moved crates in lib/ to src/, renamed crates, modified some files' text (#660)

2019-01-28 18:56:54 -05:00
parent 54959cf5bb
commit 747ad3c4c5
508 changed files with 94 additions and 92 deletions
--- a/cranelift/codegen/src/divconst_magic_numbers.rs
+++ b/cranelift/codegen/src/divconst_magic_numbers.rs
@@ -0,0 +1,590 @@
+//! Compute "magic numbers" for division-by-constants transformations.
+//!
+//! Math helpers for division by (non-power-of-2) constants. This is based
+//! on the presentation in "Hacker's Delight" by Henry Warren, 2003. There
+//! are four cases: {unsigned, signed} x {32 bit, 64 bit}. The word size
+//! makes little difference, but the signed-vs-unsigned aspect has a large
+//! effect. Therefore everything is presented in the order U32 U64 S32 S64
+//! so as to emphasise the similarity of the U32 and U64 cases and the S32
+//! and S64 cases.
+
+// Structures to hold the "magic numbers" computed.
+
+#[derive(PartialEq, Debug)]
+pub struct MU32 {
+    pub mul_by: u32,
+    pub do_add: bool,
+    pub shift_by: i32,
+}
+
+#[derive(PartialEq, Debug)]
+pub struct MU64 {
+    pub mul_by: u64,
+    pub do_add: bool,
+    pub shift_by: i32,
+}
+
+#[derive(PartialEq, Debug)]
+pub struct MS32 {
+    pub mul_by: i32,
+    pub shift_by: i32,
+}
+
+#[derive(PartialEq, Debug)]
+pub struct MS64 {
+    pub mul_by: i64,
+    pub shift_by: i32,
+}
+
+// The actual "magic number" generators follow.
+
+pub fn magic_u32(d: u32) -> MU32 {
+    debug_assert_ne!(d, 0);
+    debug_assert_ne!(d, 1); // d==1 generates out of range shifts.
+
+    let mut do_add: bool = false;
+    let mut p: i32 = 31;
+    let nc: u32 = 0xFFFFFFFFu32 - u32::wrapping_neg(d) % d;
+    let mut q1: u32 = 0x80000000u32 / nc;
+    let mut r1: u32 = 0x80000000u32 - q1 * nc;
+    let mut q2: u32 = 0x7FFFFFFFu32 / d;
+    let mut r2: u32 = 0x7FFFFFFFu32 - q2 * d;
+    loop {
+        p = p + 1;
+        if r1 >= nc - r1 {
+            q1 = u32::wrapping_add(u32::wrapping_mul(2, q1), 1);
+            r1 = u32::wrapping_sub(u32::wrapping_mul(2, r1), nc);
+        } else {
+            q1 = 2 * q1;
+            r1 = 2 * r1;
+        }
+        if r2 + 1 >= d - r2 {
+            if q2 >= 0x7FFFFFFFu32 {
+                do_add = true;
+            }
+            q2 = 2 * q2 + 1;
+            r2 = u32::wrapping_sub(u32::wrapping_add(u32::wrapping_mul(2, r2), 1), d);
+        } else {
+            if q2 >= 0x80000000u32 {
+                do_add = true;
+            }
+            q2 = u32::wrapping_mul(2, q2);
+            r2 = 2 * r2 + 1;
+        }
+        let delta: u32 = d - 1 - r2;
+        if !(p < 64 && (q1 < delta || (q1 == delta && r1 == 0))) {
+            break;
+        }
+    }
+
+    MU32 {
+        mul_by: q2 + 1,
+        do_add: do_add,
+        shift_by: p - 32,
+    }
+}
+
+pub fn magic_u64(d: u64) -> MU64 {
+    debug_assert_ne!(d, 0);
+    debug_assert_ne!(d, 1); // d==1 generates out of range shifts.
