/* libgcc1 routines for 68000 w/o floating-point hardware. */
/* Copyright (C) 1994 Free Software Foundation, Inc.
This file 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 2, or (at your option) any
later version.
In addition to the permissions in the GNU General Public License, the
Free Software Foundation gives you unlimited permission to link the
compiled version of this file with other programs, and to distribute
those programs without any restriction coming from the use of this
file. (The General Public License restrictions do apply in other
respects; for example, they cover modification of the file, and
distribution when not linked into another program.)
This file is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; see the file COPYING. If not, write to
the Free Software Foundation, 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
/* As a special exception, if you link this library with files
compiled with GCC to produce an executable, this does not cause
the resulting executable to be covered by the GNU General Public License.
This exception does not however invalidate any other reasons why
the executable file might be covered by the GNU General Public License. */
/* Use this one for any 680x0; assumes no floating point hardware.
The trailing " '" appearing on some lines is for ANSI preprocessors. Yuk.
Some of this code comes from MINIX, via the folks at ericsson.
D. V. Henkel-Wallace (gumby@cygnus.com) Fete Bastille, 1992
*/
/* These are predefined by new versions of GNU cpp. */
#ifndef __USER_LABEL_PREFIX__
#define __USER_LABEL_PREFIX__ _
#endif
#ifndef __REGISTER_PREFIX__
#define __REGISTER_PREFIX__
#endif
#ifndef __IMMEDIATE_PREFIX__
#define __IMMEDIATE_PREFIX__ #
#endif
/* ANSI concatenation macros. */
#define CONCAT1(a, b) CONCAT2(a, b)
#define CONCAT2(a, b) a ## b
/* Use the right prefix for global labels. */
#define SYM(x) CONCAT1 (__USER_LABEL_PREFIX__, x)
/* Use the right prefix for registers. */
#define REG(x) CONCAT1 (__REGISTER_PREFIX__, x)
/* Use the right prefix for immediate values. */
#define IMM(x) CONCAT1 (__IMMEDIATE_PREFIX__, x)
#define d0 REG (d0)
#define d1 REG (d1)
#define d2 REG (d2)
#define d3 REG (d3)
#define d4 REG (d4)
#define d5 REG (d5)
#define d6 REG (d6)
#define d7 REG (d7)
#define a0 REG (a0)
#define a1 REG (a1)
#define a2 REG (a2)
#define a3 REG (a3)
#define a4 REG (a4)
#define a5 REG (a5)
#define a6 REG (a6)
#define fp REG (fp)
#define sp REG (sp)
#ifdef L_floatex
| This is an attempt at a decent floating point (single, double and
| extended double) code for the GNU C compiler. It should be easy to
| adapt to other compilers (but beware of the local labels!).
| Starting date: 21 October, 1990
| It is convenient to introduce the notation (s,e,f) for a floating point
| number, where s=sign, e=exponent, f=fraction. We will call a floating
| point number fpn to abbreviate, independently of the precision.
| Let MAX_EXP be in each case the maximum exponent (255 for floats, 1023
| for doubles and 16383 for long doubles). We then have the following
| different cases:
| 1. Normalized fpns have 0 < e < MAX_EXP. They correspond to
| (-1)^s x 1.f x 2^(e-bias-1).
| 2. Denormalized fpns have e=0. They correspond to numbers of the form
| (-1)^s x 0.f x 2^(-bias).
| 3. +/-INFINITY have e=MAX_EXP, f=0.
| 4. Quiet NaN (Not a Number) have all bits set.
| 5. Signaling NaN (Not a Number) have s=0, e=MAX_EXP, f=1.
|=============================================================================
| exceptions
|=============================================================================
| This is the floating point condition code register (_fpCCR):
|
| struct {
| short _exception_bits;
| short _trap_enable_bits;
| short _sticky_bits;
| short _rounding_mode;
| short _format;
| short _last_operation;
| union {
| float sf;
| double df;
| } _operand1;
| union {
| float sf;
| double df;
| } _operand2;
| } _fpCCR;
.data
.even
.globl SYM (_fpCCR)
SYM (_fpCCR):
__exception_bits:
.word 0
__trap_enable_bits:
.word 0
__sticky_bits:
.word 0
__rounding_mode:
.word ROUND_TO_NEAREST
__format:
.word NIL
__last_operation:
.word NOOP
__operand1:
.long 0
.long 0
__operand2:
.long 0
.long 0
| Offsets:
EBITS = __exception_bits - SYM (_fpCCR)
TRAPE = __trap_enable_bits - SYM (_fpCCR)
STICK = __sticky_bits - SYM (_fpCCR)
ROUND = __rounding_mode - SYM (_fpCCR)
FORMT = __format - SYM (_fpCCR)
LASTO = __last_operation - SYM (_fpCCR)
OPER1 = __operand1 - SYM (_fpCCR)
OPER2 = __operand2 - SYM (_fpCCR)
| The following exception types are supported:
INEXACT_RESULT = 0x0001
UNDERFLOW = 0x0002
OVERFLOW = 0x0004
DIVIDE_BY_ZERO = 0x0008
INVALID_OPERATION = 0x0010
| The allowed rounding modes are:
UNKNOWN = -1
ROUND_TO_NEAREST = 0 | round result to nearest representable value
ROUND_TO_ZERO = 1 | round result towards zero
ROUND_TO_PLUS = 2 | round result towards plus infinity
ROUND_TO_MINUS = 3 | round result towards minus infinity
| The allowed values of format are:
NIL = 0
SINGLE_FLOAT = 1
DOUBLE_FLOAT = 2
LONG_FLOAT = 3
| The allowed values for the last operation are:
NOOP = 0
ADD = 1
MULTIPLY = 2
DIVIDE = 3
NEGATE = 4
COMPARE = 5
EXTENDSFDF = 6
TRUNCDFSF = 7
|=============================================================================
| __clear_sticky_bits
|=============================================================================
| The sticky bits are normally not cleared (thus the name), whereas the
| exception type and exception value reflect the last computation.
| This routine is provided to clear them (you can also write to _fpCCR,
| since it is globally visible).
.globl SYM (__clear_sticky_bit)
.text
.even
| void __clear_sticky_bits(void);
SYM (__clear_sticky_bit):
lea SYM (_fpCCR),a0
movew IMM (0),a0@(STICK)
rts
|=============================================================================
| $_exception_handler
|=============================================================================
.globl $_exception_handler
.text
.even
| This is the common exit point if an exception occurs.
| NOTE: it is NOT callable from C!
| It expects the exception type in d7, the format (SINGLE_FLOAT,
| DOUBLE_FLOAT or LONG_FLOAT) in d6, and the last operation code in d5.
| It sets the corresponding exception and sticky bits, and the format.
| Depending on the format if fills the corresponding slots for the
| operands which produced the exception (all this information is provided
| so if you write your own exception handlers you have enough information
| to deal with the problem).
| Then checks to see if the corresponding exception is trap-enabled,
| in which case it pushes the address of _fpCCR and traps through
| trap FPTRAP (15 for the moment).
FPTRAP = 15
$_exception_handler:
lea SYM (_fpCCR),a0
movew d7,a0@(EBITS) | set __exception_bits
orw d7,a0@(STICK) | and __sticky_bits
movew d6,a0@(FORMT) | and __format
movew d5,a0@(LASTO) | and __last_operation
| Now put the operands in place:
cmpw IMM (SINGLE_FLOAT),d6
beq 1f
movel a6@(8),a0@(OPER1)
movel a6@(12),a0@(OPER1+4)
movel a6@(16),a0@(OPER2)
movel a6@(20),a0@(OPER2+4)
bra 2f
1: movel a6@(8),a0@(OPER1)
movel a6@(12),a0@(OPER2)
2:
| And check whether the exception is trap-enabled:
andw a0@(TRAPE),d7 | is exception trap-enabled?
beq 1f | no, exit
pea SYM (_fpCCR) | yes, push address of _fpCCR
trap IMM (FPTRAP) | and trap
1: moveml sp@+,d2-d7 | restore data registers
unlk a6 | and return
rts
#endif /* L_floatex */
#ifdef L_mulsi3
.text
.proc
.globl SYM (__mulsi3)
SYM (__mulsi3):
movew sp@(4), d0 /* x0 -> d0 */
muluw sp@(10), d0 /* x0*y1 */
movew sp@(6), d1 /* x1 -> d1 */
muluw sp@(8), d1 /* x1*y0 */
addw d1, d0
swap d0
clrw d0
movew sp@(6), d1 /* x1 -> d1 */
muluw sp@(10), d1 /* x1*y1 */
addl d1, d0
rts
#endif /* L_mulsi3 */
#ifdef L_udivsi3
.text
.proc
.globl SYM (__udivsi3)
SYM (__udivsi3):
movel d2, sp@-
movel sp@(12), d1 /* d1 = divisor */
movel sp@(8), d0 /* d0 = dividend */
cmpl IMM (0x10000), d1 /* divisor >= 2 ^ 16 ? */
jcc L3 /* then try next algorithm */
movel d0, d2
clrw d2
swap d2
divu d1, d2 /* high quotient in lower word */
movew d2, d0 /* save high quotient */
swap d0
movew sp@(10), d2 /* get low dividend + high rest */
divu d1, d2 /* low quotient */
movew d2, d0
jra L6
L3: movel d1, d2 /* use d2 as divisor backup */
L4: lsrl IMM (1), d1 /* shift divisor */
lsrl IMM (1), d0 /* shift dividend */
cmpl IMM (0x10000), d1 /* still divisor >= 2 ^ 16 ? */
jcc L4
divu d1, d0 /* now we have 16 bit divisor */
andl IMM (0xffff), d0 /* mask out divisor, ignore remainder */
/* Multiply the 16 bit tentative quotient with the 32 bit divisor. Because of
the operand ranges, this might give a 33 bit product. If this product is
greater than the dividend, the tentative quotient was too large. */
movel d2, d1
mulu d0, d1 /* low part, 32 bits */
swap d2
mulu d0, d2 /* high part, at most 17 bits */
swap d2 /* align high part with low part */
btst IMM (0), d2 /* high part 17 bits? */
jne L5 /* if 17 bits, quotient was too large */
addl d2, d1 /* add parts */
jcs L5 /* if sum is 33 bits, quotient was too large */
cmpl sp@(8), d1 /* compare the sum with the dividend */
jls L6 /* if sum > dividend, quotient was too large */
L5: subql IMM (1), d0 /* adjust quotient */
L6: movel sp@+, d2
rts
#endif /* L_udivsi3 */
#ifdef L_divsi3
.text
.proc
.globl SYM (__divsi3)
SYM (__divsi3):
movel d2, sp@-
moveb IMM (1), d2 /* sign of result stored in d2 (=1 or =-1) */
movel sp@(12), d1 /* d1 = divisor */
jpl L1
negl d1
negb d2 /* change sign because divisor <0 */
L1: movel sp@(8), d0 /* d0 = dividend */
jpl L2
negl d0
negb d2
L2: movel d1, sp@-
movel d0, sp@-
jbsr SYM (__udivsi3) /* divide abs(dividend) by abs(divisor) */
addql IMM (8), sp
tstb d2
jpl L3
negl d0
L3: movel sp@+, d2
rts
#endif /* L_divsi3 */
#ifdef L_umodsi3
.text
.proc
.globl SYM (__umodsi3)
SYM (__umodsi3):
movel sp@(8), d1 /* d1 = divisor */
movel sp@(4), d0 /* d0 = dividend */
movel d1, sp@-
movel d0, sp@-
jbsr SYM (__udivsi3)
addql IMM (8), sp
movel sp@(8), d1 /* d1 = divisor */
movel d1, sp@-
movel d0, sp@-
jbsr SYM (__mulsi3) /* d0 = (a/b)*b */
addql IMM (8), sp
movel sp@(4), d1 /* d1 = dividend */
subl d0, d1 /* d1 = a - (a/b)*b */
movel d1, d0
rts
#endif /* L_umodsi3 */
#ifdef L_modsi3
.text
.proc
.globl SYM (__modsi3)
SYM (__modsi3):
movel sp@(8), d1 /* d1 = divisor */
movel sp@(4), d0 /* d0 = dividend */
movel d1, sp@-
movel d0, sp@-
jbsr SYM (__divsi3)
addql IMM (8), sp
movel sp@(8), d1 /* d1 = divisor */
movel d1, sp@-
movel d0, sp@-
jbsr SYM (__mulsi3) /* d0 = (a/b)*b */
addql IMM (8), sp
movel sp@(4), d1 /* d1 = dividend */
subl d0, d1 /* d1 = a - (a/b)*b */
movel d1, d0
rts
#endif /* L_modsi3 */
#ifdef L_double
.globl SYM (_fpCCR)
.globl $_exception_handler
QUIET_NaN = 0xffffffff
D_MAX_EXP = 0x07ff
D_BIAS = 1022
DBL_MAX_EXP = D_MAX_EXP - D_BIAS
DBL_MIN_EXP = 1 - D_BIAS
DBL_MANT_DIG = 53
INEXACT_RESULT = 0x0001
UNDERFLOW = 0x0002
OVERFLOW = 0x0004
DIVIDE_BY_ZERO = 0x0008
INVALID_OPERATION = 0x0010
DOUBLE_FLOAT = 2
NOOP = 0
ADD = 1
MULTIPLY = 2
DIVIDE = 3
NEGATE = 4
COMPARE = 5
EXTENDSFDF = 6
TRUNCDFSF = 7
UNKNOWN = -1
ROUND_TO_NEAREST = 0 | round result to nearest representable value
ROUND_TO_ZERO = 1 | round result towards zero
ROUND_TO_PLUS = 2 | round result towards plus infinity
ROUND_TO_MINUS = 3 | round result towards minus infinity
| Entry points:
.globl SYM (__adddf3)
.globl SYM (__subdf3)
.globl SYM (__muldf3)
.globl SYM (__divdf3)
.globl SYM (__negdf2)
.globl SYM (__cmpdf2)
.text
.even
| These are common routines to return and signal exceptions.
