vendor/compiler_builtins/libm/src/math/j1f.rs

   1 /* origin: FreeBSD /usr/src/lib/msun/src/e_j1f.c */
   2 /*
   3  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   4  */
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 use super::{cosf, fabsf, logf, sinf, sqrtf};
  17
  18 const INVSQRTPI: f32 = 5.6418961287e-01; /* 0x3f106ebb */
  19 const TPI: f32 = 6.3661974669e-01; /* 0x3f22f983 */
  20
  21 fn common(ix: u32, x: f32, y1: bool, sign: bool) -> f32 {
  22     let z: f64;
  23     let mut s: f64;
  24     let c: f64;
  25     let mut ss: f64;
  26     let mut cc: f64;
  27
  28     s = sinf(x) as f64;
  29     if y1 {
  30         s = -s;
  31     }
  32     c = cosf(x) as f64;
  33     cc = s - c;
  34     if ix < 0x7f000000 {
  35         ss = -s - c;
  36         z = cosf(2.0 * x) as f64;
  37         if s * c > 0.0 {
  38             cc = z / ss;
  39         } else {
  40             ss = z / cc;
  41         }
  42         if ix < 0x58800000 {
  43             if y1 {
  44                 ss = -ss;
  45             }
  46             cc = (ponef(x) as f64) * cc - (qonef(x) as f64) * ss;
  47         }
  48     }
  49     if sign {
  50         cc = -cc;
  51     }
  52     return (((INVSQRTPI as f64) * cc) / (sqrtf(x) as f64)) as f32;
  53 }
  54
  55 /* R0/S0 on [0,2] */
  56 const R00: f32 = -6.2500000000e-02; /* 0xbd800000 */
  57 const R01: f32 = 1.4070566976e-03; /* 0x3ab86cfd */
  58 const R02: f32 = -1.5995563444e-05; /* 0xb7862e36 */
  59 const R03: f32 = 4.9672799207e-08; /* 0x335557d2 */
  60 const S01: f32 = 1.9153760746e-02; /* 0x3c9ce859 */
  61 const S02: f32 = 1.8594678841e-04; /* 0x3942fab6 */
  62 const S03: f32 = 1.1771846857e-06; /* 0x359dffc2 */
  63 const S04: f32 = 5.0463624390e-09; /* 0x31ad6446 */
  64 const S05: f32 = 1.2354227016e-11; /* 0x2d59567e */
  65
  66 pub fn j1f(x: f32) -> f32 {
  67     let mut z: f32;
  68     let r: f32;
  69     let s: f32;
  70     let mut ix: u32;
  71     let sign: bool;
  72
  73     ix = x.to_bits();
  74     sign = (ix >> 31) != 0;
  75     ix &= 0x7fffffff;
  76     if ix >= 0x7f800000 {
  77         return 1.0 / (x * x);
  78     }
  79     if ix >= 0x40000000 {
  80         /* |x| >= 2 */
  81         return common(ix, fabsf(x), false, sign);
  82     }
  83     if ix >= 0x39000000 {
  84         /* |x| >= 2**-13 */
  85         z = x * x;
  86         r = z * (R00 + z * (R01 + z * (R02 + z * R03)));
  87         s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * (S04 + z * S05))));
  88         z = 0.5 + r / s;
  89     } else {
  90         z = 0.5;
  91     }
  92     return z * x;
  93 }
  94
  95 const U0: [f32; 5] = [
  96     -1.9605709612e-01, /* 0xbe48c331 */
  97     5.0443872809e-02,  /* 0x3d4e9e3c */
  98     -1.9125689287e-03, /* 0xbafaaf2a */
  99     2.3525259166e-05,  /* 0x37c5581c */
 100     -9.1909917899e-08, /* 0xb3c56003 */
 101 ];
 102 const V0: [f32; 5] = [
