Rollup merge of #128417 - tgross35:f16-f128-math, r=dtolnay

Add `f16` and `f128` math functions

This adds intrinsics and math functions for `f16` and `f128` floating point types. Support is quite limited and some things are broken so tests don't run on many platforms, but this provides a starting point.

library/std/src/f128/tests.rs

@@ -4,6 +4,21 @@
 use crate::f128::consts;
 use crate::num::{FpCategory as Fp, *};
 
+// Note these tolerances make sense around zero, but not for more extreme exponents.
+
+/// For operations that are near exact, usually not involving math of different
+/// signs.
+const TOL_PRECISE: f128 = 1e-28;
+
+/// Default tolerances. Works for values that should be near precise but not exact. Roughly
+/// the precision carried by `100 * 100`.
+const TOL: f128 = 1e-12;
+
+/// Tolerances for math that is allowed to be imprecise, usually due to multiple chained
+/// operations.
+#[cfg(reliable_f128_math)]
+const TOL_IMPR: f128 = 1e-10;
+
 /// Smallest number
 const TINY_BITS: u128 = 0x1;
 
@@ -41,7 +56,33 @@ fn test_num_f128() {
     test_num(10f128, 2f128);
 }
 
-// FIXME(f16_f128): add min and max tests when available
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_min_nan() {
+    assert_eq!(f128::NAN.min(2.0), 2.0);
+    assert_eq!(2.0f128.min(f128::NAN), 2.0);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_max_nan() {
+    assert_eq!(f128::NAN.max(2.0), 2.0);
+    assert_eq!(2.0f128.max(f128::NAN), 2.0);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_minimum() {
+    assert!(f128::NAN.minimum(2.0).is_nan());
+    assert!(2.0f128.minimum(f128::NAN).is_nan());
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_maximum() {
+    assert!(f128::NAN.maximum(2.0).is_nan());
+    assert!(2.0f128.maximum(f128::NAN).is_nan());
+}
 
 #[test]
 fn test_nan() {
@@ -191,9 +232,100 @@ fn test_classify() {
     assert_eq!(1e-4932f128.classify(), Fp::Subnormal);
 }
 
-// FIXME(f16_f128): add missing math functions when available
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_floor() {
+    assert_approx_eq!(1.0f128.floor(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.3f128.floor(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.5f128.floor(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.7f128.floor(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(0.0f128.floor(), 0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-0.0f128).floor(), -0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.0f128).floor(), -1.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.3f128).floor(), -2.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.5f128).floor(), -2.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.7f128).floor(), -2.0f128, TOL_PRECISE);
+}
 
 #[test]
+#[cfg(reliable_f128_math)]
+fn test_ceil() {
+    assert_approx_eq!(1.0f128.ceil(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.3f128.ceil(), 2.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.5f128.ceil(), 2.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.7f128.ceil(), 2.0f128, TOL_PRECISE);
+    assert_approx_eq!(0.0f128.ceil(), 0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-0.0f128).ceil(), -0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.0f128).ceil(), -1.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.3f128).ceil(), -1.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.5f128).ceil(), -1.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.7f128).ceil(), -1.0f128, TOL_PRECISE);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_round() {
+    assert_approx_eq!(2.5f128.round(), 3.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.0f128.round(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.3f128.round(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.5f128.round(), 2.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.7f128.round(), 2.0f128, TOL_PRECISE);
+    assert_approx_eq!(0.0f128.round(), 0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-0.0f128).round(), -0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.0f128).round(), -1.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.3f128).round(), -1.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.5f128).round(), -2.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.7f128).round(), -2.0f128, TOL_PRECISE);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_round_ties_even() {
+    assert_approx_eq!(2.5f128.round_ties_even(), 2.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.0f128.round_ties_even(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.3f128.round_ties_even(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.5f128.round_ties_even(), 2.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.7f128.round_ties_even(), 2.0f128, TOL_PRECISE);
+    assert_approx_eq!(0.0f128.round_ties_even(), 0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-0.0f128).round_ties_even(), -0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.0f128).round_ties_even(), -1.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.3f128).round_ties_even(), -1.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.5f128).round_ties_even(), -2.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.7f128).round_ties_even(), -2.0f128, TOL_PRECISE);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_trunc() {
+    assert_approx_eq!(1.0f128.trunc(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.3f128.trunc(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.5f128.trunc(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.7f128.trunc(), 1.0f128, TOL_PRECISE);
+    assert_approx_eq!(0.0f128.trunc(), 0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-0.0f128).trunc(), -0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.0f128).trunc(), -1.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.3f128).trunc(), -1.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.5f128).trunc(), -1.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.7f128).trunc(), -1.0f128, TOL_PRECISE);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_fract() {
+    assert_approx_eq!(1.0f128.fract(), 0.0f128, TOL_PRECISE);
+    assert_approx_eq!(1.3f128.fract(), 0.3f128, TOL_PRECISE);
+    assert_approx_eq!(1.5f128.fract(), 0.5f128, TOL_PRECISE);
+    assert_approx_eq!(1.7f128.fract(), 0.7f128, TOL_PRECISE);
+    assert_approx_eq!(0.0f128.fract(), 0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-0.0f128).fract(), -0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.0f128).fract(), -0.0f128, TOL_PRECISE);
+    assert_approx_eq!((-1.3f128).fract(), -0.3f128, TOL_PRECISE);
+    assert_approx_eq!((-1.5f128).fract(), -0.5f128, TOL_PRECISE);
+    assert_approx_eq!((-1.7f128).fract(), -0.7f128, TOL_PRECISE);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
 fn test_abs() {
     assert_eq!(f128::INFINITY.abs(), f128::INFINITY);
     assert_eq!(1f128.abs(), 1f128);
@@ -293,6 +425,24 @@ fn test_next_down() {
 }
 
 #[test]
+#[cfg(reliable_f128_math)]
+fn test_mul_add() {
+    let nan: f128 = f128::NAN;
+    let inf: f128 = f128::INFINITY;
+    let neg_inf: f128 = f128::NEG_INFINITY;
+    assert_approx_eq!(12.3f128.mul_add(4.5, 6.7), 62.05, TOL_PRECISE);
+    assert_approx_eq!((-12.3f128).mul_add(-4.5, -6.7), 48.65, TOL_PRECISE);
+    assert_approx_eq!(0.0f128.mul_add(8.9, 1.2), 1.2, TOL_PRECISE);
+    assert_approx_eq!(3.4f128.mul_add(-0.0, 5.6), 5.6, TOL_PRECISE);
+    assert!(nan.mul_add(7.8, 9.0).is_nan());
+    assert_eq!(inf.mul_add(7.8, 9.0), inf);
+    assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
+    assert_eq!(8.9f128.mul_add(inf, 3.2), inf);
+    assert_eq!((-3.2f128).mul_add(2.4, neg_inf), neg_inf);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
 fn test_recip() {
     let nan: f128 = f128::NAN;
     let inf: f128 = f128::INFINITY;
@@ -301,11 +451,161 @@ fn test_recip() {
     assert_eq!(2.0f128.recip(), 0.5);
     assert_eq!((-0.4f128).recip(), -2.5);
     assert_eq!(0.0f128.recip(), inf);
+    assert_approx_eq!(
+        f128::MAX.recip(),
+        8.40525785778023376565669454330438228902076605e-4933,
+        1e-4900
+    );
     assert!(nan.recip().is_nan());
     assert_eq!(inf.recip(), 0.0);
     assert_eq!(neg_inf.recip(), 0.0);
 }
 
