/* origin: FreeBSD /usr/src/lib/msun/src/e_j1f.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
/*
* ====================================================
* 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.
* ====================================================
*/
use super::{cosf, fabsf, logf, sinf, sqrtf};
const INVSQRTPI: f32 = 5.6418961287e-01; /* 0x3f106ebb */
const TPI: f32 = 6.3661974669e-01; /* 0x3f22f983 */
fn common(ix: u32, x: f32, y1: bool, sign: bool) -> f32 {
let z: f64;
let mut s: f64;
let c: f64;
let mut ss: f64;
let mut cc: f64;
s = sinf(x) as f64;
if y1 {
s = -s;
}
c = cosf(x) as f64;
cc = s - c;
if ix < 0x7f000000 {
ss = -s - c;
z = cosf(2.0 * x) as f64;
if s * c > 0.0 {
cc = z / ss;
} else {
ss = z / cc;
}
if ix < 0x58800000 {
if y1 {
ss = -ss;
}
cc = (ponef(x) as f64) * cc - (qonef(x) as f64) * ss;
}
}
if sign {
cc = -cc;
}
return (((INVSQRTPI as f64) * cc) / (sqrtf(x) as f64)) as f32;
}
/* R0/S0 on [0,2] */
const R00: f32 = -6.2500000000e-02; /* 0xbd800000 */
const R01: f32 = 1.4070566976e-03; /* 0x3ab86cfd */
const R02: f32 = -1.5995563444e-05; /* 0xb7862e36 */
const R03: f32 = 4.9672799207e-08; /* 0x335557d2 */
const S01: f32 = 1.9153760746e-02; /* 0x3c9ce859 */
const S02: f32 = 1.8594678841e-04; /* 0x3942fab6 */
const S03: f32 = 1.1771846857e-06; /* 0x359dffc2 */
const S04: f32 = 5.0463624390e-09; /* 0x31ad6446 */
const S05: f32 = 1.2354227016e-11; /* 0x2d59567e */
pub fn j1f(x: f32) -> f32 {
let mut z: f32;
let r: f32;
let s: f32;
let mut ix: u32;
let sign: bool;
ix = x.to_bits();
sign = (ix >> 31) != 0;
ix &= 0x7fffffff;
if ix >= 0x7f800000 {
return 1.0 / (x * x);
}
if ix >= 0x40000000 {
/* |x| >= 2 */
return common(ix, fabsf(x), false, sign);
}
if ix >= 0x39000000 {
/* |x| >= 2**-13 */
z = x * x;
r = z * (R00 + z * (R01 + z * (R02 + z * R03)));
s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * (S04 + z * S05))));
z = 0.5 + r / s;
} else {
z = 0.5;
}
return z * x;
}
const U0: [f32; 5] = [
-1.9605709612e-01, /* 0xbe48c331 */
5.0443872809e-02, /* 0x3d4e9e3c */
-1.9125689287e-03, /* 0xbafaaf2a */
2.3525259166e-05, /* 0x37c5581c */
-9.1909917899e-08, /* 0xb3c56003 */
];
const V0: [f32; 5] = [
1.9916731864e-02, /* 0x3ca3286a */
2.0255257550e-04, /* 0x3954644b */
1.3560879779e-06, /* 0x35b602d4 */
6.2274145840e-09, /* 0x31d5f8eb */
1.6655924903e-11, /* 0x2d9281cf */
];
pub fn y1f(x: f32) -> f32 {
let z: f32;
let u: f32;
let v: f32;
let ix: u32;
ix = x.to_bits();
if (ix & 0x7fffffff) == 0 {
return -1.0 / 0.0;
}
if (ix >> 31) != 0 {
return 0.0 / 0.0;
}
if ix >= 0x7f800000 {
return 1.0 / x;
}
if ix >= 0x40000000 {
/* |x| >= 2.0 */
return common(ix, x, true, false);
}
if ix < 0x33000000 {
/* x < 2**-25 */
return -TPI / x;
}
z = x * x;
u = U0[0] + z * (U0[1] + z * (U0[2] + z * (U0[3] + z * U0[4])));
v = 1.0 + z * (V0[0] + z * (V0[1] + z * (V0[2] + z * (V0[3] + z * V0[4]))));
return x * (u / v) + TPI * (j1f(x) * logf(x) - 1.0 / x);
}
/* For x >= 8, the asymptotic expansions of pone is
