Merge rust-lang/libm#117

117: implement cosh r=japaric a=kirch7

`cosh(f64)` implemented. I had to implement `__expo2(f64)` also.

Co-authored-by: Cássio Kirch <cassio.kirch@inf.ufrgs.br>
Co-authored-by: Jorge Aparicio <jorge@japaric.io>

library/compiler-builtins/libm/src/lib.rs

@@ -394,7 +394,6 @@ pub trait F64Ext: private::Sealed + Sized {
 
     fn sinh(self) -> Self;
 
-    #[cfg(todo)]
     fn cosh(self) -> Self;
 
     fn tanh(self) -> Self;
@@ -569,7 +568,6 @@ impl F64Ext for f64 {
         sinh(self)
     }
 
-    #[cfg(todo)]
     #[inline]
     fn cosh(self) -> Self {
         cosh(self)

library/compiler-builtins/libm/src/math/cosh.rs

@@ -0,0 +1,33 @@
+use super::exp;
+use super::expm1;
+use super::k_expo2;
+
+#[inline]
+pub fn cosh(mut x: f64) -> f64 {
+    /* |x| */
+    let mut ix = x.to_bits();
+    ix &= 0x7fffffffffffffff;
+    x = f64::from_bits(ix);
+    let w = ix >> 32;
+
+    /* |x| < log(2) */
+    if w < 0x3fe62e42 {
+        if w < 0x3ff00000 - (26 << 20) {
+            let x1p120 = f64::from_bits(0x4770000000000000);
+            force_eval!(x + x1p120);
+            return 1.;
+        }
+        let t = expm1(x); // exponential minus 1
+        return 1. + t * t / (2. * (1. + t));
+    }
+
+    /* |x| < log(DBL_MAX) */
+    if w < 0x40862e42 {
+        let t = exp(x);
+        /* note: if x>log(0x1p26) then the 1/t is not needed */
+        return 0.5 * (t + 1. / t);
+    }
+
+    /* |x| > log(DBL_MAX) or nan */
+    k_expo2(x)
+}

library/compiler-builtins/libm/src/math/k_expo2.rs

@@ -0,0 +1,14 @@
+use super::exp;
+
+/* k is such that k*ln2 has minimal relative error and x - kln2 > log(FLT_MIN) */
+const K: i32 = 2043;
+
+/* expf(x)/2 for x >= log(FLT_MAX), slightly better than 0.5f*expf(x/2)*expf(x/2) */
+#[inline]
+pub(crate) fn k_expo2(x: f64) -> f64 {
+    let k_ln2 = f64::from_bits(0x40962066151add8b);
+    /* note that k is odd and scale*scale overflows */
+    let scale = f64::from_bits(((((0x3ff + K / 2) as u32) << 20) as u64) << 32);
+    /* exp(x - k ln2) * 2**(k-1) */
+    exp(x - k_ln2) * scale * scale
+}

library/compiler-builtins/libm/src/math/mod.rs

@@ -19,6 +19,7 @@ mod ceil;
 mod ceilf;
 mod cos;
 mod cosf;
+mod cosh;
 mod coshf;
 mod exp;
 mod exp2;
@@ -77,6 +78,7 @@ pub use self::ceil::ceil;
 pub use self::ceilf::ceilf;
 pub use self::cos::cos;
 pub use self::cosf::cosf;
+pub use self::cosh::cosh;
 pub use self::coshf::coshf;
 pub use self::exp::exp;
 pub use self::exp2::exp2;
@@ -127,6 +129,7 @@ mod expo2;
 mod fenv;
 mod k_cos;
 mod k_cosf;
+mod k_expo2;
 mod k_expo2f;
 mod k_sin;
 mod k_sinf;
@@ -140,6 +143,7 @@ mod rem_pio2f;
 use self::expo2::expo2;
 use self::k_cos::k_cos;
 use self::k_cosf::k_cosf;
+use self::k_expo2::k_expo2;
 use self::k_expo2f::k_expo2f;
 use self::k_sin::k_sin;
 use self::k_sinf::k_sinf;

library/compiler-builtins/libm/test-generator/src/main.rs

@@ -703,7 +703,7 @@ f64_f64! {
     cbrt,
     ceil,
     cos,
-    // cosh,
+    cosh,
     exp,
     exp2,
     expm1,