diff options
Diffstat (limited to 'src/math/hypotl.c')
| -rw-r--r-- | src/math/hypotl.c | 178 |
1 files changed, 48 insertions, 130 deletions
diff --git a/src/math/hypotl.c b/src/math/hypotl.c index f4a64f74..479aa92c 100644 --- a/src/math/hypotl.c +++ b/src/math/hypotl.c @@ -1,16 +1,3 @@ -/* 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 @@ -19,130 +6,61 @@ long double hypotl(long double x, long double y) 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 |