Initial coarse pass

Author: tgross35

crates/libm-test/src/f8_impl.rs

@@ -39,6 +39,13 @@ impl Float for f8 {
     const NEG_PI: Self = Self::ZERO;
     const FRAC_PI_2: Self = Self::ZERO;
 
+    /// `2^sig_bits`
+    const TWO_POW_SIG_BITS: Self =
+        Self(((Self::SIG_BITS + Self::EXP_BIAS) as Self::Int) << Self::SIG_BITS);
+    /// `2^-sig_bits`
+    const TWO_POW_NEG_SIG_BITS: Self =
+        Self(((-(Self::SIG_BITS as i32) + Self::EXP_BIAS as i32) as Self::Int) << Self::SIG_BITS);
+
     const BITS: u32 = 8;
     const SIG_BITS: u32 = 3;
     const SIGN_MASK: Self::Int = 0b1_0000_000;

etc/update-api-list.py

@@ -25,6 +25,8 @@
 
 # These files do not trigger a retest.
 IGNORED_SOURCES = ["src/libm_helper.rs"]
+# Same as above, limited to specific functions
+IGNORED_SOURCES_MAP = {"fma": ["src/math/cbrt.rs"]}
 
 IndexTy: TypeAlias = dict[str, dict[str, Any]]
 """Type of the `index` item in rustdoc's JSON output"""
@@ -138,6 +140,8 @@ def _init_defs(self, index: IndexTy) -> None:
 
             for src in IGNORED_SOURCES:
                 sources.discard(src)
+            for src in IGNORED_SOURCES_MAP.get(name, []):
+                sources.discard(src)
 
         # Sort the set
         self.defs = {k: sorted(v) for (k, v) in defs.items()}

src/math/cbrt.rs

@@ -5,208 +5,253 @@
  */
 
 use super::Float;
-use super::support::{FpResult, Round, cold_path};
+use super::support::{CastFrom, FpResult, Int, MinInt, Round, cold_path};
 
 /// Compute the cube root of the argument.
 #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
 pub fn cbrt(x: f64) -> f64 {
     cbrt_round(x, Round::Nearest).val
 }
 
-pub fn cbrt_round(x: f64, round: Round) -> FpResult<f64> {
-    const ESCALE: [f64; 3] = [
-        1.0,
-        hf64!("0x1.428a2f98d728bp+0"), /* 2^(1/3) */
-        hf64!("0x1.965fea53d6e3dp+0"), /* 2^(2/3) */
-    ];
-
-    /* the polynomial c0+c1*x+c2*x^2+c3*x^3 approximates x^(1/3) on [1,2]
-    with maximal error < 9.2e-5 (attained at x=2) */
-    const C: [f64; 4] = [
-        hf64!("0x1.1b0babccfef9cp-1"),
-        hf64!("0x1.2c9a3e94d1da5p-1"),
-        hf64!("-0x1.4dc30b1a1ddbap-3"),
-        hf64!("0x1.7a8d3e4ec9b07p-6"),
-    ];
-
-    let u0: f64 = hf64!("0x1.5555555555555p-2");
-    let u1: f64 = hf64!("0x1.c71c71c71c71cp-3");
-
-    let rsc = [1.0, -1.0, 0.5, -0.5, 0.25, -0.25];
-
-    let off = [hf64!("0x1p-53"), 0.0, 0.0, 0.0];
+pub fn cbrt_round<F: Float + CbrtHelper>(x: F, round: Round) -> FpResult<F>
+where
+    F::Int: CastFrom<u64>,
+    F::Int: CastFrom<u32>,
+    F::Int: From<u8>,
+{
+    let zero = F::Int::ZERO;
+    let one = F::Int::ONE;
+    let u0: F = F::U0;
+    let u1: F = F::U1;
+    let rsc = F::RSC;
+    let off = F::OFF;
 
     /* rm=0 for rounding to nearest, and other values for directed roundings */
-    let hx: u64 = x.to_bits();
-    let mut mant: u64 = hx & f64::SIG_MASK;
-    let sign: u64 = hx >> 63;
+    let hx = x.to_bits();
+    let mut mant: F::Int = hx & F::SIG_MASK;
+    let sign: F::Int = hx >> (F::BITS - 1);
+    let neg = x.is_sign_negative();
 
