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Implement {float}::asin_acos(), {float}::asin(), and {float}::acos() #48

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merged 5 commits into from
Aug 28, 2020
Merged

Implement {float}::asin_acos(), {float}::asin(), and {float}::acos() #48

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b57bdce
f64x2::asin_acos, f64x2::asin, f64x2::acos
fu5ha Aug 21, 2020
7275c67
f32x4::asin_acos, f32x4::asin, f32x4::acos
fu5ha Aug 21, 2020
e2c42cb
tests for asin and acos
fu5ha Aug 21, 2020
d965e80
fix polynomial_4, make test thresholds tighter
fu5ha Aug 21, 2020
d75d769
impl asin_acos, asin, acos for avx/256bit types
fu5ha Aug 28, 2020
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121 changes: 121 additions & 0 deletions src/f32x4_.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -448,6 +448,119 @@ impl f32x4 {
self ^ (signs & Self::from(-0.0))
}

#[inline]
#[must_use]
#[allow(non_upper_case_globals)]
pub fn asin_acos(self) -> (Self, Self) {
// Based on the Agner Fog "vector class library":
// https://github.com/vectorclass/version2/blob/master/vectormath_trig.h
const_f32_as_f32x4!(P4asinf, 4.2163199048E-2);
const_f32_as_f32x4!(P3asinf, 2.4181311049E-2);
const_f32_as_f32x4!(P2asinf, 4.5470025998E-2);
const_f32_as_f32x4!(P1asinf, 7.4953002686E-2);
const_f32_as_f32x4!(P0asinf, 1.6666752422E-1);

let xa = self.abs();
let big = xa.cmp_ge(f32x4::splat(0.5));

let x1 = f32x4::splat(0.5) * (f32x4::ONE - xa);
let x2 = xa * xa;
let x3 = big.blend(x1, x2);

let xb = x1.sqrt();

let x4 = big.blend(xb, xa);

let z = polynomial_4(x3, P0asinf, P1asinf, P2asinf, P3asinf, P4asinf);
let z = z.mul_add(x3 * x4, x4);

let z1 = z + z;

// acos
let z3 = self.cmp_lt(f32x4::ZERO).blend(f32x4::PI - z1, z1);
let z4 = f32x4::FRAC_PI_2 - z.flip_signs(self);
let acos = big.blend(z3, z4);

// asin
let z3 = f32x4::FRAC_PI_2 - z1;
let asin = big.blend(z3, z);
let asin = asin.flip_signs(self);

(asin, acos)
}

#[inline]
#[must_use]
#[allow(non_upper_case_globals)]
pub fn asin(self) -> Self {
// Based on the Agner Fog "vector class library":
// https://github.com/vectorclass/version2/blob/master/vectormath_trig.h
const_f32_as_f32x4!(P4asinf, 4.2163199048E-2);
const_f32_as_f32x4!(P3asinf, 2.4181311049E-2);
const_f32_as_f32x4!(P2asinf, 4.5470025998E-2);
const_f32_as_f32x4!(P1asinf, 7.4953002686E-2);
const_f32_as_f32x4!(P0asinf, 1.6666752422E-1);

let xa = self.abs();
let big = xa.cmp_ge(f32x4::splat(0.5));

let x1 = f32x4::splat(0.5) * (f32x4::ONE - xa);
let x2 = xa * xa;
let x3 = big.blend(x1, x2);

let xb = x1.sqrt();

let x4 = big.blend(xb, xa);

let z = polynomial_4(x3, P0asinf, P1asinf, P2asinf, P3asinf, P4asinf);
let z = z.mul_add(x3 * x4, x4);

let z1 = z + z;

// asin
let z3 = f32x4::FRAC_PI_2 - z1;
let asin = big.blend(z3, z);
let asin = asin.flip_signs(self);

asin
}

#[inline]
#[must_use]
#[allow(non_upper_case_globals)]
pub fn acos(self) -> Self {
// Based on the Agner Fog "vector class library":
// https://github.com/vectorclass/version2/blob/master/vectormath_trig.h
const_f32_as_f32x4!(P4asinf, 4.2163199048E-2);
const_f32_as_f32x4!(P3asinf, 2.4181311049E-2);
const_f32_as_f32x4!(P2asinf, 4.5470025998E-2);
const_f32_as_f32x4!(P1asinf, 7.4953002686E-2);
const_f32_as_f32x4!(P0asinf, 1.6666752422E-1);

let xa = self.abs();
let big = xa.cmp_ge(f32x4::splat(0.5));

let x1 = f32x4::splat(0.5) * (f32x4::ONE - xa);
let x2 = xa * xa;
let x3 = big.blend(x1, x2);

let xb = x1.sqrt();

let x4 = big.blend(xb, xa);

let z = polynomial_4(x3, P0asinf, P1asinf, P2asinf, P3asinf, P4asinf);
let z = z.mul_add(x3 * x4, x4);

let z1 = z + z;

// acos
let z3 = self.cmp_lt(f32x4::ZERO).blend(f32x4::PI - z1, z1);
let z4 = f32x4::FRAC_PI_2 - z.flip_signs(self);
let acos = big.blend(z3, z4);

acos
}

#[inline]
#[must_use]
#[allow(non_upper_case_globals)]
Expand Down Expand Up @@ -691,3 +804,11 @@ impl f32x4 {
Self::ln(self) * Self::LOG10_E
}
}

