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authorSrikant Patnaik2015-01-11 12:28:04 +0530
committerSrikant Patnaik2015-01-11 12:28:04 +0530
commit871480933a1c28f8a9fed4c4d34d06c439a7a422 (patch)
tree8718f573808810c2a1e8cb8fb6ac469093ca2784 /ANDROID_3.4.5/arch/m68k/fpsp040/stwotox.S
parent9d40ac5867b9aefe0722bc1f110b965ff294d30d (diff)
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Diffstat (limited to 'ANDROID_3.4.5/arch/m68k/fpsp040/stwotox.S')
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-|
-| stwotox.sa 3.1 12/10/90
-|
-| stwotox --- 2**X
-| stwotoxd --- 2**X for denormalized X
-| stentox --- 10**X
-| stentoxd --- 10**X for denormalized X
-|
-| Input: Double-extended number X in location pointed to
-| by address register a0.
-|
-| Output: The function values are returned in Fp0.
-|
-| Accuracy and Monotonicity: The returned result is within 2 ulps in
-| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
-| result is subsequently rounded to double precision. The
-| result is provably monotonic in double precision.
-|
-| Speed: The program stwotox takes approximately 190 cycles and the
-| program stentox takes approximately 200 cycles.
-|
-| Algorithm:
-|
-| twotox
-| 1. If |X| > 16480, go to ExpBig.
-|
-| 2. If |X| < 2**(-70), go to ExpSm.
-|
-| 3. Decompose X as X = N/64 + r where |r| <= 1/128. Furthermore
-| decompose N as
-| N = 64(M + M') + j, j = 0,1,2,...,63.
-|
-| 4. Overwrite r := r * log2. Then
-| 2**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r).
-| Go to expr to compute that expression.
-|
-| tentox
-| 1. If |X| > 16480*log_10(2) (base 10 log of 2), go to ExpBig.
-|
-| 2. If |X| < 2**(-70), go to ExpSm.
-|
-| 3. Set y := X*log_2(10)*64 (base 2 log of 10). Set
-| N := round-to-int(y). Decompose N as
-| N = 64(M + M') + j, j = 0,1,2,...,63.
-|
-| 4. Define r as
-| r := ((X - N*L1)-N*L2) * L10
-| where L1, L2 are the leading and trailing parts of log_10(2)/64
-| and L10 is the natural log of 10. Then
-| 10**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r).
-| Go to expr to compute that expression.
-|
-| expr
-| 1. Fetch 2**(j/64) from table as Fact1 and Fact2.
-|
-| 2. Overwrite Fact1 and Fact2 by
-| Fact1 := 2**(M) * Fact1
-| Fact2 := 2**(M) * Fact2
-| Thus Fact1 + Fact2 = 2**(M) * 2**(j/64).
-|
-| 3. Calculate P where 1 + P approximates exp(r):
-| P = r + r*r*(A1+r*(A2+...+r*A5)).
-|
-| 4. Let AdjFact := 2**(M'). Return
-| AdjFact * ( Fact1 + ((Fact1*P) + Fact2) ).
-| Exit.
-|
-| ExpBig
-| 1. Generate overflow by Huge * Huge if X > 0; otherwise, generate
-| underflow by Tiny * Tiny.
-|
-| ExpSm
-| 1. Return 1 + X.
-|
-
-| Copyright (C) Motorola, Inc. 1990
-| All Rights Reserved
-|
-| For details on the license for this file, please see the
-| file, README, in this same directory.
