s_expm1l.s

glibc 库, 不仅可以学习使用库函数,还可以学习函数的具体实现,是提高功力的好资料

      nop.m 999
      mov FR_Y_hi = FR_T                   // Assume Y_hi = T
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fma.s1 FR_poly = FR_rsq, FR_poly, FR_r // poly = rsq * poly + r
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fma.s1 FR_Wp1_T_scale = FR_W, FR_T_scale, FR_T_scale // (W+1)*T*scale
      nop.i 999
}
{ .mfi
      nop.m 999
      fma.s1 FR_W_T_scale = FR_W, FR_T_scale, f0 // W*T*scale
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p9)  fsub.s1 FR_Y_hi = f0, FR_2_mk      // If expm1, if K < -10 set Y_hi
      nop.i 999
}
{ .mfi
      nop.m 999
(p10) fsub.s1 FR_Y_hi = FR_T, FR_2_mk    // If expm1, if |K|<=10 set Y_hi
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fma.s1 FR_result_lo = FR_Wp1_T_scale, FR_poly, FR_W_T_scale
      nop.i 999
}
;;

.pred.rel "mutex",p8,p9
// If K > 10 adjust result_lo = result_lo - scale * 2^-k
// If |K| <= 10 adjust result_lo = result_lo + scale * T
{ .mfi
      nop.m 999
(p8)  fnma.s1 FR_result_lo = FR_scale, FR_2_mk, FR_result_lo // If K > 10
      nop.i 999
}
{ .mfi
      nop.m 999
(p9)  fma.s1 FR_result_lo = FR_T_scale, f1, FR_result_lo // If |K| <= 10
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fmpy.s0 FR_tmp = FR_A1, FR_A1         // Dummy op to set inexact
      nop.i 999
}
{ .mfb
      nop.m 999
(p15) fma.s0 f8 = FR_Y_hi, FR_scale, FR_result_lo  // Safe result
(p15) br.ret.sptk b0                        // Safe exit for normal path
}
;;

// Here if unsafe, will only be here for exp with K < big_expo_neg
{ .mfb
      nop.m 999
      fma.s0 FR_RESULT = FR_Y_hi, FR_scale, FR_result_lo  // Prelim result
      br.cond.sptk EXP_POSSIBLE_UNDERFLOW  // Branch to unsafe code
}
;;

 
EXP_SMALL: 
// Here if 2^-60 < |x| < 2^-m, m=12 for exp, m=7 for expm1
{ .mfi
(p7)  ldfe FR_Q3 = [GR_ad_Q],16          // Get Q3 for small path, if expm1
(p6)  fma.s1 FR_p65 = FR_P6, FR_r, FR_P5  // If exp, p65 = P6 * r + P5
      nop.i 999
}
{ .mfi
      mov GR_minus_one = -1
(p7)  fma.s1 FR_q98 = FR_Q9, FR_r, FR_Q8  // If expm1, q98 = Q9 * r + Q8
      nop.i 999
}
;;

{ .mfi
(p7)  ldfe FR_Q2 = [GR_ad_Q],16           // Get Q2 for small path, if expm1
(p7)  fma.s1 FR_q65 = FR_Q6, FR_r, FR_Q5  // If expm1, q65 = Q6 * r + Q5
      nop.i 999
}
;;

{ .mfi
      setf.sig FR_tmp = GR_minus_one      // Create value to force inexact
(p6)  fma.s1 FR_p21 = FR_P2, FR_r, FR_P1  // If exp, p21 = P2 * r + P1
      nop.i 999
}
{ .mfi
(p7)  ldfe FR_Q1 = [GR_ad_Q],16           // Get Q1 for small path, if expm1
(p7)  fma.s1 FR_q43 = FR_Q4, FR_r, FR_Q3  // If expm1, q43 = Q4 * r + Q3
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fma.s1 FR_p654 = FR_p65, FR_r, FR_P4 // If exp, p654 = p65 * r + P4
      nop.i 999
}
{ .mfi
      nop.m 999
(p7)  fma.s1 FR_q987 = FR_q98, FR_r, FR_Q7 // If expm1, q987 = q98 * r + Q7
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p7)  fma.s1 FR_q21 = FR_Q2, FR_r, FR_Q1  // If expm1, q21 = Q2 * r + Q1
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fma.s1 FR_p210 = FR_p21, FR_rsq, FR_r // If exp, p210 = p21 * r + P0
      nop.i 999
}
{ .mfi
      nop.m 999
(p7)  fma.s1 FR_q6543 = FR_q65, FR_rsq, FR_q43 // If expm1, q6543 = q65*r2+q43
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fma.s1 FR_p6543 = FR_p654, FR_r, FR_P3 // If exp, p6543 = p654 * r + P3
      nop.i 999
}
{ .mfi
      nop.m 999
(p7)  fma.s1 FR_q9876543 = FR_q987, FR_r4, FR_q6543 // If expm1, q9876543 = ...
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fma.s1 FR_Y_lo = FR_p6543, FR_r4, FR_p210 // If exp, form Y_lo
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p7)  fma.s1 FR_Y_lo = FR_q9876543, FR_rsq, FR_q21 // If expm1, form Y_lo
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fmpy.s0  FR_tmp = FR_tmp, FR_tmp   // Dummy op to set inexact
      nop.i 999
}
;;

