1 /* @(#)e_fmod.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 #include <float.h> 17 #include <stdint.h> 18 19 #include "fpmath.h" 20 #include "math.h" 21 #include "math_private.h" 22 23 #define BIAS (LDBL_MAX_EXP - 1) 24 25 #if LDBL_MANL_SIZE > 32 26 typedef uint64_t manl_t; 27 #else 28 typedef uint32_t manl_t; 29 #endif 30 31 #if LDBL_MANH_SIZE > 32 32 typedef uint64_t manh_t; 33 #else 34 typedef uint32_t manh_t; 35 #endif 36 37 /* 38 * These macros add and remove an explicit integer bit in front of the 39 * fractional mantissa, if the architecture doesn't have such a bit by 40 * default already. 41 */ 42 #ifdef LDBL_IMPLICIT_NBIT 43 #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) 44 #define HFRAC_BITS LDBL_MANH_SIZE 45 #else 46 #define SET_NBIT(hx) (hx) 47 #define HFRAC_BITS (LDBL_MANH_SIZE - 1) 48 #endif 49 50 #define MANL_SHIFT (LDBL_MANL_SIZE - 1) 51 52 static const long double Zero[] = {0.0L, -0.0L}; 53 54 /* 55 * Return the IEEE remainder and set *quo to the last n bits of the 56 * quotient, rounded to the nearest integer. We choose n=31 because 57 * we wind up computing all the integer bits of the quotient anyway as 58 * a side-effect of computing the remainder by the shift and subtract 59 * method. In practice, this is far more bits than are needed to use 60 * remquo in reduction algorithms. 61 * 62 * Assumptions: 63 * - The low part of the mantissa fits in a manl_t exactly. 64 * - The high part of the mantissa fits in an int64_t with enough room 65 * for an explicit integer bit in front of the fractional bits. 66 */ 67 long double 68 remquol(long double x, long double y, int *quo) 69 { 70 union IEEEl2bits ux, uy; 71 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ 72 manh_t hy; 73 manl_t lx,ly,lz; 74 int ix,iy,n,q,sx,sxy; 75 76 ux.e = x; 77 uy.e = y; 78 sx = ux.bits.sign; 79 sxy = sx ^ uy.bits.sign; 80 ux.bits.sign = 0; /* |x| */ 81 uy.bits.sign = 0; /* |y| */ 82 x = ux.e; 83 84 /* purge off exception values */ 85 if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */ 86 (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ 87 (uy.bits.exp == BIAS + LDBL_MAX_EXP && 88 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */ 89 return (x*y)/(x*y); 90 if(ux.bits.exp<=uy.bits.exp) { 91 if((ux.bits.exp<uy.bits.exp) || 92 (ux.bits.manh<=uy.bits.manh && 93 (ux.bits.manh<uy.bits.manh || 94 ux.bits.manl<uy.bits.manl))) { 95 q = 0; 96 goto fixup; /* |x|<|y| return x or x-y */ 97 } 98 if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) { 99 *quo = (sxy ? -1 : 1); 100 return Zero[sx]; /* |x|=|y| return x*0*/ 101 } 102 } 103 104 /* determine ix = ilogb(x) */ 105 if(ux.bits.exp == 0) { /* subnormal x */ 106 ux.e *= 0x1.0p512; 107 ix = ux.bits.exp - (BIAS + 512); 108 } else { 109 ix = ux.bits.exp - BIAS; 110 } 111 112 /* determine iy = ilogb(y) */ 113 if(uy.bits.exp == 0) { /* subnormal y */ 114 uy.e *= 0x1.0p512; 115 iy = uy.bits.exp - (BIAS + 512); 116 } else { 117 iy = uy.bits.exp - BIAS; 118 } 119 120 /* set up {hx,lx}, {hy,ly} and align y to x */ 121 hx = SET_NBIT(ux.bits.manh); 122 hy = SET_NBIT(uy.bits.manh); 123 lx = ux.bits.manl; 124 ly = uy.bits.manl; 125 126 /* fix point fmod */ 127 n = ix - iy; 128 q = 0; 129 130 while(n--) { 131 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 132 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;} 133 else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;} 134 q <<= 1; 135 } 136 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 137 if(hz>=0) {hx=hz;lx=lz;q++;} 138 139 /* convert back to floating value and restore the sign */ 140 if((hx|lx)==0) { /* return sign(x)*0 */ 141 q &= 0x7fffffff; 142 *quo = (sxy ? -q : q); 143 return Zero[sx]; 144 } 145 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */ 146 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx; 147 iy -= 1; 148 } 149 ux.bits.manh = hx; /* The integer bit is truncated here if needed. */ 150 ux.bits.manl = lx; 151 if (iy < LDBL_MIN_EXP) { 152 ux.bits.exp = iy + (BIAS + 512); 153 ux.e *= 0x1p-512; 154 } else { 155 ux.bits.exp = iy + BIAS; 156 } 157 ux.bits.sign = 0; 158 x = ux.e; 159 fixup: 160 y = fabsl(y); 161 if (y < LDBL_MIN * 2) { 162 if (x+x>y || (x+x==y && (q & 1))) { 163 q++; 164 x-=y; 165 } 166 } else if (x>0.5*y || (x==0.5*y && (q & 1))) { 167 q++; 168 x-=y; 169 } 170 171 ux.e = x; 172 ux.bits.sign ^= sx; 173 x = ux.e; 174 175 q &= 0x7fffffff; 176 *quo = (sxy ? -q : q); 177 return x; 178 } 179