Change integer to float conversions to be generic

Reduce duplicate code and make it easier to add `f128` operations.

Author: tgross35

src/float/conv.rs

@@ -10,141 +10,148 @@ use super::Float;
 /// which unfortunately isn't the easiest kind of code to read.
 ///
 /// The algorithm is explained here: <https://blog.m-ou.se/floats/>
-mod int_to_float {
-    pub fn u32_to_f32_bits(i: u32) -> u32 {
-        if i == 0 {
-            return 0;
-        }
-        let n = i.leading_zeros();
-        let a = (i << n) >> 8; // Significant bits, with bit 24 still in tact.
-        let b = (i << n) << 24; // Insignificant bits, only relevant for rounding.
-        let m = a + ((b - (b >> 31 & !a)) >> 31); // Add one when we need to round up. Break ties to even.
-        let e = 157 - n; // Exponent plus 127, minus one.
-        (e << 23) + m // + not |, so the mantissa can overflow into the exponent.
-    }
-
-    pub fn u32_to_f64_bits(i: u32) -> u64 {
-        if i == 0 {
-            return 0;
-        }
-        let n = i.leading_zeros();
-        let m = (i as u64) << (21 + n); // Significant bits, with bit 53 still in tact.
-        let e = 1053 - n as u64; // Exponent plus 1023, minus one.
-        (e << 52) + m // Bit 53 of m will overflow into e.
-    }
-
-    pub fn u64_to_f32_bits(i: u64) -> u32 {
-        let n = i.leading_zeros();
-        let y = i.wrapping_shl(n);
-        let a = (y >> 40) as u32; // Significant bits, with bit 24 still in tact.
-        let b = (y >> 8 | y & 0xFFFF) as u32; // Insignificant bits, only relevant for rounding.
-        let m = a + ((b - (b >> 31 & !a)) >> 31); // Add one when we need to round up. Break ties to even.
-        let e = if i == 0 { 0 } else { 189 - n }; // Exponent plus 127, minus one, except for zero.
-        (e << 23) + m // + not |, so the mantissa can overflow into the exponent.
-    }
-
-    pub fn u64_to_f64_bits(i: u64) -> u64 {
-        if i == 0 {
-            return 0;
-        }
-        let n = i.leading_zeros();
-        let a = (i << n) >> 11; // Significant bits, with bit 53 still in tact.
-        let b = (i << n) << 53; // Insignificant bits, only relevant for rounding.
-        let m = a + ((b - (b >> 63 & !a)) >> 63); // Add one when we need to round up. Break ties to even.
-        let e = 1085 - n as u64; // Exponent plus 1023, minus one.
-        (e << 52) + m // + not |, so the mantissa can overflow into the exponent.
-    }
-
-    pub fn u128_to_f32_bits(i: u128) -> u32 {
-        let n = i.leading_zeros();
-        let y = i.wrapping_shl(n);
-        let a = (y >> 104) as u32; // Significant bits, with bit 24 still in tact.
-        let b = (y >> 72) as u32 | ((y << 32) >> 32 != 0) as u32; // Insignificant bits, only relevant for rounding.
-        let m = a + ((b - (b >> 31 & !a)) >> 31); // Add one when we need to round up. Break ties to even.
-        let e = if i == 0 { 0 } else { 253 - n }; // Exponent plus 127, minus one, except for zero.
-        (e << 23) + m // + not |, so the mantissa can overflow into the exponent.
-    }
-
-    pub fn u128_to_f64_bits(i: u128) -> u64 {
-        let n = i.leading_zeros();
-        let y = i.wrapping_shl(n);
-        let a = (y >> 75) as u64; // Significant bits, with bit 53 still in tact.
-        let b = (y >> 11 | y & 0xFFFF_FFFF) as u64; // Insignificant bits, only relevant for rounding.
-        let m = a + ((b - (b >> 63 & !a)) >> 63); // Add one when we need to round up. Break ties to even.
-        let e = if i == 0 { 0 } else { 1149 - n as u64 }; // Exponent plus 1023, minus one, except for zero.
-        (e << 52) + m // + not |, so the mantissa can overflow into the exponent.
+fn int_to_float<I, F>(i: I) -> F
+where
+    F: Float,
+    I: Int<UnsignedInt: Int>,
+    I::UnsignedInt: CastInto<F::Int>,
+    F::Int: CastFrom<u32>,
+    F::Int: CastFrom<I>,
+    F::Int: From<bool>,
+    F::Int: CastInto<I::UnsignedInt>,
+{
+    if i == I::ZERO {
+        return F::ZERO;
     }
+
+    let sign_bit: F::Int = if I::SIGNED {
+        F::Int::cast_from(i >> (I::BITS - 1)) << (F::BITS - 1)
+    } else {
+        // Never used
+        F::Int::ZERO
+    };
+
+    let i = i.unsigned_abs();
+    let n = i.leading_zeros();
+
+    // Calculate the exponent from the integer's significant digits
+    let e = F::Int::cast_from(I::BITS + F::EXPONENT_BIAS - 2 - n);
+
+    // The mantissa of `i`, still in `I`'s form (left shifted so the first bit is nonzero)
+    let i_m = i.wrapping_shl(n);
+
+    let m: F::Int = if F::BITS > I::BITS {
+        F::Int::cast_from(i) << (F::SIGNIFICAND_BITS - I::BITS + 1 + n)
+    } else {
+        // Shift the integer into the float's mantissa bits. Keep the lowest
+        // exponent bit intact.
+        let m_base = F::Int::cast_from(i_m >> ((I::BITS - F::BITS) + F::EXPONENT_BITS));
+
+        // Squash
+        let dropped_bits: F::Int = if F::BITS == I::BITS {
+            // Simple case
+
+            // Only the lowest `F::EXPONENT_BITS` bits will be truncated. Shift them
+            // to the highest position
+            (i_m << (F::SIGNIFICAND_BITS + 1)).cast()
+        } else if F::BITS * 2 == I::BITS {
+            // Specialized case where the float is half the integer size
+
+            // The entire lower half of `i` will be truncated (masked portion), plus the
+            // next `EXPONENT_BITS` bits.
+            let mask: I::UnsignedInt = (F::Int::MAX >> (F::Int::BITS / 2)).cast();
+            (i_m >> F::EXPONENT_BITS | i_m & mask).cast()
+        } else {
+            // Generic case
+
+            // Within the upper `F::BITS`, everything except for the signifcand
+            // gets truncated
+            let d1: F::Int = (i_m >> (I::BITS - F::BITS - F::SIGNIFICAND_BITS - 1)).cast();
+
+            // The entire rest of `i_m` gets truncated. Zero the upper `F::BITS` then just
+            // check if it is nonzero.
+            let d2: F::Int = (i_m << F::BITS >> F::BITS != I::UnsignedInt::ZERO).into();
+
+            d1 | d2
+        };
+
+        // Branchlessly extract a `1` if rounding up should happen
+        let m_adj = (dropped_bits - (dropped_bits >> (F::BITS - 1) & !m_base)) >> (F::BITS - 1);
+
+        // Add one when we need to round up. Break ties to even.
+        m_base + m_adj
+    };
+
+    // + not |, so the mantissa can overflow into the exponent.
+    let urepr = (e << F::SIGNIFICAND_BITS) + m;
+    let repr: F::Int = if I::SIGNED { urepr | sign_bit } else { urepr };
+
+    F::from_repr(repr)
 }
 
