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mac-rom/Toolbox/InSANE/ELEMS020_2.a
Elliot Nunn 4325cdcc78 Bring in CubeE sources 
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;
; File: ELEMS020_2.a
;
; Contains: xxx put contents here xxx
;
; Written by: The Apple Numerics Group
;
; Copyright: © 1990-1992 by Apple Computer, Inc., all rights reserved.
;
; This file is used in these builds: Mac32
;
; Change History (most recent first):
;
; <SM2> 2/3/93 CSS Update from Horror:
; <H2> 9/29/92 BG Rolling in Jon Okada's latest fixes.
; <1> 11/14/90 BG Added to BBS for the first time.
;
; To Do:
;
;-----------------------------------------------------------
; CHANGE HISTORY, kept for historical purposes:
;
; 21 MAY 90 Signal underflow for all inexact, subnormal results
; of EXP and EXP2 [see EXPROOT below] and do faster test
; for extended zero [see EXP1ROOT and EXPAPPROX below] (JPO)
; 29 APR 92 Filter out very large and small magnitude inputs for
; exponential functions, thus avoiding spurious exceptions and
; large magnitude SCALB factors (JPO)
;-----------------------------------------------------------
;-----------------------------------------------------------
;-----------------------------------------------------------
; EXP(x) and EXP2(x) share the same exception code. To compute
; numerical results, express result as 2^K * ((2^frac - 1) + 1),
; and use EXPAPPROX to figure (2^frac - 1).
;-----------------------------------------------------------
;-----------------------------------------------------------
EXPTOP:
SUBQ.B #1,D1 ; HAVE SUB #CLINF ALREADY
; BEQ.S P1STUFF ; EXP(+-0) IS +1 MOVED below <4/29/92, JPO>
BGT.S EXPNONZERO
BEQ.S P1STUFF ; EXP(+-0) IS +1 <4/29/92, JPO>
TST.W D1
BMI.S P0STUFF ; EXP(-INF) IS +0
BRA.S RESULTDELIVERED ; ALREADY HAVE +INF
;-----------------------------------------------------------
; Limit argument to range |arg| >= 2^(-64) and |arg| <= 16447. This will guarantee
; that the integral scale parameter will fit in 16-bit integer format. <4/29/92, JPO>
;-----------------------------------------------------------
EXPNONZERO:
BFEXTU (A4){1:31},D0 ; D0 <- first 32 bits of |arg| <4/29/92, JPO>
CMPI.L #$3FBF8000,D0 ; |arg| < 2.0^(-64)? <4/29/92, JPO>
BLT.B P1XSTUFF ; exp(+-tiny) is inexact +1 <4/29/92, JPO>
CMPI.L #$400D807E,D0 ; |arg| > 16447.0? <4/29/92, JPO>
BLE.B @expok ; no <4/29/92, JPO>
TST.W D1 ; yes. check sign of arg <4/29/92, JPO>
BMI P0XSTUFF ; exp(-large) underflows to zero <4/29/92, JPO>
BRA.B PINFXSTUFF ; exp(large) overflows to +INF <4/29/92, JPO>
@expok: ; label ADDED <4/29/92, JPO>
BTST #BTLOGBASE2,D3 ; NONZERO IF EXP2X
BEQ.S EXPR
;-----------------------------------------------------------
; 2^T is easy, for general T.
; Set cell W to integer part of T.
; Set T to fraction part of itself.
; Use root computation to evaluate 2^T - 1 with LOGAPPROX;
; add 1 to T, and scale by W.
;-----------------------------------------------------------
;EXP2R: ; label DELETED <4/29/92, JPO>
BSR.S SPLIT2
BRA.S EXPROOT
;-----------------------------------------------------------
; EXP(T) is just slightly more complicated than EXP2(T) above.
; Let T = K * LN(2) + F
; Then EXP(T) is 2^K + ((2^(F/LN(2)) - 1) + 1).
; So use EXP2ROOT with W set to K and T set to F/LN(2).
; Find F with REM modulo LN(2); then subtract from T and divide by LN(2)
; to get K.
;-----------------------------------------------------------
; ***NOTE*** Spurious OVERFLOW is prevented by pre-filtering of input <4/29/92, JPO>
EXPR:
BSR.S SPLIT
; BSR TESTOFLOW ; DELETED <4/29/92, JPO>
; BEQ.S EXPROOT ; DELETED <4/29/92, JPO>
; BSR FORCEINEXACT ; EITHER O/UFLOW DELETED <4/29/92, JPO>
; TST.W D1 ; OPERAND SIGN DELETED <4/29/92, JPO>
; BPL.S PINFSTUFF ; OFLOW TO +INF DELETED <4/29/92, JPO>
; BSR CLEAROFLOW ; DELETED <4/29/92, JPO>
; BSR FORCEUFLOW ; DELETED <4/29/92, JPO>
; BRA P0STUFF ; DELETED <4/29/92, JPO>
;-----------------------------------------------------------
; This is the root of V^X where V is 2 or E.
