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 one = 1.0, Zero[] = {0.0, -0.0,}; 51 52 /* 53 * fmodl(x,y) 54 * Return x mod y in exact arithmetic 55 * Method: shift and subtract 56 * 57 * Assumptions: 58 * - The low part of the mantissa fits in a manl_t exactly. 59 * - The high part of the mantissa fits in an int64_t with enough room 60 * for an explicit integer bit in front of the fractional bits. 61 */ 62 long double 63 fmodl(long double x, long double y) 64 { 65 union IEEEl2bits ux, uy; 66 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ 67 manh_t hy; 68 manl_t lx,ly,lz; 69 int ix,iy,n,sx; 70 71 ux.e = x; 72 uy.e = y; 73 sx = ux.bits.sign; 74 75 /* purge off exception values */ 76 if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */ 77 (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ 78 (uy.bits.exp == BIAS + LDBL_MAX_EXP && 79 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */ 80 return nan_mix_op(x, y, *)/nan_mix_op(x, y, *); 81 if(ux.bits.exp<=uy.bits.exp) { 82 if((ux.bits.exp<uy.bits.exp) || 83 (ux.bits.manh<=uy.bits.manh && 84 (ux.bits.manh<uy.bits.manh || 85 ux.bits.manl<uy.bits.manl))) { 86 return x; /* |x|<|y| return x or x-y */ 87 } 88 if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) { 89 return Zero[sx]; /* |x|=|y| return x*0*/ 90 } 91 } 92 93 /* determine ix = ilogb(x) */ 94 if(ux.bits.exp == 0) { /* subnormal x */ 95 ux.e *= 0x1.0p512; 96 ix = ux.bits.exp - (BIAS + 512); 97 } else { 98 ix = ux.bits.exp - BIAS; 99 } 100 101 /* determine iy = ilogb(y) */ 102 if(uy.bits.exp == 0) { /* subnormal y */ 103 uy.e *= 0x1.0p512; 104 iy = uy.bits.exp - (BIAS + 512); 105 } else { 106 iy = uy.bits.exp - BIAS; 107 } 108 109 /* set up {hx,lx}, {hy,ly} and align y to x */ 110 hx = SET_NBIT(ux.bits.manh); 111 hy = SET_NBIT(uy.bits.manh); 112 lx = ux.bits.manl; 113 ly = uy.bits.manl; 114 115 /* fix point fmod */ 116 n = ix - iy; 117 118 while(n--) { 119 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 120 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;} 121 else { 122 if ((hz|lz)==0) /* return sign(x)*0 */ 123 return Zero[sx]; 124 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; 125 } 126 } 127 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 128 if(hz>=0) {hx=hz;lx=lz;} 129 130 /* convert back to floating value and restore the sign */ 131 if((hx|lx)==0) /* return sign(x)*0 */ 132 return Zero[sx]; 133 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */ 134 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx; 135 iy -= 1; 136 } 137 ux.bits.manh = hx; /* The mantissa is truncated here if needed. */ 138 ux.bits.manl = lx; 139 if (iy < LDBL_MIN_EXP) { 140 ux.bits.exp = iy + (BIAS + 512); 141 ux.e *= 0x1p-512; 142 } else { 143 ux.bits.exp = iy + BIAS; 144 } 145 x = ux.e * one; /* create necessary signal */ 146 return x; /* exact output */ 147 } 148