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Add constants based on Archimedes' original circle constant #15248

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4d40d59
Add constants based on Archimedes' original circle constant
bugQ Jun 30, 2014
7f7bef2
Removing many redundant circle constants. Users can bitshift/divide …
bugQ Jun 30, 2014
ff7a454
More aggressive redundancy elimination among Float constants.
bugQ Jun 30, 2014
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66 changes: 19 additions & 47 deletions src/libcore/num/f32.rs
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Expand Up @@ -51,39 +51,27 @@ pub mod consts {
// of `Float`.

/// Archimedes' constant
pub static PI: f32 = 3.14159265358979323846264338327950288_f32;
pub static TAU: f32 = 6.28318530717958647692528676655900576_f32;

/// pi * 2.0
pub static PI_2: f32 = 6.28318530717958647692528676655900576_f32;
/// pi = tau / 2.0
pub static PI: f32 = 3.14159265358979323846264338327950288_f32;

/// pi/2.0
pub static FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;
/// tau / 3.0 = 2.0 * pi / 3.0
pub static FRAC_TAU_3: f32 = 2.094395102393195492308428922186335256_f32;

/// pi/3.0
/// pi / 3.0 = tau / 6.0
pub static FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32;

/// pi/4.0
pub static FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;

/// pi/6.0
pub static FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32;
/// 1.0 / tau = 1.0 / (pi * 2.0)
pub static FRAC_1_TAU: f32 = 0.159154943091895335768883763372514362_f32;

/// pi/8.0
pub static FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32;

/// 1.0/pi
/// 1.0 / pi = 2.0 / tau
pub static FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;

/// 2.0/pi
pub static FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;

/// 2.0/sqrt(pi)
pub static FRAC_2_SQRTPI: f32 = 1.12837916709551257389615890312154517_f32;

/// sqrt(2.0)
pub static SQRT2: f32 = 1.41421356237309504880168872420969808_f32;

/// 1.0/sqrt(2.0)
/// 1.0 / sqrt(2.0)
pub static FRAC_1_SQRT2: f32 = 0.707106781186547524400844362104849039_f32;

/// Euler's number
Expand Down Expand Up @@ -265,44 +253,28 @@ impl Float for f32 {

/// Archimedes' constant
#[inline]
fn pi() -> f32 { consts::PI }
fn tau() -> f32 { consts::TAU }

/// 2.0 * pi
/// pi = tau / 2.0
#[inline]
fn two_pi() -> f32 { consts::PI_2 }
fn pi() -> f32 { consts::PI }

/// pi / 2.0
/// tau / 3.0 = 2.0 * pi / 3.0
#[inline]
fn frac_pi_2() -> f32 { consts::FRAC_PI_2 }
fn frac_tau_3() -> f32 { consts::FRAC_TAU_3 }

/// pi / 3.0
/// pi / 3.0 = tau / 6.0
#[inline]
fn frac_pi_3() -> f32 { consts::FRAC_PI_3 }

/// pi / 4.0
/// 1.0 / tau = 1.0 / (pi * 2.0)
#[inline]
fn frac_pi_4() -> f32 { consts::FRAC_PI_4 }
fn frac_1_tau() -> f32 { consts::FRAC_1_TAU }

/// pi / 6.0
#[inline]
fn frac_pi_6() -> f32 { consts::FRAC_PI_6 }

/// pi / 8.0
#[inline]
fn frac_pi_8() -> f32 { consts::FRAC_PI_8 }

/// 1 .0/ pi
/// 1.0 / pi = 2.0 / tau
#[inline]
fn frac_1_pi() -> f32 { consts::FRAC_1_PI }

/// 2.0 / pi
#[inline]
fn frac_2_pi() -> f32 { consts::FRAC_2_PI }

/// 2.0 / sqrt(pi)
#[inline]
fn frac_2_sqrtpi() -> f32 { consts::FRAC_2_SQRTPI }

/// Euler's number
#[inline]
fn e() -> f32 { consts::E }
Expand Down
68 changes: 19 additions & 49 deletions src/libcore/num/f64.rs
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Expand Up @@ -43,9 +43,7 @@ pub static MIN_10_EXP: int = -307;
pub static MAX_10_EXP: int = 308;

pub static NAN: f64 = 0.0_f64/0.0_f64;

pub static INFINITY: f64 = 1.0_f64/0.0_f64;

pub static NEG_INFINITY: f64 = -1.0_f64/0.0_f64;

/// Various useful constants.
Expand All @@ -57,39 +55,27 @@ pub mod consts {
// of `Float`.