; Compute ((2^T - 1) + 1) * 2*W. EXPAPPROX gives the innermost
; expression. W is presumed to be an integer, possibly huge.
;-----------------------------------------------------------
EXPROOT:
BSR EXPAPPROX ; 2^T - 1
PEA FPK1 ; (2^T - 1) + 1
PEA (A4)
ELFADDX
MOVEA.L A4,A0 ; RESULT PTR
LEA STW(A6),A1 ; INTEGER PART
BSR SCALBXX
; TST.W 2(A4) ; if result is subnormal and inexact, DELETED <4/29/92, JPO>
; BMI.S RESULTDELIVERED ; raise UNDERFLOW exception <21 MAY 90, JPO> DELETED <4/29/92, JPO>
; BFEXTU (A4){1:15},D0 ; DELETED <4/29/92, JPO>
; BNE.S RESULTDELIVERED ; DELETED <4/29/92, JPO>
BFTST (A4){1:16} ; if result is subnormal or zero and inexact, <4/29/92, JPO>
BNE.S RESULTDELIVERED ; raise underflow exception <4/29/92, JPO>
BSR TESTINEXACT
BEQ.S RESULTDELIVERED
BSR FORCEUFLOW
BRA.S RESULTDELIVERED
;-----------------------------------------------------------
; Given general number in T, split into integer part in W
; and fraction in T, rounding.
;-----------------------------------------------------------
SPLIT2:
MOVEA.L A4,A0
LEA STW(A6),A1
BSR A0TOA1 ; COPY T
PEA (A1) ; CELL W
ELFRINTX ; INTEGER PART OF T, ROUNDED
; BSR CLEARINEXACT ; DON'T RECORD ROUNDING ERROR DELETED <4/29/92, JPO>
PEA (A1) ; INTEGER PART
PEA (A4) ; ALL OF NUMBER
ELFSUBX
RTS
;-----------------------------------------------------------
; Split T for EXP(x) and EXP(x)-1.
; Let T = K * LN(2) + F. Want W=K and T=F/LN(2).
; Find F with REM modulo LN(2); then subtract from T and divide by LN(2)
; to get K.
;-----------------------------------------------------------
SPLIT:
MOVEA.L A4,A0 ; T POINTER
LEA STW(A6),A1 ; COPY T INTO CELL W
BSR A0TOA1
PEA FPKLOGE2 ; NEED 3 COPIES OF LN(2)
MOVE.L (SP),-(SP)
MOVE.L (SP),-(SP)
PEA (A4)
ELFREMX ; T REM LN(2) IN T
PEA (A4)
PEA (A1)
ELFSUBX ; T - (T REM LN(2)) IN W
PEA (A1)
ELFDIVX ; T - (T REM...) / LN(2)
PEA (A1)
ELFRINTX ; MAKE SURE IT'S AN INT
PEA (A4)
ELFDIVX ; (T REM LN(2)) / LN(2)
; BRA CLEARINEXACT ; ...AND EXIT DELETED <4/29/92, JPO>
RTS ; EXIT <4/29/92, JPO>
;-----------------------------------------------------------
; EXP(x)-1 and EXP2(x)-1 share the same exception code. They both exploit
; EXPAPPROX for the root computation 2^frac - 1.
;-----------------------------------------------------------
EXP1TOP:
SUBQ.B #1,D1 ; SUBTRACTED #CLINF BEFORE
BGT.S EXP1FINITE ; FINITE, NONZERO
BEQ.S EXPEASY ; Y^+-0 - 1 IS +-0
TST.W D1 ; TEST SIGN OF INF
BMI M1STUFF ; Y^-INF - 1 IS -1
EXPEASY:
BRA RESULTDELIVERED ; Y^+INF - 1 IS +INF
EXP1FINITE:
;-----------------------------------------------------------
; If the number is denormalized, have easy case whether EXP1 or EXP21.
; Have subtracted #CLZERO so far. Subtracting 1 more from D1.B leaves
; 0 if normalized, 1 if denormalized.
;-----------------------------------------------------------
; SUBQ.B #1,D1 ; 0-NORM 1-DENORM DELETED <4/29/92, JPO>
;-----------------------------------------------------------
; Limit argument to range -64.0 <= arg <= +16384. This will guarantee
; that the integral scale parameter will fit in 16-bit integer format. <4/29/92, JPO>
;-----------------------------------------------------------
BFEXTU (A4){1:31},D0 ; D0 <- first 32 bits of |arg| <4/29/92, JPO>
TST.W D1 ; check sign of arg <4/29/92, JPO>
BPL.B @exp1pos ; check for overflow <4/29/92, JPO>
CMPI.L #$40058000,D0 ; arg < -64.0 <4/29/92, JPO>
BLE.B @exp1ok ; no. <4/29/92, JPO>
BRA M1XSTUFF ; yes, return -1.0 and signal inexact <4/29/92, JPO>
@exp1pos:
CMPI.L #$400D8000,D0 ; arg > 16384? <4/29/92, JPO>
BGT PINFXSTUFF ; yes, overflow to +INF <4/29/92, JPO>
@exp1ok: ; label ADDED <4/29/92, JPO>
BTST #BTLOGBASE2,D3 ; NONZERO IF EXP2X
BEQ.S EXP1R
;-----------------------------------------------------------
; As above, for 2^T-1 split T into fraction part in T and integer
; in W, and go to root computation.
