1 /*
2  * Single-precision sinh(x) function.
3  *
4  * Copyright (c) 2022-2023, Arm Limited.
5  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6  */
7 
8 #include "math_config.h"
9 #include "pl_sig.h"
10 #include "pl_test.h"
11 
12 #define AbsMask 0x7fffffff
13 #define Half 0x3f000000
14 #define Expm1OFlowLimit                                                        \
15   0x42b17218 /* 0x1.62e43p+6, 2^7*ln2, minimum value for which expm1f          \
16 		overflows.  */
17 #define OFlowLimit                                                             \
18   0x42b2d4fd /* 0x1.65a9fap+6, minimum positive value for which sinhf should   \
19 		overflow.  */
20 
21 float
22 optr_aor_exp_f32 (float);
23 
24 /* Approximation for single-precision sinh(x) using expm1.
25    sinh(x) = (exp(x) - exp(-x)) / 2.
26    The maximum error is 2.26 ULP:
27    sinhf(0x1.e34a9ep-4) got 0x1.e469ep-4 want 0x1.e469e4p-4.  */
28 float
29 sinhf (float x)
30 {
31   uint32_t ix = asuint (x);
32   uint32_t iax = ix & AbsMask;
33   float ax = asfloat (iax);
34   uint32_t sign = ix & ~AbsMask;
35   float halfsign = asfloat (Half | sign);
36 
37   if (unlikely (iax >= Expm1OFlowLimit))
38     {
39       /* Special values and overflow.  */
40       if (iax >= 0x7fc00001 || iax == 0x7f800000)
41 	return x;
42       if (iax >= 0x7f800000)
43 	return __math_invalidf (x);
44       if (iax >= OFlowLimit)
45 	return __math_oflowf (sign);
46 
47       /* expm1f overflows a little before sinhf, (~88.7 vs ~89.4). We have to
48 	 fill this gap by using a different algorithm, in this case we use a
49 	 double-precision exp helper. For large x sinh(x) dominated by exp(x),
50 	 however we cannot compute exp without overflow either. We use the
51 	 identity:
52 	 exp(a) = (exp(a / 2)) ^ 2.
53 	 to compute sinh(x) ~= (exp(|x| / 2)) ^ 2 / 2    for x > 0
54 			    ~= (exp(|x| / 2)) ^ 2 / -2   for x < 0.
55 	 Greatest error in this region is 1.89 ULP:
56 	 sinhf(0x1.65898cp+6) got 0x1.f00aep+127  want 0x1.f00adcp+127.  */
57       float e = optr_aor_exp_f32 (ax / 2);
58       return (e * halfsign) * e;
59     }
60 
61   /* Use expm1f to retain acceptable precision for small numbers.
62      Let t = e^(|x|) - 1.  */
63   float t = expm1f (ax);
64   /* Then sinh(x) = (t + t / (t + 1)) / 2   for x > 0
65 		    (t + t / (t + 1)) / -2  for x < 0.  */
66   return (t + t / (t + 1)) * halfsign;
67 }
68 
69 PL_SIG (S, F, 1, sinh, -10.0, 10.0)
70 PL_TEST_ULP (sinhf, 1.76)
71 PL_TEST_INTERVAL (sinhf, 0, 0x1.62e43p+6, 100000)
72 PL_TEST_INTERVAL (sinhf, -0, -0x1.62e43p+6, 100000)
73 PL_TEST_INTERVAL (sinhf, 0x1.62e43p+6, 0x1.65a9fap+6, 100)
74 PL_TEST_INTERVAL (sinhf, -0x1.62e43p+6, -0x1.65a9fap+6, 100)
75 PL_TEST_INTERVAL (sinhf, 0x1.65a9fap+6, inf, 100)
76 PL_TEST_INTERVAL (sinhf, -0x1.65a9fap+6, -inf, 100)
77