+// Many math functions allow for less accurate results, so the next tolerance up is used
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_powi() {
+    let nan: f128 = f128::NAN;
+    let inf: f128 = f128::INFINITY;
+    let neg_inf: f128 = f128::NEG_INFINITY;
+    assert_eq!(1.0f128.powi(1), 1.0);
+    assert_approx_eq!((-3.1f128).powi(2), 9.6100000000000005506706202140776519387, TOL);
+    assert_approx_eq!(5.9f128.powi(-2), 0.028727377190462507313100483690639638451, TOL);
+    assert_eq!(8.3f128.powi(0), 1.0);
+    assert!(nan.powi(2).is_nan());
+    assert_eq!(inf.powi(3), inf);
+    assert_eq!(neg_inf.powi(2), inf);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_powf() {
+    let nan: f128 = f128::NAN;
+    let inf: f128 = f128::INFINITY;
+    let neg_inf: f128 = f128::NEG_INFINITY;
+    assert_eq!(1.0f128.powf(1.0), 1.0);
+    assert_approx_eq!(3.4f128.powf(4.5), 246.40818323761892815995637964326426756, TOL_IMPR);
+    assert_approx_eq!(2.7f128.powf(-3.2), 0.041652009108526178281070304373500889273, TOL_IMPR);
+    assert_approx_eq!((-3.1f128).powf(2.0), 9.6100000000000005506706202140776519387, TOL_IMPR);
+    assert_approx_eq!(5.9f128.powf(-2.0), 0.028727377190462507313100483690639638451, TOL_IMPR);
+    assert_eq!(8.3f128.powf(0.0), 1.0);
+    assert!(nan.powf(2.0).is_nan());
+    assert_eq!(inf.powf(2.0), inf);
+    assert_eq!(neg_inf.powf(3.0), neg_inf);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_sqrt_domain() {
+    assert!(f128::NAN.sqrt().is_nan());
+    assert!(f128::NEG_INFINITY.sqrt().is_nan());
+    assert!((-1.0f128).sqrt().is_nan());
+    assert_eq!((-0.0f128).sqrt(), -0.0);
+    assert_eq!(0.0f128.sqrt(), 0.0);
+    assert_eq!(1.0f128.sqrt(), 1.0);
+    assert_eq!(f128::INFINITY.sqrt(), f128::INFINITY);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_exp() {
+    assert_eq!(1.0, 0.0f128.exp());
+    assert_approx_eq!(consts::E, 1.0f128.exp(), TOL);
+    assert_approx_eq!(148.41315910257660342111558004055227962348775, 5.0f128.exp(), TOL);
+
+    let inf: f128 = f128::INFINITY;
+    let neg_inf: f128 = f128::NEG_INFINITY;
+    let nan: f128 = f128::NAN;
+    assert_eq!(inf, inf.exp());
+    assert_eq!(0.0, neg_inf.exp());
+    assert!(nan.exp().is_nan());
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_exp2() {
+    assert_eq!(32.0, 5.0f128.exp2());
+    assert_eq!(1.0, 0.0f128.exp2());
+
+    let inf: f128 = f128::INFINITY;
+    let neg_inf: f128 = f128::NEG_INFINITY;
+    let nan: f128 = f128::NAN;
+    assert_eq!(inf, inf.exp2());
+    assert_eq!(0.0, neg_inf.exp2());
+    assert!(nan.exp2().is_nan());
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_ln() {
+    let nan: f128 = f128::NAN;
+    let inf: f128 = f128::INFINITY;
+    let neg_inf: f128 = f128::NEG_INFINITY;
+    assert_approx_eq!(1.0f128.exp().ln(), 1.0, TOL);
+    assert!(nan.ln().is_nan());
+    assert_eq!(inf.ln(), inf);
+    assert!(neg_inf.ln().is_nan());
+    assert!((-2.3f128).ln().is_nan());
+    assert_eq!((-0.0f128).ln(), neg_inf);
+    assert_eq!(0.0f128.ln(), neg_inf);
+    assert_approx_eq!(4.0f128.ln(), 1.3862943611198906188344642429163531366, TOL);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_log() {
+    let nan: f128 = f128::NAN;
+    let inf: f128 = f128::INFINITY;
+    let neg_inf: f128 = f128::NEG_INFINITY;
+    assert_eq!(10.0f128.log(10.0), 1.0);
+    assert_approx_eq!(2.3f128.log(3.5), 0.66485771361478710036766645911922010272, TOL);
+    assert_eq!(1.0f128.exp().log(1.0f128.exp()), 1.0);
+    assert!(1.0f128.log(1.0).is_nan());
+    assert!(1.0f128.log(-13.9).is_nan());
+    assert!(nan.log(2.3).is_nan());
+    assert_eq!(inf.log(10.0), inf);
+    assert!(neg_inf.log(8.8).is_nan());
+    assert!((-2.3f128).log(0.1).is_nan());
+    assert_eq!((-0.0f128).log(2.0), neg_inf);
+    assert_eq!(0.0f128.log(7.0), neg_inf);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_log2() {
+    let nan: f128 = f128::NAN;
+    let inf: f128 = f128::INFINITY;
+    let neg_inf: f128 = f128::NEG_INFINITY;
+    assert_approx_eq!(10.0f128.log2(), 3.32192809488736234787031942948939017, TOL);
+    assert_approx_eq!(2.3f128.log2(), 1.2016338611696504130002982471978765921, TOL);
+    assert_approx_eq!(1.0f128.exp().log2(), 1.4426950408889634073599246810018921381, TOL);
+    assert!(nan.log2().is_nan());
+    assert_eq!(inf.log2(), inf);
+    assert!(neg_inf.log2().is_nan());
+    assert!((-2.3f128).log2().is_nan());
+    assert_eq!((-0.0f128).log2(), neg_inf);
+    assert_eq!(0.0f128.log2(), neg_inf);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_log10() {
+    let nan: f128 = f128::NAN;
+    let inf: f128 = f128::INFINITY;
+    let neg_inf: f128 = f128::NEG_INFINITY;
+    assert_eq!(10.0f128.log10(), 1.0);
+    assert_approx_eq!(2.3f128.log10(), 0.36172783601759284532595218865859309898, TOL);
+    assert_approx_eq!(1.0f128.exp().log10(), 0.43429448190325182765112891891660508222, TOL);
+    assert_eq!(1.0f128.log10(), 0.0);
+    assert!(nan.log10().is_nan());
+    assert_eq!(inf.log10(), inf);
+    assert!(neg_inf.log10().is_nan());
+    assert!((-2.3f128).log10().is_nan());
+    assert_eq!((-0.0f128).log10(), neg_inf);
+    assert_eq!(0.0f128.log10(), neg_inf);
+}
+
 #[test]
 fn test_to_degrees() {
     let pi: f128 = consts::PI;
@@ -313,8 +613,8 @@ fn test_to_degrees() {
     let inf: f128 = f128::INFINITY;
     let neg_inf: f128 = f128::NEG_INFINITY;
     assert_eq!(0.0f128.to_degrees(), 0.0);
-    assert_approx_eq!((-5.8f128).to_degrees(), -332.315521);
-    assert_eq!(pi.to_degrees(), 180.0);
+    assert_approx_eq!((-5.8f128).to_degrees(), -332.31552117587745090765431723855668471, TOL);
+    assert_approx_eq!(pi.to_degrees(), 180.0, TOL);
     assert!(nan.to_degrees().is_nan());
     assert_eq!(inf.to_degrees(), inf);
     assert_eq!(neg_inf.to_degrees(), neg_inf);
@@ -328,19 +628,122 @@ fn test_to_radians() {
     let inf: f128 = f128::INFINITY;
     let neg_inf: f128 = f128::NEG_INFINITY;
     assert_eq!(0.0f128.to_radians(), 0.0);
-    assert_approx_eq!(154.6f128.to_radians(), 2.698279);
-    assert_approx_eq!((-332.31f128).to_radians(), -5.799903);
+    assert_approx_eq!(154.6f128.to_radians(), 2.6982790235832334267135442069489767804, TOL);
+    assert_approx_eq!((-332.31f128).to_radians(), -5.7999036373023566567593094812182763013, TOL);
     // check approx rather than exact because round trip for pi doesn't fall on an exactly
     // representable value (unlike `f32` and `f64`).
-    assert_approx_eq!(180.0f128.to_radians(), pi);
+    assert_approx_eq!(180.0f128.to_radians(), pi, TOL_PRECISE);
     assert!(nan.to_radians().is_nan());
     assert_eq!(inf.to_radians(), inf);
     assert_eq!(neg_inf.to_radians(), neg_inf);
 }
 
