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path: root/src/math/hypot.c
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 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 ``` ``````/* origin: FreeBSD /usr/src/lib/msun/src/e_hypot.c */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* hypot(x,y) * * Method : * If (assume round-to-nearest) z=x*x+y*y * has error less than sqrt(2)/2 ulp, then * sqrt(z) has error less than 1 ulp (exercise). * * So, compute sqrt(x*x+y*y) with some care as * follows to get the error below 1 ulp: * * Assume x>y>0; * (if possible, set rounding to round-to-nearest) * 1. if x > 2y use * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y * where x1 = x with lower 32 bits cleared, x2 = x-x1; else * 2. if x <= 2y use * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, * y1= y with lower 32 bits chopped, y2 = y-y1. * * NOTE: scaling may be necessary if some argument is too * large or too tiny * * Special cases: * hypot(x,y) is INF if x or y is +INF or -INF; else * hypot(x,y) is NAN if x or y is NAN. * * Accuracy: * hypot(x,y) returns sqrt(x^2+y^2) with error less * than 1 ulps (units in the last place) */ #include "libm.h" double hypot(double x, double y) { double a,b,t1,t2,y1,y2,w; int32_t j,k,ha,hb; GET_HIGH_WORD(ha, x); ha &= 0x7fffffff; GET_HIGH_WORD(hb, y); hb &= 0x7fffffff; if (hb > ha) { a = y; b = x; j=ha; ha=hb; hb=j; } else { a = x; b = y; } a = fabs(a); b = fabs(b); if (ha - hb > 0x3c00000) /* x/y > 2**60 */ return a+b; k = 0; if (ha > 0x5f300000) { /* a > 2**500 */ if(ha >= 0x7ff00000) { /* Inf or NaN */ uint32_t low; /* Use original arg order iff result is NaN; quieten sNaNs. */ w = fabs(x+0.0) - fabs(y+0.0); GET_LOW_WORD(low, a); if (((ha&0xfffff)|low) == 0) w = a; GET_LOW_WORD(low, b); if (((hb^0x7ff00000)|low) == 0) w = b; return w; } /* scale a and b by 2**-600 */ ha -= 0x25800000; hb -= 0x25800000; k += 600; SET_HIGH_WORD(a, ha); SET_HIGH_WORD(b, hb); } if (hb < 0x20b00000) { /* b < 2**-500 */ if (hb <= 0x000fffff) { /* subnormal b or 0 */ uint32_t low; GET_LOW_WORD(low, b); if ((hb|low) == 0) return a; t1 = 0; SET_HIGH_WORD(t1, 0x7fd00000); /* t1 = 2^1022 */ b *= t1; a *= t1; k -= 1022; } else { /* scale a and b by 2^600 */ ha += 0x25800000; /* a *= 2^600 */ hb += 0x25800000; /* b *= 2^600 */ k -= 600; SET_HIGH_WORD(a, ha); SET_HIGH_WORD(b, hb); } } /* medium size a and b */ w = a - b; if (w > b) { t1 = 0; SET_HIGH_WORD(t1, ha); t2 = a-t1; w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); } else { a = a + a; y1 = 0; SET_HIGH_WORD(y1, hb); y2 = b - y1; t1 = 0; SET_HIGH_WORD(t1, ha+0x00100000); t2 = a - t1; w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); } if (k != 0) { uint32_t high; t1 = 1.0; GET_HIGH_WORD(high, t1); SET_HIGH_WORD(t1, high+(k<<20)); return t1*w; } return w; } ``````