diff --git a/README.md b/README.md
index 61a6ebfb3..6299687d4 100644
--- a/README.md
+++ b/README.md
@@ -1,3 +1,7 @@
+[![crates.io](https://img.shields.io/crates/v/libm.svg)](https://crates.io/crates/libm)
+[![docs.rs](https://docs.rs/libm/badge.svg)](https://docs.rs/libm/)
+[![Build Status](https://dev.azure.com/rust-lang/libm/_apis/build/status/rust-lang-nursery.libm?branchName=master)](https://dev.azure.com/rust-lang/libm/_build/latest?definitionId=7&branchName=master)
+
 # `libm`
 
 A port of [MUSL]'s libm to Rust.
diff --git a/src/lib.rs b/src/lib.rs
index e228af9b3..0727c8e5f 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,10 +1,7 @@
 //! libm in pure Rust
 #![deny(warnings)]
 #![no_std]
-#![cfg_attr(
-    all(target_arch = "wasm32", feature = "unstable"),
-    feature(core_intrinsics)
-)]
+#![cfg_attr(feature = "unstable", feature(core_intrinsics))]
 #![allow(clippy::unreadable_literal)]
 #![allow(clippy::many_single_char_names)]
 #![allow(clippy::needless_return)]
diff --git a/src/math/sqrt.rs b/src/math/sqrt.rs
index f06b209a4..b2bcfbd2a 100644
--- a/src/math/sqrt.rs
+++ b/src/math/sqrt.rs
@@ -1,3 +1,54 @@
+/// [Square root](https://en.wikipedia.org/wiki/Square_root) of an `f64`.
+///
+/// This function is intended to exactly match the
+/// [`sqrt`](https://en.cppreference.com/w/c/numeric/math/sqrt) function as
+/// defined by the C/C++ spec.
+#[allow(unreachable_code)]
+pub fn sqrt(x: f64) -> f64 {
+    // On most targets LLVM will issue a hardware sqrt instruction instead of a
+    // call to this function when you call `core::intrinsics::sqrtf64(x)`.
+    // However, not all targets have hardware sqrt, and also people might end up
+    // calling this function directly, so we must still do our best to get a
+    // hardware instruction used, and then go with a software fallback if
+    // necessary.
+
+    // Nightly: if we're *sure* that LLVM supports a hardware instruction then
+    // we'll call the LLVM intrinsic. We have to be conservative in our
+    // selection for when to do this, because if the intrinsic usage ends up
+    // calling back here it's infinite recursion.
+    #[cfg(all(
+        feature = "unstable",
+        any(
+            all(target_arch = "x86", not(target_feature = "soft-float")),
+            all(target_arch = "x86_64", not(target_feature = "soft-float")),
+            all(target_arch = "aarch64", not(target_feature = "soft-float")),
+            all(target_arch = "powerpc", target_feature = "hard-float"),
+            all(target_arch = "powerpc64", target_feature = "hard-float"),
+            all(target_arch = "risc", target_feature = "d"),
+            target_arch = "wasm32",
+        )
+    ))]
+    {
+        return unsafe { core::intrinsics::sqrtf64(x) };
+    }
+    // Stable: We can use `sse2` if available. As more intrinsic sets stabilize
+    // we can expand this to use hardware more often.
+    #[cfg(target_feature = "sse2")]
+    {
+        #[cfg(target_arch = "x86")]
+        use core::arch::x86::*;
+        #[cfg(target_arch = "x86_64")]
+        use core::arch::x86_64::*;
+        return unsafe {
+            let m = _mm_set_sd(x);
+            let m_sqrt = _mm_sqrt_pd(m);
+            _mm_cvtsd_f64(m_sqrt)
+        };
+    }
+    // Finally, if we must, we use the software version (below).
+    software_sqrt(x)
+}
+
 /* origin: FreeBSD /usr/src/lib/msun/src/e_sqrt.c */
 /*
  * ====================================================
@@ -75,169 +126,136 @@
  *      sqrt(-ve) = NaN         ... with invalid signal
  *      sqrt(NaN) = NaN         ... with invalid signal for signaling NaN
  */
-
-use core::f64;
-
 #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
-pub fn sqrt(x: f64) -> f64 {
-    // On wasm32 we know that LLVM's intrinsic will compile to an optimized
-    // `f64.sqrt` native instruction, so we can leverage this for both code size
-    // and speed.
-    llvm_intrinsically_optimized! {
-        #[cfg(target_arch = "wasm32")] {
-            return if x < 0.0 {
-                f64::NAN
-            } else {
-                unsafe { ::core::intrinsics::sqrtf64(x) }
-            }
-        }
-    }
-    #[cfg(target_feature = "sse2")]
-    {
-        // Note: This path is unlikely since LLVM will usually have already
-        // optimized sqrt calls into hardware instructions if sse2 is available,
-        // but if someone does end up here they'll apprected the speed increase.
-        #[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"))]
-    {
-        use core::num::Wrapping;
+fn software_sqrt(x: f64) -> f64 {
+    use core::num::Wrapping;
 
