1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_csqrtf.c */
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2 | /*-
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3 | * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
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4 | * All rights reserved.
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5 | *
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6 | * Redistribution and use in source and binary forms, with or without
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7 | * modification, are permitted provided that the following conditions
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8 | * are met:
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9 | * 1. Redistributions of source code must retain the above copyright
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10 | * notice, this list of conditions and the following disclaimer.
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11 | * 2. Redistributions in binary form must reproduce the above copyright
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12 | * notice, this list of conditions and the following disclaimer in the
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13 | * documentation and/or other materials provided with the distribution.
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14 | *
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15 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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16 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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17 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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18 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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19 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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20 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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21 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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22 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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23 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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24 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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25 | * SUCH DAMAGE.
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26 | */
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27 |
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28 | #include "libm.h"
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29 |
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30 | /*
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31 | * gcc doesn't implement complex multiplication or division correctly,
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32 | * so we need to handle infinities specially. We turn on this pragma to
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33 | * notify conforming c99 compilers that the fast-but-incorrect code that
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34 | * gcc generates is acceptable, since the special cases have already been
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35 | * handled.
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36 | */
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37 | #pragma STDC CX_LIMITED_RANGE ON
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38 |
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39 | float complex csqrtf(float complex z)
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40 | {
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41 | float a = crealf(z), b = cimagf(z);
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42 | double t;
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43 |
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44 | /* Handle special cases. */
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45 | if (z == 0)
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46 | return CMPLXF(0, b);
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47 | if (isinf(b))
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48 | return CMPLXF(INFINITY, b);
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49 | if (isnan(a)) {
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50 | t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
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51 | return CMPLXF(a, t); /* return NaN + NaN i */
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52 | }
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53 | if (isinf(a)) {
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54 | /*
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55 | * csqrtf(inf + NaN i) = inf + NaN i
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56 | * csqrtf(inf + y i) = inf + 0 i
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57 | * csqrtf(-inf + NaN i) = NaN +- inf i
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58 | * csqrtf(-inf + y i) = 0 + inf i
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59 | */
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60 | if (signbit(a))
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61 | return CMPLXF(fabsf(b - b), copysignf(a, b));
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62 | else
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63 | return CMPLXF(a, copysignf(b - b, b));
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64 | }
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65 | /*
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66 | * The remaining special case (b is NaN) is handled just fine by
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67 | * the normal code path below.
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68 | */
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69 |
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70 | /*
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71 | * We compute t in double precision to avoid overflow and to
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72 | * provide correct rounding in nearly all cases.
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73 | * This is Algorithm 312, CACM vol 10, Oct 1967.
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74 | */
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75 | if (a >= 0) {
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76 | t = sqrt((a + hypot(a, b)) * 0.5);
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77 | return CMPLXF(t, b / (2.0 * t));
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78 | } else {
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79 | t = sqrt((-a + hypot(a, b)) * 0.5);
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80 | return CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b));
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81 | }
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82 | }
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