diff --git a/include/linkdefs.hpp b/include/linkdefs.hpp
index 9216a222f..2a18c6f43 100644
--- a/include/linkdefs.hpp
+++ b/include/linkdefs.hpp
@@ -55,6 +55,8 @@ enum RPNCommand {
 
 	RPN_HIGH = 0x70,
 	RPN_LOW = 0x71,
+	RPN_BITWIDTH = 0x72,
+	RPN_TZCOUNT = 0x73,
 
 	RPN_CONST = 0x80,
 	RPN_SYM = 0x81
diff --git a/man/rgbasm.5 b/man/rgbasm.5
index a57159377..a7cc5f8a1 100644
--- a/man/rgbasm.5
+++ b/man/rgbasm.5
@@ -9,9 +9,9 @@
 .Nm rgbasm
 .Nd language documentation
 .Sh DESCRIPTION
-This is the full description of the language used by
+This is the full description of the assembly language used by
 .Xr rgbasm 1 .
-The description of the instructions supported by the Game Boy CPU is in
+For the full description of instructions in the machine language supported by the Game Boy CPU, see
 .Xr gbz80 7 .
 .Pp
 It is advisable to have some familiarity with the Game Boy hardware before reading this document.
@@ -47,6 +47,23 @@ Instructions are assembled into Game Boy opcodes.
 Multiple instructions on one line can be separated by double colons
 .Ql :: .
 .Pp
+The available instructions are documented in
+.Xr gbz80 7 .
+Note that where an instruction requires an 8-bit register
+.Ar r8 ,
+.Nm
+can interpret
+.Ic HIGH Ns Pq Ar r16
+as the top 8-bit register of the given
+.Ar r16 ,
+and
+.Ic LOW Ns Pq Ar r16
+as the bottom one (except for
+.Ic LOW Ns Pq Ic AF ,
+since
+.Ic F
+is not a valid register).
+.Pp
 All reserved keywords (directives, register names, etc.) are case-insensitive;
 all identifiers (labels and other symbol names) are case-sensitive.
 .Pp
@@ -324,9 +341,33 @@ with a zero constant as either operand will be constant 0, and
 .Sq ||
 with a non-zero constant as either operand will be constant 1, even if the other operand is non-constant.
 .Pp
-.Ic \&!
+.Sq \&!
 returns 1 if the operand was 0, and 0 otherwise.
 Even a non-constant operand with any non-zero bits will return 0.
+.Ss Integer functions
+Besides operators, there are also some functions which have more specialized uses.
+.Bl -column "BITWIDTH(n)"
+.It Sy Name Ta Sy Operation
+.It Fn HIGH n Ta Equivalent to Ql Ar n No & $FF .
+.It Fn LOW n Ta Equivalent to Ql Po Ns Ar n No & $FF00 Pc >> 8 .
+.EQ
+delim $$
+.EN
+.It Fn BITWIDTH n Ta Returns the number of bits necessary to represent
+.Ar n .
+Some useful formulas:
+.Ic BITWIDTH Ns ( Ar n Ns )\ \-\ 1
+equals $\[lf] log sub 2 ( n ) \[rf]$,
+.Ic BITWIDTH Ns Pq Ar n Ns \ \-\ 1
+equals $\[lc] log sub 2 ( n ) \[rc]$, and
+.No 32\ \-\  Ns Ic BITWIDTH Ns Pq Ar n
+equals $roman clz ( n )$.
+.It Fn TZCOUNT n Ta Returns $roman ctz ( n )$, the count of trailing zero bits at the end of the binary representation of
+.Ar n .
+.El
+.EQ
+delim off
+.EN
 .Ss Fixed-point expressions
 Fixed-point numbers are basically normal (32-bit) integers, which count fractions instead of whole numbers.
 They offer better precision than integers but limit the range of values.
@@ -345,8 +386,11 @@ Some integer operators like