;-----------------------------------------------------------
;EXP21R: ; label DELETED <4/29/92, JPO>
; TST.B D1 ; DELETED <4/29/92, JPO>
; BEQ.S EXP21RNORM ; DELETED <4/29/92, JPO>
CMPI.L #$3FBF8000,D0 ; |arg| < 2.0^(-64)? <4/29/92, JPO>
BGE.B EXP21RNORM ; no <4/29/92, JPO>
PEA FPKLOGE2 ; 2^T-1 IS T*LN(2) FOR TINY T
PEA (A4)
ELFMULX
EXP1OUT:
; BSR FORCEUFLOW ; DELETED <4/29/92, JPO>
; BSR FORCEINEXACT ; DELETED <4/29/92, JPO>
; BRA.S EXP1RDONE ; DELETED <4/29/92, JPO>
BRA TINYX ; <4/29/92, JPO>
EXP21RNORM:
BSR SPLIT2 ; ???? WAS BSR.S
BRA.S EXP1ROOT
;-----------------------------------------------------------
; For E^T-1, split T into K and F/LN(2), where T = K*LN(2) + F.
; If overflow, then force INF or -1...
;-----------------------------------------------------------
EXP1R:
; TST.B D1 ; DELETED <4/29/92, JPO>
; BNE.S EXP1OUT ; E^T-1 IS T, WITH UFLOW FOR NOW DELETED <4/29/92, JPO>
CMPI.L #$3FBF8000,D0 ; |arg| < 2.0^(-64)? <4/29/92, JPO>
BLT.B EXP1OUT ; yes, return arg with proper flags <4/29/92, JPO>
; BSR.S SPLIT ; DELETED <4/29/92, JPO>
BSR SPLIT ; word branch <4/29/92, JPO>
; BSR TESTOFLOW ; DELETED <4/29/92, JPO>
; BEQ.S EXP1ROOT ; DELETED <4/29/92, JPO>
; BSR FORCEINEXACT ; EITHER O/UFLOW DELETED <4/29/92, JPO>
; TST.W D1 ; OPERAND SIGN DELETED <4/29/92, JPO>
; BPL PINFSTUFF ; OFLOW TO +INF DELETED <4/29/92, JPO>
; BSR CLEAROFLOW ; LEAVE INEXACT SET DELETED <4/29/92, JPO>
; BRA M1STUFF ; FORCE -1 DELETED <4/29/92, JPO>
;-----------------------------------------------------------
; This is the root of V^X-1 where V is 2 or E.
; Compute (2^T - 1) for fraction T. Then if (integer) W is
; nonzero, finish off with (((2^T - 1) + 1) * 2^W) - 1.
;-----------------------------------------------------------
EXP1ROOT:
BSR.S EXPAPPROX ; 2^T - 1
MOVE.L 2+STW(A6),D0 ; quick check if W = 0.0
OR.L 6+STW(A6),D0
BEQ.S EXP1RDONE
PEA FPK1 ; (2^T - 1) + 1
PEA (A4)
ELFADDX
MOVEA.L A4,A0 ; RESULT PTR
LEA STW(A6),A1 ; INTEGER PART
BSR SCALBXX ; ((2^T - 1) + 1) * 2^W
PEA FPK1 ; FINALLY, SUBTRACT 1
PEA (A4)
ELFSUBX
;-----------------------------------------------------------
; Reset underflow, which cannot occur if W (as in 2^W) is nonzero.
;-----------------------------------------------------------
; BSR CLEARUFLOW ; DELETED <4/29/92, JPO>
EXP1RDONE:
BRA RESULTDELIVERED
;-----------------------------------------------------------
; Compute approximate (2^T - 1) for T in (A4).
; Uses cells X and Y, regs D0-D2/A0-A2.
; Expression has the form
; ( 2 * T * P(T*T) ) / ( Q(T*T) - (T * P(T*T)) )
; One special case: if T is 0, just return 0, and don't set
; the inexact flag.
;-----------------------------------------------------------
EXPAPPROX:
MOVE.L 2(A4),D0 ; fast comparison of input with 0.0
OR.L 6(A4),D0
BNE.S EXPHARD
RTS ; EASY IF 0
EXPHARD:
LEA STY(A6),A1 ; CELL Y
MOVEA.L A4,A0
BSR A0TOA1 ; COPY INPUT T
PEA (A1)
PEA (A1)
ELFMULX ; T^2 INTO CELL Y
LEA STX(A6),A0 ; PLACE P(Y) INTO X
LEA EXP21P,A1 ; EXPONENT P COEFS
LEA STY(A6),A2 ; VAR IS T^2 IN Y
BSR POLYEVAL
PEA STX(A6)
PEA (A4)
ELFMULX ; T * P(T^2) IN RESULT
LEA STX(A6),A0 ; PLACE Q(Y) INTO X
LEA EXP21Q,A1
LEA STY(A6),A2
BSR POLYEVAL
PEA (A4)
PEA STX(A6)
ELFSUBX ; Q(Y) - T*P(Y)
PEA FPK2 ; 2.0
PEA (A4) ; Y*P(Y)
ELFMULX
PEA STX(A6)
PEA (A4)
ELFDIVX
;-----------------------------------------------------------
; Finally, set inexact and clear any underflow messages.