 103     1.9916731864e-02, /* 0x3ca3286a */
 104     2.0255257550e-04, /* 0x3954644b */
 105     1.3560879779e-06, /* 0x35b602d4 */
 106     6.2274145840e-09, /* 0x31d5f8eb */
 107     1.6655924903e-11, /* 0x2d9281cf */
 108 ];
 109
 110 pub fn y1f(x: f32) -> f32 {
 111     let z: f32;
 112     let u: f32;
 113     let v: f32;
 114     let ix: u32;
 115
 116     ix = x.to_bits();
 117     if (ix & 0x7fffffff) == 0 {
 118         return -1.0 / 0.0;
 119     }
 120     if (ix >> 31) != 0 {
 121         return 0.0 / 0.0;
 122     }
 123     if ix >= 0x7f800000 {
 124         return 1.0 / x;
 125     }
 126     if ix >= 0x40000000 {
 127         /* |x| >= 2.0 */
 128         return common(ix, x, true, false);
 129     }
 130     if ix < 0x33000000 {
 131         /* x < 2**-25 */
 132         return -TPI / x;
 133     }
 134     z = x * x;
 135     u = U0[0] + z * (U0[1] + z * (U0[2] + z * (U0[3] + z * U0[4])));
 136     v = 1.0 + z * (V0[0] + z * (V0[1] + z * (V0[2] + z * (V0[3] + z * V0[4]))));
 137     return x * (u / v) + TPI * (j1f(x) * logf(x) - 1.0 / x);
 138 }
 139
 140 /* For x >= 8, the asymptotic expansions of pone is
 141  *      1 + 15/128 s^2 - 4725/2^15 s^4 - ...,   where s = 1/x.
 142  * We approximate pone by
 143  *      pone(x) = 1 + (R/S)
 144  * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
 145  *        S = 1 + ps0*s^2 + ... + ps4*s^10
 146  * and
 147  *      | pone(x)-1-R/S | <= 2  ** ( -60.06)
 148  */
 149
 150 const PR8: [f32; 6] = [
 151     /* for x in [inf, 8]=1/[0,0.125] */
 152     0.0000000000e+00, /* 0x00000000 */
 153     1.1718750000e-01, /* 0x3df00000 */
 154     1.3239480972e+01, /* 0x4153d4ea */
 155     4.1205184937e+02, /* 0x43ce06a3 */
 156     3.8747453613e+03, /* 0x45722bed */
 157     7.9144794922e+03, /* 0x45f753d6 */
 158 ];
 159 const PS8: [f32; 5] = [
 160     1.1420736694e+02, /* 0x42e46a2c */
 161     3.6509309082e+03, /* 0x45642ee5 */
 162     3.6956207031e+04, /* 0x47105c35 */
 163     9.7602796875e+04, /* 0x47bea166 */
 164     3.0804271484e+04, /* 0x46f0a88b */
 165 ];
 166
 167 const PR5: [f32; 6] = [
 168     /* for x in [8,4.5454]=1/[0.125,0.22001] */
 169     1.3199052094e-11, /* 0x2d68333f */
 170     1.1718749255e-01, /* 0x3defffff */
 171     6.8027510643e+00, /* 0x40d9b023 */
 172     1.0830818176e+02, /* 0x42d89dca */
 173     5.1763616943e+02, /* 0x440168b7 */
 174     5.2871520996e+02, /* 0x44042dc6 */
 175 ];
 176 const PS5: [f32; 5] = [
 177     5.9280597687e+01, /* 0x426d1f55 */
 178     9.9140142822e+02, /* 0x4477d9b1 */
 179     5.3532670898e+03, /* 0x45a74a23 */
 180     7.8446904297e+03, /* 0x45f52586 */
 181     1.5040468750e+03, /* 0x44bc0180 */
 182 ];
 183
 184 const PR3: [f32; 6] = [
 185     3.0250391081e-09, /* 0x314fe10d */
 186     1.1718686670e-01, /* 0x3defffab */
 187     3.9329774380e+00, /* 0x407bb5e7 */
 188     3.5119403839e+01, /* 0x420c7a45 */
 189     9.1055007935e+01, /* 0x42b61c2a */
