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calc_arithm.S
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calc_arithm.S
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; ****************************************************************************
;
; Calculator arithmetics and bitwise operations (2 operands)
;
; ****************************************************************************
#include "include.inc"
.text
; ----------------------------------------------------------------------------
; Prepare number for multiplication and division
; ----------------------------------------------------------------------------
; INPUT: R23 = previous sign flag
; R31:R30 (Z) = pointer to the number
; R_ZERO = 0
; OUTPUT: R23 = new sign flag
; flag Z = number is zero (and C is not set)
; flag C = number is overflow (and Z is not set)
; DESTROYS: R24, R25
; ----------------------------------------------------------------------------
; Get sign bit and restore hidden bit '1' of mantissa.
CalcPrepMul:
; ----- get exponent
ldd r25,Z+0 ; fetch exponent HIGH
ldd r24,Z+1 ; fetch exponent LOW
; ----- test for overflow (set C) and zero (set Z)
adiw r24,1
sbiw r24,1 ; check for zero (0x0001->0x0000->ZY) and overflow (0x0000->0xFFFF->CY)
breq CalcPrepMul9 ; number is zero
; ----- check sign and restore highest bit of the mantissa
; C will be not affected
ldd r24,Z+2 ; highest byte of the mantissa
eor r23,r24 ; flip sign flag
ori r24,B7 ; restore hidden highest bit of the mantissa
std Z+2,r24 ; save new highest byte
; here is Z flag cleared
CalcPrepMul9:
ret
; ===== here is rest of CalcMul function
; ----- 2nd number is overflow
CalcMul6:
; INPUT and OUTPUT: R31:R30 (Z), R27:R26 (X) = registers to exchange
; DESTROYS: -
rcall ExcXZ ; exchange pointers
; INPUT: R23 = previous sign flag
; R31:R30 (Z) = pointer to the number
; R_ZERO = 0
; OUTPUT: R23 = new sign flag
; flag Z = number is zero (and C is not set)
; flag C = number is overflow (and Z is not set)
; DESTROYS: R24, R25
rcall CalcPrepMul ; prepare 1st number
breq CalcMul7 ; 1st number is 0, result will be 1
; ----- 1st number is not 0, result will be overflow
CalcMul62:
; OUTPUT: CY = error flag
; DESTROYS: -
rcall CalcError ; set error flag
; OUTPUT: R31:R30 (Z) = pre-last number on calculator stack
; DESTROYS: -
rcall CalcPreTop ; get pre-last number -> Z
; INPUT: R31:R30 = float number
; DESTROYS: R_M1,...R_M10
rcall CalcZOver ; set number Z to overflow
rjmp CalcDel ; delete 2nd operand
; ----- result is 1 with error
CalcMul7:
; OUTPUT: CY = error flag
; DESTROYS: -
rcall CalcError ; set error flag
; OUTPUT: R31:R30 (Z) = pre-last number on calculator stack
; DESTROYS: -
rcall CalcPreTop ; get pre-last number -> Z
; INPUT: R31:R30 = float number
; DESTROYS: R_M1,...R_M10
push r23
rcall CalcZ1 ; set number Z to 1
pop r23
tst r23 ; check sign
brpl 2f ; result is positive
; DESTROYS: R31, R30, R25, R24
rcall CalcNeg ; result will be -1
; DESTROYS: R31, R30
; CALCULATOR STACK: -1
2: rjmp CalcDel ; delete 2nd operand
; ----- 2nd number is 0
CalcMul81:
; INPUT and OUTPUT: R31:R30 (Z), R27:R26 (X) = registers to exchange
; DESTROYS: -
rcall ExcXZ ; exchange pointers
; INPUT: R23 = previous sign flag
; R31:R30 (Z) = pointer to the number
; R_ZERO = 0
; OUTPUT: R23 = new sign flag
; flag Z = number is zero (and C is not set)
; flag C = number is overflow (and Z is not set)
; DESTROYS: R24, R25
rcall CalcPrepMul ; prepare 1st number
brcs CalcMul7 ; 1st number is overflow, result will be 1
; ----- result will be 0
CalcMul82:
; OUTPUT: R31:R30 (Z) = pre-last number on calculator stack
; DESTROYS: -
rcall CalcPreTop ; get pre-last number -> Z