+
+    let mut do_add: bool = false;
+    let mut p: i32 = 63;
+    let nc: u64 = 0xFFFFFFFFFFFFFFFFu64 - u64::wrapping_neg(d) % d;
+    let mut q1: u64 = 0x8000000000000000u64 / nc;
+    let mut r1: u64 = 0x8000000000000000u64 - q1 * nc;
+    let mut q2: u64 = 0x7FFFFFFFFFFFFFFFu64 / d;
+    let mut r2: u64 = 0x7FFFFFFFFFFFFFFFu64 - q2 * d;
+    loop {
+        p = p + 1;
+        if r1 >= nc - r1 {
+            q1 = u64::wrapping_add(u64::wrapping_mul(2, q1), 1);
+            r1 = u64::wrapping_sub(u64::wrapping_mul(2, r1), nc);
+        } else {
+            q1 = 2 * q1;
+            r1 = 2 * r1;
+        }
+        if r2 + 1 >= d - r2 {
+            if q2 >= 0x7FFFFFFFFFFFFFFFu64 {
+                do_add = true;
+            }
+            q2 = 2 * q2 + 1;
+            r2 = u64::wrapping_sub(u64::wrapping_add(u64::wrapping_mul(2, r2), 1), d);
+        } else {
+            if q2 >= 0x8000000000000000u64 {
+                do_add = true;
+            }
+            q2 = u64::wrapping_mul(2, q2);
+            r2 = 2 * r2 + 1;
+        }
+        let delta: u64 = d - 1 - r2;
+        if !(p < 128 && (q1 < delta || (q1 == delta && r1 == 0))) {
+            break;
+        }
+    }
+
+    MU64 {
+        mul_by: q2 + 1,
+        do_add: do_add,
+        shift_by: p - 64,
+    }
+}
+
+pub fn magic_s32(d: i32) -> MS32 {
+    debug_assert_ne!(d, -1);
+    debug_assert_ne!(d, 0);
+    debug_assert_ne!(d, 1);
+    let two31: u32 = 0x80000000u32;
+    let mut p: i32 = 31;
+    let ad: u32 = i32::wrapping_abs(d) as u32;
+    let t: u32 = two31 + ((d as u32) >> 31);
+    let anc: u32 = u32::wrapping_sub(t - 1, t % ad);
+    let mut q1: u32 = two31 / anc;
+    let mut r1: u32 = two31 - q1 * anc;
+    let mut q2: u32 = two31 / ad;
+    let mut r2: u32 = two31 - q2 * ad;
+    loop {
+        p = p + 1;
+        q1 = 2 * q1;
+        r1 = 2 * r1;
+        if r1 >= anc {
+            q1 = q1 + 1;
+            r1 = r1 - anc;
+        }
+        q2 = 2 * q2;
+        r2 = 2 * r2;
+        if r2 >= ad {
+            q2 = q2 + 1;
+            r2 = r2 - ad;
+        }
+        let delta: u32 = ad - r2;
+        if !(q1 < delta || (q1 == delta && r1 == 0)) {
+            break;
+        }
+    }
+
+    MS32 {
+        mul_by: (if d < 0 {
+            u32::wrapping_neg(q2 + 1)
+        } else {
+            q2 + 1
+        }) as i32,
+        shift_by: p - 32,
+    }
+}
+
+pub fn magic_s64(d: i64) -> MS64 {
+    debug_assert_ne!(d, -1);
+    debug_assert_ne!(d, 0);
+    debug_assert_ne!(d, 1);
+    let two63: u64 = 0x8000000000000000u64;
+    let mut p: i32 = 63;
+    let ad: u64 = i64::wrapping_abs(d) as u64;
+    let t: u64 = two63 + ((d as u64) >> 63);
+    let anc: u64 = u64::wrapping_sub(t - 1, t % ad);
+    let mut q1: u64 = two63 / anc;
+    let mut r1: u64 = two63 - q1 * anc;
+    let mut q2: u64 = two63 / ad;
+    let mut r2: u64 = two63 - q2 * ad;
+    loop {
+        p = p + 1;
+        q1 = 2 * q1;
+        r1 = 2 * r1;
+        if r1 >= anc {
+            q1 = q1 + 1;
+            r1 = r1 - anc;
+        }
+        q2 = 2 * q2;
+        r2 = 2 * r2;
+        if r2 >= ad {
+            q2 = q2 + 1;
+            r2 = r2 - ad;
+        }
+        let delta: u64 = ad - r2;
