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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 "fdlibm.h" |
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| 47 | |
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| 48 | #ifndef _DOUBLE_IS_32BITS |
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| 49 | |
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| 50 | #ifdef __STDC__ |
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| 51 | double __ieee754_hypot(double x, double y) |
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| 52 | #else |
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| 53 | double __ieee754_hypot(x,y) |
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| 54 | double x, y; |
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| 55 | #endif |
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| 56 | { |
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| 57 | double a=x,b=y,t1,t2,y1,y2,w; |
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| 58 | __int32_t j,k,ha,hb; |
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| 59 | |
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| 60 | GET_HIGH_WORD(ha,x); |
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| 61 | ha &= 0x7fffffff; |
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| 62 | GET_HIGH_WORD(hb,y); |
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| 63 | hb &= 0x7fffffff; |
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| 64 | if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} |
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| 65 | SET_HIGH_WORD(a,ha); /* a <- |a| */ |
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| 66 | SET_HIGH_WORD(b,hb); /* b <- |b| */ |
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| 67 | if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ |
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| 68 | k=0; |
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| 69 | if(ha > 0x5f300000) { /* a>2**500 */ |
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| 70 | if(ha >= 0x7ff00000) { /* Inf or NaN */ |
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| 71 | __uint32_t low; |
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| 72 | w = a+b; /* for sNaN */ |
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| 73 | GET_LOW_WORD(low,a); |
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| 74 | if(((ha&0xfffff)|low)==0) w = a; |
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| 75 | GET_LOW_WORD(low,b); |
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| 76 | if(((hb^0x7ff00000)|low)==0) w = b; |
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| 77 | return w; |
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| 78 | } |
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| 79 | /* scale a and b by 2**-600 */ |
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| 80 | ha -= 0x25800000; hb -= 0x25800000; k += 600; |
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| 81 | SET_HIGH_WORD(a,ha); |
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| 82 | SET_HIGH_WORD(b,hb); |
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| 83 | } |
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| 84 | if(hb < 0x20b00000) { /* b < 2**-500 */ |
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| 85 | if(hb <= 0x000fffff) { /* subnormal b or 0 */ |
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| 86 | __uint32_t low; |
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| 87 | GET_LOW_WORD(low,b); |
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| 88 | if((hb|low)==0) return a; |
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| 89 | t1=0; |
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| 90 | SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ |
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| 91 | b *= t1; |
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| 92 | a *= t1; |
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| 93 | k -= 1022; |
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| 94 | } else { /* scale a and b by 2^600 */ |
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| 95 | ha += 0x25800000; /* a *= 2^600 */ |
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| 96 | hb += 0x25800000; /* b *= 2^600 */ |
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| 97 | k -= 600; |
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| 98 | SET_HIGH_WORD(a,ha); |
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| 99 | SET_HIGH_WORD(b,hb); |
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| 100 | } |
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| 101 | } |
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| 102 | /* medium size a and b */ |
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| 103 | w = a-b; |
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| 104 | if (w>b) { |
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| 105 | t1 = 0; |
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| 106 | SET_HIGH_WORD(t1,ha); |
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| 107 | t2 = a-t1; |
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| 108 | w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1))); |
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| 109 | } else { |
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| 110 | a = a+a; |
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| 111 | y1 = 0; |
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| 112 | SET_HIGH_WORD(y1,hb); |
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| 113 | y2 = b - y1; |
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| 114 | t1 = 0; |
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| 115 | SET_HIGH_WORD(t1,ha+0x00100000); |
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| 116 | t2 = a - t1; |
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| 117 | w = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); |
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| 118 | } |
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| 119 | if(k!=0) { |
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| 120 | __uint32_t high; |
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| 121 | t1 = 1.0; |
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| 122 | GET_HIGH_WORD(high,t1); |
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| 123 | SET_HIGH_WORD(t1,high+(k<<20)); |
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| 124 | return t1*w; |
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| 125 | } else return w; |
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| 126 | } |
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| 127 | |
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| 128 | #endif /* defined(_DOUBLE_IS_32BITS) */ |
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