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Diffstat (limited to 'vendor/libm/src/math/atan.rs')
| -rw-r--r-- | vendor/libm/src/math/atan.rs | 185 |
1 files changed, 185 insertions, 0 deletions
diff --git a/vendor/libm/src/math/atan.rs b/vendor/libm/src/math/atan.rs new file mode 100644 index 000000000..d2684ece8 --- /dev/null +++ b/vendor/libm/src/math/atan.rs @@ -0,0 +1,185 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_atan.c */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ +/* atan(x) + * Method + * 1. Reduce x to positive by atan(x) = -atan(-x). + * 2. According to the integer k=4t+0.25 chopped, t=x, the argument + * is further reduced to one of the following intervals and the + * arctangent of t is evaluated by the corresponding formula: + * + * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) + * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) + * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) + * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) + * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +use super::fabs; +use core::f64; + +const ATANHI: [f64; 4] = [ + 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ + 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ + 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ + 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ +]; + +const ATANLO: [f64; 4] = [ + 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ + 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ + 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ + 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ +]; + +const AT: [f64; 11] = [ + 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ + -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ + 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ + -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ + 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ + -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ + 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ + -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ + 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ + -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ + 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ +]; + +/// Arctangent (f64) +/// +/// Computes the inverse tangent (arc tangent) of the input value. +/// Returns a value in radians, in the range of -pi/2 to pi/2. +#[inline] +#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] +pub fn atan(x: f64) -> f64 { + let mut x = x; + let mut ix = (x.to_bits() >> 32) as u32; + let sign = ix >> 31; + ix &= 0x7fff_ffff; + if ix >= 0x4410_0000 { + if x.is_nan() { + return x; + } + + let z = ATANHI[3] + f64::from_bits(0x0380_0000); // 0x1p-120f + return if sign != 0 { -z } else { z }; + } + + let id = if ix < 0x3fdc_0000 { + /* |x| < 0.4375 */ + if ix < 0x3e40_0000 { + /* |x| < 2^-27 */ + if ix < 0x0010_0000 { + /* raise underflow for subnormal x */ + force_eval!(x as f32); + } + + return x; + } + + -1 + } else { + x = fabs(x); + if ix < 0x3ff30000 { + /* |x| < 1.1875 */ + if ix < 0x3fe60000 { + /* 7/16 <= |x| < 11/16 */ + x = (2. * x - 1.) / (2. + x); + 0 + } else { + /* 11/16 <= |x| < 19/16 */ + x = (x - 1.) / (x + 1.); + 1 + } + } else if ix < 0x40038000 { + /* |x| < 2.4375 */ + x = (x - 1.5) / (1. + 1.5 * x); + 2 + } else { + /* 2.4375 <= |x| < 2^66 */ + x = -1. / x; + 3 + } + }; + + let z = x * x; + let w = z * z; + /* break sum from i=0 to 10 AT[i]z**(i+1) into odd and even poly */ + let s1 = z * (AT[0] + w * (AT[2] + w * (AT[4] + w * (AT[6] + w * (AT[8] + w * AT[10]))))); + let s2 = w * (AT[1] + w * (AT[3] + w * (AT[5] + w * (AT[7] + w * AT[9])))); + + if id < 0 { + return x - x * (s1 + s2); + } + + let z = i!(ATANHI, id as usize) - (x * (s1 + s2) - i!(ATANLO, id as usize) - x); + + if sign != 0 { + -z + } else { + z + } +} + +#[cfg(test)] +mod tests { + use super::atan; + use core::f64; + + #[test] + fn sanity_check() { + for (input, answer) in [ + (3.0_f64.sqrt() / 3.0, f64::consts::FRAC_PI_6), + (1.0, f64::consts::FRAC_PI_4), + (3.0_f64.sqrt(), f64::consts::FRAC_PI_3), + (-3.0_f64.sqrt() / 3.0, -f64::consts::FRAC_PI_6), + (-1.0, -f64::consts::FRAC_PI_4), + (-3.0_f64.sqrt(), -f64::consts::FRAC_PI_3), + ] + .iter() + { + assert!( + (atan(*input) - answer) / answer < 1e-5, + "\natan({:.4}/16) = {:.4}, actual: {}", + input * 16.0, + answer, + atan(*input) + ); + } + } + + #[test] + fn zero() { + assert_eq!(atan(0.0), 0.0); + } + + #[test] + fn infinity() { + assert_eq!(atan(f64::INFINITY), f64::consts::FRAC_PI_2); + } + + #[test] + fn minus_infinity() { + assert_eq!(atan(f64::NEG_INFINITY), -f64::consts::FRAC_PI_2); + } + + #[test] + fn nan() { + assert!(atan(f64::NAN).is_nan()); + } +} |