; INPUT: R31:R30 = float number
; DESTROYS: R_M1,...R_M10
rcall CalcZ0 ; clear number Z
rjmp CalcDel ; delete 2nd operand
; ----------------------------------------------------------------------------
; Multiplicate two numbers on top of stack (C_MUL)
; ----------------------------------------------------------------------------
; DESTROYS: all
; CALCULATOR STACK: -1
; ----------------------------------------------------------------------------
.global CalcMul
CalcMul:
; ----- get last 2 numbers (1st -> X, 2nd -> Z)
; OUTPUT: R27:R26 (X) = pre-last number on calculator stack
; R31:R30 (Z) = last number on calculator stack
; DESTROYS: -
rcall CalcTop2
; ----- prepare numbers for multiplication; -> 1st number Z, 2nd number X, sign bit R_MS (not masked)
; INPUT: R23 = previous sign flag
; R31:R30 (Z) = pointer to the number
; R_ZERO = 0
; OUTPUT: R23 = new sign flag
; flag Z = number is zero (and C is not set)
; flag C = number is overflow (and Z is not set)
; DESTROYS: R24, R25
clr r23 ; prepare sign flag = 0
rcall CalcPrepMul ; prepare 2nd number
brcs CalcMul6 ; 2nd number is overflow
breq CalcMul81 ; 2nd number is zero
; INPUT and OUTPUT: R31:R30 (Z), R27:R26 (X) = registers to exchange
; DESTROYS: -
rcall ExcXZ ; exchange pointers
; INPUT: R23 = previous sign flag
; R31:R30 (Z) = pointer to the number
; R_ZERO = 0
; OUTPUT: R23 = new sign flag
; flag Z = number is zero (and C is not set)
; flag C = number is overflow (and Z is not set)
; DESTROYS: R24, R25
rcall CalcPrepMul ; prepare 1st number
brcs CalcMul62 ; 1st number is overflow, result is overflow
breq CalcMul82 ; 1st number is zero, result will be 0
mov R_MS,r23 ; sign flag
; ----- fetch 2 numbers and delete 2nd number:
; 1st number Z -> R_M1..R_M10
; 2nd number X -> R_N1..R_N10
; INPUT: R31:R30 (Z) = pointer to 1st number
; R27:R26 (X) = pointer to 2nd number
; OUTPUT: R_M1..R_M10 = 1st number (from Z)
; R_N1..R:N10 = 2nd number (from X)
; DESTROYS: R31, R30, R27, R26
; CALCULATOR STACK: -1
rcall CalcFetch2
; ----- sum exponents -> R_MT:R_M1:R_M2
clr R_MT ; exponent HIGH
add R_M2,R_N2 ; sum both exponents
adc R_M1,R_N1
adc R_MT,R_MT ; high carry
; ----- multiplication of mantissas, R_M3..R_M10 * R_N3..R_N10 -> R_M3..R_M10, R_M11
; INPUT: R_M3..R_M10 = 1st multiplier
; R_N3..R_N10 = 2nd multiplier
; OUTPUT: R_M3..R_M10, R_M11 = result (not rounded)
; R1 = 0
; DESTROYS: R_A3 (R31), R_A4 (R30), R_A7 (R27), R_A8 (R26), R0
rcall MulMant
; ----- prepare exponent -> R_MT:R_EXH:R_EXL
movw R_EXL,R_M2 ; exponent
subi R_EXL,lo8(EXP_BIAS-1) ; subtract exponent bias
sbci R_EXH,hi8(EXP_BIAS-1)
sbc R_MT,R_ZERO
; ----- normalize number: R_MS sign, R_M3..R_M10(:R_M11) mantissa, R_MT:R_EXH:R_EXL exponent
CalcMulNorm:
ldi R_M1,MANT_BITS-TRIM ; max. number of shifts (trim last bits for case of small differences)
CalcMulNorm2:
sbrc R_M3,7 ; check highest bit of mantissa
rjmp CalcMulNorm5 ; highest bit is on the position, number is normalized
lsl R_M11 ; get lower bit to round
; INPUT: R_M3..R_M10 mantissa
; C = input carry
; OUTPUT: R_M3..R_M10 mantissa shifted left
; C = output carry
; DESTROYS: -
rcall CalcMantRol ; rotate mantissa left (with carry)
sbiw R_EXL,1 ; decrement exponent
sbc R_MT,R_ZERO ; carry
dec R_M1 ; bit counter
brne CalcMulNorm2
; ----- underflow, reset result to 0
; OUTPUT: R_M1..R_M10 number (= 0)
; DESTROYS: -
CalcMulUnder:
rcall CalcClearNum ; clear result
rjmp CalcMulSave ; save result
; ----- round up
CalcMulNorm5:
lsl R_M11 ; check lowest bit
brcc CalcMulNorm6 ; no carry
; INPUT: R_M3..R_M10 = mantissa
; R_ZERO = 0
; OUTPUT: returns Z flag if result is 0 (overflow from 0xFF 0xFF 0xFF...)
