1 | /* Optimized sinf function. |
2 | Copyright (C) 2012-2017 Free Software Foundation, Inc. |
3 | This file is part of the GNU C Library. |
4 | |
5 | The GNU C Library is free software; you can redistribute it and/or |
6 | modify it under the terms of the GNU Lesser General Public |
7 | License as published by the Free Software Foundation; either |
8 | version 2.1 of the License, or (at your option) any later version. |
9 | |
10 | The GNU C Library is distributed in the hope that it will be useful, |
11 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
13 | Lesser General Public License for more details. |
14 | |
15 | You should have received a copy of the GNU Lesser General Public |
16 | License along with the GNU C Library; if not, see |
17 | <http://www.gnu.org/licenses/>. */ |
18 | |
19 | #include <sysdep.h> |
20 | #include <errno.h> |
21 | |
22 | /* Short algorithm description: |
23 | * |
24 | * 1) if |x| == 0: return x. |
25 | * 2) if |x| < 2^-27: return x-x*DP_SMALL, raise underflow only when needed. |
26 | * 3) if |x| < 2^-5 : return x+x^3*DP_SIN2_0+x^5*DP_SIN2_1. |
27 | * 4) if |x| < Pi/4: return x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). |
28 | * 5) if |x| < 9*Pi/4: |
29 | * 5.1) Range reduction: k=trunc(|x|/(Pi/4)), j=(k+1)&0x0e, n=k+1, |
30 | * t=|x|-j*Pi/4. |
31 | * 5.2) Reconstruction: |
32 | * s = sign(x) * (-1.0)^((n>>2)&1) |
33 | * if(n&2 != 0) { |
34 | * using cos(t) polynomial for |t|<Pi/4, result is |
35 | * s * (1.0+t^2*(C0+t^2*(C1+t^2*(C2+t^2*(C3+t^2*C4))))). |
36 | * } else { |
37 | * using sin(t) polynomial for |t|<Pi/4, result is |
38 | * s * t * (1.0+t^2*(S0+t^2*(S1+t^2*(S2+t^2*(S3+t^2*S4))))). |
39 | * } |
40 | * 6) if |x| < 2^23, large args: |
41 | * 6.1) Range reduction: k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, |
42 | * t=|x|-j*Pi/4. |
43 | * 6.2) Reconstruction same as (5.2). |
44 | * 7) if |x| >= 2^23, very large args: |
45 | * 7.1) Range reduction: k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, |
46 | * t=|x|-j*Pi/4. |
47 | * 7.2) Reconstruction same as (5.2). |
48 | * 8) if x is Inf, return x-x, and set errno=EDOM. |
49 | * 9) if x is NaN, return x-x. |
50 | * |
51 | * Special cases: |
52 | * sin(+-0) = +-0 not raising inexact/underflow, |
53 | * sin(subnormal) raises inexact/underflow, |
54 | * sin(min_normalized) raises inexact/underflow, |
55 | * sin(normalized) raises inexact, |
56 | * sin(Inf) = NaN, raises invalid, sets errno to EDOM, |