* 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
* We approximate pone by
* pone(x) = 1 + (R/S)
* where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
* S = 1 + ps0*s^2 + ... + ps4*s^10
* and
* | pone(x)-1-R/S | <= 2 ** ( -60.06)
*/
const PR8: [f32; 6] = [
/* for x in [inf, 8]=1/[0,0.125] */
0.0000000000e+00, /* 0x00000000 */
1.1718750000e-01, /* 0x3df00000 */
1.3239480972e+01, /* 0x4153d4ea */
4.1205184937e+02, /* 0x43ce06a3 */
3.8747453613e+03, /* 0x45722bed */
7.9144794922e+03, /* 0x45f753d6 */
];
const PS8: [f32; 5] = [
1.1420736694e+02, /* 0x42e46a2c */
3.6509309082e+03, /* 0x45642ee5 */
3.6956207031e+04, /* 0x47105c35 */
9.7602796875e+04, /* 0x47bea166 */
3.0804271484e+04, /* 0x46f0a88b */
];
const PR5: [f32; 6] = [
/* for x in [8,4.5454]=1/[0.125,0.22001] */
1.3199052094e-11, /* 0x2d68333f */
1.1718749255e-01, /* 0x3defffff */
6.8027510643e+00, /* 0x40d9b023 */
1.0830818176e+02, /* 0x42d89dca */
5.1763616943e+02, /* 0x440168b7 */
5.2871520996e+02, /* 0x44042dc6 */
];
const PS5: [f32; 5] = [
5.9280597687e+01, /* 0x426d1f55 */
9.9140142822e+02, /* 0x4477d9b1 */
5.3532670898e+03, /* 0x45a74a23 */
7.8446904297e+03, /* 0x45f52586 */
1.5040468750e+03, /* 0x44bc0180 */
];
const PR3: [f32; 6] = [
3.0250391081e-09, /* 0x314fe10d */
1.1718686670e-01, /* 0x3defffab */
3.9329774380e+00, /* 0x407bb5e7 */
3.5119403839e+01, /* 0x420c7a45 */
9.1055007935e+01, /* 0x42b61c2a */
4.8559066772e+01, /* 0x42423c7c */
];
const PS3: [f32; 5] = [
3.4791309357e+01, /* 0x420b2a4d */
3.3676245117e+02, /* 0x43a86198 */
1.0468714600e+03, /* 0x4482dbe3 */
8.9081134033e+02, /* 0x445eb3ed */
1.0378793335e+02, /* 0x42cf936c */
];
const PR2: [f32; 6] = [
/* for x in [2.8570,2]=1/[0.3499,0.5] */
1.0771083225e-07, /* 0x33e74ea8 */
1.1717621982e-01, /* 0x3deffa16 */
2.3685150146e+00, /* 0x401795c0 */
1.2242610931e+01, /* 0x4143e1bc */
1.7693971634e+01, /* 0x418d8d41 */
5.0735230446e+00, /* 0x40a25a4d */
];
const PS2: [f32; 5] = [
2.1436485291e+01, /* 0x41ab7dec */
1.2529022980e+02, /* 0x42fa9499 */
2.3227647400e+02, /* 0x436846c7 */
1.1767937469e+02, /* 0x42eb5bd7 */
8.3646392822e+00, /* 0x4105d590 */
];
fn ponef(x: f32) -> f32 {
let p: &[f32; 6];
let q: &[f32; 5];
let z: f32;
let r: f32;
let s: f32;
let mut ix: u32;
ix = x.to_bits();
ix &= 0x7fffffff;
if ix >= 0x41000000 {
p = &PR8;
q = &PS8;
} else if ix >= 0x409173eb {
p = &PR5;
q = &PS5;
} else if ix >= 0x4036d917 {
p = &PR3;
q = &PS3;
} else
/*ix >= 0x40000000*/
{
p = &PR2;
q = &PS2;
}
z = 1.0 / (x * x);
r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
return 1.0 + r / s;
}
/* For x >= 8, the asymptotic expansions of qone is
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
* We approximate pone by
* qone(x) = s*(0.375 + (R/S))
* where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
* S = 1 + qs1*s^2 + ... + qs6*s^12
* and
* | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
*/
const QR8: [f32; 6] = [
/* for x in [inf, 8]=1/[0,0.125] */