Ld$den:
| Return and signal a denormalized number
orl d7,d0
movew IMM (UNDERFLOW),d7
orw IMM (INEXACT_RESULT),d7
movew IMM (DOUBLE_FLOAT),d6
jmp $_exception_handler
Ld$infty:
Ld$overflow:
| Return a properly signed INFINITY and set the exception flags
movel IMM (0x7ff00000),d0
movel IMM (0),d1
orl d7,d0
movew IMM (OVERFLOW),d7
orw IMM (INEXACT_RESULT),d7
movew IMM (DOUBLE_FLOAT),d6
jmp $_exception_handler
Ld$underflow:
| Return 0 and set the exception flags
movel IMM (0),d0
movel d0,d1
movew IMM (UNDERFLOW),d7
orw IMM (INEXACT_RESULT),d7
movew IMM (DOUBLE_FLOAT),d6
jmp $_exception_handler
Ld$inop:
| Return a quiet NaN and set the exception flags
movel IMM (QUIET_NaN),d0
movel d0,d1
movew IMM (INVALID_OPERATION),d7
orw IMM (INEXACT_RESULT),d7
movew IMM (DOUBLE_FLOAT),d6
jmp $_exception_handler
Ld$div$0:
| Return a properly signed INFINITY and set the exception flags
movel IMM (0x7ff00000),d0
movel IMM (0),d1
orl d7,d0
movew IMM (DIVIDE_BY_ZERO),d7
orw IMM (INEXACT_RESULT),d7
movew IMM (DOUBLE_FLOAT),d6
jmp $_exception_handler
|=============================================================================
|=============================================================================
| double precision routines
|=============================================================================
|=============================================================================
| A double precision floating point number (double) has the format:
|
| struct _double {
| unsigned int sign : 1; /* sign bit */
| unsigned int exponent : 11; /* exponent, shifted by 126 */
| unsigned int fraction : 52; /* fraction */
| } double;
|
| Thus sizeof(double) = 8 (64 bits).
|
| All the routines are callable from C programs, and return the result
| in the register pair d0-d1. They also preserve all registers except
| d0-d1 and a0-a1.
|=============================================================================
| __subdf3
|=============================================================================
| double __subdf3(double, double);
SYM (__subdf3):
bchg IMM (31),sp@(12) | change sign of second operand
| and fall through, so we always add
|=============================================================================
| __adddf3
|=============================================================================
| double __adddf3(double, double);
SYM (__adddf3):
link a6,IMM (0) | everything will be done in registers
moveml d2-d7,sp@- | save all data registers and a2 (but d0-d1)
movel a6@(8),d0 | get first operand
movel a6@(12),d1 |
movel a6@(16),d2 | get second operand
movel a6@(20),d3 |
movel d0,d7 | get d0's sign bit in d7 '
addl d1,d1 | check and clear sign bit of a, and gain one
addxl d0,d0 | bit of extra precision
beq Ladddf$b | if zero return second operand
movel d2,d6 | save sign in d6
addl d3,d3 | get rid of sign bit and gain one bit of
addxl d2,d2 | extra precision
beq Ladddf$a | if zero return first operand
andl IMM (0x80000000),d7 | isolate a's sign bit '
swap d6 | and also b's sign bit '
andw IMM (0x8000),d6 |
orw d6,d7 | and combine them into d7, so that a's sign '
| bit is in the high word and b's is in the '
| low word, so d6 is free to be used
movel d7,a0 | now save d7 into a0, so d7 is free to
| be used also
| Get the exponents and check for denormalized and/or infinity.
movel IMM (0x001fffff),d6 | mask for the fraction
movel IMM (0x00200000),d7 | mask to put hidden bit back
movel d0,d4 |
andl d6,d0 | get fraction in d0
notl d6 | make d6 into mask for the exponent
andl d6,d4 | get exponent in d4
beq Ladddf$a$den | branch if a is denormalized
cmpl d6,d4 | check for INFINITY or NaN
beq Ladddf$nf |
orl d7,d0 | and put hidden bit back
Ladddf$1:
swap d4 | shift right exponent so that it starts
lsrw IMM (5),d4 | in bit 0 and not bit 20
| Now we have a's exponent in d4 and fraction in d0-d1 '
movel d2,d5 | save b to get exponent
andl d6,d5 | get exponent in d5
beq Ladddf$b$den | branch if b is denormalized
cmpl d6,d5 | check for INFINITY or NaN
beq Ladddf$nf
notl d6 | make d6 into mask for the fraction again
andl d6,d2 | and get fraction in d2
orl d7,d2 | and put hidden bit back
Ladddf$2:
swap d5 | shift right exponent so that it starts
lsrw IMM (5),d5 | in bit 0 and not bit 20
| Now we have b's exponent in d5 and fraction in d2-d3. '
| The situation now is as follows: the signs are combined in a0, the
| numbers are in d0-d1 (a) and d2-d3 (b), and the exponents in d4 (a)
| and d5 (b). To do the rounding correctly we need to keep all the
| bits until the end, so we need to use d0-d1-d2-d3 for the first number
| and d4-d5-d6-d7 for the second. To do this we store (temporarily) the
| exponents in a2-a3.
moveml a2-a3,sp@- | save the address registers
movel d4,a2 | save the exponents
movel d5,a3 |
movel IMM (0),d7 | and move the numbers around
movel d7,d6 |
movel d3,d5 |
movel d2,d4 |
movel d7,d3 |
movel d7,d2 |
| Here we shift the numbers until the exponents are the same, and put
| the largest exponent in a2.
exg d4,a2 | get exponents back
exg d5,a3 |
cmpw d4,d5 | compare the exponents
beq Ladddf$3 | if equal don't shift '
bhi 9f | branch if second exponent is higher
| Here we have a's exponent larger than b's, so we have to shift b. We do
| this by using as counter d2:
1: movew d4,d2 | move largest exponent to d2
subw d5,d2 | and subtract second exponent
exg d4,a2 | get back the longs we saved
exg d5,a3 |
| if difference is too large we don't shift (actually, we can just exit) '
cmpw IMM (DBL_MANT_DIG+2),d2
bge Ladddf$b$small
cmpw IMM (32),d2 | if difference >= 32, shift by longs
bge 5f
2: cmpw IMM (16),d2 | if difference >= 16, shift by words
bge 6f
bra 3f | enter dbra loop
4: lsrl IMM (1),d4
roxrl IMM (1),d5
roxrl IMM (1),d6
roxrl IMM (1),d7
3: dbra d2,4b
movel IMM (0),d2
movel d2,d3
bra Ladddf$4
5:
movel d6,d7
movel d5,d6
movel d4,d5
movel IMM (0),d4
subw IMM (32),d2
bra 2b
6:
movew d6,d7
swap d7
movew d5,d6
swap d6
movew d4,d5
swap d5
movew IMM (0),d4
swap d4
subw IMM (16),d2
bra 3b
9: exg d4,d5
movew d4,d6
subw d5,d6 | keep d5 (largest exponent) in d4
exg d4,a2
exg d5,a3
| if difference is too large we don't shift (actually, we can just exit) '
cmpw IMM (DBL_MANT_DIG+2),d6
bge Ladddf$a$small
cmpw IMM (32),d6 | if difference >= 32, shift by longs
bge 5f
2: cmpw IMM (16),d6 | if difference >= 16, shift by words
bge 6f
bra 3f | enter dbra loop
4: lsrl IMM (1),d0
roxrl IMM (1),d1
roxrl IMM (1),d2
roxrl IMM (1),d3
3: dbra d6,4b
movel IMM (0),d7
movel d7,d6
bra Ladddf$4
5:
movel d2,d3
movel d1,d2
movel d0,d1
movel IMM (0),d0
subw IMM (32),d6
bra 2b
6:
movew d2,d3
swap d3
movew d1,d2
swap d2
movew d0,d1
swap d1
movew IMM (0),d0
swap d0
subw IMM (16),d6
bra 3b
Ladddf$3:
exg d4,a2
exg d5,a3
Ladddf$4:
| Now we have the numbers in d0--d3 and d4--d7, the exponent in a2, and
| the signs in a4.
| Here we have to decide whether to add or subtract the numbers:
exg d7,a0 | get the signs
exg d6,a3 | a3 is free to be used
movel d7,d6 |
movew IMM (0),d7 | get a's sign in d7 '
swap d6 |
movew IMM (0),d6 | and b's sign in d6 '
eorl d7,d6 | compare the signs
bmi Lsubdf$0 | if the signs are different we have
| to subtract
exg d7,a0 | else we add the numbers
exg d6,a3 |
addl d7,d3 |
addxl d6,d2 |
addxl d5,d1 |
addxl d4,d0 |
movel a2,d4 | return exponent to d4
movel a0,d7 |
andl IMM (0x80000000),d7 | d7 now has the sign
moveml sp@+,a2-a3
| Before rounding normalize so bit #DBL_MANT_DIG is set (we will consider
| the case of denormalized numbers in the rounding routine itself).
| As in the addition (not in the subtraction!) we could have set
| one more bit we check this:
btst IMM (DBL_MANT_DIG+1),d0
beq 1f
lsrl IMM (1),d0
roxrl IMM (1),d1
roxrl IMM (1),d2
roxrl IMM (1),d3
addw IMM (1),d4
1:
lea Ladddf$5,a0 | to return from rounding routine
lea SYM (_fpCCR),a1 | check the rounding mode
movew a1@(6),d6 | rounding mode in d6
beq Lround$to$nearest
cmpw IMM (ROUND_TO_PLUS),d6
bhi Lround$to$minus
blt Lround$to$zero
bra Lround$to$plus
Ladddf$5:
| Put back the exponent and check for overflow
cmpw IMM (0x7ff),d4 | is the exponent big?
bge 1f
bclr IMM (DBL_MANT_DIG-1),d0
lslw IMM (4),d4 | put exponent back into position
swap d0 |
orw d4,d0 |
swap d0 |
bra Ladddf$ret
1:
movew IMM (ADD),d5
bra Ld$overflow
Lsubdf$0:
| Here we do the subtraction.
exg d7,a0 | put sign back in a0
exg d6,a3 |
subl d7,d3 |
subxl d6,d2 |
subxl d5,d1 |
subxl d4,d0 |
beq Ladddf$ret$1 | if zero just exit
bpl 1f | if positive skip the following
exg d7,a0 |
bchg IMM (31),d7 | change sign bit in d7
exg d7,a0 |
negl d3 |
negxl d2 |
negxl d1 | and negate result
negxl d0 |
1:
movel a2,d4 | return exponent to d4
movel a0,d7
andl IMM (0x80000000),d7 | isolate sign bit
moveml sp@+,a2-a3 |
| Before rounding normalize so bit #DBL_MANT_DIG is set (we will consider
| the case of denormalized numbers in the rounding routine itself).
| As in the addition (not in the subtraction!) we could have set
| one more bit we check this:
btst IMM (DBL_MANT_DIG+1),d0
beq 1f
lsrl IMM (1),d0
roxrl IMM (1),d1
roxrl IMM (1),d2
roxrl IMM (1),d3
addw IMM (1),d4
1:
lea Lsubdf$1,a0 | to return from rounding routine
lea SYM (_fpCCR),a1 | check the rounding mode
movew a1@(6),d6 | rounding mode in d6
beq Lround$to$nearest
cmpw IMM (ROUND_TO_PLUS),d6
bhi Lround$to$minus
blt Lround$to$zero
bra Lround$to$plus
Lsubdf$1:
| Put back the exponent and sign (we don't have overflow). '
bclr IMM (DBL_MANT_DIG-1),d0
lslw IMM (4),d4 | put exponent back into position
swap d0 |
orw d4,d0 |
swap d0 |
bra Ladddf$ret
| If one of the numbers was too small (difference of exponents >=
| DBL_MANT_DIG+1) we return the other (and now we don't have to '
| check for finiteness or zero).
