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Diffstat (limited to 'src/math/hypot.c')
| -rw-r--r-- | src/math/hypot.c | 174 |
1 files changed, 59 insertions, 115 deletions
diff --git a/src/math/hypot.c b/src/math/hypot.c index 9a4cbdb3..29ec6a47 100644 --- a/src/math/hypot.c +++ b/src/math/hypot.c @@ -1,123 +1,67 @@ -/* 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); } |