;-----------------------------------------------------------
BSR FORCEINEXACT
; BRA CLEARUFLOW ; AND EXIT... DELETED <4/29/92, JPO>
RTS ; EXIT <4/29/92, JPO>
;-----------------------------------------------------------
;-----------------------------------------------------------
; XPWRITOP---Raise extended dst to integer src power.
;-----------------------------------------------------------
;-----------------------------------------------------------
XPWRITOP:
MOVEA.L D4,A0 ; SRC PTR
MOVE.W (A0),D2 ; I OVERWRITES BOGUS CLASS
BEQ P1STUFF ; ANY^0 IS 1
SUBQ.B #1,D1 ; #CLINF ALREADY SUBTRACTED
BGT.S FINPWRI ; GT MEANS NONZERO^I
;-----------------------------------------------------------
; Get here if INF^I or 0^I. If I is negative, must reciprocate
; (signaling div by 0 in case of 0^-N). If I is even, must clear
; sign.
;-----------------------------------------------------------
ASR.W #1,D2 ; GET ODD BIT OF I INTO C,X
BCS.S @1 ; CARRY SET IF ODD
BCLR #7,(A4) ; ABS OF DST (LEAVES X BIT ALONE)
@1:
ADDX.W D2,D2 ; REGAIN ORIGINAL VALUE I
BPL RESULTDELIVERED ; (INF OR ZERO)^POS ???? WAS BPL.S
TST.B D1 ; INF OR ZERO?
BPL.S ZPWRNEG
TST.B (A4)
BPL P0STUFF ; +INF^NEG IS +0
BRA M0STUFF ; -INF^NEG IS -0
ZPWRNEG:
TST.B (A4)
BPL DIVP0STUFF ; +0^NEG IS +INF
BRA DIVM0STUFF ; -0^NEG IS -INF
;-----------------------------------------------------------
; NONZERO^I is broken into two cases:
; If I is small, then just multiply out. Note that sign perseveres if
; I is odd.
; Otherwise, convert I to extended and evaluate with exponentials.
;-----------------------------------------------------------
FINPWRI:
MOVE.W D2,D0 ; ABS(D2) --> D0
BPL.S @1
NEG.W D0
@1:
CMPI.W #SMALLEXP,D0
BHI.S XPWRBIG ; USE LOG AND EXP
BSR.S XPWRK ; MULTIPLY OUT
BRA RESULTDELIVERED
;-----------------------------------------------------------
; Integer power is too large to multiply out, so convert to extended
; and use general x^y routine. Make copy of integer in cell W.
;-----------------------------------------------------------
XPWRBIG:
MOVE.W (A4),-(SP) ; SAVE SIGN OF INPUT
BCLR #7,(A4) ; ABS(DST) IN T
MOVE.L D4,-(SP) ; ADRS OF INT
PEA STW(A6) ; ADRS OF CELL W
MOVE.L (SP),D4 ; PRETEND IT'S SRC
ELFI2X ; CONVERT INT TO EXT IN W
BSR XPWRY ; COMPUTE (A4)^(D4)
;-----------------------------------------------------------
; Note that XPWRY must preserve the integer value in D2.
;-----------------------------------------------------------
MOVE.W (SP)+,D0 ; RETRIEVE SIGN OF INPUT
BPL.S @3 ; IF POSITIVE, DON'T CARE
ASR.W #1,D2 ; LOW BIT TO CARRY
BCC.S @3
BSET #7,(A4) ; NEGATE OUTPUT
@3:
BRA RESULTDELIVERED
;-----------------------------------------------------------
; Raise T to the power D2, leaving the result in (A4). D0 = abs(D2).
; If D2 is negative, evaluate the positive power and reciprocate at
; the end. Know D2 is nonzero. Sign of (A4) is propagated correctly.
; Trash A0, A1, D0, and cells I, W and X.
;-----------------------------------------------------------
XPWRK:
MOVEA.L A4,A0 ; COPY T
LEA STX(A6),A1 ; INTO CELL W
BSR A0TOA1
BSR.S XPWRKLOOP
;-----------------------------------------------------------
; Now that loop is finished, produce 1 * T^|I| or 1 / T^|I|, depending
; on sign of I. If overflow or underflow has occurred and I is negative,
; redo computation with pre-reciprocated T.
;-----------------------------------------------------------
TST.W D2 ; IS I NEGATIVE?