Ladddf$a$small:
moveml sp@+,a2-a3
movel a6@(16),d0
movel a6@(20),d1
lea SYM (_fpCCR),a0
movew IMM (0),a0@
moveml sp@+,d2-d7 | restore data registers
unlk a6 | and return
rts
Ladddf$b$small:
moveml sp@+,a2-a3
movel a6@(8),d0
movel a6@(12),d1
lea SYM (_fpCCR),a0
movew IMM (0),a0@
moveml sp@+,d2-d7 | restore data registers
unlk a6 | and return
rts
Ladddf$a$den:
movel d7,d4 | d7 contains 0x00200000
bra Ladddf$1
Ladddf$b$den:
movel d7,d5 | d7 contains 0x00200000
notl d6
bra Ladddf$2
Ladddf$b:
| Return b (if a is zero)
movel d2,d0
movel d3,d1
bra 1f
Ladddf$a:
movel a6@(8),d0
movel a6@(12),d1
1:
movew IMM (ADD),d5
| Check for NaN and +/-INFINITY.
movel d0,d7 |
andl IMM (0x80000000),d7 |
bclr IMM (31),d0 |
cmpl IMM (0x7ff00000),d0 |
bge 2f |
movel d0,d0 | check for zero, since we don't '
bne Ladddf$ret | want to return -0 by mistake
bclr IMM (31),d7 |
bra Ladddf$ret |
2:
andl IMM (0x000fffff),d0 | check for NaN (nonzero fraction)
orl d1,d0 |
bne Ld$inop |
bra Ld$infty |
Ladddf$ret$1:
moveml sp@+,a2-a3 | restore regs and exit
Ladddf$ret:
| Normal exit.
lea SYM (_fpCCR),a0
movew IMM (0),a0@
orl d7,d0 | put sign bit back
moveml sp@+,d2-d7
unlk a6
rts
Ladddf$ret$den:
| Return a denormalized number.
lsrl IMM (1),d0 | shift right once more
roxrl IMM (1),d1 |
bra Ladddf$ret
Ladddf$nf:
movew IMM (ADD),d5
| This could be faster but it is not worth the effort, since it is not
| executed very often. We sacrifice speed for clarity here.
movel a6@(8),d0 | get the numbers back (remember that we
movel a6@(12),d1 | did some processing already)
movel a6@(16),d2 |
movel a6@(20),d3 |
movel IMM (0x7ff00000),d4 | useful constant (INFINITY)
movel d0,d7 | save sign bits
movel d2,d6 |
bclr IMM (31),d0 | clear sign bits
bclr IMM (31),d2 |
| We know that one of them is either NaN of +/-INFINITY
| Check for NaN (if either one is NaN return NaN)
cmpl d4,d0 | check first a (d0)
bhi Ld$inop | if d0 > 0x7ff00000 or equal and
bne 2f
tstl d1 | d1 > 0, a is NaN
bne Ld$inop |
2: cmpl d4,d2 | check now b (d1)
bhi Ld$inop |
bne 3f
tstl d3 |
bne Ld$inop |
3:
| Now comes the check for +/-INFINITY. We know that both are (maybe not
| finite) numbers, but we have to check if both are infinite whether we
| are adding or subtracting them.
eorl d7,d6 | to check sign bits
bmi 1f
andl IMM (0x80000000),d7 | get (common) sign bit
bra Ld$infty
1:
| We know one (or both) are infinite, so we test for equality between the
| two numbers (if they are equal they have to be infinite both, so we
| return NaN).
cmpl d2,d0 | are both infinite?
bne 1f | if d0 <> d2 they are not equal
cmpl d3,d1 | if d0 == d2 test d3 and d1
beq Ld$inop | if equal return NaN
1:
andl IMM (0x80000000),d7 | get a's sign bit '
cmpl d4,d0 | test now for infinity
beq Ld$infty | if a is INFINITY return with this sign
bchg IMM (31),d7 | else we know b is INFINITY and has
bra Ld$infty | the opposite sign
|=============================================================================
| __muldf3
|=============================================================================
| double __muldf3(double, double);
SYM (__muldf3):
link a6,IMM (0)
moveml d2-d7,sp@-
movel a6@(8),d0 | get a into d0-d1
movel a6@(12),d1 |
movel a6@(16),d2 | and b into d2-d3
movel a6@(20),d3 |
movel d0,d7 | d7 will hold the sign of the product
eorl d2,d7 |
andl IMM (0x80000000),d7 |
movel d7,a0 | save sign bit into a0
movel IMM (0x7ff00000),d7 | useful constant (+INFINITY)
movel d7,d6 | another (mask for fraction)
notl d6 |
bclr IMM (31),d0 | get rid of a's sign bit '
movel d0,d4 |
orl d1,d4 |
beq Lmuldf$a$0 | branch if a is zero
movel d0,d4 |
bclr IMM (31),d2 | get rid of b's sign bit '
movel d2,d5 |
orl d3,d5 |
beq Lmuldf$b$0 | branch if b is zero
movel d2,d5 |
cmpl d7,d0 | is a big?
bhi Lmuldf$inop | if a is NaN return NaN
beq Lmuldf$a$nf | we still have to check d1 and b ...
cmpl d7,d2 | now compare b with INFINITY
bhi Lmuldf$inop | is b NaN?
beq Lmuldf$b$nf | we still have to check d3 ...
| Here we have both numbers finite and nonzero (and with no sign bit).
| Now we get the exponents into d4 and d5.
andl d7,d4 | isolate exponent in d4
beq Lmuldf$a$den | if exponent zero, have denormalized
andl d6,d0 | isolate fraction
orl IMM (0x00100000),d0 | and put hidden bit back
swap d4 | I like exponents in the first byte
lsrw IMM (4),d4 |
Lmuldf$1:
andl d7,d5 |
beq Lmuldf$b$den |
andl d6,d2 |
orl IMM (0x00100000),d2 | and put hidden bit back
swap d5 |
lsrw IMM (4),d5 |
Lmuldf$2: |
addw d5,d4 | add exponents
subw IMM (D_BIAS+1),d4 | and subtract bias (plus one)
| We are now ready to do the multiplication. The situation is as follows:
| both a and b have bit 52 ( bit 20 of d0 and d2) set (even if they were
| denormalized to start with!), which means that in the product bit 104
| (which will correspond to bit 8 of the fourth long) is set.
| Here we have to do the product.
| To do it we have to juggle the registers back and forth, as there are not
| enough to keep everything in them. So we use the address registers to keep
| some intermediate data.
moveml a2-a3,sp@- | save a2 and a3 for temporary use
movel IMM (0),a2 | a2 is a null register
movel d4,a3 | and a3 will preserve the exponent
| First, shift d2-d3 so bit 20 becomes bit 31:
rorl IMM (5),d2 | rotate d2 5 places right
swap d2 | and swap it
rorl IMM (5),d3 | do the same thing with d3
swap d3 |
movew d3,d6 | get the rightmost 11 bits of d3
andw IMM (0x07ff),d6 |
orw d6,d2 | and put them into d2
andw IMM (0xf800),d3 | clear those bits in d3
movel d2,d6 | move b into d6-d7
movel d3,d7 | move a into d4-d5
movel d0,d4 | and clear d0-d1-d2-d3 (to put result)
movel d1,d5 |
movel IMM (0),d3 |
movel d3,d2 |
movel d3,d1 |
movel d3,d0 |
| We use a1 as counter:
movel IMM (DBL_MANT_DIG-1),a1
exg d7,a1
1: exg d7,a1 | put counter back in a1
addl d3,d3 | shift sum once left
addxl d2,d2 |
addxl d1,d1 |
addxl d0,d0 |
addl d7,d7 |
addxl d6,d6 |
bcc 2f | if bit clear skip the following
exg d7,a2 |
addl d5,d3 | else add a to the sum
addxl d4,d2 |
addxl d7,d1 |
addxl d7,d0 |
exg d7,a2 |
2: exg d7,a1 | put counter in d7
dbf d7,1b | decrement and branch
movel a3,d4 | restore exponent
moveml sp@+,a2-a3
| Now we have the product in d0-d1-d2-d3, with bit 8 of d0 set. The
| first thing to do now is to normalize it so bit 8 becomes bit
| DBL_MANT_DIG-32 (to do the rounding); later we will shift right.
swap d0
swap d1
movew d1,d0
swap d2
movew d2,d1
swap d3
movew d3,d2
movew IMM (0),d3
lsrl IMM (1),d0
roxrl IMM (1),d1
roxrl IMM (1),d2
roxrl IMM (1),d3
lsrl IMM (1),d0
roxrl IMM (1),d1
roxrl IMM (1),d2
roxrl IMM (1),d3
lsrl IMM (1),d0
roxrl IMM (1),d1
roxrl IMM (1),d2
roxrl IMM (1),d3
| Now round, check for over- and underflow, and exit.
movel a0,d7 | get sign bit back into d7
movew IMM (MULTIPLY),d5
btst IMM (DBL_MANT_DIG+1-32),d0
beq Lround$exit
lsrl IMM (1),d0
roxrl IMM (1),d1
addw IMM (1),d4
bra Lround$exit
Lmuldf$inop:
movew IMM (MULTIPLY),d5
bra Ld$inop
Lmuldf$b$nf:
movew IMM (MULTIPLY),d5
movel a0,d7 | get sign bit back into d7
tstl d3 | we know d2 == 0x7ff00000, so check d3
bne Ld$inop | if d3 <> 0 b is NaN
bra Ld$overflow | else we have overflow (since a is finite)
Lmuldf$a$nf:
movew IMM (MULTIPLY),d5
movel a0,d7 | get sign bit back into d7
tstl d1 | we know d0 == 0x7ff00000, so check d1
bne Ld$inop | if d1 <> 0 a is NaN
bra Ld$overflow | else signal overflow
| If either number is zero return zero, unless the other is +/-INFINITY or
| NaN, in which case we return NaN.
Lmuldf$b$0:
movew IMM (MULTIPLY),d5
exg d2,d0 | put b (==0) into d0-d1
exg d3,d1 | and a (with sign bit cleared) into d2-d3
bra 1f
Lmuldf$a$0:
movel a6@(16),d2 | put b into d2-d3 again
movel a6@(20),d3 |
bclr IMM (31),d2 | clear sign bit
1: cmpl IMM (0x7ff00000),d2 | check for non-finiteness
bge Ld$inop | in case NaN or +/-INFINITY return NaN
lea SYM (_fpCCR),a0
movew IMM (0),a0@
moveml sp@+,d2-d7
unlk a6
rts
| If a number is denormalized we put an exponent of 1 but do not put the
| hidden bit back into the fraction; instead we shift left until bit 21
| (the hidden bit) is set, adjusting the exponent accordingly. We do this
| to ensure that the product of the fractions is close to 1.
