/* $NetBSD: fpu_emu.h,v 1.12 2022/09/07 02:41:39 rin 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 ISSNAN(fp) ((fp)->fp_class == FPC_SNAN)
#define ISQNAN(fp) ((fp)->fp_class == FPC_QNAN)
#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; \
}
/*
* FPU data types.
*/
#define FTYPE_INT 0x00 /* data = 32-bit signed integer */
#define FTYPE_LNG 0x01 /* data = 64-bit signed long integer */
#define FTYPE_SNG 0x02 /* data = 32-bit float */
#define FTYPE_DBL 0x04 /* data = 64-bit double */
#define FTYPE_RD_RZ 0x08
#define FTYPE_FPSCR 0x10
#define FTYPE_FLAG_MASK (FTYPE_RD_RZ | FTYPE_FPSCR)
/*
* Emulator state.
*/
struct fpemu {
struct fpreg *fe_fpstate; /* registers, etc */
int fe_fpscr; /* fpscr copy (modified during op) */
int fe_cx; /* keep track of exceptions */
struct fpn fe_f1; /* operand 1 */
struct fpn fe_f2; /* operand 2, if required */
struct fpn fe_f3; /* available storage for result */
vaddr_t fe_addr; /* last address accessed */
};
/*
* 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 *);
struct fpn *fpu_mul(struct fpemu *);
struct fpn *fpu_div(struct fpemu *);
struct fpn *fpu_sqrt(struct fpemu *);
static inline struct fpn *
fpu_sub(struct fpemu *fe)
{
struct fpn *fp = &fe->fe_f2;
if (!ISNAN(fp))
fp->fp_sign ^= 1;
return fpu_add(fe);
}
/*
* 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_norm(struct fpn *);
void fpu_explode(struct fpemu *, struct fpn *, int, uint64_t);
void fpu_implode(struct fpemu *, struct fpn *, int, uint64_t *);
#ifdef DEBUG
#define FPE_EX 0x1
#define FPE_INSN 0x2
#define FPE_OP 0x4
#define FPE_REG 0x8
extern int fpe_debug;
void fpu_dumpfpn(struct fpn *);
#define DPRINTF(x, y) if (fpe_debug & (x)) printf y
#define DUMPFPN(x, f) if (fpe_debug & (x)) fpu_dumpfpn((f))
#else
#define DPRINTF(x, y)
#define DUMPFPN(x, f)
#endif