| | |
| | ssinh.sa 3.1 12/10/90 |
| | |
| | The entry point sSinh computes the hyperbolic sine of |
| | an input argument; sSinhd does the same except for denormalized |
| | input. |
| | |
| | Input: Double-extended number X in location pointed to |
| | by address register a0. |
| | |
| | Output: The value sinh(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 sSINH takes approximately 280 cycles. |
| | |
| | Algorithm: |
| | |
| | SINH |
| | 1. If |X| > 16380 log2, go to 3. |
| | |
| | 2. (|X| <= 16380 log2) Sinh(X) is obtained by the formulae |
| | y = |X|, sgn = sign(X), and z = expm1(Y), |
| | sinh(X) = sgn*(1/2)*( z + z/(1+z) ). |
| | Exit. |
| | |
| | 3. If |X| > 16480 log2, go to 5. |
| | |
| | 4. (16380 log2 < |X| <= 16480 log2) |
| | sinh(X) = sign(X) * exp(|X|)/2. |
| | However, invoking exp(|X|) may cause premature overflow. |
| | Thus, we calculate sinh(X) as follows: |
| | Y := |X| |
| | sgn := sign(X) |
| | sgnFact := sgn * 2**(16380) |
| | Y' := Y - 16381 log2 |
| | sinh(X) := sgnFact * exp(Y'). |
| | Exit. |
| | |
| | 5. (|X| > 16480 log2) sinh(X) must overflow. Return |
| | sign(X)*Huge*Huge to generate overflow and an infinity with |
| | the appropriate sign. Huge is the largest finite number in |
| | extended format. 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. |
| |
| |SSINH idnt 2,1 | Motorola 040 Floating Point Software Package |
| |
| |section 8 |
| |
| T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD |
| T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL |
| |
| |xref t_frcinx |
| |xref t_ovfl |
| |xref t_extdnrm |
| |xref setox |
| |xref setoxm1 |
| |
| .global ssinhd |
| ssinhd: |
| |--SINH(X) = X FOR DENORMALIZED X |
| |
| bra t_extdnrm |
| |
| .global ssinh |
| ssinh: |
| fmovex (%a0),%fp0 | ...LOAD INPUT |
| |
| movel (%a0),%d0 |
| movew 4(%a0),%d0 |
| movel %d0,%a1 | save a copy of original (compacted) operand |
| andl #0x7FFFFFFF,%d0 |
| cmpl #0x400CB167,%d0 |
| bgts SINHBIG |
| |
| |--THIS IS THE USUAL CASE, |X| < 16380 LOG2 |
| |--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) ) |
| |
| fabsx %fp0 | ...Y = |X| |
| |
| moveml %a1/%d1,-(%sp) |
| fmovemx %fp0-%fp0,(%a0) |
| clrl %d1 |
| bsr setoxm1 | ...FP0 IS Z = EXPM1(Y) |
| fmovel #0,%fpcr |
| moveml (%sp)+,%a1/%d1 |
| |
| fmovex %fp0,%fp1 |
| fadds #0x3F800000,%fp1 | ...1+Z |
| fmovex %fp0,-(%sp) |
| fdivx %fp1,%fp0 | ...Z/(1+Z) |
| movel %a1,%d0 |
| andl #0x80000000,%d0 |
| orl #0x3F000000,%d0 |
| faddx (%sp)+,%fp0 |
| movel %d0,-(%sp) |
| |
| fmovel %d1,%fpcr |
| fmuls (%sp)+,%fp0 |last fp inst - possible exceptions set |
| |
| bra t_frcinx |
| |
| SINHBIG: |
| cmpl #0x400CB2B3,%d0 |
| bgt t_ovfl |
| fabsx %fp0 |
| fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD) |
| movel #0,-(%sp) |
| movel #0x80000000,-(%sp) |
| movel %a1,%d0 |
| andl #0x80000000,%d0 |
| orl #0x7FFB0000,%d0 |
| movel %d0,-(%sp) | ...EXTENDED FMT |
| fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE |
| |
| movel %d1,-(%sp) |
| clrl %d1 |
| fmovemx %fp0-%fp0,(%a0) |
| bsr setox |
| fmovel (%sp)+,%fpcr |
| |
| fmulx (%sp)+,%fp0 |possible exception |
| bra t_frcinx |
| |
| |end |
