2  * Double-precision scalar sincospi function.
5  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
16    C2_hi = 4, C2_lo = C2 - C2_hi (~=1.16771278)
21   double poly[10];
24   .poly = { 0x1.921fb54442d184p1, -0x1.2aef39896f94bp0, 0x1.466bc6775ab16p1,
25 	    -0x1.32d2cce62dc33p-1, 0x1.507834891188ep-4, -0x1.e30750a28c88ep-8,
26 	    0x1.e8f48308acda4p-12, -0x1.6fc0032b3c29fp-16,
27 	    0x1.af86ae521260bp-21, -0x1.012a9870eeb7dp-25 },
30 /* Top 12 bits of a double (sign and exponent bits).  */
32 abstop12 (double x)  in abstop12()
38      -1 or +1 if iy represents half an integer
39        -1 if round(y) is odd.
41      -2 or +2 if iy represents and integer.
42        -2 if iy is odd.
44    The argument is the bit representation of a positive non-zero
45    finite floating-point value which is either a half or an integer.  */
52   if (iy & ((1ULL << (0x3ff + 52 - e)) - 1))  in checkint()
54       if ((iy - 1) & 2)  in checkint()
55 	return -1;  in checkint()
59   if (iy & (1 << (0x3ff + 52 - e)))  in checkint()
60     return -2;  in checkint()
64 /* Approximation for scalar double-precision sincospi(x).
66       sincospif_sin(0x1.3d8a067cd8961p+14) got 0x1.ffe609a279008p-1 want
67    0x1.ffe609a27900cp-1.
69       sincospif_cos(0x1.a0ec6997557eep-24) got 0x1.ffffffffffe59p-1 want
70    0x1.ffffffffffe5dp-1.  */
72 arm_math_sincospi (double x, double *out_sin, double *out_cos)  in arm_math_sincospi()
79       /* ax = |x| - n (range reduction into -1/2 .. 1/2).  */  in arm_math_sincospi()
80       double ar_s = x - rint (x);  in arm_math_sincospi()
82       /* We know that cospi(x) = sinpi(0.5 - x)  in arm_math_sincospi()
83 	 range reduction and offset into sinpi range -1/2 .. 1/2  in arm_math_sincospi()
84 	 ax = 0.5 - |x - rint(x)|.  */  in arm_math_sincospi()
85       double ar_c = 0.5 - fabs (ar_s);  in arm_math_sincospi()
88       double ar2_s = ar_s * ar_s;  in arm_math_sincospi()
89       double ar2_c = ar_c * ar_c;  in arm_math_sincospi()
90       double ar4_s = ar2_s * ar2_s;  in arm_math_sincospi()
91       double ar4_c = ar2_c * ar2_c;  in arm_math_sincospi()
98       double ss = pw_horner_9_f64 (ar2_s, ar4_s, d->poly);  in arm_math_sincospi()
99       double cc = pw_horner_9_f64 (ar2_c, ar4_c, d->poly);  in arm_math_sincospi()
101       /* As all values are reduced to -1/2 .. 1/2, the result of cos(x)  in arm_math_sincospi()
106 	  = asdouble (asuint64 (fma (-4 * ar2_s, ar_s, ss * ar_s)) ^ ss_sign);  in arm_math_sincospi()
108 	  = asdouble (asuint64 (fma (-4 * ar2_c, ar_c, cc * ar_c)) ^ cc_sign);  in arm_math_sincospi()
113 	    - Half integer (relevant if abs(x) in [0x1p51, 0x1p52])  in arm_math_sincospi()
114 	    - Odd integer  (relevant if abs(x) in [0x1p52, 0x1p53])  in arm_math_sincospi()
115 	    - Even integer (relevant if abs(x) in [0x1p53, inf])  in arm_math_sincospi()
116 	    - Inf or NaN.  */  in arm_math_sincospi()
119 	  double inv_result = __math_invalid (x);  in arm_math_sincospi()
131 	      *out_sin = sign ? -m : m;  in arm_math_sincospi()
154 SINCOS_INTERVAL (0, 0x1p-63, 10000)
155 SINCOS_INTERVAL (0x1p-63, 0.5, 50000)