+        if !(q1 < delta || (q1 == delta && r1 == 0)) {
+            break;
+        }
+    }
+
+    MS64 {
+        mul_by: (if d < 0 {
+            u64::wrapping_neg(q2 + 1)
+        } else {
+            q2 + 1
+        }) as i64,
+        shift_by: p - 64,
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::{magic_s32, magic_s64, magic_u32, magic_u64};
+    use super::{MS32, MS64, MU32, MU64};
+
+    fn make_mu32(mul_by: u32, do_add: bool, shift_by: i32) -> MU32 {
+        MU32 {
+            mul_by,
+            do_add,
+            shift_by,
+        }
+    }
+
+    fn make_mu64(mul_by: u64, do_add: bool, shift_by: i32) -> MU64 {
+        MU64 {
+            mul_by,
+            do_add,
+            shift_by,
+        }
+    }
+
+    fn make_ms32(mul_by: i32, shift_by: i32) -> MS32 {
+        MS32 { mul_by, shift_by }
+    }
+
+    fn make_ms64(mul_by: i64, shift_by: i32) -> MS64 {
+        MS64 { mul_by, shift_by }
+    }
+
+    #[test]
+    fn test_magicU32() {
+        assert_eq!(magic_u32(2u32), make_mu32(0x80000000u32, false, 0));
+        assert_eq!(magic_u32(3u32), make_mu32(0xaaaaaaabu32, false, 1));
+        assert_eq!(magic_u32(4u32), make_mu32(0x40000000u32, false, 0));
+        assert_eq!(magic_u32(5u32), make_mu32(0xcccccccdu32, false, 2));
+        assert_eq!(magic_u32(6u32), make_mu32(0xaaaaaaabu32, false, 2));
+        assert_eq!(magic_u32(7u32), make_mu32(0x24924925u32, true, 3));
+        assert_eq!(magic_u32(9u32), make_mu32(0x38e38e39u32, false, 1));
+        assert_eq!(magic_u32(10u32), make_mu32(0xcccccccdu32, false, 3));
+        assert_eq!(magic_u32(11u32), make_mu32(0xba2e8ba3u32, false, 3));
+        assert_eq!(magic_u32(12u32), make_mu32(0xaaaaaaabu32, false, 3));
+        assert_eq!(magic_u32(25u32), make_mu32(0x51eb851fu32, false, 3));
+        assert_eq!(magic_u32(125u32), make_mu32(0x10624dd3u32, false, 3));
+        assert_eq!(magic_u32(625u32), make_mu32(0xd1b71759u32, false, 9));
+        assert_eq!(magic_u32(1337u32), make_mu32(0x88233b2bu32, true, 11));
+        assert_eq!(magic_u32(65535u32), make_mu32(0x80008001u32, false, 15));
+        assert_eq!(magic_u32(65536u32), make_mu32(0x00010000u32, false, 0));
+        assert_eq!(magic_u32(65537u32), make_mu32(0xffff0001u32, false, 16));
+        assert_eq!(magic_u32(31415927u32), make_mu32(0x445b4553u32, false, 23));
+        assert_eq!(
+            magic_u32(0xdeadbeefu32),
+            make_mu32(0x93275ab3u32, false, 31)
+        );
+        assert_eq!(
+            magic_u32(0xfffffffdu32),
+            make_mu32(0x40000001u32, false, 30)
+        );
+        assert_eq!(magic_u32(0xfffffffeu32), make_mu32(0x00000003u32, true, 32));
+        assert_eq!(
+            magic_u32(0xffffffffu32),
+            make_mu32(0x80000001u32, false, 31)
+        );
+    }
+    #[test]
+    fn test_magicU64() {
+        assert_eq!(magic_u64(2u64), make_mu64(0x8000000000000000u64, false, 0));
+        assert_eq!(magic_u64(3u64), make_mu64(0xaaaaaaaaaaaaaaabu64, false, 1));
+        assert_eq!(magic_u64(4u64), make_mu64(0x4000000000000000u64, false, 0));
+        assert_eq!(magic_u64(5u64), make_mu64(0xcccccccccccccccdu64, false, 2));
+        assert_eq!(magic_u64(6u64), make_mu64(0xaaaaaaaaaaaaaaabu64, false, 2));