#[must_use]
#[inline]
fn polynomial_4(x: f32x4, c0: f32x4, c1: f32x4, c2: f32x4, c3: f32x4, c4: f32x4) -> f32x4 {
let x2 = x * x;
let x4 = x2 * x2;
c3.mul_add(x, c2).mul_add(x2, c1.mul_add(x, c0) + c4 * x4)
}
121 changes: 121 additions & 0 deletions src/f32x8_.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -567,6 +567,119 @@ impl f32x8 {
self ^ (signs & Self::from(-0.0))
}

#[inline]
#[must_use]
#[allow(non_upper_case_globals)]
pub fn asin_acos(self) -> (Self, Self) {
// Based on the Agner Fog "vector class library":
// https://github.com/vectorclass/version2/blob/master/vectormath_trig.h
const_f32_as_f32x8!(P4asinf, 4.2163199048E-2);
const_f32_as_f32x8!(P3asinf, 2.4181311049E-2);
const_f32_as_f32x8!(P2asinf, 4.5470025998E-2);
const_f32_as_f32x8!(P1asinf, 7.4953002686E-2);
const_f32_as_f32x8!(P0asinf, 1.6666752422E-1);

let xa = self.abs();
let big = xa.cmp_ge(f32x8::splat(0.5));

let x1 = f32x8::splat(0.5) * (f32x8::ONE - xa);
let x2 = xa * xa;
let x3 = big.blend(x1, x2);

let xb = x1.sqrt();

let x4 = big.blend(xb, xa);

let z = polynomial_4(x3, P0asinf, P1asinf, P2asinf, P3asinf, P4asinf);
let z = z.mul_add(x3 * x4, x4);

let z1 = z + z;

// acos
let z3 = self.cmp_lt(f32x8::ZERO).blend(f32x8::PI - z1, z1);
let z4 = f32x8::FRAC_PI_2 - z.flip_signs(self);
let acos = big.blend(z3, z4);

// asin
let z3 = f32x8::FRAC_PI_2 - z1;
let asin = big.blend(z3, z);
let asin = asin.flip_signs(self);

(asin, acos)
}

#[inline]
#[must_use]
#[allow(non_upper_case_globals)]
pub fn asin(self) -> Self {
// Based on the Agner Fog "vector class library":
// https://github.com/vectorclass/version2/blob/master/vectormath_trig.h
const_f32_as_f32x8!(P4asinf, 4.2163199048E-2);
const_f32_as_f32x8!(P3asinf, 2.4181311049E-2);
const_f32_as_f32x8!(P2asinf, 4.5470025998E-2);
const_f32_as_f32x8!(P1asinf, 7.4953002686E-2);
const_f32_as_f32x8!(P0asinf, 1.6666752422E-1);

let xa = self.abs();
let big = xa.cmp_ge(f32x8::splat(0.5));

let x1 = f32x8::splat(0.5) * (f32x8::ONE - xa);
let x2 = xa * xa;
let x3 = big.blend(x1, x2);

let xb = x1.sqrt();

let x4 = big.blend(xb, xa);

let z = polynomial_4(x3, P0asinf, P1asinf, P2asinf, P3asinf, P4asinf);
let z = z.mul_add(x3 * x4, x4);

let z1 = z + z;

// asin
let z3 = f32x8::FRAC_PI_2 - z1;
let asin = big.blend(z3, z);
let asin = asin.flip_signs(self);

asin
}

#[inline]
#[must_use]
#[allow(non_upper_case_globals)]
pub fn acos(self) -> Self {
// Based on the Agner Fog "vector class library":
// https://github.com/vectorclass/version2/blob/master/vectormath_trig.h
const_f32_as_f32x8!(P4asinf, 4.2163199048E-2);
const_f32_as_f32x8!(P3asinf, 2.4181311049E-2);
const_f32_as_f32x8!(P2asinf, 4.5470025998E-2);
const_f32_as_f32x8!(P1asinf, 7.4953002686E-2);
const_f32_as_f32x8!(P0asinf, 1.6666752422E-1);

let xa = self.abs();
let big = xa.cmp_ge(f32x8::splat(0.5));

let x1 = f32x8::splat(0.5) * (f32x8::ONE - xa);
let x2 = xa * xa;
let x3 = big.blend(x1, x2);

let xb = x1.sqrt();

let x4 = big.blend(xb, xa);

let z = polynomial_4(x3, P0asinf, P1asinf, P2asinf, P3asinf, P4asinf);
let z = z.mul_add(x3 * x4, x4);

let z1 = z + z;

// acos
let z3 = self.cmp_lt(f32x8::ZERO).blend(f32x8::PI - z1, z1);
let z4 = f32x8::FRAC_PI_2 - z.flip_signs(self);
let acos = big.blend(z3, z4);

acos
}

#[inline]
#[must_use]
#[allow(non_upper_case_globals)]
Expand Down Expand Up @@ -863,3 +976,11 @@ impl Not for f32x8 {
}
}
}

#[must_use]
#[inline]
fn polynomial_4(x: f32x8, c0: f32x8, c1: f32x8, c2: f32x8, c3: f32x8, c4: f32x8) -> f32x8 {
let x2 = x * x;
let x4 = x2 * x2;
c3.mul_add(x, c2).mul_add(x2, c1.mul_add(x, c0) + c4 * x4)
}
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