_1, 0.5);
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char* name_2 = "cdf_squared_0_1";
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if(result_2.empty){
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printf("Inverse for %s not calculated\n", name_2);
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exit(1);
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}else{
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printf("Inverse of %s at %f is: %f\n", name_2, 0.5, result_2.content);
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}
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// Squared cdf
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struct box result_2 = inverse_cdf(cdf_squared_0_1, 0.5);
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char* name_2 = "cdf_squared_0_1";
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if (result_2.empty) {
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printf("Inverse for %s not calculated\n", name_2);
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exit(1);
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} else {
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printf("Inverse of %s at %f is: %f\n", name_2, 0.5, result_2.content);
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}
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// Normal cdf
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struct box result_3 = inverse_cdf(cdf_normal_0_1, 0.5);
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char* name_3 = "cdf_normal_0_1";
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if(result_3.empty){
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printf("Inverse for %s not calculated\n", name_3);
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exit(1);
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}else{
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printf("Inverse of %s at %f is: %f\n", name_3, 0.5, result_3.content);
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}
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// Normal cdf
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struct box result_3 = inverse_cdf(cdf_normal_0_1, 0.5);
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char* name_3 = "cdf_normal_0_1";
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if (result_3.empty) {
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printf("Inverse for %s not calculated\n", name_3);
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exit(1);
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} else {
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printf("Inverse of %s at %f is: %f\n", name_3, 0.5, result_3.content);
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}
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// set randomness seed
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uint32_t* seed = malloc(sizeof(uint32_t));
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*seed = 1000; // xorshift can't start with 0
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printf("\n\nGetting some samples from %s:\n", name_3);
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int n=100;
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for(int i=0;i<n; i++){
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struct box sample = sampler(cdf_normal_0_1, seed);
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if(sample.empty){
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printf("Error in sampler function");
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}else{
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printf("%f\n", sample.content);
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}
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}
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return 0;
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// set randomness seed
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uint32_t* seed = malloc(sizeof(uint32_t));
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*seed = 1000; // xorshift can't start with 0
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printf("\n\nGetting some samples from %s:\n", name_3);
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int n = 100;
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for (int i = 0; i < n; i++) {
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struct box sample = sampler(cdf_normal_0_1, seed);
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if (sample.empty) {
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printf("Error in sampler function");
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} else {
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printf("%f\n", sample.content);
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}
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}
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return 0;
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}
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