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 #include <float.h> 15 #include <stdint.h> 16 17 #include "fpmath.h" 18 #include "math.h" 19 #include "math_private.h" 20 21 #define BIAS (LDBL_MAX_EXP - 1) 22 23 #if LDBL_MANL_SIZE > 32 24 typedef uint64_t manl_t; 25 #else 26 typedef uint32_t manl_t; 27 #endif 28 29 #if LDBL_MANH_SIZE > 32 30 typedef uint64_t manh_t; 31 #else 32 typedef uint32_t manh_t; 33 #endif 34 35 /* 36 * These macros add and remove an explicit integer bit in front of the 37 * fractional mantissa, if the architecture doesn't have such a bit by 38 * default already. 39 */ 40 #ifdef LDBL_IMPLICIT_NBIT 41 #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) 42 #define HFRAC_BITS LDBL_MANH_SIZE 43 #else 44 #define SET_NBIT(hx) (hx) 45 #define HFRAC_BITS (LDBL_MANH_SIZE - 1) 46 #endif 47 48 #define MANL_SHIFT (LDBL_MANL_SIZE - 1) 49 50 static const long double Zero[] = {0.0L, -0.0L}; 51 52 /* 53 * Return the IEEE remainder and set *quo to the last n bits of the 54 * quotient, rounded to the nearest integer. We choose n=31 because 55 * we wind up computing all the integer bits of the quotient anyway as 56 * a side-effect of computing the remainder by the shift and subtract 57 * method. In practice, this is far more bits than are needed to use 58 * remquo in reduction algorithms. 59 * 60 * Assumptions: 61 * - The low part of the mantissa fits in a manl_t exactly. 62 * - The high part of the mantissa fits in an int64_t with enough room 63 * for an explicit integer bit in front of the fractional bits. 64 */ 65 long double 66 remquol(long double x, long double y, int *quo) 67 { 68 union IEEEl2bits ux, uy; 69 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ 70 manh_t hy; 71 manl_t lx,ly,lz; 72 int ix,iy,n,q,sx,sxy; 73 74 ux.e = x; 75 uy.e = y; 76 sx = ux.bits.sign; 77 sxy = sx ^ uy.bits.sign; 78 ux.bits.sign = 0; /* |x| */ 79 uy.bits.sign = 0; /* |y| */ 80 81 /* purge off exception values */ 82 if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */ 83 (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ 84 (uy.bits.exp == BIAS + LDBL_MAX_EXP && 85 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */ 86 return nan_mix_op(x, y, *)/nan_mix_op(x, y, *); 87 if(ux.bits.exp<=uy.bits.exp) { 88 if((ux.bits.exp<uy.bits.exp) || 89 (ux.bits.manh<=uy.bits.manh && 90 (ux.bits.manh<uy.bits.manh || 91 ux.bits.manl<uy.bits.manl))) { 92 q = 0; 93 goto fixup; /* |x|<|y| return x or x-y */ 94 } 95 if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) { 96 *quo = (sxy ? -1 : 1); 97 return Zero[sx]; /* |x|=|y| return x*0*/ 98 } 99 } 100 101 /* determine ix = ilogb(x) */ 102 if(ux.bits.exp == 0) { /* subnormal x */ 103 ux.e *= 0x1.0p512; 104 ix = ux.bits.exp - (BIAS + 512); 105 } else { 106 ix = ux.bits.exp - BIAS; 107 } 108 109 /* determine iy = ilogb(y) */ 110 if(uy.bits.exp == 0) { /* subnormal y */ 111 uy.e *= 0x1.0p512; 112 iy = uy.bits.exp - (BIAS + 512); 113 } else { 114 iy = uy.bits.exp - BIAS; 115 } 116 117 /* set up {hx,lx}, {hy,ly} and align y to x */ 118 hx = SET_NBIT(ux.bits.manh); 119 hy = SET_NBIT(uy.bits.manh); 120 lx = ux.bits.manl; 121 ly = uy.bits.manl; 122 123 /* fix point fmod */ 124 n = ix - iy; 125 q = 0; 126 while(n--) { 127 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 128 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;} 129 else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;} 130 q <<= 1; 131 } 132 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 133 if(hz>=0) {hx=hz;lx=lz;q++;} 134 135 /* convert back to floating value and restore the sign */ 136 if((hx|lx)==0) { /* return sign(x)*0 */ 137 q &= 0x7fffffff; 138 *quo = (sxy ? -q : q); 139 return Zero[sx]; 140 } 141 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */ 142 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx; 143 iy -= 1; 144 } 145 ux.bits.manh = hx; /* The integer bit is truncated here if needed. */ 146 ux.bits.manl = lx; 147 if (iy < LDBL_MIN_EXP) { 148 ux.bits.exp = iy + (BIAS + 512); 149 ux.e *= 0x1p-512; 150 } else { 151 ux.bits.exp = iy + BIAS; 152 } 153 fixup: 154 x = ux.e; /* |x| */ 155 y = fabsl(y); 156 if (y < LDBL_MIN * 2) { 157 if (x+x>y || (x+x==y && (q & 1))) { 158 q++; 159 x-=y; 160 } 161 } else if (x>0.5*y || (x==0.5*y && (q & 1))) { 162 q++; 163 x-=y; 164 } 165 ux.e = x; 166 ux.bits.sign ^= sx; 167 x = ux.e; 168 q &= 0x7fffffff; 169 *quo = (sxy ? -q : q); 170 return x; 171 } 172