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_asinh() {
+    // Lower accuracy results are allowed, use increased tolerances
+    assert_eq!(0.0f128.asinh(), 0.0f128);
+    assert_eq!((-0.0f128).asinh(), -0.0f128);
+
+    let inf: f128 = f128::INFINITY;
+    let neg_inf: f128 = f128::NEG_INFINITY;
+    let nan: f128 = f128::NAN;
+    assert_eq!(inf.asinh(), inf);
+    assert_eq!(neg_inf.asinh(), neg_inf);
+    assert!(nan.asinh().is_nan());
+    assert!((-0.0f128).asinh().is_sign_negative());
+
+    // issue 63271
+    assert_approx_eq!(2.0f128.asinh(), 1.443635475178810342493276740273105f128, TOL_IMPR);
+    assert_approx_eq!((-2.0f128).asinh(), -1.443635475178810342493276740273105f128, TOL_IMPR);
+    // regression test for the catastrophic cancellation fixed in 72486
+    assert_approx_eq!(
+        (-67452098.07139316f128).asinh(),
+        -18.720075426274544393985484294000831757220,
+        TOL_IMPR
+    );
+
+    // test for low accuracy from issue 104548
+    assert_approx_eq!(60.0f128, 60.0f128.sinh().asinh(), TOL_IMPR);
+    // mul needed for approximate comparison to be meaningful
+    assert_approx_eq!(1.0f128, 1e-15f128.sinh().asinh() * 1e15f128, TOL_IMPR);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_acosh() {
+    assert_eq!(1.0f128.acosh(), 0.0f128);
+    assert!(0.999f128.acosh().is_nan());
+
+    let inf: f128 = f128::INFINITY;
+    let neg_inf: f128 = f128::NEG_INFINITY;
+    let nan: f128 = f128::NAN;
+    assert_eq!(inf.acosh(), inf);
+    assert!(neg_inf.acosh().is_nan());
+    assert!(nan.acosh().is_nan());
+    assert_approx_eq!(2.0f128.acosh(), 1.31695789692481670862504634730796844f128, TOL_IMPR);
+    assert_approx_eq!(3.0f128.acosh(), 1.76274717403908605046521864995958461f128, TOL_IMPR);
+
+    // test for low accuracy from issue 104548
+    assert_approx_eq!(60.0f128, 60.0f128.cosh().acosh(), TOL_IMPR);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_atanh() {
+    assert_eq!(0.0f128.atanh(), 0.0f128);
+    assert_eq!((-0.0f128).atanh(), -0.0f128);
+
+    let inf: f128 = f128::INFINITY;
+    let neg_inf: f128 = f128::NEG_INFINITY;
+    let nan: f128 = f128::NAN;
+    assert_eq!(1.0f128.atanh(), inf);
+    assert_eq!((-1.0f128).atanh(), neg_inf);
+    assert!(2f128.atanh().atanh().is_nan());
+    assert!((-2f128).atanh().atanh().is_nan());
+    assert!(inf.atanh().is_nan());
+    assert!(neg_inf.atanh().is_nan());
+    assert!(nan.atanh().is_nan());
+    assert_approx_eq!(0.5f128.atanh(), 0.54930614433405484569762261846126285f128, TOL_IMPR);
+    assert_approx_eq!((-0.5f128).atanh(), -0.54930614433405484569762261846126285f128, TOL_IMPR);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_gamma() {
+    // precision can differ among platforms
+    assert_approx_eq!(1.0f128.gamma(), 1.0f128, TOL_IMPR);
+    assert_approx_eq!(2.0f128.gamma(), 1.0f128, TOL_IMPR);
+    assert_approx_eq!(3.0f128.gamma(), 2.0f128, TOL_IMPR);
+    assert_approx_eq!(4.0f128.gamma(), 6.0f128, TOL_IMPR);
+    assert_approx_eq!(5.0f128.gamma(), 24.0f128, TOL_IMPR);
+    assert_approx_eq!(0.5f128.gamma(), consts::PI.sqrt(), TOL_IMPR);
+    assert_approx_eq!((-0.5f128).gamma(), -2.0 * consts::PI.sqrt(), TOL_IMPR);
+    assert_eq!(0.0f128.gamma(), f128::INFINITY);
+    assert_eq!((-0.0f128).gamma(), f128::NEG_INFINITY);
+    assert!((-1.0f128).gamma().is_nan());
+    assert!((-2.0f128).gamma().is_nan());
+    assert!(f128::NAN.gamma().is_nan());
+    assert!(f128::NEG_INFINITY.gamma().is_nan());
+    assert_eq!(f128::INFINITY.gamma(), f128::INFINITY);
+    assert_eq!(1760.9f128.gamma(), f128::INFINITY);
+}
+
+#[test]
+#[cfg(reliable_f128_math)]
+fn test_ln_gamma() {
+    assert_approx_eq!(1.0f128.ln_gamma().0, 0.0f128, TOL_IMPR);
+    assert_eq!(1.0f128.ln_gamma().1, 1);
+    assert_approx_eq!(2.0f128.ln_gamma().0, 0.0f128, TOL_IMPR);
+    assert_eq!(2.0f128.ln_gamma().1, 1);
+    assert_approx_eq!(3.0f128.ln_gamma().0, 2.0f128.ln(), TOL_IMPR);
+    assert_eq!(3.0f128.ln_gamma().1, 1);
+    assert_approx_eq!((-0.5f128).ln_gamma().0, (2.0 * consts::PI.sqrt()).ln(), TOL_IMPR);
+    assert_eq!((-0.5f128).ln_gamma().1, -1);
+}
+
 #[test]
 fn test_real_consts() {
-    // FIXME(f16_f128): add math tests when available
     use super::consts;
 
