1 /*
2 * Single-precision sinh(x) function.
3 *
4 * Copyright (c) 2022-2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "mathlib.h"
9 #include "math_config.h"
10 #include "test_sig.h"
11 #include "test_defs.h"
12
13 #define AbsMask 0x7fffffff
14 #define Half 0x3f000000
15 /* 0x1.62e43p+6, 2^7*ln2, minimum value for which expm1f overflows. */
16 #define Expm1OFlowLimit 0x42b17218
17 /* 0x1.65a9fap+6, minimum positive value for which sinhf should overflow. */
18 #define OFlowLimit 0x42b2d4fd
19
20 /* Approximation for single-precision sinh(x) using expm1.
21 sinh(x) = (exp(x) - exp(-x)) / 2.
22 The maximum error is 2.26 ULP:
23 sinhf(0x1.e34a9ep-4) got 0x1.e469ep-4 want 0x1.e469e4p-4. */
24 float
sinhf(float x)25 sinhf (float x)
26 {
27 uint32_t ix = asuint (x);
28 uint32_t iax = ix & AbsMask;
29 float ax = asfloat (iax);
30 uint32_t sign = ix & ~AbsMask;
31 float halfsign = asfloat (Half | sign);
32
33 if (unlikely (iax >= Expm1OFlowLimit))
34 {
35 /* Special values and overflow. */
36 if (iax >= 0x7fc00001 || iax == 0x7f800000)
37 return x;
38 if (iax >= 0x7f800000)
39 return __math_invalidf (x);
40 if (iax >= OFlowLimit)
41 return __math_oflowf (sign);
42
43 /* expm1f overflows a little before sinhf, (~88.7 vs ~89.4). We have to
44 fill this gap by using a different algorithm, in this case we use a
45 double-precision exp helper. For large x sinh(x) dominated by exp(x),
46 however we cannot compute exp without overflow either. We use the
47 identity:
48 exp(a) = (exp(a / 2)) ^ 2.
49 to compute sinh(x) ~= (exp(|x| / 2)) ^ 2 / 2 for x > 0
50 ~= (exp(|x| / 2)) ^ 2 / -2 for x < 0.
51 Greatest error in this region is 1.89 ULP:
52 sinhf(0x1.65898cp+6) got 0x1.f00aep+127 want 0x1.f00adcp+127. */
53 float e = expf (ax / 2);
54 return (e * halfsign) * e;
55 }
56
57 /* Use expm1f to retain acceptable precision for small numbers.
58 Let t = e^(|x|) - 1. */
59 float t = expm1f (ax);
60 /* Then sinh(x) = (t + t / (t + 1)) / 2 for x > 0
61 (t + t / (t + 1)) / -2 for x < 0. */
62 return (t + t / (t + 1)) * halfsign;
63 }
64
65 TEST_SIG (S, F, 1, sinh, -10.0, 10.0)
66 TEST_ULP (sinhf, 1.76)
67 TEST_SYM_INTERVAL (sinhf, 0, 0x1.62e43p+6, 100000)
68 TEST_SYM_INTERVAL (sinhf, 0x1.62e43p+6, 0x1.65a9fap+6, 100)
69 TEST_SYM_INTERVAL (sinhf, 0x1.65a9fap+6, inf, 100)
70