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/types.h> 14 #include <machine/ieee.h> 15 16 #include <float.h> 17 #include <math.h> 18 #include <stdint.h> 19 20 #include "math_private.h" 21 22 #define BIAS (LDBL_MAX_EXP - 1) 23 24 /* 25 * These macros add and remove an explicit integer bit in front of the 26 * fractional mantissa, if the architecture doesn't have such a bit by 27 * default already. 28 */ 29 #ifdef LDBL_IMPLICIT_NBIT 30 #define LDBL_NBIT 0 31 #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) 32 #define HFRAC_BITS EXT_FRACHBITS 33 #else 34 #define LDBL_NBIT 0x80000000 35 #define SET_NBIT(hx) (hx) 36 #define HFRAC_BITS (EXT_FRACHBITS - 1) 37 #endif 38 39 #define MANL_SHIFT (EXT_FRACLBITS - 1) 40 41 static const long double one = 1.0, Zero[] = {0.0, -0.0,}; 42 43 /* 44 * fmodl(x,y) 45 * Return x mod y in exact arithmetic 46 * Method: shift and subtract 47 * 48 * Assumptions: 49 * - The low part of the mantissa fits in a manl_t exactly. 50 * - The high part of the mantissa fits in an int64_t with enough room 51 * for an explicit integer bit in front of the fractional bits. 52 */ 53 long double 54 fmodl(long double x, long double y) 55 { 56 union { 57 long double e; 58 struct ieee_ext bits; 59 } ux, uy; 60 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ 61 uint32_t hy; 62 uint32_t lx,ly,lz; 63 int ix,iy,n,sx; 64 65 ux.e = x; 66 uy.e = y; 67 sx = ux.bits.ext_sign; 68 69 /* purge off exception values */ 70 if((uy.bits.ext_exp|uy.bits.ext_frach|uy.bits.ext_fracl)==0 || /* y=0 */ 71 (ux.bits.ext_exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ 72 (uy.bits.ext_exp == BIAS + LDBL_MAX_EXP && 73 ((uy.bits.ext_frach&~LDBL_NBIT)|uy.bits.ext_fracl)!=0)) /* or y is NaN */ 74 return (x*y)/(x*y); 75 if(ux.bits.ext_exp<=uy.bits.ext_exp) { 76 if((ux.bits.ext_exp<uy.bits.ext_exp) || 77 (ux.bits.ext_frach<=uy.bits.ext_frach && 78 (ux.bits.ext_frach<uy.bits.ext_frach || 79 ux.bits.ext_fracl<uy.bits.ext_fracl))) { 80 return x; /* |x|<|y| return x or x-y */ 81 } 82 if(ux.bits.ext_frach==uy.bits.ext_frach && 83 ux.bits.ext_fracl==uy.bits.ext_fracl) { 84 return Zero[sx]; /* |x|=|y| return x*0*/ 85 } 86 } 87 88 /* determine ix = ilogb(x) */ 89 if(ux.bits.ext_exp == 0) { /* subnormal x */ 90 ux.e *= 0x1.0p512; 91 ix = ux.bits.ext_exp - (BIAS + 512); 92 } else { 93 ix = ux.bits.ext_exp - BIAS; 94 } 95 96 /* determine iy = ilogb(y) */ 97 if(uy.bits.ext_exp == 0) { /* subnormal y */ 98 uy.e *= 0x1.0p512; 99 iy = uy.bits.ext_exp - (BIAS + 512); 100 } else { 101 iy = uy.bits.ext_exp - BIAS; 102 } 103 104 /* set up {hx,lx}, {hy,ly} and align y to x */ 105 hx = SET_NBIT(ux.bits.ext_frach); 106 hy = SET_NBIT(uy.bits.ext_frach); 107 lx = ux.bits.ext_fracl; 108 ly = uy.bits.ext_fracl; 109 110 /* fix point fmod */ 111 n = ix - iy; 112 113 while(n--) { 114 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 115 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;} 116 else { 117 if ((hz|lz)==0) /* return sign(x)*0 */ 118 return Zero[sx]; 119 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; 120 } 121 } 122 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 123 if(hz>=0) {hx=hz;lx=lz;} 124 125 /* convert back to floating value and restore the sign */ 126 if((hx|lx)==0) /* return sign(x)*0 */ 127 return Zero[sx]; 128 while(hx<(int64_t)(1ULL<<HFRAC_BITS)) { /* normalize x */ 129 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx; 130 iy -= 1; 131 } 132 ux.bits.ext_frach = hx; /* The mantissa is truncated here if needed. */ 133 ux.bits.ext_fracl = lx; 134 if (iy < LDBL_MIN_EXP) { 135 ux.bits.ext_exp = iy + (BIAS + 512); 136 ux.e *= 0x1p-512; 137 } else { 138 ux.bits.ext_exp = iy + BIAS; 139 } 140 x = ux.e * one; /* create necessary signal */ 141 return x; /* exact output */ 142 } 143