+        assert_eq!(magic_u64(7u64), make_mu64(0x2492492492492493u64, true, 3));
+        assert_eq!(magic_u64(9u64), make_mu64(0xe38e38e38e38e38fu64, false, 3));
+        assert_eq!(magic_u64(10u64), make_mu64(0xcccccccccccccccdu64, false, 3));
+        assert_eq!(magic_u64(11u64), make_mu64(0x2e8ba2e8ba2e8ba3u64, false, 1));
+        assert_eq!(magic_u64(12u64), make_mu64(0xaaaaaaaaaaaaaaabu64, false, 3));
+        assert_eq!(magic_u64(25u64), make_mu64(0x47ae147ae147ae15u64, true, 5));
+        assert_eq!(magic_u64(125u64), make_mu64(0x0624dd2f1a9fbe77u64, true, 7));
+        assert_eq!(
+            magic_u64(625u64),
+            make_mu64(0x346dc5d63886594bu64, false, 7)
+        );
+        assert_eq!(
+            magic_u64(1337u64),
+            make_mu64(0xc4119d952866a139u64, false, 10)
+        );
+        assert_eq!(
+            magic_u64(31415927u64),
+            make_mu64(0x116d154b9c3d2f85u64, true, 25)
+        );
+        assert_eq!(
+            magic_u64(0x00000000deadbeefu64),
+            make_mu64(0x93275ab2dfc9094bu64, false, 31)
+        );
+        assert_eq!(
+            magic_u64(0x00000000fffffffdu64),
+            make_mu64(0x8000000180000005u64, false, 31)
+        );
+        assert_eq!(
+            magic_u64(0x00000000fffffffeu64),
+            make_mu64(0x0000000200000005u64, true, 32)
+        );
+        assert_eq!(
+            magic_u64(0x00000000ffffffffu64),
+            make_mu64(0x8000000080000001u64, false, 31)
+        );
+        assert_eq!(
+            magic_u64(0x0000000100000000u64),
+            make_mu64(0x0000000100000000u64, false, 0)
+        );
+        assert_eq!(
+            magic_u64(0x0000000100000001u64),
+            make_mu64(0xffffffff00000001u64, false, 32)
+        );
+        assert_eq!(
+            magic_u64(0x0ddc0ffeebadf00du64),
+            make_mu64(0x2788e9d394b77da1u64, true, 60)
+        );
+        assert_eq!(
+            magic_u64(0xfffffffffffffffdu64),
+            make_mu64(0x4000000000000001u64, false, 62)
+        );
+        assert_eq!(
+            magic_u64(0xfffffffffffffffeu64),
+            make_mu64(0x0000000000000003u64, true, 64)
+        );
+        assert_eq!(
+            magic_u64(0xffffffffffffffffu64),
+            make_mu64(0x8000000000000001u64, false, 63)
+        );
+    }
+    #[test]
+    fn test_magicS32() {
+        assert_eq!(
+            magic_s32(-0x80000000i32),
+            make_ms32(0x7fffffffu32 as i32, 30)
+        );
+        assert_eq!(
+            magic_s32(-0x7FFFFFFFi32),
+            make_ms32(0xbfffffffu32 as i32, 29)
+        );
+        assert_eq!(
+            magic_s32(-0x7FFFFFFEi32),
+            make_ms32(0x7ffffffdu32 as i32, 30)
+        );
+        assert_eq!(magic_s32(-31415927i32), make_ms32(0xbba4baadu32 as i32, 23));
+        assert_eq!(magic_s32(-1337i32), make_ms32(0x9df73135u32 as i32, 9));
+        assert_eq!(magic_s32(-256i32), make_ms32(0x7fffffffu32 as i32, 7));
+        assert_eq!(magic_s32(-5i32), make_ms32(0x99999999u32 as i32, 1));
+        assert_eq!(magic_s32(-3i32), make_ms32(0x55555555u32 as i32, 1));
+        assert_eq!(magic_s32(-2i32), make_ms32(0x7fffffffu32 as i32, 0));