 and
 .Sq -
 don't care whether the operands are integers or fixed-point.
-You can easily truncate a fixed-point number into an integer by shifting it right by 16 bits.
-It follows that you can convert an integer to a fixed-point number by shifting it left.
+You can easily truncate a fixed-point number into an integer by shifting it right by the number of fractional bits.
+It follows that you can convert an integer to a fixed-point number by shifting it left that same amount.
+.Pp
+Note that the current number of fractional bits can be computed as
+.Ic TZCOUNT Ns Pq 1.0 .
 .Pp
 The following functions are designed to operate with fixed-point numbers:
 .EQ
@@ -513,8 +557,8 @@ There is also a character map stack that can be used to save and restore which c
 .Sy Note :
 Modifications to a character map take effect immediately from that point onward.
 .Ss Other functions
-There are a few other functions that do various useful things:
-.Bl -column "DEF(symbol)"
+There are a few other functions that do things beyond numeric or string operations:
+.Bl -column "SECTION(symbol)"
 .It Sy Name Ta Sy Operation
 .It Fn BANK arg Ta Returns a bank number.
 If
@@ -552,15 +596,10 @@ If
 .Ar arg
 is a section type keyword, it returns the starting address of that section type.
 The result is not constant, since only RGBLINK can compute its value.
-.It Fn DEF symbol Ta Returns TRUE (1) if
+.It Fn DEF symbol Ta Returns 1 if
 .Ar symbol
-has been defined, FALSE (0) otherwise.
+has been defined, 0 otherwise.
 String constants are not expanded within the parentheses.
-.It Fn HIGH arg Ta Returns the top 8 bits of the operand if Ar arg No is a label or constant, or the top 8-bit register if it is a 16-bit register .
-.It Fn LOW arg Ta Returns the bottom 8 bits of the operand if Ar arg No is a label or constant, or the bottom 8-bit register if it is a 16-bit register Pq Cm AF No isn't a valid register for this function .
-The result may be constant if
-.Nm
-is able to compute it.
 .It Fn ISCONST arg Ta Returns 1 if Ar arg Ap s value is known by RGBASM (e.g. if it can be an argument to
 .Ic IF ) ,
 or 0 if only RGBLINK can compute its value.
diff --git a/man/rgbds.5 b/man/rgbds.5
index f76456ee1..17cd4251c 100644
--- a/man/rgbds.5
+++ b/man/rgbds.5
@@ -391,10 +391,14 @@ The value is then ORed with $C7
 .It Li $80 Ta Integer literal; followed by the
 .Cm LONG
 integer.
-.It Li $70 Ta Ql HIGH
+.It Li $70 Ta Cm HIGH
 byte.
-.It Li $71 Ta Ql LOW
+.It Li $71 Ta Cm LOW
 byte.
+.It Li $72 Ta Cm BITWIDTH
+value.
+.It Li $73 Ta Cm TZCOUNT
+value.
 .It Li $81 Ta A symbol's value; followed by the symbol's
 .Cm LONG
 ID.
diff --git a/src/asm/lexer.cpp b/src/asm/lexer.cpp
index 37fa3ace5..ed8e21e9a 100644
--- a/src/asm/lexer.cpp
+++ b/src/asm/lexer.cpp
@@ -237,6 +237,9 @@ static std::unordered_map<std::string, int, CaseInsensitive, CaseInsensitive> ke
     {"LOW",           T_(OP_LOW)           },
     {"ISCONST",       T_(OP_ISCONST)       },
 
