1 | /*- |
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2 | * Copyright (c) 2007-2008 David Schultz <das@FreeBSD.ORG> |
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3 | * All rights reserved. |
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4 | * |
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5 | * Redistribution and use in source and binary forms, with or without |
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6 | * modification, are permitted provided that the following conditions |
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7 | * are met: |
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8 | * 1. Redistributions of source code must retain the above copyright |
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9 | * notice, this list of conditions and the following disclaimer. |
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10 | * 2. Redistributions in binary form must reproduce the above copyright |
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11 | * notice, this list of conditions and the following disclaimer in the |
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12 | * documentation and/or other materials provided with the distribution. |
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13 | * |
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14 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND |
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15 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
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16 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
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17 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
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18 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
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19 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
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20 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
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21 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
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22 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
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23 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
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24 | * SUCH DAMAGE. |
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25 | */ |
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26 | |
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27 | #include <sys/cdefs.h> |
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28 | #if 0 |
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29 | __FBSDID("$FreeBSD: head/lib/msun/src/s_csqrtl.c 181402 2008-08-08 00:15:16Z das $"); |
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30 | #else |
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31 | __RCSID("$NetBSD: csqrtl.c,v 1.2 2014/10/11 00:43:51 christos Exp $"); |
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32 | #endif |
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33 | |
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34 | #include <complex.h> |
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35 | #include <float.h> |
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36 | #include <math.h> |
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37 | #include <stdbool.h> |
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38 | /* |
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39 | * gcc doesn't implement complex multiplication or division correctly, |
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40 | * so we need to handle infinities specially. We turn on this pragma to |
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41 | * notify conforming c99 compilers that the fast-but-incorrect code that |
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42 | * gcc generates is acceptable, since the special cases have already been |
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43 | * handled. |
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44 | */ |
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45 | // #pragma STDC CX_LIMITED_RANGE ON |
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46 | |
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47 | /* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */ |
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48 | #define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L) |
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49 | |
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50 | #define cpackl(r, i) ((r) + (i) * I) |
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51 | |
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52 | long double complex |
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53 | csqrtl(long double complex z) |
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54 | { |
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55 | long double complex result; |
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56 | long double a, b; |
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57 | long double t; |
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58 | bool scale; |
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59 | |
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60 | a = creall(z); |
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61 | b = cimagl(z); |
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62 | |
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63 | /* Handle special cases. */ |
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64 | if (z == 0.0L) |
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65 | return (cpackl(0.0L, b)); |
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66 | if (isinf(b)) |
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67 | return (cpackl(INFINITY, b)); |
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68 | if (isnan(a)) { |
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69 | t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ |
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70 | return (cpackl(a, t)); /* return NaN + NaN i */ |
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71 | } |
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72 | if (isinf(a)) { |
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73 | /* |
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74 | * csqrt(inf + NaN i) = inf + NaN i |
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75 | * csqrt(inf + y i) = inf + 0 i |
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76 | * csqrt(-inf + NaN i) = NaN +- inf i |
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77 | * csqrt(-inf + y i) = 0 + inf i |
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78 | */ |
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79 | if (signbit(a)) |
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80 | return (cpackl(fabsl(b - b), copysignl(a, b))); |
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81 | else |
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82 | return (cpackl(a, copysignl(b - b, b))); |
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83 | } |
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84 | /* |
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85 | * The remaining special case (b is NaN) is handled just fine by |
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86 | * the normal code path below. |
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87 | */ |
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88 | |
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89 | /* Scale to avoid overflow. */ |
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90 | if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { |
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91 | a *= 0.25L; |
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92 | b *= 0.25L; |
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93 | scale = true; |
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94 | } else { |
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95 | scale = false; |
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96 | } |
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97 | |
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98 | /* Algorithm 312, CACM vol 10, Oct 1967. */ |
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99 | if (a >= 0L) { |
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100 | t = sqrtl((a + hypotl(a, b)) * 0.5L); |
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101 | result = cpackl(t, b / (2.0L * t)); |
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102 | } else { |
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103 | t = sqrtl((-a + hypotl(a, b)) * 0.5L); |
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104 | result = cpackl(fabsl(b) / (2.0L * t), copysignl(t, b)); |
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105 | } |
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106 | |
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107 | /* Rescale. */ |
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108 | if (scale) |
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109 | return (result * 2.0L); |
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110 | else |
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111 | return (result); |
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112 | } |
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