feat(agent): MemoryConfig::float16 stores half-precision embeddings

The setting was persisted in /meta and otherwise ignored: embeddings
were always written as f32. It now does what it says.

clawhdf5-format:
- `DatasetBuilder::with_f16_data` writes IEEE binary16 (numpy float16),
  rounding to nearest-even, and `make_f16_type`.
- `clawhdf5_format::float16` holds the f32 <-> f16 conversions, the one
  implementation the writer, the reader and the agent all use. Checked
  against the `half` crate on 16.7M f32 values and round-trips all 65536
  half values; the h5py interop tests confirm the rounding matches
  numpy's bit for bit (4020 values incl. ties, subnormals, overflow).
- Reading little-endian float16 as f32 has a fast path.

clawhdf5-agent:
- A float16 store writes /memory/embeddings as half precision, and
  `MemoryCache::half_precision` rounds each embedding as it enters the
  cache (save, update, WAL replay, and on load of a store still f32 on
  disk), so memory and file agree bit for bit and a store searches the
  same before and after a reopen (tested).
- Values beyond +-65504 are refused with the new
  `MemoryError::InvalidEntry` rather than stored as infinity, on every
  save path; batches are all or nothing, and a rejected ephemeral entry
  stays in the ephemeral tier. Breaking for exhaustive matches.
- CLI: `create --float16`. Off by default.

Measured on tank, 384-dim, six runs alternating order, medians
(search_harness --float16-study --full): at 100K the file goes from
154.0 to 80.8 MiB (-48%), checkpoint 752 -> 512 ms, open 300 -> 252 ms;
vector recall@10 against an exact scan and hybrid_search latency do not
change. At 10K open is 3 ms slower. Also a test that h5py opens a whole
agent store, f32 and float16, and decodes every dataset.

Docs: README, BENCHMARKS.md ("float16 embedding storage"), CHANGELOG
(including the h5py interop fixes in the previous commit), CLAUDE.md.