-
-|STWOTOX idnt 2,1 | Motorola 040 Floating Point Software Package
-
- |section 8
-
-#include "fpsp.h"
-
-BOUNDS1: .long 0x3FB98000,0x400D80C0 | ... 2^(-70),16480
-BOUNDS2: .long 0x3FB98000,0x400B9B07 | ... 2^(-70),16480 LOG2/LOG10
-
-L2TEN64: .long 0x406A934F,0x0979A371 | ... 64LOG10/LOG2
-L10TWO1: .long 0x3F734413,0x509F8000 | ... LOG2/64LOG10
-
-L10TWO2: .long 0xBFCD0000,0xC0219DC1,0xDA994FD2,0x00000000
-
-LOG10: .long 0x40000000,0x935D8DDD,0xAAA8AC17,0x00000000
-
-LOG2: .long 0x3FFE0000,0xB17217F7,0xD1CF79AC,0x00000000
-
-EXPA5: .long 0x3F56C16D,0x6F7BD0B2
-EXPA4: .long 0x3F811112,0x302C712C
-EXPA3: .long 0x3FA55555,0x55554CC1
-EXPA2: .long 0x3FC55555,0x55554A54
-EXPA1: .long 0x3FE00000,0x00000000,0x00000000,0x00000000
-
-HUGE: .long 0x7FFE0000,0xFFFFFFFF,0xFFFFFFFF,0x00000000
-TINY: .long 0x00010000,0xFFFFFFFF,0xFFFFFFFF,0x00000000
-
-EXPTBL:
- .long 0x3FFF0000,0x80000000,0x00000000,0x3F738000
- .long 0x3FFF0000,0x8164D1F3,0xBC030773,0x3FBEF7CA
- .long 0x3FFF0000,0x82CD8698,0xAC2BA1D7,0x3FBDF8A9
- .long 0x3FFF0000,0x843A28C3,0xACDE4046,0x3FBCD7C9
- .long 0x3FFF0000,0x85AAC367,0xCC487B15,0xBFBDE8DA
- .long 0x3FFF0000,0x871F6196,0x9E8D1010,0x3FBDE85C
- .long 0x3FFF0000,0x88980E80,0x92DA8527,0x3FBEBBF1
- .long 0x3FFF0000,0x8A14D575,0x496EFD9A,0x3FBB80CA
- .long 0x3FFF0000,0x8B95C1E3,0xEA8BD6E7,0xBFBA8373
- .long 0x3FFF0000,0x8D1ADF5B,0x7E5BA9E6,0xBFBE9670
- .long 0x3FFF0000,0x8EA4398B,0x45CD53C0,0x3FBDB700
- .long 0x3FFF0000,0x9031DC43,0x1466B1DC,0x3FBEEEB0
- .long 0x3FFF0000,0x91C3D373,0xAB11C336,0x3FBBFD6D
- .long 0x3FFF0000,0x935A2B2F,0x13E6E92C,0xBFBDB319
- .long 0x3FFF0000,0x94F4EFA8,0xFEF70961,0x3FBDBA2B
- .long 0x3FFF0000,0x96942D37,0x20185A00,0x3FBE91D5
- .long 0x3FFF0000,0x9837F051,0x8DB8A96F,0x3FBE8D5A
- .long 0x3FFF0000,0x99E04593,0x20B7FA65,0xBFBCDE7B
- .long 0x3FFF0000,0x9B8D39B9,0xD54E5539,0xBFBEBAAF
- .long 0x3FFF0000,0x9D3ED9A7,0x2CFFB751,0xBFBD86DA
- .long 0x3FFF0000,0x9EF53260,0x91A111AE,0xBFBEBEDD
- .long 0x3FFF0000,0xA0B0510F,0xB9714FC2,0x3FBCC96E
- .long 0x3FFF0000,0xA2704303,0x0C496819,0xBFBEC90B
- .long 0x3FFF0000,0xA43515AE,0x09E6809E,0x3FBBD1DB
- .long 0x3FFF0000,0xA5FED6A9,0xB15138EA,0x3FBCE5EB
- .long 0x3FFF0000,0xA7CD93B4,0xE965356A,0xBFBEC274
- .long 0x3FFF0000,0xA9A15AB4,0xEA7C0EF8,0x3FBEA83C
- .long 0x3FFF0000,0xAB7A39B5,0xA93ED337,0x3FBECB00
- .long 0x3FFF0000,0xAD583EEA,0x42A14AC6,0x3FBE9301
- .long 0x3FFF0000,0xAF3B78AD,0x690A4375,0xBFBD8367
- .long 0x3FFF0000,0xB123F581,0xD2AC2590,0xBFBEF05F
- .long 0x3FFF0000,0xB311C412,0xA9112489,0x3FBDFB3C
- .long 0x3FFF0000,0xB504F333,0xF9DE6484,0x3FBEB2FB
