seq: compute correct width for scientific notation

Change the way `seq` computes the number of digits needed to print a
number so that it works for inputs given in scientific notation.
Specifically, this commit parses the input string to determine whether
it is an integer, a float in decimal notation, or a float in scientific
notation, and then computes the number of integral digits and the number
of fractional digits based on that. This also supports floating point
negative zero, expressed in both decimal and scientific notation.

tests/by-util/test_seq.rs

@@ -23,6 +23,56 @@ fn test_rejects_non_floats() {
     ));
 }
 
+#[test]
+fn test_invalid_float() {
+    new_ucmd!()
+        .args(&["1e2.3"])
+        .fails()
+        .no_stdout()
+        .stderr_contains("invalid floating point argument: '1e2.3'")
+        .stderr_contains("for more information.");
+    new_ucmd!()
+        .args(&["1e2.3", "2"])
+        .fails()
+        .no_stdout()
+        .stderr_contains("invalid floating point argument: '1e2.3'")
+        .stderr_contains("for more information.");
+    new_ucmd!()
+        .args(&["1", "1e2.3"])
+        .fails()
+        .no_stdout()
+        .stderr_contains("invalid floating point argument: '1e2.3'")
+        .stderr_contains("for more information.");
+    new_ucmd!()
+        .args(&["1e2.3", "2", "3"])
+        .fails()
+        .no_stdout()
+        .stderr_contains("invalid floating point argument: '1e2.3'")
+        .stderr_contains("for more information.");
+    new_ucmd!()
+        .args(&["1", "1e2.3", "3"])
+        .fails()
+        .no_stdout()
+        .stderr_contains("invalid floating point argument: '1e2.3'")
+        .stderr_contains("for more information.");
+    new_ucmd!()
+        .args(&["1", "2", "1e2.3"])
+        .fails()
+        .no_stdout()
+        .stderr_contains("invalid floating point argument: '1e2.3'")
+        .stderr_contains("for more information.");
+}
+
+#[test]
+fn test_width_invalid_float() {
+    new_ucmd!()
+        .args(&["-w", "1e2.3"])
+        .fails()
+        .no_stdout()
+        .stderr_contains("invalid floating point argument: '1e2.3'")
+        .stderr_contains("for more information.");
+}
+
 // ---- Tests for the big integer based path ----
 
 #[test]
@@ -178,6 +228,90 @@ fn test_width_negative_zero() {
         .no_stderr();
 }
 
+#[test]
+fn test_width_negative_zero_scientific_notation() {
+    new_ucmd!()
+        .args(&["-w", "-0e0", "1"])
+        .succeeds()
+        .stdout_is("-0\n01\n")
+        .no_stderr();
+
+    new_ucmd!()
+        .args(&["-w", "-0e+1", "1"])
+        .succeeds()
+        .stdout_is("-00\n001\n")
+        .no_stderr();
+
+    new_ucmd!()
+        .args(&["-w", "-0.000e0", "1"])
+        .succeeds()
+        .stdout_is("-0.000\n01.000\n")
+        .no_stderr();
+
+    new_ucmd!()
+        .args(&["-w", "-0.000e-2", "1"])
+        .succeeds()
+        .stdout_is("-0.00000\n01.00000\n")
+        .no_stderr();
+
+    new_ucmd!()
+        .args(&["-w", "-0.000e5", "1"])
+        .succeeds()
+        .stdout_is("-000000\n0000001\n")
+        .no_stderr();
+
+    new_ucmd!()
+        .args(&["-w", "-0.000e5", "1"])
+        .succeeds()
+        .stdout_is("-000000\n0000001\n")
+        .no_stderr();
+}
+
+#[test]
+fn test_width_decimal_scientific_notation_increment() {
+    new_ucmd!()
+        .args(&["-w", ".1", "1e-2", ".11"])
+        .succeeds()
+        .stdout_is("0.10\n0.11\n")
+        .no_stderr();
+
+    new_ucmd!()
+        .args(&["-w", ".0", "1.500e-1", ".2"])
+        .succeeds()
+        .stdout_is("0.0000\n0.1500\n")
+        .no_stderr();
+}
+
+/// Test that trailing zeros in the start argument contribute to precision.
+#[test]
+fn test_width_decimal_scientific_notation_trailing_zeros_start() {
+    new_ucmd!()
+        .args(&["-w", ".1000", "1e-2", ".11"])
+        .succeeds()
+        .stdout_is("0.1000\n0.1100\n")
+        .no_stderr();
+}
+
+/// Test that trailing zeros in the increment argument contribute to precision.
+#[test]
+fn test_width_decimal_scientific_notation_trailing_zeros_increment() {
+    new_ucmd!()
+        .args(&["-w", "1e-1", "0.0100", ".11"])
+        .succeeds()
+        .stdout_is("0.1000\n0.1100\n")
+        .no_stderr();
+}
+
+/// Test that trailing zeros in the end argument do not contribute to width.
+#[test]
+fn test_width_decimal_scientific_notation_trailing_zeros_end() {
+    new_ucmd!()
+        .args(&["-w", "1e-1", "1e-2", ".1100"])
+        .succeeds()
+        .stdout_is("0.10\n0.11\n")
+        .no_stderr();
+}
+
 // TODO This is duplicated from `test_yes.rs`; refactor them.
 /// Run `seq`, capture some of the output, close the pipe, and verify it.
 fn run(args: &[&str], expected: &[u8]) {