integration tests for large prec, fix typos

astro-float-num/src/ops/cos.rs

@@ -163,8 +163,8 @@ impl BigFloatNumber {
 
         // Reduction gives 2^(-p+1) per iteration.
         // Restore gives 2^(-p+5) per iteration.
-        // First parts of the series for any e_eff >= 0 give 2^(-p+6) at most.
-        // The error of the remaining parts of the series is compensated (see doc/README.md).
+        // First terms of the series for any e_eff >= 0 give 2^(-p+6) at most.
+        // The error of the remaining terms of the series is compensated (see doc/README.md).
         let add_prec = reduction_times as isize * 6 + 6 - e_eff as isize;
         let p_arg = p + if add_prec > 0 { add_prec as usize } else { 0 };
         self.set_precision(p_arg, rm)?;

astro-float-num/src/ops/sin.rs

@@ -154,8 +154,8 @@ impl BigFloatNumber {
 
         // Reduction gives 2^(-p+3) once.
         // Restore gives 2^(-p+6) per iteration.
-        // First parts of the series for any e_eff >= 0 give 2^(-p+6) at most.
-        // The error of the remaining parts of the series is compensated (see doc/README.md).
+        // First terms of the series for any e_eff >= 0 give 2^(-p+6) at most.
+        // The error of the remaining terms of the series is compensated (see doc/README.md).
         let add_prec = reduction_times as isize * 6 + 9 - e_eff as isize;
         let p_arg = p + if add_prec > 0 { add_prec as usize } else { 0 };
         self.set_precision(p_arg, rm)?;

astro-float-num/tests/mpfr/compare_ops_test.rs

@@ -17,10 +17,29 @@ use rug::{
 #[test]
 fn mpfr_compare_ops() {
     let run_cnt = 1000;
-
     let p_rng = get_prec_rng();
     let p_min = 1;
 
+    run_compare_ops(run_cnt, p_rng, p_min);
+
+    let run_cnt_large = 5;
+    let p_rng_large = 1;
+    let p_min_large;
+
+    #[cfg(not(debug_assertions))]
+    {
+        p_min_large = 1563;
+    }
+
+    #[cfg(debug_assertions)]
+    {
+        p_min_large = 156;
+    }
+
+    run_compare_ops(run_cnt_large, p_rng_large, p_min_large);
+}
+
+fn run_compare_ops(run_cnt: usize, p_rng: usize, p_min: usize) {
     let mut cc = Consts::new().unwrap();
 
     unsafe {

doc/README.md

@@ -50,7 +50,7 @@ Error `err = nroot(m * 2^e + 2^(e - p)) - nroot(m * 2^e)` <= (does not exceed) *
 
 7. Error for series of sin, cos and sinh.
 
-Error of Maclaurin series M(x) of a function f(x) for x < 1 in which absolute value of the function derivatives near 0 never exceeds 1 need to be estimated only for several first parts of the series.
+Error of Maclaurin series M(x) of a function f(x) for x < 1 in which absolute value of the function derivatives near 0 never exceeds 1 need to be estimated only for several first terms of the series.
 
 Proof.
 
@@ -78,7 +78,7 @@ follows `2^(n - p) / n! < 2^(n - p) * (e/n)^n = 2^(-p) * (2 * e / n)^n`.
 The residual error of the series can be received from Lagrange's error bound,
 and it is smaller than `2^(-p) * (2 * e / (n + 1))^(n + 1)`.
 
-For n+1 parts of the series `err < 2^(-p) * sum((2 * e / k)^k), k=1..n+1`.
+For n+1 terms of the series `err < 2^(-p) * sum((2 * e / k)^k), k=1..n+1`.
 
 Starting from k = 6 `sum((2 * e / k)^k) < 1` and `err < 2^(-p)`.