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fpu_trig.c
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fpu_trig.c
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/*---------------------------------------------------------------------------+
| fpu_trig.c |
| |
| Implementation of the FPU "transcendental" functions. |
| |
| Copyright (C) 1992,1993,1994,1997,1999 |
| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, |
| Australia. E-mail [email protected] |
| |
| |
+---------------------------------------------------------------------------*/
#include "fpu_system.h"
#include "exception.h"
#include "fpu_emu.h"
#include "status_w.h"
#include "control_w.h"
#include "reg_constant.h"
static void rem_kernel(unsigned long long st0, unsigned long long *y,
unsigned long long st1, unsigned long long q, int n);
#define BETTER_THAN_486
#define FCOS 4
/* Used only by fptan, fsin, fcos, and fsincos. */
/* This routine produces very accurate results, similar to
using a value of pi with more than 128 bits precision. */
/* Limited measurements show no results worse than 64 bit precision
except for the results for arguments close to 2^63, where the
precision of the result sometimes degrades to about 63.9 bits */
static int trig_arg(FPU_REG *st0_ptr, int even)
{
FPU_REG tmp;
u_char tmptag;
unsigned long long q;
int old_cw = control_word, saved_status = partial_status;
int tag, st0_tag = TAG_Valid;
if (exponent(st0_ptr) >= 63) {
partial_status |= SW_C2; /* Reduction incomplete. */
return -1;
}
control_word &= ~CW_RC;
control_word |= RC_CHOP;
setpositive(st0_ptr);
tag = FPU_u_div(st0_ptr, &CONST_PI2, &tmp, PR_64_BITS | RC_CHOP | 0x3f,
SIGN_POS);
FPU_round_to_int(&tmp, tag); /* Fortunately, this can't overflow
to 2^64 */
q = significand(&tmp);
if (q) {
rem_kernel(significand(st0_ptr),
&significand(&tmp),
significand(&CONST_PI2),
q, exponent(st0_ptr) - exponent(&CONST_PI2));
setexponent16(&tmp, exponent(&CONST_PI2));
st0_tag = FPU_normalize(&tmp);
FPU_copy_to_reg0(&tmp, st0_tag);
}
if ((even && !(q & 1)) || (!even && (q & 1))) {
st0_tag =
FPU_sub(REV | LOADED | TAG_Valid, (int)&CONST_PI2,
FULL_PRECISION);
#ifdef BETTER_THAN_486
/* So far, the results are exact but based upon a 64 bit
precision approximation to pi/2. The technique used
now is equivalent to using an approximation to pi/2 which
is accurate to about 128 bits. */
if ((exponent(st0_ptr) <= exponent(&CONST_PI2extra) + 64)
|| (q > 1)) {
/* This code gives the effect of having pi/2 to better than
128 bits precision. */
significand(&tmp) = q + 1;
setexponent16(&tmp, 63);
FPU_normalize(&tmp);
tmptag =
FPU_u_mul(&CONST_PI2extra, &tmp, &tmp,
FULL_PRECISION, SIGN_POS,
exponent(&CONST_PI2extra) +
exponent(&tmp));
setsign(&tmp, getsign(&CONST_PI2extra));
st0_tag = FPU_add(&tmp, tmptag, 0, FULL_PRECISION);
if (signnegative(st0_ptr)) {
/* CONST_PI2extra is negative, so the result of the addition
can be negative. This means that the argument is actually
in a different quadrant. The correction is always < pi/2,
so it can't overflow into yet another quadrant. */
setpositive(st0_ptr);
q++;
}
}
#endif /* BETTER_THAN_486 */
}
#ifdef BETTER_THAN_486
else {
/* So far, the results are exact but based upon a 64 bit
precision approximation to pi/2. The technique used
now is equivalent to using an approximation to pi/2 which
is accurate to about 128 bits. */
if (((q > 0)
&& (exponent(st0_ptr) <= exponent(&CONST_PI2extra) + 64))
|| (q > 1)) {
/* This code gives the effect of having p/2 to better than
128 bits precision. */
significand(&tmp) = q;
setexponent16(&tmp, 63);
FPU_normalize(&tmp); /* This must return TAG_Valid */
tmptag =
FPU_u_mul(&CONST_PI2extra, &tmp, &tmp,
FULL_PRECISION, SIGN_POS,
exponent(&CONST_PI2extra) +
exponent(&tmp));
setsign(&tmp, getsign(&CONST_PI2extra));
st0_tag = FPU_sub(LOADED | (tmptag & 0x0f), (int)&tmp,
FULL_PRECISION);
if ((exponent(st0_ptr) == exponent(&CONST_PI2)) &&
((st0_ptr->sigh > CONST_PI2.sigh)
|| ((st0_ptr->sigh == CONST_PI2.sigh)
&& (st0_ptr->sigl > CONST_PI2.sigl)))) {
/* CONST_PI2extra is negative, so the result of the
subtraction can be larger than pi/2. This means
that the argument is actually in a different quadrant.
