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147 lines
3.6 KiB
C
147 lines
3.6 KiB
C
/* @(#)e_hypot.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* __ieee754_hypot(x,y)
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*
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* Method :
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* If (assume round-to-nearest) z=x*x+y*y
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* has error less than sqrt(2)/2 ulp, than
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* sqrt(z) has error less than 1 ulp (exercise).
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*
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* So, compute sqrt(x*x+y*y) with some care as
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* follows to get the error below 1 ulp:
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*
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* Assume x>y>0;
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* (if possible, set rounding to round-to-nearest)
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* 1. if x > 2y use
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* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
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* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
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* 2. if x <= 2y use
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* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
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* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
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* y1= y with lower 32 bits chopped, y2 = y-y1.
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*
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* NOTE: scaling may be necessary if some argument is too
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* large or too tiny
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*
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* Special cases:
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* hypot(x,y) is INF if x or y is +INF or -INF; else
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* hypot(x,y) is NAN if x or y is NAN.
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*
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* Accuracy:
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* hypot(x,y) returns sqrt(x^2+y^2) with error less
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* than 1 ulps (units in the last place)
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*/
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#include <math.h>
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#include <math_private.h>
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double
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__ieee754_hypot (double x, double y)
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{
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double a, b, t1, t2, y1, y2, w;
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int32_t j, k, ha, hb;
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GET_HIGH_WORD (ha, x);
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ha &= 0x7fffffff;
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GET_HIGH_WORD (hb, y);
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hb &= 0x7fffffff;
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if (hb > ha)
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{
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a = y; b = x; j = ha; ha = hb; hb = j;
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}
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else
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{
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a = x; b = y;
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}
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SET_HIGH_WORD (a, ha); /* a <- |a| */
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SET_HIGH_WORD (b, hb); /* b <- |b| */
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if ((ha - hb) > 0x3c00000)
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{
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return a + b;
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} /* x/y > 2**60 */
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k = 0;
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if (__builtin_expect (ha > 0x5f300000, 0)) /* a>2**500 */
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{
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if (ha >= 0x7ff00000) /* Inf or NaN */
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{
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u_int32_t low;
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w = a + b; /* for sNaN */
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GET_LOW_WORD (low, a);
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if (((ha & 0xfffff) | low) == 0)
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w = a;
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GET_LOW_WORD (low, b);
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if (((hb ^ 0x7ff00000) | low) == 0)
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w = b;
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return w;
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}
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/* scale a and b by 2**-600 */
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ha -= 0x25800000; hb -= 0x25800000; k += 600;
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SET_HIGH_WORD (a, ha);
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SET_HIGH_WORD (b, hb);
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}
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if (__builtin_expect (hb < 0x20b00000, 0)) /* b < 2**-500 */
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{
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if (hb <= 0x000fffff) /* subnormal b or 0 */
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{
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u_int32_t low;
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GET_LOW_WORD (low, b);
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if ((hb | low) == 0)
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return a;
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t1 = 0;
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SET_HIGH_WORD (t1, 0x7fd00000); /* t1=2^1022 */
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b *= t1;
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a *= t1;
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k -= 1022;
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}
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else /* scale a and b by 2^600 */
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{
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ha += 0x25800000; /* a *= 2^600 */
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hb += 0x25800000; /* b *= 2^600 */
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k -= 600;
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SET_HIGH_WORD (a, ha);
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SET_HIGH_WORD (b, hb);
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}
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}
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/* medium size a and b */
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w = a - b;
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if (w > b)
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{
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t1 = 0;
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SET_HIGH_WORD (t1, ha);
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t2 = a - t1;
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w = __ieee754_sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1)));
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}
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else
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{
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a = a + a;
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y1 = 0;
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SET_HIGH_WORD (y1, hb);
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y2 = b - y1;
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t1 = 0;
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SET_HIGH_WORD (t1, ha + 0x00100000);
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t2 = a - t1;
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w = __ieee754_sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));
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}
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if (k != 0)
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{
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u_int32_t high;
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t1 = 1.0;
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GET_HIGH_WORD (high, t1);
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SET_HIGH_WORD (t1, high + (k << 20));
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return t1 * w;
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}
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else
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return w;
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}
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strong_alias (__ieee754_hypot, __hypot_finite)
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