Lmuldf$a$den:
movel IMM (1),d4
andl d6,d0
1: addl d1,d1 | shift a left until bit 20 is set
addxl d0,d0 |
subw IMM (1),d4 | and adjust exponent
btst IMM (20),d0 |
bne Lmuldf$1 |
bra 1b
Lmuldf$b$den:
movel IMM (1),d5
andl d6,d2
1: addl d3,d3 | shift b left until bit 20 is set
addxl d2,d2 |
subw IMM (1),d5 | and adjust exponent
btst IMM (20),d2 |
bne Lmuldf$2 |
bra 1b
|=============================================================================
| __divdf3
|=============================================================================
| double __divdf3(double, double);
SYM (__divdf3):
link a6,IMM (0)
moveml d2-d7,sp@-
movel a6@(8),d0 | get a into d0-d1
movel a6@(12),d1 |
movel a6@(16),d2 | and b into d2-d3
movel a6@(20),d3 |
movel d0,d7 | d7 will hold the sign of the result
eorl d2,d7 |
andl IMM (0x80000000),d7
movel d7,a0 | save sign into a0
movel IMM (0x7ff00000),d7 | useful constant (+INFINITY)
movel d7,d6 | another (mask for fraction)
notl d6 |
bclr IMM (31),d0 | get rid of a's sign bit '
movel d0,d4 |
orl d1,d4 |
beq Ldivdf$a$0 | branch if a is zero
movel d0,d4 |
bclr IMM (31),d2 | get rid of b's sign bit '
movel d2,d5 |
orl d3,d5 |
beq Ldivdf$b$0 | branch if b is zero
movel d2,d5
cmpl d7,d0 | is a big?
bhi Ldivdf$inop | if a is NaN return NaN
beq Ldivdf$a$nf | if d0 == 0x7ff00000 we check d1
cmpl d7,d2 | now compare b with INFINITY
bhi Ldivdf$inop | if b is NaN return NaN
beq Ldivdf$b$nf | if d2 == 0x7ff00000 we check d3
| Here we have both numbers finite and nonzero (and with no sign bit).
| Now we get the exponents into d4 and d5 and normalize the numbers to
| ensure that the ratio of the fractions is around 1. We do this by
| making sure that both numbers have bit #DBL_MANT_DIG-32-1 (hidden bit)
| set, even if they were denormalized to start with.
| Thus, the result will satisfy: 2 > result > 1/2.
andl d7,d4 | and isolate exponent in d4
beq Ldivdf$a$den | if exponent is zero we have a denormalized
andl d6,d0 | and isolate fraction
orl IMM (0x00100000),d0 | and put hidden bit back
swap d4 | I like exponents in the first byte
lsrw IMM (4),d4 |
Ldivdf$1: |
andl d7,d5 |
beq Ldivdf$b$den |
andl d6,d2 |
orl IMM (0x00100000),d2
swap d5 |
lsrw IMM (4),d5 |
Ldivdf$2: |
subw d5,d4 | subtract exponents
addw IMM (D_BIAS),d4 | and add bias
| We are now ready to do the division. We have prepared things in such a way
| that the ratio of the fractions will be less than 2 but greater than 1/2.
| At this point the registers in use are:
| d0-d1 hold a (first operand, bit DBL_MANT_DIG-32=0, bit
| DBL_MANT_DIG-1-32=1)
| d2-d3 hold b (second operand, bit DBL_MANT_DIG-32=1)
| d4 holds the difference of the exponents, corrected by the bias
| a0 holds the sign of the ratio
| To do the rounding correctly we need to keep information about the
| nonsignificant bits. One way to do this would be to do the division
| using four registers; another is to use two registers (as originally
| I did), but use a sticky bit to preserve information about the
| fractional part. Note that we can keep that info in a1, which is not
| used.
movel IMM (0),d6 | d6-d7 will hold the result
movel d6,d7 |
movel IMM (0),a1 | and a1 will hold the sticky bit
movel IMM (DBL_MANT_DIG-32+1),d5
1: cmpl d0,d2 | is a < b?
bhi 3f | if b > a skip the following
beq 4f | if d0==d2 check d1 and d3
2: subl d3,d1 |
subxl d2,d0 | a <-- a - b
bset d5,d6 | set the corresponding bit in d6
3: addl d1,d1 | shift a by 1
addxl d0,d0 |
dbra d5,1b | and branch back
bra 5f
4: cmpl d1,d3 | here d0==d2, so check d1 and d3
bhi 3b | if d1 > d2 skip the subtraction
bra 2b | else go do it
5:
| Here we have to start setting the bits in the second long.
movel IMM (31),d5 | again d5 is counter
1: cmpl d0,d2 | is a < b?
bhi 3f | if b > a skip the following
beq 4f | if d0==d2 check d1 and d3
2: subl d3,d1 |
subxl d2,d0 | a <-- a - b
bset d5,d7 | set the corresponding bit in d7
3: addl d1,d1 | shift a by 1
addxl d0,d0 |
dbra d5,1b | and branch back
bra 5f
4: cmpl d1,d3 | here d0==d2, so check d1 and d3
bhi 3b | if d1 > d2 skip the subtraction
bra 2b | else go do it
5:
| Now go ahead checking until we hit a one, which we store in d2.
movel IMM (DBL_MANT_DIG),d5
1: cmpl d2,d0 | is a < b?
bhi 4f | if b < a, exit
beq 3f | if d0==d2 check d1 and d3
2: addl d1,d1 | shift a by 1
addxl d0,d0 |
dbra d5,1b | and branch back
movel IMM (0),d2 | here no sticky bit was found
movel d2,d3
bra 5f
3: cmpl d1,d3 | here d0==d2, so check d1 and d3
bhi 2b | if d1 > d2 go back
4:
| Here put the sticky bit in d2-d3 (in the position which actually corresponds
| to it; if you don't do this the algorithm loses in some cases). '
movel IMM (0),d2
movel d2,d3
subw IMM (DBL_MANT_DIG),d5
addw IMM (63),d5
cmpw IMM (31),d5
bhi 2f
1: bset d5,d3
bra 5f
subw IMM (32),d5
2: bset d5,d2
5:
| Finally we are finished! Move the longs in the address registers to
| their final destination:
movel d6,d0
movel d7,d1
movel IMM (0),d3
| Here we have finished the division, with the result in d0-d1-d2-d3, with
| 2^21 <= d6 < 2^23. Thus bit 23 is not set, but bit 22 could be set.
| If it is not, then definitely bit 21 is set. Normalize so bit 22 is
| not set:
btst IMM (DBL_MANT_DIG-32+1),d0
beq 1f
lsrl IMM (1),d0
roxrl IMM (1),d1
roxrl IMM (1),d2
roxrl IMM (1),d3
addw IMM (1),d4
1:
| Now round, check for over- and underflow, and exit.
movel a0,d7 | restore sign bit to d7
movew IMM (DIVIDE),d5
bra Lround$exit
Ldivdf$inop:
movew IMM (DIVIDE),d5
bra Ld$inop
Ldivdf$a$0:
| If a is zero check to see whether b is zero also. In that case return
| NaN; then check if b is NaN, and return NaN also in that case. Else
| return zero.
movew IMM (DIVIDE),d5
bclr IMM (31),d2 |
movel d2,d4 |
orl d3,d4 |
beq Ld$inop | if b is also zero return NaN
cmpl IMM (0x7ff00000),d2 | check for NaN
bhi Ld$inop |
blt 1f |
tstl d3 |
bne Ld$inop |
1: movel IMM (0),d0 | else return zero
movel d0,d1 |
lea SYM (_fpCCR),a0 | clear exception flags
movew IMM (0),a0@ |
moveml sp@+,d2-d7 |
unlk a6 |
rts |
Ldivdf$b$0:
movew IMM (DIVIDE),d5
| If we got here a is not zero. Check if a is NaN; in that case return NaN,
| else return +/-INFINITY. Remember that a is in d0 with the sign bit
| cleared already.
movel a0,d7 | put a's sign bit back in d7 '
cmpl IMM (0x7ff00000),d0 | compare d0 with INFINITY
bhi Ld$inop | if larger it is NaN
tstl d1 |
bne Ld$inop |
bra Ld$div$0 | else signal DIVIDE_BY_ZERO
Ldivdf$b$nf:
movew IMM (DIVIDE),d5
| If d2 == 0x7ff00000 we have to check d3.
tstl d3 |
bne Ld$inop | if d3 <> 0, b is NaN
bra Ld$underflow | else b is +/-INFINITY, so signal underflow
Ldivdf$a$nf:
movew IMM (DIVIDE),d5
| If d0 == 0x7ff00000 we have to check d1.
tstl d1 |
bne Ld$inop | if d1 <> 0, a is NaN
| If a is INFINITY we have to check b
cmpl d7,d2 | compare b with INFINITY
bge Ld$inop | if b is NaN or INFINITY return NaN
tstl d3 |
bne Ld$inop |
bra Ld$overflow | else return overflow
| If a number is denormalized we put an exponent of 1 but do not put the
| bit back into the fraction.
Ldivdf$a$den:
movel IMM (1),d4
andl d6,d0
1: addl d1,d1 | shift a left until bit 20 is set
addxl d0,d0
subw IMM (1),d4 | and adjust exponent
btst IMM (DBL_MANT_DIG-32-1),d0
bne Ldivdf$1
bra 1b
Ldivdf$b$den:
movel IMM (1),d5
andl d6,d2
1: addl d3,d3 | shift b left until bit 20 is set
addxl d2,d2
subw IMM (1),d5 | and adjust exponent
btst IMM (DBL_MANT_DIG-32-1),d2
bne Ldivdf$2
bra 1b
Lround$exit:
| This is a common exit point for __muldf3 and __divdf3. When they enter
| this point the sign of the result is in d7, the result in d0-d1, normalized
| so that 2^21 <= d0 < 2^22, and the exponent is in the lower byte of d4.
| First check for underlow in the exponent:
cmpw IMM (-DBL_MANT_DIG-1),d4
blt Ld$underflow
| It could happen that the exponent is less than 1, in which case the
| number is denormalized. In this case we shift right and adjust the
| exponent until it becomes 1 or the fraction is zero (in the latter case
| we signal underflow and return zero).
movel d7,a0 |
movel IMM (0),d6 | use d6-d7 to collect bits flushed right
movel d6,d7 | use d6-d7 to collect bits flushed right
cmpw IMM (1),d4 | if the exponent is less than 1 we
bge 2f | have to shift right (denormalize)
1: addw IMM (1),d4 | adjust the exponent
lsrl IMM (1),d0 | shift right once
roxrl IMM (1),d1 |
roxrl IMM (1),d2 |
roxrl IMM (1),d3 |
roxrl IMM (1),d6 |
roxrl IMM (1),d7 |
cmpw IMM (1),d4 | is the exponent 1 already?
beq 2f | if not loop back
bra 1b |
bra Ld$underflow | safety check, shouldn't execute '
2: orl d6,d2 | this is a trick so we don't lose '
orl d7,d3 | the bits which were flushed right
movel a0,d7 | get back sign bit into d7
| Now call the rounding routine (which takes care of denormalized numbers):
lea Lround$0,a0 | to return from rounding routine
lea SYM (_fpCCR),a1 | check the rounding mode
movew a1@(6),d6 | rounding mode in d6
beq Lround$to$nearest
cmpw IMM (ROUND_TO_PLUS),d6
bhi Lround$to$minus
blt Lround$to$zero
bra Lround$to$plus
Lround$0:
| Here we have a correctly rounded result (either normalized or denormalized).
| Here we should have either a normalized number or a denormalized one, and
| the exponent is necessarily larger or equal to 1 (so we don't have to '
| check again for underflow!). We have to check for overflow or for a
| denormalized number (which also signals underflow).
| Check for overflow (i.e., exponent >= 0x7ff).
cmpw IMM (0x07ff),d4
bge Ld$overflow
| Now check for a denormalized number (exponent==0):
movew d4,d4
beq Ld$den
1:
| Put back the exponents and sign and return.