- .long 0x3FFF0000,0xB6FD91E3,0x28D17791,0x3FBAE2CB
- .long 0x3FFF0000,0xB8FBAF47,0x62FB9EE9,0x3FBCDC3C
- .long 0x3FFF0000,0xBAFF5AB2,0x133E45FB,0x3FBEE9AA
- .long 0x3FFF0000,0xBD08A39F,0x580C36BF,0xBFBEAEFD
- .long 0x3FFF0000,0xBF1799B6,0x7A731083,0xBFBCBF51
- .long 0x3FFF0000,0xC12C4CCA,0x66709456,0x3FBEF88A
- .long 0x3FFF0000,0xC346CCDA,0x24976407,0x3FBD83B2
- .long 0x3FFF0000,0xC5672A11,0x5506DADD,0x3FBDF8AB
- .long 0x3FFF0000,0xC78D74C8,0xABB9B15D,0xBFBDFB17
- .long 0x3FFF0000,0xC9B9BD86,0x6E2F27A3,0xBFBEFE3C
- .long 0x3FFF0000,0xCBEC14FE,0xF2727C5D,0xBFBBB6F8
- .long 0x3FFF0000,0xCE248C15,0x1F8480E4,0xBFBCEE53
- .long 0x3FFF0000,0xD06333DA,0xEF2B2595,0xBFBDA4AE
- .long 0x3FFF0000,0xD2A81D91,0xF12AE45A,0x3FBC9124
- .long 0x3FFF0000,0xD4F35AAB,0xCFEDFA1F,0x3FBEB243
- .long 0x3FFF0000,0xD744FCCA,0xD69D6AF4,0x3FBDE69A
- .long 0x3FFF0000,0xD99D15C2,0x78AFD7B6,0xBFB8BC61
- .long 0x3FFF0000,0xDBFBB797,0xDAF23755,0x3FBDF610
- .long 0x3FFF0000,0xDE60F482,0x5E0E9124,0xBFBD8BE1
- .long 0x3FFF0000,0xE0CCDEEC,0x2A94E111,0x3FBACB12
- .long 0x3FFF0000,0xE33F8972,0xBE8A5A51,0x3FBB9BFE
- .long 0x3FFF0000,0xE5B906E7,0x7C8348A8,0x3FBCF2F4
- .long 0x3FFF0000,0xE8396A50,0x3C4BDC68,0x3FBEF22F
- .long 0x3FFF0000,0xEAC0C6E7,0xDD24392F,0xBFBDBF4A
- .long 0x3FFF0000,0xED4F301E,0xD9942B84,0x3FBEC01A
- .long 0x3FFF0000,0xEFE4B99B,0xDCDAF5CB,0x3FBE8CAC
- .long 0x3FFF0000,0xF281773C,0x59FFB13A,0xBFBCBB3F
- .long 0x3FFF0000,0xF5257D15,0x2486CC2C,0x3FBEF73A
- .long 0x3FFF0000,0xF7D0DF73,0x0AD13BB9,0xBFB8B795
- .long 0x3FFF0000,0xFA83B2DB,0x722A033A,0x3FBEF84B
- .long 0x3FFF0000,0xFD3E0C0C,0xF486C175,0xBFBEF581
-
- .set N,L_SCR1
-
- .set X,FP_SCR1
- .set XDCARE,X+2
- .set XFRAC,X+4
-
- .set ADJFACT,FP_SCR2
-
- .set FACT1,FP_SCR3
- .set FACT1HI,FACT1+4
- .set FACT1LOW,FACT1+8
-
- .set FACT2,FP_SCR4
- .set FACT2HI,FACT2+4
- .set FACT2LOW,FACT2+8
-
- | xref t_unfl
- |xref t_ovfl
- |xref t_frcinx
-
- .global stwotoxd
-stwotoxd:
-|--ENTRY POINT FOR 2**(X) FOR DENORMALIZED ARGUMENT
-
- fmovel %d1,%fpcr | ...set user's rounding mode/precision
- fmoves #0x3F800000,%fp0 | ...RETURN 1 + X
- movel (%a0),%d0
- orl #0x00800001,%d0
- fadds %d0,%fp0
- bra t_frcinx
-
- .global stwotox
-stwotox:
-|--ENTRY POINT FOR 2**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
- fmovemx (%a0),%fp0-%fp0 | ...LOAD INPUT, do not set cc's
-
- movel (%a0),%d0
- movew 4(%a0),%d0
- fmovex %fp0,X(%a6)
- andil #0x7FFFFFFF,%d0
-
- cmpil #0x3FB98000,%d0 | ...|X| >= 2**(-70)?
- bges TWOOK1
- bra EXPBORS
-
-TWOOK1:
- cmpil #0x400D80C0,%d0 | ...|X| > 16480?
