4 // Copyright (c) 2001 - 2004, Intel Corporation
5 // All rights reserved.
7 // Contributed 2001 by the Intel Numerics Group, Intel Corporation
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41 //==============================================================
42 // 08/15/01 Initial version
43 // 08/23/01 Corrected error tag number
44 // 05/20/02 Cleaned up namespace and sf0 syntax
45 // 02/10/03 Reordered header: .section, .global, .proc, .align
46 // 12/14/04 Added error handling on underflow.
49 //==============================================================
50 // long double nexttowardl( long double x, long double y );
51 // input floating point f8, f9
52 // output floating point f8
55 //==============================================================
70 // r36-39 parameters for libm_error_support
78 GR_Parameter_RESULT = r38
79 GR_Parameter_TAG = r39
97 // Overview of operation
98 //==============================================================
99 // nexttowardl determines the next representable value
100 // after x in the direction of y.
104 GLOBAL_LIBM_ENTRY(nexttowardl)
106 // Extract signexp from x
107 // Is x < y ? p10 if yes, p11 if no
108 // Form smallest denormal significand = ulp size
111 fcmp.lt.s1 p10,p11 = f8, f9
112 addl GR_sden_sig = 0x1, r0
114 // Form largest normal significand 0xffffffffffffffff
115 // Form smallest normal exponent
117 addl GR_lnorm_sig = -0x1,r0
119 addl GR_min_pexp = 0x0c001, r0 ;;
122 // Extract significand from x
123 // Is x=y? This fcmp also sets Invalid and Denormal if required
124 // Form largest normal exponent
127 fcmp.eq.s0 p6,p0 = f8, f9
128 addl GR_max_pexp = 0x13ffe, r0
130 // Move largest normal significand to fp reg for special cases
132 setf.sig FR_lnorm_sig = GR_lnorm_sig
134 addl GR_sign_mask = 0x20000, r0 ;;
137 // Move smallest denormal significand and exp to fp regs
139 // Set p12 and p13 based on whether significand increases or decreases
140 // It increases (p12 set) if x<y and x>=0 or if x>y and x<0
141 // It decreases (p13 set) if x<y and x<0 or if x>y and x>=0
143 setf.sig FR_sden_sig = GR_sden_sig
144 fclass.m p8,p0 = f8, 0xc3
145 (p10) cmp.lt p12,p13 = GR_exp, GR_sign_mask
147 // Move smallest normal exp to fp regs
149 setf.exp FR_snorm_exp = GR_min_pexp
151 (p11) cmp.ge p12,p13 = GR_exp, GR_sign_mask ;;
154 .pred.rel "mutex",p12,p13
156 // Form expected new significand, adding or subtracting 1 ulp increment
157 // If x=y set result to y
158 // Form smallest normal significand and largest denormal significand
160 (p12) add GR_new_sig = GR_sig, GR_sden_sig
161 (p6) fmerge.s f8=f9,f9
162 dep.z GR_snorm_sig = 1,63,1 // 0x8000000000000000
165 (p13) sub GR_new_sig = GR_sig, GR_sden_sig
166 movl GR_lden_sig = 0x7fffffffffffffff ;;
169 // Move expected result significand and signexp to fp regs
171 // Form new exponent in case result exponent needs incrementing or decrementing
173 setf.exp FR_new_exp = GR_exp
174 fclass.m p9,p0 = f9, 0xc3
175 (p12) add GR_exp1 = 1, GR_exp
178 setf.sig FR_new_sig = GR_new_sig
179 (p13) add GR_exp1 = -1, GR_exp
180 (p6) br.ret.spnt b0 ;; // Exit if x=y
183 // Move largest normal signexp to fp reg for special cases
186 setf.exp FR_lnorm_exp = GR_max_pexp
187 fclass.m p7,p0 = f8, 0x7
191 setf.exp FR_den_exp = GR_min_pexp
192 (p8) fma.s0 f8 = f8,f1,f9
193 (p8) br.ret.spnt b0 ;; // Exit if x=nan
196 // Move exp+-1 and smallest normal significand to fp regs for special cases
199 setf.exp FR_exp1 = GR_exp1
200 fclass.m p6,p0 = f8, 0x23
201 addl GR_exp_mask = 0x1ffff, r0
204 setf.sig FR_snorm_sig = GR_snorm_sig
205 (p9) fma.s0 f8 = f8,f1,f9
206 (p9) br.ret.spnt b0 ;; // Exit if y=nan
209 // Move largest denormal significand to fp regs for special cases
212 setf.sig FR_lden_sig = GR_lden_sig
214 (p7) br.cond.spnt NEXT_ZERO ;; // Exit if x=0
217 // Mask off the sign to get x_exp
219 and GR_x_exp = GR_exp_mask, GR_exp
221 (p6) br.cond.spnt NEXT_INF ;; // Exit if x=inf
224 // Check 5 special cases when significand rolls over:
225 // 1 sig size incr, x_sig=max_sig, x_exp < max_exp
226 // Set p6, result is sig=min_sig, exp++
227 // 2 sig size incr, x_sig=max_sig, x_exp >= max_exp
228 // Set p7, result is inf, signal overflow
229 // 3 sig size decr, x_sig=min_sig, x_exp > min_exp
230 // Set p8, result is sig=max_sig, exp--
231 // 4 sig size decr, x_sig=min_sig, x_exp = min_exp
232 // Set p9, result is sig=max_den_sig, exp same, signal underflow and inexact
233 // 5 sig size decr, x_sig=min_den_sig, x_exp = min_exp
234 // Set p10, result is zero, sign of x, signal underflow and inexact
