1 // origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c
2 //
3 // ====================================================
4 // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 //
6 // Developed at SunPro, a Sun Microsystems, Inc. business.
7 // Permission to use, copy, modify, and distribute this
8 // software is freely granted, provided that this notice
9 // is preserved.
10 // ====================================================
11 //
12 // Optimized by Bruce D. Evans. */
13 use super::rem_pio2_large;
14
15 // #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
16 // #define EPS DBL_EPSILON
17 const EPS: f64 = 2.2204460492503131e-16;
18 // #elif FLT_EVAL_METHOD==2
19 // #define EPS LDBL_EPSILON
20 // #endif
21
22 // TODO: Support FLT_EVAL_METHOD?
23
24 const TO_INT: f64 = 1.5 / EPS;
25 /// 53 bits of 2/pi
26 const INV_PIO2: f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
27 /// first 33 bits of pi/2
28 const PIO2_1: f64 = 1.57079632673412561417e+00; /* 0x3FF921FB, 0x54400000 */
29 /// pi/2 - PIO2_1
30 const PIO2_1T: f64 = 6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */
31 /// second 33 bits of pi/2
32 const PIO2_2: f64 = 6.07710050630396597660e-11; /* 0x3DD0B461, 0x1A600000 */
33 /// pi/2 - (PIO2_1+PIO2_2)
34 const PIO2_2T: f64 = 2.02226624879595063154e-21; /* 0x3BA3198A, 0x2E037073 */
35 /// third 33 bits of pi/2
36 const PIO2_3: f64 = 2.02226624871116645580e-21; /* 0x3BA3198A, 0x2E000000 */
37 /// pi/2 - (PIO2_1+PIO2_2+PIO2_3)
38 const PIO2_3T: f64 = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
39
40 // return the remainder of x rem pi/2 in y[0]+y[1]
41 // use rem_pio2_large() for large x
42 //
43 // caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
44 #[inline]
45 #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
rem_pio2(x: f64) -> (i32, f64, f64)46 pub(crate) fn rem_pio2(x: f64) -> (i32, f64, f64) {
47 let x1p24 = f64::from_bits(0x4170000000000000);
48
49 let sign = (f64::to_bits(x) >> 63) as i32;
50 let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
51
52 #[inline]
53 fn medium(x: f64, ix: u32) -> (i32, f64, f64) {
54 /* rint(x/(pi/2)), Assume round-to-nearest. */
55 let f_n = x as f64 * INV_PIO2 + TO_INT - TO_INT;
56 let n = f_n as i32;
57 let mut r = x - f_n * PIO2_1;
58 let mut w = f_n * PIO2_1T; /* 1st round, good to 85 bits */
59 let mut y0 = r - w;
60 let ui = f64::to_bits(y0);
61 let ey = (ui >> 52) as i32 & 0x7ff;
62 let ex = (ix >> 20) as i32;
63 if ex - ey > 16 {
64 /* 2nd round, good to 118 bits */
65 let t = r;
66 w = f_n * PIO2_2;
67 r = t - w;
68 w = f_n * PIO2_2T - ((t - r) - w);
69 y0 = r - w;
70 let ey = (f64::to_bits(y0) >> 52) as i32 & 0x7ff;
71 if ex - ey > 49 {
72 /* 3rd round, good to 151 bits, covers all cases */
73 let t = r;
74 w = f_n * PIO2_3;
75 r = t - w;
76 w = f_n * PIO2_3T - ((t - r) - w);
77 y0 = r - w;
78 }
79 }
80 let y1 = (r - y0) - w;
81 (n, y0, y1)
82 }
83
84 if ix <= 0x400f6a7a {
85 /* |x| ~<= 5pi/4 */
86 if (ix & 0xfffff) == 0x921fb {