lslw IMM (4),d4 | exponent back to fourth byte
bclr IMM (DBL_MANT_DIG-32-1),d0
swap d0 | and put back exponent
orw d4,d0 |
swap d0 |
orl d7,d0 | and sign also
lea SYM (_fpCCR),a0
movew IMM (0),a0@
moveml sp@+,d2-d7
unlk a6
rts
|=============================================================================
| __negdf2
|=============================================================================
| double __negdf2(double, double);
SYM (__negdf2):
link a6,IMM (0)
moveml d2-d7,sp@-
movew IMM (NEGATE),d5
movel a6@(8),d0 | get number to negate in d0-d1
movel a6@(12),d1 |
bchg IMM (31),d0 | negate
movel d0,d2 | make a positive copy (for the tests)
bclr IMM (31),d2 |
movel d2,d4 | check for zero
orl d1,d4 |
beq 2f | if zero (either sign) return +zero
cmpl IMM (0x7ff00000),d2 | compare to +INFINITY
blt 1f | if finite, return
bhi Ld$inop | if larger (fraction not zero) is NaN
tstl d1 | if d2 == 0x7ff00000 check d1
bne Ld$inop |
movel d0,d7 | else get sign and return INFINITY
andl IMM (0x80000000),d7
bra Ld$infty
1: lea SYM (_fpCCR),a0
movew IMM (0),a0@
moveml sp@+,d2-d7
unlk a6
rts
2: bclr IMM (31),d0
bra 1b
|=============================================================================
| __cmpdf2
|=============================================================================
GREATER = 1
LESS = -1
EQUAL = 0
| int __cmpdf2(double, double);
SYM (__cmpdf2):
link a6,IMM (0)
moveml d2-d7,sp@- | save registers
movew IMM (COMPARE),d5
movel a6@(8),d0 | get first operand
movel a6@(12),d1 |
movel a6@(16),d2 | get second operand
movel a6@(20),d3 |
| First check if a and/or b are (+/-) zero and in that case clear
| the sign bit.
movel d0,d6 | copy signs into d6 (a) and d7(b)
bclr IMM (31),d0 | and clear signs in d0 and d2
movel d2,d7 |
bclr IMM (31),d2 |
cmpl IMM (0x7fff0000),d0 | check for a == NaN
bhi Ld$inop | if d0 > 0x7ff00000, a is NaN
beq Lcmpdf$a$nf | if equal can be INFINITY, so check d1
movel d0,d4 | copy into d4 to test for zero
orl d1,d4 |
beq Lcmpdf$a$0 |
Lcmpdf$0:
cmpl IMM (0x7fff0000),d2 | check for b == NaN
bhi Ld$inop | if d2 > 0x7ff00000, b is NaN
beq Lcmpdf$b$nf | if equal can be INFINITY, so check d3
movel d2,d4 |
orl d3,d4 |
beq Lcmpdf$b$0 |
Lcmpdf$1:
| Check the signs
eorl d6,d7
bpl 1f
| If the signs are not equal check if a >= 0
tstl d6
bpl Lcmpdf$a$gt$b | if (a >= 0 && b < 0) => a > b
bmi Lcmpdf$b$gt$a | if (a < 0 && b >= 0) => a < b
1:
| If the signs are equal check for < 0
tstl d6
bpl 1f
| If both are negative exchange them
exg d0,d2
exg d1,d3
1:
| Now that they are positive we just compare them as longs (does this also
| work for denormalized numbers?).
cmpl d0,d2
bhi Lcmpdf$b$gt$a | |b| > |a|
bne Lcmpdf$a$gt$b | |b| < |a|
| If we got here d0 == d2, so we compare d1 and d3.
cmpl d1,d3
bhi Lcmpdf$b$gt$a | |b| > |a|
bne Lcmpdf$a$gt$b | |b| < |a|
| If we got here a == b.
movel IMM (EQUAL),d0
moveml sp@+,d2-d7 | put back the registers
unlk a6
rts
Lcmpdf$a$gt$b:
movel IMM (GREATER),d0
moveml sp@+,d2-d7 | put back the registers
unlk a6
rts
Lcmpdf$b$gt$a:
movel IMM (LESS),d0
moveml sp@+,d2-d7 | put back the registers
unlk a6
rts
Lcmpdf$a$0:
bclr IMM (31),d6
bra Lcmpdf$0
Lcmpdf$b$0:
bclr IMM (31),d7
bra Lcmpdf$1
Lcmpdf$a$nf:
tstl d1
bne Ld$inop
bra Lcmpdf$0
Lcmpdf$b$nf:
tstl d3
bne Ld$inop
bra Lcmpdf$1
|=============================================================================
| rounding routines
|=============================================================================
| The rounding routines expect the number to be normalized in registers
| d0-d1-d2-d3, with the exponent in register d4. They assume that the
| exponent is larger or equal to 1. They return a properly normalized number
| if possible, and a denormalized number otherwise. The exponent is returned
| in d4.
Lround$to$nearest:
| We now normalize as suggested by D. Knuth ("Seminumerical Algorithms"):
| Here we assume that the exponent is not too small (this should be checked
| before entering the rounding routine), but the number could be denormalized.
| Check for denormalized numbers:
1: btst IMM (DBL_MANT_DIG-32),d0
bne 2f | if set the number is normalized
| Normalize shifting left until bit #DBL_MANT_DIG-32 is set or the exponent
| is one (remember that a denormalized number corresponds to an
| exponent of -D_BIAS+1).
cmpw IMM (1),d4 | remember that the exponent is at least one
beq 2f | an exponent of one means denormalized
addl d3,d3 | else shift and adjust the exponent
addxl d2,d2 |
addxl d1,d1 |
addxl d0,d0 |
dbra d4,1b |
2:
| Now round: we do it as follows: after the shifting we can write the
| fraction part as f + delta, where 1 < f < 2^25, and 0 <= delta <= 2.
| If delta < 1, do nothing. If delta > 1, add 1 to f.
| If delta == 1, we make sure the rounded number will be even (odd?)
| (after shifting).
btst IMM (0),d1 | is delta < 1?
beq 2f | if so, do not do anything
orl d2,d3 | is delta == 1?
bne 1f | if so round to even
movel d1,d3 |
andl IMM (2),d3 | bit 1 is the last significant bit
movel IMM (0),d2 |
addl d3,d1 |
addxl d2,d0 |
bra 2f |
1: movel IMM (1),d3 | else add 1
movel IMM (0),d2 |
addl d3,d1 |
addxl d2,d0
| Shift right once (because we used bit #DBL_MANT_DIG-32!).
2: lsrl IMM (1),d0
roxrl IMM (1),d1
| Now check again bit #DBL_MANT_DIG-32 (rounding could have produced a
| 'fraction overflow' ...).
btst IMM (DBL_MANT_DIG-32),d0
beq 1f
lsrl IMM (1),d0
roxrl IMM (1),d1
addw IMM (1),d4
1:
| If bit #DBL_MANT_DIG-32-1 is clear we have a denormalized number, so we
| have to put the exponent to zero and return a denormalized number.
btst IMM (DBL_MANT_DIG-32-1),d0
beq 1f
jmp a0@
1: movel IMM (0),d4
jmp a0@
Lround$to$zero:
Lround$to$plus:
Lround$to$minus:
jmp a0@
#endif /* L_double */
#ifdef L_float
.globl SYM (_fpCCR)
.globl $_exception_handler
QUIET_NaN = 0xffffffff
SIGNL_NaN = 0x7f800001
INFINITY = 0x7f800000
F_MAX_EXP = 0xff
F_BIAS = 126
FLT_MAX_EXP = F_MAX_EXP - F_BIAS
FLT_MIN_EXP = 1 - F_BIAS
FLT_MANT_DIG = 24
INEXACT_RESULT = 0x0001
UNDERFLOW = 0x0002
OVERFLOW = 0x0004
DIVIDE_BY_ZERO = 0x0008
INVALID_OPERATION = 0x0010
SINGLE_FLOAT = 1
NOOP = 0
ADD = 1
MULTIPLY = 2
DIVIDE = 3
NEGATE = 4
COMPARE = 5
EXTENDSFDF = 6
TRUNCDFSF = 7
UNKNOWN = -1
ROUND_TO_NEAREST = 0 | round result to nearest representable value
ROUND_TO_ZERO = 1 | round result towards zero
ROUND_TO_PLUS = 2 | round result towards plus infinity
ROUND_TO_MINUS = 3 | round result towards minus infinity
| Entry points:
.globl SYM (__addsf3)
.globl SYM (__subsf3)
.globl SYM (__mulsf3)
.globl SYM (__divsf3)
.globl SYM (__negsf2)
.globl SYM (__cmpsf2)
| These are common routines to return and signal exceptions.
.text
.even
Lf$den:
| Return and signal a denormalized number
orl d7,d0
movew IMM (UNDERFLOW),d7
orw IMM (INEXACT_RESULT),d7
movew IMM (SINGLE_FLOAT),d6
jmp $_exception_handler
Lf$infty:
Lf$overflow:
| Return a properly signed INFINITY and set the exception flags
movel IMM (INFINITY),d0
orl d7,d0
movew IMM (OVERFLOW),d7
orw IMM (INEXACT_RESULT),d7
movew IMM (SINGLE_FLOAT),d6
jmp $_exception_handler
Lf$underflow:
| Return 0 and set the exception flags
movel IMM (0),d0
movew IMM (UNDERFLOW),d7
orw IMM (INEXACT_RESULT),d7
movew IMM (SINGLE_FLOAT),d6
jmp $_exception_handler
Lf$inop:
| Return a quiet NaN and set the exception flags
movel IMM (QUIET_NaN),d0
movew IMM (INVALID_OPERATION),d7
orw IMM (INEXACT_RESULT),d7
movew IMM (SINGLE_FLOAT),d6
jmp $_exception_handler
Lf$div$0:
| Return a properly signed INFINITY and set the exception flags
movel IMM (INFINITY),d0
orl d7,d0
movew IMM (DIVIDE_BY_ZERO),d7
orw IMM (INEXACT_RESULT),d7
movew IMM (SINGLE_FLOAT),d6
jmp $_exception_handler
|=============================================================================
|=============================================================================
| single precision routines
|=============================================================================
|=============================================================================
| A single precision floating point number (float) has the format:
|
| struct _float {
| unsigned int sign : 1; /* sign bit */
| unsigned int exponent : 8; /* exponent, shifted by 126 */
| unsigned int fraction : 23; /* fraction */
| } float;
|
| Thus sizeof(float) = 4 (32 bits).
|
| All the routines are callable from C programs, and return the result
| in the single register d0. They also preserve all registers except
| d0-d1 and a0-a1.
|=============================================================================
| __subsf3
|=============================================================================
| float __subsf3(float, float);
SYM (__subsf3):
bchg IMM (31),sp@(8) | change sign of second operand
| and fall through
|=============================================================================
| __addsf3
|=============================================================================
| float __addsf3(float, float);
SYM (__addsf3):
link a6,IMM (0) | everything will be done in registers
moveml d2-d7,sp@- | save all data registers but d0-d1
movel a6@(8),d0 | get first operand
movel a6@(12),d1 | get second operand
movel d0,d6 | get d0's sign bit '
addl d0,d0 | check and clear sign bit of a
beq Laddsf$b | if zero return second operand
movel d1,d7 | save b's sign bit '
addl d1,d1 | get rid of sign bit
beq Laddsf$a | if zero return first operand
movel d6,a0 | save signs in address registers
movel d7,a1 | so we can use d6 and d7
| Get the exponents and check for denormalized and/or infinity.
movel IMM (0x00ffffff),d4 | mask to get fraction
movel IMM (0x01000000),d5 | mask to put hidden bit back
movel d0,d6 | save a to get exponent
andl d4,d0 | get fraction in d0
notl d4 | make d4 into a mask for the exponent
andl d4,d6 | get exponent in d6
beq Laddsf$a$den | branch if a is denormalized
cmpl d4,d6 | check for INFINITY or NaN
beq Laddsf$nf
swap d6 | put exponent into first word
orl d5,d0 | and put hidden bit back
Laddsf$1:
| Now we have a's exponent in d6 (second byte) and the mantissa in d0. '
movel d1,d7 | get exponent in d7
andl d4,d7 |
beq Laddsf$b$den | branch if b is denormalized
cmpl d4,d7 | check for INFINITY or NaN
beq Laddsf$nf
swap d7 | put exponent into first word
notl d4 | make d4 into a mask for the fraction
andl d4,d1 | get fraction in d1
orl d5,d1 | and put hidden bit back
Laddsf$2:
| Now we have b's exponent in d7 (second byte) and the mantissa in d1. '
| Note that the hidden bit corresponds to bit #FLT_MANT_DIG-1, and we
| shifted right once, so bit #FLT_MANT_DIG is set (so we have one extra
| bit).