 190     4.8559066772e+01, /* 0x42423c7c */
 191 ];
 192 const PS3: [f32; 5] = [
 193     3.4791309357e+01, /* 0x420b2a4d */
 194     3.3676245117e+02, /* 0x43a86198 */
 195     1.0468714600e+03, /* 0x4482dbe3 */
 196     8.9081134033e+02, /* 0x445eb3ed */
 197     1.0378793335e+02, /* 0x42cf936c */
 198 ];
 199
 200 const PR2: [f32; 6] = [
 201     /* for x in [2.8570,2]=1/[0.3499,0.5] */
 202     1.0771083225e-07, /* 0x33e74ea8 */
 203     1.1717621982e-01, /* 0x3deffa16 */
 204     2.3685150146e+00, /* 0x401795c0 */
 205     1.2242610931e+01, /* 0x4143e1bc */
 206     1.7693971634e+01, /* 0x418d8d41 */
 207     5.0735230446e+00, /* 0x40a25a4d */
 208 ];
 209 const PS2: [f32; 5] = [
 210     2.1436485291e+01, /* 0x41ab7dec */
 211     1.2529022980e+02, /* 0x42fa9499 */
 212     2.3227647400e+02, /* 0x436846c7 */
 213     1.1767937469e+02, /* 0x42eb5bd7 */
 214     8.3646392822e+00, /* 0x4105d590 */
 215 ];
 216
 217 fn ponef(x: f32) -> f32 {
 218     let p: &[f32; 6];
 219     let q: &[f32; 5];
 220     let z: f32;
 221     let r: f32;
 222     let s: f32;
 223     let mut ix: u32;
 224
 225     ix = x.to_bits();
 226     ix &= 0x7fffffff;
 227     if ix >= 0x41000000 {
 228         p = &PR8;
 229         q = &PS8;
 230     } else if ix >= 0x409173eb {
 231         p = &PR5;
 232         q = &PS5;
 233     } else if ix >= 0x4036d917 {
 234         p = &PR3;
 235         q = &PS3;
 236     } else
 237     /*ix >= 0x40000000*/
 238     {
 239         p = &PR2;
 240         q = &PS2;
 241     }
 242     z = 1.0 / (x * x);
 243     r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
 244     s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
 245     return 1.0 + r / s;
 246 }
 247
 248 /* For x >= 8, the asymptotic expansions of qone is
 249  *      3/8 s - 105/1024 s^3 - ..., where s = 1/x.
 250  * We approximate pone by
 251  *      qone(x) = s*(0.375 + (R/S))
 252  * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
 253  *        S = 1 + qs1*s^2 + ... + qs6*s^12
 254  * and
 255  *      | qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
 256  */
 257
 258 const QR8: [f32; 6] = [
 259     /* for x in [inf, 8]=1/[0,0.125] */
 260     0.0000000000e+00,  /* 0x00000000 */
 261     -1.0253906250e-01, /* 0xbdd20000 */
 262     -1.6271753311e+01, /* 0xc1822c8d */
 263     -7.5960174561e+02, /* 0xc43de683 */
 264     -1.1849806641e+04, /* 0xc639273a */
 265     -4.8438511719e+04, /* 0xc73d3683 */
 266 ];
 267 const QS8: [f32; 6] = [
 268     1.6139537048e+02,  /* 0x43216537 */
 269     7.8253862305e+03,  /* 0x45f48b17 */
 270     1.3387534375e+05,  /* 0x4802bcd6 */
 271     7.1965775000e+05,  /* 0x492fb29c */
 272     6.6660125000e+05,  /* 0x4922be94 */
 273     -2.9449025000e+05, /* 0xc88fcb48 */
 274 ];
 275
 276 const QR5: [f32; 6] = [
 277     /* for x in [8,4.5454]=1/[0.125,0.22001] */
 278     -2.0897993405e-11, /* 0xadb7d219 */
 279     -1.0253904760e-01, /* 0xbdd1fffe */
