| //===----------------------------------------------------------------------===// |
| // |
| // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
| // See https://llvm.org/LICENSE.txt for license information. |
| // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| // |
| //===----------------------------------------------------------------------===// |
| |
| #if __CLC_FPSIZE == 32 |
| |
| _CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_cosh(__CLC_GENTYPE x) { |
| // After dealing with special cases the computation is split into regions as |
| // follows. abs(x) >= max_cosh_arg: cosh(x) = sign(x)*Inf abs(x) >= |
| // small_threshold: cosh(x) = sign(x)*exp(abs(x))/2 computed using the |
| // splitexp and scaleDouble functions as for exp_amd(). |
| // abs(x) < small_threshold: |
| // compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0))) |
| // cosh(x) is then z. |
| |
| const __CLC_GENTYPE max_cosh_arg = 0x1.65a9fap+6f; |
| const __CLC_GENTYPE small_threshold = 0x1.0a2b24p+3f; |
| |
| __CLC_UINTN ux = __CLC_AS_UINTN(x); |
| __CLC_GENTYPE y = __clc_fabs(x); |
| __CLC_UINTN aux = __CLC_AS_UINTN(y); |
| |
| // Find the integer part y0 of y and the increment dy = y - y0. We then |
| // compute z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy) z = cosh(y) = |
| // cosh(y0)cosh(dy) + sinh(y0)sinh(dy) where sinh(y0) and cosh(y0) are |
| // tabulated above. |
| |
| __CLC_INTN ind = __CLC_CONVERT_INTN(y); |
| ind = __CLC_CONVERT_UINTN(ind) > 36U ? 0 : ind; |
| |
| __CLC_GENTYPE dy = y - __CLC_CONVERT_GENTYPE(ind); |
| __CLC_GENTYPE dy2 = dy * dy; |
| |
| __CLC_GENTYPE sdy = __clc_mad( |
| dy2, |
| __clc_mad( |
| dy2, |
| __clc_mad( |
| dy2, |
| __clc_mad( |
| dy2, |
| __clc_mad(dy2, |
| __clc_mad(dy2, 0.7746188980094184251527126e-12f, |
| 0.160576793121939886190847e-9f), |
| 0.250521176994133472333666e-7f), |
| 0.275573191913636406057211e-5f), |
| 0.198412698413242405162014e-3f), |
| 0.833333333333329931873097e-2f), |
| 0.166666666666666667013899e0f); |
| sdy = __clc_mad(sdy, dy * dy2, dy); |
| |
| __CLC_GENTYPE cdy = __clc_mad( |
| dy2, |
| __clc_mad( |
| dy2, |
| __clc_mad( |
| dy2, |
| __clc_mad( |
| dy2, |
| __clc_mad(dy2, |
| __clc_mad(dy2, 0.1163921388172173692062032e-10f, |
| 0.208744349831471353536305e-8f), |
| 0.275573350756016588011357e-6f), |
| 0.248015872460622433115785e-4f), |
| 0.138888888889814854814536e-2f), |
| 0.416666666666660876512776e-1f), |
| 0.500000000000000005911074e0f); |
| cdy = __clc_mad(cdy, dy2, 1.0f); |
| |
| __CLC_GENTYPE sinhcoshh = __CLC_USE_TABLE(sinhcosh_tbl_head, ind); |
| __CLC_GENTYPE sinhcosht = __CLC_USE_TABLE(sinhcosh_tbl_tail, ind); |
| __CLC_GENTYPE z = __clc_mad(sinhcoshh, sdy, sinhcosht * cdy); |
| |
| // When exp(-x) is insignificant compared to exp(x), return exp(x)/2 |
| __CLC_GENTYPE t = __clc_exp(y - 0x1.62e500p-1f); |
| __CLC_GENTYPE zsmall = __clc_mad(0x1.a0210ep-18f, t, t); |
| z = y >= small_threshold ? zsmall : z; |
| |
| // Corner cases |
| z = y >= max_cosh_arg ? __CLC_AS_GENTYPE((__CLC_UINTN)PINFBITPATT_SP32) : z; |
| z = aux > PINFBITPATT_SP32 ? __CLC_GENTYPE_NAN : z; |
| z = aux < 0x38800000 ? 1.0f : z; |
| |
| return z; |
| } |
| |
| #elif __CLC_FPSIZE == 64 |
