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 <float.h> 13 #include <stdint.h> 14 15 #include "fpmath.h" 16 #include "math.h" 17 #include "math_private.h" 18 19 #define BIAS (LDBL_MAX_EXP - 1) 20 21 #if LDBL_MANL_SIZE > 32 22 typedef uint64_t manl_t; 23 #else 24 typedef uint32_t manl_t; 25 #endif 26 27 #if LDBL_MANH_SIZE > 32 28 typedef uint64_t manh_t; 29 #else 30 typedef uint32_t manh_t; 31 #endif 32 33 /* 34 * These macros add and remove an explicit integer bit in front of the 35 * fractional mantissa, if the architecture doesn't have such a bit by 36 * default already. 37 */ 38 #ifdef LDBL_IMPLICIT_NBIT 39 #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) 40 #define HFRAC_BITS LDBL_MANH_SIZE 41 #else 42 #define SET_NBIT(hx) (hx) 43 #define HFRAC_BITS (LDBL_MANH_SIZE - 1) 44 #endif 45 46 #define MANL_SHIFT (LDBL_MANL_SIZE - 1) 47 48 static const long double one = 1.0, Zero[] = {0.0, -0.0,}; 49 50 /* 51 * fmodl(x,y) 52 * Return x mod y in exact arithmetic 53 * Method: shift and subtract 54 * 55 * Assumptions: 56 * - The low part of the mantissa fits in a manl_t exactly. 57 * - The high part of the mantissa fits in an int64_t with enough room 58 * for an explicit integer bit in front of the fractional bits. 59 */ 60 long double 61 fmodl(long double x, long double y) 62 { 63 union IEEEl2bits ux, uy; 64 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ 65 manh_t hy; 66 manl_t lx,ly,lz; 67 int ix,iy,n,sx; 68 69 ux.e = x; 70 uy.e = y; 71 sx = ux.bits.sign; 72 73 /* purge off exception values */ 74 if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */ 75 (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ 76 (uy.bits.exp == BIAS + LDBL_MAX_EXP && 77 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */ 78 return nan_mix_op(x, y, *)/nan_mix_op(x, y, *); 79 if(ux.bits.exp<=uy.bits.exp) { 80 if((ux.bits.exp<uy.bits.exp) || 81 (ux.bits.manh<=uy.bits.manh && 82 (ux.bits.manh<uy.bits.manh || 83 ux.bits.manl<uy.bits.manl))) { 84 return x; /* |x|<|y| return x or x-y */ 85 } 86 if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) { 87 return Zero[sx]; /* |x|=|y| return x*0*/ 88 } 89 } 90 91 /* determine ix = ilogb(x) */ 92 if(ux.bits.exp == 0) { /* subnormal x */ 93 ux.e *= 0x1.0p512; 94 ix = ux.bits.exp - (BIAS + 512); 95 } else { 96 ix = ux.bits.exp - BIAS; 97 } 98 99 /* determine iy = ilogb(y) */ 100 if(uy.bits.exp == 0) { /* subnormal y */ 101 uy.e *= 0x1.0p512; 102 iy = uy.bits.exp - (BIAS + 512); 103 } else { 104 iy = uy.bits.exp - BIAS; 105 } 106 107 /* set up {hx,lx}, {hy,ly} and align y to x */ 108 hx = SET_NBIT(ux.bits.manh); 109 hy = SET_NBIT(uy.bits.manh); 110 lx = ux.bits.manl; 111 ly = uy.bits.manl; 112 113 /* fix point fmod */ 114 n = ix - iy; 115 116 while(n--) { 117 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 118 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;} 119 else { 120 if ((hz|lz)==0) /* return sign(x)*0 */ 121 return Zero[sx]; 122 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; 123 } 124 } 125 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 126 if(hz>=0) {hx=hz;lx=lz;} 127 128 /* convert back to floating value and restore the sign */ 129 if((hx|lx)==0) /* return sign(x)*0 */ 130 return Zero[sx]; 131 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */ 132 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx; 133 iy -= 1; 134 } 135 ux.bits.manh = hx; /* The mantissa is truncated here if needed. */ 136 ux.bits.manl = lx; 137 if (iy < LDBL_MIN_EXP) { 138 ux.bits.exp = iy + (BIAS + 512); 139 ux.e *= 0x1p-512; 140 } else { 141 ux.bits.exp = iy + BIAS; 142 } 143 x = ux.e * one; /* create necessary signal */ 144 return x; /* exact output */ 145 } 146