57 | * sin(NaN) = NaN. |
58 | */ |
59 | |
60 | .text |
61 | ENTRY(__sinf) |
62 | /* Input: single precision x in %xmm0 */ |
63 | |
64 | movd %xmm0, %eax /* Bits of x */ |
65 | movaps %xmm0, %xmm7 /* Copy of x */ |
66 | cvtss2sd %xmm0, %xmm0 /* DP x */ |
67 | movss L(SP_ABS_MASK)(%rip), %xmm3 |
68 | movl %eax, %edi /* Copy of x bits */ |
69 | andl $0x7fffffff, %eax /* |x| */ |
70 | |
71 | cmpl $0x3f490fdb, %eax /* |x|<Pi/4? */ |
72 | jb L(arg_less_pio4) |
73 | |
74 | /* Here if |x|>=Pi/4 */ |
75 | andps %xmm7, %xmm3 /* SP |x| */ |
76 | andpd L(DP_ABS_MASK)(%rip),%xmm0 /* DP |x| */ |
77 | movss L(SP_INVPIO4)(%rip), %xmm2 /* SP 1/(Pi/4) */ |
78 | |
79 | cmpl $0x40e231d6, %eax /* |x|<9*Pi/4? */ |
80 | jae L(large_args) |
81 | |
82 | /* Here if Pi/4<=|x|<9*Pi/4 */ |
83 | mulss %xmm3, %xmm2 /* SP |x|/(Pi/4) */ |
84 | movl %edi, %ecx /* Load x */ |
85 | cvttss2si %xmm2, %eax /* k, number of Pi/4 in x */ |
86 | lea L(PIO4J)(%rip), %rsi |
87 | shrl $31, %ecx /* sign of x */ |
88 | addl $1, %eax /* k+1 */ |
89 | movl $0x0e, %edx |
90 | andl %eax, %edx /* j = (k+1)&0x0e */ |
91 | subsd (%rsi,%rdx,8), %xmm0 /* t = |x| - j * Pi/4 */ |
92 | |
93 | L(reconstruction): |
94 | /* Input: %eax=n, %xmm0=t, %ecx=sign(x) */ |
95 | testl $2, %eax /* n&2 != 0? */ |
96 | jz L(sin_poly) |
97 | |
98 | /*L(cos_poly):*/ |
99 | /* Here if sin(x) calculated using cos(t) polynomial for |t|<Pi/4: |
100 | * y = t*t; z = y*y; |
101 | * s = sign(x) * (-1.0)^((n>>2)&1) |
102 | * result = s * (1.0+t^2*(C0+t^2*(C1+t^2*(C2+t^2*(C3+t^2*C4))))) |
103 | */ |
104 | shrl $2, %eax /* n>>2 */ |
105 | mulsd %xmm0, %xmm0 /* y=t^2 */ |
106 | andl $1, %eax /* (n>>2)&1 */ |
107 | movaps %xmm0, %xmm1 /* y */ |
108 | mulsd %xmm0, %xmm0 /* z=t^4 */ |
109 | |
110 | movsd L(DP_C4)(%rip), %xmm4 /* C4 */ |
111 | mulsd %xmm0, %xmm4 /* z*C4 */ |
112 | xorl %eax, %ecx /* (-1.0)^((n>>2)&1) XOR sign(x) */ |
113 | movsd L(DP_C3)(%rip), %xmm3 /* C3 */ |
114 | mulsd %xmm0, %xmm3 /* z*C3 */ |
115 | lea L(DP_ONES)(%rip), %rsi |
116 | addsd L(DP_C2)(%rip), %xmm4 /* C2+z*C4 */ |
117 | mulsd %xmm0, %xmm4 /* z*(C2+z*C4) */ |
118 | addsd L(DP_C1)(%rip), %xmm3 /* C1+z*C3 */ |
119 | mulsd %xmm0, %xmm3 /* z*(C1+z*C3) */ |
120 | addsd L(DP_C0)(%rip), %xmm4 /* C0+z*(C2+z*C4) */ |
121 | mulsd %xmm1, %xmm4 /* y*(C0+z*(C2+z*C4)) */ |
122 | |
123 | /* y*(C0+y*(C1+y*(C2+y*(C3+y*C4)))) */ |
124 | addsd %xmm4, %xmm3 |
125 | /* 1.0+y*(C0+y*(C1+y*(C2+y*(C3+y*C4)))) */ |
126 | addsd L(DP_ONES)(%rip), %xmm3 |