The correction is always < pi/2, so it can't overflow
into yet another quadrant. */
st0_tag =
FPU_sub(REV | LOADED | TAG_Valid,
(int)&CONST_PI2, FULL_PRECISION);
q++;
}
}
}
#endif /* BETTER_THAN_486 */
FPU_settag0(st0_tag);
control_word = old_cw;
partial_status = saved_status & ~SW_C2; /* Reduction complete. */
return (q & 3) | even;
}
/* Convert a long to register */
static void convert_l2reg(long const *arg, int deststnr)
{
int tag;
long num = *arg;
u_char sign;
FPU_REG *dest = &st(deststnr);
if (num == 0) {
FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
return;
}
if (num > 0) {
sign = SIGN_POS;
} else {
num = -num;
sign = SIGN_NEG;
}
dest->sigh = num;
dest->sigl = 0;
setexponent16(dest, 31);
tag = FPU_normalize(dest);
FPU_settagi(deststnr, tag);
setsign(dest, sign);
return;
}
static void single_arg_error(FPU_REG *st0_ptr, u_char st0_tag)
{
if (st0_tag == TAG_Empty)
FPU_stack_underflow(); /* Puts a QNaN in st(0) */
else if (st0_tag == TW_NaN)
real_1op_NaN(st0_ptr); /* return with a NaN in st(0) */
#ifdef PARANOID
else
EXCEPTION(EX_INTERNAL | 0x0112);
#endif /* PARANOID */
}
static void single_arg_2_error(FPU_REG *st0_ptr, u_char st0_tag)
{
int isNaN;
switch (st0_tag) {
case TW_NaN:
isNaN = (exponent(st0_ptr) == EXP_OVER)
&& (st0_ptr->sigh & 0x80000000);
if (isNaN && !(st0_ptr->sigh & 0x40000000)) { /* Signaling ? */
EXCEPTION(EX_Invalid);
if (control_word & CW_Invalid) {
/* The masked response */
/* Convert to a QNaN */
st0_ptr->sigh |= 0x40000000;
push();
FPU_copy_to_reg0(st0_ptr, TAG_Special);
}
} else if (isNaN) {
/* A QNaN */
push();
FPU_copy_to_reg0(st0_ptr, TAG_Special);
} else {
/* pseudoNaN or other unsupported */
EXCEPTION(EX_Invalid);
if (control_word & CW_Invalid) {
/* The masked response */
FPU_copy_to_reg0(&CONST_QNaN, TAG_Special);
push();
FPU_copy_to_reg0(&CONST_QNaN, TAG_Special);
}
}
break; /* return with a NaN in st(0) */
#ifdef PARANOID
default:
EXCEPTION(EX_INTERNAL | 0x0112);
#endif /* PARANOID */
}
}
/*---------------------------------------------------------------------------*/
static void f2xm1(FPU_REG *st0_ptr, u_char tag)
{
FPU_REG a;
clear_C1();
if (tag == TAG_Valid) {
/* For an 80486 FPU, the result is undefined if the arg is >= 1.0 */
if (exponent(st0_ptr) < 0) {
denormal_arg:
FPU_to_exp16(st0_ptr, &a);
/* poly_2xm1(x) requires 0 < st(0) < 1. */
poly_2xm1(getsign(st0_ptr), &a, st0_ptr);
}
set_precision_flag_up(); /* 80486 appears to always do this */
return;
}
if (tag == TAG_Zero)
return;
if (tag == TAG_Special)
tag = FPU_Special(st0_ptr);
switch (tag) {
case TW_Denormal:
if (denormal_operand() < 0)
return;
goto denormal_arg;
case TW_Infinity:
if (signnegative(st0_ptr)) {
/* -infinity gives -1 (p16-10) */
FPU_copy_to_reg0(&CONST_1, TAG_Valid);
setnegative(st0_ptr);
}
return;
default:
single_arg_error(st0_ptr, tag);
}
}
