1177764Sdas/* @(#)e_fmod.c 1.3 95/01/18 */ 2177764Sdas/*- 3177764Sdas * ==================================================== 4177764Sdas * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5177764Sdas * 6177764Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business. 7177764Sdas * Permission to use, copy, modify, and distribute this 8177764Sdas * software is freely granted, provided that this notice 9177764Sdas * is preserved. 10177764Sdas * ==================================================== 11177764Sdas */ 12177764Sdas 13177764Sdas#include <sys/cdefs.h> 14177764Sdas__FBSDID("$FreeBSD$"); 15177764Sdas 16177764Sdas#include <float.h> 17177764Sdas#include <stdint.h> 18177764Sdas 19177764Sdas#include "fpmath.h" 20177764Sdas#include "math.h" 21177764Sdas#include "math_private.h" 22177764Sdas 23177764Sdas#define BIAS (LDBL_MAX_EXP - 1) 24177764Sdas 25177764Sdas#if LDBL_MANL_SIZE > 32 26177764Sdastypedef uint64_t manl_t; 27177764Sdas#else 28177764Sdastypedef uint32_t manl_t; 29177764Sdas#endif 30177764Sdas 31177764Sdas#if LDBL_MANH_SIZE > 32 32177764Sdastypedef uint64_t manh_t; 33177764Sdas#else 34177764Sdastypedef uint32_t manh_t; 35177764Sdas#endif 36177764Sdas 37177764Sdas/* 38177764Sdas * These macros add and remove an explicit integer bit in front of the 39177764Sdas * fractional mantissa, if the architecture doesn't have such a bit by 40177764Sdas * default already. 41177764Sdas */ 42177764Sdas#ifdef LDBL_IMPLICIT_NBIT 43177764Sdas#define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) 44177764Sdas#define HFRAC_BITS LDBL_MANH_SIZE 45177764Sdas#else 46177764Sdas#define SET_NBIT(hx) (hx) 47177764Sdas#define HFRAC_BITS (LDBL_MANH_SIZE - 1) 48177764Sdas#endif 49177764Sdas 50177764Sdas#define MANL_SHIFT (LDBL_MANL_SIZE - 1) 51177764Sdas 52177764Sdasstatic const long double Zero[] = {0.0L, -0.0L}; 53177764Sdas 54177764Sdas/* 55177764Sdas * Return the IEEE remainder and set *quo to the last n bits of the 56177764Sdas * quotient, rounded to the nearest integer. We choose n=31 because 57177764Sdas * we wind up computing all the integer bits of the quotient anyway as 58177764Sdas * a side-effect of computing the remainder by the shift and subtract 59177764Sdas * method. In practice, this is far more bits than are needed to use 60177764Sdas * remquo in reduction algorithms. 61177764Sdas * 62177764Sdas * Assumptions: 63177764Sdas * - The low part of the mantissa fits in a manl_t exactly. 64177764Sdas * - The high part of the mantissa fits in an int64_t with enough room 65177764Sdas * for an explicit integer bit in front of the fractional bits. 66177764Sdas */ 67177764Sdaslong double 68177764Sdasremquol(long double x, long double y, int *quo) 69177764Sdas{ 70177764Sdas union IEEEl2bits ux, uy; 71177764Sdas int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ 72177764Sdas manh_t hy; 73177764Sdas manl_t lx,ly,lz; 74177764Sdas int ix,iy,n,q,sx,sxy; 75177764Sdas 76177764Sdas ux.e = x; 77177764Sdas uy.e = y; 78177764Sdas sx = ux.bits.sign; 79177764Sdas sxy = sx ^ uy.bits.sign; 80177764Sdas ux.bits.sign = 0; /* |x| */ 81177764Sdas uy.bits.sign = 0; /* |y| */ 82177764Sdas x = ux.e; 83177764Sdas 84177764Sdas /* purge off exception values */ 85177764Sdas if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */ 86177764Sdas (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ 87177764Sdas (uy.bits.exp == BIAS + LDBL_MAX_EXP && 88177764Sdas ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */ 89177764Sdas return (x*y)/(x*y); 90177764Sdas if(ux.bits.exp<=uy.bits.exp) { 91177764Sdas if((ux.bits.exp<uy.bits.exp) || 92177764Sdas (ux.bits.manh<=uy.bits.manh && 93177764Sdas (ux.bits.manh<uy.bits.manh || 94177764Sdas ux.bits.manl<uy.bits.manl))) { 95177764Sdas q = 0; 96177764Sdas goto fixup; /* |x|<|y| return x or x-y */ 97177764Sdas } 98177764Sdas if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) { 99233973Sdas *quo = (sxy ? -1 : 1); 100177764Sdas return Zero[sx]; /* |x|=|y| return x*0*/ 101177764Sdas } 102177764Sdas } 103177764Sdas 104177764Sdas /* determine ix = ilogb(x) */ 105177764Sdas if(ux.bits.exp == 0) { /* subnormal x */ 106177764Sdas ux.e *= 0x1.0p512; 107177764Sdas ix = ux.bits.exp - (BIAS + 512); 108177764Sdas } else { 109177764Sdas ix = ux.bits.exp - BIAS; 110177764Sdas } 111177764Sdas 112177764Sdas /* determine iy = ilogb(y) */ 113177764Sdas if(uy.bits.exp == 0) { /* subnormal y */ 114177764Sdas uy.e *= 0x1.0p512; 115177764Sdas iy = uy.bits.exp - (BIAS + 512); 116177764Sdas } else { 117177764Sdas iy = uy.bits.exp - BIAS; 118177764Sdas } 119177764Sdas 120177764Sdas /* set up {hx,lx}, {hy,ly} and align y to x */ 121177764Sdas hx = SET_NBIT(ux.bits.manh); 122177764Sdas hy = SET_NBIT(uy.bits.manh); 123177764Sdas lx = ux.bits.manl; 124177764Sdas ly = uy.bits.manl; 125177764Sdas 126177764Sdas /* fix point fmod */ 127177764Sdas n = ix - iy; 128177764Sdas q = 0; 129177764Sdas 130177764Sdas while(n--) { 131177764Sdas hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 132177764Sdas if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;} 133177764Sdas else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;} 134177764Sdas q <<= 1; 135177764Sdas } 136177764Sdas hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 137177764Sdas if(hz>=0) {hx=hz;lx=lz;q++;} 138177764Sdas 139177764Sdas /* convert back to floating value and restore the sign */ 140177764Sdas if((hx|lx)==0) { /* return sign(x)*0 */ 141233973Sdas q &= 0x7fffffff; 142177764Sdas *quo = (sxy ? -q : q); 143177764Sdas return Zero[sx]; 144177764Sdas } 145181063Sdas while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */ 146177764Sdas hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx; 147177764Sdas iy -= 1; 148177764Sdas } 149177764Sdas ux.bits.manh = hx; /* The integer bit is truncated here if needed. */ 150177764Sdas ux.bits.manl = lx; 151177764Sdas if (iy < LDBL_MIN_EXP) { 152177764Sdas ux.bits.exp = iy + (BIAS + 512); 153177764Sdas ux.e *= 0x1p-512; 154177764Sdas } else { 155177764Sdas ux.bits.exp = iy + BIAS; 156177764Sdas } 157177764Sdas ux.bits.sign = 0; 158177764Sdas x = ux.e; 159177764Sdasfixup: 160177764Sdas y = fabsl(y); 161177764Sdas if (y < LDBL_MIN * 2) { 162177764Sdas if (x+x>y || (x+x==y && (q & 1))) { 163177764Sdas q++; 164177764Sdas x-=y; 165177764Sdas } 166177764Sdas } else if (x>0.5*y || (x==0.5*y && (q & 1))) { 167177764Sdas q++; 168177764Sdas x-=y; 169177764Sdas } 170177764Sdas 171177764Sdas ux.e = x; 172177764Sdas ux.bits.sign ^= sx; 173177764Sdas x = ux.e; 174177764Sdas 175177764Sdas q &= 0x7fffffff; 176177764Sdas *quo = (sxy ? -q : q); 177177764Sdas return x; 178177764Sdas} 179