; DESTROYS: -
rcall CalcMantInc ; increment mantissa
brne CalcMulNorm6 ; result is not 0
ldi R_M3,0x80 ; overflow, set value to 0x80 0x00 0x00 0x00 0x00 0x00
adiw R_EXL,1 ; increment exponent R_EXH:R_EXL
adc R_MT,R_ZERO ; carry
; ----- check exponent
CalcMulNorm6:
tst R_MT ; check exponent HIGH
brmi CalcMulUnder ; underflow
brne CalcMulOver ; overflow
cp R_EXL,R_ZERO ; check minimal exponent
cpc R_EXH,R_ZERO
breq CalcMulUnder ; underflow
ldi R_M1,hi8(EXP_MAX+1)
cpi R_EXL,lo8(EXP_MAX+1) ; check maximal exponent
cpc R_EXH,R_M1
brcc CalcMulOver ; overflow
; ----- prepare 1st byte of mantissa -> R_M3
andi R_M3,0x7f ; reset hidden highest bit "1"
andi R_MS,0x80 ; mask sign flag
or R_M3,R_MS ; put bits together
; ----- exponent -> R_M1:R_M2
movw R_M2,R_EXL
; ----- save result R_M1..R_M9
; OUTPUT: R31:R30 (Z) = last number on calculator stack
; DESTROYS: -
CalcMulSave:
rcall CalcTop ; get pointer to top number -> Z
; INPUT: R31:R30 (Z) = pointer to number
; R_M1..R_M10 number
; DESTROYS: -
rjmp CalcSaveNum ; save number
; ----- overflow error
CalcMulOver:
; OUTPUT: R31:R30 (Z) = last number on calculator stack
; DESTROYS: -
rcall CalcTop ; get pointer to top number -> Z
rcall CalcZOver ; set overflow value
; OUTPUT: CY = error flag
; DESTROYS: -
rjmp CalcError ; set error flag
; ----------------------------------------------------------------------------
; divide/2/4/8/16 (C_DIV2)
; ----------------------------------------------------------------------------
; DESTROYS: R31, R30, R25, R24
; ----------------------------------------------------------------------------
.global CalcDiv16
CalcDiv16:
rcall CalcDiv2
.global CalcDiv8
CalcDiv8:
rcall CalcDiv2
.global CalcDiv4
CalcDiv4:
rcall CalcDiv2
.global CalcDiv2
CalcDiv2:
; OUTPUT: R31:R30 (Z) = last number on calculator stack
; R25:R24 = exponent (0 = number is zero, 0xFFFF = overflow)
; ZY = number is 0
; CY = number is overflow
; DESTROYS: -
rcall CalcTopCheck ; get top number -> Z, R24
brcs CalcMulOver ; number is overflow
breq CalcDiv29 ; number is zero
sbiw r24,1 ; decrement exponent
CalcDiv26:
std Z+1,r24 ; set new exponent
std Z+0,r25
CalcDiv29:
ret
; ----------------------------------------------------------------------------
; multiply*2/4/8/16 (C_MUL2)
; ----------------------------------------------------------------------------
; DESTROYS: R31, R30, R25, R24
; ----------------------------------------------------------------------------
.global CalcMul16
CalcMul16:
rcall CalcMul2
.global CalcMul8
CalcMul8:
rcall CalcMul2
.global CalcMul4
CalcMul4:
rcall CalcMul2
.global CalcMul2
CalcMul2:
; OUTPUT: R31:R30 (Z) = last number on calculator stack
; R25:R24 = exponent (0 = number is zero, 0xFFFF = overflow)
; ZY = number is 0
; CY = number is overflow
; DESTROYS: -
rcall CalcTopCheck ; get top number -> Z, R24
brcs CalcMulOver ; number is overflow
breq CalcDiv29 ; number is zero
adiw r24,1 ; increment exponent
rjmp CalcDiv26 ; set new exponent
; ----------------------------------------------------------------------------
; < (C_LEFT)
; ----------------------------------------------------------------------------
.global CalcLeft
CalcLeft:
; ----- load 2nd operand - number of shifts
; OUTPUT: R25:R24 = unsigned integer