127 | |
128 | mulsd (%rsi,%rcx,8), %xmm3 /* DP result */ |
129 | cvtsd2ss %xmm3, %xmm0 /* SP result */ |
130 | ret |
131 | |
132 | .p2align 4 |
133 | L(sin_poly): |
134 | /* Here if sin(x) calculated using sin(t) polynomial for |t|<Pi/4: |
135 | * y = t*t; z = y*y; |
136 | * s = sign(x) * (-1.0)^((n>>2)&1) |
137 | * result = s * t * (1.0+t^2*(S0+t^2*(S1+t^2*(S2+t^2*(S3+t^2*S4))))) |
138 | */ |
139 | |
140 | movaps %xmm0, %xmm4 /* t */ |
141 | shrl $2, %eax /* n>>2 */ |
142 | mulsd %xmm0, %xmm0 /* y=t^2 */ |
143 | andl $1, %eax /* (n>>2)&1 */ |
144 | movaps %xmm0, %xmm1 /* y */ |
145 | xorl %eax, %ecx /* (-1.0)^((n>>2)&1) XOR sign(x) */ |
146 | mulsd %xmm0, %xmm0 /* z=t^4 */ |
147 | |
148 | movsd L(DP_S4)(%rip), %xmm2 /* S4 */ |
149 | mulsd %xmm0, %xmm2 /* z*S4 */ |
150 | movsd L(DP_S3)(%rip), %xmm3 /* S3 */ |
151 | mulsd %xmm0, %xmm3 /* z*S3 */ |
152 | lea L(DP_ONES)(%rip), %rsi |
153 | addsd L(DP_S2)(%rip), %xmm2 /* S2+z*S4 */ |
154 | mulsd %xmm0, %xmm2 /* z*(S2+z*S4) */ |
155 | addsd L(DP_S1)(%rip), %xmm3 /* S1+z*S3 */ |
156 | mulsd %xmm0, %xmm3 /* z*(S1+z*S3) */ |
157 | addsd L(DP_S0)(%rip), %xmm2 /* S0+z*(S2+z*S4) */ |
158 | mulsd %xmm1, %xmm2 /* y*(S0+z*(S2+z*S4)) */ |
159 | /* t*s, where s = sign(x) * (-1.0)^((n>>2)&1) */ |
160 | mulsd (%rsi,%rcx,8), %xmm4 |
161 | /* y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ |
162 | addsd %xmm2, %xmm3 |
163 | /* t*s*y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ |
164 | mulsd %xmm4, %xmm3 |
165 | /* t*s*(1.0+y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ |
166 | addsd %xmm4, %xmm3 |
167 | cvtsd2ss %xmm3, %xmm0 /* SP result */ |
168 | ret |
169 | |
170 | .p2align 4 |
171 | L(large_args): |
172 | /* Here if |x|>=9*Pi/4 */ |
173 | cmpl $0x7f800000, %eax /* x is Inf or NaN? */ |
174 | jae L(arg_inf_or_nan) |
175 | |
176 | /* Here if finite |x|>=9*Pi/4 */ |
177 | cmpl $0x4b000000, %eax /* |x|<2^23? */ |
178 | jae L(very_large_args) |
179 | |
180 | /* Here if 9*Pi/4<=|x|<2^23 */ |
181 | movsd L(DP_INVPIO4)(%rip), %xmm1 /* 1/(Pi/4) */ |
182 | mulsd %xmm0, %xmm1 /* |x|/(Pi/4) */ |
183 | cvttsd2si %xmm1, %eax /* k=trunc(|x|/(Pi/4)) */ |
184 | addl $1, %eax /* k+1 */ |
185 | movl %eax, %edx |
186 | andl $0xfffffffe, %edx /* j=(k+1)&0xfffffffe */ |
187 | cvtsi2sdl %edx, %xmm4 /* DP j */ |
188 | movl %edi, %ecx /* Load x */ |
189 | movsd L(DP_PIO4HI)(%rip), %xmm2 /* -PIO4HI = high part of -Pi/4 */ |
190 | shrl $31, %ecx /* sign bit of x */ |