+        assert_eq!(magic_s32(2i32), make_ms32(0x80000001u32 as i32, 0));
+        assert_eq!(magic_s32(3i32), make_ms32(0x55555556u32 as i32, 0));
+        assert_eq!(magic_s32(4i32), make_ms32(0x80000001u32 as i32, 1));
+        assert_eq!(magic_s32(5i32), make_ms32(0x66666667u32 as i32, 1));
+        assert_eq!(magic_s32(6i32), make_ms32(0x2aaaaaabu32 as i32, 0));
+        assert_eq!(magic_s32(7i32), make_ms32(0x92492493u32 as i32, 2));
+        assert_eq!(magic_s32(9i32), make_ms32(0x38e38e39u32 as i32, 1));
+        assert_eq!(magic_s32(10i32), make_ms32(0x66666667u32 as i32, 2));
+        assert_eq!(magic_s32(11i32), make_ms32(0x2e8ba2e9u32 as i32, 1));
+        assert_eq!(magic_s32(12i32), make_ms32(0x2aaaaaabu32 as i32, 1));
+        assert_eq!(magic_s32(25i32), make_ms32(0x51eb851fu32 as i32, 3));
+        assert_eq!(magic_s32(125i32), make_ms32(0x10624dd3u32 as i32, 3));
+        assert_eq!(magic_s32(625i32), make_ms32(0x68db8badu32 as i32, 8));
+        assert_eq!(magic_s32(1337i32), make_ms32(0x6208cecbu32 as i32, 9));
+        assert_eq!(magic_s32(31415927i32), make_ms32(0x445b4553u32 as i32, 23));
+        assert_eq!(
+            magic_s32(0x7ffffffei32),
+            make_ms32(0x80000003u32 as i32, 30)
+        );
+        assert_eq!(
+            magic_s32(0x7fffffffi32),
+            make_ms32(0x40000001u32 as i32, 29)
+        );
+    }
+    #[test]
+    fn test_magicS64() {
+        assert_eq!(
+            magic_s64(-0x8000000000000000i64),
+            make_ms64(0x7fffffffffffffffu64 as i64, 62)
+        );
+        assert_eq!(
+            magic_s64(-0x7FFFFFFFFFFFFFFFi64),
+            make_ms64(0xbfffffffffffffffu64 as i64, 61)
+        );
+        assert_eq!(
+            magic_s64(-0x7FFFFFFFFFFFFFFEi64),
+            make_ms64(0x7ffffffffffffffdu64 as i64, 62)
+        );
+        assert_eq!(
+            magic_s64(-0x0ddC0ffeeBadF00di64),
+            make_ms64(0x6c3b8b1635a4412fu64 as i64, 59)
+        );
+        assert_eq!(
+            magic_s64(-0x100000001i64),
+            make_ms64(0x800000007fffffffu64 as i64, 31)
+        );
+        assert_eq!(
+            magic_s64(-0x100000000i64),
+            make_ms64(0x7fffffffffffffffu64 as i64, 31)
+        );
+        assert_eq!(
+            magic_s64(-0xFFFFFFFFi64),
+            make_ms64(0x7fffffff7fffffffu64 as i64, 31)
+        );
+        assert_eq!(
+            magic_s64(-0xFFFFFFFEi64),
+            make_ms64(0x7ffffffefffffffdu64 as i64, 31)
+        );
+        assert_eq!(
+            magic_s64(-0xFFFFFFFDi64),
+            make_ms64(0x7ffffffe7ffffffbu64 as i64, 31)
+        );
+        assert_eq!(
+            magic_s64(-0xDeadBeefi64),
+            make_ms64(0x6cd8a54d2036f6b5u64 as i64, 31)
+        );
+        assert_eq!(
+            magic_s64(-31415927i64),
+            make_ms64(0x7749755a31e1683du64 as i64, 24)
+        );
+        assert_eq!(
+            magic_s64(-1337i64),
+            make_ms64(0x9df731356bccaf63u64 as i64, 9)
+        );
+        assert_eq!(
+            magic_s64(-256i64),
+            make_ms64(0x7fffffffffffffffu64 as i64, 7)
+        );
+        assert_eq!(magic_s64(-5i64), make_ms64(0x9999999999999999u64 as i64, 1));
