add float support to spec

.kiro/specs/calculator/design.md

@@ -645,6 +645,30 @@ Text/ASCII literals:
 - Useful for: magic numbers (`'ELF'`), protocol tags, inspecting
   how string bytes pack into integer registers
 
+IEEE 754 float interpretation:
+- A sub-view within programmer mode (toggle with a key, e.g. Ctrl-F)
+- Reinterprets the current bit pattern as an IEEE 754 float
+- Supported formats:
+  - float32 (1 sign + 8 exponent + 23 significand, bias 127)
+  - float64 (1 sign + 11 exponent + 52 significand, bias 1023)
+- Bit grid color-codes the three fields:
+  - Sign bit: one color (e.g. pink)
+  - Exponent: another color (e.g. cyan)
+  - Significand: another color (e.g. green)
+- Display below the bit grid shows:
+  - Decimal value (exact)
+  - Formula: (-1)^s * 2^(e-bias) * 1.mantissa
+  - Classification: normal, denormal, zero, infinity, NaN
+  - ULP: delta to next representable value
+  - Raw fields: sign=0, exp=127 (unbiased: 0), frac=0x000000
+- Input: can type a decimal float value (e.g. `3.14`) and it
+  shows the closest representable bit pattern, noting if rounding
+  occurred
+- Toggling bits in the grid updates the float interpretation live
+- Does NOT change bit_width setting - float32 uses 32-bit view,
+  float64 uses 64-bit view (auto-switches width when toggling
+  float format)
+
 ### 8.3 Struct Visualizer (sub-view of Programmer Mode)
 ```
 ┌─ Tally ────────────────── [Programmer > Struct Layout] ─────────────┐

.kiro/specs/calculator/requirements.md

@@ -31,6 +31,16 @@ A calculator application with three frontends (CLI, TUI, Android) sharing a comm
 - **FR-2.8**: Configurable endianness display (little-endian default, big-endian available). Affects byte order in HEX display and byte-level visualizations. Does not change the underlying value - purely a display/interpretation toggle.
 - **FR-2.9**: ASCII/text literal input via single-quoted strings: `'hello'` packs ASCII bytes into the integer value. First character occupies the most significant used byte (big-endian packing when display is BE) or least significant byte (when display is LE). Useful for examining magic numbers, file signatures, protocol headers.
 - **FR-2.10**: ASCII interpretation display - when the current value contains printable ASCII bytes, show the text representation alongside the numeric bases (e.g., `ASCII: "ELF."` or `ASCII: ..lf` with dots for non-printable bytes).
+- **FR-2.11**: IEEE 754 floating-point interpretation (float.exposed style):
+  - Support float32 (single) and float64 (double) formats, selectable
+  - Decompose bit pattern into sign bit, exponent field, and significand/mantissa field with visual color-coding in the bit grid
+  - Display the evaluation formula: (-1)^sign * 2^(exponent - bias) * 1.mantissa
+  - Display the exact decimal value represented by the bit pattern
+  - Display delta to next and previous representable float (ULP - unit in last place)
+  - Handle special values: +/-infinity, NaN, denormals/subnormals, +/-zero
+  - Allow toggling individual bits and seeing the float value update in real-time
+  - Allow entering a decimal float value and seeing the closest IEEE 754 representation
+  - Show when a value is not exactly representable (rounding occurred)
 
 ### FR-3: Struct Layout Visualizer (Programmer Mode Extension)
 

.kiro/specs/calculator/tasks.md

@@ -267,6 +267,22 @@ Subcommands deferred until Phase 2 engine work is done.
 - 128-bit width also added (u64 -> u128 throughout engine)
 - Verify: `'A'` = 0x41, `'ELF'` = 0x454C46, overflow on too-long strings
 
+### Task 5.3.3: Implement IEEE 754 float interpretation [NOT STARTED]
+- Add float interpretation engine module (`engine/src/float_interp.zig`)
+- Given a u32 or u64 bit pattern, decompose into sign, exponent, significand
+- Compute exact decimal value (including denormals, infinities, NaN)
+- Compute ULP (delta to next/previous representable value)
+- Classify: normal, denormal, zero, +inf, -inf, quiet NaN, signaling NaN
+- Given a decimal float, find the closest IEEE 754 bit pattern and report rounding
+- TUI sub-view (Ctrl-F toggles float interpretation overlay in programmer mode):
+  - Color-coded bit grid (sign=pink, exponent=cyan, significand=green)
+  - Formula display, classification, ULP, exact value
+  - Typing a float value shows its bit pattern
+  - Auto-switch to 32-bit or 64-bit width based on selected float format
+- Support float32 and float64 formats
+- Verify: 0x3F800000 = 1.0 (float32), special values display correctly,
+  bit toggling updates float display, `3.14` shows nearest representation
+
 ### Task 5.4: Implement programmer mode TUI view - bit grid [DONE - merged into 5.3]
 - Bit grid widget: 8 bits per group, groups separated by space
 - Arrow key navigation (left/right moves cursor across bits, up/down between rows for 32/64-bit)