191 | mulsd %xmm4, %xmm2 /* -j*PIO4HI */ |
192 | movsd L(DP_PIO4LO)(%rip), %xmm3 /* -PIO4LO = low part of -Pi/4 */ |
193 | addsd %xmm2, %xmm0 /* |x| - j*PIO4HI */ |
194 | mulsd %xmm3, %xmm4 /* j*PIO4LO */ |
195 | addsd %xmm4, %xmm0 /* t = |x| - j*PIO4HI - j*PIO4LO */ |
196 | jmp L(reconstruction) |
197 | |
198 | .p2align 4 |
199 | L(very_large_args): |
200 | /* Here if finite |x|>=2^23 */ |
201 | |
202 | /* bitpos = (ix>>23) - BIAS_32 + 59; */ |
203 | shrl $23, %eax /* eb = biased exponent of x */ |
204 | /* bitpos = eb - 0x7f + 59, where 0x7f is exponent bias */ |
205 | subl $68, %eax |
206 | movl $28, %ecx /* %cl=28 */ |
207 | movl %eax, %edx /* bitpos copy */ |
208 | |
209 | /* j = bitpos/28; */ |
210 | div %cl /* j in register %al=%ax/%cl */ |
211 | movapd %xmm0, %xmm3 /* |x| */ |
212 | /* clear unneeded remainder from %ah */ |
213 | andl $0xff, %eax |
214 | |
215 | imull $28, %eax, %ecx /* j*28 */ |
216 | lea L(_FPI)(%rip), %rsi |
217 | movsd L(DP_HI_MASK)(%rip), %xmm4 /* DP_HI_MASK */ |
218 | movapd %xmm0, %xmm5 /* |x| */ |
219 | mulsd -16(%rsi,%rax,8), %xmm3 /* tmp3 = FPI[j-2]*|x| */ |
220 | movapd %xmm0, %xmm1 /* |x| */ |
221 | mulsd -8(%rsi,%rax,8), %xmm5 /* tmp2 = FPI[j-1]*|x| */ |
222 | mulsd (%rsi,%rax,8), %xmm0 /* tmp0 = FPI[j]*|x| */ |
223 | addl $19, %ecx /* j*28+19 */ |
224 | mulsd 8(%rsi,%rax,8), %xmm1 /* tmp1 = FPI[j+1]*|x| */ |
225 | cmpl %ecx, %edx /* bitpos>=j*28+19? */ |
226 | jl L(very_large_skip1) |
227 | |
228 | /* Here if bitpos>=j*28+19 */ |
229 | andpd %xmm3, %xmm4 /* HI(tmp3) */ |
230 | subsd %xmm4, %xmm3 /* tmp3 = tmp3 - HI(tmp3) */ |
231 | L(very_large_skip1): |
232 | |
233 | movsd L(DP_2POW52)(%rip), %xmm6 |
234 | movapd %xmm5, %xmm2 /* tmp2 copy */ |
235 | addsd %xmm3, %xmm5 /* tmp5 = tmp3 + tmp2 */ |
236 | movl $1, %edx |
237 | addsd %xmm5, %xmm6 /* tmp6 = tmp5 + 2^52 */ |
238 | movsd 8+L(DP_2POW52)(%rip), %xmm4 |
239 | movd %xmm6, %eax /* k = I64_LO(tmp6); */ |
240 | addsd %xmm6, %xmm4 /* tmp4 = tmp6 - 2^52 */ |
241 | movl %edi, %ecx /* Load x */ |
242 | comisd %xmm5, %xmm4 /* tmp4 > tmp5? */ |
243 | jbe L(very_large_skip2) |
244 | |
245 | /* Here if tmp4 > tmp5 */ |
246 | subl $1, %eax /* k-- */ |
247 | addsd 8+L(DP_ONES)(%rip), %xmm4 /* tmp4 -= 1.0 */ |
248 | L(very_large_skip2): |
249 | |
250 | andl %eax, %edx /* k&1 */ |
251 | lea L(DP_ZERONE)(%rip), %rsi |
252 | subsd %xmm4, %xmm3 /* tmp3 -= tmp4 */ |
253 | addsd (%rsi,%rdx,8), %xmm3 /* t = DP_ZERONE[k&1] + tmp3 */ |