+        assert_eq!(magic_s64(-3i64), make_ms64(0x5555555555555555u64 as i64, 1));
+        assert_eq!(magic_s64(-2i64), make_ms64(0x7fffffffffffffffu64 as i64, 0));
+        assert_eq!(magic_s64(2i64), make_ms64(0x8000000000000001u64 as i64, 0));
+        assert_eq!(magic_s64(3i64), make_ms64(0x5555555555555556u64 as i64, 0));
+        assert_eq!(magic_s64(4i64), make_ms64(0x8000000000000001u64 as i64, 1));
+        assert_eq!(magic_s64(5i64), make_ms64(0x6666666666666667u64 as i64, 1));
+        assert_eq!(magic_s64(6i64), make_ms64(0x2aaaaaaaaaaaaaabu64 as i64, 0));
+        assert_eq!(magic_s64(7i64), make_ms64(0x4924924924924925u64 as i64, 1));
+        assert_eq!(magic_s64(9i64), make_ms64(0x1c71c71c71c71c72u64 as i64, 0));
+        assert_eq!(magic_s64(10i64), make_ms64(0x6666666666666667u64 as i64, 2));
+        assert_eq!(magic_s64(11i64), make_ms64(0x2e8ba2e8ba2e8ba3u64 as i64, 1));
+        assert_eq!(magic_s64(12i64), make_ms64(0x2aaaaaaaaaaaaaabu64 as i64, 1));
+        assert_eq!(magic_s64(25i64), make_ms64(0xa3d70a3d70a3d70bu64 as i64, 4));
+        assert_eq!(
+            magic_s64(125i64),
+            make_ms64(0x20c49ba5e353f7cfu64 as i64, 4)
+        );
+        assert_eq!(
+            magic_s64(625i64),
+            make_ms64(0x346dc5d63886594bu64 as i64, 7)
+        );
+        assert_eq!(
+            magic_s64(1337i64),
+            make_ms64(0x6208ceca9433509du64 as i64, 9)
+        );
+        assert_eq!(
+            magic_s64(31415927i64),
+            make_ms64(0x88b68aa5ce1e97c3u64 as i64, 24)
+        );
+        assert_eq!(
+            magic_s64(0x00000000deadbeefi64),
+            make_ms64(0x93275ab2dfc9094bu64 as i64, 31)
+        );
+        assert_eq!(
+            magic_s64(0x00000000fffffffdi64),
+            make_ms64(0x8000000180000005u64 as i64, 31)
+        );
+        assert_eq!(
+            magic_s64(0x00000000fffffffei64),
+            make_ms64(0x8000000100000003u64 as i64, 31)
+        );
+        assert_eq!(
+            magic_s64(0x00000000ffffffffi64),
+            make_ms64(0x8000000080000001u64 as i64, 31)
+        );
+        assert_eq!(
+            magic_s64(0x0000000100000000i64),
+            make_ms64(0x8000000000000001u64 as i64, 31)
+        );
+        assert_eq!(
+            magic_s64(0x0000000100000001i64),
+            make_ms64(0x7fffffff80000001u64 as i64, 31)
+        );
+        assert_eq!(
+            magic_s64(0x0ddc0ffeebadf00di64),
+            make_ms64(0x93c474e9ca5bbed1u64 as i64, 59)
+        );
+        assert_eq!(
+            magic_s64(0x7ffffffffffffffdi64),
+            make_ms64(0x2000000000000001u64 as i64, 60)
+        );
+        assert_eq!(
+            magic_s64(0x7ffffffffffffffei64),
+            make_ms64(0x8000000000000003u64 as i64, 62)
+        );
+        assert_eq!(
+            magic_s64(0x7fffffffffffffffi64),
+            make_ms64(0x4000000000000001u64 as i64, 61)
+        );
+    }
+    #[test]
+    fn test_magic_generators_dont_panic() {
+        // The point of this is to check that the magic number generators
+        // don't panic with integer wraparounds, especially at boundary
+        // cases for their arguments. The actual results are thrown away.