.pred.rel "mutex",p6,p7
{ .mfi
      nop.m 999
(p6)  fma.s0 f8 = FR_Y_lo, f1, f1          // If exp, result = 1 + Y_lo
      nop.i 999
}
{ .mfb
      nop.m 999
(p7)  fma.s0 f8 = FR_Y_lo, FR_rsq, FR_norm_x // If expm1, result = Y_lo*r2+x
      br.ret.sptk  b0                      // Exit for 2^-60 <= |x| < 2^-m
                                           // m=12 for exp, m=7 for expm1
}
;;


EXP_VERY_SMALL: 
//
// Here if 0 < |x| < 2^-60
// If exp, result = 1.0 + x
// If expm1, result = x +x*x/2, but have to check for possible underflow
//

{ .mfi
(p7)  mov GR_exp_underflow = -16381        // Exponent for possible underflow
(p6)  fadd.s0 f8 = f1, FR_norm_x           // If exp, result = 1+x
      nop.i 999
}
{ .mfi
      nop.m 999
(p7)  fmpy.s1 FR_result_lo = FR_half_x, FR_norm_x  // If expm1 result_lo = x*x/2
      nop.i 999
}
;;

{ .mfi
(p7)  cmp.lt.unc p0, p8 = GR_exp_x, GR_exp_underflow // Unsafe if expm1 x small
(p7)  mov FR_Y_hi = FR_norm_x              // If expm1, Y_hi = x
(p7)  cmp.lt p0, p15 = GR_exp_x, GR_exp_underflow // Unsafe if expm1 x small
}
;;

{ .mfb
      nop.m 999
(p8)  fma.s0 f8 = FR_norm_x, f1, FR_result_lo // If expm1, result=x+x*x/2
(p15) br.ret.sptk b0                       // If Safe, exit
}
;;

// Here if expm1 and 0 < |x| < 2^-16381;  may be possible underflow
{ .mfb
      nop.m 999
      fma.s0 FR_RESULT = FR_Y_hi, FR_scale, FR_result_lo // Prelim result
      br.cond.sptk EXP_POSSIBLE_UNDERFLOW  // Branch to unsafe code
}
;;

EXP_CERTAIN_UNDERFLOW_ZERO:
// Here if x < zero_uflow_x
// For exp, set result to tiny+0.0 and set I, U, and branch to error handling
// For expm1, set result to tiny-1.0 and set I, and exit
{ .mmi
      alloc GR_SAVE_PFS = ar.pfs,0,3,4,0
      nop.m 999
      mov GR_one = 1
}
;;

{ .mmi
      setf.exp FR_small = GR_one               // Form small value
      nop.m 999
(p6)  mov GR_Parameter_TAG = 13                // Error tag for exp underflow
}
;;

{ .mfi
      nop.m 999
      fmerge.s FR_X = f8,f8                    // Save x for error call
      nop.i 999
}
;;

.pred.rel "mutex",p6,p7
{ .mfb
      nop.m 999
(p6)  fma.s0 FR_RESULT = FR_small, FR_small, f0 // If exp, set I,U, tiny result
(p6)  br.cond.sptk __libm_error_region          // If exp, go to error handling
}
{ .mfb
      nop.m 999
(p7)  fms.s0 f8 = FR_small, FR_small, f1        // If expm1, set I, result -1.0
(p7)  br.ret.sptk  b0                           // If expm1, exit
}
;;
     
  
EXP_OVERFLOW:
// Here if x >= min_oflow_x
{ .mmi
      alloc GR_SAVE_PFS = ar.pfs,0,3,4,0
      mov GR_huge_exp = 0x1fffe
      nop.i 999
}
{ .mfi
      mov GR_huge_signif = -0x1
      nop.f 999
(p6)  mov GR_Parameter_TAG = 12                // Error tag for exp overflow
}
;;

{ .mmf
      setf.exp FR_huge_exp = GR_huge_exp       // Create huge value
      setf.sig FR_huge_signif = GR_huge_signif // Create huge value
      fmerge.s FR_X = f8,f8                    // Save x for error call
}
;;

{ .mfi
      nop.m 999
      fmerge.se FR_huge = FR_huge_exp, FR_huge_signif
(p7)  mov GR_Parameter_TAG = 39                // Error tag for expm1 overflow
}
;;

