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 // double nexttoward( double x, long double y );
51 // input floating point f8, f9
52 // output floating point f8
55 //==============================================================
71 // r36-39 parameters for libm_error_support
79 GR_Parameter_RESULT = r38
80 GR_Parameter_TAG = r39
97 // Overview of operation
98 //==============================================================
99 // nexttoward determines the next representable value
100 // after x in the direction of y.
104 GLOBAL_LIBM_ENTRY(nexttoward)
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 = 0x800, r0
114 // Form largest normal significand 0xfffffffffffff800
115 // Form smallest normal exponent
117 addl GR_lnorm_sig = -0x800,r0
119 addl GR_min_pexp = 0x0fc01, r0 ;;
121 // Extract significand from x
123 // Form largest normal exponent
126 fcmp.eq.s0 p6,p0 = f8, f9
127 addl GR_max_pexp = 0x103fe, r0
129 // Move largest normal significand to fp reg for special cases
131 setf.sig FR_lnorm_sig = GR_lnorm_sig
133 addl GR_sign_mask = 0x20000, r0 ;;
136 // Move smallest denormal significand and signexp to fp regs
138 // Set p12 and p13 based on whether significand increases or decreases
139 // It increases (p12 set) if x<y and x>=0 or if x>y and x<0
140 // It decreases (p13 set) if x<y and x<0 or if x>y and x>=0
142 setf.sig FR_sden_sig = GR_sden_sig
143 fclass.m p8,p0 = f8, 0xc3
144 (p10) cmp.lt p12,p13 = GR_exp, GR_sign_mask
147 setf.exp FR_sden_exp = GR_min_pexp
148 (p11) cmp.ge p12,p13 = GR_exp, GR_sign_mask ;;
151 .pred.rel "mutex",p12,p13
153 // Form expected new significand, adding or subtracting 1 ulp increment
154 // If x=y set result to y
155 // Form smallest normal significand and largest denormal significand
157 (p12) add GR_new_sig = GR_sig, GR_sden_sig
158 (p6) fnorm.d.s0 f8=f9 //Normalise
159 dep.z GR_snorm_sig = 1,63,1 // 0x8000000000000000
162 (p13) sub GR_new_sig = GR_sig, GR_sden_sig
163 movl GR_lden_sig = 0x7ffffffffffff800 ;;
166 // Move expected result significand and signexp to fp regs
168 // Form new exponent in case result exponent needs incrementing or decrementing
170 setf.exp FR_new_exp = GR_exp
171 fclass.m p9,p0 = f9, 0xc3
172 (p12) add GR_exp1 = 1, GR_exp
175 setf.sig FR_new_sig = GR_new_sig
176 (p13) add GR_exp1 = -1, GR_exp
177 (p6) br.ret.spnt b0 ;; // Exit if x=y
180 // Move largest normal signexp to fp reg for special cases
183 setf.exp FR_lnorm_exp = GR_max_pexp
184 fclass.m p7,p0 = f8, 0x7
189 (p8) fma.s0 f8 = f8,f1,f9
190 (p8) br.ret.spnt b0 ;; // Exit if x=nan
193 // Move exp+-1 and smallest normal significand to fp regs for special cases
196 setf.exp FR_exp1 = GR_exp1
197 fclass.m p6,p0 = f8, 0x23
198 addl GR_exp_mask = 0x1ffff, r0
201 setf.sig FR_snorm_sig = GR_snorm_sig
202 (p9) fma.s0 f8 = f8,f1,f9
203 (p9) br.ret.spnt b0 ;; // Exit if y=nan
206 // Move largest denormal significand to fp regs for special cases
209 setf.sig FR_lden_sig = GR_lden_sig
211 (p7) br.cond.spnt NEXT_ZERO ;; // Exit if x=0
214 // Mask off the sign to get x_exp
216 and GR_x_exp = GR_exp_mask, GR_exp
218 (p6) br.cond.spnt NEXT_INF ;; // Exit if x=inf
221 // Check 6 special cases when significand rolls over:
222 // 1 sig size incr, x_sig=max_sig, x_exp < max_exp
223 // Set p6, result is sig=min_sig, exp++
224 // 2 sig size incr, x_sig=max_sig, x_exp >= max_exp
225 // Set p7, result is inf, signal overflow
226 // 3 sig size decr, x_sig=min_sig, x_exp > min_exp
227 // Set p8, result is sig=max_sig, exp--
228 // 4 sig size decr, x_sig=min_sig, x_exp = min_exp
229 // Set p9, result is sig=max_den_sig, exp same, signal underflow and inexact
230 // 5 sig size decr, x_sig=min_den_sig, x_exp = min_exp
231 // Set p10, result is zero, sign of x, signal underflow and inexact
232 // 6 sig size decr, x_sig=min_sig, x_exp < min_exp
233 // Set p14, result is zero, sign of x, signal underflow and inexact
235 // Form exponent of smallest double denormal (if normalized register format)
237 adds GR_min_den_rexp = -52, GR_min_pexp
238 (p12) cmp.eq.unc p6,p0 = GR_new_sig, r0
239 (p13) cmp.eq.unc p8,p10 = GR_new_sig, GR_lden_sig ;;
243 (p6) cmp.lt.unc p6,p7 = GR_x_exp, GR_max_pexp
244 (p8) cmp.gt.unc p8,p9 = GR_x_exp, GR_min_pexp
245 (p10) cmp.eq.unc p10,p0 = GR_new_sig, r0 ;;
248 // Create small normal in case need to generate underflow flag
