-/* 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 <math.h>
+#include <stdint.h>
+#include <float.h>
-#include "libm.h"
+#if FLT_EVAL_METHOD > 1U && LDBL_MANT_DIG == 64
+#define SPLIT (0x1p32 + 1)
+#else
+#define SPLIT (0x1p27 + 1)
+#endif
+
+static void sq(double_t *hi, double_t *lo, double x)
+{
+ double_t xh, xl, xc;
+
+ xc = (double_t)x*SPLIT;
+ xh = x - xc + xc;
+ xl = x - xh;
+ *hi = (double_t)x*x;
+ *lo = xh*xh - *hi + 2*xh*xl + xl*xl;
+}
double hypot(double x, double y)
{
- double a,b,t1,t2,y1,y2,w;
- int32_t j,k,ha,hb;
+ union {double f; uint64_t i;} ux = {x}, uy = {y}, ut;
+ int ex, ey;
+ double_t hx, lx, hy, ly, z;
- 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;
+ /* arrange |x| >= |y| */
+ ux.i &= -1ULL>>1;
+ uy.i &= -1ULL>>1;
+ if (ux.i < uy.i) {
+ ut = ux;
+ ux = uy;
+ uy = ut;
}
- 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)));
+
+ /* special cases */
+ ex = ux.i>>52;
+ ey = uy.i>>52;
+ x = ux.f;
+ y = uy.f;
+ /* note: hypot(inf,nan) == inf */
+ if (ey == 0x7ff)
+ return y;
+ if (ex == 0x7ff || uy.i == 0)
+ return x;
+ /* note: hypot(x,y) ~= x + y*y/x/2 with inexact for small y/x */
+ /* 64 difference is enough for ld80 double_t */
+ if (ex - ey > 64)
+ return x + y;
+
+ /* precise sqrt argument in nearest rounding mode without overflow */
+ /* xh*xh must not overflow and xl*xl must not underflow in sq */
+ z = 1;
+ if (ex > 0x3ff+510) {
+ z = 0x1p700;
+ x *= 0x1p-700;
+ y *= 0x1p-700;
+ } else if (ey < 0x3ff-450) {
+ z = 0x1p-700;
+ x *= 0x1p700;
+ y *= 0x1p700;
}
- if (k)
- w = scalbn(w, k);
- return w;
+ sq(&hx, &lx, x);
+ sq(&hy, &ly, y);
+ return z*sqrt(ly+lx+hy+hx);
}
projects / musl / blobdiff