Co-Authored-By: Claude Opus 5.5 (1M context) <[email protected]>

crates/clawhdf5-format/src/float16.rs

@@ -0,0 +1,155 @@
+//! IEEE-754 half precision (binary16) conversions.
+//!
+//! Pure integer bit manipulation, so it works under `no_std` and needs no
+//! `libm`. The writer ([`crate::type_builders::DatasetBuilder::with_f16_data`]),
+//! the reader and `clawhdf5-agent`'s half-precision embedding store all use
+//! these two functions, so a value rounded in memory is bit-for-bit the value
+//! that reads back from the file.
+
+/// Largest finite half-precision value. Anything larger in magnitude rounds
+/// to infinity.
+pub const F16_MAX: f32 = 65504.0;
+
+/// Convert an `f32` to the bit pattern of the nearest half-precision value,
+/// rounding ties to even (the IEEE default, and what numpy and the `half`
+/// crate do).
+///
+/// Values beyond ±[`F16_MAX`] become ±infinity, values too small for a
+/// subnormal become signed zero, and NaN stays NaN (quiet, payload
+/// truncated).
+pub fn f32_to_f16_bits(value: f32) -> u16 {
+    let x = value.to_bits();
+    let sign = (x >> 16) & 0x8000;
+    let exp = x & 0x7F80_0000;
+    let man = x & 0x007F_FFFF;
+
+    // Infinity and NaN.
+    if exp == 0x7F80_0000 {
+        let quiet_nan = if man == 0 { 0 } else { 0x0200 };
+        return (sign | 0x7C00 | quiet_nan | (man >> 13)) as u16;
+    }
+
+    let half_exp = ((exp >> 23) as i32) - 127 + 15;
+
+    // Too large: infinity.
+    if half_exp >= 0x1F {
+        return (sign | 0x7C00) as u16;
+    }
+
+    // Subnormal half, or zero.
+    if half_exp <= 0 {
+        if 14 - half_exp > 24 {
+            return sign as u16;
+        }
+        let man = man | 0x0080_0000; // implicit leading bit
+        let shift = (14 - half_exp) as u32;
+        let mut half_man = man >> shift;
+        let round_bit = 1u32 << (shift - 1);
+        // Round half to even: up if above half, or exactly half and odd.
+        if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
+            half_man += 1;
+        }
+        return (sign | half_man) as u16;
+    }
+
+    // Normal half. A mantissa carry correctly rolls into the exponent (and
+    // from the largest finite value into infinity).
+    let half = sign | ((half_exp as u32) << 10) | (man >> 13);
+    let round_bit = 0x0000_1000;
+    if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
+        (half + 1) as u16
+    } else {
+        half as u16
+    }
+}
+
+/// Convert the bit pattern of a half-precision value to `f32` (exact: every
+/// half value is representable as an `f32`).
+pub fn f16_bits_to_f32(h: u16) -> f32 {
+    let h = h as u32;
+    let sign = (h & 0x8000) << 16;
+    let exp = (h >> 10) & 0x1f;
+    let mant = h & 0x3ff;
+    let bits = if exp == 0 {
+        if mant == 0 {
+            sign // signed zero
+        } else {
+            // Subnormal: normalize into an f32 normal.
+            let mut e: i32 = -1;
+            let mut m = mant;
+            loop {
+                e += 1;
+                m <<= 1;
+                if m & 0x400 != 0 {
+                    break;
+                }
+            }
+            let m = m & 0x3ff;
+            sign | (((127 - 15 - e) as u32) << 23) | (m << 13)
+        }
+    } else if exp == 0x1f {
+        sign | 0x7f80_0000 | (mant << 13) // inf / NaN
+    } else {
+        sign | ((exp + 127 - 15) << 23) | (mant << 13)
+    };
+    f32::from_bits(bits)
+}
+
+/// Round an `f32` to the nearest half-precision value, returned as `f32`.
+pub fn round_to_f16(value: f32) -> f32 {
+    f16_bits_to_f32(f32_to_f16_bits(value))
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn every_half_value_round_trips() {
+        for bits in 0..=u16::MAX {
+            let v = f16_bits_to_f32(bits);
+            if v.is_nan() {
+                assert!(f16_bits_to_f32(f32_to_f16_bits(v)).is_nan(), "{bits:#06x}");
+            } else {
+                assert_eq!(f32_to_f16_bits(v), bits, "{bits:#06x} -> {v}");
+            }
+        }
+    }
+
+    #[test]
+    fn matches_the_half_crate() {
+        // Every 257th f32 bit pattern (~16.7M values) covers every exponent,
+        // the subnormal range, both signs, ties and the overflow boundary.
+        let mut bits: u32 = 0;
+        loop {
+            let v = f32::from_bits(bits);
+            let ours = f32_to_f16_bits(v);
+            let theirs = half::f16::from_f32(v);
+            if v.is_nan() {
+                assert!(theirs.is_nan() && f16_bits_to_f32(ours).is_nan());
+            } else {
+                assert_eq!(ours, theirs.to_bits(), "{bits:#010x} ({v:e})");
+                assert_eq!(f16_bits_to_f32(ours).to_bits(), theirs.to_f32().to_bits());
+            }
+            match bits.checked_add(257) {
+                Some(b) => bits = b,
+                None => break,
+            }
+        }
+    }
+
+    #[test]
+    fn rounds_ties_to_even_and_saturates_to_infinity() {
+        // 1 + 2^-11 is exactly halfway between 1.0 and the next half (1 + 2^-10).
+        assert_eq!(round_to_f16(1.0 + 2f32.powi(-11)), 1.0);
+        assert_eq!(
+            round_to_f16(1.0 + 3.0 * 2f32.powi(-11)),
+            1.0 + 2.0 * 2f32.powi(-10)
+        );
+        assert_eq!(round_to_f16(F16_MAX), F16_MAX);
+        assert_eq!(round_to_f16(65520.0), f32::INFINITY); // halfway to 2^16 rounds up
+        assert_eq!(round_to_f16(-1e9), f32::NEG_INFINITY);
+        assert_eq!(round_to_f16(1e-9).to_bits(), 0);
+        assert_eq!(round_to_f16(-1e-9).to_bits(), (-0.0f32).to_bits());
+    }
+}