BMI.S XPWRKDIV
XPWRKSTORE:
MOVEA.L A1,A0 ; T^|I|
MOVEA.L A4,A1 ; RESULT ADRS
BRA A0TOA1 ; T <-- T^|I|, AND EXIT
XPWRKDIV:
LEA FPK1,A0
LEA (A4),A1 ; LOSE ADRS OF CELL X FROM LOOP
BSR A0TOA1 ; T <-- 1
BSR TESTUFLOW
BNE.S XPWRKCLEAR
BSR TESTOFLOW
BNE.S XPWRKCLEAR
PEA STW(A6) ; W = T^|I| FROM XPWRKLOOP
PEA (A4) ; RES=1
ELFDIVX
RTS
XPWRKCLEAR:
BSR CLEAROFLOW
BSR CLEARUFLOW
PEA STX(A6) ; SAVED INPUT T ATOP T^|I|
PEA (A4)
ELFDIVX
MOVE.W D2,D0 ; GET K AGAIN
BPL.S @11
NEG.W D0
@11:
BSR.S XPWRKLOOP
BRA.S XPWRKSTORE
;-----------------------------------------------------------
; Input: D0 = positive integer K
; A4 = X
; Output: A1 = W = X^K
; Uses: cell W, A0
; Trashes: D0
;-----------------------------------------------------------
XPWRKLOOP:
LEA FPK1,A0
LEA STW(A6),A1
BSR A0TOA1 ; SEED RESULT WITH 1.0
BRA.S XKLPENTRY
XKLPTOP:
PEA (A4)
PEA (A4)
ELFMULX ; T^(2^(I+1))
XKLPENTRY:
LSR.W #1,D0 ; GET LOW BIT INTO C
BCC.S XKLPSKIP
PEA (A4) ; T^(2^I)
PEA (A1) ; RESULT SO FAR
ELFMULX
XKLPSKIP:
TST.W D0 ; ANY MORE BITS?
BNE.S XKLPTOP
RTS
;-----------------------------------------------------------
; Simple routine to compute (A4)^(D4) into (A4).
; Know that (A4) is positive. Know that the FMULX will never
; encounter 0 * INF, so extreme cases, like INF^3, will be handled
; correctly. Fixed to use temp X while computing, in case sources and
; dest are the same.
;-----------------------------------------------------------
XPWRY:
MOVEA.L A4,A0 ; COPY DST ARG
LEA STX(A6),A1
BSR A0TOA1 ; CELL X <-- INPUT X
PEA (A1) ; X = INPUT
MOVE.W #FOLOG2X,-(SP)
BSR ELEMS020 ; LOG2((A1))
MOVE.L D4,-(SP)
PEA (A1)
ELFMULX ; (D4) * LOG2((A1))
PEA (A1)
MOVE.W #FOEXP2X,-(SP)
BSR ELEMS020 ; (A1) ^ (D4)
MOVEA.L A1,A0
MOVEA.L A4,A1
BRA A0TOA1
;-----------------------------------------------------------
;-----------------------------------------------------------
; XPWRYTOP---General function x^y is beset by exceptional cases.
;-----------------------------------------------------------
;-----------------------------------------------------------
XPWRYTOP:
TST.W D1 ; IS X=DST NEG?
BMI.S NEGPWRY
BSR.S XPWRYCOM
BRA RESULTDELIVERED
;-----------------------------------------------------------
; Signal X^Y error and stuff a NAN. Special entry accommodates branches from
; within subroutines, in which case a return address must be popped.
;-----------------------------------------------------------
XPWRY9ERR:
ADDQ.L #4,SP ; KILL RETURN ADDRESS
XPWRYERR:
BSR CLEARINEXACT ; SIGNAL INVALID ONLY
MOVEQ #NANPOWER,D0
BRA ERRORNAN
;-----------------------------------------------------------
; If X is negative, check that Y is integral; otherwise error.
; Save parity of Y to fix sign at end of XPWRYCOM.
;-----------------------------------------------------------
NEGPWRY:
TST.B D2 ; Y CLASS - INF
BEQ.S XPWRYERR
MOVEA.L D4,A0 ; Y=SRC
LEA STW(A6),A1 ; CELL W TEMP
BSR A0TOA1
PEA (A1) ; Y=SRC
ELFRINTX ; ROUND TO INTEGER
BSR TESTINEXACT
BNE.S XPWRYERR
;-----------------------------------------------------------
; NEG ^ INT requires that parity of Y be saved in cell J for later
; setting of sign. To find low bit of floating integer, divide by
; 2 and test inexact.
;-----------------------------------------------------------
PEA FPK2 ; 2.0
PEA (A1) ; CELL W
ELFDIVX ; W/2
PEA (A1)
ELFRINTX ; STRIP OFF ODD BIT OF W
MOVE.W (FPSTATE).W,STJ(A6) ; save env in J cell
BSR CLEARINEXACT
BCLR #7,(A4) ; ABS((A4))
BSR.S XPWRYCOM ; ABS((A4))^(D4)
;-----------------------------------------------------------
; Fix sign of power, according to parity of Y. The parity is stored in
; the inexact flag, saved in cell J. It's in the high byte so just to
; a bit test.