; R_M3 = negative flag (0 or B7)
; C flag is set = overflow valid range
; Z flag is set = number is positive or 0 (breq), NZ = number is negative (brne)
; DESTROYS: R31, R30, R_M1..R_M10
; CALCULATOR STACK: -1
rcall CalcUnstackW
brcs CalcMulOver ; number is overflow
movw r22,r24 ; save number of shifts
; ----- load current exponent
; OUTPUT: R31:R30 (Z) = last number on calculator stack
; R25:R24 = exponent (0 = number is zero, 0xFFFF = overflow)
; ZY = number is 0
; CY = number is overflow
; DESTROYS: -
rcall CalcTopCheck ; get top number -> Z, R24
brcs CalcMulOver ; number is overflow
breq CalcDiv29 ; number is zero
; ----- shift exponent
add r24,r22
adc r25,r23
brcs CalcMulOver ; overflow
rjmp CalcDiv26 ; set new exponent
; ----------------------------------------------------------------------------
; > (C_RIGHT)
; ----------------------------------------------------------------------------
.global CalcRight
CalcRight:
; ----- load 2nd operand - number of shifts
; OUTPUT: R25:R24 = unsigned integer
; R_M3 = negative flag (0 or B7)
; C flag is set = overflow valid range
; Z flag is set = number is positive or 0 (breq), NZ = number is negative (brne)
; DESTROYS: R31, R30, R_M1..R_M10
; CALCULATOR STACK: -1
rcall CalcUnstackW
brcs CalcMulOver ; number is overflow
movw r22,r24 ; save number of shifts
; ----- load current exponent
; OUTPUT: R31:R30 (Z) = last number on calculator stack
; R25:R24 = exponent (0 = number is zero, 0xFFFF = overflow)
; ZY = number is 0
; CY = number is overflow
; DESTROYS: -
rcall CalcTopCheck ; get top number -> Z, R24
brcs CalcMulOver ; number is overflow
breq CalcDiv29 ; number is zero
; ----- shift exponent
sub r24,r22
sbc r25,r23
brcc CalcDiv26 ; set new exponent
clr r24
clr r25 ; number will be 0
rjmp CalcDiv26 ; set new exponent
; ===== here is rest of CalcDiv function
; ----- 2nd number is 0
CalcDiv6:
; INPUT and OUTPUT: R31:R30 (Z), R27:R26 (X) = registers to exchange
; DESTROYS: -
rcall ExcXZ ; exchange pointers
; INPUT: R23 = previous sign flag
; R31:R30 (Z) = pointer to the number
; R_ZERO = 0
; OUTPUT: R23 = new sign flag
; flag Z = number is zero (and C is not set)
; flag C = number is overflow (and Z is not set)
; DESTROYS: R24, R25
rcall CalcPrepMul ; prepare 1st number
breq CalcDiv7 ; 1st number is 0, result will be 1
; ----- 1st number is not zero, result will be overflow
CalcDiv62:
rjmp CalcMul62
; ----- result is 1 with error
CalcDiv7:
rjmp CalcMul7
; ----- 2nd number is overflow
CalcDiv81:
; INPUT and OUTPUT: R31:R30 (Z), R27:R26 (X) = registers to exchange
; DESTROYS: -
rcall ExcXZ ; exchange pointers
; INPUT: R23 = previous sign flag
; R31:R30 (Z) = pointer to the number
; R_ZERO = 0
; OUTPUT: R23 = new sign flag
; flag Z = number is zero (and C is not set)
; flag C = number is overflow (and Z is not set)
; DESTROYS: R24, R25
rcall CalcPrepMul ; prepare 1st number
brcs CalcDiv7 ; 1st number is overflow, result will be 1
; ----- result will be 0
CalcDiv82:
rjmp CalcMul82
; ----------------------------------------------------------------------------
; Division (C_DIV)
; ----------------------------------------------------------------------------
; DESTROYS: all
; CALCULATOR STACK: -1
; ----------------------------------------------------------------------------
