diff --git a/bfloat16.tal b/bfloat16.tal
index 7358854..4cf8060 100644
--- a/bfloat16.tal
+++ b/bfloat16.tal
@@ -152,18 +152,6 @@
 %EXPONENT { #10 SFT2 POP }
 %MANTISSA { NIP #7f AND }
 
-( returns sign: #00 or #01 )
-@sign ( x* -> sgn^ )
-    SIGN JMP2r
-
-( returns exp: #00 to #ff )
-@exponent ( x* -> exp^ )
-    EXPONENT JMP2r
-
-( returns mta: #00 to #7f )
-@mantissa ( x* -> mta^ )
-    MANTISSA JMP2r
-
 ( returns full mta: #00 to #ff )
 ( normal numbers will be >= #80 ) 
 ( subnormal numbers will be < #80 )
@@ -175,11 +163,14 @@
 @negate-bf16 ( x* -> z* )
     #8000 EOR2 JMP2r
 
+@abs-bf16 ( x* -> z* )
+    #7fff AND2 JMP2r
+
 @is-zero ( x* -> bool^ )
-    #7fff AND2 #0000 EQU2
+    #7fff AND2 #0000 EQU2 JMP2r
 
 @non-zero ( x* -> bool^ )
-    #7fff AND2 #0000 NEQ2
+    #7fff AND2 #0000 NEQ2 JMP2r
 
 ( Shift mantissa m right by n bits, with rounding         )
 ( )
@@ -262,19 +253,19 @@
 @ne-bf16 ( x* y* -> bool^ )
     ;eq-bf16 JSR2 #00 EQU JMP2r
 
-( rules for sentinels (in order):     )
-(   1.  x < x is false                )
-(   2a. nan < x is false              )
-(   2b. x < nan is false              )
-(   3a. x < +inf is true              )
-(   3b. +inf < x is false             )
-(   4a. -inf < x is true              )
-(   4b. x < -inf is false             )
-(   5. -0 < +0 is false               )
-(   6. -x < +x (or 0)                 )
-(   7. 0 < +x                         )
-(   8. x*2^p < y*2^q if p < q         )
-(   9. x*2^p < y*2^p if x < y         )
+( rules for sentinels (in order): )
+(   1.  x < x is false            )
+(   2a. nan < x is false          )
+(   2b. x < nan is false          )
+(   3a. x < +inf is true          )
+(   3b. +inf < x is false         )
+(   4a. -inf < x is true          )
+(   4b. x < -inf is false         )
+(   5. -0 < +0 is false           )
+(   6. -x < +x (or 0)             )
+(   7. 0 < +x                     )
+(   8. x*2^p < y*2^q if p < q     )
+(   9. x*2^p < y*2^p if x < y     )
 @lt-bf16 ( x* y* -> bool^ )
     ,&y STR2 ,&x STR2
     ,&y LDR2 ;non-nan JSR2 ( is y not nan? )
@@ -285,16 +276,26 @@
     ,&x ;non-zero JSR2 ( is x non-zero? )
     ORA ,&not-zero JCN #00 JMP2r ( false if x and y are zero )
     &not-zero
-    ,&x LDR2 ;sign JSR2 ( sign of x )
-    ,&y LDR2 ;sign JSR2 ( sign of y )
+    ,&x LDR2 SIGN ( sign of x )
+    ,&y LDR2 SIGN ( sign of y )
     EQUk ,&same-sign JCN GTH JMP2r ( return unless signs are eq )
     [ &x $2 &y $2 ]
-    &same-sign POP
-    ,&x LDR2 ;exponent JSR2 ( exponent of x )
-    ,&y LDR2 ;exponent JSR2 ( exponent of y )
-    EQUk ,&exp-eq JCN LTH JMP2r ( return ex < ey unless exps are eq )
-    &exp-eq POP
-    ,&x LDR2 ;mantissa JSR2 ( mantissa of x )
-    ,&y LDR2 ;exponent JSR2 ( mantissa of y )
-    LTH JMP2r ( mx < my )
-    
\ No newline at end of file
+    &same-sign
+    POP ,&is-negative JCN
+    ,&x LDR2 ,&y LDR2 LTH2 JMP2r ( for positives, use integer x < y )
+    &is-negative
+    ,&x LDR2 ,&y LDR2 GTH2 JMP2r ( for negatives, use integer x > y )
+
+( see lt-bf16; (x < y) = (y < x) )
+@gt-bf16 ( x* y* -> bool^ )
+    SWP2 ;lt-bf16 JMP2
+
+( special cases: )
+(   1.        x + y  =  y + x )
+(   2.      nan + x  =  nan   )
+(   3.        0 + x  =  x     )
+(   4.  inf + (-inf) =  nan   )
+(   5.      inf + x  =  inf   )
+(   6.     -inf + x  = -inf   )
+@add-bf16 ( x* y* -> z* )
+    JMP2r