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 #if 0 15 __FBSDID("$FreeBSD: src/lib/msun/src/s_remquol.c,v 1.2 2008/07/31 20:09:47 das Exp $"); 16 #endif 17 18 #include <sys/types.h> 19 #include <machine/ieee.h> 20 21 #include <float.h> 22 #include <math.h> 23 #include <stdint.h> 24 25 #include "math_private.h" 26 27 #define BIAS (LDBL_MAX_EXP - 1) 28 29 /* 30 * These macros add and remove an explicit integer bit in front of the 31 * fractional mantissa, if the architecture doesn't have such a bit by 32 * default already. 33 */ 34 #ifdef LDBL_IMPLICIT_NBIT 35 #define LDBL_NBIT 0 36 #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) 37 #define HFRAC_BITS EXT_FRACHBITS 38 #else 39 #define LDBL_NBIT 0x80000000 40 #define SET_NBIT(hx) (hx) 41 #define HFRAC_BITS (EXT_FRACHBITS - 1) 42 #endif 43 44 #define MANL_SHIFT (EXT_FRACLBITS - 1) 45 46 static const long double Zero[] = {0.0L, -0.0L}; 47 48 /* 49 * Return the IEEE remainder and set *quo to the last n bits of the 50 * quotient, rounded to the nearest integer. We choose n=31 because 51 * we wind up computing all the integer bits of the quotient anyway as 52 * a side-effect of computing the remainder by the shift and subtract 53 * method. In practice, this is far more bits than are needed to use 54 * remquo in reduction algorithms. 55 * 56 * Assumptions: 57 * - The low part of the mantissa fits in a manl_t exactly. 58 * - The high part of the mantissa fits in an int64_t with enough room 59 * for an explicit integer bit in front of the fractional bits. 60 */ 61 long double 62 remquol(long double x, long double y, int *quo) 63 { 64 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ 65 uint32_t hy; 66 uint32_t lx,ly,lz; 67 uint32_t esx, esy; 68 int ix,iy,n,q,sx,sxy; 69 70 GET_LDOUBLE_WORDS(esx,hx,lx,x); 71 GET_LDOUBLE_WORDS(esy,hy,ly,y); 72 sx = esx & 0x8000; 73 sxy = sx ^ (esy & 0x8000); 74 esx &= 0x7fff; /* |x| */ 75 esy &= 0x7fff; /* |y| */ 76 SET_LDOUBLE_EXP(x,esx); 77 SET_LDOUBLE_EXP(y,esy); 78 79 /* purge off exception values */ 80 if((esy|hy|ly)==0 || /* y=0 */ 81 (esx == BIAS + LDBL_MAX_EXP) || /* or x not finite */ 82 (esy == BIAS + LDBL_MAX_EXP && 83 ((hy&~LDBL_NBIT)|ly)!=0)) /* or y is NaN */ 84 return (x*y)/(x*y); 85 if(esx<=esy) { 86 if((esx<esy) || 87 (hx<=hy && 88 (hx<hy || 89 lx<ly))) { 90 q = 0; 91 goto fixup; /* |x|<|y| return x or x-y */ 92 } 93 if(hx==hy && lx==ly) { 94 *quo = 1; 95 return Zero[sx!=0]; /* |x|=|y| return x*0*/ 96 } 97 } 98 99 /* determine ix = ilogb(x) */ 100 if(esx == 0) { /* subnormal x */ 101 x *= 0x1.0p512; 102 GET_LDOUBLE_WORDS(esx,hx,lx,x); 103 ix = esx - (BIAS + 512); 104 } else { 105 ix = esx - BIAS; 106 } 107 108 /* determine iy = ilogb(y) */ 109 if(esy == 0) { /* subnormal y */ 110 y *= 0x1.0p512; 111 GET_LDOUBLE_WORDS(esy,hy,ly,y); 112 iy = esy - (BIAS + 512); 113 } else { 114 iy = esy - BIAS; 115 } 116 117 /* set up {hx,lx}, {hy,ly} and align y to x */ 118 hx = SET_NBIT(hx); 119 lx = SET_NBIT(lx); 120 121 /* fix point fmod */ 122 n = ix - iy; 123 q = 0; 124 125 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 *quo = (sxy ? -q : q); 137 return Zero[sx!=0]; 138 } 139 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */ 140 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx; 141 iy -= 1; 142 } 143 if (iy < LDBL_MIN_EXP) { 144 esx = (iy + BIAS + 512) & 0x7fff; 145 SET_LDOUBLE_WORDS(x,esx,hx,lx); 146 x *= 0x1p-512; 147 GET_LDOUBLE_WORDS(esx,hx,lx,x); 148 } else { 149 esx = (iy + BIAS) & 0x7fff; 150 } 151 SET_LDOUBLE_WORDS(x,esx,hx,lx); 152 fixup: 153 y = fabsl(y); 154 if (y < LDBL_MIN * 2) { 155 if (x+x>y || (x+x==y && (q & 1))) { 156 q++; 157 x-=y; 158 } 159 } else if (x>0.5*y || (x==0.5*y && (q & 1))) { 160 q++; 161 x-=y; 162 } 163 164 GET_LDOUBLE_EXP(esx,x); 165 esx ^= sx; 166 SET_LDOUBLE_EXP(x,esx); 167 168 q &= 0x7fffffff; 169 *quo = (sxy ? -q : q); 170 return x; 171 } 172