movel d1,d2 | move b to d2, since we want to use
| two registers to do the sum
movel IMM (0),d1 | and clear the new ones
movel d1,d3 |
| Here we shift the numbers in registers d0 and d1 so the exponents are the
| same, and put the largest exponent in d6. Note that we are using two
| registers for each number (see the discussion by D. Knuth in "Seminumerical
| Algorithms").
cmpw d6,d7 | compare exponents
beq Laddsf$3 | if equal don't shift '
bhi 5f | branch if second exponent largest
1:
subl d6,d7 | keep the largest exponent
negl d7
lsrw IMM (8),d7 | put difference in lower byte
| if difference is too large we don't shift (actually, we can just exit) '
cmpw IMM (FLT_MANT_DIG+2),d7
bge Laddsf$b$small
cmpw IMM (16),d7 | if difference >= 16 swap
bge 4f
2:
subw IMM (1),d7
3: lsrl IMM (1),d2 | shift right second operand
roxrl IMM (1),d3
dbra d7,3b
bra Laddsf$3
4:
movew d2,d3
swap d3
movew d3,d2
swap d2
subw IMM (16),d7
bne 2b | if still more bits, go back to normal case
bra Laddsf$3
5:
exg d6,d7 | exchange the exponents
subl d6,d7 | keep the largest exponent
negl d7 |
lsrw IMM (8),d7 | put difference in lower byte
| if difference is too large we don't shift (and exit!) '
cmpw IMM (FLT_MANT_DIG+2),d7
bge Laddsf$a$small
cmpw IMM (16),d7 | if difference >= 16 swap
bge 8f
6:
subw IMM (1),d7
7: lsrl IMM (1),d0 | shift right first operand
roxrl IMM (1),d1
dbra d7,7b
bra Laddsf$3
8:
movew d0,d1
swap d1
movew d1,d0
swap d0
subw IMM (16),d7
bne 6b | if still more bits, go back to normal case
| otherwise we fall through
| Now we have a in d0-d1, b in d2-d3, and the largest exponent in d6 (the
| signs are stored in a0 and a1).
Laddsf$3:
| Here we have to decide whether to add or subtract the numbers
exg d6,a0 | get signs back
exg d7,a1 | and save the exponents
eorl d6,d7 | combine sign bits
bmi Lsubsf$0 | if negative a and b have opposite
| sign so we actually subtract the
| numbers
| Here we have both positive or both negative
exg d6,a0 | now we have the exponent in d6
movel a0,d7 | and sign in d7
andl IMM (0x80000000),d7
| Here we do the addition.
addl d3,d1
addxl d2,d0
| Note: now we have d2, d3, d4 and d5 to play with!
| Put the exponent, in the first byte, in d2, to use the "standard" rounding
| routines:
movel d6,d2
lsrw IMM (8),d2
| Before rounding normalize so bit #FLT_MANT_DIG is set (we will consider
| the case of denormalized numbers in the rounding routine itself).
| As in the addition (not in the subtraction!) we could have set
| one more bit we check this:
btst IMM (FLT_MANT_DIG+1),d0
beq 1f
lsrl IMM (1),d0
roxrl IMM (1),d1
addl IMM (1),d2
1:
lea Laddsf$4,a0 | to return from rounding routine
lea SYM (_fpCCR),a1 | check the rounding mode
movew a1@(6),d6 | rounding mode in d6
beq Lround$to$nearest
cmpw IMM (ROUND_TO_PLUS),d6
bhi Lround$to$minus
blt Lround$to$zero
bra Lround$to$plus
Laddsf$4:
| Put back the exponent, but check for overflow.
cmpw IMM (0xff),d2
bhi 1f
bclr IMM (FLT_MANT_DIG-1),d0
lslw IMM (7),d2
swap d2
orl d2,d0
bra Laddsf$ret
1:
movew IMM (ADD),d5
bra Lf$overflow
Lsubsf$0:
| We are here if a > 0 and b < 0 (sign bits cleared).
| Here we do the subtraction.
movel d6,d7 | put sign in d7
andl IMM (0x80000000),d7
subl d3,d1 | result in d0-d1
subxl d2,d0 |
beq Laddsf$ret | if zero just exit
bpl 1f | if positive skip the following
bchg IMM (31),d7 | change sign bit in d7
negl d1
negxl d0
1:
exg d2,a0 | now we have the exponent in d2
lsrw IMM (8),d2 | put it in the first byte
| Now d0-d1 is positive and the sign bit is in d7.
| Note that we do not have to normalize, since in the subtraction bit
| #FLT_MANT_DIG+1 is never set, and denormalized numbers are handled by
| the rounding routines themselves.
lea Lsubsf$1,a0 | to return from rounding routine
lea SYM (_fpCCR),a1 | check the rounding mode
movew a1@(6),d6 | rounding mode in d6
beq Lround$to$nearest
cmpw IMM (ROUND_TO_PLUS),d6
bhi Lround$to$minus
blt Lround$to$zero
bra Lround$to$plus
Lsubsf$1:
| Put back the exponent (we can't have overflow!). '
bclr IMM (FLT_MANT_DIG-1),d0
lslw IMM (7),d2
swap d2
orl d2,d0
bra Laddsf$ret
| If one of the numbers was too small (difference of exponents >=
| FLT_MANT_DIG+2) we return the other (and now we don't have to '
| check for finiteness or zero).
Laddsf$a$small:
movel a6@(12),d0
lea SYM (_fpCCR),a0
movew IMM (0),a0@
moveml sp@+,d2-d7 | restore data registers
unlk a6 | and return
rts
Laddsf$b$small:
movel a6@(8),d0
lea SYM (_fpCCR),a0
movew IMM (0),a0@
moveml sp@+,d2-d7 | restore data registers
unlk a6 | and return
rts
| If the numbers are denormalized remember to put exponent equal to 1.
Laddsf$a$den:
movel d5,d6 | d5 contains 0x01000000
swap d6
bra Laddsf$1
Laddsf$b$den:
movel d5,d7
swap d7
notl d4 | make d4 into a mask for the fraction
| (this was not executed after the jump)
bra Laddsf$2
| The rest is mainly code for the different results which can be
| returned (checking always for +/-INFINITY and NaN).
Laddsf$b:
| Return b (if a is zero).
movel a6@(12),d0
bra 1f
Laddsf$a:
| Return a (if b is zero).
movel a6@(8),d0
1:
movew IMM (ADD),d5
| We have to check for NaN and +/-infty.
movel d0,d7
andl IMM (0x80000000),d7 | put sign in d7
bclr IMM (31),d0 | clear sign
cmpl IMM (INFINITY),d0 | check for infty or NaN
bge 2f
movel d0,d0 | check for zero (we do this because we don't '
bne Laddsf$ret | want to return -0 by mistake
bclr IMM (31),d7 | if zero be sure to clear sign
bra Laddsf$ret | if everything OK just return
2:
| The value to be returned is either +/-infty or NaN
andl IMM (0x007fffff),d0 | check for NaN
bne Lf$inop | if mantissa not zero is NaN
bra Lf$infty
Laddsf$ret:
| Normal exit (a and b nonzero, result is not NaN nor +/-infty).
| We have to clear the exception flags (just the exception type).
lea SYM (_fpCCR),a0
movew IMM (0),a0@
orl d7,d0 | put sign bit
moveml sp@+,d2-d7 | restore data registers
unlk a6 | and return
rts
Laddsf$ret$den:
| Return a denormalized number (for addition we don't signal underflow) '
lsrl IMM (1),d0 | remember to shift right back once
bra Laddsf$ret | and return
| Note: when adding two floats of the same sign if either one is
| NaN we return NaN without regard to whether the other is finite or
| not. When subtracting them (i.e., when adding two numbers of
| opposite signs) things are more complicated: if both are INFINITY
| we return NaN, if only one is INFINITY and the other is NaN we return
| NaN, but if it is finite we return INFINITY with the corresponding sign.
Laddsf$nf:
movew IMM (ADD),d5
| This could be faster but it is not worth the effort, since it is not
| executed very often. We sacrifice speed for clarity here.
movel a6@(8),d0 | get the numbers back (remember that we
movel a6@(12),d1 | did some processing already)
movel IMM (INFINITY),d4 | useful constant (INFINITY)
movel d0,d2 | save sign bits
movel d1,d3
bclr IMM (31),d0 | clear sign bits
bclr IMM (31),d1
| We know that one of them is either NaN of +/-INFINITY
| Check for NaN (if either one is NaN return NaN)
cmpl d4,d0 | check first a (d0)
bhi Lf$inop
cmpl d4,d1 | check now b (d1)
bhi Lf$inop
| Now comes the check for +/-INFINITY. We know that both are (maybe not
| finite) numbers, but we have to check if both are infinite whether we
| are adding or subtracting them.
eorl d3,d2 | to check sign bits
bmi 1f
movel d0,d7
andl IMM (0x80000000),d7 | get (common) sign bit
bra Lf$infty
1:
| We know one (or both) are infinite, so we test for equality between the
| two numbers (if they are equal they have to be infinite both, so we
| return NaN).
cmpl d1,d0 | are both infinite?
beq Lf$inop | if so return NaN
movel d0,d7
andl IMM (0x80000000),d7 | get a's sign bit '
cmpl d4,d0 | test now for infinity
beq Lf$infty | if a is INFINITY return with this sign
bchg IMM (31),d7 | else we know b is INFINITY and has
bra Lf$infty | the opposite sign
|=============================================================================
| __mulsf3
|=============================================================================
| float __mulsf3(float, float);
SYM (__mulsf3):
link a6,IMM (0)
moveml d2-d7,sp@-
movel a6@(8),d0 | get a into d0
movel a6@(12),d1 | and b into d1
movel d0,d7 | d7 will hold the sign of the product
eorl d1,d7 |
andl IMM (0x80000000),d7
movel IMM (INFINITY),d6 | useful constant (+INFINITY)
movel d6,d5 | another (mask for fraction)
notl d5 |
movel IMM (0x00800000),d4 | this is to put hidden bit back
bclr IMM (31),d0 | get rid of a's sign bit '
movel d0,d2 |
beq Lmulsf$a$0 | branch if a is zero
bclr IMM (31),d1 | get rid of b's sign bit '
movel d1,d3 |
beq Lmulsf$b$0 | branch if b is zero
cmpl d6,d0 | is a big?
bhi Lmulsf$inop | if a is NaN return NaN
beq Lmulsf$inf | if a is INFINITY we have to check b
cmpl d6,d1 | now compare b with INFINITY
bhi Lmulsf$inop | is b NaN?
beq Lmulsf$overflow | is b INFINITY?
| Here we have both numbers finite and nonzero (and with no sign bit).
| Now we get the exponents into d2 and d3.
andl d6,d2 | and isolate exponent in d2
beq Lmulsf$a$den | if exponent is zero we have a denormalized
andl d5,d0 | and isolate fraction
orl d4,d0 | and put hidden bit back
swap d2 | I like exponents in the first byte
lsrw IMM (7),d2 |
Lmulsf$1: | number
andl d6,d3 |
beq Lmulsf$b$den |
andl d5,d1 |
orl d4,d1 |
swap d3 |
lsrw IMM (7),d3 |
Lmulsf$2: |
addw d3,d2 | add exponents
subw IMM (F_BIAS+1),d2 | and subtract bias (plus one)
| We are now ready to do the multiplication. The situation is as follows:
| both a and b have bit FLT_MANT_DIG-1 set (even if they were
| denormalized to start with!), which means that in the product
| bit 2*(FLT_MANT_DIG-1) (that is, bit 2*FLT_MANT_DIG-2-32 of the
| high long) is set.
| To do the multiplication let us move the number a little bit around ...
movel d1,d6 | second operand in d6
movel d0,d5 | first operand in d4-d5
movel IMM (0),d4
movel d4,d1 | the sums will go in d0-d1
movel d4,d0
| now bit FLT_MANT_DIG-1 becomes bit 31:
lsll IMM (31-FLT_MANT_DIG+1),d6
| Start the loop (we loop #FLT_MANT_DIG times):
movew IMM (FLT_MANT_DIG-1),d3
1: addl d1,d1 | shift sum
addxl d0,d0
lsll IMM (1),d6 | get bit bn
bcc 2f | if not set skip sum
addl d5,d1 | add a
addxl d4,d0
2: dbf d3,1b | loop back
| Now we have the product in d0-d1, with bit (FLT_MANT_DIG - 1) + FLT_MANT_DIG
| (mod 32) of d0 set. The first thing to do now is to normalize it so bit
| FLT_MANT_DIG is set (to do the rounding).
rorl IMM (6),d1
swap d1
movew d1,d3
andw IMM (0x03ff),d3
andw IMM (0xfd00),d1
lsll IMM (8),d0
addl d0,d0
addl d0,d0
orw d3,d0
movew IMM (MULTIPLY),d5
btst IMM (FLT_MANT_DIG+1),d0
beq Lround$exit
lsrl IMM (1),d0
roxrl IMM (1),d1
addw IMM (1),d2
bra Lround$exit
Lmulsf$inop:
movew IMM (MULTIPLY),d5
bra Lf$inop
Lmulsf$overflow:
movew IMM (MULTIPLY),d5
bra Lf$overflow
Lmulsf$inf:
movew IMM (MULTIPLY),d5
| If either is NaN return NaN; else both are (maybe infinite) numbers, so
| return INFINITY with the correct sign (which is in d7).
cmpl d6,d1 | is b NaN?
bhi Lf$inop | if so return NaN
bra Lf$overflow | else return +/-INFINITY
| If either number is zero return zero, unless the other is +/-INFINITY,
| or NaN, in which case we return NaN.
