start adding inverse_cdf to scratchpad

scratchpad/scratchpad.c

@@ -1,7 +1,97 @@
 #include <stdint.h>
 #include <stdlib.h>
 #include <stdio.h>
+#include <float.h> // FLT_MAX, FLT_MIN
 
+// Errors
+// https://mccue.dev/pages/7-27-22-c-errors
+// Huh, first time I've really needed a struct
+// https://en.wikipedia.org/wiki/Struct_(C_programming_language)
+// https://www.cs.yale.edu/homes/aspnes/pinewiki/C(2f)Structs.html
+// https://stackoverflow.com/questions/9653072/return-a-struct-from-a-function-in-c
+// options: 
+//   - exit
+//   - pass structs
+struct box {
+	int empty;
+	float content; 
+};
+
+// Example cdf
+float cdf_uniform_0_1(float x){
+  if(x < 0){
+		return 0;
+	} else if (x > 1){
+		return 1;
+	} else {
+		return x;
+	}
+}
+
+// Inverse cdf
+struct box inverse_cdf(float (*cdf(float)), float p){
+	// given a cdf: [-Inf, Inf] => [0,1]
+	// returns x such that cdf(x) = p
+	// to do: add bounds, add error checking
+	// [x] maybe return a struct or smth.
+	
+  struct box result;
+	float start = -1.0;
+	float end = 1.0;
+
+	// 1. Make sure that cdf(start) < p < cdf(end)
+	// [x] to do: do smth with float min and float max?
+	int interval_found = 0;
+	while((!interval_found) && (start > FLT_MIN/4) && (end < FLT_MAX/4)){
+		// ^ Using FLT_MIN and FLT_MAX is overkill
+		// but it's also the *correct* thing to do.
+
+		int start_condition = (*cdf(start) < p); 
+		int end_condition = (p < *cdf(end));
+		if( start_condition && end_condition ){
+			interval_found = 1;
+		}else if(!start_condition){
+			start = start * 2;
+		}else if (!end_condition){
+			end = end * 2 ;
+		}
+	}
+  
+	if(!interval_found){
+		result.empty = 1;
+		return result;
+	} else{
+		int convergence_condition = 0;
+		while(!convergence_condition){
+			float mid = (end - start)/2;
+			int mid_not_new = (mid == start) || (mid == end);
+			if(mid_not_new){
+				convergence_condition = 1;
+			}else{
+				float mid_sign = *cdf(mid) - p;
+				if(mid_sign < 0){
+					start = mid;
+				} else if  (mid_sign > 0){
+					end = mid;
+				} else {
+					result.content = mid;
+					result.empty = 0;
+					return result;
+				}
+
+			}
+		}
+		return result;
+	}
+
+}
+
+// sampler based on inverse cdf
+
+// to-do: integrals
+
+// main with an example
 int main(){
 	printf("Hello world");
+	return 0;
 }