-/* origin: FreeBSD /usr/src/lib/msun/src/e_hypotl.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.
- * ====================================================
- */
-/* long double version of hypot(). See comments in hypot.c. */
-
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
return hypot(x, y);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-
-#define GET_LDBL_EXPSIGN(i, v) do { \
- union IEEEl2bits uv; \
- \
- uv.e = v; \
- i = uv.xbits.expsign; \
-} while (0)
-
-#define GET_LDBL_MAN(h, l, v) do { \
- union IEEEl2bits uv; \
- \
- uv.e = v; \
- h = uv.bits.manh; \
- l = uv.bits.manl; \
-} while (0)
-
-#define SET_LDBL_EXPSIGN(v, i) do { \
- union IEEEl2bits uv; \
- \
- uv.e = v; \
- uv.xbits.expsign = i; \
- v = uv.e; \
-} while (0)
-
-#undef GET_HIGH_WORD
-#define GET_HIGH_WORD(i, v) GET_LDBL_EXPSIGN(i, v)
-#undef SET_HIGH_WORD
-#define SET_HIGH_WORD(v, i) SET_LDBL_EXPSIGN(v, i)
-
-#define DESW(exp) (exp) /* delta expsign word */
-#define ESW(exp) (MAX_EXP - 1 + (exp)) /* expsign word */
-#define MANT_DIG LDBL_MANT_DIG
-#define MAX_EXP LDBL_MAX_EXP
-
-#if LDBL_MANL_SIZE > 32
-typedef uint64_t man_t;
-#else
-typedef uint32_t man_t;
+#if LDBL_MANT_DIG == 64
+#define SPLIT (0x1p32L+1)
+#elif LDBL_MANT_DIG == 113
+#define SPLIT (0x1p57L+1)
#endif
+static void sq(long double *hi, long double *lo, long double x)
+{
+ long double xh, xl, xc;
+ xc = x*SPLIT;
+ xh = x - xc + xc;
+ xl = x - xh;
+ *hi = x*x;
+ *lo = xh*xh - *hi + 2*xh*xl + xl*xl;
+}
+
long double hypotl(long double x, long double y)
{
- long double a=x,b=y,t1,t2,y1,y2,w;
- int32_t j,k,ha,hb;
+ union ldshape ux = {x}, uy = {y};
+ int ex, ey;
+ long double hx, lx, hy, ly, z;
- GET_HIGH_WORD(ha, x);
- ha &= 0x7fff;
- GET_HIGH_WORD(hb, y);
- hb &= 0x7fff;
- if (hb > ha) {
- a = y;
- b = x;
- j=ha; ha=hb; hb=j;
- } else {
- a = x;
- b = y;
- }
- a = fabsl(a);
- b = fabsl(b);
- if (ha - hb > DESW(MANT_DIG+7)) /* x/y > 2**(MANT_DIG+7) */
- return a+b;
- k = 0;
- if (ha > ESW(MAX_EXP/2-12)) { /* a>2**(MAX_EXP/2-12) */
- if (ha >= ESW(MAX_EXP)) { /* Inf or NaN */
- man_t manh, manl;
- /* Use original arg order iff result is NaN; quieten sNaNs. */
- w = fabsl(x+0.0)-fabsl(y+0.0);
- GET_LDBL_MAN(manh,manl,a);
- if (manh == LDBL_NBIT && manl == 0) w = a;
- GET_LDBL_MAN(manh,manl,b);
- if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
- return w;
- }
- /* scale a and b by 2**-(MAX_EXP/2+88) */
- ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
- k += MAX_EXP/2+88;
- SET_HIGH_WORD(a, ha);
- SET_HIGH_WORD(b, hb);
- }
- if (hb < ESW(-(MAX_EXP/2-12))) { /* b < 2**-(MAX_EXP/2-12) */
- if (hb <= 0) { /* subnormal b or 0 */
- man_t manh, manl;
- GET_LDBL_MAN(manh,manl,b);
- if ((manh|manl) == 0)
- return a;
- t1 = 0;
- SET_HIGH_WORD(t1, ESW(MAX_EXP-2)); /* t1 = 2^(MAX_EXP-2) */
- b *= t1;
- a *= t1;
- k -= MAX_EXP-2;
- } else { /* scale a and b by 2^(MAX_EXP/2+88) */
- ha += DESW(MAX_EXP/2+88);
- hb += DESW(MAX_EXP/2+88);
- k -= MAX_EXP/2+88;
- SET_HIGH_WORD(a, ha);
- SET_HIGH_WORD(b, hb);
- }
- }
- /* medium size a and b */
- w = a - b;
- if (w > b) {
- t1 = a;
- union IEEEl2bits uv;
- uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
- t2 = a-t1;
- w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
+ ux.i.se &= 0x7fff;
+ uy.i.se &= 0x7fff;
+ if (ux.i.se < uy.i.se) {
+ ex = uy.i.se;
+ ey = ux.i.se;
+ x = uy.f;
+ y = ux.f;
} else {
- a = a+a;
- y1 = b;
- union IEEEl2bits uv;
- uv.e = y1; uv.bits.manl = 0; y1 = uv.e;
- y2 = b - y1;
- t1 = a;
- uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
- t2 = a - t1;
- w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
+ ex = ux.i.se;
+ ey = uy.i.se;
+ x = ux.f;
+ y = uy.f;
}
- if(k!=0) {
- uint32_t high;
- t1 = 1.0;
- GET_HIGH_WORD(high, t1);
- SET_HIGH_WORD(t1, high+DESW(k));
- return t1*w;
+
+ if (ex == 0x7fff && isinf(y))
+ return y;
+ if (ex == 0x7fff || y == 0)
+ return x;
+ if (ex - ey > LDBL_MANT_DIG)
+ return x + y;
+
+ z = 1;
+ if (ex > 0x3fff+8000) {
+ z = 0x1p10000L;
+ x *= 0x1p-10000L;
+ y *= 0x1p-10000L;
+ } else if (ey < 0x3fff-8000) {
+ z = 0x1p-10000L;
+ x *= 0x1p10000L;
+ y *= 0x1p10000L;
}
- return w;
+ sq(&hx, &lx, x);
+ sq(&hy, &ly, y);
+ return z*sqrtl(ly+lx+hy+hx);
}
#endif
projects / musl / blobdiff