1 /* From: @(#)e_hypot.c 1.3 95/01/18 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #include <sys/cdefs.h> 14 __FBSDID("$FreeBSD$"); 15 16 /* long double version of hypot(). See e_hypot.c for most comments. */ 17 18 #include <float.h> 19 20 #include "fpmath.h" 21 #include "math.h" 22 #include "math_private.h" 23 24 #define GET_LDBL_MAN(h, l, v) do { \ 25 union IEEEl2bits uv; \ 26 \ 27 uv.e = v; \ 28 h = uv.bits.manh; \ 29 l = uv.bits.manl; \ 30 } while (0) 31 32 #undef GET_HIGH_WORD 33 #define GET_HIGH_WORD(i, v) GET_LDBL_EXPSIGN(i, v) 34 #undef SET_HIGH_WORD 35 #define SET_HIGH_WORD(v, i) SET_LDBL_EXPSIGN(v, i) 36 37 #define DESW(exp) (exp) /* delta expsign word */ 38 #define ESW(exp) (MAX_EXP - 1 + (exp)) /* expsign word */ 39 #define MANT_DIG LDBL_MANT_DIG 40 #define MAX_EXP LDBL_MAX_EXP 41 42 #if LDBL_MANL_SIZE > 32 43 typedef uint64_t man_t; 44 #else 45 typedef uint32_t man_t; 46 #endif 47 48 long double 49 hypotl(long double x, long double y) 50 { 51 long double a=x,b=y,t1,t2,y1,y2,w; 52 int32_t j,k,ha,hb; 53 54 GET_HIGH_WORD(ha,x); 55 ha &= 0x7fff; 56 GET_HIGH_WORD(hb,y); 57 hb &= 0x7fff; 58 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 59 a = fabsl(a); 60 b = fabsl(b); 61 if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */ 62 k=0; 63 if(ha > ESW(MAX_EXP/2-12)) { /* a>2**(MAX_EXP/2-12) */ 64 if(ha >= ESW(MAX_EXP)) { /* Inf or NaN */ 65 man_t manh, manl; 66 /* Use original arg order iff result is NaN; quieten sNaNs. */ 67 w = fabsl(x+0.0)-fabsl(y+0.0); 68 GET_LDBL_MAN(manh,manl,a); 69 if (manh == LDBL_NBIT && manl == 0) w = a; 70 GET_LDBL_MAN(manh,manl,b); 71 if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b; 72 return w; 73 } 74 /* scale a and b by 2**-(MAX_EXP/2+88) */ 75 ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88); 76 k += MAX_EXP/2+88; 77 SET_HIGH_WORD(a,ha); 78 SET_HIGH_WORD(b,hb); 79 } 80 if(hb < ESW(-(MAX_EXP/2-12))) { /* b < 2**-(MAX_EXP/2-12) */ 81 if(hb <= 0) { /* subnormal b or 0 */ 82 man_t manh, manl; 83 GET_LDBL_MAN(manh,manl,b); 84 if((manh|manl)==0) return a; 85 t1=0; 86 SET_HIGH_WORD(t1,ESW(MAX_EXP-2)); /* t1=2^(MAX_EXP-2) */ 87 b *= t1; 88 a *= t1; 89 k -= MAX_EXP-2; 90 } else { /* scale a and b by 2^(MAX_EXP/2+88) */ 91 ha += DESW(MAX_EXP/2+88); 92 hb += DESW(MAX_EXP/2+88); 93 k -= MAX_EXP/2+88; 94 SET_HIGH_WORD(a,ha); 95 SET_HIGH_WORD(b,hb); 96 } 97 } 98 /* medium size a and b */ 99 w = a-b; 100 if (w>b) { 101 t1 = a; 102 union IEEEl2bits uv; 103 uv.e = t1; uv.bits.manl = 0; t1 = uv.e; 104 t2 = a-t1; 105 w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); 106 } else { 107 a = a+a; 108 y1 = b; 109 union IEEEl2bits uv; 110 uv.e = y1; uv.bits.manl = 0; y1 = uv.e; 111 y2 = b - y1; 112 t1 = a; 113 uv.e = t1; uv.bits.manl = 0; t1 = uv.e; 114 t2 = a - t1; 115 w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b))); 116 } 117 if(k!=0) { 118 u_int32_t high; 119 t1 = 1.0; 120 GET_HIGH_WORD(high,t1); 121 SET_HIGH_WORD(t1,high+DESW(k)); 122 return t1*w; 123 } else return w; 124 } 125