.global CalcDiv
CalcDiv:
; ----- get last 2 numbers (1st -> X, 2nd -> Z)
; OUTPUT: R27:R26 (X) = pre-last number on calculator stack
; R31:R30 (Z) = last number on calculator stack
; DESTROYS: -
rcall CalcTop2
; ----- prepare numbers for division; -> 1st number Z, 2nd number X, sign bit R_MS (not masked)
; INPUT: R23 = previous sign flag
; R31:R30 (Z) = pointer to the number
; R_ZERO = 0
; OUTPUT: R23 = new sign flag
; flag Z = number is zero (and C is not set)
; flag C = number is overflow (and Z is not set)
; DESTROYS: R24, R25
clr r23 ; prepare sign flag = 0
rcall CalcPrepMul ; prepare 2nd number
brcs CalcDiv81 ; 2nd number is overflow
breq CalcDiv6 ; 2nd number is zero
; INPUT and OUTPUT: R31:R30 (Z), R27:R26 (X) = registers to exchange
; DESTROYS: -
rcall ExcXZ ; exchange pointers
; INPUT: R23 = previous sign flag
; R31:R30 (Z) = pointer to the number
; R_ZERO = 0
; OUTPUT: R23 = new sign flag
; flag Z = number is zero (and C is not set)
; flag C = number is overflow (and Z is not set)
; DESTROYS: R24, R25
rcall CalcPrepMul ; prepare 1st number
brcs CalcDiv62 ; 1st number is overflow, result is overflow
breq CalcDiv82 ; 1st number is zero, result will be 0
mov R_MS,r23 ; sign flag
; ----- fetch 2 numbers and delete 2nd number:
; 1st number Z -> R_M1..R_M10
; 2nd number X -> R_N1..R_N10
; INPUT: R31:R30 (Z) = pointer to 1st number
; R27:R26 (X) = pointer to 2nd number
; OUTPUT: R_M1..R_M10 = 1st number (from Z)
; R_N1..R_N10 = 2nd number (from X)
; DESTROYS: R31, R30, R27, R26
; CALCULATOR STACK: -1
rcall CalcFetch2
; ----- division of mantissas, dividend R_M3..R_M10 / divisor R_N3..R_N10 -> quotient R_R3..R_R10
push R_MS ; push result sign
; push registers
push r28
push r29
; prepare loop counter
ldi r31,-(MANT_BITS+1) ; negative 'number of loops + 1'
mov r1,r31 ; loop counter
; clear quotient result LOW
clr R_R10
clr r0 ; accumulator of 2 extra bits
rjmp CalcDivLoop4 ; start loop (carry is undefined, but not needed now)
CalcDivLoop:
; shift quotient left, adding result carry from right
rol R_R10
rol R_R9
rol R_R8
rol R_R7
rol R_R6
rol R_R5
rol R_R4
rol R_R3
CalcDivLoop2:
; shift dividend left
clc ; clear carry
; INPUT: R_M3..R_M10 mantissa
; C = input carry
; OUTPUT: R_M3..R_M10 mantissa shifted left
; C = output carry
; DESTROYS: -
rcall CalcMantRol ; rotate mantissa left
brcs CalcDivLoop6 ; carry - dividend is higher than divisor, subtract only (result bit will be 1)
CalcDivLoop4:
; try to subtract divisor from dividend
; INPUT: R_M3..R_M10 mantissa 1
; R_N3..R_N10 mantissa 2
; OUTPUT: R_M3..R_M10 result
; C = output borrow
; DESTROYS: -
rcall CalcMantSub
brcc CalcDivLoop8 ; no cary, no restore (dividend is not smaller than divisor, result bit will be 1)
; carry is set - dividend is smaler than divisor, restore dividend (result bit will be 0)
; INPUT: R_M3..R_M10 mantissa 1
; R_N3..R_N10 mantissa 2
; OUTPUT: R_M3..R_M10 result
; C = output carry
; DESTROYS: -
rcall CalcMantAdd
clc ; clear carry flag
rjmp CalcDivLoop9 ; result bit will be 0
CalcDivLoop6:
; subtract only, result bit will be 1
; INPUT: R_M3..R_M10 mantissa 1
; R_N3..R_N10 mantissa 2
; OUTPUT: R_M3..R_M10 result
; C = output borrow
; DESTROYS: -
rcall CalcMantSub
CalcDivLoop8:
; result bit is 1