     let pi: f128 = consts::PI;
@@ -351,29 +754,34 @@ fn test_real_consts() {
     let frac_pi_8: f128 = consts::FRAC_PI_8;
     let frac_1_pi: f128 = consts::FRAC_1_PI;
     let frac_2_pi: f128 = consts::FRAC_2_PI;
-    // let frac_2_sqrtpi: f128 = consts::FRAC_2_SQRT_PI;
-    // let sqrt2: f128 = consts::SQRT_2;
-    // let frac_1_sqrt2: f128 = consts::FRAC_1_SQRT_2;
-    // let e: f128 = consts::E;
-    // let log2_e: f128 = consts::LOG2_E;
-    // let log10_e: f128 = consts::LOG10_E;
-    // let ln_2: f128 = consts::LN_2;
-    // let ln_10: f128 = consts::LN_10;
 
-    assert_approx_eq!(frac_pi_2, pi / 2f128);
-    assert_approx_eq!(frac_pi_3, pi / 3f128);
-    assert_approx_eq!(frac_pi_4, pi / 4f128);
-    assert_approx_eq!(frac_pi_6, pi / 6f128);
-    assert_approx_eq!(frac_pi_8, pi / 8f128);
-    assert_approx_eq!(frac_1_pi, 1f128 / pi);
-    assert_approx_eq!(frac_2_pi, 2f128 / pi);
-    // assert_approx_eq!(frac_2_sqrtpi, 2f128 / pi.sqrt());
-    // assert_approx_eq!(sqrt2, 2f128.sqrt());
-    // assert_approx_eq!(frac_1_sqrt2, 1f128 / 2f128.sqrt());
-    // assert_approx_eq!(log2_e, e.log2());
-    // assert_approx_eq!(log10_e, e.log10());
-    // assert_approx_eq!(ln_2, 2f128.ln());
-    // assert_approx_eq!(ln_10, 10f128.ln());
+    assert_approx_eq!(frac_pi_2, pi / 2f128, TOL_PRECISE);
+    assert_approx_eq!(frac_pi_3, pi / 3f128, TOL_PRECISE);
+    assert_approx_eq!(frac_pi_4, pi / 4f128, TOL_PRECISE);
+    assert_approx_eq!(frac_pi_6, pi / 6f128, TOL_PRECISE);
+    assert_approx_eq!(frac_pi_8, pi / 8f128, TOL_PRECISE);
+    assert_approx_eq!(frac_1_pi, 1f128 / pi, TOL_PRECISE);
+    assert_approx_eq!(frac_2_pi, 2f128 / pi, TOL_PRECISE);
+
+    #[cfg(reliable_f128_math)]
+    {
+        let frac_2_sqrtpi: f128 = consts::FRAC_2_SQRT_PI;
+        let sqrt2: f128 = consts::SQRT_2;
+        let frac_1_sqrt2: f128 = consts::FRAC_1_SQRT_2;
+        let e: f128 = consts::E;
+        let log2_e: f128 = consts::LOG2_E;
+        let log10_e: f128 = consts::LOG10_E;
+        let ln_2: f128 = consts::LN_2;
+        let ln_10: f128 = consts::LN_10;
+
+        assert_approx_eq!(frac_2_sqrtpi, 2f128 / pi.sqrt(), TOL_PRECISE);
+        assert_approx_eq!(sqrt2, 2f128.sqrt(), TOL_PRECISE);
+        assert_approx_eq!(frac_1_sqrt2, 1f128 / 2f128.sqrt(), TOL_PRECISE);
+        assert_approx_eq!(log2_e, e.log2(), TOL_PRECISE);
+        assert_approx_eq!(log10_e, e.log10(), TOL_PRECISE);
+        assert_approx_eq!(ln_2, 2f128.ln(), TOL_PRECISE);
+        assert_approx_eq!(ln_10, 10f128.ln(), TOL_PRECISE);
+    }
 }
 
 #[test]
@@ -382,10 +790,10 @@ fn test_float_bits_conv() {
     assert_eq!((12.5f128).to_bits(), 0x40029000000000000000000000000000);
     assert_eq!((1337f128).to_bits(), 0x40094e40000000000000000000000000);
     assert_eq!((-14.25f128).to_bits(), 0xc002c800000000000000000000000000);
-    assert_approx_eq!(f128::from_bits(0x3fff0000000000000000000000000000), 1.0);
-    assert_approx_eq!(f128::from_bits(0x40029000000000000000000000000000), 12.5);
-    assert_approx_eq!(f128::from_bits(0x40094e40000000000000000000000000), 1337.0);
-    assert_approx_eq!(f128::from_bits(0xc002c800000000000000000000000000), -14.25);
+    assert_approx_eq!(f128::from_bits(0x3fff0000000000000000000000000000), 1.0, TOL_PRECISE);
+    assert_approx_eq!(f128::from_bits(0x40029000000000000000000000000000), 12.5, TOL_PRECISE);
+    assert_approx_eq!(f128::from_bits(0x40094e40000000000000000000000000), 1337.0, TOL_PRECISE);
+    assert_approx_eq!(f128::from_bits(0xc002c800000000000000000000000000), -14.25, TOL_PRECISE);
 
     // Check that NaNs roundtrip their bits regardless of signaling-ness
     // 0xA is 0b1010; 0x5 is 0b0101 -- so these two together clobbers all the mantissa bits

library/std/src/f16/tests.rs

@@ -4,11 +4,21 @@
 use crate::f16::consts;
 use crate::num::{FpCategory as Fp, *};
 
-// We run out of precision pretty quickly with f16
-// const F16_APPROX_L1: f16 = 0.001;
-const F16_APPROX_L2: f16 = 0.01;
-// const F16_APPROX_L3: f16 = 0.1;
-const F16_APPROX_L4: f16 = 0.5;
+/// Tolerance for results on the order of 10.0e-2;
+#[cfg(reliable_f16_math)]
+const TOL_N2: f16 = 0.0001;
+
+/// Tolerance for results on the order of 10.0e+0
+#[cfg(reliable_f16_math)]
+const TOL_0: f16 = 0.01;
+
+/// Tolerance for results on the order of 10.0e+2
+#[cfg(reliable_f16_math)]
+const TOL_P2: f16 = 0.5;
+
+/// Tolerance for results on the order of 10.0e+4
+#[cfg(reliable_f16_math)]
+const TOL_P4: f16 = 10.0;
 
 /// Smallest number
 const TINY_BITS: u16 = 0x1;
@@ -47,7 +57,33 @@ fn test_num_f16() {
     test_num(10f16, 2f16);
 }
 
