-/* 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 = x*SPLIT;
+ xh = x - xc + xc;
+ xl = x - xh;
+ *hi = 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);
}
-/* origin: FreeBSD /usr/src/lib/msun/src/e_hypotf.c */
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-#include "libm.h"
+#include <math.h>
+#include <stdint.h>
float hypotf(float x, float y)
{
- float a,b,t1,t2,y1,y2,w;
- int32_t j,k,ha,hb;
+ union {float f; uint32_t i;} ux = {x}, uy = {y}, ut;
+ float_t z;
- GET_FLOAT_WORD(ha,x);
- ha &= 0x7fffffff;
- GET_FLOAT_WORD(hb,y);
- hb &= 0x7fffffff;
- if (hb > ha) {
- a = y;
- b = x;
- j=ha; ha=hb; hb=j;
- } else {
- a = x;
- b = y;
- }
- a = fabsf(a);
- b = fabsf(b);
- if (ha - hb > 0xf000000) /* x/y > 2**30 */
- return a+b;
- k = 0;
- if (ha > 0x58800000) { /* a > 2**50 */
- if(ha >= 0x7f800000) { /* Inf or NaN */
- /* Use original arg order iff result is NaN; quieten sNaNs. */
- w = fabsf(x+0.0f) - fabsf(y+0.0f);
- if (ha == 0x7f800000) w = a;
- if (hb == 0x7f800000) w = b;
- return w;
- }
- /* scale a and b by 2**-68 */
- ha -= 0x22000000; hb -= 0x22000000; k += 68;
- SET_FLOAT_WORD(a, ha);
- SET_FLOAT_WORD(b, hb);
- }
- if (hb < 0x26800000) { /* b < 2**-50 */
- if (hb <= 0x007fffff) { /* subnormal b or 0 */
- if (hb == 0)
- return a;
- SET_FLOAT_WORD(t1, 0x7e800000); /* t1 = 2^126 */
- b *= t1;
- a *= t1;
- k -= 126;
- } else { /* scale a and b by 2^68 */
- ha += 0x22000000; /* a *= 2^68 */
- hb += 0x22000000; /* b *= 2^68 */
- k -= 68;
- SET_FLOAT_WORD(a, ha);
- SET_FLOAT_WORD(b, hb);
- }
+ ux.i &= -1U>>1;
+ uy.i &= -1U>>1;
+ if (ux.i < uy.i) {
+ ut = ux;
+ ux = uy;
+ uy = ut;
}
- /* medium size a and b */
- w = a - b;
- if (w > b) {
- SET_FLOAT_WORD(t1, ha&0xfffff000);
- t2 = a - t1;
- w = sqrtf(t1*t1-(b*(-b)-t2*(a+t1)));
- } else {
- a = a + a;
- SET_FLOAT_WORD(y1, hb&0xfffff000);
- y2 = b - y1;
- SET_FLOAT_WORD(t1,(ha+0x00800000)&0xfffff000);
- t2 = a - t1;
- w = sqrtf(t1*y1-(w*(-w)-(t1*y2+t2*b)));
+
+ x = ux.f;
+ y = uy.f;
+ if (uy.i == 0xff<<23)
+ return y;
+ if (ux.i >= 0xff<<23 || uy.i == 0 || ux.i - uy.i >= 25<<23)
+ return x + y;
+
+ z = 1;
+ if (ux.i >= (0x7f+60)<<23) {
+ z = 0x1p90f;
+ x *= 0x1p-90f;
+ y *= 0x1p-90f;
+ } else if (uy.i < (0x7f-60)<<23) {
+ z = 0x1p-90f;
+ x *= 0x1p90f;
+ y *= 0x1p90f;
}
- if (k)
- w = scalbnf(w, k);
- return w;
+ return z*sqrtf((double)x*x + (double)y*y);
}
-/* 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 / oweals / musl.git / commitdiff