-    let mut e: u32 = (hx >> f64::SIG_BITS) as u32 & f64::EXP_SAT;
+    let mut e: u32 = x.exp();
 
-    if ((e + 1) & f64::EXP_SAT) < 2 {
+    if ((e + 1) & F::EXP_SAT) < 2 {
         cold_path();
 
-        let ix: u64 = hx & !f64::SIGN_MASK;
+        let ix = hx & !F::SIGN_MASK;
 
         /* 0, inf, nan: we return x + x instead of simply x,
         to that for x a signaling NaN, it correctly triggers
         the invalid exception. */
-        if e == f64::EXP_SAT || ix == 0 {
+        if e == F::EXP_SAT || ix == zero {
             return FpResult::ok(x + x);
         }
 
         let nz = ix.leading_zeros() - 11; /* subnormal */
         mant <<= nz;
-        mant &= f64::SIG_MASK;
+        mant &= F::SIG_MASK;
         e = e.wrapping_sub(nz - 1);
     }
 
     e = e.wrapping_add(3072);
-    let cvt1: u64 = mant | (0x3ffu64 << 52);
-    let mut cvt5: u64 = cvt1;
+    let cvt1 = mant | (F::Int::cast_from(F::EXP_BIAS) << F::SIG_BITS);
+    let mut cvt5 = cvt1;
 
     let et: u32 = e / 3;
     let it: u32 = e % 3;
 
     /* 2^(3k+it) <= x < 2^(3k+it+1), with 0 <= it <= 3 */
-    cvt5 += u64::from(it) << f64::SIG_BITS;
-    cvt5 |= sign << 63;
-    let zz: f64 = f64::from_bits(cvt5);
+    cvt5 += F::Int::cast_from(it) << F::SIG_BITS;
+    cvt5 |= sign << (F::BITS - 1);
+    let zz: F = F::from_bits(cvt5);
 
     /* cbrt(x) = cbrt(zz)*2^(et-1365) where 1 <= zz < 8 */
-    let mut isc: u64 = ESCALE[it as usize].to_bits(); // todo: index
-    isc |= sign << 63;
-    let cvt2: u64 = isc;
-    let z: f64 = f64::from_bits(cvt1);
+    let mut isc = F::ESCALE[it as usize].to_bits(); // todo: index
+    isc |= sign << (F::BITS - 1);
+    let cvt2 = isc;
+    let z: F = F::from_bits(cvt1);
 
     /* cbrt(zz) = cbrt(z)*isc, where isc encodes 1, 2^(1/3) or 2^(2/3),
     and 1 <= z < 2 */
-    let r: f64 = 1.0 / z;
-    let rr: f64 = r * rsc[((it as usize) << 1) | sign as usize];
-    let z2: f64 = z * z;
-    let c0: f64 = C[0] + z * C[1];
-    let c2: f64 = C[2] + z * C[3];
-    let mut y: f64 = c0 + z2 * c2;
-    let mut y2: f64 = y * y;
+    let r: F = F::ONE / z;
+    let rr: F = r * rsc[((it as usize) << 1) | neg as usize];
+    let z2: F = z * z;
+    let c0: F = F::C[0] + z * F::C[1];
+    let c2: F = F::C[2] + z * F::C[3];
+    let mut y: F = c0 + z2 * c2;
+    let mut y2: F = y * y;
 
     /* y is an approximation of z^(1/3) */
-    let mut h: f64 = y2 * (y * r) - 1.0;
+    let mut h: F = y2 * (y * r) - F::ONE;
 
     /* h determines the error between y and z^(1/3) */
     y -= (h * y) * (u0 - u1 * h);
 
     /* The correction y -= (h*y)*(u0 - u1*h) corresponds to a cubic variant
     of Newton's method, with the function f(y) = 1-z/y^3. */
-    y *= f64::from_bits(cvt2);
+    y *= F::from_bits(cvt2);
 
