Improve sqrt/sqrtf if stable intrinsics allow

Author: Lokathor

src/math/sqrt.rs

@@ -95,128 +95,146 @@ pub fn sqrt(x: f64) -> f64 {
             }
         }
     }
-    let mut z: f64;
-    let sign: Wrapping<u32> = Wrapping(0x80000000);
-    let mut ix0: i32;
-    let mut s0: i32;
-    let mut q: i32;
-    let mut m: i32;
-    let mut t: i32;
-    let mut i: i32;
-    let mut r: Wrapping<u32>;
-    let mut t1: Wrapping<u32>;
-    let mut s1: Wrapping<u32>;
-    let mut ix1: Wrapping<u32>;
-    let mut q1: Wrapping<u32>;
+    #[cfg(target_feature="sse2")]
+    {
+      // Note(Lokathor): If compile time settings allow, we just use SSE2, since
+      // the sqrt in `std` on these platforms also compiles down to an SSE2
+      // instruction.
+      #[cfg(target_arch="x86")]
+      use core::arch::x86::*;
+      #[cfg(target_arch="x86_64")]
+      use core::arch::x86_64::*;
+      unsafe {
+        let m = _mm_set_sd(x);
+        let m_sqrt = _mm_sqrt_pd(m);
+        _mm_cvtsd_f64(m_sqrt)
+      }
+    }
+    #[cfg(not(target_feature="sse2"))]
+    {
+      let mut z: f64;
+      let sign: Wrapping<u32> = Wrapping(0x80000000);
+      let mut ix0: i32;
+      let mut s0: i32;
+      let mut q: i32;
+      let mut m: i32;
+      let mut t: i32;
+      let mut i: i32;
+      let mut r: Wrapping<u32>;
+      let mut t1: Wrapping<u32>;
+      let mut s1: Wrapping<u32>;
+      let mut ix1: Wrapping<u32>;
+      let mut q1: Wrapping<u32>;
 
-    ix0 = (x.to_bits() >> 32) as i32;
-    ix1 = Wrapping(x.to_bits() as u32);
+      ix0 = (x.to_bits() >> 32) as i32;
+      ix1 = Wrapping(x.to_bits() as u32);
 
-    /* take care of Inf and NaN */
-    if (ix0 & 0x7ff00000) == 0x7ff00000 {
-        return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
-    }
-    /* take care of zero */
-    if ix0 <= 0 {
-        if ((ix0 & !(sign.0 as i32)) | ix1.0 as i32) == 0 {
-            return x; /* sqrt(+-0) = +-0 */
-        }
-        if ix0 < 0 {
-            return (x - x) / (x - x); /* sqrt(-ve) = sNaN */
-        }
-    }
-    /* normalize x */
-    m = ix0 >> 20;
-    if m == 0 {
-        /* subnormal x */
-        while ix0 == 0 {
-            m -= 21;
-            ix0 |= (ix1 >> 11).0 as i32;
-            ix1 <<= 21;
-        }
-        i = 0;
-        while (ix0 & 0x00100000) == 0 {
-            i += 1;
-            ix0 <<= 1;
-        }
-        m -= i - 1;
-        ix0 |= (ix1 >> (32 - i) as usize).0 as i32;
-        ix1 = ix1 << i as usize;
-    }
-    m -= 1023; /* unbias exponent */
-    ix0 = (ix0 & 0x000fffff) | 0x00100000;
-    if (m & 1) == 1 {
-        /* odd m, double x to make it even */
-        ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
-        ix1 += ix1;
-    }
-    m >>= 1; /* m = [m/2] */
+      /* take care of Inf and NaN */
+      if (ix0 & 0x7ff00000) == 0x7ff00000 {
+          return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
+      }
+      /* take care of zero */
+      if ix0 <= 0 {
+          if ((ix0 & !(sign.0 as i32)) | ix1.0 as i32) == 0 {
+              return x; /* sqrt(+-0) = +-0 */
+          }
+          if ix0 < 0 {
+              return (x - x) / (x - x); /* sqrt(-ve) = sNaN */
+          }
+      }
+      /* normalize x */
+      m = ix0 >> 20;
+      if m == 0 {
+          /* subnormal x */
+          while ix0 == 0 {
+              m -= 21;
+              ix0 |= (ix1 >> 11).0 as i32;
+              ix1 <<= 21;
+          }
+          i = 0;
+          while (ix0 & 0x00100000) == 0 {
+              i += 1;
+              ix0 <<= 1;
+          }
+          m -= i - 1;
+          ix0 |= (ix1 >> (32 - i) as usize).0 as i32;
+          ix1 = ix1 << i as usize;
+      }
+      m -= 1023; /* unbias exponent */
+      ix0 = (ix0 & 0x000fffff) | 0x00100000;
+      if (m & 1) == 1 {
+          /* odd m, double x to make it even */
+          ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
+          ix1 += ix1;
+      }
+      m >>= 1; /* m = [m/2] */
 