static void fptan(FPU_REG *st0_ptr, u_char st0_tag)
{
FPU_REG *st_new_ptr;
int q;
u_char arg_sign = getsign(st0_ptr);
/* Stack underflow has higher priority */
if (st0_tag == TAG_Empty) {
FPU_stack_underflow(); /* Puts a QNaN in st(0) */
if (control_word & CW_Invalid) {
st_new_ptr = &st(-1);
push();
FPU_stack_underflow(); /* Puts a QNaN in the new st(0) */
}
return;
}
if (STACK_OVERFLOW) {
FPU_stack_overflow();
return;
}
if (st0_tag == TAG_Valid) {
if (exponent(st0_ptr) > -40) {
if ((q = trig_arg(st0_ptr, 0)) == -1) {
/* Operand is out of range */
return;
}
poly_tan(st0_ptr);
setsign(st0_ptr, (q & 1) ^ (arg_sign != 0));
set_precision_flag_up(); /* We do not really know if up or down */
} else {
/* For a small arg, the result == the argument */
/* Underflow may happen */
denormal_arg:
FPU_to_exp16(st0_ptr, st0_ptr);
st0_tag =
FPU_round(st0_ptr, 1, 0, FULL_PRECISION, arg_sign);
FPU_settag0(st0_tag);
}
push();
FPU_copy_to_reg0(&CONST_1, TAG_Valid);
return;
}
if (st0_tag == TAG_Zero) {
push();
FPU_copy_to_reg0(&CONST_1, TAG_Valid);
setcc(0);
return;
}
if (st0_tag == TAG_Special)
st0_tag = FPU_Special(st0_ptr);
if (st0_tag == TW_Denormal) {
if (denormal_operand() < 0)
return;
goto denormal_arg;
}
if (st0_tag == TW_Infinity) {
/* The 80486 treats infinity as an invalid operand */
if (arith_invalid(0) >= 0) {
st_new_ptr = &st(-1);
push();
arith_invalid(0);
}
return;
}
single_arg_2_error(st0_ptr, st0_tag);
}
static void fxtract(FPU_REG *st0_ptr, u_char st0_tag)
{
FPU_REG *st_new_ptr;
u_char sign;
register FPU_REG *st1_ptr = st0_ptr; /* anticipate */
if (STACK_OVERFLOW) {
FPU_stack_overflow();
return;
}
clear_C1();
if (st0_tag == TAG_Valid) {
long e;
push();
sign = getsign(st1_ptr);
reg_copy(st1_ptr, st_new_ptr);
setexponent16(st_new_ptr, exponent(st_new_ptr));
denormal_arg:
e = exponent16(st_new_ptr);
convert_l2reg(&e, 1);
setexponentpos(st_new_ptr, 0);
setsign(st_new_ptr, sign);
FPU_settag0(TAG_Valid); /* Needed if arg was a denormal */
return;
} else if (st0_tag == TAG_Zero) {
sign = getsign(st0_ptr);
if (FPU_divide_by_zero(0, SIGN_NEG) < 0)
return;
push();
FPU_copy_to_reg0(&CONST_Z, TAG_Zero);
setsign(st_new_ptr, sign);
return;
}
if (st0_tag == TAG_Special)
st0_tag = FPU_Special(st0_ptr);
if (st0_tag == TW_Denormal) {
if (denormal_operand() < 0)
return;
push();
sign = getsign(st1_ptr);
FPU_to_exp16(st1_ptr, st_new_ptr);
goto denormal_arg;
} else if (st0_tag == TW_Infinity) {
sign = getsign(st0_ptr);
setpositive(st0_ptr);
push();
FPU_copy_to_reg0(&CONST_INF, TAG_Special);
setsign(st_new_ptr, sign);
return;
} else if (st0_tag == TW_NaN) {
if (real_1op_NaN(st0_ptr) < 0)
return;
push();
FPU_copy_to_reg0(st0_ptr, TAG_Special);
return;
} else if (st0_tag == TAG_Empty) {
/* Is this the correct behaviour? */
if (control_word & EX_Invalid) {
FPU_stack_underflow();
push();
FPU_stack_underflow();
} else