-// FIXME(f16_f128): add min and max tests when available
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_min_nan() {
+    assert_eq!(f16::NAN.min(2.0), 2.0);
+    assert_eq!(2.0f16.min(f16::NAN), 2.0);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_max_nan() {
+    assert_eq!(f16::NAN.max(2.0), 2.0);
+    assert_eq!(2.0f16.max(f16::NAN), 2.0);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_minimum() {
+    assert!(f16::NAN.minimum(2.0).is_nan());
+    assert!(2.0f16.minimum(f16::NAN).is_nan());
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_maximum() {
+    assert!(f16::NAN.maximum(2.0).is_nan());
+    assert!(2.0f16.maximum(f16::NAN).is_nan());
+}
 
 #[test]
 fn test_nan() {
@@ -197,9 +233,100 @@ fn test_classify() {
     assert_eq!(1e-5f16.classify(), Fp::Subnormal);
 }
 
-// FIXME(f16_f128): add missing math functions when available
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_floor() {
+    assert_approx_eq!(1.0f16.floor(), 1.0f16, TOL_0);
+    assert_approx_eq!(1.3f16.floor(), 1.0f16, TOL_0);
+    assert_approx_eq!(1.5f16.floor(), 1.0f16, TOL_0);
+    assert_approx_eq!(1.7f16.floor(), 1.0f16, TOL_0);
+    assert_approx_eq!(0.0f16.floor(), 0.0f16, TOL_0);
+    assert_approx_eq!((-0.0f16).floor(), -0.0f16, TOL_0);
+    assert_approx_eq!((-1.0f16).floor(), -1.0f16, TOL_0);
+    assert_approx_eq!((-1.3f16).floor(), -2.0f16, TOL_0);
+    assert_approx_eq!((-1.5f16).floor(), -2.0f16, TOL_0);
+    assert_approx_eq!((-1.7f16).floor(), -2.0f16, TOL_0);
+}
 
 #[test]
+#[cfg(reliable_f16_math)]
+fn test_ceil() {
+    assert_approx_eq!(1.0f16.ceil(), 1.0f16, TOL_0);
+    assert_approx_eq!(1.3f16.ceil(), 2.0f16, TOL_0);
+    assert_approx_eq!(1.5f16.ceil(), 2.0f16, TOL_0);
+    assert_approx_eq!(1.7f16.ceil(), 2.0f16, TOL_0);
+    assert_approx_eq!(0.0f16.ceil(), 0.0f16, TOL_0);
+    assert_approx_eq!((-0.0f16).ceil(), -0.0f16, TOL_0);
+    assert_approx_eq!((-1.0f16).ceil(), -1.0f16, TOL_0);
+    assert_approx_eq!((-1.3f16).ceil(), -1.0f16, TOL_0);
+    assert_approx_eq!((-1.5f16).ceil(), -1.0f16, TOL_0);
+    assert_approx_eq!((-1.7f16).ceil(), -1.0f16, TOL_0);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_round() {
+    assert_approx_eq!(2.5f16.round(), 3.0f16, TOL_0);
+    assert_approx_eq!(1.0f16.round(), 1.0f16, TOL_0);
+    assert_approx_eq!(1.3f16.round(), 1.0f16, TOL_0);
+    assert_approx_eq!(1.5f16.round(), 2.0f16, TOL_0);
+    assert_approx_eq!(1.7f16.round(), 2.0f16, TOL_0);
+    assert_approx_eq!(0.0f16.round(), 0.0f16, TOL_0);
+    assert_approx_eq!((-0.0f16).round(), -0.0f16, TOL_0);
+    assert_approx_eq!((-1.0f16).round(), -1.0f16, TOL_0);
+    assert_approx_eq!((-1.3f16).round(), -1.0f16, TOL_0);
+    assert_approx_eq!((-1.5f16).round(), -2.0f16, TOL_0);
+    assert_approx_eq!((-1.7f16).round(), -2.0f16, TOL_0);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_round_ties_even() {
+    assert_approx_eq!(2.5f16.round_ties_even(), 2.0f16, TOL_0);
+    assert_approx_eq!(1.0f16.round_ties_even(), 1.0f16, TOL_0);
+    assert_approx_eq!(1.3f16.round_ties_even(), 1.0f16, TOL_0);
+    assert_approx_eq!(1.5f16.round_ties_even(), 2.0f16, TOL_0);
+    assert_approx_eq!(1.7f16.round_ties_even(), 2.0f16, TOL_0);
+    assert_approx_eq!(0.0f16.round_ties_even(), 0.0f16, TOL_0);
+    assert_approx_eq!((-0.0f16).round_ties_even(), -0.0f16, TOL_0);
+    assert_approx_eq!((-1.0f16).round_ties_even(), -1.0f16, TOL_0);
+    assert_approx_eq!((-1.3f16).round_ties_even(), -1.0f16, TOL_0);
+    assert_approx_eq!((-1.5f16).round_ties_even(), -2.0f16, TOL_0);
+    assert_approx_eq!((-1.7f16).round_ties_even(), -2.0f16, TOL_0);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_trunc() {
+    assert_approx_eq!(1.0f16.trunc(), 1.0f16, TOL_0);
+    assert_approx_eq!(1.3f16.trunc(), 1.0f16, TOL_0);
+    assert_approx_eq!(1.5f16.trunc(), 1.0f16, TOL_0);
+    assert_approx_eq!(1.7f16.trunc(), 1.0f16, TOL_0);
+    assert_approx_eq!(0.0f16.trunc(), 0.0f16, TOL_0);
+    assert_approx_eq!((-0.0f16).trunc(), -0.0f16, TOL_0);
+    assert_approx_eq!((-1.0f16).trunc(), -1.0f16, TOL_0);
+    assert_approx_eq!((-1.3f16).trunc(), -1.0f16, TOL_0);
+    assert_approx_eq!((-1.5f16).trunc(), -1.0f16, TOL_0);
+    assert_approx_eq!((-1.7f16).trunc(), -1.0f16, TOL_0);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_fract() {
+    assert_approx_eq!(1.0f16.fract(), 0.0f16, TOL_0);
+    assert_approx_eq!(1.3f16.fract(), 0.3f16, TOL_0);
+    assert_approx_eq!(1.5f16.fract(), 0.5f16, TOL_0);
+    assert_approx_eq!(1.7f16.fract(), 0.7f16, TOL_0);
+    assert_approx_eq!(0.0f16.fract(), 0.0f16, TOL_0);
+    assert_approx_eq!((-0.0f16).fract(), -0.0f16, TOL_0);
+    assert_approx_eq!((-1.0f16).fract(), -0.0f16, TOL_0);
+    assert_approx_eq!((-1.3f16).fract(), -0.3f16, TOL_0);
+    assert_approx_eq!((-1.5f16).fract(), -0.5f16, TOL_0);
+    assert_approx_eq!((-1.7f16).fract(), -0.7f16, TOL_0);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
 fn test_abs() {
     assert_eq!(f16::INFINITY.abs(), f16::INFINITY);
     assert_eq!(1f16.abs(), 1f16);
@@ -299,6 +426,24 @@ fn test_next_down() {
 }
 