Lmulsf$b$0:
| Here d1 (==b) is zero.
movel d1,d0 | put b into d0 (just a zero)
movel a6@(8),d1 | get a again to check for non-finiteness
bra 1f
Lmulsf$a$0:
movel a6@(12),d1 | get b again to check for non-finiteness
1: bclr IMM (31),d1 | clear sign bit
cmpl IMM (INFINITY),d1 | and check for a large exponent
bge Lf$inop | if b is +/-INFINITY or NaN return NaN
lea SYM (_fpCCR),a0 | else return zero
movew IMM (0),a0@ |
moveml sp@+,d2-d7 |
unlk a6 |
rts |
| If a number is denormalized we put an exponent of 1 but do not put the
| hidden bit back into the fraction; instead we shift left until bit 23
| (the hidden bit) is set, adjusting the exponent accordingly. We do this
| to ensure that the product of the fractions is close to 1.
Lmulsf$a$den:
movel IMM (1),d2
andl d5,d0
1: addl d0,d0 | shift a left (until bit 23 is set)
subw IMM (1),d2 | and adjust exponent
btst IMM (FLT_MANT_DIG-1),d0
bne Lmulsf$1 |
bra 1b | else loop back
Lmulsf$b$den:
movel IMM (1),d3
andl d5,d1
1: addl d1,d1 | shift b left until bit 23 is set
subw IMM (1),d3 | and adjust exponent
btst IMM (FLT_MANT_DIG-1),d1
bne Lmulsf$2 |
bra 1b | else loop back
|=============================================================================
| __divsf3
|=============================================================================
| float __divsf3(float, float);
SYM (__divsf3):
link a6,IMM (0)
moveml d2-d7,sp@-
movel a6@(8),d0 | get a into d0
movel a6@(12),d1 | and b into d1
movel d0,d7 | d7 will hold the sign of the result
eorl d1,d7 |
andl IMM (0x80000000),d7 |
movel IMM (INFINITY),d6 | useful constant (+INFINITY)
movel d6,d5 | another (mask for fraction)
notl d5 |
movel IMM (0x00800000),d4 | this is to put hidden bit back
bclr IMM (31),d0 | get rid of a's sign bit '
movel d0,d2 |
beq Ldivsf$a$0 | branch if a is zero
bclr IMM (31),d1 | get rid of b's sign bit '
movel d1,d3 |
beq Ldivsf$b$0 | branch if b is zero
cmpl d6,d0 | is a big?
bhi Ldivsf$inop | if a is NaN return NaN
beq Ldivsf$inf | if a is INFINITY we have to check b
cmpl d6,d1 | now compare b with INFINITY
bhi Ldivsf$inop | if b is NaN return NaN
beq Ldivsf$underflow
| Here we have both numbers finite and nonzero (and with no sign bit).
| Now we get the exponents into d2 and d3 and normalize the numbers to
| ensure that the ratio of the fractions is close to 1. We do this by
| making sure that bit #FLT_MANT_DIG-1 (hidden bit) is set.
andl d6,d2 | and isolate exponent in d2
beq Ldivsf$a$den | if exponent is zero we have a denormalized
andl d5,d0 | and isolate fraction
orl d4,d0 | and put hidden bit back
swap d2 | I like exponents in the first byte
lsrw IMM (7),d2 |
Ldivsf$1: |
andl d6,d3 |
beq Ldivsf$b$den |
andl d5,d1 |
orl d4,d1 |
swap d3 |
lsrw IMM (7),d3 |
Ldivsf$2: |
subw d3,d2 | subtract exponents
addw IMM (F_BIAS),d2 | and add bias
| We are now ready to do the division. We have prepared things in such a way
| that the ratio of the fractions will be less than 2 but greater than 1/2.
| At this point the registers in use are:
| d0 holds a (first operand, bit FLT_MANT_DIG=0, bit FLT_MANT_DIG-1=1)
| d1 holds b (second operand, bit FLT_MANT_DIG=1)
| d2 holds the difference of the exponents, corrected by the bias
| d7 holds the sign of the ratio
| d4, d5, d6 hold some constants
movel d7,a0 | d6-d7 will hold the ratio of the fractions
movel IMM (0),d6 |
movel d6,d7
movew IMM (FLT_MANT_DIG+1),d3
1: cmpl d0,d1 | is a < b?
bhi 2f |
bset d3,d6 | set a bit in d6
subl d1,d0 | if a >= b a <-- a-b
beq 3f | if a is zero, exit
2: addl d0,d0 | multiply a by 2
dbra d3,1b
| Now we keep going to set the sticky bit ...
movew IMM (FLT_MANT_DIG),d3
1: cmpl d0,d1
ble 2f
addl d0,d0
dbra d3,1b
movel IMM (0),d1
bra 3f
2: movel IMM (0),d1
subw IMM (FLT_MANT_DIG),d3
addw IMM (31),d3
bset d3,d1
3:
movel d6,d0 | put the ratio in d0-d1
movel a0,d7 | get sign back
| Because of the normalization we did before we are guaranteed that
| d0 is smaller than 2^26 but larger than 2^24. Thus bit 26 is not set,
| bit 25 could be set, and if it is not set then bit 24 is necessarily set.
btst IMM (FLT_MANT_DIG+1),d0
beq 1f | if it is not set, then bit 24 is set
lsrl IMM (1),d0 |
addw IMM (1),d2 |
1:
| Now round, check for over- and underflow, and exit.
movew IMM (DIVIDE),d5
bra Lround$exit
Ldivsf$inop:
movew IMM (DIVIDE),d5
bra Lf$inop
Ldivsf$overflow:
movew IMM (DIVIDE),d5
bra Lf$overflow
Ldivsf$underflow:
movew IMM (DIVIDE),d5
bra Lf$underflow
Ldivsf$a$0:
movew IMM (DIVIDE),d5
| If a is zero check to see whether b is zero also. In that case return
| NaN; then check if b is NaN, and return NaN also in that case. Else
| return zero.
andl IMM (0x7fffffff),d1 | clear sign bit and test b
beq Lf$inop | if b is also zero return NaN
cmpl IMM (INFINITY),d1 | check for NaN
bhi Lf$inop |
movel IMM (0),d0 | else return zero
lea SYM (_fpCCR),a0 |
movew IMM (0),a0@ |
moveml sp@+,d2-d7 |
unlk a6 |
rts |
Ldivsf$b$0:
movew IMM (DIVIDE),d5
| If we got here a is not zero. Check if a is NaN; in that case return NaN,
| else return +/-INFINITY. Remember that a is in d0 with the sign bit
| cleared already.
cmpl IMM (INFINITY),d0 | compare d0 with INFINITY
bhi Lf$inop | if larger it is NaN
bra Lf$div$0 | else signal DIVIDE_BY_ZERO
Ldivsf$inf:
movew IMM (DIVIDE),d5
| If a is INFINITY we have to check b
cmpl IMM (INFINITY),d1 | compare b with INFINITY
bge Lf$inop | if b is NaN or INFINITY return NaN
bra Lf$overflow | else return overflow
| If a number is denormalized we put an exponent of 1 but do not put the
| bit back into the fraction.
Ldivsf$a$den:
movel IMM (1),d2
andl d5,d0
1: addl d0,d0 | shift a left until bit FLT_MANT_DIG-1 is set
subw IMM (1),d2 | and adjust exponent
btst IMM (FLT_MANT_DIG-1),d0
bne Ldivsf$1
bra 1b
Ldivsf$b$den:
movel IMM (1),d3
andl d5,d1
1: addl d1,d1 | shift b left until bit FLT_MANT_DIG is set
subw IMM (1),d3 | and adjust exponent
btst IMM (FLT_MANT_DIG-1),d1
bne Ldivsf$2
bra 1b
Lround$exit:
| This is a common exit point for __mulsf3 and __divsf3.
| First check for underlow in the exponent:
cmpw IMM (-FLT_MANT_DIG-1),d2
blt Lf$underflow
| It could happen that the exponent is less than 1, in which case the
| number is denormalized. In this case we shift right and adjust the
| exponent until it becomes 1 or the fraction is zero (in the latter case
| we signal underflow and return zero).
movel IMM (0),d6 | d6 is used temporarily
cmpw IMM (1),d2 | if the exponent is less than 1 we
bge 2f | have to shift right (denormalize)
1: addw IMM (1),d2 | adjust the exponent
lsrl IMM (1),d0 | shift right once
roxrl IMM (1),d1 |
roxrl IMM (1),d6 | d6 collect bits we would lose otherwise
cmpw IMM (1),d2 | is the exponent 1 already?
beq 2f | if not loop back
bra 1b |
bra Lf$underflow | safety check, shouldn't execute '
2: orl d6,d1 | this is a trick so we don't lose '
| the extra bits which were flushed right
| Now call the rounding routine (which takes care of denormalized numbers):
lea Lround$0,a0 | to return from rounding routine
lea SYM (_fpCCR),a1 | check the rounding mode
movew a1@(6),d6 | rounding mode in d6
beq Lround$to$nearest
cmpw IMM (ROUND_TO_PLUS),d6
bhi Lround$to$minus
blt Lround$to$zero
bra Lround$to$plus
Lround$0:
| Here we have a correctly rounded result (either normalized or denormalized).
| Here we should have either a normalized number or a denormalized one, and
| the exponent is necessarily larger or equal to 1 (so we don't have to '
| check again for underflow!). We have to check for overflow or for a
| denormalized number (which also signals underflow).
| Check for overflow (i.e., exponent >= 255).
cmpw IMM (0x00ff),d2
bge Lf$overflow
| Now check for a denormalized number (exponent==0).
movew d2,d2
beq Lf$den
1:
| Put back the exponents and sign and return.
lslw IMM (7),d2 | exponent back to fourth byte
bclr IMM (FLT_MANT_DIG-1),d0
swap d0 | and put back exponent
orw d2,d0 |
swap d0 |
orl d7,d0 | and sign also
lea SYM (_fpCCR),a0
movew IMM (0),a0@
moveml sp@+,d2-d7
unlk a6
rts
|=============================================================================
| __negsf2
|=============================================================================
| This is trivial and could be shorter if we didn't bother checking for NaN '
| and +/-INFINITY.
| float __negsf2(float);
SYM (__negsf2):
link a6,IMM (0)
moveml d2-d7,sp@-
movew IMM (NEGATE),d5
movel a6@(8),d0 | get number to negate in d0
bchg IMM (31),d0 | negate
movel d0,d1 | make a positive copy
bclr IMM (31),d1 |
tstl d1 | check for zero
beq 2f | if zero (either sign) return +zero
cmpl IMM (INFINITY),d1 | compare to +INFINITY
blt 1f |
bhi Lf$inop | if larger (fraction not zero) is NaN
movel d0,d7 | else get sign and return INFINITY
andl IMM (0x80000000),d7
bra Lf$infty
1: lea SYM (_fpCCR),a0
movew IMM (0),a0@
moveml sp@+,d2-d7
unlk a6
rts
2: bclr IMM (31),d0
bra 1b
|=============================================================================
| __cmpsf2
|=============================================================================
GREATER = 1
LESS = -1
EQUAL = 0
| int __cmpsf2(float, float);
SYM (__cmpsf2):
link a6,IMM (0)
moveml d2-d7,sp@- | save registers
movew IMM (COMPARE),d5
movel a6@(8),d0 | get first operand
movel a6@(12),d1 | get second operand
| Check if either is NaN, and in that case return garbage and signal
| INVALID_OPERATION. Check also if either is zero, and clear the signs
| if necessary.