| |
| _CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_cosh(__CLC_GENTYPE x) { |
| // After dealing with special cases the computation is split into |
| // regions as follows: |
| // |
| // abs(x) >= max_cosh_arg: |
| // cosh(x) = sign(x)*Inf |
| // |
| // abs(x) >= small_threshold: |
| // cosh(x) = sign(x)*exp(abs(x))/2 computed using the |
| // splitexp and scaleDouble functions as for exp_amd(). |
| // |
| // abs(x) < small_threshold: |
| // compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0))) |
| // cosh(x) is then sign(x)*z. |
| |
| // This is ln(2^1025) = 0x408633ce8fb9f87e |
| const __CLC_GENTYPE max_cosh_arg = 7.10475860073943977113e+02; |
| |
| // This is where exp(-x) is insignificant compared to exp(x) = ln(2^27) |
| const __CLC_GENTYPE small_threshold = 0x1.2b708872320e2p+4; |
| |
| __CLC_GENTYPE y = __clc_fabs(x); |
| |
| // In this range we find the integer part y0 of y |
| // and the increment dy = y - y0. We then compute |
| // z = cosh(y) = cosh(y0)cosh(dy) + sinh(y0)sinh(dy) |
| // where sinh(y0) and cosh(y0) are tabulated above. |
| |
| __CLC_INTN ind = __clc_min(__CLC_CONVERT_INTN(y), 36); |
| __CLC_GENTYPE dy = y - __CLC_CONVERT_GENTYPE(ind); |
| __CLC_GENTYPE dy2 = dy * dy; |
| |
| __CLC_GENTYPE sdy = |
| dy * dy2 * |
| __clc_fma( |
| dy2, |
| __clc_fma( |
| dy2, |
| __clc_fma( |
| dy2, |
| __clc_fma( |
| dy2, |
| __clc_fma(dy2, |
| __clc_fma(dy2, 0.7746188980094184251527126e-12, |
| 0.160576793121939886190847e-9), |
| 0.250521176994133472333666e-7), |
| 0.275573191913636406057211e-5), |
| 0.198412698413242405162014e-3), |
| 0.833333333333329931873097e-2), |
| 0.166666666666666667013899e0); |
| |
| __CLC_GENTYPE cdy = |
| dy2 * |
| __clc_fma( |
| dy2, |
| __clc_fma( |
| dy2, |
| __clc_fma( |
| dy2, |
| __clc_fma( |
| dy2, |
| __clc_fma(dy2, |
| __clc_fma(dy2, 0.1163921388172173692062032e-10, |
| 0.208744349831471353536305e-8), |
| 0.275573350756016588011357e-6), |
| 0.248015872460622433115785e-4), |
| 0.138888888889814854814536e-2), |
| 0.416666666666660876512776e-1), |
| 0.500000000000000005911074e0); |
| |
| // At this point sinh(dy) is approximated by dy + sdy, |
| // and cosh(dy) is approximated by 1 + cdy. |
| __CLC_GENTYPE cl = __CLC_USE_TABLE(cosh_tbl_head, ind); |
| __CLC_GENTYPE ct = __CLC_USE_TABLE(cosh_tbl_tail, ind); |
| __CLC_GENTYPE sl = __CLC_USE_TABLE(sinh_tbl_head, ind); |
| __CLC_GENTYPE st = __CLC_USE_TABLE(sinh_tbl_tail, ind); |
| |
| __CLC_GENTYPE z = |
| __clc_fma( |
| sl, dy, |
| __clc_fma(sl, sdy, |
| __clc_fma(cl, cdy, |
| __clc_fma(st, dy, __clc_fma(st, sdy, ct * cdy)) + |
| ct))) + |
| cl; |
| |
| // Other cases |
| z = y < 0x1.0p-28 ? 1.0 : z; |
| |
| __CLC_GENTYPE t = __clc_exp(y - 0x1.62e42fefa3800p-1); |
| t = __clc_fma(t, -0x1.ef35793c76641p-45, t); |
| z = y >= small_threshold ? t : z; |
| |
| z = y >= max_cosh_arg ? __CLC_AS_GENTYPE((__CLC_ULONGN)PINFBITPATT_DP64) : z; |
| |
| z = __clc_isinf(x) || __clc_isnan(x) ? y : z; |
| |
| return z; |
| } |
| |
| #elif __CLC_FPSIZE == 16 |
| |
| _CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_cosh(__CLC_GENTYPE x) { |
| return __CLC_CONVERT_GENTYPE(__clc_cosh(__CLC_CONVERT_FLOATN(x))); |
| } |
| |
| #endif |
