1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_asinl.c */
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2 | /*
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3 | * ====================================================
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4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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5 | *
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6 | * Developed at SunSoft, a Sun Microsystems, Inc. business.
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7 | * Permission to use, copy, modify, and distribute this
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8 | * software is freely granted, provided that this notice
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9 | * is preserved.
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10 | * ====================================================
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11 | */
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12 | /*
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13 | * See comments in asin.c.
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14 | * Converted to long double by David Schultz <das@FreeBSD.ORG>.
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15 | */
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16 |
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17 | #include "libm.h"
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18 |
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19 | #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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20 | long double asinl(long double x)
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21 | {
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22 | return asin(x);
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23 | }
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24 | #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
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25 | #include "__invtrigl.h"
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26 | #if LDBL_MANT_DIG == 64
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27 | #define CLOSETO1(u) (u.i.m>>56 >= 0xf7)
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28 | #define CLEARBOTTOM(u) (u.i.m &= -1ULL << 32)
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29 | #elif LDBL_MANT_DIG == 113
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30 | #define CLOSETO1(u) (u.i.top >= 0xee00)
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31 | #define CLEARBOTTOM(u) (u.i.lo = 0)
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32 | #endif
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33 |
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34 | long double asinl(long double x)
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35 | {
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36 | union ldshape u = {x};
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37 | long double z, r, s;
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38 | uint16_t e = u.i.se & 0x7fff;
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39 | int sign = u.i.se >> 15;
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40 |
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41 | if (e >= 0x3fff) { /* |x| >= 1 or nan */
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42 | /* asin(+-1)=+-pi/2 with inexact */
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43 | if (x == 1 || x == -1)
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44 | return x*pio2_hi + 0x1p-120f;
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45 | return 0/(x-x);
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46 | }
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47 | if (e < 0x3fff - 1) { /* |x| < 0.5 */
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48 | if (e < 0x3fff - (LDBL_MANT_DIG+1)/2) {
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49 | /* return x with inexact if x!=0 */
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50 | FORCE_EVAL(x + 0x1p120f);
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51 | return x;
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52 | }
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53 | return x + x*__invtrigl_R(x*x);
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54 | }
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55 | /* 1 > |x| >= 0.5 */
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56 | z = (1.0 - fabsl(x))*0.5;
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57 | s = sqrtl(z);
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58 | r = __invtrigl_R(z);
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59 | if (CLOSETO1(u)) {
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60 | x = pio2_hi - (2*(s+s*r)-pio2_lo);
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61 | } else {
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62 | long double f, c;
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63 | u.f = s;
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64 | CLEARBOTTOM(u);
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65 | f = u.f;
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66 | c = (z - f*f)/(s + f);
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67 | x = 0.5*pio2_hi-(2*s*r - (pio2_lo-2*c) - (0.5*pio2_hi-2*f));
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68 | }
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69 | return sign ? -x : x;
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70 | }
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71 | #endif
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