1 | |
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2 | /* @(#)e_hypot.c 5.1 93/09/24 */ |
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3 | /* |
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4 | * ==================================================== |
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5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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6 | * |
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7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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8 | * Permission to use, copy, modify, and distribute this |
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9 | * software is freely granted, provided that this notice |
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10 | * is preserved. |
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11 | * ==================================================== |
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12 | */ |
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13 | |
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14 | /* __ieee754_hypot(x,y) |
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15 | * |
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16 | * Method : |
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17 | * If (assume round-to-nearest) z=x*x+y*y |
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18 | * has error less than sqrt(2)/2 ulp, than |
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19 | * sqrt(z) has error less than 1 ulp (exercise). |
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20 | * |
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21 | * So, compute sqrt(x*x+y*y) with some care as |
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22 | * follows to get the error below 1 ulp: |
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23 | * |
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24 | * Assume x>y>0; |
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25 | * (if possible, set rounding to round-to-nearest) |
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26 | * 1. if x > 2y use |
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27 | * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y |
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28 | * where x1 = x with lower 32 bits cleared, x2 = x-x1; else |
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29 | * 2. if x <= 2y use |
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30 | * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) |
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31 | * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, |
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32 | * y1= y with lower 32 bits chopped, y2 = y-y1. |
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33 | * |
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34 | * NOTE: scaling may be necessary if some argument is too |
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35 | * large or too tiny |
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36 | * |
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37 | * Special cases: |
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38 | * hypot(x,y) is INF if x or y is +INF or -INF; else |
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39 | * hypot(x,y) is NAN if x or y is NAN. |
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40 | * |
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41 | * Accuracy: |
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42 | * hypot(x,y) returns sqrt(x^2+y^2) with error less |
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43 | * than 1 ulps (units in the last place) |
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44 | */ |
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45 | |
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46 | #include <libm/fdlibm.h> |
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47 | |
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48 | #ifdef __STDC__ |
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49 | static const double one = 1.0; |
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50 | #else |
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51 | static double one = 1.0; |
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52 | #endif |
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53 | |
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54 | #ifdef __STDC__ |
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55 | double __ieee754_hypot(double x, double y) |
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56 | #else |
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57 | double __ieee754_hypot(x,y) |
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58 | double x, y; |
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59 | #endif |
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60 | { |
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61 | int n0; |
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62 | double a=x,b=y,t1,t2,y1,y2,w; |
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63 | int j,k,ha,hb; |
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64 | |
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65 | n0 = ((*(int*)&one)>>29)^1; /* high word index */ |
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66 | ha = *(n0+(int*)&x)&0x7fffffff; /* high word of x */ |
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67 | hb = *(n0+(int*)&y)&0x7fffffff; /* high word of y */ |
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68 | if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} |
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69 | *(n0+(int*)&a) = ha; /* a <- |a| */ |
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70 | *(n0+(int*)&b) = hb; /* b <- |b| */ |
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71 | if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ |
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72 | k=0; |
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73 | if(ha > 0x5f300000) { /* a>2**500 */ |
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74 | if(ha >= 0x7ff00000) { /* Inf or NaN */ |
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75 | w = a+b; /* for sNaN */ |
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76 | if(((ha&0xfffff)|*(1-n0+(int*)&a))==0) w = a; |
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77 | if(((hb^0x7ff00000)|*(1-n0+(int*)&b))==0) w = b; |
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78 | return w; |
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79 | } |
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80 | /* scale a and b by 2**-600 */ |
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81 | ha -= 0x25800000; hb -= 0x25800000; k += 600; |
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82 | *(n0+(int*)&a) = ha; |
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83 | *(n0+(int*)&b) = hb; |
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84 | } |
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85 | if(hb < 0x20b00000) { /* b < 2**-500 */ |
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86 | if(hb <= 0x000fffff) { /* subnormal b or 0 */ |
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87 | if((hb|(*(1-n0+(int*)&b)))==0) return a; |
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88 | t1=0; |
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89 | *(n0+(int*)&t1) = 0x7fd00000; /* t1=2^1022 */ |
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90 | b *= t1; |
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91 | a *= t1; |
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92 | k -= 1022; |
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93 | } else { /* scale a and b by 2^600 */ |
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94 | ha += 0x25800000; /* a *= 2^600 */ |
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95 | hb += 0x25800000; /* b *= 2^600 */ |
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96 | k -= 600; |
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97 | *(n0+(int*)&a) = ha; |
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98 | *(n0+(int*)&b) = hb; |
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99 | } |
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100 | } |
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101 | /* medium size a and b */ |
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102 | w = a-b; |
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103 | if (w>b) { |
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104 | t1 = 0; |
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105 | *(n0+(int*)&t1) = ha; |
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106 | t2 = a-t1; |
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107 | w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); |
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108 | } else { |
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109 | a = a+a; |
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110 | y1 = 0; |
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111 | *(n0+(int*)&y1) = hb; |
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112 | y2 = b - y1; |
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113 | t1 = 0; |
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114 | *(n0+(int*)&t1) = ha+0x00100000; |
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115 | t2 = a - t1; |
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116 | w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); |
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117 | } |
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118 | if(k!=0) { |
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119 | t1 = 1.0; |
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120 | *(n0+(int*)&t1) += (k<<20); |
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121 | return t1*w; |
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122 | } else return w; |
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123 | } |
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