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| ssinh.sa 3.1 12/10/90
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| The entry point sSinh computes the hyperbolic sine of
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| an input argument; sSinhd 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 sinh(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 sSINH takes approximately 280 cycles.
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| Algorithm:
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| SINH
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| 1. If |X| > 16380 log2, go to 3.
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| 2. (|X| <= 16380 log2) Sinh(X) is obtained by the formulae
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| y = |X|, sgn = sign(X), and z = expm1(Y),
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| sinh(X) = sgn*(1/2)*( z + z/(1+z) ).
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| Exit.
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| 3. If |X| > 16480 log2, go to 5.
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| 4. (16380 log2 < |X| <= 16480 log2)
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| sinh(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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| sgn := sign(X)
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| sgnFact := sgn * 2**(16380)
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| Y' := Y - 16381 log2
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| sinh(X) := sgnFact * exp(Y').
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| Exit.
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| 5. (|X| > 16480 log2) sinh(X) must overflow. Return
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| sign(X)*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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| 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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|
|SSINH idnt 2,1 | Motorola 040 Floating Point Software Package
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|section 8
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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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|xref t_frcinx
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|xref t_ovfl
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|xref t_extdnrm
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|xref setox
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|xref setoxm1
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.global ssinhd
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ssinhd:
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|--SINH(X) = X FOR DENORMALIZED X
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bra t_extdnrm
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.global ssinh
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ssinh:
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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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movel %d0,%a1 | save a copy of original (compacted) operand
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andl #0x7FFFFFFF,%d0
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cmpl #0x400CB167,%d0
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bgts SINHBIG
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|--THIS IS THE USUAL CASE, |X| < 16380 LOG2
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|--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
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fabsx %fp0 | ...Y = |X|
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moveml %a1/%d1,-(%sp)
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fmovemx %fp0-%fp0,(%a0)
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clrl %d1
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bsr setoxm1 | ...FP0 IS Z = EXPM1(Y)
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fmovel #0,%fpcr
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moveml (%sp)+,%a1/%d1
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fmovex %fp0,%fp1
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fadds #0x3F800000,%fp1 | ...1+Z
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fmovex %fp0,-(%sp)
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fdivx %fp1,%fp0 | ...Z/(1+Z)
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movel %a1,%d0
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andl #0x80000000,%d0
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orl #0x3F000000,%d0
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faddx (%sp)+,%fp0
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movel %d0,-(%sp)
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fmovel %d1,%fpcr
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fmuls (%sp)+,%fp0 |last fp inst - possible exceptions set
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bra t_frcinx
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SINHBIG:
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cmpl #0x400CB2B3,%d0
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bgt t_ovfl
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fabsx %fp0
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fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD)
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movel #0,-(%sp)
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movel #0x80000000,-(%sp)
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movel %a1,%d0
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andl #0x80000000,%d0
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orl #0x7FFB0000,%d0
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movel %d0,-(%sp) | ...EXTENDED FMT
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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 (%sp)+,%fp0 |possible exception
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bra t_frcinx
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|end
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