sec ; set carry flag, result bit is 1
CalcDivLoop9:
; loop counter
inc r1 ; loop counter (C stays untouched)
brmi CalcDivLoop ; do MANT_BITS loops, while loop counter is negativ
; one extra loop, to get one extra bit (we already have one bit in carry)
rol r0 ; save last 2 bits
tst r1 ; check loop counter
breq CalcDivLoop2 ; one extra loop
; ----- difference of exponents (warning R_M11 = R_N1)
sub R_M2,R_N2 ; difference of exponents
sbc R_M1,R_N1
sbc r1,r1 ; high carry
; ----- prepare extra result byte -> R_M11 (extra 2 bits)
mov R_M11,r0 ; extra bits accumulator
ror R_M11
ror R_M11
ror R_M11 ; sihft last 2 bits to position 6 and 7
; ----- prepare mantissa -> R_M3..R_M10
movw R_M10,R_R10
movw R_M8,R_R8
movw R_M6,R_R6
movw R_M4,R_R4
; ----- prepare exponent -> R1:R_EXH:R_EXL
ldi r28,-1
movw R_EXL,R_M2 ; exponent
subi R_EXL,lo8(-EXP_BIAS) ; add exponent bias
sbci R_EXH,hi8(-EXP_BIAS)
sbc r1,r28
mov R_MT,r1 ; exponent HIGH
; ----- pop registers
pop r29
pop r28
clr R_ZERO ; restore R1
; ----- prepare sign -> R_MS
pop R_MS ; pop result sign
; ----- normalize number: R_MS sign, R_M3..R_M10(:R_M11) mantissa, R_MT:R_EXH:R_EXL exponent
rjmp CalcMulNorm
; ----------------------------------------------------------------------------
; Modulus with trunc rounding (C_MOD)
; ----------------------------------------------------------------------------
; DESTROYS: stack, R31, R30
; ----------------------------------------------------------------------------
; - result has same sign as divisor
.global CalcMod
CalcMod:
rcall Calc
.byte C_DUP2 ; pre-duplicate (a,b,a)
.byte C_DUP2 ; pre-duplicate (a,b,a,b)
.byte C_DIV ; division (a,b,a/b)
.byte C_TRUNC ; trunc (a,b,trunc(a/b))
.byte C_MUL ; multiply (a,b*trunc(a/b))
.byte C_SUB ; subtract (a-b*trunc(a/b))
.byte C_END ; end
.balign 2 ; align
ret
; ----------------------------------------------------------------------------
; Modulus with floor rounding (C_MOD2)
; ----------------------------------------------------------------------------
; DESTROYS: stack, R31, R30
; ----------------------------------------------------------------------------
; - result has same sign as dividend
.global CalcMod2
CalcMod2:
rcall Calc
.byte C_DUP2 ; pre-duplicate (a,b,a)
.byte C_DUP2 ; pre-duplicate (a,b,a,b)
.byte C_DIV ; division (a,b,a/b)
.byte C_FLOOR ; floor (a,b,floor(a/b))
.byte C_MUL ; multiply (a,b*floor(a/b))
.byte C_SUB ; subtract (a-b*floor(a/b))
.byte C_END ; end
.balign 2 ; align
ret
; ----------------------------------------------------------------------------
; Prepare number for addition and bit operation
; ----------------------------------------------------------------------------
; INPUT: R31:R30 (Z) = pointer to the number
; OUTPUT: R_R9:R_R10 = exponent
; DESTROYS: R_M1..R_M10
; ----------------------------------------------------------------------------
; Clear exponent and expand mantissa to 9 bytes signed.
CalcPrepAdd:
; ----- load number -> R_M1..R_M10
; INPUT: R31:R30 (Z) = pointer to number
; OUTPUT: R_M1..R_M10 number
; DESTROYS: -
rcall CalcLoadNum
; ----- get exponent and test for zero, clear 2nd byte - next highest byte of mantissa
movw R_R10,R_M2 ; exponent LOW and HIGH
clr R_M2 ; clear exponent LOW byte
adiw R_R10,0 ; zero number?