EXCEPTION(EX_StackUnder);
}
#ifdef PARANOID
else
EXCEPTION(EX_INTERNAL | 0x119);
#endif /* PARANOID */
}
static void fdecstp(void)
{
clear_C1();
top--;
}
static void fincstp(void)
{
clear_C1();
top++;
}
static void fsqrt_(FPU_REG *st0_ptr, u_char st0_tag)
{
int expon;
clear_C1();
if (st0_tag == TAG_Valid) {
u_char tag;
if (signnegative(st0_ptr)) {
arith_invalid(0); /* sqrt(negative) is invalid */
return;
}
/* make st(0) in [1.0 .. 4.0) */
expon = exponent(st0_ptr);
denormal_arg:
setexponent16(st0_ptr, (expon & 1));
/* Do the computation, the sign of the result will be positive. */
tag = wm_sqrt(st0_ptr, 0, 0, control_word, SIGN_POS);
addexponent(st0_ptr, expon >> 1);
FPU_settag0(tag);
return;
}
if (st0_tag == TAG_Zero)
return;
if (st0_tag == TAG_Special)
st0_tag = FPU_Special(st0_ptr);
if (st0_tag == TW_Infinity) {
if (signnegative(st0_ptr))
arith_invalid(0); /* sqrt(-Infinity) is invalid */
return;
} else if (st0_tag == TW_Denormal) {
if (signnegative(st0_ptr)) {
arith_invalid(0); /* sqrt(negative) is invalid */
return;
}
if (denormal_operand() < 0)
return;
FPU_to_exp16(st0_ptr, st0_ptr);
expon = exponent16(st0_ptr);
goto denormal_arg;
}
single_arg_error(st0_ptr, st0_tag);
}
static void frndint_(FPU_REG *st0_ptr, u_char st0_tag)
{
int flags, tag;
if (st0_tag == TAG_Valid) {
u_char sign;
denormal_arg:
sign = getsign(st0_ptr);
if (exponent(st0_ptr) > 63)
return;
if (st0_tag == TW_Denormal) {
if (denormal_operand() < 0)
return;
}
/* Fortunately, this can't overflow to 2^64 */
if ((flags = FPU_round_to_int(st0_ptr, st0_tag)))
set_precision_flag(flags);
setexponent16(st0_ptr, 63);
tag = FPU_normalize(st0_ptr);
setsign(st0_ptr, sign);
FPU_settag0(tag);
return;
}
if (st0_tag == TAG_Zero)
return;
if (st0_tag == TAG_Special)
st0_tag = FPU_Special(st0_ptr);
if (st0_tag == TW_Denormal)
goto denormal_arg;
else if (st0_tag == TW_Infinity)
return;
else
single_arg_error(st0_ptr, st0_tag);
}
static int fsin(FPU_REG *st0_ptr, u_char tag)
{
u_char arg_sign = getsign(st0_ptr);
if (tag == TAG_Valid) {
int q;
if (exponent(st0_ptr) > -40) {
if ((q = trig_arg(st0_ptr, 0)) == -1) {
/* Operand is out of range */
return 1;
}
poly_sine(st0_ptr);
if (q & 2)
changesign(st0_ptr);
setsign(st0_ptr, getsign(st0_ptr) ^ arg_sign);
/* We do not really know if up or down */
set_precision_flag_up();
return 0;
} else {
/* For a small arg, the result == the argument */
set_precision_flag_up(); /* Must be up. */
return 0;
}
}
if (tag == TAG_Zero) {
setcc(0);
return 0;
}
if (tag == TAG_Special)
tag = FPU_Special(st0_ptr);
if (tag == TW_Denormal) {
if (denormal_operand() < 0)
return 1;
/* For a small arg, the result == the argument */
/* Underflow may happen */
FPU_to_exp16(st0_ptr, st0_ptr);
tag = FPU_round(st0_ptr, 1, 0, FULL_PRECISION, arg_sign);
FPU_settag0(tag);
return 0;
} else if (tag == TW_Infinity) {
