vendor/libm-0.1.4/src/math/j1f.rs - toolchain/rustc - Git at Google

 /* origin: FreeBSD /usr/src/lib/msun/src/e_j1f.c */
 /*
  * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
  */
 /*
  * ====================================================
  * 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 * (cc as f32) / sqrtf(x);
 }

 /* 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;
 }
	/* origin: FreeBSD /usr/src/lib/msun/src/e_j1f.c */
	/*
	* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
	*/
	/*
	* ====================================================
	* 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 * (cc as f32) / sqrtf(x);
	}

	/* 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 + pr1s^2 + pr2s^4 + ... + pr5*s^10
	* S = 1 + ps0s^2 + ... + ps4s^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 = qr1s^2 + qr2s^4 + ... + qr5*s^10
	* S = 1 + qs1s^2 + ... + qs6s^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;
	}