250 (p10) cmp.le.unc p10,p0 = GR_x_exp, GR_min_pexp
251 fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig
252 (p9) cmp.gt.unc p9,p14 = GR_x_exp, GR_min_den_rexp
254 // Branch if cases 1, 2, 3
256 (p6) br.cond.spnt NEXT_EXPUP
257 (p7) br.cond.spnt NEXT_OVERFLOW
258 (p8) br.cond.spnt NEXT_EXPDOWN ;;
261 // Branch if cases 4, 5, 6
263 (p9) br.cond.spnt NEXT_NORM_TO_DENORM
264 (p10) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO
265 (p14) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO ;;
268 // Here if no special cases
269 // Set p6 if result will be a denormal, so can force underflow flag
270 // Case 1: x_exp=min_exp, x_sig=unnormalized
271 // Case 2: x_exp<min_exp
273 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
274 fmerge.se f8 = FR_new_exp, FR_new_sig
281 (p7) tbit.z p6,p0 = GR_new_sig, 63 ;;
285 // Force underflow and inexact if denormal result
288 (p6) fma.d.s0 FR_tmp = FR_tmp,FR_tmp,f0
293 fnorm.d.s0 f8 = f8 // Final normalization to result precision
294 (p6) br.cond.spnt NEXT_UNDERFLOW ;;
306 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
307 fmerge.se f8 = FR_exp1, FR_snorm_sig
308 br.cond.sptk NEXT_COMMON_FINISH ;;
313 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
314 fmerge.se f8 = FR_exp1, FR_lnorm_sig
315 br.cond.sptk NEXT_COMMON_FINISH ;;
321 fmerge.se f8 = FR_new_exp, FR_lden_sig
324 // Force underflow and inexact if denormal result
327 fma.d.s0 FR_tmp = FR_tmp,FR_tmp,f0
328 br.cond.sptk NEXT_UNDERFLOW ;;
331 NEXT_UNDERFLOW_TO_ZERO:
334 fmerge.s f8 = FR_save_f8,f0
335 br.cond.sptk NEXT_COMMON_FINISH ;;
339 // Here if f8 is +- infinity
341 // if f8 is +inf, no matter what y is return largest double
342 // if f8 is -inf, no matter what y is return -largest double
346 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
352 fmerge.s f8 = f8,FR_lnorm
358 // Here if f8 is +- zero
360 // if f8 is zero and y is +, return + smallest double denormal
361 // if f8 is zero and y is -, return - smallest double denormal
365 fmerge.se FR_sden = FR_sden_exp,FR_sden_sig
369 // Create small normal to generate underflow flag
372 fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig
376 // Add correct sign from direction arg
379 fmerge.s f8 = f9,FR_sden
383 // Force underflow and inexact flags
386 fma.d.s0 FR_tmp = FR_tmp,FR_tmp,f0
387 br.cond.sptk NEXT_UNDERFLOW ;;
391 // Here if result is a denorm, or input is finite and result is zero
392 // Call error support to report possible range error
394 alloc r32=ar.pfs,2,2,4,0
395 mov GR_Parameter_TAG = 271 // Error code
396 br.cond.sptk __libm_error_region // Branch to error call
401 // Here if input is finite, but result will be infinite
402 // Use frcpa to generate infinity of correct sign
403 // Call error support to report possible range error
405 alloc r32=ar.pfs,2,2,4,0
406 frcpa.s1 f8,p6 = FR_save_f8, f0
410 // Create largest double
413 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
417 // Force overflow and inexact flags to be set
419 mov GR_Parameter_TAG = 199 // Error code
420 fma.d.s0 FR_tmp = FR_lnorm,FR_lnorm,f0
421 br.cond.sptk __libm_error_region // Branch to error call
425 GLOBAL_LIBM_END(nexttoward)
428 LOCAL_LIBM_ENTRY(__libm_error_region)
433 add GR_Parameter_Y=-32,sp // Parameter 2 value
435 .save ar.pfs,GR_SAVE_PFS
436 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
440 add sp=-64,sp // Create new stack
442 mov GR_SAVE_GP=gp // Save gp
448 stfd [GR_Parameter_Y] = f9,16 // STORE Parameter 2 on stack
449 add GR_Parameter_X = 16,sp // Parameter 1 address
451 mov GR_SAVE_B0=b0 // Save b0
457 stfd [GR_Parameter_X] = FR_save_f8 // STORE Parameter 1 on stack
458 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
462 stfd [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
463 add GR_Parameter_Y = -16,GR_Parameter_Y
464 br.call.sptk b0=__libm_error_support# // Call error handling function
469 add GR_Parameter_RESULT = 48,sp
474 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
476 add sp = 64,sp // Restore stack pointer
477 mov b0 = GR_SAVE_B0 // Restore return address
480 mov gp = GR_SAVE_GP // Restore gp
481 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
482 br.ret.sptk b0 // Return
485 LOCAL_LIBM_END(__libm_error_region)
488 .type __libm_error_support#,@function
489 .global __libm_error_support#