1 /* 2 * ==================================================== 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * 5 * Developed at SunSoft, a Sun Microsystems, Inc. business. 6 * Permission to use, copy, modify, and distribute this 7 * software is freely granted, provided that this notice 8 * is preserved. 9 * ==================================================== 10 */ 11 12 #include <sys/cdefs.h> 13 /* long double version of hypot(). See e_hypot.c for most comments. */ 14 15 #include "namespace.h" 16 17 18 #include <float.h> 19 20 __weak_alias(hypotl, _hypotl) 21 22 #ifdef __HAVE_LONG_DOUBLE 23 #include "math.h" 24 #include "math_private.h" 25 26 #ifdef LDBL_IMPLICIT_NBIT 27 #define LDBL_NBIT 0 28 #endif 29 30 #define GET_LDBL_MAN(h, l, v) do { \ 31 union ieee_ext_u uv; \ 32 \ 33 uv.extu_ld = v; \ 34 h = uv.extu_frach; \ 35 l = uv.extu_fracl; \ 36 } while (0) 37 38 #undef GET_HIGH_WORD 39 #define GET_HIGH_WORD(i, v) GET_LDBL_EXPSIGN(i, v) 40 #undef SET_HIGH_WORD 41 #define SET_HIGH_WORD(v, i) SET_LDBL_EXPSIGN(v, i) 42 43 #define DESW(exp) (exp) /* delta expsign word */ 44 #define ESW(exp) (MAX_EXP - 1 + (exp)) /* expsign word */ 45 #define MANT_DIG LDBL_MANT_DIG 46 #define MAX_EXP LDBL_MAX_EXP 47 48 #if LDBL_MANL_SIZE > 32 49 typedef uint64_t man_t; 50 #else 51 typedef uint32_t man_t; 52 #endif 53 54 long double 55 hypotl(long double x, long double y) 56 { 57 long double a=x,b=y,t1,t2,y1,y2,w; 58 int32_t j,k,ha,hb; 59 60 GET_HIGH_WORD(ha,x); 61 ha &= 0x7fff; 62 GET_HIGH_WORD(hb,y); 63 hb &= 0x7fff; 64 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 65 a = fabsl(a); 66 b = fabsl(b); 67 if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */ 68 k=0; 69 if(ha > ESW(MAX_EXP/2-12)) { /* a>2**(MAX_EXP/2-12) */ 70 if(ha >= ESW(MAX_EXP)) { /* Inf or NaN */ 71 man_t manh, manl; 72 /* Use original arg order iff result is NaN; quieten sNaNs. */ 73 w = fabsl(x+0.0L)-fabsl(y+0); 74 GET_LDBL_MAN(manh,manl,a); 75 if (manh == LDBL_NBIT && manl == 0) w = a; 76 GET_LDBL_MAN(manh,manl,b); 77 if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b; 78 return w; 79 } 80 /* scale a and b by 2**-(MAX_EXP/2+88) */ 81 ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88); 82 k += MAX_EXP/2+88; 83 SET_HIGH_WORD(a,ha); 84 SET_HIGH_WORD(b,hb); 85 } 86 if(hb < ESW(-(MAX_EXP/2-12))) { /* b < 2**-(MAX_EXP/2-12) */ 87 if(hb <= 0) { /* subnormal b or 0 */ 88 man_t manh, manl; 89 GET_LDBL_MAN(manh,manl,b); 90 if((manh|manl)==0) return a; 91 t1=1; 92 SET_HIGH_WORD(t1,ESW(MAX_EXP-2)); /* t1=2^(MAX_EXP-2) */ 93 b *= t1; 94 a *= t1; 95 k -= MAX_EXP-2; 96 } else { /* scale a and b by 2^(MAX_EXP/2+88) */ 97 ha += DESW(MAX_EXP/2+88); 98 hb += DESW(MAX_EXP/2+88); 99 k -= MAX_EXP/2+88; 100 SET_HIGH_WORD(a,ha); 101 SET_HIGH_WORD(b,hb); 102 } 103 } 104 /* medium size a and b */ 105 w = a-b; 106 if (w>b) { 107 t1 = a; 108 union ieee_ext_u uv; 109 uv.extu_ld = t1; uv.extu_fracl = 0; t1 = uv.extu_ld; 110 t2 = a-t1; 111 w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); 112 } else { 113 a = a+a; 114 y1 = b; 115 union ieee_ext_u uv; 116 uv.extu_ld = y1; uv.extu_fracl = 0; y1 = uv.extu_ld; 117 y2 = b - y1; 118 t1 = a; 119 uv.extu_ld = t1; uv.extu_fracl = 0; t1 = uv.extu_ld; 120 t2 = a - t1; 121 w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b))); 122 } 123 if(k!=0) { 124 u_int32_t high; 125 t1 = 1.0; 126 GET_HIGH_WORD(high,t1); 127 SET_HIGH_WORD(t1,high+DESW(k)); 128 return t1*w; 129 } else return w; 130 } 131 #else 132 #include "math.h" 133 134 long double 135 hypotl(long double x, long double y) 136 { 137 return hypot(x, y); 138 } 139 #endif 140