 280     -8.0564479828e+00, /* 0xc100e736 */
 281     -1.8366960144e+02, /* 0xc337ab6b */
 282     -1.3731937256e+03, /* 0xc4aba633 */
 283     -2.6124443359e+03, /* 0xc523471c */
 284 ];
 285 const QS5: [f32; 6] = [
 286     8.1276550293e+01,  /* 0x42a28d98 */
 287     1.9917987061e+03,  /* 0x44f8f98f */
 288     1.7468484375e+04,  /* 0x468878f8 */
 289     4.9851425781e+04,  /* 0x4742bb6d */
 290     2.7948074219e+04,  /* 0x46da5826 */
 291     -4.7191835938e+03, /* 0xc5937978 */
 292 ];
 293
 294 const QR3: [f32; 6] = [
 295     -5.0783124372e-09, /* 0xb1ae7d4f */
 296     -1.0253783315e-01, /* 0xbdd1ff5b */
 297     -4.6101160049e+00, /* 0xc0938612 */
 298     -5.7847221375e+01, /* 0xc267638e */
 299     -2.2824453735e+02, /* 0xc3643e9a */
 300     -2.1921012878e+02, /* 0xc35b35cb */
 301 ];
 302 const QS3: [f32; 6] = [
 303     4.7665153503e+01,  /* 0x423ea91e */
 304     6.7386511230e+02,  /* 0x4428775e */
 305     3.3801528320e+03,  /* 0x45534272 */
 306     5.5477290039e+03,  /* 0x45ad5dd5 */
 307     1.9031191406e+03,  /* 0x44ede3d0 */
 308     -1.3520118713e+02, /* 0xc3073381 */
 309 ];
 310
 311 const QR2: [f32; 6] = [
 312     /* for x in [2.8570,2]=1/[0.3499,0.5] */
 313     -1.7838172539e-07, /* 0xb43f8932 */
 314     -1.0251704603e-01, /* 0xbdd1f475 */
 315     -2.7522056103e+00, /* 0xc0302423 */
 316     -1.9663616180e+01, /* 0xc19d4f16 */
 317     -4.2325313568e+01, /* 0xc2294d1f */
 318     -2.1371921539e+01, /* 0xc1aaf9b2 */
 319 ];
 320 const QS2: [f32; 6] = [
 321     2.9533363342e+01,  /* 0x41ec4454 */
 322     2.5298155212e+02,  /* 0x437cfb47 */
 323     7.5750280762e+02,  /* 0x443d602e */
 324     7.3939318848e+02,  /* 0x4438d92a */
 325     1.5594900513e+02,  /* 0x431bf2f2 */
 326     -4.9594988823e+00, /* 0xc09eb437 */
 327 ];
 328
 329 fn qonef(x: f32) -> f32 {
 330     let p: &[f32; 6];
 331     let q: &[f32; 6];
 332     let s: f32;
 333     let r: f32;
 334     let z: f32;
 335     let mut ix: u32;
 336
 337     ix = x.to_bits();
 338     ix &= 0x7fffffff;
 339     if ix >= 0x41000000 {
 340         p = &QR8;
 341         q = &QS8;
 342     } else if ix >= 0x409173eb {
 343         p = &QR5;
 344         q = &QS5;
 345     } else if ix >= 0x4036d917 {
 346         p = &QR3;
 347         q = &QS3;
 348     } else
 349     /*ix >= 0x40000000*/
 350     {
 351         p = &QR2;
 352         q = &QS2;
 353     }
 354     z = 1.0 / (x * x);
 355     r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
 356     s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
 357     return (0.375 + r / s) / x;
 358 }
 359
 360 #[cfg(test)]
 361 mod tests {
 362     use super::{j1f, y1f};
 363     #[test]
 364     fn test_j1f_2488() {
 365         // 0x401F3E49
 366         assert_eq!(j1f(2.4881766_f32), 0.49999475_f32);
 367     }
 368     #[test]
 369     fn test_y1f_2002() {
 370         assert_eq!(y1f(2.0000002_f32), -0.10703229_f32);
 371     }
 372 }