254 | addsd %xmm2, %xmm3 /* t += tmp2 */ |
255 | shrl $31, %ecx /* sign of x */ |
256 | addsd %xmm3, %xmm0 /* t += tmp0 */ |
257 | addl $1, %eax /* n=k+1 */ |
258 | addsd %xmm1, %xmm0 /* t += tmp1 */ |
259 | mulsd L(DP_PIO4)(%rip), %xmm0 /* t *= PI04 */ |
260 | |
261 | jmp L(reconstruction) /* end of very_large_args peth */ |
262 | |
263 | .p2align 4 |
264 | L(arg_less_pio4): |
265 | /* Here if |x|<Pi/4 */ |
266 | cmpl $0x3d000000, %eax /* |x|<2^-5? */ |
267 | jl L(arg_less_2pn5) |
268 | |
269 | /* Here if 2^-5<=|x|<Pi/4 */ |
270 | movaps %xmm0, %xmm3 /* x */ |
271 | mulsd %xmm0, %xmm0 /* y=x^2 */ |
272 | movaps %xmm0, %xmm1 /* y */ |
273 | mulsd %xmm0, %xmm0 /* z=x^4 */ |
274 | movsd L(DP_S4)(%rip), %xmm4 /* S4 */ |
275 | mulsd %xmm0, %xmm4 /* z*S4 */ |
276 | movsd L(DP_S3)(%rip), %xmm5 /* S3 */ |
277 | mulsd %xmm0, %xmm5 /* z*S3 */ |
278 | addsd L(DP_S2)(%rip), %xmm4 /* S2+z*S4 */ |
279 | mulsd %xmm0, %xmm4 /* z*(S2+z*S4) */ |
280 | addsd L(DP_S1)(%rip), %xmm5 /* S1+z*S3 */ |
281 | mulsd %xmm0, %xmm5 /* z*(S1+z*S3) */ |
282 | addsd L(DP_S0)(%rip), %xmm4 /* S0+z*(S2+z*S4) */ |
283 | mulsd %xmm1, %xmm4 /* y*(S0+z*(S2+z*S4)) */ |
284 | mulsd %xmm3, %xmm5 /* x*z*(S1+z*S3) */ |
285 | mulsd %xmm3, %xmm4 /* x*y*(S0+z*(S2+z*S4)) */ |
286 | /* x*y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ |
287 | addsd %xmm5, %xmm4 |
288 | /* x + x*y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */ |
289 | addsd %xmm4, %xmm3 |
290 | cvtsd2ss %xmm3, %xmm0 /* SP result */ |
291 | ret |
292 | |
293 | .p2align 4 |
294 | L(arg_less_2pn5): |
295 | /* Here if |x|<2^-5 */ |
296 | cmpl $0x32000000, %eax /* |x|<2^-27? */ |
297 | jl L(arg_less_2pn27) |
298 | |
299 | /* Here if 2^-27<=|x|<2^-5 */ |
300 | movaps %xmm0, %xmm1 /* DP x */ |
301 | mulsd %xmm0, %xmm0 /* DP x^2 */ |
302 | movsd L(DP_SIN2_1)(%rip), %xmm3 /* DP DP_SIN2_1 */ |
303 | mulsd %xmm0, %xmm3 /* DP x^2*DP_SIN2_1 */ |
304 | addsd L(DP_SIN2_0)(%rip), %xmm3 /* DP DP_SIN2_0+x^2*DP_SIN2_1 */ |
305 | mulsd %xmm0, %xmm3 /* DP x^2*DP_SIN2_0+x^4*DP_SIN2_1 */ |
306 | mulsd %xmm1, %xmm3 /* DP x^3*DP_SIN2_0+x^5*DP_SIN2_1 */ |
307 | addsd %xmm1, %xmm3 /* DP x+x^3*DP_SIN2_0+x^5*DP_SIN2_1 */ |
308 | cvtsd2ss %xmm3, %xmm0 /* SP result */ |
309 | ret |
310 | |
311 | .p2align 4 |
312 | L(arg_less_2pn27): |
313 | cmpl $0, %eax /* x=0? */ |
314 | je L(arg_zero) /* in case x=0 return sin(+-0)==+-0 */ |
315 | /* Here if |x|<2^-27 */ |
316 | /* |
317 | * Special cases here: |
318 | * sin(subnormal) raises inexact/underflow |