/* The 80486 treats infinity as an invalid operand */
arith_invalid(0);
return 1;
} else {
single_arg_error(st0_ptr, tag);
return 1;
}
}
static int f_cos(FPU_REG *st0_ptr, u_char tag)
{
u_char st0_sign;
st0_sign = getsign(st0_ptr);
if (tag == TAG_Valid) {
int q;
if (exponent(st0_ptr) > -40) {
if ((exponent(st0_ptr) < 0)
|| ((exponent(st0_ptr) == 0)
&& (significand(st0_ptr) <=
0xc90fdaa22168c234LL))) {
poly_cos(st0_ptr);
/* We do not really know if up or down */
set_precision_flag_down();
return 0;
} else if ((q = trig_arg(st0_ptr, FCOS)) != -1) {
poly_sine(st0_ptr);
if ((q + 1) & 2)
changesign(st0_ptr);
/* We do not really know if up or down */
set_precision_flag_down();
return 0;
} else {
/* Operand is out of range */
return 1;
}
} else {
denormal_arg:
setcc(0);
FPU_copy_to_reg0(&CONST_1, TAG_Valid);
#ifdef PECULIAR_486
set_precision_flag_down(); /* 80486 appears to do this. */
#else
set_precision_flag_up(); /* Must be up. */
#endif /* PECULIAR_486 */
return 0;
}
} else if (tag == TAG_Zero) {
FPU_copy_to_reg0(&CONST_1, TAG_Valid);
setcc(0);
return 0;
}
if (tag == TAG_Special)
tag = FPU_Special(st0_ptr);
if (tag == TW_Denormal) {
if (denormal_operand() < 0)
return 1;
goto denormal_arg;
} else if (tag == TW_Infinity) {
/* The 80486 treats infinity as an invalid operand */
arith_invalid(0);
return 1;
} else {
single_arg_error(st0_ptr, tag); /* requires st0_ptr == &st(0) */
return 1;
}
}
static void fcos(FPU_REG *st0_ptr, u_char st0_tag)
{
f_cos(st0_ptr, st0_tag);
}
static void fsincos(FPU_REG *st0_ptr, u_char st0_tag)
{
FPU_REG *st_new_ptr;
FPU_REG arg;
u_char tag;
/* Stack underflow has higher priority */
if (st0_tag == TAG_Empty) {
FPU_stack_underflow(); /* Puts a QNaN in st(0) */
if (control_word & CW_Invalid) {
st_new_ptr = &st(-1);
push();
FPU_stack_underflow(); /* Puts a QNaN in the new st(0) */
}
return;
}
if (STACK_OVERFLOW) {
FPU_stack_overflow();
return;
}
if (st0_tag == TAG_Special)
tag = FPU_Special(st0_ptr);
else
tag = st0_tag;
if (tag == TW_NaN) {
single_arg_2_error(st0_ptr, TW_NaN);
return;
} else if (tag == TW_Infinity) {
/* The 80486 treats infinity as an invalid operand */
if (arith_invalid(0) >= 0) {
/* Masked response */
push();
arith_invalid(0);
}
return;
}
reg_copy(st0_ptr, &arg);
if (!fsin(st0_ptr, st0_tag)) {
push();
FPU_copy_to_reg0(&arg, st0_tag);
f_cos(&st(0), st0_tag);
} else {
/* An error, so restore st(0) */
FPU_copy_to_reg0(&arg, st0_tag);
}
}
/*---------------------------------------------------------------------------*/
/* The following all require two arguments: st(0) and st(1) */
/* A lean, mean kernel for the fprem instructions. This relies upon
the division and rounding to an integer in do_fprem giving an
exact result. Because of this, rem_kernel() needs to deal only with
the least significant 64 bits, the more significant bits of the
result must be zero.
