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 #include <float.h> 14 #include <stdint.h> 15 16 #include "fpmath.h" 17 #include "math.h" 18 #include "math_private.h" 19 20 #define BIAS (LDBL_MAX_EXP - 1) 21 22 #if LDBL_MANL_SIZE > 32 23 typedef uint64_t manl_t; 24 #else 25 typedef uint32_t manl_t; 26 #endif 27 28 #if LDBL_MANH_SIZE > 32 29 typedef uint64_t manh_t; 30 #else 31 typedef uint32_t manh_t; 32 #endif 33 34 /* 35 * These macros add and remove an explicit integer bit in front of the 36 * fractional mantissa, if the architecture doesn't have such a bit by 37 * default already. 38 */ 39 #ifdef LDBL_IMPLICIT_NBIT 40 #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) 41 #define HFRAC_BITS LDBL_MANH_SIZE 42 #else 43 #define SET_NBIT(hx) (hx) 44 #define HFRAC_BITS (LDBL_MANH_SIZE - 1) 45 #endif 46 47 #define MANL_SHIFT (LDBL_MANL_SIZE - 1) 48 49 static const long double Zero[] = {0.0L, -0.0L}; 50 51 /* 52 * Return the IEEE remainder and set *quo to the last n bits of the 53 * quotient, rounded to the nearest integer. We choose n=31 because 54 * we wind up computing all the integer bits of the quotient anyway as 55 * a side-effect of computing the remainder by the shift and subtract 56 * method. In practice, this is far more bits than are needed to use 57 * remquo in reduction algorithms. 58 * 59 * Assumptions: 60 * - The low part of the mantissa fits in a manl_t exactly. 61 * - The high part of the mantissa fits in an int64_t with enough room 62 * for an explicit integer bit in front of the fractional bits. 63 */ 64 long double 65 remquol(long double x, long double y, int *quo) 66 { 67 union IEEEl2bits ux, uy; 68 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ 69 manh_t hy; 70 manl_t lx,ly,lz; 71 int ix,iy,n,q,sx,sxy; 72 73 ux.e = x; 74 uy.e = y; 75 sx = ux.bits.sign; 76 sxy = sx ^ uy.bits.sign; 77 ux.bits.sign = 0; /* |x| */ 78 uy.bits.sign = 0; /* |y| */ 79 80 /* purge off exception values */ 81 if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */ 82 (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ 83 (uy.bits.exp == BIAS + LDBL_MAX_EXP && 84 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */ 85 return nan_mix_op(x, y, *)/nan_mix_op(x, y, *); 86 if(ux.bits.exp<=uy.bits.exp) { 87 if((ux.bits.exp<uy.bits.exp) || 88 (ux.bits.manh<=uy.bits.manh && 89 (ux.bits.manh<uy.bits.manh || 90 ux.bits.manl<uy.bits.manl))) { 91 q = 0; 92 goto fixup; /* |x|<|y| return x or x-y */ 93 } 94 if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) { 95 *quo = (sxy ? -1 : 1); 96 return Zero[sx]; /* |x|=|y| return x*0*/ 97 } 98 } 99 100 /* determine ix = ilogb(x) */ 101 if(ux.bits.exp == 0) { /* subnormal x */ 102 ux.e *= 0x1.0p512; 103 ix = ux.bits.exp - (BIAS + 512); 104 } else { 105 ix = ux.bits.exp - BIAS; 106 } 107 108 /* determine iy = ilogb(y) */ 109 if(uy.bits.exp == 0) { /* subnormal y */ 110 uy.e *= 0x1.0p512; 111 iy = uy.bits.exp - (BIAS + 512); 112 } else { 113 iy = uy.bits.exp - BIAS; 114 } 115 116 /* set up {hx,lx}, {hy,ly} and align y to x */ 117 hx = SET_NBIT(ux.bits.manh); 118 hy = SET_NBIT(uy.bits.manh); 119 lx = ux.bits.manl; 120 ly = uy.bits.manl; 121 122 /* fix point fmod */ 123 n = ix - iy; 124 q = 0; 125 while(n--) { 126 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 127 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;} 128 else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;} 129 q <<= 1; 130 } 131 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 132 if(hz>=0) {hx=hz;lx=lz;q++;} 133 134 /* convert back to floating value and restore the sign */ 135 if((hx|lx)==0) { /* return sign(x)*0 */ 136 q &= 0x7fffffff; 137 *quo = (sxy ? -q : q); 138 return Zero[sx]; 139 } 140 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */ 141 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx; 142 iy -= 1; 143 } 144 ux.bits.manh = hx; /* The integer bit is truncated here if needed. */ 145 ux.bits.manl = lx; 146 if (iy < LDBL_MIN_EXP) { 147 ux.bits.exp = iy + (BIAS + 512); 148 ux.e *= 0x1p-512; 149 } else { 150 ux.bits.exp = iy + BIAS; 151 } 152 fixup: 153 x = ux.e; /* |x| */ 154 y = fabsl(y); 155 if (y < LDBL_MIN * 2) { 156 if (x+x>y || (x+x==y && (q & 1))) { 157 q++; 158 x-=y; 159 } 160 } else if (x>0.5*y || (x==0.5*y && (q & 1))) { 161 q++; 162 x-=y; 163 } 164 ux.e = x; 165 ux.bits.sign ^= sx; 166 x = ux.e; 167 q &= 0x7fffffff; 168 *quo = (sxy ? -q : q); 169 return x; 170 } 171