     /* Now y is an approximation of zz^(1/3),
      * and rr an approximation of 1/zz. We now perform another iteration of
      * Newton-Raphson, this time with a linear approximation only. */
     y2 = y * y;
-    let mut y2l: f64 = fmaf64(y, y, -y2);
+    let mut y2l: F = y.fma(y, -y2);
 
     /* y2 + y2l = y^2 exactly */
-    let mut y3: f64 = y2 * y;
-    let mut y3l: f64 = fmaf64(y, y2, -y3) + y * y2l;
+    let mut y3: F = y2 * y;
+    let mut y3l: F = y.fma(y2, -y3) + y * y2l;
 
     /* y3 + y3l approximates y^3 with about 106 bits of accuracy */
     h = ((y3 - zz) + y3l) * rr;
-    let mut dy: f64 = h * (y * u0);
+    let mut dy: F = h * (y * u0);
 
     /* the approximation of zz^(1/3) is y - dy */
-    let mut y1: f64 = y - dy;
+    let mut y1: F = y - dy;
     dy = (y - y1) - dy;
 
     /* the approximation of zz^(1/3) is now y1 + dy, where |dy| < 1/2 ulp(y)
      * (for rounding to nearest) */
-    let mut ady: f64 = dy.abs();
+    let mut ady: F = dy.abs();
 
     /* For directed roundings, ady0 is tiny when dy is tiny, or ady0 is near
      * from ulp(1);
      * for rounding to nearest, ady0 is tiny when dy is near from 1/2 ulp(1),
      * or from 3/2 ulp(1). */
-    let mut ady0: f64 = (ady - off[round as usize]).abs();
-    let mut ady1: f64 = (ady - (hf64!("0x1p-52") + off[round as usize])).abs();
+    let mut ady0: F = (ady - off[round as usize]).abs();
+    let mut ady1: F = (ady - (F::TWO_POW_NEG_SIG_BITS + off[round as usize])).abs();
 
-    if ady0 < hf64!("0x1p-75") || ady1 < hf64!("0x1p-75") {
+    let magic = F::from_parts(false, (-75 + F::EXP_BIAS as i32) as u32, zero);
+
+    if ady0 < magic || ady1 < magic {
         cold_path();
 
         y2 = y1 * y1;
-        y2l = fmaf64(y1, y1, -y2);
+        y2l = y1.fma(y1, -y2);
         y3 = y2 * y1;
-        y3l = fmaf64(y1, y2, -y3) + y1 * y2l;
+        y3l = y1.fma(y2, -y3) + y1 * y2l;
         h = ((y3 - zz) + y3l) * rr;
         dy = h * (y1 * u0);
         y = y1 - dy;
         dy = (y1 - y) - dy;
         y1 = y;
         ady = dy.abs();
         ady0 = (ady - off[round as usize]).abs();
-        ady1 = (ady - (hf64!("0x1p-52") + off[round as usize])).abs();
+        ady1 = (ady - (F::TWO_POW_NEG_SIG_BITS + off[round as usize])).abs();
 
-        if ady0 < hf64!("0x1p-98") || ady1 < hf64!("0x1p-98") {
+        let magic2 = F::from_parts(false, (-98 + F::EXP_BIAS as i32) as u32, zero);
+        if ady0 < magic2 || ady1 < magic2 {
             cold_path();
-            let azz: f64 = zz.abs();
+            let azz: F = zz.abs();
 
             // ~ 0x1.79d15d0e8d59b80000000000000ffc3dp+0
-            if azz == hf64!("0x1.9b78223aa307cp+1") {
-                y1 = hf64!("0x1.79d15d0e8d59cp+0").copysign(zz);
+            if azz == F::AZMAGIC1 {
+                y1 = F::AZMAGIC2.copysign(zz);
             }
 
