blob: 8a560edc7653e903580c74490b0f4d69a2f43f2a [file] [log] [blame]
 | | 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