{ .mfi          nop.m 999          fma.s1 POW_q                  = POW_Z3sq, POW_q, POW_Z3          nop.i 999};;// p8 TRUE ==> |Y(G + r)| >= 10// double//     -2^10  -2^9             2^9   2^10// -----+-----+----+ ... +-----+-----+-----//  p8  |             p9             |  p8//      |     |       p10      |     |// Form signexp of constants to indicate overflow{ .mfi          mov         pow_GR_big_pos    = 0x103ff          fma.s1 POW_ssq                = POW_s, POW_s, f0          cmp.le p8,p9                  = 10, pow_GR_true_exp_Y_Gpr}{ .mfi          mov         pow_GR_big_neg    = 0x303ff          fma.s1 POW_v4                 = POW_s, POW_Q3, POW_Q2          andcm pow_GR_sign_Y_Gpr       = pow_GR_signexp_Y_Gpr, pow_GR_17ones};;// Form big positive and negative constants to test for possible overflow{ .mfi          setf.exp POW_big_pos          = pow_GR_big_pos          fma.s1 POW_v2                 = POW_s, POW_Q1, POW_Q0_half(p9)      cmp.le.unc p0,p10             = 9, pow_GR_true_exp_Y_Gpr}{ .mfb          setf.exp POW_big_neg          = pow_GR_big_neg          fma.s1 POW_1ps                = f1,f1,POW_s(p8)      br.cond.spnt POW_OVER_UNDER_X_NOT_INF};;// f123 = f12*(e123+1) = f12*e123+f12{ .mfi          nop.m 999          fma.s1 POW_f123               = POW_e123,POW_f12,POW_f12          nop.i 999};;{ .mfi          nop.m 999          fma.s1 POW_T1T2               = POW_T1, POW_T2, f0          nop.i 999}{ .mfi          nop.m 999          fma.s1 POW_v3                 = POW_ssq, POW_Q4, POW_v4          cmp.ne p12,p13 = pow_GR_xneg_yodd, r0};;{ .mfi          nop.m 999          fma.s1 POW_v21ps              = POW_ssq, POW_v2, POW_1ps          nop.i 999}{ .mfi          nop.m 999          fma.s1 POW_s4                 = POW_ssq, POW_ssq, f0          nop.i 999};;{ .mfi          nop.m 999(p12)     fnma.s1 POW_A                 =  POW_2M, POW_f123, f0          nop.i 999}{ .mfi          nop.m 999(p13)     fma.s1 POW_A                  =  POW_2M, POW_f123, f0          cmp.eq p14,p11 = r0,r0   // Initialize p14 on, p11 off};;{ .mfi          nop.m 999          fmerge.s POW_abs_q = f0, POW_q // Form |q| so can test its size          nop.i 999};;{ .mfi(p10)     cmp.eq p0,p14 = r0,r0    // Turn off p14 if no overflow          fma.s1 POW_es                 = POW_s4,  POW_v3, POW_v21ps          nop.i 999}{ .mfi          nop.m 999          fma.s1 POW_A                  = POW_A, POW_T1T2, f0          nop.i 999};;{ .mfi// Test for |q| < 2^-63.  If so then reverse last two steps of the result// to avoid monotonicity problems for results near 1.0 in round up/down/zero.// p11 will be set if need to reverse the order, p14 if not.          nop.m 999(p10)     fcmp.lt.s0 p11,p14 = POW_abs_q, POW_2toM63 // Test |q| <2^-63          nop.i 999};;.pred.rel "mutex",p11,p14{ .mfi          nop.m 999(p14)     fma.s1 POW_A                  = POW_A, POW_es, f0          nop.i 999}{ .mfi          nop.m 999(p11)     fma.s1 POW_A                  = POW_A, POW_q, POW_A          nop.i 999};;// Dummy op to set inexact if |q| < 2^-63{ .mfi          nop.m 999(p11)     fma.d.s0 POW_tmp              = POW_A, POW_q, POW_A          nop.i 999};;{ .mfi          nop.m 999(p14)     fma.d.s0 f8                   = POW_A, POW_q, POW_A          nop.i 999}{ .mfb          nop.m 999(p11)     fma.d.s0 f8                   = POW_A, POW_es, f0(p10)     br.ret.sptk     b0            // Exit main branch if no over/underflow};;// POSSIBLE_OVER_UNDER// p6 = TRUE ==> Y_Gpr negative// Result is already computed.  We just need to know if over/underflow occurred.{ .mfb        cmp.eq p0,p6                    = pow_GR_sign_Y_Gpr, r0        nop.f 999(p6)    br.cond.spnt POW_POSSIBLE_UNDER};;// POSSIBLE_OVER// We got an answer.// overflow is a possibility, not a certainty// We define an overflow when the answer with//    WRE set//    user-defined rounding mode// double// Largest double is 7FE (biased double)//                   7FE - 3FF + FFFF = 103FE// Create + largest_double_plus_ulp// Create - largest_double_plus_ulp// Calculate answer with WRE set.