             // ~ 0x1.de87aa837820e80000000000001c0f08p+0
-            if azz == hf64!("0x1.a202bfc89ddffp+2") {
-                y1 = hf64!("0x1.de87aa837820fp+0").copysign(zz);
+            if azz == F::AZMAGIC3 {
+                y1 = F::AZMAGIC4.copysign(zz);
             }
 
             if round != Round::Nearest {
-                let wlist = [
-                    (hf64!("0x1.3a9ccd7f022dbp+0"), hf64!("0x1.1236160ba9b93p+0")), // ~ 0x1.1236160ba9b930000000000001e7e8fap+0
-                    (hf64!("0x1.7845d2faac6fep+0"), hf64!("0x1.23115e657e49cp+0")), // ~ 0x1.23115e657e49c0000000000001d7a799p+0
-                    (hf64!("0x1.d1ef81cbbbe71p+0"), hf64!("0x1.388fb44cdcf5ap+0")), // ~ 0x1.388fb44cdcf5a0000000000002202c55p+0
-                    (hf64!("0x1.0a2014f62987cp+1"), hf64!("0x1.46bcbf47dc1e8p+0")), // ~ 0x1.46bcbf47dc1e8000000000000303aa2dp+0
-                    (hf64!("0x1.fe18a044a5501p+1"), hf64!("0x1.95decfec9c904p+0")), // ~ 0x1.95decfec9c9040000000000000159e8ep+0
-                    (hf64!("0x1.a6bb8c803147bp+2"), hf64!("0x1.e05335a6401dep+0")), // ~ 0x1.e05335a6401de00000000000027ca017p+0
-                    (hf64!("0x1.ac8538a031cbdp+2"), hf64!("0x1.e281d87098de8p+0")), // ~ 0x1.e281d87098de80000000000000ee9314p+0
-                ];
-
-                for (a, b) in wlist {
+                for (a, b) in F::WLIST {
                     if azz == a {
-                        let tmp = if round as u64 + sign == 2 { hf64!("0x1p-52") } else { 0.0 };
+                        let tmp = if F::Int::from(round as u8) + sign == F::Int::cast_from(2) {
+                            F::TWO_POW_NEG_SIG_BITS
+                        } else {
+                            F::ZERO
+                        };
                         y1 = (b + tmp).copysign(zz);
                     }
                 }
             }
         }
     }
 
-    let mut cvt3: u64 = y1.to_bits();
-    cvt3 = cvt3.wrapping_add(((et.wrapping_sub(342).wrapping_sub(1023)) as u64) << 52);
-    let m0: u64 = cvt3 << 30;
+    let mut cvt3 = y1.to_bits();
+    cvt3 = cvt3.wrapping_add((F::Int::cast_from(et.wrapping_sub(342).wrapping_sub(1023))) << 52);
+    let m0 = cvt3 << 30;
     let m1 = m0 >> 63;
 
-    if (m0 ^ m1) <= (1u64 << 30) {
+    if (m0 ^ m1) <= (one << 30) {
         cold_path();
 
-        let mut cvt4: u64 = y1.to_bits();
-        cvt4 = (cvt4 + (164 << 15)) & 0xffffffffffff0000u64;
+        let mut cvt4 = y1.to_bits();
+        cvt4 = (cvt4 + (F::Int::cast_from(164) << 15)) & F::Int::cast_from(0xffffffffffff0000u64);
 
-        if ((f64::from_bits(cvt4) - y1) - dy).abs() < hf64!("0x1p-60") || (zz).abs() == 1.0 {
-            cvt3 = (cvt3 + (1u64 << 15)) & 0xffffffffffff0000u64;
+        let magic3 = F::from_parts(false, (-60 + F::EXP_BIAS as i32) as u32, zero);
+        if ((F::from_bits(cvt4) - y1) - dy).abs() < magic3 || (zz).abs() == F::ONE {
+            cvt3 = (cvt3 + (one << 15)) & F::Int::cast_from(0xffffffffffff0000u64);
         }
     }
 