 // Conversions from unsigned integers to floats.
 intrinsics! {
     #[arm_aeabi_alias = __aeabi_ui2f]
     pub extern "C" fn __floatunsisf(i: u32) -> f32 {
-        f32::from_bits(int_to_float::u32_to_f32_bits(i))
+        int_to_float(i)
     }
 
     #[arm_aeabi_alias = __aeabi_ui2d]
     pub extern "C" fn __floatunsidf(i: u32) -> f64 {
-        f64::from_bits(int_to_float::u32_to_f64_bits(i))
+        int_to_float(i)
     }
 
     #[arm_aeabi_alias = __aeabi_ul2f]
     pub extern "C" fn __floatundisf(i: u64) -> f32 {
-        f32::from_bits(int_to_float::u64_to_f32_bits(i))
+        int_to_float(i)
     }
 
     #[arm_aeabi_alias = __aeabi_ul2d]
     pub extern "C" fn __floatundidf(i: u64) -> f64 {
-        f64::from_bits(int_to_float::u64_to_f64_bits(i))
+        int_to_float(i)
     }
 
     #[cfg_attr(target_os = "uefi", unadjusted_on_win64)]
     pub extern "C" fn __floatuntisf(i: u128) -> f32 {
-        f32::from_bits(int_to_float::u128_to_f32_bits(i))
+        int_to_float(i)
     }
 
