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 one = 1.0, Zero[] = {0.0, -0.0,}; 53 54 /* 55 * fmodl(x,y) 56 * Return x mod y in exact arithmetic 57 * Method: shift and subtract 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 fmodl(long double x, long double y) 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,sx; 72 73 ux.e = x; 74 uy.e = y; 75 sx = ux.bits.sign; 76 77 /* purge off exception values */ 78 if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */ 79 (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ 80 (uy.bits.exp == BIAS + LDBL_MAX_EXP && 81 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */ 82 return (x*y)/(x*y); 83 if(ux.bits.exp<=uy.bits.exp) { 84 if((ux.bits.exp<uy.bits.exp) || 85 (ux.bits.manh<=uy.bits.manh && 86 (ux.bits.manh<uy.bits.manh || 87 ux.bits.manl<uy.bits.manl))) { 88 return x; /* |x|<|y| return x or x-y */ 89 } 90 if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) { 91 return Zero[sx]; /* |x|=|y| return x*0*/ 92 } 93 } 94 95 /* determine ix = ilogb(x) */ 96 if(ux.bits.exp == 0) { /* subnormal x */ 97 ux.e *= 0x1.0p512; 98 ix = ux.bits.exp - (BIAS + 512); 99 } else { 100 ix = ux.bits.exp - BIAS; 101 } 102 103 /* determine iy = ilogb(y) */ 104 if(uy.bits.exp == 0) { /* subnormal y */ 105 uy.e *= 0x1.0p512; 106 iy = uy.bits.exp - (BIAS + 512); 107 } else { 108 iy = uy.bits.exp - BIAS; 109 } 110 111 /* set up {hx,lx}, {hy,ly} and align y to x */ 112 hx = SET_NBIT(ux.bits.manh); 113 hy = SET_NBIT(uy.bits.manh); 114 lx = ux.bits.manl; 115 ly = uy.bits.manl; 116 117 /* fix point fmod */ 118 n = ix - iy; 119 120 while(n--) { 121 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 122 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;} 123 else { 124 if ((hz|lz)==0) /* return sign(x)*0 */ 125 return Zero[sx]; 126 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; 127 } 128 } 129 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 130 if(hz>=0) {hx=hz;lx=lz;} 131 132 /* convert back to floating value and restore the sign */ 133 if((hx|lx)==0) /* return sign(x)*0 */ 134 return Zero[sx]; 135 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */ 136 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx; 137 iy -= 1; 138 } 139 ux.bits.manh = hx; /* The mantissa is truncated here if needed. */ 140 ux.bits.manl = lx; 141 if (iy < LDBL_MIN_EXP) { 142 ux.bits.exp = iy + (BIAS + 512); 143 ux.e *= 0x1p-512; 144 } else { 145 ux.bits.exp = iy + BIAS; 146 } 147 x = ux.e * one; /* create necessary signal */ 148 return x; /* exact output */ 149 } 150
