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/* Simulator Floating-point support.
Copyright 1997-2021 Free Software Foundation, Inc.
Contributed by Cygnus Support.
This file is part of GDB, the GNU debugger.
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <>. */
#ifndef SIM_FPU_H
#define SIM_FPU_H
/* The FPU intermediate type - this object, passed by reference,
should be treated as opaque.
Pragmatics - pass struct by ref:
The alternatives for this object/interface that were considered
were: a packed 64 bit value; an unpacked structure passed by value;
and an unpacked structure passed by reference.
The packed 64 bit value was rejected because: it limited the
precision of intermediate values; reasonable performance would only
be achieved when the sim_fpu package was in-lined allowing repeated
unpacking operations to be eliminated.
For unpacked structures (passed by value and reference), the code
quality of GCC-2.7 (on x86) for each alternative was compared.
Needless to say the results, while better than for a packed 64 bit
object, were still poor (GCC had only limited support for the
optimization of references to structure members). Regardless, the
struct-by-ref alternative achieved better results when compiled
with (better speed) and without (better code density) in-lining.
Here's looking forward to an improved GCC optimizer.
Pragmatics - avoid host FP hardware:
FP operations can be implemented by either: the host's floating
point hardware; or by emulating the FP operations using integer
only routines. This is direct tradeoff between speed, portability
and correctness.
The two principal reasons for selecting portability and correctness
over speed are:
1 - Correctness. The assumption that FP correctness wasn't an
issue for code being run on simulators was wrong. Instead of
running FP tolerant (?) code, simulator users instead typically run
very aggressive FP code sequences. The sole purpose of those
sequences being to test the target ISA's FP implementation.
2 - Portability. The host FP implementation is not predictable. A
simulator modeling aggressive FP code sequences using the hosts FPU
relies heavily on the correctness of the hosts FP implementation.
It turns out that such trust can be misplaced. The behavior of
host FP implementations when handling edge conditions such as SNaNs
and exceptions varied widely.
typedef enum
} sim_fpu_class;
typedef struct _sim_fpu {
sim_fpu_class class;
int sign;
unsigned64 fraction;
int normal_exp;
} sim_fpu;
/* Rounding options.
The value zero (sim_fpu_round_default) for ALU operations indicates
that, when possible, rounding should be avoided. */
typedef enum
sim_fpu_round_default = 0,
sim_fpu_round_near = 1,
sim_fpu_round_zero = 2,
sim_fpu_round_up = 3,
sim_fpu_round_down = 4,
} sim_fpu_round;
/* Options when handling denormalized numbers. */
typedef enum
sim_fpu_denorm_default = 0,
sim_fpu_denorm_underflow_inexact = 1,
sim_fpu_denorm_zero = 2,
} sim_fpu_denorm;
/* Status values returned by FPU operators.
When checking the result of an FP sequence (ex 32to, add, single,
to32) the caller may either: check the return value of each FP
operator; or form the union (OR) of the returned values and examine
them once at the end.
FIXME: This facility is still being developed. The choice of
status values returned and their exact meaning may changed in the
future. */
typedef enum
sim_fpu_status_invalid_snan = 1,
sim_fpu_status_invalid_qnan = 2,
sim_fpu_status_invalid_isi = 4, /* (inf - inf) */
sim_fpu_status_invalid_idi = 8, /* (inf / inf) */
sim_fpu_status_invalid_zdz = 16, /* (0 / 0) */
sim_fpu_status_invalid_imz = 32, /* (inf * 0) */
sim_fpu_status_invalid_cvi = 64, /* convert to integer */
sim_fpu_status_invalid_div0 = 128, /* (X / 0) */
sim_fpu_status_invalid_cmp = 256, /* compare */
sim_fpu_status_invalid_sqrt = 512,
sim_fpu_status_invalid_irx = 1024, /* (inf % X) */
sim_fpu_status_rounded = 2048,
sim_fpu_status_inexact = 4096,
sim_fpu_status_overflow = 8192,
sim_fpu_status_underflow = 16384,
sim_fpu_status_denorm = 32768,
} sim_fpu_status;
/* Directly map between a 32/64 bit register and the sim_fpu internal
When converting from the 32/64 bit packed format to the sim_fpu
internal type, the operation is exact.
