1 |
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2 /* |
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3 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. |
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4 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
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5 * |
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6 * This code is free software; you can redistribute it and/or modify it |
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7 * under the terms of the GNU General Public License version 2 only, as |
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8 * published by the Free Software Foundation. Oracle designates this |
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9 * particular file as subject to the "Classpath" exception as provided |
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10 * by Oracle in the LICENSE file that accompanied this code. |
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11 * |
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12 * This code is distributed in the hope that it will be useful, but WITHOUT |
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13 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 * version 2 for more details (a copy is included in the LICENSE file that |
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16 * accompanied this code). |
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17 * |
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18 * You should have received a copy of the GNU General Public License version |
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19 * 2 along with this work; if not, write to the Free Software Foundation, |
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20 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
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21 * |
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22 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
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23 * or visit www.oracle.com if you need additional information or have any |
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24 * questions. |
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25 */ |
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26 |
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27 /* __ieee754_hypot(x,y) |
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28 * |
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29 * Method : |
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30 * If (assume round-to-nearest) z=x*x+y*y |
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31 * has error less than sqrt(2)/2 ulp, than |
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32 * sqrt(z) has error less than 1 ulp (exercise). |
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33 * |
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34 * So, compute sqrt(x*x+y*y) with some care as |
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35 * follows to get the error below 1 ulp: |
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36 * |
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37 * Assume x>y>0; |
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38 * (if possible, set rounding to round-to-nearest) |
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39 * 1. if x > 2y use |
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40 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y |
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41 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else |
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42 * 2. if x <= 2y use |
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43 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) |
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44 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, |
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45 * y1= y with lower 32 bits chopped, y2 = y-y1. |
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46 * |
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47 * NOTE: scaling may be necessary if some argument is too |
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48 * large or too tiny |
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49 * |
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50 * Special cases: |
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51 * hypot(x,y) is INF if x or y is +INF or -INF; else |
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52 * hypot(x,y) is NAN if x or y is NAN. |
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53 * |
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54 * Accuracy: |
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55 * hypot(x,y) returns sqrt(x^2+y^2) with error less |
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56 * than 1 ulps (units in the last place) |
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57 */ |
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58 |
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59 #include "fdlibm.h" |
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60 |
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61 #ifdef __STDC__ |
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62 double __ieee754_hypot(double x, double y) |
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63 #else |
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64 double __ieee754_hypot(x,y) |
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65 double x, y; |
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66 #endif |
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67 { |
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68 double a=x,b=y,t1,t2,y1,y2,w; |
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69 int j,k,ha,hb; |
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70 |
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71 ha = __HI(x)&0x7fffffff; /* high word of x */ |
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72 hb = __HI(y)&0x7fffffff; /* high word of y */ |
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73 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} |
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74 __HI(a) = ha; /* a <- |a| */ |
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75 __HI(b) = hb; /* b <- |b| */ |
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76 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ |
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77 k=0; |
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78 if(ha > 0x5f300000) { /* a>2**500 */ |
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79 if(ha >= 0x7ff00000) { /* Inf or NaN */ |
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80 w = a+b; /* for sNaN */ |
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81 if(((ha&0xfffff)|__LO(a))==0) w = a; |
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82 if(((hb^0x7ff00000)|__LO(b))==0) w = b; |
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83 return w; |
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84 } |
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85 /* scale a and b by 2**-600 */ |
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86 ha -= 0x25800000; hb -= 0x25800000; k += 600; |
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87 __HI(a) = ha; |
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88 __HI(b) = hb; |
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89 } |
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90 if(hb < 0x20b00000) { /* b < 2**-500 */ |
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91 if(hb <= 0x000fffff) { /* subnormal b or 0 */ |
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92 if((hb|(__LO(b)))==0) return a; |
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93 t1=0; |
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94 __HI(t1) = 0x7fd00000; /* t1=2^1022 */ |
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95 b *= t1; |
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96 a *= t1; |
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97 k -= 1022; |
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98 } else { /* scale a and b by 2^600 */ |
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99 ha += 0x25800000; /* a *= 2^600 */ |
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100 hb += 0x25800000; /* b *= 2^600 */ |
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101 k -= 600; |
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102 __HI(a) = ha; |
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103 __HI(b) = hb; |
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104 } |
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105 } |
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106 /* medium size a and b */ |
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107 w = a-b; |
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108 if (w>b) { |
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109 t1 = 0; |
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110 __HI(t1) = ha; |
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111 t2 = a-t1; |
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112 w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); |
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113 } else { |
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114 a = a+a; |
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115 y1 = 0; |
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116 __HI(y1) = hb; |
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117 y2 = b - y1; |
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118 t1 = 0; |
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119 __HI(t1) = ha+0x00100000; |
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120 t2 = a - t1; |
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121 w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); |
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122 } |
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123 if(k!=0) { |
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124 t1 = 1.0; |
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125 __HI(t1) += (k<<20); |
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126 return t1*w; |
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127 } else return w; |
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128 } |
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