/* $OpenBSD: fpu_emu.h,v 1.7 2024/03/29 21:07:11 miod Exp $ */ /* $NetBSD: fpu_emu.h,v 1.4 2000/08/03 18:32:07 eeh Exp $ */ /* * Copyright (c) 1992, 1993 * The Regents of the University of California. All rights reserved. * * This software was developed by the Computer Systems Engineering group * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and * contributed to Berkeley. * * All advertising materials mentioning features or use of this software * must display the following acknowledgement: * This product includes software developed by the University of * California, Lawrence Berkeley Laboratory. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * * @(#)fpu_emu.h 8.1 (Berkeley) 6/11/93 */ /* * Floating point emulator (tailored for SPARC, but structurally * machine-independent). * * Floating point numbers are carried around internally in an `expanded' * or `unpacked' form consisting of: * - sign * - unbiased exponent * - mantissa (`1.' + 112-bit fraction + guard + round) * - sticky bit * Any implied `1' bit is inserted, giving a 113-bit mantissa that is * always nonzero. Additional low-order `guard' and `round' bits are * scrunched in, making the entire mantissa 115 bits long. This is divided * into four 32-bit words, with `spare' bits left over in the upper part * of the top word (the high bits of fp_mant[0]). An internal `exploded' * number is thus kept within the half-open interval [1.0,2.0) (but see * the `number classes' below). This holds even for denormalized numbers: * when we explode an external denorm, we normalize it, introducing low-order * zero bits, so that the rest of the code always sees normalized values. * * Note that a number of our algorithms use the `spare' bits at the top. * The most demanding algorithm---the one for sqrt---depends on two such * bits, so that it can represent values up to (but not including) 8.0, * and then it needs a carry on top of that, so that we need three `spares'. * * The sticky-word is 32 bits so that we can use `OR' operators to goosh * whole words from the mantissa into it. * * All operations are done in this internal extended precision. According * to Hennesey & Patterson, Appendix A, rounding can be repeated---that is, * it is OK to do a+b in extended precision and then round the result to * single precision---provided single, double, and extended precisions are * `far enough apart' (they always are), but we will try to avoid any such * extra work where possible. */ struct fpn { int fp_class; /* see below */ int fp_sign; /* 0 => positive, 1 => negative */ int fp_exp; /* exponent (unbiased) */ int fp_sticky; /* nonzero bits lost at right end */ u_int fp_mant[4]; /* 115-bit mantissa */ }; #define FP_NMANT 115 /* total bits in mantissa (incl g,r) */ #define FP_NG 2 /* number of low-order guard bits */ #define FP_LG ((FP_NMANT - 1) & 31) /* log2(1.0) for fp_mant[0] */ #define FP_LG2 ((FP_NMANT - 1) & 63) /* log2(1.0) for fp_mant[0] and fp_mant[1] */ #define FP_QUIETBIT (1 << (FP_LG - 1)) /* Quiet bit in NaNs (0.5) */ #define FP_1 (1 << FP_LG) /* 1.0 in fp_mant[0] */ #define FP_2 (1 << (FP_LG + 1)) /* 2.0 in fp_mant[0] */ /* * Number classes. Since zero, Inf, and NaN cannot be represented using * the above layout, we distinguish these from other numbers via a class. * In addition, to make computation easier and to follow Appendix N of * the SPARC Version 8 standard, we give each kind of NaN a separate class. */ #define FPC_SNAN -2 /* signalling NaN (sign irrelevant) */ #define FPC_QNAN -1 /* quiet NaN (sign irrelevant) */ #define FPC_ZERO 0 /* zero (sign matters) */ #define FPC_NUM 1 /* number (sign matters) */ #define FPC_INF 2 /* infinity (sign matters) */ #define ISNAN(fp) ((fp)->fp_class < 0) #define ISZERO(fp) ((fp)->fp_class == 0) #define ISINF(fp) ((fp)->fp_class == FPC_INF) /* * ORDER(x,y) `sorts' a pair of `fpn *'s so that the right operand (y) points * to the `more significant' operand for our purposes. Appendix N says that * the result of a computation involving two numbers are: * * If both are SNaN: operand 2, converted to Quiet * If only one is SNaN: the SNaN operand, converted to Quiet * If both are QNaN: operand 2 * If only one is QNaN: the QNaN operand * * In addition, in operations with an Inf operand, the result is usually * Inf. The class numbers are carefully arranged so that if * (unsigned)class(op1) > (unsigned)class(op2) * then op1 is the one we want; otherwise op2 is the one we want. */ #define ORDER(x, y) { \ if ((u_int)(x)->fp_class > (u_int)(y)->fp_class) \ SWAP(x, y); \ } #define SWAP(x, y) { \ struct fpn *swap; \ swap = (x), (x) = (y), (y) = swap; \ } /* * Emulator state. */ struct fpemu { struct fpstate *fe_fpstate; /* registers, etc */ int fe_fsr; /* fsr copy (modified during op) */ int fe_cx; /* exceptions */ struct fpn fe_f1; /* operand 1 */ struct fpn fe_f2; /* operand 2, if required */ struct fpn fe_f3; /* available storage for result */ }; /* * Arithmetic functions. * Each of these may modify its inputs (f1,f2) and/or the temporary. * Each returns a pointer to the result and/or sets exceptions. */ struct fpn *fpu_add(struct fpemu *); #define fpu_sub(fe) ((fe)->fe_f2.fp_sign ^= 1, fpu_add(fe)) struct fpn *fpu_mul(struct fpemu *); struct fpn *fpu_div(struct fpemu *); struct fpn *fpu_sqrt(struct fpemu *); /* * Other functions. */ /* Perform a compare instruction (with or without unordered exception). */ void fpu_compare(struct fpemu *, int); /* Build a new Quiet NaN (sign=0, frac=all 1's). */ struct fpn *fpu_newnan(struct fpemu *); /* * Shift a number right some number of bits, taking care of round/sticky. * Note that the result is probably not a well-formed number (it will lack * the normal 1-bit mant[0]&FP_1). */ int fpu_shr(struct fpn *, int); void fpu_explode(struct fpemu *, struct fpn *, int, int); void fpu_implode(struct fpemu *, struct fpn *, int, u_int *); #ifdef DEBUG #define FPE_INSN 0x1 #define FPE_REG 0x2 #define FPE_STATE 0x4 extern int fpe_debug; void fpu_dumpfpn(struct fpn *); void fpu_dumpstate(struct fpstate *); #define DPRINTF(x, y) if (fpe_debug & (x)) printf y #define DUMPFPN(x, f) if (fpe_debug & (x)) fpu_dumpfpn((f)) #define DUMPSTATE(x, s) if (fpe_debug & (x)) fpu_dumpstate((s)) #else #define DPRINTF(x, y) #define DUMPFPN(x, f) #define DUMPSTATE(x, s) #endif