// single// Largest single is FE (biased double)//                   FE - 7F + FFFF = 1007E// Create + largest_single_plus_ulp// Create - largest_single_plus_ulp// Calculate answer with WRE set.// Cases when answer is ldn+1  are as follows://  ldn                   ldn+1// --+----------|----------+------------//              |//    +inf          +inf      -inf//                  RN         RN//                             RZ// Put in s2 (td set, wre set){ .mfi        nop.m 999        fsetc.s2 0x7F,0x42        nop.i 999};;{ .mfi        nop.m 999        fma.d.s2 POW_wre_urm_f8         = POW_A, POW_q, POW_A        nop.i 999};;// Return s2 to default{ .mfi        nop.m 999        fsetc.s2 0x7F,0x40        nop.i 999};;// p7 = TRUE ==> yes, we have an overflow{ .mfi        nop.m 999        fcmp.ge.s1 p7, p8               =  POW_wre_urm_f8, POW_big_pos        nop.i 999};;{ .mfi        nop.m 999(p8)    fcmp.le.s1 p7, p0               =  POW_wre_urm_f8, POW_big_neg        nop.i 999};;{ .mbb(p7)   mov pow_GR_tag                   = 24(p7)   br.cond.spnt __libm_error_region // Branch if overflow       br.ret.sptk     b0               // Exit if did not overflow};;// Here if |y*log(x)| < 2^(-11)// pow(x,y) ~ exp(d) ~ 1 + d + 0.5*d^2 + Q1*d^3 + Q2*d^4, where d = y*log(x).align 32POW_NEAR_ONE:{ .mfi          nop.m 999          fma.s1 POW_d2                 = POW_d, POW_d, f0          nop.i 999};;{ .mfi          nop.m 999          fma.s1 POW_poly_d_hi          = POW_d, POW_Q0_half, f1          nop.i 999}{ .mfi          nop.m 999          fma.s1 POW_poly_d_lo          = POW_d, POW_Q2, POW_Q1          nop.i 999};;{ .mfi          nop.m 999          fma.s1 POW_poly_d             = POW_d2, POW_poly_d_lo, POW_poly_d_hi          nop.i 999};;{ .mfb          nop.m 999          fma.d.s0 f8                   = POW_d, POW_poly_d, f1          br.ret.sptk b0 // exit function for arguments |y*log(x)| < 2^(-11)};;POW_POSSIBLE_UNDER:// We got an answer. input was < -2^9 but > -2^10 (double)// We got an answer. input was < -2^6 but > -2^7  (float)// underflow is a possibility, not a certainty// We define an underflow when the answer with//    ftz set// is zero (tiny numbers become zero)// Notice (from below) that if we have an unlimited exponent range,// then there is an extra machine number E between the largest denormal and// the smallest normal.// So if with unbounded exponent we round to E or below, then we are// tiny and underflow has occurred.// But notice that you can be in a situation where we are tiny, namely// rounded to E, but when the exponent is bounded we round to smallest// normal. So the answer can be the smallest normal with underflow.//                           E// -----+--------------------+--------------------+-----//      |                    |                    |//   1.1...10 2^-3fff    1.1...11 2^-3fff    1.0...00 2^-3ffe//   0.1...11 2^-3ffe                                   (biased, 1)//    largest dn                               smallest normal// Put in s2 (td set, ftz set){ .mfi        nop.m 999        fsetc.s2 0x7F,0x41        nop.i 999};;{ .mfi        nop.m 999        fma.d.s2 POW_ftz_urm_f8         = POW_A, POW_q, POW_A        nop.i 999};;// Return s2 to default{ .mfi        nop.m 999        fsetc.s2 0x7F,0x40        nop.i 999};;// p7 = TRUE ==> yes, we have an underflow{ .mfi        nop.m 999        fcmp.eq.s1 p7, p0               =  POW_ftz_urm_f8, f0        nop.i 999};;{ .mbb(p7)    mov pow_GR_tag                  = 25(p7)    br.cond.spnt __libm_error_region // Branch if underflow        br.ret.sptk     b0               // Exit if did not underflow};;POW_X_DENORM:// Here if x unorm. Use the NORM_X for getf instructions, and then back// to normal path{ .mfi        getf.exp      pow_GR_signexp_X  = POW_NORM_X        nop.f 999        nop.i 999};;{ .mmi        getf.sig      pow_GR_sig_X      = POW_NORM_X;;        and           pow_GR_exp_X      = pow_GR_signexp_X, pow_GR_17ones        nop.i 999};;{ .mib        sub       pow_G