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+# Chapter 14: Narrow types
+
+## Narrow or sub-word types
+
+As a prelude to arrays, especially arrays of bytes common in all networking
+codes, Simple needs some way to manipulate sub-word integer types.
+Computations are always done in 64 bits for both integer and float ops, but
+will be truncated (rounded) on a variable or field assignment, and (sign)
+extended on a load.
+
+```java
+i8 x = 123456789;
+if( x != 21 ) 
+  return false;
+return true;
+```
+
+The variable `x` is limited to 8 bits signed.  Assigning the vary large value
+`123456789` (hex `0x75BCD15`) simply truncates to 8 bits yielding `21 (0x15)`.
+The value is sign-extended on a load.
+
+```java
+i16 x = 123456789;
+if( x != -13035 ) 
+  return false;
+return true;
+```
+
+The variable `x` is limited to 16 bits signed.  Assigning the vary large value
+`0x75BCD15` simply truncates to 16 bits yielding `0xCD15`.  The value is
+sign-extended on a load yielding `-13035 (0xFFFF FFFF FFFF CD15)`.
+
+```java
+u16 x = 123456789;
+if( x != 52501 ) 
+  return false;
+return true;
+```
+
+The variable `x` is limited to 16 bits unsigned.  Assigning the vary large value
+`0x75BCD15` simply truncates to 16 bits yielding `0xCD15`.  The value is
+zero-extended on a load yielding `52501 (0x0000 0000 0000 CD15)`.
+
+Similarly, floats can be limited to IEEE754 32-bit standard format and will be
+rounded when assigned, and inflated to 64-bits when loaded.
+
+The complete list of primitive types is now:
+```java
+int, i64  // 64-bits, matching modern hardware
+// u64    // NOT implemented, as it hints at some kind of >64 bit behavior
+i32, u32  // 32 bits, sign or zero extended on load
+i16, u16  // 16 bits, sign or zero extended on load
+ i8,  u8  //  8 bits, sign or zero extended on load
+ i1,  u1  //  1 bit , sign or zero extended on load
+bool      // Same as u1 
+flt, f64  // IEEE 754 64-bit float, sometimes called a "double"
+f32       // IEEE 754 32-bit float
+```
+
+
+
+## Type Implementation
+
+The TypeInteger class is reworked to support a full range of min/max values.
+At this time, only some power-of-2 sized ranges are exposed but the optimizer
+internally supports all ranges.  The MEET operation takes the min-of-mins and
+max-of-maxes.  The DUAL operation inverts the min and max.
+
+The TypeFloat class is also reworked to support 32-bit and 64-bit sizes.
+
+
+## Nodes
+
+Added this Chapter are some bit-manipulation Nodes representing common hardware
+ops to mask, shift, sign-extend and round bits.  The truncation and extension
+logic uses these.  They are otherwise very similar to the previous
+`Add/Sub/Mul/Div` Nodes but with slightly different constant math and
+slightly different `idealize()` calls.
+
+
+