;-----------------------------------------------------------
BTST #FBINEXACT,STJ(A6)
BEQ.S @1
BCHG #7,(A4) ; NEGATE IF ODD (INEXACT)
@1:
BRA RESULTDELIVERED
;-----------------------------------------------------------
; Common routine to raise (A4) to (D4) power.
; Know (A4) >= 0 and (D4) is not a NAN.
; Have class codes, less CLINF, in D1 and D2, respectively.
; Can run through 2 ^ Y*LOG2(X) code so long as won't multiply
; INF and 0 to compute exponent. As a minor detail, if Y is 0 or INF,
; clear any inexact that may have been set by LOG2(X).
;
; Since this is called as a subroutine, exits to XPWRYERR must have a special
; pop for the return address.
;-----------------------------------------------------------
XPWRYCOM:
SUBQ.B #1,D1 ; CLINF ALREADY SUBTRACTED
BNE.S NONPWRY
;-----------------------------------------------------------
; 0 ^ some
;-----------------------------------------------------------
SUBQ.B #1,D2 ; CLINF ALREADY SUBTRACTED
BEQ.S XPWRY9ERR ; 0^0, 0^INF ERRORS, WITH RTS POP
TST.W D2 ; SIGN OF Y
BPL.S @1
;-----------------------------------------------------------
; 0 ^ nonzero
;-----------------------------------------------------------
BSR FORCEDIVZER ; SIGNAL DIV BY ZERO
LEA FPKINF,A0
BRA.S @2
@1:
LEA FPK0,A0
@2:
MOVEA.L A4,A1 ; RESULT PTR
BRA A0TOA1 ; STUFF RESULT AND EXIT
;-----------------------------------------------------------
; nonzero ^ some
;-----------------------------------------------------------
NONPWRY:
BPL.S FINPWRY ; EXIT IF X FINITE
;-----------------------------------------------------------
; inf ^ some
;-----------------------------------------------------------
SUBQ.B #1,D2 ; CLINF ALREADY SUBTRACTED
BNE.S XPWRYOK
BRA XPWRY9ERR ; INF^O IS AN ERROR
;-----------------------------------------------------------
; finite ^ some
;-----------------------------------------------------------
FINPWRY:
SUBQ.B #1,D2
BPL.S XPWRYOK ; FIN ^ FIN IS OK
;-----------------------------------------------------------
; finite ^ inf has the special case 1^INF which is an error.
;-----------------------------------------------------------
PEA FPK1
PEA (A4)
ELFCMPX
FBEQL XPWRY9ERR
;-----------------------------------------------------------
; Finally, compute finite^reasonable and return.
; Two cases: if exponent is a small integer, then just multiply;
; else use log and exp. To check for an integer, try converting to
; 16 bits. Overflow is Invalid, rounding error is Inexact.
; Must reset Invalid, but if Inexact the result will be anyway.
; Save D2=YClass in D6 across possible call to XPWRK.
;-----------------------------------------------------------
XPWRYOK:
MOVE.W D2,D6 ; COPY OF Y'S CLASS LESS CLNORM
MOVE.L D4,-(SP) ; EXPONENT ADDRESS
PEA STI(A6) ; INTEGER CELL I
ELFX2I ; CONVERT TO INTEGER
BSR TESTINVALID ; X2I OFLOW IS INVALID
SNE D7
BSR CLEARINVALID ; CLEAR UNDESERVED ERROR
BSR TESTINEXACT ; MAY HAVE JUST ROUNDED OFF
SNE D1
OR.B D1,D7 ; EITHER ERROR?
BNE.S XPWRYHARD
MOVE.W STI(A6),D2 ; GET INTEGER TO REG.
MOVE.W D2,D0
BPL.S @1
NEG.W D0
@1:
CMPI.W #SMALLEXP,D0
BLE XPWRK ; DO IT AS INTEGER AND EXIT
XPWRYHARD:
BSR CLEARINEXACT
BSR XPWRY
TST.B D6 ; CHECK FOR Y 0 OR INF
BMI CLEARINEXACT ; AND RETURN FROM THERE
RTS
;-----------------------------------------------------------
; Compute dst <-- (1 + src2)^src r = src2 n = src
; Watch for special cases:
; src2 < -1 is invalid
; else src = 0 yields 1
; else src2 = 0 and src = INF is invalid
; else src = INF yields 0 or INF according to src2
; else src2 = -1 yields 0, 1, or INF according to src
; else actually compute (1 + r)^n !!
;-----------------------------------------------------------
COMPOUNDTOP:
PEA FPKM1 ; -1
MOVE.L D5,-(SP) ; SRC2
ELFCMPX
FBULTL ERRFINAN ; UNORDERED OR LESS THAN -1
FBGTS CMPGTM1
;-----------------------------------------------------------
; Get here if SRC2 is -1. Check SRC (D2) for 0 or nonzero.
;-----------------------------------------------------------
SUBQ.B #1,D2 ; CLINF ALREADY SUBTRACTED
BNE.S CMPM1N
CMPTOZERO:
BRA P1STUFF ; (1 + SOME)^0 IS +1
CMPM1N:
MOVEA.L D4,A0 ; CHECK SIGN OF SRC
TST.B (A0)
BMI DIVP0STUFF ; (1 - 1)^NEG IS +INF
CMPZERO:
BRA P0STUFF ; (1 - 1)^POS IS +0
;-----------------------------------------------------------
; Get here if SRC2 (r) is > -1.