 #[test]
+#[cfg(reliable_f16_math)]
+fn test_mul_add() {
+    let nan: f16 = f16::NAN;
+    let inf: f16 = f16::INFINITY;
+    let neg_inf: f16 = f16::NEG_INFINITY;
+    assert_approx_eq!(12.3f16.mul_add(4.5, 6.7), 62.05, TOL_P2);
+    assert_approx_eq!((-12.3f16).mul_add(-4.5, -6.7), 48.65, TOL_P2);
+    assert_approx_eq!(0.0f16.mul_add(8.9, 1.2), 1.2, TOL_0);
+    assert_approx_eq!(3.4f16.mul_add(-0.0, 5.6), 5.6, TOL_0);
+    assert!(nan.mul_add(7.8, 9.0).is_nan());
+    assert_eq!(inf.mul_add(7.8, 9.0), inf);
+    assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
+    assert_eq!(8.9f16.mul_add(inf, 3.2), inf);
+    assert_eq!((-3.2f16).mul_add(2.4, neg_inf), neg_inf);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
 fn test_recip() {
     let nan: f16 = f16::NAN;
     let inf: f16 = f16::INFINITY;
@@ -307,11 +452,157 @@ fn test_recip() {
     assert_eq!(2.0f16.recip(), 0.5);
     assert_eq!((-0.4f16).recip(), -2.5);
     assert_eq!(0.0f16.recip(), inf);
+    assert_approx_eq!(f16::MAX.recip(), 1.526624e-5f16, 1e-4);
     assert!(nan.recip().is_nan());
     assert_eq!(inf.recip(), 0.0);
     assert_eq!(neg_inf.recip(), 0.0);
 }
 
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_powi() {
+    // FIXME(llvm19): LLVM misoptimizes `powi.f16`
+    // <https://github.com/llvm/llvm-project/issues/98665>
+    // let nan: f16 = f16::NAN;
+    // let inf: f16 = f16::INFINITY;
+    // let neg_inf: f16 = f16::NEG_INFINITY;
+    // assert_eq!(1.0f16.powi(1), 1.0);
+    // assert_approx_eq!((-3.1f16).powi(2), 9.61, TOL_0);
+    // assert_approx_eq!(5.9f16.powi(-2), 0.028727, TOL_N2);
+    // assert_eq!(8.3f16.powi(0), 1.0);
+    // assert!(nan.powi(2).is_nan());
+    // assert_eq!(inf.powi(3), inf);
+    // assert_eq!(neg_inf.powi(2), inf);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_powf() {
+    let nan: f16 = f16::NAN;
+    let inf: f16 = f16::INFINITY;
+    let neg_inf: f16 = f16::NEG_INFINITY;
+    assert_eq!(1.0f16.powf(1.0), 1.0);
+    assert_approx_eq!(3.4f16.powf(4.5), 246.408183, TOL_P2);
+    assert_approx_eq!(2.7f16.powf(-3.2), 0.041652, TOL_N2);
+    assert_approx_eq!((-3.1f16).powf(2.0), 9.61, TOL_P2);
+    assert_approx_eq!(5.9f16.powf(-2.0), 0.028727, TOL_N2);
+    assert_eq!(8.3f16.powf(0.0), 1.0);
+    assert!(nan.powf(2.0).is_nan());
+    assert_eq!(inf.powf(2.0), inf);
+    assert_eq!(neg_inf.powf(3.0), neg_inf);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_sqrt_domain() {
+    assert!(f16::NAN.sqrt().is_nan());
+    assert!(f16::NEG_INFINITY.sqrt().is_nan());
+    assert!((-1.0f16).sqrt().is_nan());
+    assert_eq!((-0.0f16).sqrt(), -0.0);
+    assert_eq!(0.0f16.sqrt(), 0.0);
+    assert_eq!(1.0f16.sqrt(), 1.0);
+    assert_eq!(f16::INFINITY.sqrt(), f16::INFINITY);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_exp() {
+    assert_eq!(1.0, 0.0f16.exp());
+    assert_approx_eq!(2.718282, 1.0f16.exp(), TOL_0);
+    assert_approx_eq!(148.413159, 5.0f16.exp(), TOL_0);
+
+    let inf: f16 = f16::INFINITY;
+    let neg_inf: f16 = f16::NEG_INFINITY;
+    let nan: f16 = f16::NAN;
+    assert_eq!(inf, inf.exp());
+    assert_eq!(0.0, neg_inf.exp());
+    assert!(nan.exp().is_nan());
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_exp2() {
+    assert_eq!(32.0, 5.0f16.exp2());
+    assert_eq!(1.0, 0.0f16.exp2());
+
+    let inf: f16 = f16::INFINITY;
+    let neg_inf: f16 = f16::NEG_INFINITY;
+    let nan: f16 = f16::NAN;
+    assert_eq!(inf, inf.exp2());
+    assert_eq!(0.0, neg_inf.exp2());
+    assert!(nan.exp2().is_nan());
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_ln() {
+    let nan: f16 = f16::NAN;
+    let inf: f16 = f16::INFINITY;
+    let neg_inf: f16 = f16::NEG_INFINITY;
+    assert_approx_eq!(1.0f16.exp().ln(), 1.0, TOL_0);
+    assert!(nan.ln().is_nan());
+    assert_eq!(inf.ln(), inf);
+    assert!(neg_inf.ln().is_nan());
+    assert!((-2.3f16).ln().is_nan());
+    assert_eq!((-0.0f16).ln(), neg_inf);
+    assert_eq!(0.0f16.ln(), neg_inf);
+    assert_approx_eq!(4.0f16.ln(), 1.386294, TOL_0);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_log() {
+    let nan: f16 = f16::NAN;
+    let inf: f16 = f16::INFINITY;
+    let neg_inf: f16 = f16::NEG_INFINITY;
+    assert_eq!(10.0f16.log(10.0), 1.0);
+    assert_approx_eq!(2.3f16.log(3.5), 0.664858, TOL_0);
+    assert_eq!(1.0f16.exp().log(1.0f16.exp()), 1.0);
+    assert!(1.0f16.log(1.0).is_nan());
+    assert!(1.0f16.log(-13.9).is_nan());
+    assert!(nan.log(2.3).is_nan());
+    assert_eq!(inf.log(10.0), inf);
+    assert!(neg_inf.log(8.8).is_nan());
+    assert!((-2.3f16).log(0.1).is_nan());
+    assert_eq!((-0.0f16).log(2.0), neg_inf);
+    assert_eq!(0.0f16.log(7.0), neg_inf);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_log2() {
+    let nan: f16 = f16::NAN;
+    let inf: f16 = f16::INFINITY;
+    let neg_inf: f16 = f16::NEG_INFINITY;
+    assert_approx_eq!(10.0f16.log2(), 3.321928, TOL_0);
+    assert_approx_eq!(2.3f16.log2(), 1.201634, TOL_0);
+    assert_approx_eq!(1.0f16.exp().log2(), 1.442695, TOL_0);
+    assert!(nan.log2().is_nan());
+    assert_eq!(inf.log2(), inf);
+    assert!(neg_inf.log2().is_nan());
+    assert!((-2.3f16).log2().is_nan());
+    assert_eq!((-0.0f16).log2(), neg_inf);
+    assert_eq!(0.0f16.log2(), neg_inf);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_log10() {
+    let nan: f16 = f16::NAN;
+    let inf: f16 = f16::INFINITY;
+    let neg_inf: f16 = f16::NEG_INFINITY;
+    assert_eq!(10.0f16.log10(), 1.0);
+    assert_approx_eq!(2.3f16.log10(), 0.361728, TOL_0);
+    assert_approx_eq!(1.0f16.exp().log10(), 0.434294, TOL_0);
+    assert_eq!(1.0f16.log10(), 0.0);
+    assert!(nan.log10().is_nan());
+    assert_eq!(inf.log10(), inf);
+    assert!(neg_inf.log10().is_nan());
+    assert!((-2.3f16).log10().is_nan());
+    assert_eq!((-0.0f16).log10(), neg_inf);
+    assert_eq!(0.0f16.log10(), neg_inf);
+}
+
 #[test]
 fn test_to_degrees() {
     let pi: f16 = consts::PI;
@@ -319,8 +610,8 @@ fn test_to_degrees() {
     let inf: f16 = f16::INFINITY;
     let neg_inf: f16 = f16::NEG_INFINITY;
     assert_eq!(0.0f16.to_degrees(), 0.0);
-    assert_approx_eq!((-5.8f16).to_degrees(), -332.315521);
-    assert_approx_eq!(pi.to_degrees(), 180.0, F16_APPROX_L4);
+    assert_approx_eq!((-5.8f16).to_degrees(), -332.315521, TOL_P2);
+    assert_approx_eq!(pi.to_degrees(), 180.0, TOL_P2);
     assert!(nan.to_degrees().is_nan());
     assert_eq!(inf.to_degrees(), inf);
     assert_eq!(neg_inf.to_degrees(), neg_inf);
@@ -334,14 +625,112 @@ fn test_to_radians() {
     let inf: f16 = f16::INFINITY;
     let neg_inf: f16 = f16::NEG_INFINITY;
     assert_eq!(0.0f16.to_radians(), 0.0);
-    assert_approx_eq!(154.6f16.to_radians(), 2.698279);
-    assert_approx_eq!((-332.31f16).to_radians(), -5.799903);
-    assert_approx_eq!(180.0f16.to_radians(), pi, F16_APPROX_L2);
+    assert_approx_eq!(154.6f16.to_radians(), 2.698279, TOL_0);
+    assert_approx_eq!((-332.31f16).to_radians(), -5.799903, TOL_0);
+    assert_approx_eq!(180.0f16.to_radians(), pi, TOL_0);
     assert!(nan.to_radians().is_nan());
     assert_eq!(inf.to_radians(), inf);
     assert_eq!(neg_inf.to_radians(), neg_inf);
 }
 