- bles TWOMAIN
- bra EXPBORS
-
-
-TWOMAIN:
-|--USUAL CASE, 2^(-70) <= |X| <= 16480
-
- fmovex %fp0,%fp1
- fmuls #0x42800000,%fp1 | ...64 * X
-
- fmovel %fp1,N(%a6) | ...N = ROUND-TO-INT(64 X)
- movel %d2,-(%sp)
- lea EXPTBL,%a1 | ...LOAD ADDRESS OF TABLE OF 2^(J/64)
- fmovel N(%a6),%fp1 | ...N --> FLOATING FMT
- movel N(%a6),%d0
- movel %d0,%d2
- andil #0x3F,%d0 | ...D0 IS J
- asll #4,%d0 | ...DISPLACEMENT FOR 2^(J/64)
- addal %d0,%a1 | ...ADDRESS FOR 2^(J/64)
- asrl #6,%d2 | ...d2 IS L, N = 64L + J
- movel %d2,%d0
- asrl #1,%d0 | ...D0 IS M
- subl %d0,%d2 | ...d2 IS M', N = 64(M+M') + J
- addil #0x3FFF,%d2
- movew %d2,ADJFACT(%a6) | ...ADJFACT IS 2^(M')
- movel (%sp)+,%d2
-|--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64),
-|--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN.
-|--ADJFACT = 2^(M').
-|--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2.
-
- fmuls #0x3C800000,%fp1 | ...(1/64)*N
- movel (%a1)+,FACT1(%a6)
- movel (%a1)+,FACT1HI(%a6)
- movel (%a1)+,FACT1LOW(%a6)
- movew (%a1)+,FACT2(%a6)
- clrw FACT2+2(%a6)
-
- fsubx %fp1,%fp0 | ...X - (1/64)*INT(64 X)
-
- movew (%a1)+,FACT2HI(%a6)
- clrw FACT2HI+2(%a6)
- clrl FACT2LOW(%a6)
- addw %d0,FACT1(%a6)
-
- fmulx LOG2,%fp0 | ...FP0 IS R
- addw %d0,FACT2(%a6)
-
- bra expr
-
-EXPBORS:
-|--FPCR, D0 SAVED
- cmpil #0x3FFF8000,%d0
- bgts EXPBIG
-
-EXPSM:
-|--|X| IS SMALL, RETURN 1 + X
-
- fmovel %d1,%FPCR |restore users exceptions
- fadds #0x3F800000,%fp0 | ...RETURN 1 + X
-
- bra t_frcinx
-
-EXPBIG:
-|--|X| IS LARGE, GENERATE OVERFLOW IF X > 0; ELSE GENERATE UNDERFLOW
-|--REGISTERS SAVE SO FAR ARE FPCR AND D0
- movel X(%a6),%d0
- cmpil #0,%d0
- blts EXPNEG
-
- bclrb #7,(%a0) |t_ovfl expects positive value
- bra t_ovfl
-
-EXPNEG:
- bclrb #7,(%a0) |t_unfl expects positive value
- bra t_unfl
-
- .global stentoxd
-stentoxd:
-|--ENTRY POINT FOR 10**(X) FOR DENORMALIZED ARGUMENT
-
- fmovel %d1,%fpcr | ...set user's rounding mode/precision
- fmoves #0x3F800000,%fp0 | ...RETURN 1 + X
- movel (%a0),%d0
- orl #0x00800001,%d0
- fadds %d0,%fp0
- bra t_frcinx
-
- .global stentox
-stentox:
-|--ENTRY POINT FOR 10**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
- fmovemx (%a0),%fp0-%fp0 | ...LOAD INPUT, do not set cc's
-
- movel (%a0),%d0
- movew 4(%a0),%d0
- fmovex %fp0,X(%a6)
- andil #0x7FFFFFFF,%d0
-
- cmpil #0x3FB98000,%d0 | ...|X| >= 2**(-70)?
- bges TENOK1
- bra EXPBORS
-
-TENOK1:
- cmpil #0x400B9B07,%d0 | ...|X| <= 16480*log2/log10 ?