319 | * sin(min_normalized) raises inexact/underflow |
320 | * sin(normalized) raises inexact |
321 | */ |
322 | movaps %xmm0, %xmm3 /* Copy of DP x */ |
323 | mulsd L(DP_SMALL)(%rip), %xmm0 /* x*DP_SMALL */ |
324 | subsd %xmm0, %xmm3 /* Result is x-x*DP_SMALL */ |
325 | cvtsd2ss %xmm3, %xmm0 /* Result converted to SP */ |
326 | ret |
327 | |
328 | .p2align 4 |
329 | L(arg_zero): |
330 | movaps %xmm7, %xmm0 /* SP x */ |
331 | ret |
332 | |
333 | .p2align 4 |
334 | L(arg_inf_or_nan): |
335 | /* Here if |x| is Inf or NAN */ |
336 | jne L(skip_errno_setting) /* in case of x is NaN */ |
337 | |
338 | /* Align stack to 16 bytes. */ |
339 | subq $8, %rsp |
340 | cfi_adjust_cfa_offset (8) |
341 | /* Here if x is Inf. Set errno to EDOM. */ |
342 | call JUMPTARGET(__errno_location) |
343 | addq $8, %rsp |
344 | cfi_adjust_cfa_offset (-8) |
345 | |
346 | movl $EDOM, (%rax) |
347 | |
348 | .p2align 4 |
349 | L(skip_errno_setting): |
350 | /* Here if |x| is Inf or NAN. Continued. */ |
351 | movaps %xmm7, %xmm0 /* load x */ |
352 | subss %xmm0, %xmm0 /* Result is NaN */ |
353 | ret |
354 | END(__sinf) |
355 | |
356 | .section .rodata, "a" |
357 | .p2align 3 |
358 | L(PIO4J): /* Table of j*Pi/4, for j=0,1,..,10 */ |
359 | .long 0x00000000,0x00000000 |
360 | .long 0x54442d18,0x3fe921fb |
361 | .long 0x54442d18,0x3ff921fb |
362 | .long 0x7f3321d2,0x4002d97c |
363 | .long 0x54442d18,0x400921fb |
364 | .long 0x2955385e,0x400f6a7a |
365 | .long 0x7f3321d2,0x4012d97c |
366 | .long 0xe9bba775,0x4015fdbb |
367 | .long 0x54442d18,0x401921fb |
368 | .long 0xbeccb2bb,0x401c463a |
369 | .long 0x2955385e,0x401f6a7a |
370 | .type L(PIO4J), @object |
371 | ASM_SIZE_DIRECTIVE(L(PIO4J)) |
372 | |
373 | .p2align 3 |
374 | L(_FPI): /* 4/Pi broken into sum of positive DP values */ |
375 | .long 0x00000000,0x00000000 |
376 | .long 0x6c000000,0x3ff45f30 |
377 | .long 0x2a000000,0x3e3c9c88 |
378 | .long 0xa8000000,0x3c54fe13 |
379 | .long 0xd0000000,0x3aaf47d4 |
380 | .long 0x6c000000,0x38fbb81b |
381 | .long 0xe0000000,0x3714acc9 |
382 | .long 0x7c000000,0x3560e410 |
383 | .long 0x56000000,0x33bca2c7 |
384 | .long 0xac000000,0x31fbd778 |
385 | .long 0xe0000000,0x300b7246 |
386 | .long 0xe8000000,0x2e5d2126 |
387 | .long 0x48000000,0x2c970032 |
388 | .long 0xe8000000,0x2ad77504 |
389 | .long 0xe0000000,0x290921cf |
390 | .long 0xb0000000,0x274deb1c |
391 | .long 0xe0000000,0x25829a73 |
392 | .long 0xbe000000,0x23fd1046 |
393 | .long 0x10000000,0x2224baed |