;-----------------------------------------------------------
CMPGTM1:
SUBQ.B #1,D2 ; CLINF ALREADY SUBTRACTED
BEQ.S CMPTOZERO ; (1 + SOME)^0 IS +1
BGT.S CMPTOFIN ; GO DO (1 + SOME)^FINITE
;-----------------------------------------------------------
; Get here if (1 + SOME)^INF. Check for 1^INF, an error, else have
; INF or 0 according to SRC and SRC2.
;-----------------------------------------------------------
SUBQ.B #1,D1 ; CLINF ALREADY SUBTRACTED
BEQ.S ERRFINAN
EOR.W D2,D1 ; GET XOR OF SRC, SRC2 SIGNS
BMI.S CMPZERO ; SIGNS DIFFER --> ZERO
BRA PINFSTUFF ; SIGNS SAME --> +INF
;-----------------------------------------------------------
; Finally, compute (1 + reasonable)^finite with the usual...
;-----------------------------------------------------------
CMPTOFIN:
LEA STX(A6),A1 ; CELL X
MOVEA.L D5,A0 ; R = SRC2
BSR A0TOA1 ; COPY R TO X
MOVE (a1),d0 ; D0 gets sign/exponent of R.
BCLR #15,d0 ; Clear sign.
CMP #$3f7f,d0 ; Exponent -64.
BLT.S cmpbasee ; Natural log/exp for tiny
;-----------------------------------------------------------
; COMPOUND BASE 2.
;-----------------------------------------------------------
PEA (A1)
MOVE.W #FOLOG21X,-(SP)
BSR ELEMS020 ; LOG2(1 + (A1))
MOVE.L D4,-(SP) ; N = SRC ADDRESS
PEA (A1) ; LOG2(1+R)
ELFMULX ; N * LOG2(1+R)
PEA (A1)
MOVE.W #FOEXP2X,-(SP)
BRA.S cmpresult
cmpbasee: ; COMPOUND BASE E.
MOVE.L D4,-(SP) ; N = SRC ADDRESS
PEA (A1) ; LOG2(1+R)
ELFMULX ; N * LOG2(1+R)
PEA (A1)
MOVE.W #FOEXPX,-(SP)
cmpresult:
BSR clearuflow ; Irrelevant!
BSR ELEMS020 ; EXP2 OR EXPE((A1))
MOVEA.L A1,A0 ; CELL X
MOVEA.L A4,A1
BSR A0TOA1
BRA RESULTDELIVERED
;-----------------------------------------------------------
; Routine to stuff the financial NAN and go.
;-----------------------------------------------------------
ERRFINAN:
MOVEQ #NANFINAN,D0
BRA ERRORNAN
;-----------------------------------------------------------
; Compute annuity factor:
; ( 1 - (1 + r)^-n ) / r
; for r = SRC2 and n = SRC.
; Multitudinous special cases handled piece by piece.
;-----------------------------------------------------------
ANNUITYTOP:
PEA FPKM1 ; -1
MOVE.L D5,-(SP) ; R = SRC2
ELFCMPX ; R VS. -1
FBULTS ERRFINAN ; R < -1 IS AN ERROR
FBNES ANNOK
;-----------------------------------------------------------
; Get here if have (1 - 1)^ANY. Just check n = SRC.
;-----------------------------------------------------------
SUBQ.B #1,D2 ; CLINF ALREADY SUBTRACTED
BEQ.S ANN0 ; ANN(-1, 0) IS +0
TST.W D2 ; CHECK SIGN OF NONZERO N
BPL DIVP0STUFF
ANNM1:
BRA M1STUFF
;-----------------------------------------------------------
; Know that R=SRC2 exceeds -1. Check first for N=SRC=0.
;-----------------------------------------------------------
ANNOK:
SUBQ.B #1,D2 ; CLINF ALREADY SUBTRACTED
BNE.S ANNXN
ANN0:
BRA P0STUFF
;-----------------------------------------------------------
; Now check for unusual, 0 or INF, R=SRC2.
;-----------------------------------------------------------
ANNXN:
SUBQ.B #1,D1 ; CLINF ALREADY SUBTRACTED
BGT.S ANNROK
BLT.S ANNRINF
;-----------------------------------------------------------
; R=SRC2=0. Limit gives result of N=SRC.
;-----------------------------------------------------------
ANNSRC:
MOVEA.L A4,A1 ; DST PTR
MOVEA.L D4,A0 ; SRC=N PTR
BSR A0TOA1
BRA RESULTDELIVERED
;-----------------------------------------------------------
; R=SRC2=+INF. If N=SRC is nonnegative have 0, else test N=SRC versus -1.
