put div intrinsics in their own module + some docs

Author: Jorge Aparicio

src/div.rs

@@ -0,0 +1,278 @@
+use {Int, LargeInt, U64};
+
+/// Returns `n / d`
+#[no_mangle]
+pub extern "C" fn __udivsi3(n: u32, d: u32) -> u32 {
+    let u32_bits = u32::bits() as u32;
+
+    // Special cases
+    if d == 0 {
+        return 0; // ?!
+    }
+
+    if n == 0 {
+        return 0;
+    }
+
+    let mut sr = d.leading_zeros().wrapping_sub(n.leading_zeros());
+
+    // d > n
+    if sr > u32_bits - 1 {
+        return 0;
+    }
+
+    // d == 1
+    if sr == u32_bits - 1 {
+        return n;
+    }
+
+    sr = sr + 1;
+
+    // 1 <= sr <= u32_bits - 1
+    let mut q = n << (u32_bits - sr);
+    let mut r = n >> sr;
+
+    let mut carry = 0;
+    for _ in 0..sr {
+        // r:q = ((r:q) << 1) | carry
+        r = (r << 1) | (q >> (u32_bits - 1));
+        q = (q << 1) | carry;
+
+        // carry = 0;
+        // if r > d {
+        //     r -= d;
+        //     carry = 1;
+        // }
+
+        let s = (d.wrapping_sub(r).wrapping_sub(1)) as i32 >> (u32_bits - 1);
+        carry = (s & 1) as u32;
+        r -= d & s as u32;
+    }
+
+    q = (q << 1) | carry;
+    q
+}
+
+/// Returns `n / d` and sets `*rem = n % d`
+#[no_mangle]
+pub extern "C" fn __udivmodsi4(a: u32, b: u32, rem: Option<&mut u32>) -> u32 {
+    let d = __udivsi3(a, b);
+    if let Some(rem) = rem {
+        *rem = a - (d * b);
+    }
+    return d;
+}
+
+/// Returns `n / d` and sets `*rem = n % d`
+#[no_mangle]
+pub extern "C" fn __udivmoddi4(n: u64, d: u64, rem: Option<&mut u64>) -> u64 {
+    let u32_bits = u32::bits() as u32;
+    let u64_bits = u64::bits() as u32;
+
+    // NOTE X is unknown, K != 0
+    if n.high() == 0 {
+        if d.high() == 0 {
+            // 0 X
+            // ---
+            // 0 X
+
+            if let Some(rem) = rem {
+                *rem = u64::from(n.low() % d.low());
+            }
+            return u64::from(n.low() / d.low());
+        } else
+        // d.high() != 0
+        {
+            // 0 X
+            // ---
+            // K X
+
+            if let Some(rem) = rem {
+                *rem = u64::from(n.low());
+            }
+            return 0;
+        };
+    }
+
+    let mut sr;
+    let mut q = U64 { low: 0, high: 0 };
+    let mut r = U64 { low: 0, high: 0 };
+
+    // n.high() != 0
+    if d.low() == 0 {
+        if d.high() == 0 {
+            // K X
+            // ---
+            // 0 0
+
+            // NOTE copied verbatim from compiler-rt. This probably lets the intrinsic decide how to
+            // handle the division by zero (SIGFPE, 0, etc.). But this part shouldn't be reachable
+            // from safe code.
+            if let Some(rem) = rem {
+                *rem = u64::from(n.high() % d.low());
+            }
+            return u64::from(n.high() / d.low());
+        }
+
+        // d.high() != 0
+        if n.low() == 0 {
+            // K 0
+            // ---
+            // K 0
+
+            if let Some(rem) = rem {
+                *rem = U64 {
+                    low: 0,
+                    high: n.high() % d.high(),
+                }[..];
+            }
+            return u64::from(n.high() / d.high());
+        }
+
+        // n.low() != 0
+        // K K
+        // ---
+        // K 0
+
+        if d.high().is_power_of_two() {
+            if let Some(rem) = rem {
+                *rem = U64 {
+                    low: n.low(),
+                    high: n.high() & (d.high() - 1),
+                }[..];
+            }
+
+            return u64::from(n.high() >> d.high().trailing_zeros());
+        }
+
+        sr = d.high().leading_zeros().wrapping_sub(n.high().leading_zeros());
