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Diffstat (limited to 'library/compiler-builtins/libm/src/math/cbrt.rs')
| -rw-r--r-- | library/compiler-builtins/libm/src/math/cbrt.rs | 219 |
1 files changed, 219 insertions, 0 deletions
diff --git a/library/compiler-builtins/libm/src/math/cbrt.rs b/library/compiler-builtins/libm/src/math/cbrt.rs new file mode 100644 index 00000000000..cf56f7a9792 --- /dev/null +++ b/library/compiler-builtins/libm/src/math/cbrt.rs @@ -0,0 +1,219 @@ +/* SPDX-License-Identifier: MIT */ +/* origin: core-math/src/binary64/cbrt/cbrt.c + * Copyright (c) 2021-2022 Alexei Sibidanov. + * Ported to Rust in 2025 by Trevor Gross. + */ + +use super::Float; +use super::support::{FpResult, 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]; + + /* 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 mut e: u32 = (hx >> f64::SIG_BITS) as u32 & f64::EXP_SAT; + + if ((e + 1) & f64::EXP_SAT) < 2 { + cold_path(); + + let ix: u64 = hx & !f64::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 { + return FpResult::ok(x + x); + } + + let nz = ix.leading_zeros() - 11; /* subnormal */ + mant <<= nz; + mant &= f64::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 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); + + /* 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); + + /* 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; + + /* y is an approximation of z^(1/3) */ + let mut h: f64 = y2 * (y * r) - 1.0; + + /* 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); + + /* 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 = y.fma(y, -y2); + + /* y2 + y2l = y^2 exactly */ + let mut y3: f64 = y2 * y; + let mut y3l: f64 = 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); + + /* the approximation of zz^(1/3) is y - dy */ + let mut y1: f64 = 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(); + + /* 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(); + + if ady0 < hf64!("0x1p-75") || ady1 < hf64!("0x1p-75") { + cold_path(); + + y2 = y1 * y1; + y2l = y1.fma(y1, -y2); + y3 = y2 * y1; + 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(); + + if ady0 < hf64!("0x1p-98") || ady1 < hf64!("0x1p-98") { + cold_path(); + let azz: f64 = zz.abs(); + + // ~ 0x1.79d15d0e8d59b80000000000000ffc3dp+0 + if azz == hf64!("0x1.9b78223aa307cp+1") { + y1 = hf64!("0x1.79d15d0e8d59cp+0").copysign(zz); + } + + // ~ 0x1.de87aa837820e80000000000001c0f08p+0 + if azz == hf64!("0x1.a202bfc89ddffp+2") { + y1 = hf64!("0x1.de87aa837820fp+0").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 { + if azz == a { + let tmp = if round as u64 + sign == 2 { + hf64!("0x1p-52") + } else { + 0.0 + }; + 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 m1 = m0 >> 63; + + if (m0 ^ m1) <= (1u64 << 30) { + cold_path(); + + let mut cvt4: u64 = y1.to_bits(); + cvt4 = (cvt4 + (164 << 15)) & 0xffffffffffff0000u64; + + if ((f64::from_bits(cvt4) - y1) - dy).abs() < hf64!("0x1p-60") || (zz).abs() == 1.0 { + cvt3 = (cvt3 + (1u64 << 15)) & 0xffffffffffff0000u64; + } + } + + FpResult::ok(f64::from_bits(cvt3)) +} + +#[cfg(test)] +mod tests { + use super::*; + + #[test] + fn spot_checks() { + if !cfg!(x86_no_sse) { + // Exposes a rounding mode problem. Ignored on i586 because of inaccurate FMA. + assert_biteq!( + cbrt(f64::from_bits(0xf7f792b28f600000)), + f64::from_bits(0xd29ce68655d962f3) + ); + } + } +} |