-    FpResult::ok(f64::from_bits(cvt3))
+    FpResult::ok(F::from_bits(cvt3))
 }
 
-fn fmaf64(x: f64, y: f64, z: f64) -> f64 {
-    #[cfg(intrinsics_enabled)]
-    {
-        return unsafe { core::intrinsics::fmaf64(x, y, z) };
-    }
+trait CbrtHelper: Float {
+    /// 2^(n / 3) for n = [0, 1, 2]
+    const ESCALE: [Self; 3];
+    /// The polynomial `c0+c1*x+c2*x^2+c3*x^3` approximates `x^(1/3)` on `[1,2]`
+    /// with maximal error < 9.2e-5 (attained at x=2)
+    const C: [Self; 4];
+    const U0: Self;
+    const U1: Self;
+    const RSC: [Self; 6];
+    const OFF: [Self; 4];
+    const WLIST: [(Self, Self); 7];
+    const AZMAGIC1: Self;
+    const AZMAGIC2: Self;
+    const AZMAGIC3: Self;
+    const AZMAGIC4: Self;
+    fn fma(self, y: Self, z: Self) -> Self;
+}
 
-    #[cfg(not(intrinsics_enabled))]
-    {
-        return super::fma(x, y, z);
+impl CbrtHelper for f64 {
+    const ESCALE: [Self; 3] = [
+        1.0,
+        hf64!("0x1.428a2f98d728bp+0"), /* 2^(1/3) */
+        hf64!("0x1.965fea53d6e3dp+0"), /* 2^(2/3) */
+    ];
+
+    const C: [Self; 4] = [
+        hf64!("0x1.1b0babccfef9cp-1"),
+        hf64!("0x1.2c9a3e94d1da5p-1"),
+        hf64!("-0x1.4dc30b1a1ddbap-3"),
+        hf64!("0x1.7a8d3e4ec9b07p-6"),
+    ];
+
+    const U0: Self = hf64!("0x1.5555555555555p-2");
+
+    const U1: Self = hf64!("0x1.c71c71c71c71cp-3");
+
+    const RSC: [Self; 6] = [1.0, -1.0, 0.5, -0.5, 0.25, -0.25];
+
+    const OFF: [Self; 4] = [hf64!("0x1p-53"), 0.0, 0.0, 0.0];
+
+    const WLIST: [(Self, Self); 7] = [
+        (hf64!("0x1.3a9ccd7f022dbp+0"), hf64!("0x1.1236160ba9b93p+0")), // ~ 0x1.1236160ba9b930000000000001e7e8fap+0
+        (hf64!("0x1.7845d2faac6fep+0"), hf64!("0x1.23115e657e49cp+0")), // ~ 0x1.23115e657e49c0000000000001d7a799p+0
+        (hf64!("0x1.d1ef81cbbbe71p+0"), hf64!("0x1.388fb44cdcf5ap+0")), // ~ 0x1.388fb44cdcf5a0000000000002202c55p+0
+        (hf64!("0x1.0a2014f62987cp+1"), hf64!("0x1.46bcbf47dc1e8p+0")), // ~ 0x1.46bcbf47dc1e8000000000000303aa2dp+0
+        (hf64!("0x1.fe18a044a5501p+1"), hf64!("0x1.95decfec9c904p+0")), // ~ 0x1.95decfec9c9040000000000000159e8ep+0
+        (hf64!("0x1.a6bb8c803147bp+2"), hf64!("0x1.e05335a6401dep+0")), // ~ 0x1.e05335a6401de00000000000027ca017p+0
+        (hf64!("0x1.ac8538a031cbdp+2"), hf64!("0x1.e281d87098de8p+0")), // ~ 0x1.e281d87098de80000000000000ee9314p+0
+    ];
+
+    const AZMAGIC1: Self = hf64!("0x1.9b78223aa307cp+1");
+    const AZMAGIC2: Self = hf64!("0x1.79d15d0e8d59cp+0");
+    const AZMAGIC3: Self = hf64!("0x1.a202bfc89ddffp+2");
+    const AZMAGIC4: Self = hf64!("0x1.de87aa837820fp+0");
+
+    fn fma(self, y: Self, z: Self) -> Self {
+        #[cfg(intrinsics_enabled)]
+        {
+            return unsafe { core::intrinsics::fmaf64(self, y, z) };
+        }
+
+        #[cfg(not(intrinsics_enabled))]
+        {
+            return super::fma(self, y, z);
+        }
     }
 }