+
+        // D > N
+        if sr > u32_bits - 2 {
+            if let Some(rem) = rem {
+                *rem = n;
+            }
+            return 0;
+        }
+
+        sr = sr + 1;
+
+        // 1 <= sr <= u32_bits - 1
+        // q = n << (u64_bits - sr);
+        q.low = 0;
+        q.high = n.low() << (u32_bits - sr);
+        // r = n >> sr
+        r.high = n.high() >> sr;
+        r.low = (n.high() << (u32_bits - sr)) | (n.low() >> sr);
+    } else
+    // d.low() != 0
+    {
+        if d.high() == 0 {
+            // K X
+            // ---
+            // 0 K
+            if d.low().is_power_of_two() {
+                if let Some(rem) = rem {
+                    *rem = u64::from(n.low() & (d.low() - 1));
+                }
+
+                if d.low() == 1 {
+                    return n;
+                } else {
+                    let sr = d.low().trailing_zeros();
+                    return U64 {
+                        low: (n.high() << (u32_bits - sr)) | (n.low() >> sr),
+                        high: n.high() >> sr,
+                    }[..];
+                };
+            }
+
+            sr = 1 + u32_bits + d.low().leading_zeros() - n.high().leading_zeros();
+
+            // 2 <= sr <= u64_bits - 1
+            // q = n << (u64_bits - sr)
+            // r = n >> sr;
+            if sr == u32_bits {
+                q.low = 0;
+                q.high = n.low();
+                r.high = 0;
+                r.low = n.high();
+            } else if sr < u32_bits
+            // 2 <= sr <= u32_bits - 1
+            {
+                q.low = 0;
+                q.high = n.low() << (u32_bits - sr);
+                r.high = n.high() >> sr;
+                r.low = (n.high() << (u32_bits - sr)) | (n.low() >> sr);
+            } else
+            // u32_bits + 1 <= sr <= u64_bits - 1
+            {
+                q.low = n.low() << (u64_bits - sr);
+                q.high = (n.high() << (u64_bits - sr)) | (n.low() >> (sr - u32_bits));
+                r.high = 0;
+                r.low = n.high() >> (sr - u32_bits);
+            }
+
+        } else
+        // d.high() != 0
+        {
+            // K X
+            // ---
+            // K K
+
+            sr = d.high().leading_zeros().wrapping_sub(n.high().leading_zeros());
+
+            // D > N
+            if sr > u32_bits - 1 {
+                if let Some(rem) = rem {
+                    *rem = n;
+                    return 0;
+                }
+            }
+
+            sr += 1;
+
+            // 1 <= sr <= u32_bits
+            // q = n << (u64_bits - sr)
+            q.low = 0;
+            if sr == u32_bits {
+                q.high = n.low();
+                r.high = 0;
+                r.low = n.high();
+            } else {
+                q.high = n.low() << (u32_bits - sr);
+                r.high = n.high() >> sr;
+                r.low = (n.high() << (u32_bits - sr)) | (n.low() >> sr);
+            }
+        }
+    }
+
+    // Not a special case
+    // q and r are initialized with
+    // q = n << (u64_bits - sr)
+    // r = n >> sr
+    // 1 <= sr <= u64_bits - 1
+    let mut carry = 0;
+
+    for _ in 0..sr {
+        // r:q = ((r:q) << 1) | carry
+        r[..] = (r[..] << 1) | (q[..] >> 63);
+        q[..] = (q[..] << 1) | carry as u64;
+
+        // carry = 0
+        // if r >= d {
+        //     r -= d;
+        //     carry = 1;
+        // }
+
+        let s = (d.wrapping_sub(r[..]).wrapping_sub(1)) as i64 >> (u64_bits - 1);
+        carry = (s & 1) as u32;
+        r[..] -= d & s as u64;
+    }
+
+    q[..] = (q[..] << 1) | carry as u64;
+    if let Some(rem) = rem {
+        *rem = r[..];
+    }
+    q[..]
+}