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Diffstat (limited to 'arch/m68k/fpsp040/stanh.S')
| -rw-r--r-- | arch/m68k/fpsp040/stanh.S | 184 |
1 files changed, 184 insertions, 0 deletions
diff --git a/arch/m68k/fpsp040/stanh.S b/arch/m68k/fpsp040/stanh.S new file mode 100644 index 000000000..7e12e59ee --- /dev/null +++ b/arch/m68k/fpsp040/stanh.S @@ -0,0 +1,184 @@ +| +| stanh.sa 3.1 12/10/90 +| +| The entry point sTanh computes the hyperbolic tangent of +| an input argument; sTanhd does the same except for denormalized +| input. +| +| Input: Double-extended number X in location pointed to +| by address register a0. +| +| Output: The value tanh(X) returned in floating-point register Fp0. +| +| Accuracy and Monotonicity: The returned result is within 3 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 stanh takes approximately 270 cycles. +| +| Algorithm: +| +| TANH +| 1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3. +| +| 2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by +| sgn := sign(X), y := 2|X|, z := expm1(Y), and +| tanh(X) = sgn*( z/(2+z) ). +| Exit. +| +| 3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1, +| go to 7. +| +| 4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6. +| +| 5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by +| sgn := sign(X), y := 2|X|, z := exp(Y), +| tanh(X) = sgn - [ sgn*2/(1+z) ]. +| Exit. +| +| 6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we +| calculate Tanh(X) by +| sgn := sign(X), Tiny := 2**(-126), +| tanh(X) := sgn - sgn*Tiny. +| Exit. +| +| 7. (|X| < 2**(-40)). Tanh(X) = X. Exit. +| + +| 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. + +|STANH idnt 2,1 | Motorola 040 Floating Point Software Package + + |section 8 + +#include "fpsp.h" + + .set X,FP_SCR5 + .set XDCARE,X+2 + .set XFRAC,X+4 + + .set SGN,L_SCR3 + + .set V,FP_SCR6 + +BOUNDS1: .long 0x3FD78000,0x3FFFDDCE | ... 2^(-40), (5/2)LOG2 + + |xref t_frcinx + |xref t_extdnrm + |xref setox + |xref setoxm1 + + .global stanhd +stanhd: +|--TANH(X) = X FOR DENORMALIZED X + + bra t_extdnrm + + .global stanh +stanh: + fmovex (%a0),%fp0 | ...LOAD INPUT + + fmovex %fp0,X(%a6) + movel (%a0),%d0 + movew 4(%a0),%d0 + movel %d0,X(%a6) + andl #0x7FFFFFFF,%d0 + cmp2l BOUNDS1(%pc),%d0 | ...2**(-40) < |X| < (5/2)LOG2 ? + bcss TANHBORS + +|--THIS IS THE USUAL CASE +|--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2). + + movel X(%a6),%d0 + movel %d0,SGN(%a6) + andl #0x7FFF0000,%d0 + addl #0x00010000,%d0 | ...EXPONENT OF 2|X| + movel %d0,X(%a6) + andl #0x80000000,SGN(%a6) + fmovex X(%a6),%fp0 | ...FP0 IS Y = 2|X| + + movel %d1,-(%a7) + clrl %d1 + fmovemx %fp0-%fp0,(%a0) + bsr setoxm1 | ...FP0 IS Z = EXPM1(Y) + movel (%a7)+,%d1 + + fmovex %fp0,%fp1 + fadds #0x40000000,%fp1 | ...Z+2 + movel SGN(%a6),%d0 + fmovex %fp1,V(%a6) + eorl %d0,V(%a6) + + fmovel %d1,%FPCR |restore users exceptions + fdivx V(%a6),%fp0 + bra t_frcinx + +TANHBORS: + cmpl #0x3FFF8000,%d0 + blt TANHSM + + cmpl #0x40048AA1,%d0 + bgt TANHHUGE + +|-- (5/2) LOG2 < |X| < 50 LOG2, +|--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X), +|--TANH(X) = SGN - SGN*2/[EXP(Y)+1]. + + movel X(%a6),%d0 + movel %d0,SGN(%a6) + andl #0x7FFF0000,%d0 + addl #0x00010000,%d0 | ...EXPO OF 2|X| + movel %d0,X(%a6) | ...Y = 2|X| + andl #0x80000000,SGN(%a6) + movel SGN(%a6),%d0 + fmovex X(%a6),%fp0 | ...Y = 2|X| + + movel %d1,-(%a7) + clrl %d1 + fmovemx %fp0-%fp0,(%a0) + bsr setox | ...FP0 IS EXP(Y) + movel (%a7)+,%d1 + movel SGN(%a6),%d0 + fadds #0x3F800000,%fp0 | ...EXP(Y)+1 + + eorl #0xC0000000,%d0 | ...-SIGN(X)*2 + fmoves %d0,%fp1 | ...-SIGN(X)*2 IN SGL FMT + fdivx %fp0,%fp1 | ...-SIGN(X)2 / [EXP(Y)+1 ] + + movel SGN(%a6),%d0 + orl #0x3F800000,%d0 | ...SGN + fmoves %d0,%fp0 | ...SGN IN SGL FMT + + fmovel %d1,%FPCR |restore users exceptions + faddx %fp1,%fp0 + + bra t_frcinx + +TANHSM: + movew #0x0000,XDCARE(%a6) + + fmovel %d1,%FPCR |restore users exceptions + fmovex X(%a6),%fp0 |last inst - possible exception set + + bra t_frcinx + +TANHHUGE: +|---RETURN SGN(X) - SGN(X)EPS + movel X(%a6),%d0 + andl #0x80000000,%d0 + orl #0x3F800000,%d0 + fmoves %d0,%fp0 + andl #0x80000000,%d0 + eorl #0x80800000,%d0 | ...-SIGN(X)*EPS + + fmovel %d1,%FPCR |restore users exceptions + fadds %d0,%fp0 + + bra t_frcinx + + |end |