87 /* |x| ~= pi/2 or 2pi/2 */
88 return medium(x, ix); /* cancellation -- use medium case */
89 }
90 if ix <= 0x4002d97c {
91 /* |x| ~<= 3pi/4 */
92 if sign == 0 {
93 let z = x - PIO2_1; /* one round good to 85 bits */
94 let y0 = z - PIO2_1T;
95 let y1 = (z - y0) - PIO2_1T;
96 return (1, y0, y1);
97 } else {
98 let z = x + PIO2_1;
99 let y0 = z + PIO2_1T;
100 let y1 = (z - y0) + PIO2_1T;
101 return (-1, y0, y1);
102 }
103 } else if sign == 0 {
104 let z = x - 2.0 * PIO2_1;
105 let y0 = z - 2.0 * PIO2_1T;
106 let y1 = (z - y0) - 2.0 * PIO2_1T;
107 return (2, y0, y1);
108 } else {
109 let z = x + 2.0 * PIO2_1;
110 let y0 = z + 2.0 * PIO2_1T;
111 let y1 = (z - y0) + 2.0 * PIO2_1T;
112 return (-2, y0, y1);
113 }
114 }
115 if ix <= 0x401c463b {
116 /* |x| ~<= 9pi/4 */
117 if ix <= 0x4015fdbc {
118 /* |x| ~<= 7pi/4 */
119 if ix == 0x4012d97c {
120 /* |x| ~= 3pi/2 */
121 return medium(x, ix);
122 }
123 if sign == 0 {
124 let z = x - 3.0 * PIO2_1;
125 let y0 = z - 3.0 * PIO2_1T;
126 let y1 = (z - y0) - 3.0 * PIO2_1T;
127 return (3, y0, y1);
128 } else {
129 let z = x + 3.0 * PIO2_1;
130 let y0 = z + 3.0 * PIO2_1T;
131 let y1 = (z - y0) + 3.0 * PIO2_1T;
132 return (-3, y0, y1);
133 }
134 } else {
135 if ix == 0x401921fb {
136 /* |x| ~= 4pi/2 */
137 return medium(x, ix);
138 }
139 if sign == 0 {
140 let z = x - 4.0 * PIO2_1;
141 let y0 = z - 4.0 * PIO2_1T;
142 let y1 = (z - y0) - 4.0 * PIO2_1T;
143 return (4, y0, y1);
144 } else {
145 let z = x + 4.0 * PIO2_1;
146 let y0 = z + 4.0 * PIO2_1T;
147 let y1 = (z - y0) + 4.0 * PIO2_1T;
148 return (-4, y0, y1);
149 }
150 }
151 }
152 if ix < 0x413921fb {
153 /* |x| ~< 2^20*(pi/2), medium size */
154 return medium(x, ix);
155 }
156 /*
157 * all other (large) arguments
158 */
159 if ix >= 0x7ff00000 {
160 /* x is inf or NaN */
161 let y0 = x - x;
162 let y1 = y0;
163 return (0, y0, y1);
164 }
165 /* set z = scalbn(|x|,-ilogb(x)+23) */
166 let mut ui = f64::to_bits(x);
167 ui &= (!1) >> 12;
168 ui |= (0x3ff + 23) << 52;
169 let mut z = f64::from_bits(ui);
170 let mut tx = [0.0; 3];
171 for i in 0..2 {
172 tx[i] = z as i32 as f64;
173 z = (z - tx[i]) * x1p24;
174 }
175 tx[2] = z;
176 /* skip zero terms, first term is non-zero */
177 let mut i = 2;
178 while i != 0 && tx[i] == 0.0 {
179 i -= 1;
180 }
181 let mut ty = [0.0; 3];
182 let n = rem_pio2_large(&tx[..=i], &mut ty, ((ix >> 20) - (0x3ff + 23)) as i32, 1);
183 if sign != 0 {
184 return (-n, -ty[0], -ty[1]);
185 }
186 (n, ty[0], ty[1])
187 }
188
189 #[test]
test_near_pi()190 fn test_near_pi() {
191 assert_eq!(
192 rem_pio2(3.141592025756836),
193 (2, -6.278329573009626e-7, -2.1125998133974653e-23)
194 );
195 assert_eq!(
196 rem_pio2(3.141592033207416),
197 (2, -6.20382377148128e-7, -2.1125998133974653e-23)
198 );
199 assert_eq!(
200 rem_pio2(3.141592144966125),
201 (2, -5.086236681942706e-7, -2.1125998133974653e-23)
202 );
203 assert_eq!(
204 rem_pio2(3.141592979431152),
205 (2, 3.2584135866119817e-7, -2.1125998133974653e-23)
206 );
207 }
208