When converting from the sim_fpu internal type to 32/64 bit packed
format, the operation may result in a loss of precision. The
configuration macro WITH_FPU_CONVERSION controls this. By default,
silent round to nearest is performed. Alternatively, round up,
round down and round to zero can be performed. In a simulator
emulating exact FPU behavior, sim_fpu_round_{32,64} should be
called before packing the sim_fpu value. */
INLINE_SIM_FPU (void) sim_fpu_32to (sim_fpu *f, unsigned32 s);
INLINE_SIM_FPU (void) sim_fpu_232to (sim_fpu *f, unsigned32 h, unsigned32 l);
INLINE_SIM_FPU (void) sim_fpu_64to (sim_fpu *f, unsigned64 d);
INLINE_SIM_FPU (void) sim_fpu_to32 (unsigned32 *s, const sim_fpu *f);
INLINE_SIM_FPU (void) sim_fpu_to232 (unsigned32 *h, unsigned32 *l, const sim_fpu *f);
INLINE_SIM_FPU (void) sim_fpu_to64 (unsigned64 *d, const sim_fpu *f);
/* Create a sim_fpu struct using raw information. (FRACTION & LSMASK
(PRECISION-1, 0)) is assumed to contain the fraction part of the
floating-point number. The leading bit LSBIT (PRECISION) is always
implied. The number created can be represented by:
(SIGN ? "-" : "+") "1." FRACTION{PRECISION-1,0} X 2 ^ NORMAL_EXP>
You can not specify zero using this function. */
INLINE_SIM_FPU (void) sim_fpu_fractionto (sim_fpu *f, int sign, int normal_exp, unsigned64 fraction, int precision);
/* Reverse operation. If S is a non-zero number, discards the implied
leading one and returns PRECISION fraction bits. No rounding is
performed. */
INLINE_SIM_FPU (unsigned64) sim_fpu_tofraction (const sim_fpu *s, int precision);
/* Rounding operators.
Force an intermediate result to an exact 32/64 bit
representation. */
INLINE_SIM_FPU (int) sim_fpu_round_32 (sim_fpu *f,
sim_fpu_round round,
sim_fpu_denorm denorm);
INLINE_SIM_FPU (int) sim_fpu_round_64 (sim_fpu *f,
sim_fpu_round round,
sim_fpu_denorm denorm);
/* Arithmetic operators.
FIXME: In the future, additional arguments ROUNDING and BITSIZE may
be added. */
typedef int (sim_fpu_op1) (sim_fpu *f,
const sim_fpu *l);
typedef int (sim_fpu_op2) (sim_fpu *f,
const sim_fpu *l,
const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_add (sim_fpu *f,
const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_sub (sim_fpu *f,
const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_mul (sim_fpu *f,
const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_div (sim_fpu *f,
const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_rem (sim_fpu *f,
const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_max (sim_fpu *f,
const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_min (sim_fpu *f,
const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_neg (sim_fpu *f,
const sim_fpu *a);
INLINE_SIM_FPU (int) sim_fpu_abs (sim_fpu *f,
const sim_fpu *a);
INLINE_SIM_FPU (int) sim_fpu_inv (sim_fpu *f,
const sim_fpu *a);
INLINE_SIM_FPU (int) sim_fpu_sqrt (sim_fpu *f,
const sim_fpu *sqr);
/* Conversion of integer <-> floating point. */
INLINE_SIM_FPU (int) sim_fpu_i32to (sim_fpu *f, signed32 i,
sim_fpu_round round);
INLINE_SIM_FPU (int) sim_fpu_u32to (sim_fpu *f, unsigned32 u,
sim_fpu_round round);
INLINE_SIM_FPU (int) sim_fpu_i64to (sim_fpu *f, signed64 i,
sim_fpu_round round);
INLINE_SIM_FPU (int) sim_fpu_u64to (sim_fpu *f, unsigned64 u,
sim_fpu_round round);
#if 0
INLINE_SIM_FPU (int) sim_fpu_i232to (sim_fpu *f, signed32 h, signed32 l,
sim_fpu_round round);
#if 0
INLINE_SIM_FPU (int) sim_fpu_u232to (sim_fpu *f, unsigned32 h, unsigned32 l,
sim_fpu_round round);
INLINE_SIM_FPU (int) sim_fpu_to32i (signed32 *i, const sim_fpu *f,
sim_fpu_round round);
INLINE_SIM_FPU (int) sim_fpu_to32u (unsigned32 *u, const sim_fpu *f,
sim_fpu_round round);
INLINE_SIM_FPU (int) sim_fpu_to64i (signed64 *i, const sim_fpu *f,
sim_fpu_round round);
INLINE_SIM_FPU (int) sim_fpu_to64u (unsigned64 *u, const sim_fpu *f,
sim_fpu_round round);
#if 0
INLINE_SIM_FPU (int) sim_fpu_to232i (signed64 *h, signed64 *l, const sim_fpu *f,
sim_fpu_round round);
#if 0
INLINE_SIM_FPU (int) sim_fpu_to232u (unsigned64 *h, unsigned64 *l, const sim_fpu *f,
sim_fpu_round round);
/* Conversion of internal sim_fpu type to host double format.
For debugging/tracing only. A SNaN is never returned. */
/* INLINE_SIM_FPU (float) sim_fpu_2f (const sim_fpu *f); */
INLINE_SIM_FPU (double) sim_fpu_2d (const sim_fpu *d);
/* INLINE_SIM_FPU (void) sim_fpu_f2 (sim_fpu *f, float s); */
INLINE_SIM_FPU (void) sim_fpu_d2 (sim_fpu *f, double d);
/* Specific number classes.
