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| scosh.sa 3.1 12/10/90
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| The entry point sCosh computes the hyperbolic cosine of
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| an input argument; sCoshd does the same except for denormalized
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| input.
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| Input: Double-extended number X in location pointed to
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| by address register a0.
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| Output: The value cosh(X) returned in floating-point register Fp0.
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| Accuracy and Monotonicity: The returned result is within 3 ulps in
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| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
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| result is subsequently rounded to double precision. The
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| result is provably monotonic in double precision.
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| Speed: The program sCOSH takes approximately 250 cycles.
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| Algorithm:
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| COSH
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| 1. If |X| > 16380 log2, go to 3.
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| 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae
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| y = |X|, z = exp(Y), and
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| cosh(X) = (1/2)*( z + 1/z ).
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| Exit.
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| 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5.
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| 4. (16380 log2 < |X| <= 16480 log2)
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| cosh(X) = sign(X) * exp(|X|)/2.
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| However, invoking exp(|X|) may cause premature overflow.
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| Thus, we calculate sinh(X) as follows:
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| Y := |X|
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| Fact := 2**(16380)
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| Y' := Y - 16381 log2
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| cosh(X) := Fact * exp(Y').
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| Exit.
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| 5. (|X| > 16480 log2) sinh(X) must overflow. Return
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| Huge*Huge to generate overflow and an infinity with
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| the appropriate sign. Huge is the largest finite number in
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| extended format. Exit.
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| Copyright (C) Motorola, Inc. 1990
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| All Rights Reserved
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|
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| For details on the license for this file, please see the
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| file, README, in this same directory.
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|
|SCOSH idnt 2,1 | Motorola 040 Floating Point Software Package
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|section 8
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|
|xref t_ovfl
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|xref t_frcinx
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|xref setox
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T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
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T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
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TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000
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.global scoshd
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scoshd:
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|--COSH(X) = 1 FOR DENORMALIZED X
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fmoves #0x3F800000,%fp0
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fmovel %d1,%FPCR
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fadds #0x00800000,%fp0
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bra t_frcinx
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.global scosh
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scosh:
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fmovex (%a0),%fp0 | ...LOAD INPUT
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movel (%a0),%d0
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movew 4(%a0),%d0
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andil #0x7FFFFFFF,%d0
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cmpil #0x400CB167,%d0
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bgts COSHBIG
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|--THIS IS THE USUAL CASE, |X| < 16380 LOG2
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|--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
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fabsx %fp0 | ...|X|
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movel %d1,-(%sp)
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clrl %d1
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fmovemx %fp0-%fp0,(%a0) |pass parameter to setox
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bsr setox | ...FP0 IS EXP(|X|)
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fmuls #0x3F000000,%fp0 | ...(1/2)EXP(|X|)
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movel (%sp)+,%d1
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fmoves #0x3E800000,%fp1 | ...(1/4)
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fdivx %fp0,%fp1 | ...1/(2 EXP(|X|))
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fmovel %d1,%FPCR
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faddx %fp1,%fp0
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bra t_frcinx
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COSHBIG:
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cmpil #0x400CB2B3,%d0
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bgts COSHHUGE
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fabsx %fp0
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fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD)
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fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE
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movel %d1,-(%sp)
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clrl %d1
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fmovemx %fp0-%fp0,(%a0)
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bsr setox
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fmovel (%sp)+,%fpcr
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fmulx TWO16380(%pc),%fp0
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bra t_frcinx
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COSHHUGE:
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fmovel #0,%fpsr |clr N bit if set by source
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bclrb #7,(%a0) |always return positive value
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fmovemx (%a0),%fp0-%fp0
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bra t_ovfl
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|end
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