Improve the root and cbrt API's

gen/lib2.bc

@@ -101,6 +101,7 @@ define l2(x){return log(x,2)}
 define l10(x){return log(x,A)}
 define root(x,n){
 	auto s,m,r,q,p
+	if(n<0)sqrt(n)
 	n=abs(n)$
 	if(n==0)x/n
 	if(n==1)return x

manuals/bc.1

@@ -921,10 +921,10 @@ Returns the cube root of \fBx\fR\.
 .
 .TP
 \fBroot(x, n)\fR
-Calculates the truncated absolute value of \fBn\fR, \fBr\fR, and returns the \fBr\fRth root of \fBx\fR to the current \fBscale\fR\.
+Calculates the truncated value of \fBn\fR, \fBr\fR, and returns the \fBr\fRth root of \fBx\fR to the current \fBscale\fR\.
 .
 .IP
-If \fBn\fR is \fB0\fR, this raises an error and causes bc(1) to reset (see the RESET section)\. It also raises an error and causes bc(1) to reset if \fBn\fR is even and \fBx\fR is negative\.
+If \fBr\fR is \fB0\fR or negative, this raises an error and causes bc(1) to reset (see the RESET section)\. It also raises an error and causes bc(1) to reset if \fBr\fR is even and \fBx\fR is negative\.
 .
 .TP
 \fBpi(p)\fR

manuals/bc.1.ronn

@@ -848,12 +848,12 @@ The extended library is a **non-portable extension**.
     Returns the cube root of `x`.
 
   * `root(x, n)`:
-    Calculates the truncated absolute value of `n`, `r`, and returns the `r`th
-    root of `x` to the current `scale`.
+    Calculates the truncated value of `n`, `r`, and returns the `r`th root of
+    `x` to the current `scale`.
 
-    If `n` is `0`, this raises an error and causes bc(1) to reset (see the RESET
-    section). It also raises an error and causes bc(1) to reset if `n` is even
-    and `x` is negative.
+    If `r` is `0` or negative, this raises an error and causes bc(1) to reset
+    (see the RESET section). It also raises an error and causes bc(1) to reset
+    if `r` is even and `x` is negative.
 
   * `pi(p)`:
     Returns `pi` to `p` decimal places.

tests/bc/errors.txt

@@ -145,6 +145,8 @@ sqrt(-1)
 0.000000%0.00000000
 root(-15, 4)
 root(5, 0)
+root(13, -5)
+root(1548, 0)
 scale = 10000000000000000000000000000000000
 obase += 999999999999999999999999999999999999999999999999999999999999999999999999
 ibase *= 9999999999999999999999999999999999999999999999999999999999999.9