/// Archimedes' constant
pub static PI: f64 = 3.14159265358979323846264338327950288_f64;
pub static TAU: f64 = 6.28318530717958647692528676655900576_f64;

/// pi * 2.0
pub static PI_2: f64 = 6.28318530717958647692528676655900576_f64;
/// pi = tau / 2.0
pub static PI: f64 = 3.14159265358979323846264338327950288_f64;

/// pi/2.0
pub static FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
/// tau / 3.0 = 2.0 * pi / 3.0
pub static FRAC_TAU_3: f64 = 2.094395102393195492308428922186335256_f64;

/// pi/3.0
/// pi / 3.0 = tau / 6.0
pub static FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;

/// pi/4.0
pub static FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;

/// pi/6.0
pub static FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
/// 1.0 / tau = 1.0 / (pi * 2.0)
pub static FRAC_1_TAU: f64 = 0.159154943091895335768883763372514362_f64;

/// pi/8.0
pub static FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;

/// 1.0/pi
/// 1.0 / pi = 2.0 / tau
pub static FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;

/// 2.0/pi
pub static FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;

/// 2.0/sqrt(pi)
pub static FRAC_2_SQRTPI: f64 = 1.12837916709551257389615890312154517_f64;

/// sqrt(2.0)
pub static SQRT2: f64 = 1.41421356237309504880168872420969808_f64;

/// 1.0/sqrt(2.0)
/// 1.0 / sqrt(2.0)
pub static FRAC_1_SQRT2: f64 = 0.707106781186547524400844362104849039_f64;

/// Euler's number
Expand Down Expand Up @@ -272,44 +258,28 @@ impl Float for f64 {

/// Archimedes' constant
#[inline]
fn pi() -> f64 { consts::PI }
fn tau() -> f64 { consts::TAU }

/// 2.0 * pi
/// pi = tau / 2.0
#[inline]
fn two_pi() -> f64 { consts::PI_2 }
fn pi() -> f64 { consts::PI }

/// pi / 2.0
/// tau / 3.0 = 2.0 * pi / 3.0
#[inline]
fn frac_pi_2() -> f64 { consts::FRAC_PI_2 }
fn frac_tau_3() -> f64 { consts::FRAC_TAU_3 }

/// pi / 3.0
/// pi / 3.0 = tau / 6.0
#[inline]
fn frac_pi_3() -> f64 { consts::FRAC_PI_3 }

/// pi / 4.0
#[inline]
fn frac_pi_4() -> f64 { consts::FRAC_PI_4 }

/// pi / 6.0
#[inline]
fn frac_pi_6() -> f64 { consts::FRAC_PI_6 }

/// pi / 8.0
/// 1.0 / tau = 1.0 / (pi * 2.0)
#[inline]
fn frac_pi_8() -> f64 { consts::FRAC_PI_8 }
fn frac_1_tau() -> f64 { consts::FRAC_1_TAU }

/// 1.0 / pi
/// 1.0 / pi = 2.0 / tau
#[inline]
fn frac_1_pi() -> f64 { consts::FRAC_1_PI }

/// 2.0 / pi
#[inline]
fn frac_2_pi() -> f64 { consts::FRAC_2_PI }

/// 2.0 / sqrt(pi)
#[inline]
fn frac_2_sqrtpi() -> f64 { consts::FRAC_2_SQRTPI }

/// Euler's number
#[inline]
fn e() -> f64 { consts::E }
Expand Down
24 changes: 8 additions & 16 deletions src/libcore/num/mod.rs
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Expand Up @@ -1495,25 +1495,17 @@ pub trait Float: Signed + Primitive {
// FIXME (#5527): These should be associated constants

/// Archimedes' constant.
fn tau() -> Self;
/// pi = tau / 2.0.
fn pi() -> Self;
/// 2.0 * pi.
fn two_pi() -> Self;
/// pi / 2.0.
fn frac_pi_2() -> Self;
/// pi / 3.0.
/// tau / 3.0 = 2.0 * pi / 3.0.
fn frac_tau_3() -> Self;
/// pi / 3.0 = tau / 6.0.
fn frac_pi_3() -> Self;
/// pi / 4.0.
fn frac_pi_4() -> Self;
/// pi / 6.0.
fn frac_pi_6() -> Self;
/// pi / 8.0.
fn frac_pi_8() -> Self;
/// 1.0 / pi.
/// 1.0 / tau = 1.0 / (pi * 2.0).
fn frac_1_tau() -> Self;
/// 1.0 / pi = 2.0 / tau.
fn frac_1_pi() -> Self;
/// 2.0 / pi.
fn frac_2_pi() -> Self;
/// 2.0 / sqrt(pi).
fn frac_2_sqrtpi() -> Self;

