Convert bench.h to fixed-point math

- Use 64-bit integer microsecond timestamps
- Use fixed-point math for formatting numbers

Then, remove "except in benchmarks" exception from `README.md`.

README.md

@@ -23,7 +23,7 @@ Implementation details
   * Extensive testing infrastructure.
   * Structured to facilitate review and analysis.
   * Intended to be portable to any system with a C89 compiler and uint64_t support.
-  * No use of floating types, except in benchmarks.
+  * No use of floating types.
   * Expose only higher level interfaces to minimize the API surface and improve application security. ("Be difficult to use insecurely.")
 * Field operations
   * Optimized implementation of arithmetic modulo the curve's field size (2^256 - 0x1000003D1).

src/bench.h

@@ -7,43 +7,85 @@
 #ifndef SECP256K1_BENCH_H
 #define SECP256K1_BENCH_H
 
+#include <stdint.h>
 #include <stdio.h>
 #include <string.h>
-#include <math.h>
 #include "sys/time.h"
 
-static double gettimedouble(void) {
+static int64_t gettime_i64(void) {
     struct timeval tv;
     gettimeofday(&tv, NULL);
-    return tv.tv_usec * 0.000001 + tv.tv_sec;
+    return (int64_t)tv.tv_usec + (int64_t)tv.tv_sec * 1000000LL;
 }
 
-void print_number(double x) {
-    double y = x;
-    int c = 0;
-    if (y < 0.0) {
-        y = -y;
+#define FP_EXP (6)
+#define FP_MULT (1000000LL)
+
+/* Format fixed point number. */
+void print_number(const int64_t x) {
+    int64_t x_abs, y;
+    int c, i, rounding;
+    size_t ptr;
+    char buffer[30];
+
+    if (x == INT64_MIN) {
+        /* Prevent UB. */
+        printf("ERR");
+        return;
     }
-    while (y > 0 && y < 100.0) {
-        y *= 10.0;
+    x_abs = x < 0 ? -x : x;
+
+    /* Determine how many decimals we want to show (more than FP_EXP makes no
+     * sense). */
+    y = x_abs;
+    c = 0;
+    while (y > 0LL && y < 100LL * FP_MULT && c < FP_EXP) {
+        y *= 10LL;
         c++;
     }
-    printf("%.*f", c, x);
+
+    /* Round to 'c' decimals. */
+    y = x_abs;
+    rounding = 0;
+    for (i = c; i < FP_EXP; ++i) {
+        rounding = (y % 10) >= 5;
+        y /= 10;
+    }
+    y += rounding;
+
+    /* Format and print the number. */
+    ptr = sizeof(buffer) - 1;
+    buffer[ptr] = 0;
+    if (c != 0) {
+        for (i = 0; i < c; ++i) {
+            buffer[--ptr] = '0' + (y % 10);
+            y /= 10;
+        }
+        buffer[--ptr] = '.';
+    }
+    do {
+        buffer[--ptr] = '0' + (y % 10);
+        y /= 10;
+    } while (y != 0);
+    if (x < 0) {
+        buffer[--ptr] = '-';
+    }
+    printf("%s", &buffer[ptr]);
 }
 
 void run_benchmark(char *name, void (*benchmark)(void*), void (*setup)(void*), void (*teardown)(void*), void* data, int count, int iter) {
     int i;
-    double min = HUGE_VAL;
-    double sum = 0.0;
-    double max = 0.0;
+    int64_t min = INT64_MAX;
+    int64_t sum = 0;
+    int64_t max = 0;
     for (i = 0; i < count; i++) {
-        double begin, total;
+        int64_t begin, total;
         if (setup != NULL) {
             setup(data);
         }
-        begin = gettimedouble();
+        begin = gettime_i64();
         benchmark(data);
-        total = gettimedouble() - begin;
+        total = gettime_i64() - begin;
         if (teardown != NULL) {
             teardown(data);
         }
@@ -56,11 +98,11 @@ void run_benchmark(char *name, void (*benchmark)(void*), void (*setup)(void*), v
         sum += total;
     }
     printf("%s: min ", name);
-    print_number(min * 1000000.0 / iter);
+    print_number(min * FP_MULT / iter);
     printf("us / avg ");
-    print_number((sum / count) * 1000000.0 / iter);
+    print_number(((sum * FP_MULT) / count) / iter);
     printf("us / max ");
-    print_number(max * 1000000.0 / iter);
+    print_number(max * FP_MULT / iter);
     printf("us\n");
 }