breq CalcPrepAdd9 ; number is zero
; ----- check sign and restore highest bit of the mantissa
bst R_M3,7 ; load sign bit into T flag
ori R_M3,B7 ; restore hidden highest bit of the mantissa
brtc CalcPrepAdd8 ; number is positive, all ok
; ----- negate extended mantissa (R_M2..R_M10)
; INPUT: R_M2..R_M10 extended mantissa
; R_ZERO = 0
; OUTPUT: R_M2..R_M10 extended mantissa negated
; CY = carry set if result is not 0
; DESTROYS: -
rcall CalcMantNeg ; negate number R_M2..R_M10
; ----- save number
CalcPrepAdd8:
; INPUT: R31:R30 (Z) = pointer to number
; R_M1..R_M10 number
; DESTROYS: -
rjmp CalcSaveNum
; ----- number is 0 (need to clear - mantissa may be not zeroed)
; OUTPUT: R_M1..R_M10 number (= 0)
; DESTROYS: -
CalcPrepAdd9:
rcall CalcClearNum ; clear number R_M1..R_M10
; INPUT: R31:R30 (Z) = pointer to number
; R_M1..R_M10 number
; DESTROYS: -
rjmp CalcSaveNum
; ----------------------------------------------------------------------------
; Shift 1st number right
; ----------------------------------------------------------------------------
; INPUT: R_R9:R_R10 = number of shifts
; R_M2..R_M10 = extended mantissa (R_M2=0x00 or 0xFF)
; DESTROYS: R_R10
; ----------------------------------------------------------------------------
CalcAddShift:
; ----- check number of shifts
adiw R_R10,0 ; check zero
breq CalcAddShift9 ; no shift needed
; ----- check overflow
tst R_R9 ; check number of shifts HIGH
brne CalcAddShift6 ; overflow, clear number R_M2..R_M10
cpi R_R10,MANT_BITS+1 ; max. size of mantissa
brcc CalcAddShift6 ; overflow difference, clear the number R_M2..R_M10
; ----- rotate mantissa right
CalcAddShift2:
asr R_M2 ; bit 7 unchanged
; INPUT: R_M3..R_M10 mantissa
; C = input carry
; OUTPUT: R_M3..R_M10 mantissa shifted right
; C = output carry
; DESTROYS: -
rcall CalcMantRor ; rotate mantissa right (with carry)
dec R_R10
brne CalcAddShift2
; ----- round up, if last shiftet bit was set
; INPUT: R_M3..R_M10 = mantissa
; OUTPUT: returns Z flag if result is 0 (overflow from 0xFF 0xFF 0xFF 0xFF 0xFF)
brcc CalcAddShift9 ; no carry bits
; INPUT: R_M3..R_M10 = mantissa
; R_ZERO = 0
; OUTPUT: returns Z flag if result is 0 (overflow from 0xFF 0xFF 0xFF...)
; DESTROYS: -
rcall CalcMantInc ; increment mantissa
sbci R_M2,0xff
brne CalcAddShift9 ; no overflow
CalcAddShift6:
; OUTPUT: R_M2..R_M10 number (= 0)
; DESTROYS: -
rjmp CalcClearNum2 ; clear result R_M2..R_M10
CalcAddShift9:
ret
; ----------------------------------------------------------------------------
; Subtraction (C_SUB)
; ----------------------------------------------------------------------------
; DESTROYS: all
; CALCULATOR STACK: -1
; ----------------------------------------------------------------------------
.global CalcSub
CalcSub:
; ----- negate second number
; DESTROYS: R31, R30, R25, R24
rcall CalcNeg
; CalcAdd must follow
; ----------------------------------------------------------------------------
; Addition (C_ADD)
; ----------------------------------------------------------------------------
; DESTROYS: all
; CALCULATOR STACK: -1
; ----------------------------------------------------------------------------
.global CalcAdd
CalcAdd:
; ----- get last 2 numbers (1st -> X, 2nd -> Z)
; OUTPUT: R27:R26 (X) = pre-last number on calculator stack
; R31:R30 (Z) = last number on calculator stack
; DESTROYS: -
rcall CalcTop2
; ----- prepare numbers for addition; 1st exponent -> R_R9:R_R10/Z, 2nd exponent -> R_N9:R_N10/X
; INPUT: R31:R30 (Z) = pointer to the number
; OUTPUT: R_R9:R_R10 = exponent