394 | .long 0x8e000000,0x20709d33 |
395 | .long 0x80000000,0x1e535a2f |
396 | .long 0x64000000,0x1cef904e |
397 | .long 0x30000000,0x1b0d6398 |
398 | .long 0x24000000,0x1964ce7d |
399 | .long 0x16000000,0x17b908bf |
400 | .type L(_FPI), @object |
401 | ASM_SIZE_DIRECTIVE(L(_FPI)) |
402 | |
403 | /* Coefficients of polynomial |
404 | for sin(x)~=x+x^3*DP_SIN2_0+x^5*DP_SIN2_1, |x|<2^-5. */ |
405 | .p2align 3 |
406 | L(DP_SIN2_0): |
407 | .long 0x5543d49d,0xbfc55555 |
408 | .type L(DP_SIN2_0), @object |
409 | ASM_SIZE_DIRECTIVE(L(DP_SIN2_0)) |
410 | |
411 | .p2align 3 |
412 | L(DP_SIN2_1): |
413 | .long 0x75cec8c5,0x3f8110f4 |
414 | .type L(DP_SIN2_1), @object |
415 | ASM_SIZE_DIRECTIVE(L(DP_SIN2_1)) |
416 | |
417 | .p2align 3 |
418 | L(DP_ZERONE): |
419 | .long 0x00000000,0x00000000 /* 0.0 */ |
420 | .long 0x00000000,0xbff00000 /* 1.0 */ |
421 | .type L(DP_ZERONE), @object |
422 | ASM_SIZE_DIRECTIVE(L(DP_ZERONE)) |
423 | |
424 | .p2align 3 |
425 | L(DP_ONES): |
426 | .long 0x00000000,0x3ff00000 /* +1.0 */ |
427 | .long 0x00000000,0xbff00000 /* -1.0 */ |
428 | .type L(DP_ONES), @object |
429 | ASM_SIZE_DIRECTIVE(L(DP_ONES)) |
430 | |
431 | /* Coefficients of polynomial |
432 | for sin(t)~=t+t^3*(S0+t^2*(S1+t^2*(S2+t^2*(S3+t^2*S4)))), |t|<Pi/4. */ |
433 | .p2align 3 |
434 | L(DP_S3): |
435 | .long 0x64e6b5b4,0x3ec71d72 |
436 | .type L(DP_S3), @object |
437 | ASM_SIZE_DIRECTIVE(L(DP_S3)) |
438 | |
439 | .p2align 3 |
440 | L(DP_S1): |
441 | .long 0x10c2688b,0x3f811111 |
442 | .type L(DP_S1), @object |
443 | ASM_SIZE_DIRECTIVE(L(DP_S1)) |
444 | |
445 | .p2align 3 |
446 | L(DP_S4): |
447 | .long 0x1674b58a,0xbe5a947e |
448 | .type L(DP_S4), @object |
449 | ASM_SIZE_DIRECTIVE(L(DP_S4)) |
450 | |
451 | .p2align 3 |
452 | L(DP_S2): |
453 | .long 0x8b4bd1f9,0xbf2a019f |
454 | .type L(DP_S2), @object |
455 | ASM_SIZE_DIRECTIVE(L(DP_S2)) |
456 | |
457 | .p2align 3 |
458 | L(DP_S0): |
459 | .long 0x55551cd9,0xbfc55555 |
460 | .type L(DP_S0), @object |
461 | ASM_SIZE_DIRECTIVE(L(DP_S0)) |
462 | |
463 | .p2align 3 |
464 | L(DP_SMALL): |
465 | .long 0x00000000,0x3cd00000 /* 2^(-50) */ |
466 | .type L(DP_SMALL), @object |
467 | ASM_SIZE_DIRECTIVE(L(DP_SMALL)) |
468 | |
469 | /* Coefficients of polynomial |
470 | for cos(t)~=1.0+t^2*(C0+t^2*(C1+t^2*(C2+t^2*(C3+t^2*C4)))), |t|<Pi/4. */ |
471 | .p2align 3 |
472 | L(DP_C3): |
473 | .long 0x9ac43cc0,0x3efa00eb |
474 | .type L(DP_C3), @object |
475 | ASM_SIZE_DIRECTIVE(L(DP_C3)) |