;-----------------------------------------------------------
ANNRINF:
TST.W D2 ; IT'S NONZERO, JUST TEST SIGN
BPL.S ANN0 ; FORCE +0
PEA FPKM1 ; -1
MOVE.L D4,-(SP) ; SRC
ELFCMPX
FBEQS ANNM1 ; N = -1, STUFF -1
FBGTL M0STUFF
BRA MINFSTUFF
;-----------------------------------------------------------
; Way down here, we have R=SRC2 a normal or denormal number.
; Last check is for N=SRC=INF.
;-----------------------------------------------------------
ANNROK:
TST.B D2 ; (CLINF + 1) ALREADY SUB
BPL.S ANNDOIT
EOR.W D2,D1 ; DO R AND N SIGNS MATCH
BMI.S ANNSRC
MOVEA.L D5,A0 ; ADDRESS OF 4=SRC2, DIVISOR
LEA STX(A6),A1
BSR A0TOA1
PEA (A1) ; FOR DIVIDE BELOW
MOVEA.L A4,A1
LEA FPK1,A0
BSR A0TOA1 ; DST <-- +1
PEA (A1) ; ADDRESS OF DST
ELFDIVX ; RESULT IS 1/R
BRA RESULTDELIVERED
;-----------------------------------------------------------
; Finally, compute ( 1 - (1 + r)^-n ) / r.
; Distinguish two cases:
; r normal:
; log2(1 + r)
; n * log2(1 + r)
; -n * log2(1 + r)
; 2^(...) - 1
; 1 - 2^(...)
; (1 - 2^(...)) / r
;
; r denormal:
; log(1 + r) is about r
; n * r
; -n * r
; e^(...) - 1
; 1 - e^(...)
; (1 - e^(...)) / r
; Use D1.B, from which CLZERO has already been subtracted.
; Subtracting one more (CLNORMAL) leaves D1.B 0 for normal, 1 for denormal.
;-----------------------------------------------------------
ANNDOIT:
LEA STX(A6),A1 ; CELL X FOR TEMP
MOVEA.L D5,A0 ; SRC2 PTR
BSR A0TOA1
MOVE (a1),d0 ; D0 gets sign/exponent of R.
BCLR #15,d0 ; Clear sign.
CMP #$3f7f,d0 ; Exponent -64.
BLT.S annbasee ; Natural log/exp for tiny
;-----------------------------------------------------------
; Annuity base two.
;-----------------------------------------------------------
PEA (A1) ; X
MOVE.W #FOLOG21X,-(SP)
BSR ELEMS020 ; LOG2(1 + R)
MOVE.L D4,-(SP) ; N=SRC PTR
PEA (A1)
ELFMULX ; N * LOG2(1 + R)
BCHG #7,(A1) ; -(N * LOG2(1 + R))
CMP #$4007,(a1)
BLT.S @1 ; Branch if exp(-n*log(1+r)) not huge.
MOVE.L d5,a0
CMP #$407f,(a0)
BGE.S annspecial ; Branch if r huge.
@1:
PEA (A1)
MOVE.W #FOEXP21X,-(SP)
BRA.S annresult
annbasee: ; Annuity base e.
MOVE.L D4,-(SP) ; N=SRC PTR
PEA (A1)
ELFMULX ; N * LOG2(1 + R)
BCHG #7,(A1) ; -(N * LOG2(1 + R))
PEA (A1)
MOVE.W #FOEXP1X,-(SP)
annresult:
BSR ELEMS020 ; (1 + R)^-N - 1
BCHG #7,(A1) ; 1 - (1 + R)^-N
MOVE.L D5,-(SP) ; R=SRC2
PEA (A1)
ELFDIVX ; ( 1 - (1 + R)^-N ) / R
annclear:
BSR CLEARUFLOW
BSR CLEAROFLOW
MOVEA.L A1,A0 ; SET UP REGS FOR CLASS
BSR CLASSIFY
SUBQ.B #FCINF,D0 ; IS IT INF?
BNE.S @1
BSR FORCEOFLOW
BRA.S ANNDOUT
@1:
SUBQ.B #2,D0 ; IS IT NORMAL?
BEQ.S ANNDOUT
BSR FORCEUFLOW
ANNDOUT:
LEA STX(A6),A0 ; STORE TO DESTINATION
MOVEA.L A4,A1
BSR A0TOA1
BRA RESULTDELIVERED
annspecial:
MOVEA.L D5,A0 ; SRC2 PTR
BSR A0TOA1
PEA (A1) ; X := r
MOVE.W #FOLOG2X,-(SP)
BSR ELEMS020 ; x := LOG2( R)
LEA sty(a6),a1
MOVE.L d4,a0
BSR a0toa1 ; Y gets N.
PEA fpk1
PEA (a1)
ELFADDX ; Y gets N+1.
PEA (A1)
LEA stx(a6),a1 ; A1 gets X again.
PEA (a1)
ELFMULX ; x gets (n+1) * LOG2( R)
BCHG #7,(A1) ; -(N+1) * LOG2( R)
PEA (A1)
MOVE.W #FOEXP2X,-(SP)
BSR ELEMS020 ; ( R)^-(n+1)
BCHG #7,(A1) ; - (R)^-(N+1)
BRA.S annclear
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