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_asinh() {
+    assert_eq!(0.0f16.asinh(), 0.0f16);
+    assert_eq!((-0.0f16).asinh(), -0.0f16);
+
+    let inf: f16 = f16::INFINITY;
+    let neg_inf: f16 = f16::NEG_INFINITY;
+    let nan: f16 = f16::NAN;
+    assert_eq!(inf.asinh(), inf);
+    assert_eq!(neg_inf.asinh(), neg_inf);
+    assert!(nan.asinh().is_nan());
+    assert!((-0.0f16).asinh().is_sign_negative());
+    // issue 63271
+    assert_approx_eq!(2.0f16.asinh(), 1.443635475178810342493276740273105f16, TOL_0);
+    assert_approx_eq!((-2.0f16).asinh(), -1.443635475178810342493276740273105f16, TOL_0);
+    // regression test for the catastrophic cancellation fixed in 72486
+    assert_approx_eq!((-200.0f16).asinh(), -5.991470797049389, TOL_0);
+
+    // test for low accuracy from issue 104548
+    assert_approx_eq!(10.0f16, 10.0f16.sinh().asinh(), TOL_0);
+    // mul needed for approximate comparison to be meaningful
+    assert_approx_eq!(1.0f16, 1e-3f16.sinh().asinh() * 1e3f16, TOL_0);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_acosh() {
+    assert_eq!(1.0f16.acosh(), 0.0f16);
+    assert!(0.999f16.acosh().is_nan());
+
+    let inf: f16 = f16::INFINITY;
+    let neg_inf: f16 = f16::NEG_INFINITY;
+    let nan: f16 = f16::NAN;
+    assert_eq!(inf.acosh(), inf);
+    assert!(neg_inf.acosh().is_nan());
+    assert!(nan.acosh().is_nan());
+    assert_approx_eq!(2.0f16.acosh(), 1.31695789692481670862504634730796844f16, TOL_0);
+    assert_approx_eq!(3.0f16.acosh(), 1.76274717403908605046521864995958461f16, TOL_0);
+
+    // test for low accuracy from issue 104548
+    assert_approx_eq!(10.0f16, 10.0f16.cosh().acosh(), TOL_P2);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_atanh() {
+    assert_eq!(0.0f16.atanh(), 0.0f16);
+    assert_eq!((-0.0f16).atanh(), -0.0f16);
+
+    let inf: f16 = f16::INFINITY;
+    let neg_inf: f16 = f16::NEG_INFINITY;
+    let nan: f16 = f16::NAN;
+    assert_eq!(1.0f16.atanh(), inf);
+    assert_eq!((-1.0f16).atanh(), neg_inf);
+    assert!(2f16.atanh().atanh().is_nan());
+    assert!((-2f16).atanh().atanh().is_nan());
+    assert!(inf.atanh().is_nan());
+    assert!(neg_inf.atanh().is_nan());
+    assert!(nan.atanh().is_nan());
+    assert_approx_eq!(0.5f16.atanh(), 0.54930614433405484569762261846126285f16, TOL_0);
+    assert_approx_eq!((-0.5f16).atanh(), -0.54930614433405484569762261846126285f16, TOL_0);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_gamma() {
+    // precision can differ among platforms
+    assert_approx_eq!(1.0f16.gamma(), 1.0f16, TOL_0);
+    assert_approx_eq!(2.0f16.gamma(), 1.0f16, TOL_0);
+    assert_approx_eq!(3.0f16.gamma(), 2.0f16, TOL_0);
+    assert_approx_eq!(4.0f16.gamma(), 6.0f16, TOL_0);
+    assert_approx_eq!(5.0f16.gamma(), 24.0f16, TOL_0);
+    assert_approx_eq!(0.5f16.gamma(), consts::PI.sqrt(), TOL_0);
+    assert_approx_eq!((-0.5f16).gamma(), -2.0 * consts::PI.sqrt(), TOL_0);
+    assert_eq!(0.0f16.gamma(), f16::INFINITY);
+    assert_eq!((-0.0f16).gamma(), f16::NEG_INFINITY);
+    assert!((-1.0f16).gamma().is_nan());
+    assert!((-2.0f16).gamma().is_nan());
+    assert!(f16::NAN.gamma().is_nan());
+    assert!(f16::NEG_INFINITY.gamma().is_nan());
+    assert_eq!(f16::INFINITY.gamma(), f16::INFINITY);
+    assert_eq!(171.71f16.gamma(), f16::INFINITY);
+}
+
+#[test]
+#[cfg(reliable_f16_math)]
+fn test_ln_gamma() {
+    assert_approx_eq!(1.0f16.ln_gamma().0, 0.0f16, TOL_0);
+    assert_eq!(1.0f16.ln_gamma().1, 1);
+    assert_approx_eq!(2.0f16.ln_gamma().0, 0.0f16, TOL_0);
+    assert_eq!(2.0f16.ln_gamma().1, 1);
+    assert_approx_eq!(3.0f16.ln_gamma().0, 2.0f16.ln(), TOL_0);
+    assert_eq!(3.0f16.ln_gamma().1, 1);
+    assert_approx_eq!((-0.5f16).ln_gamma().0, (2.0 * consts::PI.sqrt()).ln(), TOL_0);
+    assert_eq!((-0.5f16).ln_gamma().1, -1);
+}
+
 #[test]
 fn test_real_consts() {
     // FIXME(f16_f128): add math tests when available
@@ -355,29 +744,34 @@ fn test_real_consts() {
     let frac_pi_8: f16 = consts::FRAC_PI_8;
     let frac_1_pi: f16 = consts::FRAC_1_PI;
     let frac_2_pi: f16 = consts::FRAC_2_PI;
-    // let frac_2_sqrtpi: f16 = consts::FRAC_2_SQRT_PI;
-    // let sqrt2: f16 = consts::SQRT_2;
-    // let frac_1_sqrt2: f16 = consts::FRAC_1_SQRT_2;
-    // let e: f16 = consts::E;
-    // let log2_e: f16 = consts::LOG2_E;
-    // let log10_e: f16 = consts::LOG10_E;
-    // let ln_2: f16 = consts::LN_2;
-    // let ln_10: f16 = consts::LN_10;
 