     #[cfg_attr(target_os = "uefi", unadjusted_on_win64)]
     pub extern "C" fn __floatuntidf(i: u128) -> f64 {
-        f64::from_bits(int_to_float::u128_to_f64_bits(i))
+        int_to_float(i)
     }
 }
 
 // Conversions from signed integers to floats.
 intrinsics! {
     #[arm_aeabi_alias = __aeabi_i2f]
     pub extern "C" fn __floatsisf(i: i32) -> f32 {
-        let sign_bit = ((i >> 31) as u32) << 31;
-        f32::from_bits(int_to_float::u32_to_f32_bits(i.unsigned_abs()) | sign_bit)
+        int_to_float(i)
     }
 
     #[arm_aeabi_alias = __aeabi_i2d]
     pub extern "C" fn __floatsidf(i: i32) -> f64 {
-        let sign_bit = ((i >> 31) as u64) << 63;
-        f64::from_bits(int_to_float::u32_to_f64_bits(i.unsigned_abs()) | sign_bit)
+        int_to_float(i)
     }
 
     #[arm_aeabi_alias = __aeabi_l2f]
     pub extern "C" fn __floatdisf(i: i64) -> f32 {
-        let sign_bit = ((i >> 63) as u32) << 31;
-        f32::from_bits(int_to_float::u64_to_f32_bits(i.unsigned_abs()) | sign_bit)
+        int_to_float(i)
     }
 
     #[arm_aeabi_alias = __aeabi_l2d]
     pub extern "C" fn __floatdidf(i: i64) -> f64 {
-        let sign_bit = ((i >> 63) as u64) << 63;
-        f64::from_bits(int_to_float::u64_to_f64_bits(i.unsigned_abs()) | sign_bit)
+        int_to_float(i)
     }
 
     #[cfg_attr(target_os = "uefi", unadjusted_on_win64)]
     pub extern "C" fn __floattisf(i: i128) -> f32 {
-        let sign_bit = ((i >> 127) as u32) << 31;
-        f32::from_bits(int_to_float::u128_to_f32_bits(i.unsigned_abs()) | sign_bit)
+        int_to_float(i)
     }
 
     #[cfg_attr(target_os = "uefi", unadjusted_on_win64)]
     pub extern "C" fn __floattidf(i: i128) -> f64 {
-        let sign_bit = ((i >> 127) as u64) << 63;
-        f64::from_bits(int_to_float::u128_to_f64_bits(i.unsigned_abs()) | sign_bit)
+        int_to_float(i)
     }
 }
 

src/float/mod.rs

@@ -31,10 +31,10 @@ pub(crate) trait Float:
     + ops::Rem<Output = Self>
 {
     /// A uint of the same width as the float
-    type Int: Int;
+    type Int: Int<UnsignedInt = Self::Int, OtherSign = Self::SignedInt>;
 
     /// A int of the same width as the float
-    type SignedInt: Int;
+    type SignedInt: Int<UnsignedInt = Self::Int, OtherSign = Self::Int>;
 
     /// An int capable of containing the exponent bits plus a sign bit. This is signed.
     type ExpInt: Int;

src/int/mod.rs

@@ -82,6 +82,7 @@ pub(crate) trait Int: MinInt
 
     fn unsigned(self) -> Self::UnsignedInt;
     fn from_unsigned(unsigned: Self::UnsignedInt) -> Self;
+    fn unsigned_abs(self) -> Self::UnsignedInt;
 
     fn from_bool(b: bool) -> Self;
 
@@ -177,7 +178,6 @@ macro_rules! int_impl_common {
         fn wrapping_mul(self, other: Self) -> Self {
             <Self>::wrapping_mul(self, other)
         }
-
         fn wrapping_sub(self, other: Self) -> Self {
             <Self>::wrapping_sub(self, other)
         }
@@ -234,6 +234,10 @@ macro_rules! int_impl {
                 me
             }
 
+            fn unsigned_abs(self) -> Self {
+                self
+            }
+
             fn abs_diff(self, other: Self) -> Self {
                 if self < other {
                     other.wrapping_sub(self)
@@ -267,6 +271,10 @@ macro_rules! int_impl {
                 me as $ity
             }
 
+            fn unsigned_abs(self) -> Self::UnsignedInt {
+                self.unsigned_abs()
+            }
+
             fn abs_diff(self, other: Self) -> $uty {
                 self.wrapping_sub(other).wrapping_abs() as $uty
             }