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_EXPSIGN(i, v) do { \ 25 union IEEEl2bits uv; \ 26 \ 27 uv.e = v; \ 28 i = uv.xbits.expsign; \ 29 } while (0) 30 31 #define GET_LDBL_MAN(h, l, v) do { \ 32 union IEEEl2bits uv; \ 33 \ 34 uv.e = v; \ 35 h = uv.bits.manh; \ 36 l = uv.bits.manl; \ 37 } while (0) 38 39 #define SET_LDBL_EXPSIGN(v, i) do { \ 40 union IEEEl2bits uv; \ 41 \ 42 uv.e = v; \ 43 uv.xbits.expsign = i; \ 44 v = uv.e; \ 45 } while (0) 46 47 #undef GET_HIGH_WORD 48 #define GET_HIGH_WORD(i, v) GET_LDBL_EXPSIGN(i, v) 49 #undef SET_HIGH_WORD 50 #define SET_HIGH_WORD(v, i) SET_LDBL_EXPSIGN(v, i) 51 52 #define DESW(exp) (exp) /* delta expsign word */ 53 #define ESW(exp) (MAX_EXP - 1 + (exp)) /* expsign word */ 54 #define MANT_DIG LDBL_MANT_DIG 55 #define MAX_EXP LDBL_MAX_EXP 56 57 #if LDBL_MANL_SIZE > 32 58 typedef uint64_t man_t; 59 #else 60 typedef uint32_t man_t; 61 #endif 62 63 long double 64 hypotl(long double x, long double y) 65 { 66 long double a=x,b=y,t1,t2,y1,y2,w; 67 int32_t j,k,ha,hb; 68 69 GET_HIGH_WORD(ha,x); 70 ha &= 0x7fff; 71 GET_HIGH_WORD(hb,y); 72 hb &= 0x7fff; 73 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 74 a = fabsl(a); 75 b = fabsl(b); 76 if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */ 77 k=0; 78 if(ha > ESW(MAX_EXP/2-12)) { /* a>2**(MAX_EXP/2-12) */ 79 if(ha >= ESW(MAX_EXP)) { /* Inf or NaN */ 80 man_t manh, manl; 81 /* Use original arg order iff result is NaN; quieten sNaNs. */ 82 w = fabsl(x+0.0)-fabsl(y+0.0); 83 GET_LDBL_MAN(manh,manl,a); 84 if (manh == LDBL_NBIT && manl == 0) w = a; 85 GET_LDBL_MAN(manh,manl,b); 86 if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b; 87 return w; 88 } 89 /* scale a and b by 2**-(MAX_EXP/2+88) */ 90 ha -= DESW(MAX_EXP/2+88); 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 if(hb < ESW(-(MAX_EXP/2-12))) { /* b < 2**-(MAX_EXP/2-12) */ 96 if(hb <= 0) { /* subnormal b or 0 */ 97 man_t manh, manl; 98 GET_LDBL_MAN(manh,manl,b); 99 if((manh|manl)==0) return a; 100 t1=0; 101 SET_HIGH_WORD(t1,ESW(MAX_EXP-2)); /* t1=2^(MAX_EXP-2) */ 102 b *= t1; 103 a *= t1; 104 k -= MAX_EXP-2; 105 } else { /* scale a and b by 2^(MAX_EXP/2+88) */ 106 ha += DESW(MAX_EXP/2+88); 107 hb += DESW(MAX_EXP/2+88); 108 k -= MAX_EXP/2+88; 109 SET_HIGH_WORD(a,ha); 110 SET_HIGH_WORD(b,hb); 111 } 112 } 113 /* medium size a and b */ 114 w = a-b; 115 if (w>b) { 116 t1 = a; 117 union IEEEl2bits uv; 118 uv.e = t1; uv.bits.manl = 0; t1 = uv.e; 119 t2 = a-t1; 120 w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); 121 } else { 122 a = a+a; 123 y1 = b; 124 union IEEEl2bits uv; 125 uv.e = y1; uv.bits.manl = 0; y1 = uv.e; 126 y2 = b - y1; 127 t1 = a; 128 uv.e = t1; uv.bits.manl = 0; t1 = uv.e; 129 t2 = a - t1; 130 w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b))); 131 } 132 if(k!=0) { 133 u_int32_t high; 134 t1 = 1.0; 135 GET_HIGH_WORD(high,t1); 136 SET_HIGH_WORD(t1,high+DESW(k)); 137 return t1*w; 138 } else return w; 139 } 140