+    {"BITWIDTH",      T_(OP_BITWIDTH)      },
+    {"TZCOUNT",       T_(OP_TZCOUNT)       },
+
     {"STRCMP",        T_(OP_STRCMP)        },
     {"STRIN",         T_(OP_STRIN)         },
     {"STRRIN",        T_(OP_STRRIN)        },
diff --git a/src/asm/parser.y b/src/asm/parser.y
index 0dfc0727b..c21be6ce6 100644
--- a/src/asm/parser.y
+++ b/src/asm/parser.y
@@ -174,6 +174,8 @@
 %type <int32_t> opt_q_arg
 
 %token OP_HIGH "HIGH" OP_LOW "LOW"
+%token OP_BITWIDTH "BITWIDTH"
+%token OP_TZCOUNT "TZCOUNT"
 %token OP_ISCONST "ISCONST"
 
 %token OP_STRCMP "STRCMP"
@@ -1349,6 +1351,12 @@ relocexpr_no_str:
 	| OP_LOW LPAREN relocexpr RPAREN {
 		$$.makeUnaryOp(RPN_LOW, std::move($3));
 	}
+	| OP_BITWIDTH LPAREN relocexpr RPAREN {
+		$$.makeUnaryOp(RPN_BITWIDTH, std::move($3));
+	}
+	| OP_TZCOUNT LPAREN relocexpr RPAREN {
+		$$.makeUnaryOp(RPN_TZCOUNT, std::move($3));
+	}
 	| OP_ISCONST LPAREN relocexpr RPAREN {
 		$$.makeNumber($3.isKnown());
 	}
diff --git a/src/asm/rpn.cpp b/src/asm/rpn.cpp
index 4fbae8755..873d76495 100644
--- a/src/asm/rpn.cpp
+++ b/src/asm/rpn.cpp
@@ -9,7 +9,7 @@
 #include <string.h>
 #include <string_view>
 
-#include "helpers.hpp" // assume
+#include "helpers.hpp" // assume, clz, ctz
 #include "opmath.hpp"
 
 #include "asm/output.hpp"
@@ -315,6 +315,12 @@ void Expression::makeUnaryOp(RPNCommand op, Expression &&src) {
 		case RPN_LOW:
 			data = val & 0xFF;
 			break;
+		case RPN_BITWIDTH:
+			data = val != 0 ? 32 - clz((uint32_t)val) : 0;
+			break;
+		case RPN_TZCOUNT:
+			data = val != 0 ? ctz((uint32_t)val) : 32;
+			break;
 
 		case RPN_LOGOR:
 		case RPN_LOGAND:
@@ -494,6 +500,8 @@ void Expression::makeBinaryOp(RPNCommand op, Expression &&src1, Expression const
 		case RPN_RST:
 		case RPN_HIGH:
 		case RPN_LOW:
+		case RPN_BITWIDTH:
+		case RPN_TZCOUNT:
 		case RPN_CONST:
 		case RPN_SYM:
 			fatalerror("%d is not a binary operator\n", op);
diff --git a/src/link/patch.cpp b/src/link/patch.cpp
index 68a5d5129..24da60191 100644
--- a/src/link/patch.cpp
+++ b/src/link/patch.cpp
@@ -8,7 +8,7 @@
 #include <variant>
 #include <vector>
 
-#include "helpers.hpp" // assume
+#include "helpers.hpp" // assume, clz, ctz
 #include "linkdefs.hpp"
 #include "opmath.hpp"
 
@@ -146,6 +146,15 @@ static int32_t computeRPNExpr(Patch const &patch, std::vector<Symbol> const &fil
 			value = popRPN(patch) & 0xFF;
 			break;
 
+		case RPN_BITWIDTH:
+			value = popRPN(patch);
+			value = value != 0 ? 32 - clz((uint32_t)value) : 0;
+			break;
+		case RPN_TZCOUNT:
+			value = popRPN(patch);
+			value = value != 0 ? ctz((uint32_t)value) : 32;
+			break;
+
 		case RPN_OR:
 			value = popRPN(patch) | popRPN(patch);
 			break;
diff --git a/test/asm/bit-functions.asm b/test/asm/bit-functions.asm
new file mode 100644
index 000000000..5d8b2fe6f
--- /dev/null
+++ b/test/asm/bit-functions.asm
@@ -0,0 +1,11 @@
+assert BITWIDTH(0) == 0
+assert BITWIDTH(42) == 6
+assert BITWIDTH(-1) == 32
+assert BITWIDTH($80000000) == 32
+
+assert TZCOUNT(0) == 32
+assert TZCOUNT(42) == 1
+assert TZCOUNT(-1) == 0
+assert TZCOUNT($80000000) == 31
+
+assert TZCOUNT(1.0) == 16
diff --git a/test/link/operators.asm b/test/link/operators.asm
index 941b036f3..db50e9ab3 100644
--- a/test/link/operators.asm
+++ b/test/link/operators.asm
@@ -27,3 +27,6 @@ db @ <= 7
 dw @ << 1
 dw @ >> 1
 dw @ >>> 1
+
+db BITWIDTH(@)
+db TZCOUNT(@)
diff --git a/test/link/operators.out.bin b/test/link/operators.out.bin
index e5e08472a..0a8810887 100644
Binary files a/test/link/operators.out.bin and b/test/link/operators.out.bin differ