476 | |
477 | .p2align 3 |
478 | L(DP_C1): |
479 | .long 0x545c50c7,0x3fa55555 |
480 | .type L(DP_C1), @object |
481 | ASM_SIZE_DIRECTIVE(L(DP_C1)) |
482 | |
483 | .p2align 3 |
484 | L(DP_C4): |
485 | .long 0xdd8844d7,0xbe923c97 |
486 | .type L(DP_C4), @object |
487 | ASM_SIZE_DIRECTIVE(L(DP_C4)) |
488 | |
489 | .p2align 3 |
490 | L(DP_C2): |
491 | .long 0x348b6874,0xbf56c16b |
492 | .type L(DP_C2), @object |
493 | ASM_SIZE_DIRECTIVE(L(DP_C2)) |
494 | |
495 | .p2align 3 |
496 | L(DP_C0): |
497 | .long 0xfffe98ae,0xbfdfffff |
498 | .type L(DP_C0), @object |
499 | ASM_SIZE_DIRECTIVE(L(DP_C0)) |
500 | |
501 | .p2align 3 |
502 | L(DP_PIO4): |
503 | .long 0x54442d18,0x3fe921fb /* Pi/4 */ |
504 | .type L(DP_PIO4), @object |
505 | ASM_SIZE_DIRECTIVE(L(DP_PIO4)) |
506 | |
507 | .p2align 3 |
508 | L(DP_2POW52): |
509 | .long 0x00000000,0x43300000 /* +2^52 */ |
510 | .long 0x00000000,0xc3300000 /* -2^52 */ |
511 | .type L(DP_2POW52), @object |
512 | ASM_SIZE_DIRECTIVE(L(DP_2POW52)) |
513 | |
514 | .p2align 3 |
515 | L(DP_INVPIO4): |
516 | .long 0x6dc9c883,0x3ff45f30 /* 4/Pi */ |
517 | .type L(DP_INVPIO4), @object |
518 | ASM_SIZE_DIRECTIVE(L(DP_INVPIO4)) |
519 | |
520 | .p2align 3 |
521 | L(DP_PIO4HI): |
522 | .long 0x54000000,0xbfe921fb /* High part of Pi/4 */ |
523 | .type L(DP_PIO4HI), @object |
524 | ASM_SIZE_DIRECTIVE(L(DP_PIO4HI)) |
525 | |
526 | .p2align 3 |
527 | L(DP_PIO4LO): |
528 | .long 0x11A62633,0xbe010b46 /* Low part of Pi/4 */ |
529 | .type L(DP_PIO4LO), @object |
530 | ASM_SIZE_DIRECTIVE(L(DP_PIO4LO)) |
531 | |
532 | .p2align 2 |
533 | L(SP_INVPIO4): |
534 | .long 0x3fa2f983 /* 4/Pi */ |
535 | .type L(SP_INVPIO4), @object |
536 | ASM_SIZE_DIRECTIVE(L(SP_INVPIO4)) |
537 | |
538 | .p2align 4 |
539 | L(DP_ABS_MASK): /* Mask for getting DP absolute value */ |
540 | .long 0xffffffff,0x7fffffff |
541 | .long 0xffffffff,0x7fffffff |
542 | .type L(DP_ABS_MASK), @object |
543 | ASM_SIZE_DIRECTIVE(L(DP_ABS_MASK)) |
544 | |
545 | .p2align 3 |
546 | L(DP_HI_MASK): /* Mask for getting high 21 bits of DP value */ |
547 | .long 0x00000000,0xffffffff |
548 | .type L(DP_HI_MASK),@object |
549 | ASM_SIZE_DIRECTIVE(L(DP_HI_MASK)) |
550 | |
551 | .p2align 4 |
552 | L(SP_ABS_MASK): /* Mask for getting SP absolute value */ |
553 | .long 0x7fffffff,0x7fffffff |
554 | .long 0x7fffffff,0x7fffffff |
555 | .type L(SP_ABS_MASK), @object |
556 | ASM_SIZE_DIRECTIVE(L(SP_ABS_MASK)) |
557 | |
558 | weak_alias(__sinf, sinf) |
559 | |