/// Euler's number.
fn e() -> Self;
Expand Down
21 changes: 7 additions & 14 deletions src/libstd/num/f32.rs
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Expand Up @@ -594,16 +594,13 @@ mod tests {

#[test]
fn test_real_consts() {
let tau: f32 = Float::tau();
let frac_tau_3: f32 = Float::frac_tau_3();
let frac_1_tau: f32 = Float::frac_1_tau();
let pi: f32 = Float::pi();
let two_pi: f32 = Float::two_pi();
let frac_pi_2: f32 = Float::frac_pi_2();
let frac_pi_3: f32 = Float::frac_pi_3();
let frac_pi_4: f32 = Float::frac_pi_4();
let frac_pi_6: f32 = Float::frac_pi_6();
let frac_pi_8: f32 = Float::frac_pi_8();
let frac_1_pi: f32 = Float::frac_1_pi();
let frac_2_pi: f32 = Float::frac_2_pi();
let frac_2_sqrtpi: f32 = Float::frac_2_sqrtpi();

let sqrt2: f32 = Float::sqrt2();
let frac_1_sqrt2: f32 = Float::frac_1_sqrt2();
let e: f32 = Float::e();
Expand All @@ -612,15 +609,11 @@ mod tests {
let ln_2: f32 = Float::ln_2();
let ln_10: f32 = Float::ln_10();

assert_approx_eq!(two_pi, 2f32 * pi);
assert_approx_eq!(frac_pi_2, pi / 2f32);
assert_approx_eq!(frac_tau_3, tau / 3f32);
assert_approx_eq!(frac_1_tau, 1f32 / tau);
assert_approx_eq!(frac_pi_3, pi / 3f32);
assert_approx_eq!(frac_pi_4, pi / 4f32);
assert_approx_eq!(frac_pi_6, pi / 6f32);
assert_approx_eq!(frac_pi_8, pi / 8f32);
assert_approx_eq!(frac_1_pi, 1f32 / pi);
assert_approx_eq!(frac_2_pi, 2f32 / pi);
assert_approx_eq!(frac_2_sqrtpi, 2f32 / pi.sqrt());

assert_approx_eq!(sqrt2, 2f32.sqrt());
assert_approx_eq!(frac_1_sqrt2, 1f32 / 2f32.sqrt());
assert_approx_eq!(log2_e, e.log2());
Expand Down
21 changes: 7 additions & 14 deletions src/libstd/num/f64.rs
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Expand Up @@ -597,16 +597,13 @@ mod tests {

#[test]
fn test_real_consts() {
let tau: f64 = Float::tau();
let frac_tau_3: f64 = Float::frac_tau_3();
let frac_1_tau: f64 = Float::frac_1_tau();
let pi: f64 = Float::pi();
let two_pi: f64 = Float::two_pi();
let frac_pi_2: f64 = Float::frac_pi_2();
let frac_pi_3: f64 = Float::frac_pi_3();
let frac_pi_4: f64 = Float::frac_pi_4();
let frac_pi_6: f64 = Float::frac_pi_6();
let frac_pi_8: f64 = Float::frac_pi_8();
let frac_1_pi: f64 = Float::frac_1_pi();
let frac_2_pi: f64 = Float::frac_2_pi();
let frac_2_sqrtpi: f64 = Float::frac_2_sqrtpi();

let sqrt2: f64 = Float::sqrt2();
let frac_1_sqrt2: f64 = Float::frac_1_sqrt2();
let e: f64 = Float::e();
Expand All @@ -615,15 +612,11 @@ mod tests {
let ln_2: f64 = Float::ln_2();
let ln_10: f64 = Float::ln_10();

assert_approx_eq!(two_pi, 2.0 * pi);
assert_approx_eq!(frac_pi_2, pi / 2f64);
assert_approx_eq!(frac_tau_3, tau / 3f64);
assert_approx_eq!(frac_1_tau, 1f64 / tau);
assert_approx_eq!(frac_pi_3, pi / 3f64);
assert_approx_eq!(frac_pi_4, pi / 4f64);
assert_approx_eq!(frac_pi_6, pi / 6f64);
assert_approx_eq!(frac_pi_8, pi / 8f64);
assert_approx_eq!(frac_1_pi, 1f64 / pi);
assert_approx_eq!(frac_2_pi, 2f64 / pi);
assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt());

assert_approx_eq!(sqrt2, 2f64.sqrt());
assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt());
assert_approx_eq!(log2_e, e.log2());
Expand Down