-        const TINY: f64 = 1.0e-300;
+    const TINY: f64 = 1.0e-300;
 
-        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>;
+    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 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 */
         }
-        /* 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 */
-            }
+        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;
+    }
+    /* normalize x */
+    m = ix0 >> 20;
+    if m == 0 {
+        /* subnormal x */
+        while ix0 == 0 {
+            m -= 21;
+            ix0 |= (ix1 >> 11).0 as i32;
+            ix1 <<= 21;
         }
-        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;
+        i = 0;
+        while (ix0 & 0x00100000) == 0 {
+            i += 1;
+            ix0 <<= 1;
         }
-        m >>= 1; /* m = [m/2] */
-
-        /* generate sqrt(x) bit by bit */
+        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;
-        q = 0; /* [q,q1] = sqrt(x) */
-        q1 = Wrapping(0);
-        s0 = 0;
-        s1 = Wrapping(0);
-        r = Wrapping(0x00200000); /* r = moving bit from right to left */
+    }
+    m >>= 1; /* m = [m/2] */
 
-        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;
+    /* 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;
+    }
 
-        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;
+    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 += ix0 + ((ix1 & sign) >> 31).0 as i32;
-            ix1 += ix1;
-            r >>= 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);
+    /* 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;
-                } else if z > 1.0 {
-                    if q1.0 == 0xfffffffe {
-                        q += 1;
-                    }
-                    q1 += Wrapping(2);
-                } else {
-                    q1 += q1 & Wrapping(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 = (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)
 }
 
 #[cfg(test)]
diff --git a/src/math/sqrtf.rs b/src/math/sqrtf.rs
index ee868c8c8..b43e797dc 100644
--- a/src/math/sqrtf.rs
+++ b/src/math/sqrtf.rs
@@ -1,3 +1,47 @@
+/// [Square root](https://en.wikipedia.org/wiki/Square_root) of an `f32`.
+///
+/// This function is intended to exactly match the
+/// [`sqrtf`](https://en.cppreference.com/w/c/numeric/math/sqrt) function as
+/// defined by the C/C++ spec.
+#[allow(unreachable_code)]
+pub fn sqrtf(x: f32) -> f32 {
+    // See the notes in the `sqrt` function for an explanation of what's going on
+    // here.
+
+    // Nightly
+    #[cfg(all(
+        feature = "unstable",
+        any(
+            all(target_arch = "x86", not(target_feature = "soft-float")),
+            all(target_arch = "x86_64", not(target_feature = "soft-float")),
+            all(target_arch = "arm", not(target_feature = "soft-float")),
+            all(target_arch = "aarch64", not(target_feature = "soft-float")),
+            all(target_arch = "powerpc", target_feature = "hard-float"),
+            all(target_arch = "powerpc64", target_feature = "hard-float"),
+            all(target_arch = "risc", target_feature = "f"),
+            target_arch = "wasm32",
+        )
+    ))]
+    {
+        return unsafe { core::intrinsics::sqrtf32(x) };
+    }
+    // Stable
+    #[cfg(target_feature = "sse2")]
+    {
+        #[cfg(target_arch = "x86")]
+        use core::arch::x86::*;
+        #[cfg(target_arch = "x86_64")]
+        use core::arch::x86_64::*;
+        return unsafe {
+            let m = _mm_set_ss(x);
+            let m_sqrt = _mm_sqrt_ss(m);
+            _mm_cvtss_f32(m_sqrt)
+        };
+    }
+    // Fallback
+    software_sqrtf(x)
+}
+
 /* origin: FreeBSD /usr/src/lib/msun/src/e_sqrtf.c */
 /*
  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
@@ -12,120 +56,89 @@
  * is preserved.
  * ====================================================
  */
-
 #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
-pub fn sqrtf(x: f32) -> f32 {
-    // On wasm32 we know that LLVM's intrinsic will compile to an optimized
-    // `f32.sqrt` native instruction, so we can leverage this for both code size
-    // and speed.
-    llvm_intrinsically_optimized! {
-        #[cfg(target_arch = "wasm32")] {
-            return if x < 0.0 {
-                ::core::f32::NAN
-            } else {
-                unsafe { ::core::intrinsics::sqrtf32(x) }
-            }
-        }
-    }
-    #[cfg(target_feature = "sse")]
-    {
-        // Note: This path is unlikely since LLVM will usually have already
-        // optimized sqrt calls into hardware instructions if sse is available,
-        // but if someone does end up here they'll apprected the speed increase.
-        #[cfg(target_arch = "x86")]
-        use core::arch::x86::*;
-        #[cfg(target_arch = "x86_64")]
-        use core::arch::x86_64::*;
-        unsafe {
-            let m = _mm_set_ss(x);
-            let m_sqrt = _mm_sqrt_ss(m);
-            _mm_cvtss_f32(m_sqrt)
-        }
-    }
-    #[cfg(not(target_feature = "sse"))]
-    {
-        const TINY: f32 = 1.0e-30;
+fn software_sqrtf(x: f32) -> f32 {
+    const TINY: f32 = 1.0e-30;
 
