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