NB: When either, a 32/64 bit floating points is converted to
internal format, or an internal format number is rounded to 32/64
bit precision, a special marker is retained that indicates that the
value was normalized. For such numbers both is_number and
is_denorm return true. */
INLINE_SIM_FPU (int) sim_fpu_is_nan (const sim_fpu *s); /* 1 => SNaN or QNaN */
INLINE_SIM_FPU (int) sim_fpu_is_snan (const sim_fpu *s); /* 1 => SNaN */
INLINE_SIM_FPU (int) sim_fpu_is_qnan (const sim_fpu *s); /* 1 => QNaN */
INLINE_SIM_FPU (int) sim_fpu_is_zero (const sim_fpu *s);
INLINE_SIM_FPU (int) sim_fpu_is_infinity (const sim_fpu *s);
INLINE_SIM_FPU (int) sim_fpu_is_number (const sim_fpu *s); /* !zero */
INLINE_SIM_FPU (int) sim_fpu_is_denorm (const sim_fpu *s); /* !zero */
/* Floating point fields */
INLINE_SIM_FPU (int) sim_fpu_sign (const sim_fpu *s);
INLINE_SIM_FPU (int) sim_fpu_exp (const sim_fpu *s);
INLINE_SIM_FPU (unsigned64) sim_fpu_fraction (const sim_fpu *s);
INLINE_SIM_FPU (unsigned64) sim_fpu_guard (const sim_fpu *s, int is_double);
/* Specific comparison operators
For NaNs et al., the comparison operators will set IS to zero and
return a nonzero result. */
INLINE_SIM_FPU (int) sim_fpu_lt (int *is, const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_le (int *is, const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_eq (int *is, const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_ne (int *is, const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_ge (int *is, const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_gt (int *is, const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_is_lt (const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_is_le (const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_is_eq (const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_is_ne (const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_is_ge (const sim_fpu *l, const sim_fpu *r);
INLINE_SIM_FPU (int) sim_fpu_is_gt (const sim_fpu *l, const sim_fpu *r);
/* General number class and comparison operators.
The result of the comparison is indicated by returning one of the
values below. Efficient emulation of a target FP compare
instruction can be achieved by redefining the values below to match
corresponding target FP status bits.
For instance. SIM_FPU_QNAN may be redefined to be the bit
`INVALID' while SIM_FPU_NINF might be redefined as the bits
enum {
SIM_FPU_IS_SNAN = 1, /* Noisy not-a-number */
SIM_FPU_IS_QNAN = 2, /* Quiet not-a-number */
SIM_FPU_IS_NINF = 3, /* -infinity */
SIM_FPU_IS_PINF = 4, /* +infinity */
SIM_FPU_IS_NNUMBER = 5, /* -number - [ -MAX .. -MIN ] */
SIM_FPU_IS_PNUMBER = 6, /* +number - [ +MIN .. +MAX ] */
SIM_FPU_IS_NDENORM = 7, /* -denorm - ( MIN .. 0 ) */
SIM_FPU_IS_PDENORM = 8, /* +denorm - ( 0 .. MIN ) */
SIM_FPU_IS_NZERO = 9, /* -0 */
SIM_FPU_IS_PZERO = 10, /* +0 */
INLINE_SIM_FPU (int) sim_fpu_is (const sim_fpu *l);
INLINE_SIM_FPU (int) sim_fpu_cmp (const sim_fpu *l, const sim_fpu *r);
/* A number of useful constants. */
extern const sim_fpu sim_fpu_zero;
extern const sim_fpu sim_fpu_one;
extern const sim_fpu sim_fpu_two;
extern const sim_fpu sim_fpu_qnan;
extern const sim_fpu sim_fpu_max32;
extern const sim_fpu sim_fpu_max64;
/* Select the applicable functions for the fp_word type */
#define sim_fpu_tofp sim_fpu_to32
#define sim_fpu_fpto sim_fpu_32to
#define sim_fpu_round_fp sim_fpu_round_32
#define sim_fpu_maxfp sim_fpu_max32
#define sim_fpu_tofp sim_fpu_to64
#define sim_fpu_fpto sim_fpu_64to
#define sim_fpu_round_fp sim_fpu_round_64
#define sim_fpu_maxfp sim_fpu_max64
/* For debugging */
typedef void sim_fpu_print_func (void *, const char *, ...);
/* Print a sim_fpu with full precision. */
INLINE_SIM_FPU (void) sim_fpu_print_fpu (const sim_fpu *f,
sim_fpu_print_func *print,
void *arg);
/* Print a sim_fpu with `n' trailing digits. */
INLINE_SIM_FPU (void) sim_fpu_printn_fpu (const sim_fpu *f,
sim_fpu_print_func *print,
int digits,
void *arg);
INLINE_SIM_FPU (void) sim_fpu_print_status (int status,
sim_fpu_print_func *print,
void *arg);
#include "sim-fpu.c"