Add a generic version of ceil

Additionally, make use of this version to implement `ceil` and `ceilf`.

Musl's `ceilf` algorithm seems to work better for all versions of the
functions. Testing with a generic version of musl's `ceil` routine
showed the following regressions:

    icount::icount_bench_ceil_group::icount_bench_ceil logspace:setup_ceil()
    Performance has regressed: Instructions (14064 > 13171) regressed by +6.78005% (>+5.00000)
      Baselines:                      softfloat|softfloat
      Instructions:                       14064|13171                (+6.78005%) [+1.06780x]
      L1 Hits:                            16697|15803                (+5.65715%) [+1.05657x]
      L2 Hits:                                0|0                    (No change)
      RAM Hits:                               7|8                    (-12.5000%) [-1.14286x]
      Total read+write:                   16704|15811                (+5.64797%) [+1.05648x]
      Estimated Cycles:                   16942|16083                (+5.34104%) [+1.05341x]
    icount::icount_bench_ceilf_group::icount_bench_ceilf logspace:setup_ceilf()
    Performance has regressed: Instructions (14732 > 9901) regressed by +48.7931% (>+5.00000)
      Baselines:                      softfloat|softfloat
      Instructions:                       14732|9901                 (+48.7931%) [+1.48793x]
      L1 Hits:                            17494|12611                (+38.7202%) [+1.38720x]
      L2 Hits:                                0|0                    (No change)
      RAM Hits:                               6|6                    (No change)
      Total read+write:                   17500|12617                (+38.7018%) [+1.38702x]
      Estimated Cycles:                   17704|12821                (+38.0860%) [+1.38086x]

Author: tgross35

src/math/ceil.rs

@@ -1,8 +1,3 @@
-#![allow(unreachable_code)]
-use core::f64;
-
-const TOINT: f64 = 1. / f64::EPSILON;
-
 /// Ceil (f64)
 ///
 /// Finds the nearest integer greater than or equal to `x`.
@@ -15,40 +10,5 @@ pub fn ceil(x: f64) -> f64 {
         args: x,
     }
 
-    let u: u64 = x.to_bits();
-    let e: i64 = ((u >> 52) & 0x7ff) as i64;
-    let y: f64;
-
-    if e >= 0x3ff + 52 || x == 0. {
-        return x;
-    }
-    // y = int(x) - x, where int(x) is an integer neighbor of x
-    y = if (u >> 63) != 0 { x - TOINT + TOINT - x } else { x + TOINT - TOINT - x };
-    // special case because of non-nearest rounding modes
-    if e < 0x3ff {
-        force_eval!(y);
-        return if (u >> 63) != 0 { -0. } else { 1. };
-    }
-    if y < 0. { x + y + 1. } else { x + y }
-}
-
-#[cfg(test)]
-mod tests {
-    use super::*;
-
-    #[test]
-    fn sanity_check() {
-        assert_eq!(ceil(1.1), 2.0);
-        assert_eq!(ceil(2.9), 3.0);
-    }
-
-    /// The spec: https://en.cppreference.com/w/cpp/numeric/math/ceil
-    #[test]
-    fn spec_tests() {
-        // Not Asserted: that the current rounding mode has no effect.
-        assert!(ceil(f64::NAN).is_nan());
-        for f in [0.0, -0.0, f64::INFINITY, f64::NEG_INFINITY].iter().copied() {
-            assert_eq!(ceil(f), f);
-        }
-    }
+    super::generic::ceil(x)
 }

src/math/ceilf.rs

@@ -1,5 +1,3 @@
-use core::f32;
-
 /// Ceil (f32)
 ///
 /// Finds the nearest integer greater than or equal to `x`.
@@ -11,52 +9,5 @@ pub fn ceilf(x: f32) -> f32 {
         args: x,
     }
 
