diff --git a/basis/help/handbook/handbook.factor b/basis/help/handbook/handbook.factor
index 5db362d9bc..3effd5931e 100644
--- a/basis/help/handbook/handbook.factor
+++ b/basis/help/handbook/handbook.factor
@@ -106,10 +106,7 @@ ARTICLE: "numbers" "Numbers"
 { $subsection "complex-numbers" }
 "Advanced features:"
 { $subsection "math-vectors" }
-{ $subsection "math-intervals" }
-{ $subsection "math-bitfields" }
-"Implementation:"
-{ $subsection "math.libm" } ;
+{ $subsection "math-intervals" } ;
 
 USE: io.buffers
 
diff --git a/basis/math/bits/bits-docs.factor b/basis/math/bits/bits-docs.factor
index 36043a5576..9e69823906 100644
--- a/basis/math/bits/bits-docs.factor
+++ b/basis/math/bits/bits-docs.factor
@@ -6,6 +6,7 @@ IN: math.bits
 ABOUT: "math.bits"
 
 ARTICLE: "math.bits" "Number bits virtual sequence"
+"The " { $vocab-link "math.bits" } " vocabulary implements a virtual sequence which presents an integer as a sequence of bits, with the first element of the sequence being the least significant bit of the integer."
 { $subsection bits }
 { $subsection <bits> }
 { $subsection make-bits } ;
diff --git a/basis/math/complex/complex.factor b/basis/math/complex/complex.factor
index ce94dfaca8..c432089f4d 100644
--- a/basis/math/complex/complex.factor
+++ b/basis/math/complex/complex.factor
@@ -1,8 +1,7 @@
 ! Copyright (C) 2006, 2009 Slava Pestov.
 ! See http://factorcode.org/license.txt for BSD license.
 USING: accessors kernel kernel.private math math.private
-math.libm math.functions arrays math.functions.private sequences
-parser ;
+math.functions arrays math.functions.private sequences parser ;
 IN: math.complex.private
 
 M: real real-part ; inline
@@ -26,8 +25,8 @@ M: complex * [ *re - ] [ *im + ] 2bi rect> ; inline
 M: complex / [ / ] complex/ ; inline
 M: complex /f [ /f ] complex/ ; inline
 M: complex /i [ /i ] complex/ ; inline
-M: complex abs absq >float fsqrt ; inline
-M: complex sqrt >polar [ fsqrt ] [ 2.0 / ] bi* polar> ; inline
+M: complex abs absq sqrt ; inline
+M: complex sqrt >polar [ sqrt ] [ 2.0 / ] bi* polar> ; inline
 
 IN: syntax
 
diff --git a/basis/math/libm/libm-docs.factor b/basis/math/libm/libm-docs.factor
index a890a59c19..abbb6f1289 100644
--- a/basis/math/libm/libm-docs.factor
+++ b/basis/math/libm/libm-docs.factor
@@ -3,10 +3,10 @@ IN: math.libm
 
 ARTICLE: "math.libm" "C standard library math functions"
 "The words in the " { $vocab-link "math.libm" } " vocabulary call C standard library math functions. They are used to implement words in the " { $vocab-link "math.functions" } " vocabulary."
-$nl
-"They can be called directly, however there is little reason to do so, since they only implement real-valued functions, and in some cases place restrictions on the domain:"
-{ $example "USE: math.functions" "2 acos ." "C{ 0.0 1.316957896924817 }" }
-{ $unchecked-example "USE: math.libm" "2 facos ." "0/0." }
+{ $warning
+"These functions are unsafe. The compiler special-cases them to operate on floats only. They can be called directly, however there is little reason to do so, since they only implement real-valued functions, and in some cases place restrictions on the domain:"
+{ $example "USE: math.functions" "2.0 acos ." "C{ 0.0 1.316957896924817 }" }
+{ $unchecked-example "USE: math.libm" "2 facos ." "0/0." } }
 "Trigonometric functions:"
 { $subsection fcos }
 { $subsection fsin }
diff --git a/core/math/math-docs.factor b/core/math/math-docs.factor
index 853aca5969..ab2a5ab8be 100644
--- a/core/math/math-docs.factor
+++ b/core/math/math-docs.factor
@@ -420,6 +420,7 @@ ARTICLE: "bitwise-arithmetic" "Bitwise arithmetic"
 { $subsection 2/ }
 { $subsection 2^ }
 { $subsection bit? }
+"Advanced topics:"
 { $subsection "math.bitwise" }
 { $subsection "math.bits" }
 { $see-also "booleans" } ;