movel d0,d6
andl IMM (0x7fffffff),d0
beq Lcmpsf$a$0
cmpl IMM (0x7f800000),d0
bhi Lf$inop
Lcmpsf$1:
movel d1,d7
andl IMM (0x7fffffff),d1
beq Lcmpsf$b$0
cmpl IMM (0x7f800000),d1
bhi Lf$inop
Lcmpsf$2:
| Check the signs
eorl d6,d7
bpl 1f
| If the signs are not equal check if a >= 0
tstl d6
bpl Lcmpsf$a$gt$b | if (a >= 0 && b < 0) => a > b
bmi Lcmpsf$b$gt$a | if (a < 0 && b >= 0) => a < b
1:
| If the signs are equal check for < 0
tstl d6
bpl 1f
| If both are negative exchange them
exg d0,d1
1:
| Now that they are positive we just compare them as longs (does this also
| work for denormalized numbers?).
cmpl d0,d1
bhi Lcmpsf$b$gt$a | |b| > |a|
bne Lcmpsf$a$gt$b | |b| < |a|
| If we got here a == b.
movel IMM (EQUAL),d0
moveml sp@+,d2-d7 | put back the registers
unlk a6
rts
Lcmpsf$a$gt$b:
movel IMM (GREATER),d0
moveml sp@+,d2-d7 | put back the registers
unlk a6
rts
Lcmpsf$b$gt$a:
movel IMM (LESS),d0
moveml sp@+,d2-d7 | put back the registers
unlk a6
rts
Lcmpsf$a$0:
bclr IMM (31),d6
bra Lcmpsf$1
Lcmpsf$b$0:
bclr IMM (31),d7
bra Lcmpsf$2
|=============================================================================
| rounding routines
|=============================================================================
| The rounding routines expect the number to be normalized in registers
| d0-d1, with the exponent in register d2. They assume that the
| exponent is larger or equal to 1. They return a properly normalized number
| if possible, and a denormalized number otherwise. The exponent is returned
| in d2.
Lround$to$nearest:
| We now normalize as suggested by D. Knuth ("Seminumerical Algorithms"):
| Here we assume that the exponent is not too small (this should be checked
| before entering the rounding routine), but the number could be denormalized.
| Check for denormalized numbers:
1: btst IMM (FLT_MANT_DIG),d0
bne 2f | if set the number is normalized
| Normalize shifting left until bit #FLT_MANT_DIG is set or the exponent
| is one (remember that a denormalized number corresponds to an
| exponent of -F_BIAS+1).
cmpw IMM (1),d2 | remember that the exponent is at least one
beq 2f | an exponent of one means denormalized
addl d1,d1 | else shift and adjust the exponent
addxl d0,d0 |
dbra d2,1b |
2:
| Now round: we do it as follows: after the shifting we can write the
| fraction part as f + delta, where 1 < f < 2^25, and 0 <= delta <= 2.
| If delta < 1, do nothing. If delta > 1, add 1 to f.
| If delta == 1, we make sure the rounded number will be even (odd?)
| (after shifting).
btst IMM (0),d0 | is delta < 1?
beq 2f | if so, do not do anything
tstl d1 | is delta == 1?
bne 1f | if so round to even
movel d0,d1 |
andl IMM (2),d1 | bit 1 is the last significant bit
addl d1,d0 |
bra 2f |
1: movel IMM (1),d1 | else add 1
addl d1,d0 |
| Shift right once (because we used bit #FLT_MANT_DIG!).
2: lsrl IMM (1),d0
| Now check again bit #FLT_MANT_DIG (rounding could have produced a
| 'fraction overflow' ...).
btst IMM (FLT_MANT_DIG),d0
beq 1f
lsrl IMM (1),d0
addw IMM (1),d2
1:
| If bit #FLT_MANT_DIG-1 is clear we have a denormalized number, so we
| have to put the exponent to zero and return a denormalized number.
btst IMM (FLT_MANT_DIG-1),d0
beq 1f
jmp a0@
1: movel IMM (0),d2
jmp a0@
Lround$to$zero:
Lround$to$plus:
Lround$to$minus:
jmp a0@
#endif /* L_float */
| gcc expects the routines __eqdf2, __nedf2, __gtdf2, __gedf2,
| __ledf2, __ltdf2 to all return the same value as a direct call to
| __cmpdf2 would. In this implementation, each of these routines
| simply calls __cmpdf2. It would be more efficient to give the
| __cmpdf2 routine several names, but separating them out will make it
| easier to write efficient versions of these routines someday.
#ifdef L_eqdf2
LL0:
.text
.proc
|#PROC# 04
LF18 = 4
LS18 = 128
LFF18 = 0
LSS18 = 0
LV18 = 0
.text
.globl SYM (__eqdf2)
SYM (__eqdf2):
|#PROLOGUE# 0
link a6,IMM (0)
|#PROLOGUE# 1
movl a6@(20),sp@-
movl a6@(16),sp@-
movl a6@(12),sp@-
movl a6@(8),sp@-
jbsr SYM (__cmpdf2)
|#PROLOGUE# 2
unlk a6
|#PROLOGUE# 3
rts
#endif /* L_eqdf2 */
#ifdef L_nedf2
LL0:
.text
.proc
|#PROC# 04
LF18 = 8
LS18 = 132
LFF18 = 0
LSS18 = 0
LV18 = 0
.text
.globl SYM (__nedf2)
SYM (__nedf2):
|#PROLOGUE# 0
link a6,IMM (0)
|#PROLOGUE# 1
movl a6@(20),sp@-
movl a6@(16),sp@-
movl a6@(12),sp@-
movl a6@(8),sp@-
jbsr SYM (__cmpdf2)
|#PROLOGUE# 2
unlk a6
|#PROLOGUE# 3
rts
#endif /* L_nedf2 */
#ifdef L_gtdf2
.text
.proc
|#PROC# 04
LF18 = 8
LS18 = 132
LFF18 = 0
LSS18 = 0
LV18 = 0
.text
.globl SYM (__gtdf2)
SYM (__gtdf2):
|#PROLOGUE# 0
link a6,IMM (0)
|#PROLOGUE# 1
movl a6@(20),sp@-
movl a6@(16),sp@-
movl a6@(12),sp@-
movl a6@(8),sp@-
jbsr SYM (__cmpdf2)
|#PROLOGUE# 2
unlk a6
|#PROLOGUE# 3
rts
#endif /* L_gtdf2 */
#ifdef L_gedf2
LL0:
.text
.proc
|#PROC# 04
LF18 = 8
LS18 = 132
LFF18 = 0
LSS18 = 0
LV18 = 0
.text
.globl SYM (__gedf2)
SYM (__gedf2):
|#PROLOGUE# 0
link a6,IMM (0)
|#PROLOGUE# 1
movl a6@(20),sp@-
movl a6@(16),sp@-
movl a6@(12),sp@-
movl a6@(8),sp@-
jbsr SYM (__cmpdf2)
|#PROLOGUE# 2
unlk a6
|#PROLOGUE# 3
rts
#endif /* L_gedf2 */
#ifdef L_ltdf2
LL0:
.text
.proc
|#PROC# 04
LF18 = 8
LS18 = 132
LFF18 = 0
LSS18 = 0
LV18 = 0
.text
.globl SYM (__ltdf2)
SYM (__ltdf2):
|#PROLOGUE# 0
link a6,IMM (0)
|#PROLOGUE# 1
movl a6@(20),sp@-
movl a6@(16),sp@-
movl a6@(12),sp@-
movl a6@(8),sp@-
jbsr SYM (__cmpdf2)
|#PROLOGUE# 2
unlk a6
|#PROLOGUE# 3
rts
#endif /* L_ltdf2 */
#ifdef L_ledf2
.text
.proc
|#PROC# 04
LF18 = 8
LS18 = 132
LFF18 = 0
LSS18 = 0
LV18 = 0
.text
.globl SYM (__ledf2)
SYM (__ledf2):
|#PROLOGUE# 0
link a6,IMM (0)
|#PROLOGUE# 1
movl a6@(20),sp@-
movl a6@(16),sp@-
movl a6@(12),sp@-
movl a6@(8),sp@-
jbsr SYM (__cmpdf2)
|#PROLOGUE# 2
unlk a6
|#PROLOGUE# 3
rts
#endif /* L_ledf2 */
| The comments above about __eqdf2, et. al., also apply to __eqsf2,
| et. al., except that the latter call __cmpsf2 rather than __cmpdf2.
#ifdef L_eqsf2
.text
.proc
|#PROC# 04
LF18 = 4
LS18 = 128
LFF18 = 0
LSS18 = 0
LV18 = 0
.text
.globl SYM (__eqsf2)
SYM (__eqsf2):
|#PROLOGUE# 0
link a6,IMM (0)
|#PROLOGUE# 1
movl a6@(12),sp@-
movl a6@(8),sp@-
jbsr SYM (__cmpsf2)
|#PROLOGUE# 2
unlk a6
|#PROLOGUE# 3
rts
#endif /* L_eqsf2 */
#ifdef L_nesf2
.text
.proc
|#PROC# 04
LF18 = 8
LS18 = 132
LFF18 = 0
LSS18 = 0
LV18 = 0
.text
.globl SYM (__nesf2)
SYM (__nesf2):
|#PROLOGUE# 0
link a6,IMM (0)
|#PROLOGUE# 1
movl a6@(12),sp@-
movl a6@(8),sp@-
jbsr SYM (__cmpsf2)
|#PROLOGUE# 2
unlk a6
|#PROLOGUE# 3
rts
#endif /* L_nesf2 */
#ifdef L_gtsf2
.text
.proc
|#PROC# 04
LF18 = 8
LS18 = 132
LFF18 = 0
LSS18 = 0
LV18 = 0
.text
.globl SYM (__gtsf2)
SYM (__gtsf2):
|#PROLOGUE# 0
link a6,IMM (0)
|#PROLOGUE# 1
movl a6@(12),sp@-
movl a6@(8),sp@-
jbsr SYM (__cmpsf2)
|#PROLOGUE# 2
unlk a6
|#PROLOGUE# 3
rts
#endif /* L_gtsf2 */
#ifdef L_gesf2
.text
.proc
|#PROC# 04
LF18 = 8
LS18 = 132
LFF18 = 0
LSS18 = 0
LV18 = 0
.text
.globl SYM (__gesf2)
SYM (__gesf2):
|#PROLOGUE# 0
link a6,IMM (0)
|#PROLOGUE# 1
movl a6@(12),sp@-
movl a6@(8),sp@-
jbsr SYM (__cmpsf2)
|#PROLOGUE# 2
unlk a6
|#PROLOGUE# 3
rts
#endif /* L_gesf2 */
#ifdef L_ltsf2
.text
.proc
|#PROC# 04
LF18 = 8
LS18 = 132
LFF18 = 0
LSS18 = 0
LV18 = 0
.text
.globl SYM (__ltsf2)
SYM (__ltsf2):
|#PROLOGUE# 0
link a6,IMM (0)
|#PROLOGUE# 1
movl a6@(12),sp@-
movl a6@(8),sp@-
jbsr SYM (__cmpsf2)
|#PROLOGUE# 2
unlk a6
|#PROLOGUE# 3
rts
#endif /* L_ltsf2 */
#ifdef L_lesf2
.text
.proc
|#PROC# 04
LF18 = 8
LS18 = 132
LFF18 = 0
LSS18 = 0
LV18 = 0
.text
.globl SYM (__lesf2)
SYM (__lesf2):
|#PROLOGUE# 0
link a6,IMM (0)
|#PROLOGUE# 1
movl a6@(12),sp@-
movl a6@(8),sp@-
jbsr SYM (__cmpsf2)
|#PROLOGUE# 2
unlk a6
|#PROLOGUE# 3
rts
#endif /* L_lesf2 */
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