-        let mut z: f32;
-        let sign: i32 = 0x80000000u32 as i32;
-        let mut ix: i32;
-        let mut s: i32;
-        let mut q: i32;
-        let mut m: i32;
-        let mut t: i32;
-        let mut i: i32;
-        let mut r: u32;
+    let mut z: f32;
+    let sign: i32 = 0x80000000u32 as i32;
+    let mut ix: i32;
+    let mut s: i32;
+    let mut q: i32;
+    let mut m: i32;
+    let mut t: i32;
+    let mut i: i32;
+    let mut r: u32;
 
-        ix = x.to_bits() as i32;
+    ix = x.to_bits() as i32;
 
-        /* take care of Inf and NaN */
-        if (ix as u32 & 0x7f800000) == 0x7f800000 {
-            return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
-        }
+    /* take care of Inf and NaN */
+    if (ix as u32 & 0x7f800000) == 0x7f800000 {
+        return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
+    }
 
-        /* take care of zero */
-        if ix <= 0 {
-            if (ix & !sign) == 0 {
-                return x; /* sqrt(+-0) = +-0 */
-            }
-            if ix < 0 {
-                return (x - x) / (x - x); /* sqrt(-ve) = sNaN */
-            }
+    /* take care of zero */
+    if ix <= 0 {
+        if (ix & !sign) == 0 {
+            return x; /* sqrt(+-0) = +-0 */
         }
-
-        /* normalize x */
-        m = ix >> 23;
-        if m == 0 {
-            /* subnormal x */
-            i = 0;
-            while ix & 0x00800000 == 0 {
-                ix <<= 1;
-                i = i + 1;
-            }
-            m -= i - 1;
+        if ix < 0 {
+            return (x - x) / (x - x); /* sqrt(-ve) = sNaN */
         }
-        m -= 127; /* unbias exponent */
-        ix = (ix & 0x007fffff) | 0x00800000;
-        if m & 1 == 1 {
-            /* odd m, double x to make it even */
-            ix += ix;
-        }
-        m >>= 1; /* m = [m/2] */
+    }
 
-        /* generate sqrt(x) bit by bit */
+    /* normalize x */
+    m = ix >> 23;
+    if m == 0 {
+        /* subnormal x */
+        i = 0;
+        while ix & 0x00800000 == 0 {
+            ix <<= 1;
+            i = i + 1;
+        }
+        m -= i - 1;
+    }
+    m -= 127; /* unbias exponent */
+    ix = (ix & 0x007fffff) | 0x00800000;
+    if m & 1 == 1 {
+        /* odd m, double x to make it even */
         ix += ix;
-        q = 0;
-        s = 0;
-        r = 0x01000000; /* r = moving bit from right to left */
+    }
+    m >>= 1; /* m = [m/2] */
 
-        while r != 0 {
-            t = s + r as i32;
-            if t <= ix {
-                s = t + r as i32;
-                ix -= t;
-                q += r as i32;
-            }
-            ix += ix;
-            r >>= 1;
+    /* generate sqrt(x) bit by bit */
+    ix += ix;
+    q = 0;
+    s = 0;
+    r = 0x01000000; /* r = moving bit from right to left */
+
+    while r != 0 {
+        t = s + r as i32;
+        if t <= ix {
+            s = t + r as i32;
+            ix -= t;
+            q += r as i32;
         }
+        ix += ix;
+        r >>= 1;
+    }
 
-        /* use floating add to find out rounding direction */
-        if ix != 0 {
-            z = 1.0 - TINY; /* raise inexact flag */
-            if z >= 1.0 {
-                z = 1.0 + TINY;
-                if z > 1.0 {
-                    q += 2;
-                } else {
-                    q += q & 1;
-                }
+    /* use floating add to find out rounding direction */
+    if ix != 0 {
+        z = 1.0 - TINY; /* raise inexact flag */
+        if z >= 1.0 {
+            z = 1.0 + TINY;
+            if z > 1.0 {
+                q += 2;
+            } else {
+                q += q & 1;
             }
         }
-
-        ix = (q >> 1) + 0x3f000000;
-        ix += m << 23;
-        f32::from_bits(ix as u32)
     }
+
+    ix = (q >> 1) + 0x3f000000;
+    ix += m << 23;
+    f32::from_bits(ix as u32)
 }
 
 #[cfg(test)]