*/
static void rem_kernel(unsigned long long st0, unsigned long long *y,
unsigned long long st1, unsigned long long q, int n)
{
int dummy;
unsigned long long x;
x = st0 << n;
/* Do the required multiplication and subtraction in the one operation */
/* lsw x -= lsw st1 * lsw q */
asm volatile ("mull %4; subl %%eax,%0; sbbl %%edx,%1":"=m"
(((unsigned *)&x)[0]), "=m"(((unsigned *)&x)[1]),
"=a"(dummy)
:"2"(((unsigned *)&st1)[0]), "m"(((unsigned *)&q)[0])
:"%dx");
/* msw x -= msw st1 * lsw q */
asm volatile ("mull %3; subl %%eax,%0":"=m" (((unsigned *)&x)[1]),
"=a"(dummy)
:"1"(((unsigned *)&st1)[1]), "m"(((unsigned *)&q)[0])
:"%dx");
/* msw x -= lsw st1 * msw q */
asm volatile ("mull %3; subl %%eax,%0":"=m" (((unsigned *)&x)[1]),
"=a"(dummy)
:"1"(((unsigned *)&st1)[0]), "m"(((unsigned *)&q)[1])
:"%dx");
*y = x;
}
/* Remainder of st(0) / st(1) */
/* This routine produces exact results, i.e. there is never any
rounding or truncation, etc of the result. */
static void do_fprem(FPU_REG *st0_ptr, u_char st0_tag, int round)
{
FPU_REG *st1_ptr = &st(1);
u_char st1_tag = FPU_gettagi(1);
if (!((st0_tag ^ TAG_Valid) | (st1_tag ^ TAG_Valid))) {
FPU_REG tmp, st0, st1;
u_char st0_sign, st1_sign;
u_char tmptag;
int tag;
int old_cw;
int expdif;
long long q;
unsigned short saved_status;
int cc;
fprem_valid:
/* Convert registers for internal use. */
st0_sign = FPU_to_exp16(st0_ptr, &st0);
st1_sign = FPU_to_exp16(st1_ptr, &st1);
expdif = exponent16(&st0) - exponent16(&st1);
old_cw = control_word;
cc = 0;
/* We want the status following the denorm tests, but don't want
the status changed by the arithmetic operations. */
saved_status = partial_status;
control_word &= ~CW_RC;
control_word |= RC_CHOP;
if (expdif < 64) {
/* This should be the most common case */
if (expdif > -2) {
u_char sign = st0_sign ^ st1_sign;
tag = FPU_u_div(&st0, &st1, &tmp,
PR_64_BITS | RC_CHOP | 0x3f,
sign);
setsign(&tmp, sign);
if (exponent(&tmp) >= 0) {
FPU_round_to_int(&tmp, tag); /* Fortunately, this can't
overflow to 2^64 */
q = significand(&tmp);
rem_kernel(significand(&st0),
&significand(&tmp),
significand(&st1),
q, expdif);
setexponent16(&tmp, exponent16(&st1));
} else {
reg_copy(&st0, &tmp);
q = 0;
}
if ((round == RC_RND)
&& (tmp.sigh & 0xc0000000)) {
/* We may need to subtract st(1) once more,
to get a result <= 1/2 of st(1). */
unsigned long long x;
expdif =
exponent16(&st1) - exponent16(&tmp);
if (expdif <= 1) {
if (expdif == 0)
x = significand(&st1) -
significand(&tmp);
else /* expdif is 1 */
x = (significand(&st1)
<< 1) -
significand(&tmp);
if ((x < significand(&tmp)) ||
/* or equi-distant (from 0 & st(1)) and q is odd */
((x == significand(&tmp))
&& (q & 1))) {
st0_sign = !st0_sign;
significand(&tmp) = x;
q++;
}
}
}
if (q & 4)
cc |= SW_C0;
if (q & 2)
cc |= SW_C3;
if (q & 1)
cc |= SW_C1;
} else {
control_word = old_cw;
setcc(0);
return;
}
} else {
/* There is a large exponent difference ( >= 64 ) */
/* To make much sense, the code in this section should
be done at high precision. */
int exp_1, N;
u_char sign;
/* prevent overflow here */
/* N is 'a number between 32 and 63' (p26-113) */
reg_copy(&st0, &tmp);
tmptag = st0_tag;
N = (expdif & 0x0000001f) + 32; /* This choice gives results
identical to an AMD 486 */
setexponent16(&tmp, N);
exp_1 = exponent16(&st1);
setexponent16(&st1, 0);
expdif -= N;
sign = getsign(&tmp) ^ st1_sign;
tag =
FPU_u_div(&tmp, &st1, &tmp,
PR_64_BITS | RC_CHOP | 0x3f, sign);
setsign(&tmp, sign);
FPU_round_to_int(&tmp, tag); /* Fortunately, this can't
overflow to 2^64 */
rem_kernel(significand(&st0),
&significand(&tmp),
significand(&st1),
significand(&tmp), exponent(&tmp)
);
setexponent16(&tmp, exp_1 + expdif);
/* It is possible for the operation to be complete here.