237 (p12) cmp.eq.unc p6,p0 = GR_new_sig, r0
238 (p13) cmp.eq.unc p9,p10 = GR_new_sig, GR_lden_sig
244 (p6) cmp.lt.unc p6,p7 = GR_x_exp, GR_max_pexp
245 (p10) cmp.eq.unc p10,p0 = GR_new_sig, r0
246 (p9) cmp.le.unc p9,p8 = GR_x_exp, GR_min_pexp
250 // Create small normal in case need to generate underflow flag
253 fmerge.se FR_tmp = FR_snorm_exp, FR_lnorm_sig
256 // Branch if cases 1, 2, 3
258 (p6) br.cond.spnt NEXT_EXPUP
259 (p7) br.cond.spnt NEXT_OVERFLOW
260 (p8) br.cond.spnt NEXT_EXPDOWN ;;
263 // Branch if cases 4, 5
266 (p9) br.cond.spnt NEXT_NORM_TO_DENORM
267 (p10) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO
271 // Here if no special cases
272 // Set p6 if result will be a denormal, so can force underflow flag
273 // Case 1: x_exp=min_exp, x_sig=unnormalized
274 // Case 2: x_exp<min_exp
276 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
277 fmerge.se f8 = FR_new_exp, FR_new_sig
284 (p6) tbit.z p6,p0 = GR_new_sig, 63 ;;
288 // Force underflow and inexact if denormal result
291 (p6) fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
296 fnorm.s0 f8 = f8 // Final normalization to result precision
297 (p6) br.cond.spnt NEXT_UNDERFLOW ;;
309 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
310 fmerge.se f8 = FR_exp1, FR_snorm_sig
311 br.cond.sptk NEXT_COMMON_FINISH ;;
316 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
317 fmerge.se f8 = FR_exp1, FR_lnorm_sig
318 br.cond.sptk NEXT_COMMON_FINISH ;;
324 fmerge.se f8 = FR_exp1, FR_lden_sig
327 // Force underflow and inexact
330 fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
331 br.cond.sptk NEXT_UNDERFLOW ;;
334 NEXT_UNDERFLOW_TO_ZERO:
337 fmerge.s f8 = FR_save_f8,f0
338 br.cond.sptk NEXT_COMMON_FINISH ;;
342 // Here if f8 is +- infinity
344 // if f8 is +inf, no matter what y is return largest long double
345 // if f8 is -inf, no matter what y is return -largest long double
347 // Create largest long double
350 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
356 fmerge.s f8 = f8,FR_lnorm
362 // Here if f8 is +- zero
364 // if f8 is zero and y is +, return + smallest long double denormal
365 // if f8 is zero and y is -, return - smallest long double denormal
369 fmerge.se FR_sden = f0,FR_sden_sig
373 // Create small normal to generate underflow flag
376 fmerge.se FR_tmp = FR_snorm_exp, FR_lnorm_sig
380 // Add correct sign from direction arg
383 fmerge.s f8 = f9,FR_sden
387 // Force underflow and inexact flags
390 fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
391 br.cond.sptk NEXT_UNDERFLOW ;;
395 // Here if result is a denorm, or input is finite and result is zero
396 // Call error support to report possible range error
398 alloc r32=ar.pfs,2,2,4,0
399 mov GR_Parameter_TAG = 270 // Error code
400 br.cond.sptk __libm_error_region // Branch to error call
405 // Here if input is finite, but result will be infinite
406 // Use frcpa to generate infinity of correct sign
407 // Call error support to report possible range error
409 alloc r32=ar.pfs,2,2,4,0
410 frcpa.s1 f8,p6 = FR_save_f8, f0
414 // Create largest double
417 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
421 // Force overflow and inexact flags to be set
423 mov GR_Parameter_TAG = 198 // Error code
424 fma.s0 FR_tmp = FR_lnorm,FR_lnorm,f0
425 br.cond.sptk __libm_error_region // Branch to error call
429 GLOBAL_LIBM_END(nexttowardl)
432 LOCAL_LIBM_ENTRY(__libm_error_region)
437 add GR_Parameter_Y=-32,sp // Parameter 2 value
439 .save ar.pfs,GR_SAVE_PFS
440 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
444 add sp=-64,sp // Create new stack
446 mov GR_SAVE_GP=gp // Save gp
452 stfe [GR_Parameter_Y] = f9,16 // STORE Parameter 2 on stack
453 add GR_Parameter_X = 16,sp // Parameter 1 address
455 mov GR_SAVE_B0=b0 // Save b0
461 stfe [GR_Parameter_X] = FR_save_f8 // STORE Parameter 1 on stack
462 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
466 stfe [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
467 add GR_Parameter_Y = -16,GR_Parameter_Y
468 br.call.sptk b0=__libm_error_support# // Call error handling function
473 add GR_Parameter_RESULT = 48,sp
478 ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
480 add sp = 64,sp // Restore stack pointer
481 mov b0 = GR_SAVE_B0 // Restore return address
484 mov gp = GR_SAVE_GP // Restore gp
485 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
486 br.ret.sptk b0 // Return
489 LOCAL_LIBM_END(__libm_error_region)
492 .type __libm_error_support#,@function
493 .global __libm_error_support#