2 * Header for sinf, cosf and sincosf.
4 * Copyright (c) 2018, Arm Limited.
5 * SPDX-License-Identifier: MIT
10 #include "math_config.h"
13 static const double pi63 = 0x1.921FB54442D18p-62;
15 static const double pio4 = 0x1.921FB54442D18p-1;
17 /* The constants and polynomials for sine and cosine. */
20 double sign[4]; /* Sign of sine in quadrants 0..3. */
21 double hpi_inv; /* 2 / PI ( * 2^24 if !TOINT_INTRINSICS). */
22 double hpi; /* PI / 2. */
23 double c0, c1, c2, c3, c4; /* Cosine polynomial. */
24 double s1, s2, s3; /* Sine polynomial. */
27 /* Polynomial data (the cosine polynomial is negated in the 2nd entry). */
28 extern const sincos_t __sincosf_table[2] HIDDEN;
30 /* Table with 4/PI to 192 bit precision. */
31 extern const uint32_t __inv_pio4[] HIDDEN;
33 /* Top 12 bits of the float representation with the sign bit cleared. */
34 static inline uint32_t
37 return (asuint (x) >> 20) & 0x7ff;
40 /* Compute the sine and cosine of inputs X and X2 (X squared), using the
41 polynomial P and store the results in SINP and COSP. N is the quadrant,
42 if odd the cosine and sine polynomials are swapped. */
44 sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp,
47 double x3, x4, x5, x6, s, c, c1, c2, s1;
51 c2 = p->c3 + x2 * p->c4;
52 s1 = p->s2 + x2 * p->s3;
54 /* Swap sin/cos result based on quadrant. */
55 float *tmp = (n & 1 ? cosp : sinp);
56 cosp = (n & 1 ? sinp : cosp);
59 c1 = p->c0 + x2 * p->c1;
70 /* Return the sine of inputs X and X2 (X squared) using the polynomial P.
71 N is the quadrant, and if odd the cosine polynomial is used. */
73 sinf_poly (double x, double x2, const sincos_t *p, int n)
75 double x3, x4, x6, x7, s, c, c1, c2, s1;
80 s1 = p->s2 + x2 * p->s3;
90 c2 = p->c3 + x2 * p->c4;
91 c1 = p->c0 + x2 * p->c1;
100 /* Fast range reduction using single multiply-subtract. Return the modulo of
101 X as a value between -PI/4 and PI/4 and store the quadrant in NP.
102 The values for PI/2 and 2/PI are accessed via P. Since PI/2 as a double
103 is accurate to 55 bits and the worst-case cancellation happens at 6 * PI/4,
104 the result is accurate for |X| <= 120.0. */
106 reduce_fast (double x, const sincos_t *p, int *np)
110 /* Use fast round and lround instructions when available. */
112 *np = converttoint (r);
113 return x - roundtoint (r) * p->hpi;
115 /* Use scaled float to int conversion with explicit rounding.
116 hpi_inv is prescaled by 2^24 so the quadrant ends up in bits 24..31.
117 This avoids inaccuracies introduced by truncating negative values. */
119 int n = ((int32_t)r + 0x800000) >> 24;
121 return x - n * p->hpi;
125 /* Reduce the range of XI to a multiple of PI/2 using fast integer arithmetic.
126 XI is a reinterpreted float and must be >= 2.0f (the sign bit is ignored).
127 Return the modulo between -PI/4 and PI/4 and store the quadrant in NP.
128 Reduction uses a table of 4/PI with 192 bits of precision. A 32x96->128 bit
129 multiply computes the exact 2.62-bit fixed-point modulo. Since the result
130 can have at most 29 leading zeros after the binary point, the double
131 precision result is accurate to 33 bits. */
133 reduce_large (uint32_t xi, int *np)
135 const uint32_t *arr = &__inv_pio4[(xi >> 26) & 15];
136 int shift = (xi >> 23) & 7;
137 uint64_t n, res0, res1, res2;
139 xi = (xi & 0xffffff) | 0x800000;
143 res1 = (uint64_t)xi * arr[4];
144 res2 = (uint64_t)xi * arr[8];
145 res0 = (res2 >> 32) | (res0 << 32);
148 n = (res0 + (1ULL << 61)) >> 62;
150 double x = (int64_t)res0;