-    /* generate sqrt(x) bit by bit */
-    ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
-    ix1 += ix1;
-    q = 0; /* [q,q1] = sqrt(x) */
-    q1 = Wrapping(0);
-    s0 = 0;
-    s1 = Wrapping(0);
-    r = Wrapping(0x00200000); /* r = moving bit from right to left */
+      /* generate sqrt(x) bit by bit */
+      ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
+      ix1 += ix1;
+      q = 0; /* [q,q1] = sqrt(x) */
+      q1 = Wrapping(0);
+      s0 = 0;
+      s1 = Wrapping(0);
+      r = Wrapping(0x00200000); /* r = moving bit from right to left */
 
-    while r != Wrapping(0) {
-        t = s0 + r.0 as i32;
-        if t <= ix0 {
-            s0 = t + r.0 as i32;
-            ix0 -= t;
-            q += r.0 as i32;
-        }
-        ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
-        ix1 += ix1;
-        r >>= 1;
-    }
+      while r != Wrapping(0) {
+          t = s0 + r.0 as i32;
+          if t <= ix0 {
+              s0 = t + r.0 as i32;
+              ix0 -= t;
+              q += r.0 as i32;
+          }
+          ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
+          ix1 += ix1;
+          r >>= 1;
+      }
 
-    r = sign;
-    while r != Wrapping(0) {
-        t1 = s1 + r;
-        t = s0;
-        if t < ix0 || (t == ix0 && t1 <= ix1) {
-            s1 = t1 + r;
-            if (t1 & sign) == sign && (s1 & sign) == Wrapping(0) {
-                s0 += 1;
-            }
-            ix0 -= t;
-            if ix1 < t1 {
-                ix0 -= 1;
-            }
-            ix1 -= t1;
-            q1 += r;
-        }
-        ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
-        ix1 += ix1;
-        r >>= 1;
-    }
+      r = sign;
+      while r != Wrapping(0) {
+          t1 = s1 + r;
+          t = s0;
+          if t < ix0 || (t == ix0 && t1 <= ix1) {
+              s1 = t1 + r;
+              if (t1 & sign) == sign && (s1 & sign) == Wrapping(0) {
+                  s0 += 1;
+              }
+              ix0 -= t;
+              if ix1 < t1 {
+                  ix0 -= 1;
+              }
+              ix1 -= t1;
+              q1 += r;
+          }
+          ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
+          ix1 += ix1;
+          r >>= 1;
+      }
 
-    /* use floating add to find out rounding direction */
-    if (ix0 as u32 | ix1.0) != 0 {
-        z = 1.0 - TINY; /* raise inexact flag */
-        if z >= 1.0 {
-            z = 1.0 + TINY;
-            if q1.0 == 0xffffffff {
-                q1 = Wrapping(0);
-                q += 1;
-            } else if z > 1.0 {
-                if q1.0 == 0xfffffffe {
-                    q += 1;
-                }
-                q1 += Wrapping(2);
-            } else {
-                q1 += q1 & Wrapping(1);
-            }
-        }
-    }
-    ix0 = (q >> 1) + 0x3fe00000;
-    ix1 = q1 >> 1;
-    if (q & 1) == 1 {
-        ix1 |= sign;
+      /* use floating add to find out rounding direction */
+      if (ix0 as u32 | ix1.0) != 0 {
+          z = 1.0 - TINY; /* raise inexact flag */
+          if z >= 1.0 {
+              z = 1.0 + TINY;
+              if q1.0 == 0xffffffff {
+                  q1 = Wrapping(0);
+                  q += 1;
+              } else if z > 1.0 {
+                  if q1.0 == 0xfffffffe {
+                      q += 1;
+                  }
+                  q1 += Wrapping(2);
+              } else {
+                  q1 += q1 & Wrapping(1);
+              }
+          }
+      }
+      ix0 = (q >> 1) + 0x3fe00000;
+      ix1 = q1 >> 1;
+      if (q & 1) == 1 {
+          ix1 |= sign;
+      }
+      ix0 += m << 20;
+      f64::from_bits((ix0 as u64) << 32 | ix1.0 as u64)
     }
-    ix0 += m << 20;
-    f64::from_bits((ix0 as u64) << 32 | ix1.0 as u64)
 }