-    let mut ui = x.to_bits();
-    let e = (((ui >> 23) & 0xff).wrapping_sub(0x7f)) as i32;
-
-    if e >= 23 {
-        return x;
-    }
-    if e >= 0 {
-        let m = 0x007fffff >> e;
-        if (ui & m) == 0 {
-            return x;
-        }
-        force_eval!(x + f32::from_bits(0x7b800000));
-        if ui >> 31 == 0 {
-            ui += m;
-        }
-        ui &= !m;
-    } else {
-        force_eval!(x + f32::from_bits(0x7b800000));
-        if ui >> 31 != 0 {
-            return -0.0;
-        } else if ui << 1 != 0 {
-            return 1.0;
-        }
-    }
-    f32::from_bits(ui)
-}
-
-// PowerPC tests are failing on LLVM 13: https://github.com/rust-lang/rust/issues/88520
-#[cfg(not(target_arch = "powerpc64"))]
-#[cfg(test)]
-mod tests {
-    use super::*;
-
-    #[test]
-    fn sanity_check() {
-        assert_eq!(ceilf(1.1), 2.0);
-        assert_eq!(ceilf(2.9), 3.0);
-    }
-
-    /// The spec: https://en.cppreference.com/w/cpp/numeric/math/ceil
-    #[test]
-    fn spec_tests() {
-        // Not Asserted: that the current rounding mode has no effect.
-        assert!(ceilf(f32::NAN).is_nan());
-        for f in [0.0, -0.0, f32::INFINITY, f32::NEG_INFINITY].iter().copied() {
-            assert_eq!(ceilf(f), f);
-        }
-    }
+    super::generic::ceil(x)
 }

src/math/generic/ceil.rs

@@ -0,0 +1,87 @@
+/* SPDX-License-Identifier: MIT */
+/* origin: musl src/math/ceilf.c */
+
+//! Generic `ceil` algorithm.
+//!
+//! Note that this uses the algorithm from musl's `ceilf` rather than `ceil` or `ceill` because
+//! performance seems to be better (based on icount) and it does not seem to experience rounding
+//! errors on i386.
+
+use super::super::{Float, Int, IntTy, MinInt};
+
+pub fn ceil<F: Float>(x: F) -> F {
+    let zero = IntTy::<F>::ZERO;
+
+    let mut ix = x.to_bits();
+    let e = x.exp_unbiased();
+
+    // If the represented value has no fractional part, no truncation is needed.
+    if e >= F::SIG_BITS as i32 {
+        return x;
+    }
+
+    if e >= 0 {
+        // |x| >= 1.0
+
+        let m = F::SIG_MASK >> e.unsigned();
+        if (ix & m) == zero {
+            // Portion to be masked is already zero; no adjustment needed.
+            return x;
+        }
+
+        // Otherwise, raise an inexact exception.
+        force_eval!(x + F::MAX);
+        if x.is_sign_positive() {
+            ix += m;
+        }
+        ix &= !m;
+    } else {
+        // |x| < 1.0, raise an inexact exception since truncation will happen (unless x == 0).
+        force_eval!(x + F::MAX);
+
+        if x.is_sign_negative() {
+            // -1.0 < x <= -0.0; rounding up goes toward -0.0.
+            return F::NEG_ZERO;
+        } else if ix << 1 != zero {
+            // 0.0 < x < 1.0; rounding up goes toward +1.0.
+            return F::ONE;
+        }
+    }
+
+    F::from_bits(ix)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    /// Test against https://en.cppreference.com/w/cpp/numeric/math/ceil
+    fn spec_test<F: Float>() {
+        // Not Asserted: that the current rounding mode has no effect.
+        for f in [F::ZERO, F::NEG_ZERO, F::INFINITY, F::NEG_INFINITY].iter().copied() {
+            assert_biteq!(ceil(f), f);
+        }
+    }
+
+    #[test]
+    fn sanity_check_f32() {
+        assert_eq!(ceil(1.1f32), 2.0);
+        assert_eq!(ceil(2.9f32), 3.0);
+    }
+
+    #[test]
+    fn spec_tests_f32() {
+        spec_test::<f32>();
+    }
+
+    #[test]
+    fn sanity_check_f64() {
+        assert_eq!(ceil(1.1f64), 2.0);
+        assert_eq!(ceil(2.9f64), 3.0);
+    }
+
+    #[test]
+    fn spec_tests_f64() {
+        spec_test::<f64>();
+    }
+}

src/math/generic/mod.rs

@@ -1,9 +1,11 @@
+mod ceil;
 mod copysign;
 mod fabs;
 mod fdim;
 mod sqrt;
 mod trunc;
 
+pub use ceil::ceil;
 pub use copysign::copysign;
 pub use fabs::fabs;
 pub use fdim::fdim;