; DESTROYS: R_M1..R_M10
rcall CalcPrepAdd ; prepare 2nd number
movw R_N10,R_R10 ; save 2nd exponent -> R_N9:R_N10
; INPUT and OUTPUT: R31:R30 (Z), R27:R26 (X) = registers to exchange
; DESTROYS: -
rcall ExcXZ ; exchange pointers
rcall CalcPrepAdd ; prepare 1st number, 1st exponent -> R_R9:R_R10
; ----- sort numbers - 2nd exponent must not be less than 1st one
cp R_N10,R_R10 ; compare exponents
cpc R_N9,R_R9 ; compare exponents
brcc CalcAdd2 ; 2nd exponent is higher or equal, it is OK
; INPUT and OUTPUT: R31:R30 (Z), R27:R26 (X) = registers to exchange
; DESTROYS: -
rcall ExcXZ ; exchange pointers
eor R_R10,R_N10 ; exchange exponents
eor R_N10,R_R10
eor R_R10,R_N10
eor R_R9,R_N9 ; exchange exponents
eor R_N9,R_R9
eor R_R9,R_N9
CalcAdd2:
; ----- fetch 2 numbers and delete 2nd number:
; 1st number Z -> (R_R9:R_R10) R_M1..R_M10
; 2nd number X -> (R_R7:R_R8) R_N1..R_N10
; INPUT: R31:R30 (Z) = pointer to 1st number
; R27:R26 (X) = pointer to 2nd number
; OUTPUT: R_M1..R_M10 = 1st number (from Z)
; R_N1..R_N10 = 2nd number (from X)
; DESTROYS: R31, R30, R27, R26
; CALCULATOR STACK: -1
push R_N9
push R_N10
rcall CalcFetch2
pop R_R8
pop R_R7
; ----- save new exponent (= exponent of 2nd number) -> R_EXH:R_EXL
; ... already R_EXH:R_EXL = R_R7:R_R8
; movw R_EXL,R_R8
; ----- difference of exponents (= 2nd exponent - 1st exponent; result is >= 0) -> R_R9:R_R10
sub R_R10,R_R8 ; 1st exponent - 2nd exponent
sbc R_R9,R_R7
com R_R9
neg R_R10
sbci R_R9,0xff ; negate difference
; ----- shift 1st number right to normalize numbers to the same exponent
; INPUT: R_R9:R_R10 = number of shifts
; R_M2..R_M10 = extended mantissa (R_M2=0x00 or 0xFF)
; DESTROYS: R_R10
rcall CalcAddShift
; ----- add both numbers (here is R_M2=0x00 or 0xFF, R_N2=0x00 or 0xFF)
; INPUT: R_M3..R_M10 mantissa 1
; R_N3..R_N10 mantissa 2
; OUTPUT: R_M3..R_M10 result
; C = output carry
; DESTROYS: -
rcall CalcMantAdd ; add mantissas
adc R_M2,R_N2
; ----- negate result
mov R_MS,R_M2 ; get sign
andi R_MS,B7 ; isolate sign sign
breq CalcAdd3 ; number is not negative
; INPUT: R_M2..R_M10 extended mantissa
; R_ZERO = 0
; OUTPUT: R_M2..R_M10 extended mantissa negated
; CY = carry set if result is not 0
; DESTROYS: -
rcall CalcMantNeg ; negate mantissa
brcs CalcAdd3 ; result is not 0
rjmp CalcMulUnder ; underflow (difference is 0)
; ----- check overflow = highest byte is 0x01
CalcAdd3:
clr R_MT ; exponent HIGH = 0
tst R_M2
breq CalcAdd6 ; no overflow
; ----- overflow - shift result right and increment exponent
; INPUT: R_R9:R_R10 = number of shifts
; R_M2..R_M10 = normalized number (mantissa, R_M2=0x00 or 0xFF)
; DESTROYS: R_R10
ldi R_R10,1 ; number of shifts = 1
rcall CalcAddShift2 ; shift result right
adiw R_EXL,1 ; increment exponent R_EXH:R_EXL
adc R_MT,R_MT ; exponent HIGH
; ----- normalize number: R_MS sign, R_M3..R_M10(:R_M11) mantissa, R_MT:R_EXH:R_EXL exponent
CalcAdd6:
clr R_M11 ; R_M11 <- 0, mantissa extra lowest byte
rjmp CalcMulNorm ; normalize result
; ----------------------------------------------------------------------------
; Square root (C_SQRT)
; ----------------------------------------------------------------------------
; DESTROYS: all
; USES: TEMP_1, TEMP_2, TEMP_3, TEMP_4
; ----------------------------------------------------------------------------
.global CalcSqrt
CalcSqrt:
rcall Calc
; offset 0: number is zero, result will be zero
.byte C_JUMPZ ; jump if zero
.byte 9 ; jump to offset 5 of CalcPow (5 + 6 - 2 = 9)
; offset 2
.byte C_CONST(CONST_05) ; load constant 0.5 (x,0.5)
.byte C_END ; end