What does the IEEE standard say? The Intel 80486 manual
implies that the operation will never be completed at this
point, and the behaviour of a real 80486 confirms this.
*/
if (!(tmp.sigh | tmp.sigl)) {
/* The result is zero */
control_word = old_cw;
partial_status = saved_status;
FPU_copy_to_reg0(&CONST_Z, TAG_Zero);
setsign(&st0, st0_sign);
#ifdef PECULIAR_486
setcc(SW_C2);
#else
setcc(0);
#endif /* PECULIAR_486 */
return;
}
cc = SW_C2;
}
control_word = old_cw;
partial_status = saved_status;
tag = FPU_normalize_nuo(&tmp);
reg_copy(&tmp, st0_ptr);
/* The only condition to be looked for is underflow,
and it can occur here only if underflow is unmasked. */
if ((exponent16(&tmp) <= EXP_UNDER) && (tag != TAG_Zero)
&& !(control_word & CW_Underflow)) {
setcc(cc);
tag = arith_underflow(st0_ptr);
setsign(st0_ptr, st0_sign);
FPU_settag0(tag);
return;
} else if ((exponent16(&tmp) > EXP_UNDER) || (tag == TAG_Zero)) {
stdexp(st0_ptr);
setsign(st0_ptr, st0_sign);
} else {
tag =
FPU_round(st0_ptr, 0, 0, FULL_PRECISION, st0_sign);
}
FPU_settag0(tag);
setcc(cc);
return;
}
if (st0_tag == TAG_Special)
st0_tag = FPU_Special(st0_ptr);
if (st1_tag == TAG_Special)
st1_tag = FPU_Special(st1_ptr);
if (((st0_tag == TAG_Valid) && (st1_tag == TW_Denormal))
|| ((st0_tag == TW_Denormal) && (st1_tag == TAG_Valid))
|| ((st0_tag == TW_Denormal) && (st1_tag == TW_Denormal))) {
if (denormal_operand() < 0)
return;
goto fprem_valid;
} else if ((st0_tag == TAG_Empty) || (st1_tag == TAG_Empty)) {
FPU_stack_underflow();
return;
} else if (st0_tag == TAG_Zero) {
if (st1_tag == TAG_Valid) {
setcc(0);
return;
} else if (st1_tag == TW_Denormal) {
if (denormal_operand() < 0)
return;
setcc(0);
return;
} else if (st1_tag == TAG_Zero) {
arith_invalid(0);
return;
} /* fprem(?,0) always invalid */
else if (st1_tag == TW_Infinity) {
setcc(0);
return;
}
} else if ((st0_tag == TAG_Valid) || (st0_tag == TW_Denormal)) {
if (st1_tag == TAG_Zero) {
arith_invalid(0); /* fprem(Valid,Zero) is invalid */
return;
} else if (st1_tag != TW_NaN) {
if (((st0_tag == TW_Denormal)
|| (st1_tag == TW_Denormal))
&& (denormal_operand() < 0))
return;
if (st1_tag == TW_Infinity) {
/* fprem(Valid,Infinity) is o.k. */
setcc(0);
return;
}
}