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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
+|
+| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
+| The copyright notice above does not evidence any
+| actual or intended publication of such source code.
+
+|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