{ .mfb
      nop.m 999
      fma.s0 FR_RESULT = FR_huge, FR_huge, FR_huge // Force I, O, and Inf
      br.cond.sptk __libm_error_region         // Branch to error handling
}
;;



EXP_POSSIBLE_UNDERFLOW:
// Here if exp and zero_uflow_x < x < about -11356 [where k < -16381]
// Here if expm1 and |x| < 2^-16381
{ .mfi
      alloc GR_SAVE_PFS = ar.pfs,0,3,4,0
      fsetc.s2 0x7F,0x41                   // Set FTZ and disable traps
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fma.s2 FR_ftz = FR_Y_hi, FR_scale, FR_result_lo   // Result with FTZ
      nop.i 999
}
;;

{ .mfi
      nop.m 999
      fsetc.s2 0x7F,0x40                   // Disable traps (set s2 default)
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fclass.m.unc p11, p0 = FR_ftz, 0x00F // If exp, FTZ result denorm or zero?
      nop.i 999
}
;;

{ .mfb
(p11) mov   GR_Parameter_TAG = 13             // exp underflow
      fmerge.s FR_X = f8,f8                   // Save x for error call
(p11) br.cond.spnt __libm_error_region        // Branch on exp underflow
}
;;

{ .mfb
      nop.m 999
      mov   f8     = FR_RESULT                // Was safe after all
      br.ret.sptk   b0
}
;;


EXP_64_SPECIAL: 
// Here if x natval, nan, inf, zero
// If x natval, +inf, or if expm1 and x zero, just return x.
// The other cases must be tested for, and results set.
// These cases do not generate exceptions.
{ .mfi
      nop.m 999
      fclass.m p8, p0 =  f8, 0x0c3            // Is x nan?
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fclass.m.unc p13, p0 =  f8, 0x007       // If exp, is x zero?
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p6)  fclass.m.unc p11, p0 =  f8, 0x022       // If exp, is x -inf?
      nop.i 999
}
{ .mfi
      nop.m 999
(p8)  fadd.s0 f8 = f8, f1                     // If x nan, result quietized x
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p7)  fclass.m.unc p10, p0 =  f8, 0x022       // If expm1, is x -inf?
      nop.i 999
}
{ .mfi
      nop.m 999
(p13) fadd.s0 f8 = f0, f1                     // If exp and x zero, result 1.0
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p11) mov f8 = f0                             // If exp and x -inf, result 0
      nop.i 999
}
;;

{ .mfb
      nop.m 999
(p10) fsub.s1 f8 = f0, f1                     // If expm1, x -inf, result -1.0
      br.ret.sptk b0                          // Exit special cases
}
;;


EXP_64_UNSUPPORTED: 
// Here if x unsupported type
{ .mfb
      nop.m 999
      fmpy.s0 f8 = f8, f0                     // Return nan
      br.ret.sptk   b0
}
;;

GLOBAL_IEEE754_END(expl)

LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
{ .mfi
        add   GR_Parameter_Y=-32,sp             // Parameter 2 value
        nop.f 0
.save   ar.pfs,GR_SAVE_PFS
        mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs
}
{ .mfi
.fframe 64
        add sp=-64,sp                           // Create new stack
        nop.f 0
        mov GR_SAVE_GP=gp                       // Save gp
};;
{ .mmi
        stfe [GR_Parameter_Y] = FR_Y,16         // Save Parameter 2 on stack
        add GR_Parameter_X = 16,sp              // Parameter 1 address
.save   b0, GR_SAVE_B0
        mov GR_SAVE_B0=b0                       // Save b0
};;
.body
{ .mib
        stfe [GR_Parameter_X] = FR_X            // Store Parameter 1 on stack
        add   GR_Parameter_RESULT = 0,GR_Parameter_Y
        nop.b 0                                 // Parameter 3 address
}
{ .mib
        stfe [GR_Parameter_Y] = FR_RESULT      // Store Parameter 3 on stack
        add   GR_Parameter_Y = -16,GR_Parameter_Y
        br.call.sptk b0=__libm_error_support#  // Call error handling function
};;
{ .mmi
        add   GR_Parameter_RESULT = 48,sp
        nop.m 0
        nop.i 0
};;
{ .mmi
        ldfe  f8 = [GR_Parameter_RESULT]       // Get return result off stack
.restore sp
        add   sp = 64,sp                       // Restore stack pointer
        mov   b0 = GR_SAVE_B0                  // Restore return address
};;
{ .mib
        mov   gp = GR_SAVE_GP                  // Restore gp
        mov   ar.pfs = GR_SAVE_PFS             // Restore ar.pfs
        br.ret.sptk     b0                     // Return
};;
LOCAL_LIBM_END(__libm_error_region#)

.type   __libm_error_support#,@function
.global __libm_error_support#