+        let mut total: u64 = 0;
+        // Testing UP magic_u32
+        for x in 2..(200 * 1000u32) {
+            let m = magic_u32(x);
+            total = total ^ (m.mul_by as u64);
+            total = total + (m.shift_by as u64);
+            total = total - (if m.do_add { 123 } else { 456 });
+        }
+        assert_eq!(total, 1747815691);
+        // Testing DOWN magic_u32
+        for x in 0..(200 * 1000u32) {
+            let m = magic_u32(0xFFFF_FFFFu32 - x);
+            total = total ^ (m.mul_by as u64);
+            total = total + (m.shift_by as u64);
+            total = total - (if m.do_add { 123 } else { 456 });
+        }
+        assert_eq!(total, 2210292772);
+
+        // Testing UP magic_u64
+        for x in 2..(200 * 1000u64) {
+            let m = magic_u64(x);
+            total = total ^ m.mul_by;
+            total = total + (m.shift_by as u64);
+            total = total - (if m.do_add { 123 } else { 456 });
+        }
+        assert_eq!(total, 7430004084791260605);
+        // Testing DOWN magic_u64
+        for x in 0..(200 * 1000u64) {
+            let m = magic_u64(0xFFFF_FFFF_FFFF_FFFFu64 - x);
+            total = total ^ m.mul_by;
+            total = total + (m.shift_by as u64);
+            total = total - (if m.do_add { 123 } else { 456 });
+        }
+        assert_eq!(total, 7547519887519825919);
+
+        // Testing UP magic_s32
+        for x in 0..(200 * 1000i32) {
+            let m = magic_s32(-0x8000_0000i32 + x);
+            total = total ^ (m.mul_by as u64);
+            total = total + (m.shift_by as u64);
+        }
+        assert_eq!(total, 10899224186731671235);
+        // Testing DOWN magic_s32
+        for x in 0..(200 * 1000i32) {
+            let m = magic_s32(0x7FFF_FFFFi32 - x);
+            total = total ^ (m.mul_by as u64);
+            total = total + (m.shift_by as u64);
+        }
+        assert_eq!(total, 7547519887517897369);
+
+        // Testing UP magic_s64
+        for x in 0..(200 * 1000i64) {
+            let m = magic_s64(-0x8000_0000_0000_0000i64 + x);
+            total = total ^ (m.mul_by as u64);
+            total = total + (m.shift_by as u64);
+        }
+        assert_eq!(total, 8029756891368555163);
+        // Testing DOWN magic_s64
+        for x in 0..(200 * 1000i64) {
+            let m = magic_s64(0x7FFF_FFFF_FFFF_FFFFi64 - x);
+            total = total ^ (m.mul_by as u64);
+            total = total + (m.shift_by as u64);
+        }
+        // Force `total` -- and hence, the entire computation -- to
+        // be used, so that rustc can't optimise it out.
+        assert_eq!(total, 7547519887532559585u64);
+    }
+}