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Assembly Source File | 1995-06-15 | 79.5 KB | 2,977 lines

/* 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 */