0.0000000000e+00, /* 0x00000000 */
-1.0253906250e-01, /* 0xbdd20000 */
-1.6271753311e+01, /* 0xc1822c8d */
-7.5960174561e+02, /* 0xc43de683 */
-1.1849806641e+04, /* 0xc639273a */
-4.8438511719e+04, /* 0xc73d3683 */
];
const QS8: [f32; 6] = [
1.6139537048e+02, /* 0x43216537 */
7.8253862305e+03, /* 0x45f48b17 */
1.3387534375e+05, /* 0x4802bcd6 */
7.1965775000e+05, /* 0x492fb29c */
6.6660125000e+05, /* 0x4922be94 */
-2.9449025000e+05, /* 0xc88fcb48 */
];
const QR5: [f32; 6] = [
/* for x in [8,4.5454]=1/[0.125,0.22001] */
-2.0897993405e-11, /* 0xadb7d219 */
-1.0253904760e-01, /* 0xbdd1fffe */
-8.0564479828e+00, /* 0xc100e736 */
-1.8366960144e+02, /* 0xc337ab6b */
-1.3731937256e+03, /* 0xc4aba633 */
-2.6124443359e+03, /* 0xc523471c */
];
const QS5: [f32; 6] = [
8.1276550293e+01, /* 0x42a28d98 */
1.9917987061e+03, /* 0x44f8f98f */
1.7468484375e+04, /* 0x468878f8 */
4.9851425781e+04, /* 0x4742bb6d */
2.7948074219e+04, /* 0x46da5826 */
-4.7191835938e+03, /* 0xc5937978 */
];
const QR3: [f32; 6] = [
-5.0783124372e-09, /* 0xb1ae7d4f */
-1.0253783315e-01, /* 0xbdd1ff5b */
-4.6101160049e+00, /* 0xc0938612 */
-5.7847221375e+01, /* 0xc267638e */
-2.2824453735e+02, /* 0xc3643e9a */
-2.1921012878e+02, /* 0xc35b35cb */
];
const QS3: [f32; 6] = [
4.7665153503e+01, /* 0x423ea91e */
6.7386511230e+02, /* 0x4428775e */
3.3801528320e+03, /* 0x45534272 */
5.5477290039e+03, /* 0x45ad5dd5 */
1.9031191406e+03, /* 0x44ede3d0 */
-1.3520118713e+02, /* 0xc3073381 */
];
const QR2: [f32; 6] = [
/* for x in [2.8570,2]=1/[0.3499,0.5] */
-1.7838172539e-07, /* 0xb43f8932 */
-1.0251704603e-01, /* 0xbdd1f475 */
-2.7522056103e+00, /* 0xc0302423 */
-1.9663616180e+01, /* 0xc19d4f16 */
-4.2325313568e+01, /* 0xc2294d1f */
-2.1371921539e+01, /* 0xc1aaf9b2 */
];
const QS2: [f32; 6] = [
2.9533363342e+01, /* 0x41ec4454 */
2.5298155212e+02, /* 0x437cfb47 */
7.5750280762e+02, /* 0x443d602e */
7.3939318848e+02, /* 0x4438d92a */
1.5594900513e+02, /* 0x431bf2f2 */
-4.9594988823e+00, /* 0xc09eb437 */
];
fn qonef(x: f32) -> f32 {
let p: &[f32; 6];
let q: &[f32; 6];
let s: f32;
let r: f32;
let z: f32;
let mut ix: u32;
ix = x.to_bits();
ix &= 0x7fffffff;
if ix >= 0x41000000 {
p = &QR8;
q = &QS8;
} else if ix >= 0x409173eb {
p = &QR5;
q = &QS5;
} else if ix >= 0x4036d917 {
p = &QR3;
q = &QS3;
} else
/*ix >= 0x40000000*/
{
p = &QR2;
q = &QS2;
}
z = 1.0 / (x * x);
r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
return (0.375 + r / s) / x;
}
// PowerPC tests are failing on LLVM 13:
https://github.com/rust-lang/rust/issues/88520
#[cfg(not(target_arch = "powerpc64"))]
#[cfg(test)]
mod tests {
use super::{j1f, y1f};
#[test]
fn test_j1f_2488() {
// 0x401F3E49
assert_eq!(j1f(2.4881766_f32), 0.49999475_f32);
}
#[test]
fn test_y1f_2002() {
//allow slightly different result on x87
let res = y1f(2.0000002_f32);
if cfg!(all(target_arch = "x86", not(target_feature = "sse2"))) && (res == -0.10703231_f32)
{
return;
}
assert_eq!(res, -0.10703229_f32);
}
}