- bles TENMAIN
- bra EXPBORS
-
-TENMAIN:
-|--USUAL CASE, 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10
-
- fmovex %fp0,%fp1
- fmuld L2TEN64,%fp1 | ...X*64*LOG10/LOG2
-
- fmovel %fp1,N(%a6) | ...N=INT(X*64*LOG10/LOG2)
- movel %d2,-(%sp)
- lea EXPTBL,%a1 | ...LOAD ADDRESS OF TABLE OF 2^(J/64)
- fmovel N(%a6),%fp1 | ...N --> FLOATING FMT
- movel N(%a6),%d0
- movel %d0,%d2
- andil #0x3F,%d0 | ...D0 IS J
- asll #4,%d0 | ...DISPLACEMENT FOR 2^(J/64)
- addal %d0,%a1 | ...ADDRESS FOR 2^(J/64)
- asrl #6,%d2 | ...d2 IS L, N = 64L + J
- movel %d2,%d0
- asrl #1,%d0 | ...D0 IS M
- subl %d0,%d2 | ...d2 IS M', N = 64(M+M') + J
- addil #0x3FFF,%d2
- movew %d2,ADJFACT(%a6) | ...ADJFACT IS 2^(M')
- movel (%sp)+,%d2
-
-|--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64),
-|--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN.
-|--ADJFACT = 2^(M').
-|--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2.
-
- fmovex %fp1,%fp2
-
- fmuld L10TWO1,%fp1 | ...N*(LOG2/64LOG10)_LEAD
- movel (%a1)+,FACT1(%a6)
-
- fmulx L10TWO2,%fp2 | ...N*(LOG2/64LOG10)_TRAIL
-
- movel (%a1)+,FACT1HI(%a6)
- movel (%a1)+,FACT1LOW(%a6)
- fsubx %fp1,%fp0 | ...X - N L_LEAD
- movew (%a1)+,FACT2(%a6)
-
- fsubx %fp2,%fp0 | ...X - N L_TRAIL
-
- clrw FACT2+2(%a6)
- movew (%a1)+,FACT2HI(%a6)
- clrw FACT2HI+2(%a6)
- clrl FACT2LOW(%a6)
-
- fmulx LOG10,%fp0 | ...FP0 IS R
-
- addw %d0,FACT1(%a6)
- addw %d0,FACT2(%a6)
-
-expr:
-|--FPCR, FP2, FP3 ARE SAVED IN ORDER AS SHOWN.
-|--ADJFACT CONTAINS 2**(M'), FACT1 + FACT2 = 2**(M) * 2**(J/64).
-|--FP0 IS R. THE FOLLOWING CODE COMPUTES
-|-- 2**(M'+M) * 2**(J/64) * EXP(R)
-
- fmovex %fp0,%fp1
- fmulx %fp1,%fp1 | ...FP1 IS S = R*R
-
- fmoved EXPA5,%fp2 | ...FP2 IS A5
- fmoved EXPA4,%fp3 | ...FP3 IS A4
-
- fmulx %fp1,%fp2 | ...FP2 IS S*A5
- fmulx %fp1,%fp3 | ...FP3 IS S*A4
-
- faddd EXPA3,%fp2 | ...FP2 IS A3+S*A5
- faddd EXPA2,%fp3 | ...FP3 IS A2+S*A4
-
- fmulx %fp1,%fp2 | ...FP2 IS S*(A3+S*A5)
- fmulx %fp1,%fp3 | ...FP3 IS S*(A2+S*A4)
-
- faddd EXPA1,%fp2 | ...FP2 IS A1+S*(A3+S*A5)
- fmulx %fp0,%fp3 | ...FP3 IS R*S*(A2+S*A4)
-
- fmulx %fp1,%fp2 | ...FP2 IS S*(A1+S*(A3+S*A5))
- faddx %fp3,%fp0 | ...FP0 IS R+R*S*(A2+S*A4)
-
- faddx %fp2,%fp0 | ...FP0 IS EXP(R) - 1
-
-
-|--FINAL RECONSTRUCTION PROCESS
-|--EXP(X) = 2^M*2^(J/64) + 2^M*2^(J/64)*(EXP(R)-1) - (1 OR 0)
-
- fmulx FACT1(%a6),%fp0
- faddx FACT2(%a6),%fp0
- faddx FACT1(%a6),%fp0
-
- fmovel %d1,%FPCR |restore users exceptions
- clrw ADJFACT+2(%a6)
- movel #0x80000000,ADJFACT+4(%a6)
- clrl ADJFACT+8(%a6)
- fmulx ADJFACT(%a6),%fp0 | ...FINAL ADJUSTMENT
-
- bra t_frcinx
-
- |end