-    assert_approx_eq!(frac_pi_2, pi / 2f16);
-    assert_approx_eq!(frac_pi_3, pi / 3f16);
-    assert_approx_eq!(frac_pi_4, pi / 4f16);
-    assert_approx_eq!(frac_pi_6, pi / 6f16);
-    assert_approx_eq!(frac_pi_8, pi / 8f16);
-    assert_approx_eq!(frac_1_pi, 1f16 / pi);
-    assert_approx_eq!(frac_2_pi, 2f16 / pi);
-    // assert_approx_eq!(frac_2_sqrtpi, 2f16 / pi.sqrt());
-    // assert_approx_eq!(sqrt2, 2f16.sqrt());
-    // assert_approx_eq!(frac_1_sqrt2, 1f16 / 2f16.sqrt());
-    // assert_approx_eq!(log2_e, e.log2());
-    // assert_approx_eq!(log10_e, e.log10());
-    // assert_approx_eq!(ln_2, 2f16.ln());
-    // assert_approx_eq!(ln_10, 10f16.ln());
+    assert_approx_eq!(frac_pi_2, pi / 2f16, TOL_0);
+    assert_approx_eq!(frac_pi_3, pi / 3f16, TOL_0);
+    assert_approx_eq!(frac_pi_4, pi / 4f16, TOL_0);
+    assert_approx_eq!(frac_pi_6, pi / 6f16, TOL_0);
+    assert_approx_eq!(frac_pi_8, pi / 8f16, TOL_0);
+    assert_approx_eq!(frac_1_pi, 1f16 / pi, TOL_0);
+    assert_approx_eq!(frac_2_pi, 2f16 / pi, TOL_0);
+
+    #[cfg(reliable_f16_math)]
+    {
+        let frac_2_sqrtpi: f16 = consts::FRAC_2_SQRT_PI;
+        let sqrt2: f16 = consts::SQRT_2;
+        let frac_1_sqrt2: f16 = consts::FRAC_1_SQRT_2;
+        let e: f16 = consts::E;
+        let log2_e: f16 = consts::LOG2_E;
+        let log10_e: f16 = consts::LOG10_E;
+        let ln_2: f16 = consts::LN_2;
+        let ln_10: f16 = consts::LN_10;
+
+        assert_approx_eq!(frac_2_sqrtpi, 2f16 / pi.sqrt(), TOL_0);
+        assert_approx_eq!(sqrt2, 2f16.sqrt(), TOL_0);
+        assert_approx_eq!(frac_1_sqrt2, 1f16 / 2f16.sqrt(), TOL_0);
+        assert_approx_eq!(log2_e, e.log2(), TOL_0);
+        assert_approx_eq!(log10_e, e.log10(), TOL_0);
+        assert_approx_eq!(ln_2, 2f16.ln(), TOL_0);
+        assert_approx_eq!(ln_10, 10f16.ln(), TOL_0);
+    }
 }
 
 #[test]
@@ -386,10 +780,10 @@ fn test_float_bits_conv() {
     assert_eq!((12.5f16).to_bits(), 0x4a40);
     assert_eq!((1337f16).to_bits(), 0x6539);
     assert_eq!((-14.25f16).to_bits(), 0xcb20);
-    assert_approx_eq!(f16::from_bits(0x3c00), 1.0);
-    assert_approx_eq!(f16::from_bits(0x4a40), 12.5);
-    assert_approx_eq!(f16::from_bits(0x6539), 1337.0);
-    assert_approx_eq!(f16::from_bits(0xcb20), -14.25);
+    assert_approx_eq!(f16::from_bits(0x3c00), 1.0, TOL_0);
+    assert_approx_eq!(f16::from_bits(0x4a40), 12.5, TOL_0);
+    assert_approx_eq!(f16::from_bits(0x6539), 1337.0, TOL_P4);
+    assert_approx_eq!(f16::from_bits(0xcb20), -14.25, TOL_0);
 
     // Check that NaNs roundtrip their bits regardless of signaling-ness
     let masked_nan1 = f16::NAN.to_bits() ^ NAN_MASK1;

library/std/src/macros.rs

@@ -382,7 +382,7 @@ macro_rules! assert_approx_eq {
         let diff = (*a - *b).abs();
         assert!(
             diff < $lim,
-            "{a:?} is not approximately equal to {b:?} (threshold {lim:?}, actual {diff:?})",
+            "{a:?} is not approximately equal to {b:?} (threshold {lim:?}, difference {diff:?})",
             lim = $lim
         );
     }};

library/std/src/sys/cmath.rs

@@ -28,6 +28,21 @@ extern "C" {
     pub fn lgamma_r(n: f64, s: &mut i32) -> f64;
     pub fn lgammaf_r(n: f32, s: &mut i32) -> f32;
 
+    pub fn acosf128(n: f128) -> f128;
+    pub fn asinf128(n: f128) -> f128;
+    pub fn atanf128(n: f128) -> f128;
+    pub fn atan2f128(a: f128, b: f128) -> f128;
+    pub fn cbrtf128(n: f128) -> f128;
+    pub fn coshf128(n: f128) -> f128;
+    pub fn expm1f128(n: f128) -> f128;
+    pub fn hypotf128(x: f128, y: f128) -> f128;
+    pub fn log1pf128(n: f128) -> f128;
+    pub fn sinhf128(n: f128) -> f128;
+    pub fn tanf128(n: f128) -> f128;
+    pub fn tanhf128(n: f128) -> f128;
+    pub fn tgammaf128(n: f128) -> f128;
+    pub fn lgammaf128_r(n: f128, s: &mut i32) -> f128;
+
     cfg_if::cfg_if! {
     if #[cfg(not(all(target_os = "windows", target_env = "msvc", target_arch = "x86")))] {
         pub fn acosf(n: f32) -> f32;