^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 1) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 2) | scosh.sa 3.1 12/10/90
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 3) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 4) | The entry point sCosh computes the hyperbolic cosine of
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 5) | an input argument; sCoshd does the same except for denormalized
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 6) | input.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 7) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 8) | Input: Double-extended number X in location pointed to
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 9) | by address register a0.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 10) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 11) | Output: The value cosh(X) returned in floating-point register Fp0.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 12) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 13) | Accuracy and Monotonicity: The returned result is within 3 ulps in
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 14) | 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 15) | result is subsequently rounded to double precision. The
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 16) | result is provably monotonic in double precision.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 17) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 18) | Speed: The program sCOSH takes approximately 250 cycles.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 19) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 20) | Algorithm:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 21) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 22) | COSH
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 23) | 1. If |X| > 16380 log2, go to 3.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 24) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 25) | 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 26) | y = |X|, z = exp(Y), and
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 27) | cosh(X) = (1/2)*( z + 1/z ).
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 28) | Exit.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 29) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 30) | 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 31) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 32) | 4. (16380 log2 < |X| <= 16480 log2)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 33) | cosh(X) = sign(X) * exp(|X|)/2.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 34) | However, invoking exp(|X|) may cause premature overflow.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 35) | Thus, we calculate sinh(X) as follows:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 36) | Y := |X|
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 37) | Fact := 2**(16380)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 38) | Y' := Y - 16381 log2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 39) | cosh(X) := Fact * exp(Y').
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 40) | Exit.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 41) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 42) | 5. (|X| > 16480 log2) sinh(X) must overflow. Return
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 43) | Huge*Huge to generate overflow and an infinity with
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 44) | the appropriate sign. Huge is the largest finite number in
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 45) | extended format. Exit.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 46) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 47) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 48)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 49) | Copyright (C) Motorola, Inc. 1990
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 50) | All Rights Reserved
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 51) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 52) | For details on the license for this file, please see the
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 53) | file, README, in this same directory.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 54)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 55) |SCOSH idnt 2,1 | Motorola 040 Floating Point Software Package
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 56)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 57) |section 8
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 58)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 59) |xref t_ovfl
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 60) |xref t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 61) |xref setox
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 62)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 63) T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 64) T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 65)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 66) TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 67)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 68) .global scoshd
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 69) scoshd:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 70) |--COSH(X) = 1 FOR DENORMALIZED X
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 71)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 72) fmoves #0x3F800000,%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 73)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 74) fmovel %d1,%FPCR
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 75) fadds #0x00800000,%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 76) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 77)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 78) .global scosh
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 79) scosh:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 80) fmovex (%a0),%fp0 | ...LOAD INPUT
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 81)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 82) movel (%a0),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 83) movew 4(%a0),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 84) andil #0x7FFFFFFF,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 85) cmpil #0x400CB167,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 86) bgts COSHBIG
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 87)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 88) |--THIS IS THE USUAL CASE, |X| < 16380 LOG2
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 89) |--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 90)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 91) fabsx %fp0 | ...|X|
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 92)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 93) movel %d1,-(%sp)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 94) clrl %d1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 95) fmovemx %fp0-%fp0,(%a0) |pass parameter to setox
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 96) bsr setox | ...FP0 IS EXP(|X|)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 97) fmuls #0x3F000000,%fp0 | ...(1/2)EXP(|X|)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 98) movel (%sp)+,%d1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 99)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 100) fmoves #0x3E800000,%fp1 | ...(1/4)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 101) fdivx %fp0,%fp1 | ...1/(2 EXP(|X|))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 102)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 103) fmovel %d1,%FPCR
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 104) faddx %fp1,%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 105)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 106) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 107)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 108) COSHBIG:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 109) cmpil #0x400CB2B3,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 110) bgts COSHHUGE
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 111)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 112) fabsx %fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 113) fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 114) fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 115)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 116) movel %d1,-(%sp)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 117) clrl %d1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 118) fmovemx %fp0-%fp0,(%a0)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 119) bsr setox
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 120) fmovel (%sp)+,%fpcr
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 121)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 122) fmulx TWO16380(%pc),%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 123) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 124)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 125) COSHHUGE:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 126) fmovel #0,%fpsr |clr N bit if set by source
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 127) bclrb #7,(%a0) |always return positive value
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 128) fmovemx (%a0),%fp0-%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 129) bra t_ovfl
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 130)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 131) |end
Orange Pi5 kernel
Deprecated Linux kernel 5.10.110 for OrangePi 5/5B/5+ boards
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